Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,2,Mod(25,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, 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("504.25");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.q (of order \(3\), 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: | \(4.02446026187\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 25.10 | ||
Character | \(\chi\) | \(=\) | 504.25 |
Dual form | 504.2.q.c.121.10 |
$q$-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 \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | −0.918823 | − | 0.394669i | \(-0.870859\pi\) |
0.801205 | + | 0.598390i | \(0.204193\pi\) | |||||||
\(6\) | 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 | −0.970160 | − | 0.242466i | \(-0.922044\pi\) |
0.275098 | − | 0.961416i | \(-0.411290\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.244554 | + | 0.423580i | 0.0678270 | + | 0.117480i | 0.897945 | − | 0.440109i | \(-0.145060\pi\) |
−0.830118 | + | 0.557588i | \(0.811727\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.179749 | + | 0.893158i | −0.0464110 | + | 0.230613i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.75579 | − | 4.77318i | 0.668378 | − | 1.15767i | −0.309979 | − | 0.950743i | \(-0.600322\pi\) |
0.978357 | − | 0.206922i | \(-0.0663446\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.83782 | + | 3.18319i | 0.421624 | + | 0.730274i | 0.996099 | − | 0.0882484i | \(-0.0281269\pi\) |
−0.574475 | + | 0.818522i | \(0.694794\pi\) | |||||||
\(20\) | 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 | \(-0.831543\pi\) |
0.868824 | + | 0.495121i | \(0.164876\pi\) | |||||||
\(24\) | 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 | 0.381292 | + | 0.924455i | \(0.375479\pi\) |
−0.991247 | + | 0.132019i | \(0.957854\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.07640 | 1.09135 | 0.545676 | − | 0.837996i | \(-0.316273\pi\) | ||||
0.545676 | + | 0.837996i | \(0.316273\pi\) | |||||||
\(32\) | 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 | 0.883830 | − | 0.467808i | \(-0.154956\pi\) |
−0.847049 | + | 0.531515i | \(0.821623\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.635671 | + | 0.560002i | 0.101789 | + | 0.0896721i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.52284 | + | 4.36968i | 0.394001 | + | 0.682430i | 0.992973 | − | 0.118340i | \(-0.0377574\pi\) |
−0.598972 | + | 0.800770i | \(0.704424\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.84893 | − | 4.93449i | 0.434458 | − | 0.752503i | −0.562794 | − | 0.826598i | \(-0.690273\pi\) |
0.997251 | + | 0.0740947i | \(0.0236067\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.198934 | + | 1.56542i | 0.0296553 | + | 0.233360i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.19621 | −1.34140 | −0.670702 | − | 0.741726i | \(-0.734007\pi\) | ||||
−0.670702 | + | 0.741726i | \(0.734007\pi\) | |||||||
\(48\) | 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 | 0.392297 | + | 0.919839i | \(0.371680\pi\) |
−0.992752 | + | 0.120180i | \(0.961653\pi\) | |||||||
\(54\) | 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 | \(-0.642060\pi\) | ||||
−0.431626 | + | 0.902053i | \(0.642060\pi\) | |||||||
\(60\) | 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 | \(-0.397241\pi\) | ||||
0.317248 | + | 0.948343i | \(0.397241\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.0184374 | − | 0.0916137i | 0.00221960 | − | 0.0110290i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.76328 | 0.209263 | 0.104632 | − | 0.994511i | \(-0.466634\pi\) | ||||
0.104632 | + | 0.994511i | \(0.466634\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.23776 | + | 9.07207i | −0.613034 | + | 1.06181i | 0.377692 | + | 0.925931i | \(0.376718\pi\) |
−0.990726 | + | 0.135875i | \(0.956616\pi\) | |||||||
\(74\) | 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 | \(-0.127460\pi\) | ||||
0.920895 | + | 0.389812i | \(0.127460\pi\) | |||||||
