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 | 193.11 | ||
Character | \(\chi\) | \(=\) | 1008.193 |
Dual form | 1008.2.t.k.961.11 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.61774 | + | 0.618811i | 0.934001 | + | 0.357271i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.83657 | −0.821340 | −0.410670 | − | 0.911784i | \(-0.634705\pi\) | ||||
−0.410670 | + | 0.911784i | \(0.634705\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.45061 | − | 0.997255i | −0.926243 | − | 0.376927i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.23415 | + | 2.00215i | 0.744715 | + | 0.667383i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.09719 | 0.933838 | 0.466919 | − | 0.884300i | \(-0.345364\pi\) | ||||
0.466919 | + | 0.884300i | \(0.345364\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.40225 | − | 4.16081i | 0.666263 | − | 1.15400i | −0.312678 | − | 0.949859i | \(-0.601226\pi\) |
0.978941 | − | 0.204143i | \(-0.0654406\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.97109 | − | 1.13649i | −0.767132 | − | 0.293441i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.87185 | − | 3.24214i | 0.453990 | − | 0.786333i | −0.544640 | − | 0.838670i | \(-0.683334\pi\) |
0.998629 | + | 0.0523367i | \(0.0166669\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.71408 | + | 4.70093i | 0.622654 | + | 1.07847i | 0.988990 | + | 0.147985i | \(0.0472788\pi\) |
−0.366336 | + | 0.930483i | \(0.619388\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.34733 | − | 3.12976i | −0.730447 | − | 0.682970i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.95829 | 1.65942 | 0.829709 | − | 0.558197i | \(-0.188507\pi\) | ||||
0.829709 | + | 0.558197i | \(0.188507\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.62701 | −0.325401 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.37531 | + | 4.62146i | 0.457128 | + | 0.889401i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.325267 | − | 0.563379i | −0.0604006 | − | 0.104617i | 0.834244 | − | 0.551396i | \(-0.185904\pi\) |
−0.894645 | + | 0.446779i | \(0.852571\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.518342 | + | 0.897795i | 0.0930970 | + | 0.161249i | 0.908813 | − | 0.417204i | \(-0.136990\pi\) |
−0.815716 | + | 0.578453i | \(0.803657\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.01044 | + | 1.91658i | 0.872206 | + | 0.333633i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.50072 | + | 1.83153i | 0.760760 | + | 0.309585i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.873712 | + | 1.51331i | 0.143637 | + | 0.248787i | 0.928864 | − | 0.370422i | \(-0.120787\pi\) |
−0.785226 | + | 0.619209i | \(0.787453\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.46096 | − | 5.24456i | 1.03458 | − | 0.839802i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.52260 | − | 4.36927i | 0.393964 | − | 0.682365i | −0.599005 | − | 0.800745i | \(-0.704437\pi\) |
0.992968 | + | 0.118381i | \(0.0377703\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.09645 | + | 10.5594i | 0.929699 | + | 1.61029i | 0.783824 | + | 0.620984i | \(0.213267\pi\) |
0.145876 | + | 0.989303i | \(0.453400\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.10317 | − | 3.67709i | −0.611664 | − | 0.548148i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.30691 | + | 3.99569i | −0.336498 | + | 0.582832i | −0.983771 | − | 0.179426i | \(-0.942576\pi\) |
0.647273 | + | 0.762258i | \(0.275909\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.01096 | + | 4.88776i | 0.715852 | + | 0.698252i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.03443 | − | 4.08660i | 0.704961 | − | 0.572239i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.55082 | − | 7.88226i | 0.625104 | − | 1.08271i | −0.363417 | − | 0.931626i | \(-0.618390\pi\) |
0.988521 | − | 0.151085i | \(-0.0482766\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.68821 | −0.766998 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.48168 | + | 9.28438i | 0.196254 | + | 1.22975i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.89863 | − | 5.02058i | −0.377370 | − | 0.653624i | 0.613309 | − | 0.789843i | \(-0.289838\pi\) |
−0.990679 | + | 0.136219i | \(0.956505\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.40623 | − | 4.16771i | 0.308086 | − | 0.533620i | −0.669858 | − | 0.742489i | \(-0.733645\pi\) |
0.977944 | + | 0.208869i | \(0.0669783\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.47836 | − | 7.13449i | −0.438233 | − | 0.898862i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.41190 | + | 7.64163i | −0.547228 | + | 0.947827i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.23870 | − | 12.5378i | −0.884348 | − | 1.53174i | −0.846459 | − | 0.532454i | \(-0.821270\pi\) |
−0.0378895 | − | 0.999282i | \(-0.512063\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 12.8744 | + | 4.92468i | 1.54990 | + | 0.592861i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.00714 | 0.594238 | 0.297119 | − | 0.954840i | \(-0.403974\pi\) | ||||
0.297119 | + | 0.954840i | \(0.403974\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.81364 | + | 3.14131i | −0.212270 | + | 0.367662i | −0.952425 | − | 0.304774i | \(-0.901419\pi\) |
0.740155 | + | 0.672437i | \(0.234752\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.63207 | − | 1.00681i | −0.303925 | − | 0.116256i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.59000 | − | 3.08869i | −0.864961 | − | 0.351989i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.17904 | + | 12.4345i | −0.807705 | + | 1.39899i | 0.106745 | + | 0.994286i | \(0.465957\pi\) |
−0.914450 | + | 0.404699i | \(0.867376\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.982810 | + | 8.94618i | 0.109201 | + | 0.994020i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.83139 | − | 6.63616i | −0.420550 | − | 0.728414i | 0.575443 | − | 0.817842i | \(-0.304829\pi\) |
−0.995993 | + | 0.0894279i | \(0.971496\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.43778 | + | 5.95441i | −0.372880 | + | 0.645847i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.177571 | − | 1.11268i | −0.0190376 | − | 0.119292i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.76798 | − | 9.99043i | −0.611405 | − | 1.05898i | −0.991004 | − | 0.133833i | \(-0.957271\pi\) |
0.379599 | − | 0.925151i | \(-0.376062\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.0364 | + | 7.80087i | −1.05210 | + | 0.817753i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.282976 | + | 1.77315i | 0.0293432 | + | 0.183867i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.98461 | − | 8.63360i | −0.511410 | − | 0.885788i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.04480 | − | 1.80964i | −0.106083 | − | 0.183741i | 0.808097 | − | 0.589049i | \(-0.200498\pi\) |
