Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,2,Mod(193,1008)]
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, 2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.193");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.t (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 | 961.3 | ||
Character | \(\chi\) | \(=\) | 1008.961 |
Dual form | 1008.2.t.k.193.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(3\) | −1.34414 | − | 1.09237i | −0.776042 | − | 0.630682i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.66802 | 1.19317 | 0.596587 | − | 0.802548i | \(-0.296523\pi\) | ||||
0.596587 | + | 0.802548i | \(0.296523\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.94471 | + | 1.79391i | −0.735032 | + | 0.678033i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.613444 | + | 2.93661i | 0.204481 | + | 0.978870i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.36451 | −0.411416 | −0.205708 | − | 0.978613i | \(-0.565950\pi\) | ||||
−0.205708 | + | 0.978613i | \(0.565950\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.75597 | − | 4.77348i | −0.764368 | − | 1.32392i | −0.940580 | − | 0.339572i | \(-0.889718\pi\) |
0.176212 | − | 0.984352i | \(-0.443616\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.58620 | − | 2.91447i | −0.925953 | − | 0.752513i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.23930 | − | 2.14654i | −0.300575 | − | 0.520611i | 0.675691 | − | 0.737185i | \(-0.263845\pi\) |
−0.976266 | + | 0.216573i | \(0.930512\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.19600 | − | 3.80358i | 0.503797 | − | 0.872601i | −0.496194 | − | 0.868212i | \(-0.665269\pi\) |
0.999990 | − | 0.00438950i | \(-0.00139723\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.57358 | − | 0.286919i | 0.998038 | − | 0.0626108i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.69002 | 0.977936 | 0.488968 | − | 0.872302i | \(-0.337373\pi\) | ||||
0.488968 | + | 0.872302i | \(0.337373\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.11832 | 0.423664 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.38332 | − | 4.61734i | 0.458670 | − | 0.888607i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.94810 | − | 5.10625i | 0.547448 | − | 0.948207i | −0.451001 | − | 0.892524i | \(-0.648933\pi\) |
0.998448 | − | 0.0556837i | \(-0.0177338\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.55839 | − | 2.69921i | 0.279895 | − | 0.484792i | −0.691464 | − | 0.722411i | \(-0.743034\pi\) |
0.971358 | + | 0.237619i | \(0.0763671\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.83410 | + | 1.49056i | 0.319276 | + | 0.259473i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.18852 | + | 4.78617i | −0.877021 | + | 0.809011i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.15627 | + | 5.46681i | −0.518887 | + | 0.898739i | 0.480872 | + | 0.876791i | \(0.340320\pi\) |
−0.999759 | + | 0.0219479i | \(0.993013\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.51000 | + | 9.42678i | −0.241793 | + | 1.50949i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.38693 | + | 2.40224i | 0.216603 | + | 0.375167i | 0.953767 | − | 0.300546i | \(-0.0971690\pi\) |
−0.737164 | + | 0.675713i | \(0.763836\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.87889 | − | 8.45048i | 0.744023 | − | 1.28869i | −0.206626 | − | 0.978420i | \(-0.566248\pi\) |
0.950650 | − | 0.310267i | \(-0.100418\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.63668 | + | 7.83493i | 0.243982 | + | 1.16796i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.02505 | − | 8.70364i | −0.732979 | − | 1.26956i | −0.955605 | − | 0.294652i | \(-0.904796\pi\) |
0.222626 | − | 0.974904i | \(-0.428537\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.563800 | − | 6.97726i | 0.0805429 | − | 0.996751i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.679016 | + | 4.23903i | −0.0950812 | + | 0.593583i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.47823 | − | 2.56037i | −0.203050 | − | 0.351694i | 0.746459 | − | 0.665431i | \(-0.231752\pi\) |
−0.949510 | + | 0.313737i | \(0.898419\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.64055 | −0.490891 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.10667 | + | 2.71371i | −0.941301 | + | 0.359440i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.77809 | − | 3.07974i | 0.231487 | − | 0.400948i | −0.726759 | − | 0.686893i | \(-0.758974\pi\) |
0.958246 | + | 0.285945i | \(0.0923075\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.663043 | − | 1.14842i | −0.0848940 | − | 0.147041i | 0.820452 | − | 0.571715i | \(-0.193722\pi\) |
−0.905346 | + | 0.424675i | \(0.860388\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.46098 | − | 4.61040i | −0.814007 | − | 0.580856i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −7.35297 | − | 12.7357i | −0.912024 | − | 1.57967i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.14937 | − | 7.18692i | 0.506926 | − | 0.878021i | −0.493042 | − | 0.870006i | \(-0.664115\pi\) |
0.999968 | − | 0.00801592i | \(-0.00255158\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.30406 | − | 5.12325i | −0.758919 | − | 0.616766i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.3069 | −1.46056 | −0.730279 | − | 0.683149i | \(-0.760610\pi\) | ||||
−0.730279 | + | 0.683149i | \(0.760610\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.11577 | − | 1.93257i | −0.130591 | − | 0.226190i | 0.793314 | − | 0.608813i | \(-0.208354\pi\) |
−0.923905 | + | 0.382623i | \(0.875021\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.84733 | − | 2.31399i | −0.328781 | − | 0.267197i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.65358 | − | 2.44781i | 0.302404 | − | 0.278954i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.41535 | + | 11.1117i | 0.721783 | + | 1.25017i | 0.960284 | + | 0.279023i | \(0.0900106\pi\) |
−0.238501 | + | 0.971142i | \(0.576656\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.24737 | + | 3.60289i | −0.916375 | + | 0.400322i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.15934 | + | 8.93625i | −0.566312 | + | 0.980881i | 0.430615 | + | 0.902536i | \(0.358297\pi\) |
−0.996926 | + | 0.0783447i | \(0.975037\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.30648 | − | 5.72700i | −0.358638 | − | 0.621180i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −9.54059 | + | 3.64312i | −1.02286 | + | 0.390583i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.73159 | − | 13.3915i | 0.819547 | − | 1.41950i | −0.0864698 | − | 0.996254i | \(-0.527559\pi\) |
0.906017 | − | 0.423242i | \(-0.139108\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.9227 | + | 4.33908i | 1.45950 | + | 0.454860i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.04324 | + | 1.92578i | −0.522959 | + | 0.199694i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.85896 | − | 10.1480i | 0.601117 | − | 1.04117i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.55369 | + | 4.42311i | −0.259288 | + | 0.449099i | −0.966051 | − | 0.258351i | \(-0.916821\pi\) |
0.706764 | + | 0.707450i | \(0.250154\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.837053 | − | 4.00705i | −0.0841270 | − | 0.402723i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.69496 | −0.268159 | −0.134079 | − | 0.990971i | \(-0.542808\pi\) | ||||
−0.134079 | + | 0.990971i | \(0.542808\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.0214 | 1.28304 | 0.641519 | − | 0.767107i | \(-0.278304\pi\) | ||||
0.641519 | + | 0.767107i | \(0.278304\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 12.2024 | − | 0.765505i | 1.19083 | − | 0.0747056i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.49753 | − | 2.59379i | 0.144771 | − | 0.250751i | −0.784516 | − | 0.620108i | \(-0.787089\pi\) |
0.929288 | + | 0.369357i | \(0.120422\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.0132 | + | 17.3434i | 0.959093 | + | 1.66120i | 0.724710 | + | 0.689054i | \(0.241974\pi\) |
0.234383 | + | 0.972144i | \(0.424693\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.2143 | − | 3.90036i | 0.969496 | − | 0.370206i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.23211 | − | 10.7943i | −0.586267 | − | 1.01544i | −0.994716 | − | 0.102664i | \(-0.967263\pi\) |