\(80\) | 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 | \(-0.669191\pi\) |
0.999969 | + | 0.00792925i | \(0.00252399\pi\) | |||||||
\(84\) | 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 | −0.949040 | − | 0.315155i | \(-0.897944\pi\) |
0.201588 | − | 0.979470i | \(-0.435390\pi\) | |||||||
\(90\) | 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 | −0.468939 | − | 0.883230i | \(-0.655364\pi\) |
0.999370 | − | 0.0355020i | \(-0.0113030\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −12.7548 | − | 5.35052i | −1.28190 | − | 0.537748i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.98254 | + | 8.63001i | 0.495781 | + | 0.858718i | 0.999988 | − | 0.00486475i | \(-0.00154850\pi\) |
−0.504207 | + | 0.863583i | \(0.668215\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.82553 | + | 10.0901i | −0.574006 | + | 0.994208i | 0.422143 | + | 0.906529i | \(0.361278\pi\) |
−0.996149 | + | 0.0876783i | \(0.972055\pi\) | |||||||
\(104\) | 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 | \(-0.0903754\pi\) |
−0.722576 | + | 0.691292i | \(0.757042\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.76353 | + | 16.9109i | −0.935177 | + | 1.61977i | −0.160858 | + | 0.986978i | \(0.551426\pi\) |
−0.774319 | + | 0.632796i | \(0.781907\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.581545 | + | 0.512319i | 0.0551978 | + | 0.0486272i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.48658 | + | 9.50304i | 0.516134 | + | 0.893971i | 0.999825 | + | 0.0187317i | \(0.00596282\pi\) |
−0.483690 | + | 0.875239i | \(0.660704\pi\) | |||||||
\(114\) | 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 | \(-0.763748\pi\) | ||||
−0.736979 | + | 0.675915i | \(0.763748\pi\) | |||||||
\(128\) | 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 | \(-0.915117\pi\) |
0.710540 | + | 0.703657i | \(0.248451\pi\) | |||||||
\(132\) | 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 | 0.992989 | − | 0.118205i | \(-0.0377139\pi\) |
−0.598863 | + | 0.800852i | \(0.704381\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.88477 | + | 11.9248i | 0.583959 | + | 1.01145i | 0.995004 | + | 0.0998314i | \(0.0318303\pi\) |
−0.411046 | + | 0.911615i | \(0.634836\pi\) | |||||||
\(140\) | 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 | −0.644419 | − | 0.764673i | \(-0.722901\pi\) |
0.984435 | + | 0.175747i | \(0.0562340\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.24894 | + | 12.5555i | 0.589911 | + | 1.02176i | 0.994244 | + | 0.107143i | \(0.0341704\pi\) |
−0.404333 | + | 0.914612i | \(0.632496\pi\) | |||||||
\(152\) | 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 | \(-0.229007\pi\) |
−0.946769 | + | 0.321913i | \(0.895674\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.98060 | − | 1.34126i | 0.309889 | − | 0.104417i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −10.0088 | − | 17.3357i | −0.774504 | − | 1.34148i | −0.935073 | − | 0.354456i | \(-0.884666\pi\) |
0.160569 | − | 0.987025i | \(-0.448667\pi\) | |||||||
\(168\) | 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 | 0.421143 | + | 0.906994i | \(0.361629\pi\) |
−0.996052 | + | 0.0887763i | \(0.971704\pi\) | |||||||
\(180\) | 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 | \(-0.630827\pi\) | ||||
−0.399531 | + | 0.916720i | \(0.630827\pi\) | |||||||
\(192\) | 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 | −0.242586 | − | 0.970130i | \(-0.577996\pi\) |
0.961450 | − | 0.274979i | \(-0.0886710\pi\) | |||||||
\(200\) | 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 | \(-0.0599545\pi\) |
−0.653312 | + | 0.757088i | \(0.726621\pi\) | |||||||
\(212\) | 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 | −0.123046 | − | 0.992401i | \(-0.539266\pi\) |
0.920968 | − | 0.389639i | \(-0.127400\pi\) | |||||||
\(224\) | 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 | \(-0.138411\pi\) |