−0.914180 | + | 0.405308i | \(0.867164\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.91957 | + | 6.20103i | 0.695443 | + | 0.623227i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.4532 | −1.63716 | −0.818578 | − | 0.574395i | \(-0.805237\pi\) | ||||
−0.818578 | + | 0.574395i | \(0.805237\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.74692 | 0.763327 | 0.381663 | − | 0.924301i | \(-0.375351\pi\) | ||||
0.381663 | + | 0.924301i | \(0.375351\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.14760 | + | 5.74803i | 0.599945 | + | 0.560950i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.74746 | − | 6.49080i | −0.362281 | − | 0.627489i | 0.626055 | − | 0.779779i | \(-0.284669\pi\) |
−0.988336 | + | 0.152290i | \(0.951335\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.30644 | + | 7.45897i | −0.412482 | + | 0.714440i | −0.995160 | − | 0.0982628i | \(-0.968671\pi\) |
0.582678 | + | 0.812703i | \(0.302005\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.476981 | + | 2.98881i | 0.0452730 | + | 0.283685i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.55747 | + | 2.69762i | −0.146514 | + | 0.253771i | −0.929937 | − | 0.367719i | \(-0.880139\pi\) |
0.783422 | + | 0.621490i | \(0.213472\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −14.6160 | −1.36295 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 13.6975 | − | 4.48621i | 1.26634 | − | 0.414750i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.82040 | + | 6.07850i | −0.716895 | + | 0.557215i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.40741 | −0.127946 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.78465 | − | 5.50731i | 0.611751 | − | 0.496578i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.1710 | 1.08860 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.8866 | −0.966033 | −0.483017 | − | 0.875611i | \(-0.660459\pi\) | ||||
−0.483017 | + | 0.875611i | \(0.660459\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.32820 | + | 20.8548i | 0.293032 | + | 1.83616i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.0558 | 1.40280 | 0.701401 | − | 0.712767i | \(-0.252558\pi\) | ||||
0.701401 | + | 0.712767i | \(0.252558\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.96313 | − | 14.2268i | −0.170225 | − | 1.23362i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.36242 | − | 8.48764i | −0.375457 | − | 0.730500i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.4406 | 1.14831 | 0.574155 | − | 0.818747i | \(-0.305331\pi\) | ||||
0.574155 | + | 0.818747i | \(0.305331\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.06953 | − | 7.04863i | 0.345173 | − | 0.597857i | −0.640212 | − | 0.768198i | \(-0.721154\pi\) |
0.985385 | + | 0.170341i | \(0.0544869\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.20456 | + | 5.03644i | −0.522518 | + | 0.424144i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.44022 | − | 12.8868i | 0.622182 | − | 1.07765i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.597376 | + | 1.03469i | 0.0496094 | + | 0.0859260i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.08182 | + | 11.0080i | 0.419141 | + | 0.907921i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.52958 | 0.616847 | 0.308424 | − | 0.951249i | \(-0.400199\pi\) | ||||
0.308424 | + | 0.951249i | \(0.400199\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.67232 | 0.461607 | 0.230803 | − | 0.973000i | \(-0.425865\pi\) | ||||
0.230803 | + | 0.973000i | \(0.425865\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 10.6732 | − | 3.49569i | 0.862878 | − | 0.282610i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.951973 | − | 1.64886i | −0.0764643 | − | 0.132440i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.218381 | − | 0.378248i | −0.0174287 | − | 0.0301875i | 0.857179 | − | 0.515018i | \(-0.172215\pi\) |
−0.874608 | + | 0.484830i | \(0.838881\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 12.2397 | − | 9.93532i | 0.970668 | − | 0.787922i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −19.5026 | − | 7.93644i | −1.53702 | − | 0.625479i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.12649 | − | 15.8076i | −0.714842 | − | 1.23814i | −0.963020 | − | 0.269429i | \(-0.913165\pi\) |
0.248178 | − | 0.968714i | \(-0.420168\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −9.20203 | − | 3.51993i | −0.716377 | − | 0.274026i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.765108 | + | 1.32521i | −0.0592058 | + | 0.102548i | −0.894109 | − | 0.447849i | \(-0.852190\pi\) |
0.834903 | + | 0.550397i | \(0.185523\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.04157 | − | 8.73226i | −0.387813 | − | 0.671713i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.34830 | + | 15.9366i | −0.256051 | + | 1.21870i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.08474 | + | 1.87883i | −0.0824716 | + | 0.142845i | −0.904311 | − | 0.426874i | \(-0.859615\pi\) |
0.821839 | + | 0.569719i | \(0.192948\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.98716 | + | 1.62254i | 0.301401 | + | 0.122653i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.58244 | − | 9.91569i | −0.118943 | − | 0.745309i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.08263 | − | 1.87517i | 0.0809195 | − | 0.140157i | −0.822726 | − | 0.568439i | \(-0.807548\pi\) |
0.903645 | + | 0.428282i | \(0.140881\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.557838 | 0.0414638 | 0.0207319 | − | 0.999785i | \(-0.493400\pi\) | ||||
0.0207319 | + | 0.999785i | \(0.493400\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.47167 | − | 5.25325i | 0.478399 | − | 0.388332i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.60463 | − | 2.77931i | −0.117975 | − | 0.204339i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.79747 | − | 10.0415i | 0.423953 | − | 0.734308i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.21217 | − | 13.6942i | −0.0881725 | − | 0.996105i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.9998 | + | 20.7843i | −0.868277 | + | 1.50390i | −0.00452179 | + | 0.999990i | \(0.501439\pi\) |
−0.863756 | + | 0.503911i | \(0.831894\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.6397 | + | 18.4285i | 0.765862 | + | 1.32651i | 0.939790 | + | 0.341753i | \(0.111021\pi\) |
−0.173928 | + | 0.984758i | \(0.555646\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −11.8660 | + | 9.63201i | −0.849743 | + | 0.689763i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14.8768 | −1.05993 | −0.529964 | − | 0.848020i | \(-0.677795\pi\) | ||||
−0.529964 | + | 0.848020i | \(0.677795\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.17884 | + | 10.7021i | −0.438006 | + | 0.758649i | −0.997536 | − | 0.0701616i | \(-0.977649\pi\) |