0.408449 | − | 0.912781i | \(-0.366070\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.5130 | 1.16685 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 12.3272 | − | 11.0215i | 1.13965 | − | 1.01894i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.26077 | + | 1.95120i | 0.573924 | + | 0.178866i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.13810 | −0.830737 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.759903 | − | 4.74400i | 0.0685181 | − | 0.427753i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.68837 | −0.687669 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.0734 | −1.33754 | −0.668772 | − | 0.743467i | \(-0.733180\pi\) | ||||
−0.668772 | + | 0.743467i | \(0.733180\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −15.7890 | + | 6.02910i | −1.39014 | + | 0.530832i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.8406 | −1.29663 | −0.648316 | − | 0.761371i | \(-0.724527\pi\) | ||||
−0.648316 | + | 0.761371i | \(0.724527\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.55269 | + | 11.3363i | 0.221346 | + | 0.982980i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 6.35873 | − | 12.3191i | 0.547273 | − | 1.06026i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −20.1559 | −1.72203 | −0.861017 | − | 0.508577i | \(-0.830172\pi\) | ||||
−0.861017 | + | 0.508577i | \(0.830172\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.91552 | + | 17.1742i | 0.841023 | + | 1.45669i | 0.889031 | + | 0.457848i | \(0.151380\pi\) |
−0.0480074 | + | 0.998847i | \(0.515287\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.75323 | + | 17.1882i | −0.231864 | + | 1.44750i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.76056 | + | 6.51347i | 0.314473 | + | 0.544684i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.86557 | − | 13.6236i | 0.653200 | − | 1.13138i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −8.37959 | + | 8.76256i | −0.691137 | + | 0.722724i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 17.3033 | 1.41754 | 0.708772 | − | 0.705438i | \(-0.249250\pi\) | ||||
0.708772 | + | 0.705438i | \(0.249250\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.98976 | 0.324682 | 0.162341 | − | 0.986735i | \(-0.448096\pi\) | ||||
0.162341 | + | 0.986735i | \(0.448096\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.54330 | − | 4.95613i | 0.448149 | − | 0.400680i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.15781 | − | 7.20153i | 0.333963 | − | 0.578441i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.0994 | − | 20.9568i | 0.965637 | − | 1.67253i | 0.257742 | − | 0.966214i | \(-0.417022\pi\) |
0.707895 | − | 0.706318i | \(-0.249645\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.809924 | + | 5.05628i | −0.0642311 | + | 0.400989i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.12073 | + | 8.41345i | −0.718814 | + | 0.663073i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.34498 | + | 4.06162i | −0.183673 | + | 0.318131i | −0.943129 | − | 0.332428i | \(-0.892132\pi\) |
0.759456 | + | 0.650559i | \(0.225465\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.89342 | + | 3.97683i | 0.380952 | + | 0.309596i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.12627 | + | 10.6110i | 0.474065 | + | 0.821104i | 0.999559 | − | 0.0296928i | \(-0.00945290\pi\) |
−0.525494 | + | 0.850797i | \(0.676120\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.69072 | + | 15.0528i | −0.668517 | + | 1.15791i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 12.5168 | + | 4.11551i | 0.957181 | + | 0.314721i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.05503 | + | 7.02352i | 0.308298 | + | 0.533988i | 0.977990 | − | 0.208651i | \(-0.0669072\pi\) |
−0.669692 | + | 0.742639i | \(0.733574\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.11952 | + | 3.80007i | −0.311406 | + | 0.287258i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.75422 | + | 2.19727i | −0.432514 | + | 0.165157i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.91636 | − | 8.51538i | −0.367466 | − | 0.636469i | 0.621703 | − | 0.783253i | \(-0.286441\pi\) |
−0.989169 | + | 0.146784i | \(0.953108\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.8876 | 1.18092 | 0.590458 | − | 0.807068i | \(-0.298947\pi\) | ||||
0.590458 | + | 0.807068i | \(0.298947\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.363282 | + | 2.26794i | −0.0268546 | + | 0.167651i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.42097 | + | 14.5856i | −0.619122 | + | 1.07235i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.69105 | + | 2.92898i | 0.123661 | + | 0.214188i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.64821 | + | 13.2548i | 0.265368 | + | 0.964147i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.10949 | − | 1.92170i | −0.0802800 | − | 0.139049i | 0.823090 | − | 0.567911i | \(-0.192248\pi\) |
−0.903370 | + | 0.428862i | \(0.858915\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.92084 | + | 5.05904i | −0.210247 | + | 0.364158i | −0.951792 | − | 0.306745i | \(-0.900760\pi\) |
0.741545 | + | 0.670903i | \(0.234093\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.02870 | + | 25.1508i | −0.288501 | + | 1.80109i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.93695 | 0.138002 | 0.0690010 | − | 0.997617i | \(-0.478019\pi\) | ||||
0.0690010 | + | 0.997617i | \(0.478019\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.84540 | − | 3.19633i | −0.130817 | − | 0.226582i | 0.793175 | − | 0.608994i | \(-0.208427\pi\) |
−0.923992 | + | 0.382412i | \(0.875093\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −13.4281 | + | 5.12759i | −0.947148 | + | 0.361672i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.42694 | + | 15.2188i | 0.240524 | + | 1.06815i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.70037 | + | 6.40922i | 0.258445 | + | 0.447639i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.87706 | + | 13.7728i | 0.199970 | + | 0.957273i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.99647 | + | 5.19004i | −0.207270 | + | 0.359002i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.67097 | + | 9.82241i | 0.390406 | + | 0.676202i | 0.992503 | − | 0.122220i | \(-0.0390014\pi\) |
−0.602097 | + | 0.798423i | \(0.705668\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 16.5422 | + | 13.4437i | 1.13345 | + | 0.921147i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 13.0170 | − | 22.5460i | 0.887749 | − | 1.53763i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.81151 | + | 8.04478i | 0.122973 | + | 0.546115i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.611332 | + | 3.81649i | −0.0413100 | + | 0.257895i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.83096 | + | 11.8316i | −0.459500 | + | 0.795878i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.965547 | − | 1.67238i | 0.0646578 | − | 0.111991i | −0.831884 | − | 0.554949i | \(-0.812738\pi\) |
0.896542 | + | 0.442958i | \(0.146071\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.29947 | + | 6.22068i | 0.0866314 | + | 0.414712i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −19.7283 | −1.30941 | −0.654705 | − | 0.755884i | \(-0.727207\pi\) | ||||
−0.654705 | + | 0.755884i | \(0.727207\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 26.4197 | 1.74586 | 0.872931 | − | 0.487844i | \(-0.162216\pi\) | ||||
0.872931 | + | 0.487844i | \(0.162216\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.24072 | + | 0.391505i | −0.410609 | + | 0.0257591i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.24071 | + | 7.34513i | −0.277818 | + | 0.481196i | −0.970842 | − | 0.239719i | \(-0.922945\pi\) |
0.693024 | + | 0.720915i | \(0.256278\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −13.4069 | − | 23.2215i | −0.874571 | − | 1.51480i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.51498 | − | 21.9437i | 0.228322 | − | 1.42540i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.08023 | + | 13.9954i | 0.522667 | + | 0.905286i | 0.999652 | + | 0.0263743i | \(0.00839619\pi\) |