−0.818290 | + | 0.574806i | \(0.805078\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.16258 | + | 5.47775i | −0.208989 | + | 0.361980i | −0.951396 | − | 0.307969i | \(-0.900351\pi\) |
0.742407 | + | 0.669949i | \(0.233684\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −11.8590 | + | 17.4860i | −0.780262 | + | 1.15049i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.63381 | + | 8.02600i | 0.303571 | + | 0.525801i | 0.976942 | − | 0.213504i | \(-0.0684877\pi\) |
−0.673371 | + | 0.739305i | \(0.735154\pi\) | |||||||
\(234\) | 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 | \(-0.131755\pi\) |
−0.806092 | + | 0.591790i | \(0.798422\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.57982 | − | 11.3966i | −0.423844 | − | 0.734119i | 0.572468 | − | 0.819927i | \(-0.305986\pi\) |
−0.996312 | + | 0.0858082i | \(0.972653\pi\) | |||||||
\(242\) | 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 | \(-0.523149\pi\) | ||||
−0.0726614 | + | 0.997357i | \(0.523149\pi\) | |||||||
\(252\) | 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 | 0.0926132 | − | 0.995702i | \(-0.470478\pi\) |
0.815997 | − | 0.578056i | \(-0.196189\pi\) | |||||||
\(258\) | 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 | \(-0.139957\pi\) |
−0.821073 | + | 0.570823i | \(0.806624\pi\) | |||||||
\(264\) | 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 | −0.767620 | − | 0.640906i | \(-0.778559\pi\) |
0.938850 | + | 0.344325i | \(0.111892\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.25164 | − | 12.5602i | −0.440506 | − | 0.762978i | 0.557221 | − | 0.830364i | \(-0.311867\pi\) |
−0.997727 | + | 0.0673860i | \(0.978534\pi\) | |||||||
\(272\) | 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 | 0.891086 | − | 0.453835i | \(-0.149944\pi\) |
−0.838575 | + | 0.544786i | \(0.816611\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 14.5119 | − | 11.0321i | 0.868808 | − | 0.660473i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.35657 | − | 9.27786i | 0.319546 | − | 0.553471i | −0.660847 | − | 0.750521i | \(-0.729803\pi\) |
0.980393 | + | 0.197050i | \(0.0631361\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.5967 | −0.748793 | −0.374397 | − | 0.927269i | \(-0.622150\pi\) | ||||
−0.374397 | + | 0.927269i | \(0.622150\pi\) | |||||||
\(284\) | 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 | 0.816320 | − | 0.577600i | \(-0.196011\pi\) |
−0.908376 | + | 0.418154i | \(0.862677\pi\) | |||||||
\(294\) | 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 | \(-0.697657\pi\) | ||||
−0.581813 | + | 0.813322i | \(0.697657\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.98146 | + | 19.7836i | −0.226497 | + | 1.12545i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 22.7014 | 1.28728 | 0.643640 | − | 0.765328i | \(-0.277423\pi\) | ||||
0.643640 | + | 0.765328i | \(0.277423\pi\) | |||||||
\(312\) | 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 | \(-0.713668\pi\) | ||||
−0.621970 | + | 0.783041i | \(0.713668\pi\) | |||||||
\(332\) | 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 | 0.989482 | − | 0.144653i | \(-0.0462066\pi\) |
−0.620014 | + | 0.784590i | \(0.712873\pi\) | |||||||
\(338\) | 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 | \(-0.846850\pi\) | ||||
−0.886470 | + | 0.462786i | \(0.846850\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.1773 | + | 17.6276i | −0.544778 | + | 0.943584i | 0.453842 | + | 0.891082i | \(0.350053\pi\) |
−0.998621 | + | 0.0525019i | \(0.983280\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.53486 | + | 0.183325i | 0.135301 | + | 0.00978514i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.75381 | + | 4.76975i | 0.146571 | + | 0.253868i | 0.929958 | − | 0.367666i | \(-0.119843\pi\) |
−0.783387 | + | 0.621534i | \(0.786510\pi\) | |||||||
\(354\) | 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 | −0.998104 | − | 0.0615472i | \(-0.980397\pi\) |
0.445751 | − | 0.895157i | \(-0.352937\pi\) | |||||||