0.559530 | + | 0.828810i | \(0.310982\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.95178 | − | 24.7623i | −0.278737 | − | 1.74659i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.235270 | + | 1.70500i | 0.0165127 | + | 0.119667i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.63293 | + | 8.02447i | −0.323578 | + | 0.560453i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 17.7800 | + | 15.9337i | 1.23579 | + | 1.10747i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.40604 | + | 14.5597i | 0.581458 | + | 1.00711i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.65802 | + | 14.9961i | −0.596043 | + | 1.03238i | 0.397356 | + | 0.917664i | \(0.369928\pi\) |
−0.993399 | + | 0.114712i | \(0.963406\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.10023 | + | 3.09847i | 0.555019 | + | 0.212304i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −11.1966 | − | 19.3930i | −0.763599 | − | 1.32259i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.374923 | − | 2.71706i | −0.0254514 | − | 0.184446i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.87786 | + | 3.95951i | −0.329615 | + | 0.267559i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.99328 | − | 15.5768i | −0.604953 | − | 1.04781i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.14489 | − | 1.98301i | −0.0766677 | − | 0.132792i | 0.825143 | − | 0.564925i | \(-0.191095\pi\) |
−0.901810 | + | 0.432132i | \(0.857761\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.63497 | − | 3.25751i | −0.242331 | − | 0.217167i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.56026 | 0.236303 | 0.118152 | − | 0.992996i | \(-0.462303\pi\) | ||||
0.118152 | + | 0.992996i | \(0.462303\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −26.9597 | −1.78155 | −0.890775 | − | 0.454445i | \(-0.849837\pi\) | ||||
−0.890775 | + | 0.454445i | \(0.849837\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −10.3673 | − | 9.69347i | −0.682119 | − | 0.637783i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.7321 | + | 18.5885i | 0.703081 | + | 1.21777i | 0.967380 | + | 0.253332i | \(0.0815264\pi\) |
−0.264298 | + | 0.964441i | \(0.585140\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.23681 | − | 7.33837i | 0.276379 | − | 0.478703i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −19.3084 | + | 15.6732i | −1.25421 | + | 1.01808i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.65970 | + | 8.07083i | −0.301411 | + | 0.522059i | −0.976456 | − | 0.215718i | \(-0.930791\pi\) |
0.675045 | + | 0.737777i | \(0.264124\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20.2007 | −1.30124 | −0.650620 | − | 0.759404i | \(-0.725491\pi\) | ||||
−0.650620 | + | 0.759404i | \(0.725491\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3.94607 | + | 15.0807i | −0.253140 | + | 0.967430i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −9.20299 | − | 8.97673i | −0.587958 | − | 0.573502i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 26.0796 | 1.65940 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.09165 | − | 13.1065i | −0.132553 | − | 0.830589i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −27.1837 | −1.71582 | −0.857910 | − | 0.513800i | \(-0.828238\pi\) | ||||
−0.857910 | + | 0.513800i | \(0.828238\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 24.6483 | 1.54963 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −9.24608 | + | 7.50534i | −0.579012 | + | 0.470002i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 28.4821 | 1.77667 | 0.888333 | − | 0.459200i | \(-0.151864\pi\) | ||||
0.888333 | + | 0.459200i | \(0.151864\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.631966 | − | 4.57985i | −0.0392685 | − | 0.284578i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.401274 | − | 1.90990i | 0.0248383 | − | 0.118220i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.59814 | −0.221871 | −0.110935 | − | 0.993828i | \(-0.535385\pi\) | ||||
−0.110935 | + | 0.993828i | \(0.535385\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.35791 | + | 14.4763i | −0.513422 | + | 0.889274i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.14888 | − | 19.7312i | −0.192708 | − | 1.20753i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.2261 | − | 19.4443i | 0.684470 | − | 1.18554i | −0.289133 | − | 0.957289i | \(-0.593367\pi\) |
0.973603 | − | 0.228248i | \(-0.0732997\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.7935 | + | 25.6231i | 0.898642 | + | 1.55649i | 0.829231 | + | 0.558906i | \(0.188779\pi\) |
0.0694115 | + | 0.997588i | \(0.477888\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −21.0635 | + | 6.40914i | −1.27482 | + | 0.387899i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.03915 | −0.303872 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −20.3867 | −1.22492 | −0.612459 | − | 0.790503i | \(-0.709819\pi\) | ||||
−0.612459 | + | 0.790503i | \(0.709819\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.639467 | + | 3.04360i | −0.0382839 | + | 0.182216i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.23968 | − | 3.87924i | −0.133608 | − | 0.231416i | 0.791457 | − | 0.611225i | \(-0.209323\pi\) |
−0.925065 | + | 0.379809i | \(0.875990\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.03840 | + | 1.79856i | 0.0617264 | + | 0.106913i | 0.895237 | − | 0.445590i | \(-0.147006\pi\) |
−0.833511 | + | 0.552503i | \(0.813673\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.72122 | − | 17.0514i | −0.161191 | − | 1.01004i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.5392 | + | 8.19169i | −0.622108 | + | 0.483540i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.49237 | + | 2.58486i | 0.0877865 | + | 0.152051i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.570380 | − | 3.57405i | −0.0334362 | − | 0.209515i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.887340 | + | 1.53692i | −0.0518389 | + | 0.0897877i | −0.890780 | − | 0.454434i | \(-0.849842\pi\) |
0.838942 | + | 0.544222i | \(0.183175\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.32355 | + | 9.22066i | 0.309949 | + | 0.536847i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 7.35678 | + | 14.3136i | 0.426884 | + | 0.830556i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 19.1178 | − | 33.1129i | 1.10561 | − | 1.91497i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.40963 | − | 31.9566i | −0.254167 | − | 1.84195i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −26.6170 | − | 10.1814i | −1.52911 | − | 0.584908i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.41921 | + | 7.65429i | −0.253043 | + | 0.438283i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −19.6315 | −1.12043 | −0.560215 | − | 0.828347i | \(-0.689282\pi\) | ||||