−0.476985 | + | 0.878911i | \(0.658270\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.9735 | 0.706868 | 0.353434 | − | 0.935460i | \(-0.385014\pi\) | ||||
0.353434 | + | 0.935460i | \(0.385014\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.0214 | + | 4.16640i | 0.963620 | + | 0.267274i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.50423 | − | 18.6154i | 0.0961017 | − | 1.18930i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −24.2084 | −1.54034 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 16.6966 | − | 6.37567i | 1.05810 | − | 0.404042i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.85873 | −0.180442 | −0.0902208 | − | 0.995922i | \(-0.528757\pi\) | ||||
−0.0902208 | + | 0.995922i | \(0.528757\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.39959 | −0.402339 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.81163 | + | 11.3098i | −0.113448 | + | 0.708248i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 24.5875 | 1.53373 | 0.766864 | − | 0.641810i | \(-0.221816\pi\) | ||||
0.766864 | + | 0.641810i | \(0.221816\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.66893 | − | 16.2934i | −0.227976 | − | 1.01242i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 16.8036 | + | 5.52501i | 1.04011 | + | 0.341990i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.957972 | −0.0590711 | −0.0295355 | − | 0.999564i | \(-0.509403\pi\) | ||||
−0.0295355 | + | 0.999564i | \(0.509403\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.94394 | − | 6.83111i | −0.242274 | − | 0.419632i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −25.0209 | + | 9.55433i | −1.53125 | + | 0.584715i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.31005 | + | 14.3934i | 0.506673 | + | 0.877583i | 0.999970 | + | 0.00772245i | \(0.00245816\pi\) |
−0.493297 | + | 0.869861i | \(0.664209\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.21801 | + | 12.5020i | −0.438463 | + | 0.759440i | −0.997571 | − | 0.0696545i | \(-0.977810\pi\) |
0.559108 | + | 0.829095i | \(0.311144\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −13.9743 | − | 21.0412i | −0.845760 | − | 1.27347i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.89048 | −0.174302 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.46642 | −0.268361 | −0.134181 | − | 0.990957i | \(-0.542840\pi\) | ||||
−0.134181 | + | 0.990957i | \(0.542840\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.88251 | + | 2.92057i | 0.531782 | + | 0.174850i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.62617 | − | 4.54867i | 0.156664 | − | 0.271351i | −0.776999 | − | 0.629501i | \(-0.783259\pi\) |
0.933664 | + | 0.358151i | \(0.116593\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.65751 | − | 9.79909i | 0.336304 | − | 0.582495i | −0.647431 | − | 0.762124i | \(-0.724156\pi\) |
0.983734 | + | 0.179629i | \(0.0574898\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −18.9607 | + | 7.24023i | −1.12314 | + | 0.428874i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.00658 | − | 2.18363i | −0.413585 | − | 0.128896i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.42826 | − | 9.40201i | 0.319309 | − | 0.553060i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.26421 | − | 3.15572i | 0.484456 | − | 0.184992i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.38422 | − | 9.32574i | −0.314549 | − | 0.544815i | 0.664792 | − | 0.747028i | \(-0.268520\pi\) |
−0.979342 | + | 0.202213i | \(0.935187\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.74397 | − | 8.21679i | 0.276204 | − | 0.478400i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.25207 | + | 6.30042i | −0.188704 | + | 0.365587i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −12.9255 | − | 22.3877i | −0.747503 | − | 1.29471i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.67135 | + | 25.1860i | 0.326891 | + | 1.45170i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.62242 | + | 2.94390i | 0.208102 | + | 0.169123i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.76901 | − | 3.06402i | −0.101293 | − | 0.175445i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.42151 | −0.537714 | −0.268857 | − | 0.963180i | \(-0.586646\pi\) | ||||
−0.268857 | + | 0.963180i | \(0.586646\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −17.5027 | − | 14.2242i | −0.995692 | − | 0.809189i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.65754 | + | 9.79914i | −0.320809 | + | 0.555658i | −0.980655 | − | 0.195743i | \(-0.937288\pi\) |
0.659846 | + | 0.751401i | \(0.270622\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.8431 | − | 18.7808i | −0.612889 | − | 1.06156i | −0.990751 | − | 0.135693i | \(-0.956674\pi\) |
0.377862 | − | 0.925862i | \(-0.376660\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −17.2380 | − | 12.3006i | −0.971251 | − | 0.693062i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.6087 | + | 21.8389i | 0.708174 | + | 1.22659i | 0.965534 | + | 0.260278i | \(0.0838141\pi\) |
−0.257360 | + | 0.966316i | \(0.582853\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.02272 | + | 6.96755i | −0.225229 | + | 0.390108i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.84628 | + | 1.85057i | −0.270493 | + | 0.103289i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10.8860 | −0.605715 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.83802 | − | 10.1118i | −0.323835 | − | 0.560899i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.48626 | − | 34.2502i | 0.303391 | − | 1.89404i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 25.3858 | + | 7.91160i | 1.39956 | + | 0.436180i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.51226 | − | 14.7437i | −0.467876 | − | 0.810386i | 0.531450 | − | 0.847090i | \(-0.321647\pi\) |
−0.999326 | + | 0.0367042i | \(0.988314\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −17.9901 | − | 5.91514i | −0.985851 | − | 0.324148i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 11.0706 | − | 19.1748i | 0.604851 | − | 1.04763i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.85166 | + | 11.8674i | 0.373233 | + | 0.646459i | 0.990061 | − | 0.140639i | \(-0.0449157\pi\) |
−0.616827 | + | 0.787098i | \(0.711582\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.41458 | + | 21.3169i | −0.185455 | + | 1.15778i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.12644 | + | 3.68310i | −0.115153 | + | 0.199451i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.4201 | + | 14.5802i | 0.616628 | + | 0.787254i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −16.8193 | − | 13.6689i | −0.905523 | − | 0.735910i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.2183 | − | 21.1627i | 0.655912 | − | 1.13607i | −0.325752 | − | 0.945455i | \(-0.605618\pi\) |
0.981664 | − | 0.190618i | \(-0.0610491\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.4881 | − | 19.8979i | 0.614943 | − | 1.06511i | −0.375451 | − | 0.926842i | \(-0.622512\pi\) |
0.990394 | − | 0.138271i | \(-0.0441544\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −28.6091 | + | 1.34853i | −1.52704 | + | 0.0719790i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 24.0305 | 1.27901 | 0.639507 | − | 0.768785i | \(-0.279139\pi\) | ||||
0.639507 | + | 0.768785i | \(0.279139\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −32.8350 | −1.74270 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.28394 | − | 9.46179i | −0.332581 | − | 0.500771i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9.84234 | − | 17.0474i | 0.519459 | − | 0.899729i | −0.480285 | − | 0.877112i | \(-0.659467\pi\) |
0.999744 | − | 0.0226169i | \(-0.00719980\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.144819 | − | 0.250833i | −0.00762204 | − | 0.0132018i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 12.2829 | + | 9.98221i | 0.644686 | + | 0.523930i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.97690 | − | 5.15613i | −0.155818 | − | 0.269884i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.2006 | 0.741263 | 0.370632 | − | 0.928780i | \(-0.379141\pi\) | ||||