\(360\) | 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 | \(-0.202352\pi\) |
−0.916526 | + | 0.399976i | \(0.869018\pi\) | |||||||
\(368\) | 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 | −0.682079 | − | 0.731279i | \(-0.738924\pi\) |
0.974345 | + | 0.225058i | \(0.0722571\pi\) | |||||||
\(374\) | 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 | \(-0.677295\pi\) | ||||
−0.528634 | + | 0.848850i | \(0.677295\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −27.2644 | + | 9.18670i | −1.39680 | + | 0.470649i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.8108 | − | 18.7248i | 0.552405 | − | 0.956793i | −0.445696 | − | 0.895184i | \(-0.647044\pi\) |
0.998100 | − | 0.0616083i | \(-0.0196230\pi\) | |||||||
\(384\) | 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 | 0.989915 | − | 0.141662i | \(-0.0452446\pi\) |
−0.617640 | + | 0.786461i | \(0.711911\pi\) | |||||||
\(390\) | 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 | 0.776592 | − | 0.630003i | \(-0.216947\pi\) |
−0.933895 | + | 0.357547i | \(0.883613\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 9.45428 | − | 13.9403i | 0.473306 | − | 0.697888i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.6951 | + | 25.4526i | −0.733836 | + | 1.27104i | 0.221396 | + | 0.975184i | \(0.428939\pi\) |
−0.955232 | + | 0.295857i | \(0.904395\pi\) | |||||||
\(402\) | 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 | \(-0.311890\pi\) |
−0.997732 | + | 0.0673151i | \(0.978557\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.8278 | − | 29.1465i | 0.820135 | − | 1.42052i | −0.0854466 | − | 0.996343i | \(-0.527232\pi\) |
0.905581 | − | 0.424172i | \(-0.139435\pi\) | |||||||
\(422\) | 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 | 0.461754 | + | 0.887008i | \(0.347220\pi\) |
−0.999048 | + | 0.0436135i | \(0.986113\pi\) | |||||||
\(432\) | 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 | \(-0.700394\pi\) | ||||
−0.588785 | + | 0.808289i | \(0.700394\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −13.0125 | + | 16.4826i | −0.619643 | + | 0.784884i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 30.5363 | 1.45082 | 0.725412 | − | 0.688315i | \(-0.241649\pi\) | ||||
0.725412 | + | 0.688315i | \(0.241649\pi\) | |||||||
\(444\) | 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 | −0.966569 | − | 0.256406i | \(-0.917462\pi\) |
0.705339 | + | 0.708871i | \(0.250795\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −19.9362 | − | 34.5305i | −0.926514 | − | 1.60477i | −0.789108 | − | 0.614254i | \(-0.789457\pi\) |
−0.137405 | − | 0.990515i | \(-0.543876\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.09223 | + | 5.42718i | −0.0506508 | + | 0.251680i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.7818 | + | 20.4067i | 0.545198 | + | 0.944311i | 0.998594 | + | 0.0530016i | \(0.0168788\pi\) |
−0.453397 | + | 0.891309i | \(0.649788\pi\) | |||||||
\(468\) | 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 | \(-0.272060\pi\) |
−0.981530 | + | 0.191310i | \(0.938727\pi\) | |||||||
\(480\) | 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 | 0.353242 | + | 0.935532i | \(0.385079\pi\) |
−0.986815 | + | 0.161850i | \(0.948254\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.45794 | − | 5.68920i | −0.292038 | − | 0.257275i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.2543 | + | 29.8853i | 0.778676 | + | 1.34871i | 0.932705 | + | 0.360639i | \(0.117442\pi\) |
−0.154030 | + | 0.988066i | \(0.549225\pi\) | |||||||
\(492\) | 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 | 0.406054 | + | 0.913849i | \(0.366905\pi\) |
−0.994443 | + | 0.105272i | \(0.966429\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −26.0159 | − | 22.9191i | −1.16231 | − | 1.02395i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.09068 | 0.271570 | 0.135785 | − | 0.990738i | \(-0.456644\pi\) | ||||
0.135785 | + | 0.990738i | \(0.456644\pi\) | |||||||