−0.560215 | + | 0.828347i | \(0.689282\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12.5325 | + | 4.79388i | 0.712948 | + | 0.272714i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.65795 | − | 11.5319i | −0.377538 | − | 0.653915i | 0.613166 | − | 0.789954i | \(-0.289896\pi\) |
−0.990703 | + | 0.136040i | \(0.956563\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.32641 | + | 4.02945i | −0.131496 | + | 0.227758i | −0.924254 | − | 0.381779i | \(-0.875311\pi\) |
0.792757 | + | 0.609537i | \(0.208645\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.38826 | + | 13.1030i | 0.359938 | + | 0.738271i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.06276 | − | 3.57281i | 0.115856 | − | 0.200669i | −0.802265 | − | 0.596967i | \(-0.796372\pi\) |
0.918122 | + | 0.396299i | \(0.129705\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.00741 | − | 1.74489i | −0.0564044 | − | 0.0976953i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.04583 | − | 12.8194i | −0.114187 | − | 0.715508i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 20.3214 | 1.13071 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.90847 | + | 6.76967i | −0.216803 | + | 0.375514i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −11.5824 | + | 9.40178i | −0.640507 | + | 0.519920i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 9.63807 | − | 7.49130i | 0.531364 | − | 0.413009i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.0220297 | − | 0.0381566i | 0.00121086 | − | 0.00209727i | −0.865419 | − | 0.501048i | \(-0.832948\pi\) |
0.866630 | + | 0.498951i | \(0.166281\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.07788 | + | 5.13026i | −0.0590673 | + | 0.281137i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 13.2944 | + | 23.0266i | 0.726350 | + | 1.25808i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.3351 | + | 23.0970i | −0.726407 | + | 1.25817i | 0.231986 | + | 0.972719i | \(0.425478\pi\) |
−0.958392 | + | 0.285454i | \(0.907856\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.18889 | + | 3.40026i | −0.227509 | + | 0.184677i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.60541 | + | 2.78064i | 0.0869376 | + | 0.150580i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.40556 | − | 16.9752i | −0.399863 | − | 0.916575i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −23.6448 | − | 9.04452i | −1.27299 | − | 0.486941i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.41259 | + | 9.37488i | 0.290563 | + | 0.503270i | 0.973943 | − | 0.226793i | \(-0.0728241\pi\) |
−0.683380 | + | 0.730063i | \(0.739491\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.69555 | − | 4.66884i | −0.144290 | − | 0.249917i | 0.784818 | − | 0.619726i | \(-0.212756\pi\) |
−0.929108 | + | 0.369809i | \(0.879423\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 24.9351 | + | 1.21868i | 1.33094 | + | 0.0650483i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.94614 | −0.476155 | −0.238078 | − | 0.971246i | \(-0.576517\pi\) | ||||
−0.238078 | + | 0.971246i | \(0.576517\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.19596 | −0.488071 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −16.4128 | + | 4.99405i | −0.868657 | + | 0.264313i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.84157 | − | 3.18969i | −0.0971942 | − | 0.168345i | 0.813328 | − | 0.581805i | \(-0.197653\pi\) |
−0.910522 | + | 0.413460i | \(0.864320\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.23251 | + | 9.06297i | −0.275395 | + | 0.476998i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.27682 | − | 0.870920i | −0.119502 | − | 0.0457114i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.33087 | − | 5.76924i | 0.174346 | − | 0.301976i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.49976 | 0.391484 | 0.195742 | − | 0.980655i | \(-0.437288\pi\) | ||||
0.195742 | + | 0.980655i | \(0.437288\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 14.3838 | − | 4.71096i | 0.748789 | − | 0.245243i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −19.0129 | + | 14.7780i | −0.987101 | + | 0.767235i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.23833 | 0.426565 | 0.213282 | − | 0.976991i | \(-0.431585\pi\) | ||||
0.213282 | + | 0.976991i | \(0.431585\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 19.6894 | + | 7.53153i | 1.01676 | + | 0.388927i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.12549 | −0.160971 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.92853 | 0.201795 | 0.100897 | − | 0.994897i | \(-0.467829\pi\) | ||||
0.100897 | + | 0.994897i | \(0.467829\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −17.6117 | − | 6.73678i | −0.902276 | − | 0.345136i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −23.9265 | −1.22259 | −0.611293 | − | 0.791404i | \(-0.709350\pi\) | ||||
−0.611293 | + | 0.791404i | \(0.709350\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13.9396 | + | 5.67260i | 0.710427 | + | 0.289102i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.52104 | + | 35.7971i | −0.382316 | + | 1.81967i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12.6575 | 0.641761 | 0.320881 | − | 0.947120i | \(-0.396021\pi\) | ||||
0.320881 | + | 0.947120i | \(0.396021\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.8967 | − | 25.8018i | 0.753359 | − | 1.30486i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 25.9741 | + | 9.93551i | 1.31022 | + | 0.501180i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 13.1848 | − | 22.8368i | 0.663400 | − | 1.14904i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −17.7703 | − | 30.7791i | −0.891866 | − | 1.54476i | −0.837636 | − | 0.546229i | \(-0.816063\pi\) |
−0.0542297 | − | 0.998528i | \(-0.517270\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.62786 | − | 24.2300i | 0.281746 | − | 1.21302i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.32332 | −0.165959 | −0.0829794 | − | 0.996551i | \(-0.526444\pi\) | ||||
−0.0829794 | + | 0.996551i | \(0.526444\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.98074 | 0.248109 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.80500 | − | 16.4303i | −0.0896912 | − | 0.816428i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.70605 | + | 4.68702i | 0.134134 | + | 0.232327i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.2564 | − | 19.4967i | −0.556595 | − | 0.964051i | −0.997777 | − | 0.0666338i | \(-0.978774\pi\) |
0.441182 | − | 0.897418i | \(-0.354559\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 21.7434 | + | 8.31720i | 1.07252 | + | 0.410257i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.09662 | + | 15.1942i | 0.103168 | + | 0.747656i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.03662 | + | 12.1878i | 0.345414 | + | 0.598275i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10.9452 | − | 8.88456i | 0.535989 | − | 0.435079i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.59772 | − | 6.23144i | 0.175760 | − | 0.304426i | −0.764664 | − | 0.644429i | \(-0.777095\pi\) |