0.370632 | + | 0.928780i | \(0.379141\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.20364 | + | 5.54653i | −0.322949 | + | 0.288741i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.46779 | + | 2.32737i | 0.387708 | + | 0.120831i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −28.4669 | −1.47396 | −0.736980 | − | 0.675914i | \(-0.763749\pi\) | ||||
−0.736980 | + | 0.675914i | \(0.763749\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10.3343 | + | 8.39857i | 0.533660 | + | 0.433700i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −32.4994 | −1.67381 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.25098 | 0.218358 | 0.109179 | − | 0.994022i | \(-0.465178\pi\) | ||||
0.109179 | + | 0.994022i | \(0.465178\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 20.2608 | + | 16.4657i | 1.03799 | + | 0.843565i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 35.8428 | 1.83148 | 0.915740 | − | 0.401772i | \(-0.131605\pi\) | ||||
0.915740 | + | 0.401772i | \(0.131605\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.07981 | − | 6.53080i | 0.360820 | − | 0.332840i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 27.8087 | + | 9.14350i | 1.41360 | + | 0.464790i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −31.7944 | −1.61204 | −0.806020 | − | 0.591888i | \(-0.798383\pi\) | ||||
−0.806020 | + | 0.591888i | \(0.798383\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.81235 | − | 10.0673i | −0.293943 | − | 0.509125i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 19.9480 | + | 16.2115i | 1.00624 | + | 0.817762i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 17.1163 | + | 29.6462i | 0.861213 | + | 1.49166i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.07669 | − | 5.32899i | 0.154415 | − | 0.267454i | −0.778431 | − | 0.627730i | \(-0.783984\pi\) |
0.932846 | + | 0.360276i | \(0.117317\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8.95227 | − | 18.0261i | 0.448174 | − | 0.902432i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.8229 | −0.740222 | −0.370111 | − | 0.928988i | \(-0.620680\pi\) | ||||
−0.370111 | + | 0.928988i | \(0.620680\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −17.1795 | −0.855770 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −22.0041 | + | 9.61259i | −1.09339 | + | 0.477653i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.30677 | − | 7.45954i | 0.213479 | − | 0.369756i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.7222 | + | 18.5713i | −0.530177 | + | 0.918293i | 0.469203 | + | 0.883090i | \(0.344541\pi\) |
−0.999380 | + | 0.0352032i | \(0.988792\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 27.0924 | + | 22.0177i | 1.33637 | + | 1.08605i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.06689 | + | 9.17892i | 0.101705 | + | 0.451665i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.7652 | + | 23.8421i | −0.675708 | + | 1.17036i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.43272 | − | 33.9160i | 0.266042 | − | 1.66087i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.2332 | − | 22.9205i | −0.646483 | − | 1.11974i | −0.983957 | − | 0.178406i | \(-0.942906\pi\) |
0.337474 | − | 0.941335i | \(-0.390428\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.54824 | + | 14.8060i | −0.416616 | + | 0.721600i | −0.995597 | − | 0.0937415i | \(-0.970117\pi\) |
0.578981 | + | 0.815341i | \(0.303451\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 22.4766 | − | 20.0958i | 1.09285 | − | 0.977092i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.62524 | − | 4.54705i | −0.127343 | − | 0.220564i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.34959 | + | 1.04392i | 0.162098 | + | 0.0505186i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.06041 | − | 12.8630i | 0.0994777 | − | 0.621030i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.0292 | + | 20.8352i | 0.579425 | + | 1.00359i | 0.995545 | + | 0.0942846i | \(0.0300564\pi\) |
−0.416120 | + | 0.909310i | \(0.636610\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.58345 | −0.316380 | −0.158190 | − | 0.987409i | \(-0.550566\pi\) | ||||
−0.158190 | + | 0.987409i | \(0.550566\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −25.4545 | + | 9.71990i | −1.22045 | + | 0.466034i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 10.2993 | − | 17.8389i | 0.492681 | − | 0.853348i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.6327 | + | 18.4164i | 0.507472 | + | 0.878967i | 0.999963 | + | 0.00864927i | \(0.00275318\pi\) |
−0.492491 | + | 0.870318i | \(0.663913\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 20.8354 | − | 2.62450i | 0.992160 | − | 0.124976i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.471724 | − | 0.817050i | −0.0224123 | − | 0.0388192i | 0.854602 | − | 0.519284i | \(-0.173801\pi\) |
−0.877014 | + | 0.480465i | \(0.840468\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 20.6280 | − | 35.7288i | 0.977862 | − | 1.69371i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −23.2582 | − | 18.9017i | −1.10007 | − | 0.894019i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17.7959 | −0.839842 | −0.419921 | − | 0.907561i | \(-0.637942\pi\) | ||||
−0.419921 | + | 0.907561i | \(0.637942\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.89249 | − | 3.27789i | −0.0891139 | − | 0.154350i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.36281 | − | 4.35830i | −0.251967 | − | 0.204771i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 37.1461 | + | 11.5768i | 1.74144 | + | 0.542727i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.88851 | + | 11.9313i | 0.322231 | + | 0.558120i | 0.980948 | − | 0.194270i | \(-0.0622339\pi\) |
−0.658717 | + | 0.752391i | \(0.728901\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −12.8649 | + | 0.606405i | −0.600484 | + | 0.0283046i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.97576 | + | 5.15417i | −0.138595 | + | 0.240054i | −0.926965 | − | 0.375148i | \(-0.877592\pi\) |
0.788370 | + | 0.615201i | \(0.210925\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.7618 | + | 30.7644i | 0.825463 | + | 1.42974i | 0.901565 | + | 0.432643i | \(0.142419\pi\) |
−0.0761023 | + | 0.997100i | \(0.524248\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −13.4554 | + | 5.13802i | −0.623981 | + | 0.238270i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12.2574 | + | 21.2305i | −0.567207 | + | 0.982431i | 0.429634 | + | 0.903003i | \(0.358643\pi\) |
−0.996841 | + | 0.0794277i | \(0.974691\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.82333 | + | 21.4200i | 0.222721 | + | 0.989086i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −39.1559 | + | 14.9519i | −1.80421 | + | 0.688945i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.65731 | + | 11.5308i | −0.306103 | + | 0.530187i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.65183 | − | 8.05720i | 0.213440 | − | 0.369690i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.61200 | − | 5.91163i | 0.302743 | − | 0.270675i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −19.2352 | −0.878878 | −0.439439 | − | 0.898272i | \(-0.644823\pi\) | ||||
−0.439439 | + | 0.898272i | \(0.644823\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 34.7943 | 1.58648 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 21.4502 | − | 1.34565i | 0.976017 | − | 0.0612294i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.81328 | + | 11.8009i | −0.309375 | + | 0.535853i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.3089 | − | 21.3197i | −0.557770 | − | 0.966086i | −0.997682 | − | 0.0680455i | \(-0.978324\pi\) |
0.439912 | − | 0.898041i | \(-0.355010\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.58879 | − | 2.89781i | 0.343177 | − | 0.131044i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.73086 | − | 16.8543i | −0.439147 | − | 0.760626i | 0.558476 | − | 0.829520i | \(-0.311386\pi\) |
−0.997624 | + | 0.0688947i | \(0.978053\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −14.6143 | −0.658197 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.23327 | − | 10.6909i | −0.100378 | − | 0.480519i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 23.9333 | − | 22.0774i | 1.07356 | − | 0.990306i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.17781 | 0.321323 | 0.160661 | − | 0.987010i | \(-0.448637\pi\) | ||||