\(504\) | 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 | −0.761145 | − | 0.648582i | \(-0.775363\pi\) |
0.942261 | + | 0.334880i | \(0.108696\pi\) | |||||||
\(510\) | 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 | −0.424729 | − | 0.905321i | \(-0.639630\pi\) |
0.996395 | − | 0.0848346i | \(-0.0270362\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.6655 | + | 23.6694i | 0.597553 | + | 1.03499i | 0.993181 | + | 0.116581i | \(0.0371935\pi\) |
−0.395628 | + | 0.918411i | \(0.629473\pi\) | |||||||
\(524\) | 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 | 0.714271 | − | 0.699869i | \(-0.246758\pi\) |
−0.963240 | + | 0.268643i | \(0.913425\pi\) | |||||||
\(542\) | 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 | 0.00952755 | − | 0.999955i | \(-0.496967\pi\) |
0.861222 | − | 0.508228i | \(-0.169699\pi\) | |||||||
\(548\) | 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 | −0.572258 | − | 0.820074i | \(-0.693932\pi\) |
0.996334 | + | 0.0855533i | \(0.0272658\pi\) | |||||||
\(558\) | 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 | \(-0.323917\pi\) | ||||
0.525396 | + | 0.850858i | \(0.323917\pi\) | |||||||
\(564\) | 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 | \(-0.825521\pi\) | ||||
−0.853494 | + | 0.521103i | \(0.825521\pi\) | |||||||
\(572\) | 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 | −0.996581 | − | 0.0826259i | \(-0.973669\pi\) |
0.569846 | + | 0.821751i | \(0.307003\pi\) | |||||||
\(578\) | 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 | 0.125791 | + | 0.992057i | \(0.459853\pi\) |
−0.922042 | + | 0.387090i | \(0.873480\pi\) | |||||||
\(588\) | 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 | 0.838874 | − | 0.544326i | \(-0.183215\pi\) |
−0.890837 | + | 0.454323i | \(0.849881\pi\) | |||||||
\(594\) | 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 | \(-0.606145\pi\) | ||||
−0.327317 | + | 0.944915i | \(0.606145\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.1601 | + | 38.3824i | −0.903929 | + | 1.56565i | −0.0815796 | + | 0.996667i | \(0.525996\pi\) |
−0.822349 | + | 0.568983i | \(0.807337\pi\) | |||||||
\(602\) | 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 | \(-0.770971\pi\) |
0.946791 | + | 0.321849i | \(0.104304\pi\) | |||||||
\(608\) | 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 | −0.544761 | − | 0.838591i | \(-0.683380\pi\) |
0.998622 | + | 0.0524815i | \(0.0167131\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.35630 | + | 1.46785i | −0.175663 | + | 0.0591893i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.7056 | + | 20.2746i | 0.471248 | + | 0.816226i | 0.999459 | − | 0.0328875i | \(-0.0104703\pi\) |
−0.528211 | + | 0.849113i | \(0.677137\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.98843 | − | 13.8364i | −0.321082 | − | 0.556131i | 0.659629 | − | 0.751591i | \(-0.270713\pi\) |
−0.980712 | + | 0.195460i | \(0.937380\pi\) | |||||||
\(620\) | 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 | \(-0.505592\pi\) | ||||
−0.0175662 | + | 0.999846i | \(0.505592\pi\) | |||||||
\(632\) | 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 | −0.920652 | − | 0.390384i | \(-0.872342\pi\) |
0.122244 | − | 0.992500i | \(-0.460991\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.99047 | + | 5.17964i | 0.117932 | + | 0.204265i | 0.918948 | − | 0.394378i | \(-0.129040\pi\) |
−0.801016 | + | 0.598643i | \(0.795707\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.89519 | + | 3.43152i | 0.153373 | + | 0.135116i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −16.4743 | + | 28.5343i | −0.647672 | + | 1.12180i | 0.336005 | + | 0.941860i | \(0.390924\pi\) |
−0.983677 | + | 0.179941i | \(0.942409\pi\) | |||||||
\(648\) | 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 | 0.490561 | + | 0.871407i | \(0.336792\pi\) |
−0.999941 | + | 0.0108653i | \(0.996541\pi\) | |||||||
\(654\) | 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 | \(-0.771992\pi\) |