0.940424 | + | 0.340004i | \(0.110428\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.8121 | + | 29.1193i | 0.819370 | + | 1.41919i | 0.906147 | + | 0.422962i | \(0.139010\pi\) |
−0.0867773 | + | 0.996228i | \(0.527657\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −13.1539 | + | 4.30818i | −0.639567 | + | 0.209471i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.04551 | + | 5.27498i | −0.147729 | + | 0.255874i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.0530 | + | 7.81380i | −0.486498 | + | 0.378136i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 20.0108 | − | 16.2434i | 0.966132 | − | 0.784239i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.4871 | + | 28.5565i | −0.794156 | + | 1.37552i | 0.129217 | + | 0.991616i | \(0.458754\pi\) |
−0.923373 | + | 0.383903i | \(0.874580\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.8977 | 0.956221 | 0.478110 | − | 0.878300i | \(-0.341322\pi\) | ||||
0.478110 | + | 0.878300i | \(0.341322\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.326122 | + | 2.04351i | 0.0156364 | + | 0.0979789i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 21.5995 | + | 37.4114i | 1.03324 | + | 1.78963i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.5634 | − | 25.2246i | 0.695074 | − | 1.20390i | −0.275082 | − | 0.961421i | \(-0.588705\pi\) |
0.970156 | − | 0.242482i | \(-0.0779617\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.40920 | + | 20.9527i | 0.0671046 | + | 0.997746i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.88317 | − | 11.9220i | 0.327029 | − | 0.566431i | −0.654892 | − | 0.755723i | \(-0.727286\pi\) |
0.981921 | + | 0.189292i | \(0.0606191\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.5933 | + | 18.3481i | 0.502171 | + | 0.869785i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.1809 | + | 4.65939i | 0.576136 | + | 0.220382i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12.0958 | −0.570838 | −0.285419 | − | 0.958403i | \(-0.592133\pi\) | ||||
−0.285419 | + | 0.958403i | \(0.592133\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.81297 | − | 13.5325i | 0.367898 | − | 0.637218i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9.17632 | + | 3.51009i | 0.431141 | + | 0.164919i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 18.4325 | − | 14.3269i | 0.864128 | − | 0.671653i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.17738 | − | 7.23544i | 0.195410 | − | 0.338459i | −0.751625 | − | 0.659591i | \(-0.770730\pi\) |
0.947035 | + | 0.321131i | \(0.104063\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 19.4296 | + | 0.949604i | 0.906897 | + | 0.0443237i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.1673 | + | 19.3423i | 0.520112 | + | 0.900860i | 0.999727 | + | 0.0233807i | \(0.00744299\pi\) |
−0.479615 | + | 0.877479i | \(0.659224\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.0370790 | − | 0.0642228i | 0.00172321 | − | 0.00298469i | −0.865163 | − | 0.501492i | \(-0.832785\pi\) |
0.866886 | + | 0.498507i | \(0.166118\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.519705 | − | 3.25652i | −0.0241007 | − | 0.151018i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −14.5828 | − | 25.2581i | −0.674810 | − | 1.16880i | −0.976524 | − | 0.215407i | \(-0.930892\pi\) |
0.301715 | − | 0.953398i | \(-0.402441\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.23584 | + | 37.9441i | 0.241769 | + | 1.75209i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.119220 | − | 0.747042i | −0.00549336 | − | 0.0344219i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 18.8819 | + | 32.7043i | 0.868189 | + | 1.50375i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.41583 | − | 7.64845i | −0.202612 | − | 0.350935i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 25.9486 | − | 8.49869i | 1.18811 | − | 0.389128i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −27.9103 | −1.27525 | −0.637626 | − | 0.770346i | \(-0.720083\pi\) | ||||
−0.637626 | + | 0.770346i | \(0.720083\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.39548 | 0.382801 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −26.6390 | − | 24.9075i | −1.21212 | − | 1.13333i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.91884 | + | 3.32353i | 0.0871301 | + | 0.150914i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.14409 | − | 3.71367i | 0.0971580 | − | 0.168283i | −0.813349 | − | 0.581776i | \(-0.802358\pi\) |
0.910507 | + | 0.413493i | \(0.135691\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.98238 | − | 31.2200i | −0.225311 | − | 1.41182i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.22215 | − | 9.04503i | 0.235672 | − | 0.408196i | −0.723796 | − | 0.690015i | \(-0.757604\pi\) |
0.959468 | + | 0.281818i | \(0.0909375\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.43540 | −0.109685 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −12.7083 | − | 11.3886i | −0.571195 | − | 0.511881i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −12.2705 | − | 4.99339i | −0.550409 | − | 0.223984i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.12624 | 0.274248 | 0.137124 | − | 0.990554i | \(-0.456214\pi\) | ||||
0.137124 | + | 0.990554i | \(0.456214\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.05780 | + | 1.67038i | −0.0919355 | + | 0.0746270i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.4469 | 0.554982 | 0.277491 | − | 0.960728i | \(-0.410497\pi\) | ||||
0.277491 | + | 0.960728i | \(0.410497\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 30.2175 | 1.34466 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.75232 | − | 17.2463i | −0.122235 | − | 0.765935i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.8090 | 0.523425 | 0.261712 | − | 0.965146i | \(-0.415713\pi\) | ||||
0.261712 | + | 0.965146i | \(0.415713\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.57720 | − | 5.88946i | 0.335195 | − | 0.260534i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −15.2784 | + | 23.7092i | −0.674558 | + | 1.04679i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −14.2278 | −0.626950 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.14495 | + | 12.3754i | −0.314235 | + | 0.544271i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.91748 | + | 2.36821i | −0.128063 | + | 0.103953i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.54828 | − | 9.60991i | 0.243075 | − | 0.421018i | −0.718514 | − | 0.695513i | \(-0.755177\pi\) |
0.961589 | + | 0.274495i | \(0.0885107\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.6209 | − | 18.3960i | −0.464421 | − | 0.804401i | 0.534754 | − | 0.845008i | \(-0.320404\pi\) |