0.160661 | + | 0.987010i | \(0.448637\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.35659 | − | 20.9549i | 0.149961 | − | 0.936195i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −22.1112 | −0.985889 | −0.492945 | − | 0.870061i | \(-0.664079\pi\) | ||||
−0.492945 | + | 0.870061i | \(0.664079\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.19021 | −0.319960 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 28.1248 | − | 10.7396i | 1.24907 | − | 0.476962i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −31.3575 | −1.38989 | −0.694947 | − | 0.719061i | \(-0.744572\pi\) | ||||
−0.694947 | + | 0.719061i | \(0.744572\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.63670 | + | 1.75670i | 0.249353 | + | 0.0777120i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −12.3287 | − | 19.2048i | −0.544323 | − | 0.847913i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 34.7414 | 1.53089 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.85675 | + | 11.8762i | 0.301559 | + | 0.522316i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.22176 | − | 13.8702i | 0.0975243 | − | 0.608835i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.76588 | + | 3.05859i | 0.0773645 | + | 0.133999i | 0.902112 | − | 0.431502i | \(-0.142016\pi\) |
−0.824748 | + | 0.565501i | \(0.808683\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.03821 | − | 12.1905i | 0.307759 | − | 0.533055i | −0.670113 | − | 0.742259i | \(-0.733754\pi\) |
0.977872 | + | 0.209205i | \(0.0670875\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 9.68832 | − | 0.607786i | 0.422833 | − | 0.0265260i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.72526 | −0.336518 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00374 | −0.0436409 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.1347 | + | 3.33230i | 0.439810 | + | 0.144610i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.64469 | − | 13.2410i | 0.331128 | − | 0.573531i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.99543 | − | 6.92029i | 0.172737 | − | 0.299190i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.69368 | + | 16.8164i | −0.116241 | + | 0.725681i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.769313 | + | 9.52056i | −0.0331367 | + | 0.410080i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.5799 | − | 20.0569i | 0.497858 | − | 0.862315i | −0.502139 | − | 0.864787i | \(-0.667454\pi\) |
0.999997 | + | 0.00247207i | \(0.000786884\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −21.3552 | − | 17.3552i | −0.916440 | − | 0.744782i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 26.7155 | + | 46.2725i | 1.14436 | + | 1.98210i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.76832 | − | 9.99102i | 0.246635 | − | 0.427185i | −0.715955 | − | 0.698147i | \(-0.754008\pi\) |
0.962590 | + | 0.270962i | \(0.0873417\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.96574 | − | 2.65159i | 0.126575 | − | 0.113167i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.9480 | − | 22.4266i | −0.551605 | − | 0.955407i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −32.4094 | − | 10.1005i | −1.37819 | − | 0.429518i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 27.2519 | − | 10.4062i | 1.15678 | − | 0.441720i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.04108 | − | 1.80321i | −0.0441122 | − | 0.0764045i | 0.843126 | − | 0.537716i | \(-0.180713\pi\) |
−0.887238 | + | 0.461311i | \(0.847379\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −53.7842 | −2.27483 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.926526 | − | 5.78422i | 0.0391180 | − | 0.244210i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.35403 | + | 5.80936i | −0.141356 | + | 0.244835i | −0.928007 | − | 0.372562i | \(-0.878479\pi\) |
0.786652 | + | 0.617397i | \(0.211813\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −16.6274 | − | 28.7995i | −0.699519 | − | 1.21160i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 9.57550 | − | 21.8016i | 0.402133 | − | 0.915581i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.01112 | + | 6.94746i | 0.168155 | + | 0.291253i | 0.937771 | − | 0.347254i | \(-0.112886\pi\) |
−0.769616 | + | 0.638507i | \(0.779553\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.34215 | − | 5.78877i | 0.139865 | − | 0.242253i | −0.787581 | − | 0.616212i | \(-0.788667\pi\) |
0.927445 | + | 0.373959i | \(0.122000\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.607892 | + | 3.79501i | −0.0253951 | + | 0.158539i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.93496 | 0.414316 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14.0088 | − | 24.2639i | −0.583193 | − | 1.01012i | −0.995098 | − | 0.0988925i | \(-0.968470\pi\) |
0.411906 | − | 0.911227i | \(-0.364863\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9.45239 | − | 3.60944i | 0.392828 | − | 0.150003i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.99736 | − | 26.6338i | −0.248812 | − | 1.10496i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.01706 | + | 3.49366i | 0.0835382 | + | 0.144692i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 32.8892 | − | 29.4055i | 1.35980 | − | 1.21577i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.35952 | − | 5.81886i | 0.138662 | − | 0.240170i | −0.788328 | − | 0.615255i | \(-0.789053\pi\) |
0.926990 | + | 0.375085i | \(0.122386\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.84443 | − | 11.8549i | −0.282020 | − | 0.488473i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.60354 | − | 2.11587i | −0.107095 | − | 0.0870354i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.19462 | + | 5.53325i | −0.131187 | + | 0.227223i | −0.924135 | − | 0.382067i | \(-0.875212\pi\) |
0.792947 | + | 0.609290i | \(0.208546\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 16.7038 | + | 5.20583i | 0.684791 | + | 0.213418i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.01110 | + | 6.31219i | −0.0413815 | + | 0.258341i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.96098 | + | 5.12856i | −0.120982 | + | 0.209547i | −0.920155 | − | 0.391554i | \(-0.871938\pi\) |
0.799173 | + | 0.601101i | \(0.205271\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.97104 | + | 3.41393i | −0.0804002 | + | 0.139257i | −0.903422 | − | 0.428753i | \(-0.858953\pi\) |
0.823022 | + | 0.568010i | \(0.192287\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 23.6506 | + | 7.77631i | 0.963126 | + | 0.316676i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −24.3806 | −0.991213 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.09551 | 0.287998 | 0.143999 | − | 0.989578i | \(-0.454004\pi\) | ||||
0.143999 | + | 0.989578i | \(0.454004\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 12.0183 | − | 24.1997i | 0.487006 | − | 0.980623i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −27.6978 | + | 47.9739i | −1.12053 | + | 1.94082i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.87000 | + | 11.8992i | 0.277477 | + | 0.480604i | 0.970757 | − | 0.240064i | \(-0.0771685\pi\) |
−0.693280 | + | 0.720668i | \(0.743835\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.02743 | − | 12.6571i | 0.0817541 | − | 0.510383i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16.3605 | − | 28.3372i | −0.658649 | − | 1.14081i | −0.980966 | − | 0.194182i | \(-0.937795\pi\) |
0.322317 | − | 0.946632i | \(-0.395538\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22.6180 | −0.909094 | −0.454547 | − | 0.890723i | \(-0.650199\pi\) | ||||
−0.454547 | + | 0.890723i | \(0.650199\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 11.1778 | − | 21.6554i | 0.448550 | − | 0.869001i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.98740 | + | 39.9124i | 0.360073 | + | 1.59905i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.1043 | −1.24417 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 9.69714 | − | 3.70289i | 0.387266 | − | 0.147879i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 15.6463 | 0.623858 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 43.9355 | 1.74905 | 0.874523 | − | 0.484984i | \(-0.161175\pi\) | ||||