0.945754 | + | 0.324883i | \(0.105325\pi\) | |||||||
\(660\) | 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 | −0.188569 | − | 0.982060i | \(-0.560385\pi\) |
0.944773 | − | 0.327725i | \(-0.106282\pi\) | |||||||
\(674\) | 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 | \(-0.895924\pi\) |
0.751652 | + | 0.659560i | \(0.229257\pi\) | |||||||
\(684\) | 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 | \(-0.732499\pi\) | ||||
−0.667179 | + | 0.744897i | \(0.732499\pi\) | |||||||
\(692\) | 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 | −0.892820 | − | 0.450414i | \(-0.851277\pi\) |
0.0563403 | − | 0.998412i | \(-0.482057\pi\) | |||||||
\(720\) | 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 | \(-0.859576\pi\) |
0.821909 | + | 0.569619i | \(0.192909\pi\) | |||||||
\(728\) | 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 | −0.259233 | − | 0.965815i | \(-0.583470\pi\) |
0.966037 | − | 0.258405i | \(-0.0831968\pi\) | |||||||
\(734\) | 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 | \(-0.863751\pi\) |
0.814367 | + | 0.580350i | \(0.197084\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.614347 | + | 3.05264i | −0.0225686 | + | 0.112142i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.3351 | + | 28.2932i | 0.599276 | + | 1.03798i | 0.992928 | + | 0.118716i | \(0.0378779\pi\) |
−0.393653 | + | 0.919259i | \(0.628789\pi\) | |||||||
\(744\) | 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 | \(-0.738296\pi\) |
0.974787 | + | 0.223136i | \(0.0716294\pi\) | |||||||
\(752\) | 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 | −0.955315 | − | 0.295590i | \(-0.904484\pi\) |
0.733646 | + | 0.679532i | \(0.237817\pi\) | |||||||
\(762\) | 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 | 0.917555 | − | 0.397610i | \(-0.130160\pi\) |
−0.803117 | + | 0.595821i | \(0.796827\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.95523 | − | 49.4667i | 0.358529 | − | 1.78150i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 24.4515 | − | 42.3512i | 0.879459 | − | 1.52327i | 0.0275225 | − | 0.999621i | \(-0.491238\pi\) |
0.851936 | − | 0.523646i | \(-0.175428\pi\) | |||||||
\(774\) | 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 | \(-0.635379\pi\) | ||||
−0.412600 | + | 0.910912i | \(0.635379\pi\) | |||||||
\(788\) | 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 | 0.873631 | + | 0.486589i | \(0.161759\pi\) |
−0.0154170 | + | 0.999881i | \(0.504908\pi\) | |||||||
\(798\) | 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 | −0.988107 | − | 0.153765i | \(-0.950860\pi\) |
0.627218 | + | 0.778844i | \(0.284193\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27.7882 | 0.975776 | 0.487888 | − | 0.872906i | \(-0.337767\pi\) | ||||
0.487888 | + | 0.872906i | \(0.337767\pi\) | |||||||
\(812\) | 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 | \(-0.353587\pi\) | ||||
0.443922 | + | 0.896066i | \(0.353587\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7.44174 | − | 36.9774i | 0.259088 | − | 1.28739i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36.0798 | 1.25462 | 0.627309 | − | 0.778771i | \(-0.284156\pi\) | ||||
0.627309 | + | 0.778771i | \(0.284156\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 22.3539 | − | 38.7180i | 0.776381 | − | 1.34473i | −0.157633 | − | 0.987498i | \(-0.550386\pi\) |
0.934015 | − | 0.357234i | \(-0.116280\pi\) | |||||||
\(830\) | 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 | \(-0.920898\pi\) |
0.697645 | + | 0.716443i | \(0.254231\pi\) | |||||||
\(840\) | 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 | −0.513643 | − | 0.858004i | \(-0.671705\pi\) |
0.999875 | + | 0.0158264i | \(0.00503792\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.61744 | + | 3.51021i | −0.157913 | + | 0.120046i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.48867 | + | 7.77461i | 0.153330 | + | 0.265575i | 0.932450 | − | 0.361300i | \(-0.117667\pi\) |