−0.999175 | + | 0.0406065i | \(0.987071\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.44612 | + | 5.09214i | 0.237688 | + | 0.222239i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.88103 | 0.169060 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 40.3343 | 1.75367 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.57598 | − | 17.0202i | 0.155184 | − | 0.738614i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.1198 | − | 20.9921i | −0.524967 | − | 0.909269i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.88248 | + | 11.9208i | 0.297556 | + | 0.515382i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.91178 | − | 2.36359i | 0.125653 | − | 0.101996i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 15.5199 | + | 15.1383i | 0.668490 | + | 0.652054i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.33567 | − | 10.9737i | −0.272392 | − | 0.471796i | 0.697082 | − | 0.716991i | \(-0.254481\pi\) |
−0.969474 | + | 0.245195i | \(0.921148\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.902436 | + | 0.345197i | 0.0387272 | + | 0.0148138i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.90908 | − | 13.6989i | 0.338788 | − | 0.586798i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.4805 | + | 37.2053i | 0.918438 | + | 1.59078i | 0.801788 | + | 0.597609i | \(0.203883\pi\) |
0.116651 | + | 0.993173i | \(0.462784\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 13.7202 | − | 4.49364i | 0.585565 | − | 0.191784i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.76560 | − | 3.05812i | 0.0752173 | − | 0.130280i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 29.9933 | − | 23.3126i | 1.27545 | − | 0.991355i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.876009 | − | 5.48915i | −0.0371845 | − | 0.233002i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 16.5129 | − | 28.6012i | 0.699673 | − | 1.21187i | −0.268906 | − | 0.963166i | \(-0.586662\pi\) |
0.968580 | − | 0.248703i | \(-0.0800044\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 58.5807 | 2.47770 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 15.5926 | − | 12.6570i | 0.658319 | − | 0.534378i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 18.4066 | + | 31.8812i | 0.775746 | + | 1.34363i | 0.934374 | + | 0.356293i | \(0.115959\pi\) |
−0.158629 | + | 0.987338i | \(0.550707\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.86040 | − | 4.95437i | 0.120338 | − | 0.208432i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 6.51314 | − | 22.9037i | 0.273526 | − | 0.961865i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −22.1786 | + | 38.4144i | −0.929774 | + | 1.61042i | −0.146075 | + | 0.989273i | \(0.546664\pi\) |
−0.783698 | + | 0.621142i | \(0.786669\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.2936 | − | 36.8816i | −0.891110 | − | 1.54345i | −0.838546 | − | 0.544831i | \(-0.816594\pi\) |
−0.0525644 | − | 0.998618i | \(-0.516739\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −32.2741 | + | 26.1979i | −1.34827 | + | 1.09443i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −12.9482 | −0.539977 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16.3209 | − | 28.2687i | 0.679450 | − | 1.17684i | −0.295697 | − | 0.955282i | \(-0.595552\pi\) |
0.975147 | − | 0.221559i | \(-0.0711147\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.80847 | + | 36.3964i | 0.241392 | + | 1.51258i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.77129 | + | 20.0835i | 0.114973 | + | 0.833205i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.0948 | − | 24.4129i | 0.583746 | − | 1.01108i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −25.1565 | + | 8.23924i | −1.04009 | + | 0.340651i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13.1270 | + | 22.7366i | 0.541809 | + | 0.938441i | 0.998800 | + | 0.0489701i | \(0.0155939\pi\) |
−0.456991 | + | 0.889471i | \(0.651073\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.81365 | + | 4.87338i | −0.115934 | + | 0.200804i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −24.0667 | − | 9.20593i | −0.989974 | − | 0.378681i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.59998 | − | 4.50330i | −0.106768 | − | 0.184928i | 0.807691 | − | 0.589606i | \(-0.200717\pi\) |
−0.914459 | + | 0.404678i | \(0.867384\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 14.3627 | − | 11.1636i | 0.588814 | − | 0.457663i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −16.6183 | + | 13.4896i | −0.680141 | + | 0.552092i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 13.1837 | + | 22.8349i | 0.538673 | + | 0.933008i | 0.998976 | + | 0.0452465i | \(0.0144073\pi\) |
−0.460303 | + | 0.887762i | \(0.652259\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.4505 | − | 26.7611i | −0.630239 | − | 1.09161i | −0.987503 | − | 0.157603i | \(-0.949623\pi\) |
0.357263 | − | 0.934004i | \(-0.383710\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.93021 | − | 42.5042i | 0.363666 | − | 1.73091i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.58480 | 0.105087 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.67321 | −0.311446 | −0.155723 | − | 0.987801i | \(-0.549771\pi\) | ||||
−0.155723 | + | 0.987801i | \(0.549771\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.674467 | + | 2.90382i | −0.0273308 | + | 0.117669i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11.0836 | + | 19.1973i | 0.448393 | + | 0.776639i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.97498 | − | 13.8131i | 0.322106 | − | 0.557905i | −0.658816 | − | 0.752304i | \(-0.728942\pi\) |
0.980922 | + | 0.194399i | \(0.0622758\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −12.4605 | + | 10.1146i | −0.502456 | + | 0.407859i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.67011 | + | 6.35682i | −0.147753 | + | 0.255916i | −0.930397 | − | 0.366554i | \(-0.880537\pi\) |
0.782644 | + | 0.622470i | \(0.213871\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −20.5684 | −0.826713 | −0.413357 | − | 0.910569i | \(-0.635644\pi\) | ||||
−0.413357 | + | 0.910569i | \(0.635644\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 18.9034 | + | 36.7789i | 0.758566 | + | 1.47589i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.17205 | + | 30.2348i | 0.167150 | + | 1.21133i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −14.2178 | −0.568713 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.58906 | + | 28.7555i | 0.183269 | + | 1.14838i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.54182 | 0.260840 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.09394 | 0.202787 | 0.101393 | − | 0.994846i | \(-0.467670\pi\) | ||||