0.874523 | + | 0.484984i | \(0.161175\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.10713 | − | 19.3975i | 0.123497 | − | 0.770983i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −40.2160 | −1.59592 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −34.8596 | + | 16.5378i | −1.38119 | + | 0.655252i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.54958 | − | 36.1405i | −0.298657 | − | 1.42970i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 39.8595 | 1.57436 | 0.787178 | − | 0.616726i | \(-0.211541\pi\) | ||||
0.787178 | + | 0.616726i | \(0.211541\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.24049 | − | 16.0050i | −0.364410 | − | 0.631176i | 0.624272 | − | 0.781207i | \(-0.285396\pi\) |
−0.988681 | + | 0.150032i | \(0.952062\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −42.1253 | + | 16.0857i | −1.65868 | + | 0.633375i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.76068 | − | 15.1739i | −0.344418 | − | 0.596549i | 0.640830 | − | 0.767683i | \(-0.278590\pi\) |
−0.985248 | + | 0.171134i | \(0.945257\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.42622 | + | 4.20234i | −0.0952376 | + | 0.164956i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.35297 | − | 12.7922i | 0.248992 | − | 0.501365i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 27.4055 | 1.07246 | 0.536230 | − | 0.844072i | \(-0.319848\pi\) | ||||
0.536230 | + | 0.844072i | \(0.319848\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −39.5951 | −1.54711 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.99075 | − | 4.46211i | 0.194708 | − | 0.174083i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16.2580 | − | 28.1597i | 0.633322 | − | 1.09695i | −0.353546 | − | 0.935417i | \(-0.615024\pi\) |
0.986868 | − | 0.161529i | \(-0.0516424\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.4336 | + | 33.6599i | −0.755878 | + | 1.30922i | 0.189059 | + | 0.981966i | \(0.439456\pi\) |
−0.944937 | + | 0.327253i | \(0.893877\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 22.1063 | − | 8.44138i | 0.858537 | − | 0.327836i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.81061 | + | 30.2454i | 0.264104 | + | 1.17287i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 13.8266 | − | 23.9484i | 0.535369 | − | 0.927286i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.12469 | + | 1.19318i | −0.120808 | + | 0.0461309i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.904731 | + | 1.56704i | 0.0349268 | + | 0.0604949i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.50978 | + | 7.81117i | −0.173839 | + | 0.301099i | −0.939759 | − | 0.341838i | \(-0.888951\pi\) |
0.765920 | + | 0.642936i | \(0.222284\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.04863 | − | 9.78100i | 0.194322 | − | 0.376471i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.41435 | − | 16.3061i | −0.361823 | − | 0.626695i | 0.626438 | − | 0.779471i | \(-0.284512\pi\) |
−0.988261 | + | 0.152776i | \(0.951179\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.96847 | − | 13.1827i | −0.113919 | − | 0.505907i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 26.5176 | + | 21.5506i | 1.01616 | + | 0.825821i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.35476 | − | 9.27471i | −0.204894 | − | 0.354887i | 0.745205 | − | 0.666836i | \(-0.232352\pi\) |
−0.950099 | + | 0.311949i | \(0.899018\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −53.7763 | −2.05468 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −35.5118 | − | 28.8601i | −1.35486 | − | 1.10108i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8.14791 | + | 14.1126i | −0.310411 | + | 0.537647i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.52277 | + | 4.36956i | 0.0959705 | + | 0.166226i | 0.910013 | − | 0.414579i | \(-0.136071\pi\) |
−0.814043 | + | 0.580805i | \(0.802738\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8.81609 | + | 6.29095i | 0.334896 | + | 0.238973i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 26.4548 | + | 45.8210i | 1.00349 | + | 1.73809i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.43766 | − | 5.95421i | 0.130211 | − | 0.225532i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 13.7238 | − | 5.24047i | 0.519080 | − | 0.198213i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 44.9138 | 1.69637 | 0.848186 | − | 0.529698i | \(-0.177695\pi\) | ||||
0.848186 | + | 0.529698i | \(0.177695\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.8623 | + | 24.0102i | 0.522827 | + | 0.905563i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.34567 | + | 45.8583i | −0.276654 | + | 1.72713i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.24092 | − | 4.83451i | 0.197105 | − | 0.181820i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.72658 | − | 6.45463i | −0.139955 | − | 0.242409i | 0.787524 | − | 0.616283i | \(-0.211362\pi\) |
−0.927479 | + | 0.373875i | \(0.878029\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −28.6953 | + | 25.6558i | −1.07616 | + | 0.962168i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.30887 | − | 12.6593i | 0.273719 | − | 0.474096i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10.0332 | + | 17.3781i | 0.375222 | + | 0.649903i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.42717 | − | 27.6384i | 0.165336 | − | 1.03218i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −21.5574 | + | 37.3385i | −0.803954 | + | 1.39249i | 0.113040 | + | 0.993590i | \(0.463941\pi\) |
−0.916995 | + | 0.398899i | \(0.869392\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −25.3229 | + | 23.3592i | −0.943074 | + | 0.869943i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −14.7500 | − | 11.9872i | −0.548559 | − | 0.445808i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.24501 | − | 10.8167i | 0.231934 | − | 0.401721i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.389926 | − | 0.675372i | 0.0144616 | − | 0.0250482i | −0.858704 | − | 0.512472i | \(-0.828730\pi\) |
0.873166 | + | 0.487424i | \(0.162063\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −15.6396 | − | 22.0092i | −0.579245 | − | 0.815154i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −24.1857 | −0.894540 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15.6772 | −0.579050 | −0.289525 | − | 0.957170i | \(-0.593497\pi\) | ||||
−0.289525 | + | 0.957170i | \(0.593497\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −22.3569 | + | 23.3787i | −0.824647 | + | 0.862335i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.66187 | + | 9.80664i | −0.208558 | + | 0.361232i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.87450 | − | 15.3711i | −0.326454 | − | 0.565434i | 0.655352 | − | 0.755324i | \(-0.272520\pi\) |
−0.981805 | + | 0.189889i | \(0.939187\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 32.5396 | + | 26.4446i | 1.19537 | + | 0.971467i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.74308 | + | 6.48321i | 0.137320 | + | 0.237846i | 0.926481 | − | 0.376340i | \(-0.122818\pi\) |
−0.789161 | + | 0.614186i | \(0.789484\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 46.1656 | 1.69138 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −29.4073 | − | 9.66910i | −1.07596 | − | 0.353774i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.74076 | + | 7.73060i | 0.0636062 | + | 0.282470i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −23.3599 | −0.852415 | −0.426208 | − | 0.904625i | \(-0.640151\pi\) | ||||
−0.426208 | + | 0.904625i | \(0.640151\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.84255 | + | 3.12280i | 0.140030 | + | 0.113801i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10.6447 | 0.387402 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 31.2350 | 1.13525 | 0.567627 | − | 0.823286i | \(-0.307862\pi\) | ||||
0.567627 | + | 0.823286i | \(0.307862\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.60197 | + | 6.99074i | 0.312232 | + | 0.253748i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16.6147 | 0.602282 | 0.301141 | − | 0.953580i | \(-0.402633\pi\) | ||||