−0.779120 | + | 0.626875i | \(0.784334\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.471450 | − | 0.816575i | 0.0160857 | − | 0.0278612i | −0.857871 | − | 0.513866i | \(-0.828213\pi\) |
0.873956 | + | 0.486005i | \(0.161546\pi\) | |||||||
\(860\) | 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 | \(-0.313173\pi\) |
−0.997995 | + | 0.0632920i | \(0.979840\pi\) | |||||||
\(864\) | 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 | −0.553017 | − | 0.833170i | \(-0.686523\pi\) |
0.998055 | + | 0.0623413i | \(0.0198567\pi\) | |||||||
\(878\) | 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 | \(-0.645070\pi\) | ||||
−0.440136 | + | 0.897931i | \(0.645070\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.19187 | − | 5.92232i | 0.0400644 | − | 0.199077i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −18.5963 | + | 32.2097i | −0.624401 | + | 1.08149i | 0.364255 | + | 0.931299i | \(0.381324\pi\) |
−0.988656 | + | 0.150196i | \(0.952010\pi\) | |||||||
\(888\) | 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 | \(-0.307837\pi\) |
−0.996794 | + | 0.0800134i | \(0.974504\pi\) | |||||||
\(908\) | 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 | \(-0.858799\pi\) |
0.823297 | + | 0.567611i | \(0.192132\pi\) | |||||||
\(912\) | 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 | \(-0.0643014\pi\) |
−0.663590 | + | 0.748096i | \(0.730968\pi\) | |||||||
\(920\) | 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 | \(-0.887328\pi\) | ||||
−0.938004 | + | 0.346625i | \(0.887328\pi\) | |||||||
\(948\) | 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 | \(-0.122885\pi\) |
−0.789292 | + | 0.614019i | \(0.789552\pi\) | |||||||
\(968\) | 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 | \(-0.0688417\pi\) |
−0.674193 | + | 0.738555i | \(0.735508\pi\) | |||||||
\(972\) | 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 | \(-0.129773\pi\) |
−0.802392 | + | 0.596798i | \(0.796439\pi\) | |||||||
\(984\) | 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 | \(-0.858564\pi\) |
0.823715 | + | 0.567004i | \(0.191897\pi\) | |||||||
\(992\) | 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 | 0.890130 | − | 0.455708i | \(-0.150614\pi\) |
−0.839719 | + | 0.543021i | \(0.817280\pi\) | |||||||
\(998\) | 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 | 504.2.q.c.25.10 | ✓ | 22 | |
3.2 | odd | 2 | 1512.2.q.d.1369.7 | 22 | |||
4.3 | odd | 2 | 1008.2.q.l.529.2 | 22 | |||
7.2 | even | 3 | 504.2.t.c.457.6 | yes | 22 | ||
9.4 | even | 3 | 504.2.t.c.193.6 | yes | 22 | ||
9.5 | odd | 6 | 1512.2.t.c.361.5 | 22 | |||
12.11 | even | 2 | 3024.2.q.l.2881.7 | 22 | |||
21.2 | odd | 6 | 1512.2.t.c.289.5 | 22 | |||
28.23 | odd | 6 | 1008.2.t.l.961.6 | 22 | |||
36.23 | even | 6 | 3024.2.t.k.1873.5 | 22 | |||
36.31 | odd | 6 | 1008.2.t.l.193.6 | 22 | |||
63.23 | odd | 6 | 1512.2.q.d.793.7 | 22 | |||
63.58 | even | 3 | inner | 504.2.q.c.121.10 | yes | 22 | |
84.23 | even | 6 | 3024.2.t.k.289.5 | 22 | |||
252.23 | even | 6 | 3024.2.q.l.2305.7 | 22 | |||
252.247 | odd | 6 | 1008.2.q.l.625.2 | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.q.c.25.10 | ✓ | 22 | 1.1 | even | 1 | trivial | |
504.2.q.c.121.10 | yes | 22 | 63.58 | even | 3 | inner | |
504.2.t.c.193.6 | yes | 22 | 9.4 | even | 3 | ||
504.2.t.c.457.6 | yes | 22 | 7.2 | even | 3 | ||
1008.2.q.l.529.2 | 22 | 4.3 | odd | 2 | |||
1008.2.q.l.625.2 | 22 | 252.247 | odd | 6 | |||
1008.2.t.l.193.6 | 22 | 36.31 | odd | 6 | |||
1008.2.t.l.961.6 | 22 | 28.23 | odd | 6 | |||
1512.2.q.d.793.7 | 22 | 63.23 | odd | 6 | |||
1512.2.q.d.1369.7 | 22 | 3.2 | odd | 2 | |||
1512.2.t.c.289.5 | 22 | 21.2 | odd | 6 | |||
1512.2.t.c.361.5 | 22 | 9.5 | odd | 6 | |||
3024.2.q.l.2305.7 | 22 | 252.23 | even | 6 | |||
3024.2.q.l.2881.7 | 22 | 12.11 | even | 2 | |||
3024.2.t.k.289.5 | 22 | 84.23 | even | 6 | |||
3024.2.t.k.1873.5 | 22 | 36.23 | even | 6 |