0.101393 | + | 0.994846i | \(0.467670\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −23.2862 | + | 18.9021i | −0.925542 | + | 0.751292i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 19.9941 | 0.793442 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 32.3746 | − | 9.10807i | 1.28273 | − | 0.360875i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 11.1867 | + | 10.0250i | 0.442538 | + | 0.396584i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.6372 | 0.499140 | 0.249570 | − | 0.968357i | \(-0.419711\pi\) | ||||
0.249570 | + | 0.968357i | \(0.419711\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.4329 | + | 21.5344i | −0.490306 | + | 0.849235i | −0.999938 | − | 0.0111579i | \(-0.996448\pi\) |
0.509632 | + | 0.860393i | \(0.329782\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.11247 | − | 38.3013i | −0.240678 | − | 1.50811i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.12339 | + | 1.94577i | −0.0441650 | + | 0.0764960i | −0.887263 | − | 0.461264i | \(-0.847396\pi\) |
0.843098 | + | 0.537760i | \(0.180729\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.97762 | − | 15.5497i | −0.352403 | − | 0.610379i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.07482 | − | 4.62750i | 0.0421256 | − | 0.181366i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.05762 | 0.0805207 | 0.0402604 | − | 0.999189i | \(-0.487181\pi\) | ||||
0.0402604 | + | 0.999189i | \(0.487181\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −29.4876 | −1.15218 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −10.3413 | + | 3.38697i | −0.403452 | + | 0.132138i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.16599 | + | 7.21571i | 0.162284 | + | 0.281084i | 0.935687 | − | 0.352830i | \(-0.114781\pi\) |
−0.773403 | + | 0.633914i | \(0.781447\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.0463 | − | 29.5251i | −0.663024 | − | 1.14839i | −0.979817 | − | 0.199897i | \(-0.935939\pi\) |
0.316793 | − | 0.948495i | \(-0.397394\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.90965 | − | 30.7643i | −0.190675 | − | 1.19479i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.60543 | + | 26.1285i | 0.139812 | + | 1.01322i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.58857 | − | 4.48353i | −0.100230 | − | 0.173603i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.625025 | − | 3.91646i | −0.0241649 | − | 0.151419i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.45255 | − | 12.9082i | 0.287702 | − | 0.498315i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.571008 | + | 0.989016i | 0.0220108 | + | 0.0381237i | 0.876821 | − | 0.480817i | \(-0.159660\pi\) |
−0.854810 | + | 0.518941i | \(0.826327\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.86464 | − | 7.51915i | −0.148750 | − | 0.289412i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −18.1906 | + | 31.5070i | −0.699121 | + | 1.21091i | 0.269651 | + | 0.962958i | \(0.413092\pi\) |
−0.968772 | + | 0.247955i | \(0.920242\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.755713 | + | 5.47665i | 0.0290016 | + | 0.210174i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.75957 | + | 2.20313i | 0.220707 | + | 0.0844242i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3.11274 | + | 5.39142i | −0.119106 | + | 0.206297i | −0.919414 | − | 0.393292i | \(-0.871336\pi\) |
0.800308 | + | 0.599589i | \(0.204669\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −24.6846 | −0.943152 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −43.6138 | − | 16.6830i | −1.66397 | − | 0.636496i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −21.8644 | − | 37.8702i | −0.832967 | − | 1.44274i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.9130 | + | 34.4903i | −0.757525 | + | 1.31207i | 0.186584 | + | 0.982439i | \(0.440258\pi\) |
−0.944109 | + | 0.329633i | \(0.893075\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −10.7732 | − | 22.0969i | −0.409238 | − | 0.839391i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.47398 | + | 12.9453i | −0.283504 | + | 0.491044i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.44384 | − | 16.3572i | −0.357711 | − | 0.619573i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.85890 | + | 36.7124i | 0.221604 | + | 1.38859i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −48.3337 | −1.82554 | −0.912769 | − | 0.408477i | \(-0.866060\pi\) | ||||
−0.912769 | + | 0.408477i | \(0.866060\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.74265 | + | 8.21452i | −0.178873 | + | 0.309816i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 11.3951 | − | 9.24977i | 0.429165 | − | 0.348367i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 40.3204 | + | 16.4081i | 1.51640 | + | 0.617088i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.04198 | − | 13.9291i | 0.302023 | − | 0.523119i | −0.674571 | − | 0.738210i | \(-0.735671\pi\) |
0.976594 | + | 0.215091i | \(0.0690048\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −40.9346 | + | 13.4069i | −1.53517 | + | 0.502798i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.12512 | + | 7.14491i | 0.154487 | + | 0.267579i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −13.6645 | + | 23.6676i | −0.511023 | + | 0.885117i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −12.5325 | + | 10.1730i | −0.468034 | + | 0.379918i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −21.0734 | − | 36.5002i | −0.785906 | − | 1.36123i | −0.928456 | − | 0.371442i | \(-0.878864\pi\) |
0.142550 | − | 0.989788i | \(-0.454470\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −18.9847 | − | 7.72566i | −0.707026 | − | 0.287718i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −32.6794 | − | 12.5004i | −1.21536 | − | 0.464895i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.529212 | + | 0.916622i | 0.0196544 | + | 0.0340425i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.9548 | + | 22.4384i | 0.480467 | + | 0.832192i | 0.999749 | − | 0.0224103i | \(-0.00713401\pi\) |
−0.519282 | + | 0.854603i | \(0.673801\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −15.7158 | + | 21.9548i | −0.582068 | + | 0.813140i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 45.6465 | 1.68830 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.4054 | 0.753692 | 0.376846 | − | 0.926276i | \(-0.377009\pi\) | ||||
0.376846 | + | 0.926276i | \(0.377009\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −9.33312 | − | 20.2169i | −0.344257 | − | 0.745711i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −22.4196 | − | 38.8320i | −0.825838 | − | 1.43039i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.8953 | − | 20.6033i | 0.437576 | − | 0.757903i | −0.559926 | − | 0.828542i | \(-0.689171\pi\) |
0.997502 | + | 0.0706392i | \(0.0225039\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 42.1899 | + | 16.1383i | 1.54989 | + | 0.592857i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −21.6320 | + | 37.4678i | −0.793603 | + | 1.37456i | 0.130120 | + | 0.991498i | \(0.458464\pi\) |