0.301141 | + | 0.953580i | \(0.402633\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −50.5853 | − | 15.7651i | −1.83131 | − | 0.570736i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 14.7896 | − | 13.2230i | 0.534720 | − | 0.478080i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −19.6014 | −0.707766 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.3794 | + | 31.8340i | 0.662777 | + | 1.14796i | 0.979883 | + | 0.199573i | \(0.0639556\pi\) |
−0.317106 | + | 0.948390i | \(0.602711\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −33.0492 | − | 26.8587i | −1.19024 | − | 0.967294i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.77690 | + | 8.27382i | 0.171813 | + | 0.297589i | 0.939054 | − | 0.343770i | \(-0.111704\pi\) |
−0.767241 | + | 0.641359i | \(0.778371\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.30116 | − | 5.71778i | 0.118581 | − | 0.205389i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −12.8669 | + | 25.9085i | −0.461598 | + | 0.929463i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 12.1828 | 0.436495 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.7929 | 0.600897 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −16.5510 | − | 25.7822i | −0.591486 | − | 0.921380i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 32.2814 | − | 55.9130i | 1.15217 | − | 1.99562i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10.1339 | + | 17.5524i | −0.361233 | + | 0.625674i | −0.988164 | − | 0.153401i | \(-0.950977\pi\) |
0.626931 | + | 0.779075i | \(0.284311\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.28765 | + | 1.04646i | 0.0458416 | + | 0.0372550i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 31.4837 | + | 9.81203i | 1.11943 | + | 0.348876i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.65465 | + | 6.33004i | −0.129780 | + | 0.224786i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.16089 | + | 13.4902i | −0.0766389 | + | 0.478450i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 21.4236 | + | 37.1068i | 0.758863 | + | 1.31439i | 0.943431 | + | 0.331570i | \(0.107578\pi\) |
−0.184567 | + | 0.982820i | \(0.559088\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.4551 | + | 21.5729i | −0.440630 | + | 0.763194i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 44.0685 | + | 14.4897i | 1.55709 | + | 0.511969i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.52248 | + | 2.63702i | 0.0537273 | + | 0.0930584i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −24.3343 | + | 22.4472i | −0.857670 | + | 0.791161i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.55309 | − | 28.4245i | 0.160276 | − | 1.00059i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −10.4750 | − | 18.1432i | −0.368282 | − | 0.637883i | 0.621015 | − | 0.783798i | \(-0.286720\pi\) |
−0.989297 | + | 0.145916i | \(0.953387\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.0129 | 0.667633 | 0.333817 | − | 0.942638i | \(-0.391663\pi\) | ||||
0.333817 | + | 0.942638i | \(0.391663\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 23.3588 | − | 8.91968i | 0.819231 | − | 0.312827i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.25644 | + | 10.8365i | −0.219154 | + | 0.379585i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −21.4281 | − | 37.1145i | −0.749673 | − | 1.29847i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.20138 | + | 43.5474i | −0.146808 | + | 1.52167i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16.6953 | + | 28.9171i | 0.582669 | + | 1.00921i | 0.995162 | + | 0.0982515i | \(0.0313249\pi\) |
−0.412493 | + | 0.910961i | \(0.635342\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.52040 | + | 7.82955i | −0.157571 | + | 0.272921i | −0.933992 | − | 0.357293i | \(-0.883700\pi\) |
0.776421 | + | 0.630214i | \(0.217033\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.88521 | + | 3.15748i | 0.135266 | + | 0.109929i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −22.4071 | −0.779172 | −0.389586 | − | 0.920990i | \(-0.627382\pi\) | ||||
−0.389586 | + | 0.920990i | \(0.627382\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.4090 | − | 19.7610i | −0.396252 | − | 0.686328i | 0.597008 | − | 0.802235i | \(-0.296356\pi\) |
−0.993260 | + | 0.115907i | \(0.963023\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.00352 | + | 4.87900i | 0.208260 | + | 0.169251i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −15.6757 | + | 7.43672i | −0.543129 | + | 0.257667i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16.3450 | + | 28.3104i | 0.565642 | + | 0.979720i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.74902 | − | 13.6287i | −0.302410 | − | 0.471076i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8.05060 | − | 13.9441i | 0.277938 | − | 0.481402i | −0.692934 | − | 0.721001i | \(-0.743682\pi\) |
0.970872 | + | 0.239598i | \(0.0770158\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.88254 | − | 4.99271i | −0.0993980 | − | 0.172162i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −8.49880 | + | 3.24530i | −0.292714 | + | 0.111774i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −23.1870 | + | 40.1611i | −0.797657 | + | 1.38158i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 17.7710 | − | 16.3929i | 0.610618 | − | 0.563267i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −18.3088 | + | 6.99128i | −0.628355 | + | 0.239940i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −14.8029 | + | 25.6394i | −0.507438 | + | 0.878909i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12.7818 | − | 22.1387i | 0.437639 | − | 0.758013i | −0.559868 | − | 0.828582i | \(-0.689148\pi\) |
0.997507 | + | 0.0705689i | \(0.0224815\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 33.3949 | + | 10.9803i | 1.14208 | + | 0.375517i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −52.6556 | −1.79868 | −0.899340 | − | 0.437250i | \(-0.855952\pi\) | ||||
−0.899340 | + | 0.437250i | \(0.855952\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 30.8862 | 1.05382 | 0.526912 | − | 0.849920i | \(-0.323350\pi\) | ||||
0.526912 | + | 0.849920i | \(0.323350\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7.03251 | + | 10.5889i | 0.239667 | + | 0.360869i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0.929596 | − | 1.61011i | 0.0316438 | − | 0.0548087i | −0.849770 | − | 0.527154i | \(-0.823259\pi\) |
0.881414 | + | 0.472345i | \(0.156592\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.8189 | + | 18.7389i | 0.367853 | + | 0.637141i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −17.5669 | + | 6.70798i | −0.596602 | + | 0.227815i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.75383 | − | 15.1621i | −0.296953 | − | 0.514338i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −45.7421 | −1.54991 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −14.5555 | − | 4.78585i | −0.492629 | − | 0.161976i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 14.9517 | − | 13.7922i | 0.505459 | − | 0.466262i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13.3037 | −0.449234 | −0.224617 | − | 0.974447i | \(-0.572113\pi\) | ||||
−0.224617 | + | 0.974447i | \(0.572113\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.95002 | + | 18.4167i | −0.0995017 | + | 0.621180i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 21.2210 | 0.714954 | 0.357477 | − | 0.933922i | \(-0.383637\pi\) | ||||
0.357477 | + | 0.933922i | \(0.383637\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 49.8289 | 1.67687 | 0.838437 | − | 0.544998i | \(-0.183470\pi\) | ||||
0.838437 | + | 0.544998i | \(0.183470\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −15.3524 | + | 5.86237i | −0.516064 | + | 0.197061i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.77272 | 0.0595220 | 0.0297610 | − | 0.999557i | \(-0.490525\pi\) | ||||
0.0297610 | + | 0.999557i | \(0.490525\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 29.3133 | − | 27.0402i | 0.983138 | − | 0.906899i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 11.2536 | − | 4.91620i | 0.377011 | − | 0.164699i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −44.1400 | −1.47709 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −13.1169 | − | 22.7192i | −0.438450 | − | 0.759419i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.08192 | + | 44.2118i | −0.236458 | + | 1.47619i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.18855 | − | 15.9150i | −0.306455 | − | 0.530796i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.66395 | + | 6.34615i | −0.122064 | + | 0.211421i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 19.8894 | − | 40.0488i | 0.661878 | − | 1.33274i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 42.3884 | 1.40904 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10.5750 | 0.351136 | 0.175568 | − | 0.984467i | \(-0.443824\pi\) | ||||
0.175568 | + | 0.984467i | \(0.443824\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.65321 | − | 7.91406i | −0.0548335 | − | 0.262493i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.2693 | + | 26.4473i | −0.505896 | + | 0.876237i | 0.494081 | + | 0.869416i | \(0.335505\pi\) |
−0.999977 | + | 0.00682127i | \(0.997829\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.03999 | − | 12.1936i | 0.232990 | − | 0.403550i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.969243 | + | 6.05090i | −0.0320422 | + | 0.200037i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 28.8608 | − | 26.6227i | 0.953066 | − | 0.879160i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.552490 | − | 0.956940i | 0.0182249 | − | 0.0315665i | −0.856769 | − | 0.515700i | \(-0.827532\pi\) |
0.874994 | + | 0.484134i | \(0.160865\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 12.6639 | + | 10.2918i | 0.417288 | + | 0.339126i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 33.9174 | + | 58.7466i | 1.11640 | + | 1.93367i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.68598 | + | 11.5805i | −0.219834 | + | 0.380763i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7.98792 | + | 38.2389i | 0.262358 | + | 1.25593i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.63729 | + | 4.56792i | 0.0865266 | + | 0.149869i | 0.906041 | − | 0.423191i | \(-0.139090\pi\) |
−0.819514 | + | 0.573059i | \(0.805757\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −25.3005 | − | 17.4665i | −0.829189 | − | 0.572442i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 18.3089 | − | 6.99131i | 0.599405 | − | 0.228885i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.51174 | + | 7.81456i | 0.147550 | + | 0.255564i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17.7481 | 0.579806 | 0.289903 | − | 0.957056i | \(-0.406377\pi\) | ||||
0.289903 | + | 0.957056i | \(0.406377\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.94096 | + | 37.0889i | −0.193876 | + | 1.21035i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13.8684 | − | 24.0207i | 0.452096 | − | 0.783053i | −0.546420 | − | 0.837511i | \(-0.684010\pi\) |
0.998516 | + | 0.0544582i | \(0.0173432\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.50474 | + | 11.2665i | 0.211824 | + | 0.366889i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 9.73349 | + | 35.3641i | 0.316630 | + | 1.15040i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.63828 | + | 13.2299i | 0.248211 | + | 0.429914i | 0.963029 | − | 0.269396i | \(-0.0868241\pi\) |
−0.714819 | + | 0.699310i | \(0.753491\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.15006 | + | 10.6522i | −0.199639 | + | 0.345785i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.90831 | − | 43.1280i | 0.224017 | − | 1.39852i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −25.3569 | −0.821390 | −0.410695 | − | 0.911773i | \(-0.634714\pi\) | ||||
−0.410695 | + | 0.911773i | \(0.634714\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.96014 | − | 5.12712i | −0.0957880 | − | 0.165910i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 13.0183 | − | 4.97108i | 0.420821 | − | 0.160692i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 39.1974 | − | 36.1578i | 1.26575 | − | 1.16760i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.6429 | + | 18.4340i | 0.343318 | + | 0.594644i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.53561 | + | 2.80651i | 0.275056 | + | 0.0904385i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7.79286 | + | 13.4976i | −0.250861 | + | 0.434504i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.5566 | + | 23.4808i | 0.435952 | + | 0.755090i | 0.997373 | − | 0.0724398i | \(-0.0230785\pi\) |
−0.561421 | + | 0.827530i | \(0.689745\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 14.6324 | + | 11.8916i | 0.470060 | + | 0.382013i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.1555 | − | 36.6423i | 0.678911 | − | 1.17591i | −0.296398 | − | 0.955064i | \(-0.595786\pi\) |
0.975309 | − | 0.220844i | \(-0.0708812\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −50.0917 | − | 15.6113i | −1.60587 | − | 0.500475i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.19866 | + | 19.9689i | −0.102439 | + | 0.639518i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.18908 | + | 2.05955i | −0.0380421 | + | 0.0658908i | −0.884420 | − | 0.466693i | \(-0.845445\pi\) |
0.846377 | + | 0.532583i | \(0.178779\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.5499 | + | 18.2729i | −0.337175 | + | 0.584004i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −44.7883 | + | 40.0442i | −1.42998 | + | 1.27851i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.29283 | −0.105025 | −0.0525124 | − | 0.998620i | \(-0.516723\pi\) | ||||
−0.0525124 | + | 0.998620i | \(0.516723\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.16782 | 0.164661 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −25.4797 | − | 38.3651i | −0.811029 | − | 1.22117i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 22.8821 | − | 39.6329i | 0.727607 | − | 1.26025i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.5482 | + | 51.1790i | 0.938630 | + | 1.62575i | 0.768030 | + | 0.640414i | \(0.221237\pi\) |
0.170600 | + | 0.985340i | \(0.445429\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.66388 | + | 29.1162i | −0.148004 | + | 0.923974i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.92356 | − | 8.52786i | −0.156087 | − | 0.270351i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16.9797 | −0.537754 | −0.268877 | − | 0.963175i | \(-0.586652\pi\) | ||||
−0.268877 | + | 0.963175i | \(0.586652\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 17.7197 | + | 27.6027i | 0.560628 | + | 0.873311i |
(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.t.k.961.3 | 22 | ||
3.2 | odd | 2 | 3024.2.t.l.289.2 | 22 | |||
4.3 | odd | 2 | 504.2.t.d.457.9 | yes | 22 | ||
7.4 | even | 3 | 1008.2.q.k.529.6 | 22 | |||
9.4 | even | 3 | 1008.2.q.k.625.6 | 22 | |||
9.5 | odd | 6 | 3024.2.q.k.2305.10 | 22 | |||
12.11 | even | 2 | 1512.2.t.d.289.2 | 22 | |||
21.11 | odd | 6 | 3024.2.q.k.2881.10 | 22 | |||
28.11 | odd | 6 | 504.2.q.d.25.6 | ✓ | 22 | ||
36.23 | even | 6 | 1512.2.q.c.793.10 | 22 | |||
36.31 | odd | 6 | 504.2.q.d.121.6 | yes | 22 | ||
63.4 | even | 3 | inner | 1008.2.t.k.193.3 | 22 | ||
63.32 | odd | 6 | 3024.2.t.l.1873.2 | 22 | |||
84.11 | even | 6 | 1512.2.q.c.1369.10 | 22 | |||
252.67 | odd | 6 | 504.2.t.d.193.9 | yes | 22 | ||
252.95 | even | 6 | 1512.2.t.d.361.2 | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.q.d.25.6 | ✓ | 22 | 28.11 | odd | 6 | ||
504.2.q.d.121.6 | yes | 22 | 36.31 | odd | 6 | ||
504.2.t.d.193.9 | yes | 22 | 252.67 | odd | 6 | ||
504.2.t.d.457.9 | yes | 22 | 4.3 | odd | 2 | ||
1008.2.q.k.529.6 | 22 | 7.4 | even | 3 | |||
1008.2.q.k.625.6 | 22 | 9.4 | even | 3 | |||
1008.2.t.k.193.3 | 22 | 63.4 | even | 3 | inner | ||
1008.2.t.k.961.3 | 22 | 1.1 | even | 1 | trivial | ||
1512.2.q.c.793.10 | 22 | 36.23 | even | 6 | |||
1512.2.q.c.1369.10 | 22 | 84.11 | even | 6 | |||
1512.2.t.d.289.2 | 22 | 12.11 | even | 2 | |||
1512.2.t.d.361.2 | 22 | 252.95 | even | 6 | |||
3024.2.q.k.2305.10 | 22 | 9.5 | odd | 6 | |||
3024.2.q.k.2881.10 | 22 | 21.11 | odd | 6 | |||
3024.2.t.l.289.2 | 22 | 3.2 | odd | 2 | |||
3024.2.t.l.1873.2 | 22 | 63.32 | odd | 6 |