−0.923723 | + | 0.383062i | \(0.874870\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −13.8286 | −0.506641 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.72670 | − | 22.4972i | 0.172941 | − | 0.823128i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.71058 | + | 19.6436i | 0.0990426 | + | 0.717761i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.3693 | 0.524343 | 0.262172 | − | 0.965021i | \(-0.415561\pi\) | ||||
0.262172 | + | 0.965021i | \(0.415561\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −43.9761 | − | 16.8216i | −1.60258 | − | 0.613013i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −10.4176 | −0.379136 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 39.7854 | 1.44603 | 0.723013 | − | 0.690835i | \(-0.242757\pi\) | ||||
0.723013 | + | 0.690835i | \(0.242757\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 39.8745 | + | 15.2527i | 1.44735 | + | 0.553637i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −22.3933 | −0.811756 | −0.405878 | − | 0.913927i | \(-0.633034\pi\) | ||||
−0.405878 | + | 0.913927i | \(0.633034\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 17.9919 | − | 13.9844i | 0.651350 | − | 0.506269i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −19.6021 | + | 6.42008i | −0.708716 | + | 0.232118i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −27.8529 | −1.00571 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.45546 | + | 2.52093i | −0.0524853 | + | 0.0909071i | −0.891074 | − | 0.453857i | \(-0.850048\pi\) |
0.838589 | + | 0.544764i | \(0.183381\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 46.0766 | + | 17.6251i | 1.65941 | + | 0.634751i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −6.68612 | + | 11.5807i | −0.240483 | + | 0.416529i | −0.960852 | − | 0.277062i | \(-0.910639\pi\) |
0.720369 | + | 0.693591i | \(0.243972\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.843347 | − | 1.46072i | −0.0302939 | − | 0.0524706i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.81171 | − | 7.80006i | 0.0649947 | − | 0.279826i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 27.3862 | 0.981211 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.5081 | 0.554922 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.83103 | − | 2.84141i | 0.0654355 | − | 0.101544i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.401073 | + | 0.694679i | 0.0143149 | + | 0.0247941i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11.9264 | − | 20.6571i | −0.425130 | − | 0.736347i | 0.571302 | − | 0.820740i | \(-0.306438\pi\) |
−0.996433 | + | 0.0843925i | \(0.973105\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5.82084 | − | 2.22657i | −0.207228 | − | 0.0792680i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.50696 | − | 5.05761i | 0.231361 | − | 0.179828i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11.5607 | − | 20.0237i | −0.410533 | − | 0.711063i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −22.4790 | + | 18.2469i | −0.797248 | + | 0.647151i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6.10559 | + | 10.5752i | −0.216271 | + | 0.374593i | −0.953665 | − | 0.300870i | \(-0.902723\pi\) |
0.737394 | + | 0.675463i | \(0.236056\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.63639 | + | 14.9587i | 0.305533 | + | 0.529199i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.11582 | − | 33.8684i | 0.251425 | − | 1.19668i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.61718 | + | 9.72923i | −0.198226 | + | 0.343337i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 35.8180 | + | 14.5758i | 1.26242 | + | 0.513731i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 30.1933 | − | 24.5088i | 1.06285 | − | 0.862751i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 26.7838 | − | 46.3910i | 0.941669 | − | 1.63102i | 0.179383 | − | 0.983779i | \(-0.442590\pi\) |
0.762287 | − | 0.647240i | \(-0.224077\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.81310 | −0.0636667 | −0.0318334 | − | 0.999493i | \(-0.510135\pi\) | ||||
−0.0318334 | + | 0.999493i | \(0.510135\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8.07614 | + | 50.6059i | 0.283243 | + | 1.77483i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 16.7615 | + | 29.0317i | 0.587128 | + | 1.01694i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −33.0925 | + | 57.3180i | −1.15776 | + | 2.00530i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −38.0412 | − | 2.66599i | −1.32927 | − | 0.0931573i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19.8371 | − | 34.3589i | 0.692321 | − | 1.19913i | −0.278755 | − | 0.960362i | \(-0.589922\pi\) |
0.971076 | − | 0.238772i | \(-0.0767450\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.40656 | + | 14.5606i | 0.293034 | + | 0.507550i | 0.974526 | − | 0.224276i | \(-0.0720016\pi\) |
−0.681491 | + | 0.731826i | \(0.738668\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −8.15202 | − | 3.11828i | −0.283817 | − | 0.108565i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −37.2198 | −1.29426 | −0.647130 | − | 0.762379i | \(-0.724031\pi\) | ||||
−0.647130 | + | 0.762379i | \(0.724031\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.4365 | + | 19.8086i | −0.397206 | + | 0.687981i | −0.993380 | − | 0.114874i | \(-0.963354\pi\) |
0.596174 | + | 0.802855i | \(0.296687\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −32.9803 | − | 12.6155i | −1.14407 | − | 0.437627i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 25.2266 | − | 7.09707i | 0.874048 | − | 0.245899i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.40518 | − | 2.43384i | 0.0486281 | − | 0.0842263i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.91790 | + | 4.52804i | −0.100858 | + | 0.156512i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −18.4071 | − | 31.8820i | −0.635484 | − | 1.10069i | −0.986412 | − | 0.164288i | \(-0.947467\pi\) |
0.350929 | − | 0.936402i | \(-0.385866\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.2884 | − | 24.7482i | 0.492704 | − | 0.853388i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.22270 | − | 7.66153i | −0.0421119 | − | 0.263877i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.25921 | + | 16.0374i | 0.318527 | + | 0.551704i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.44901 | + | 1.40354i | 0.118509 | + | 0.0482264i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.566887 | + | 3.55217i | 0.0194555 | + | 0.121910i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.95325 | + | 12.0434i | 0.238354 | + | 0.412842i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.98355 | + | 12.0959i | 0.239112 | + | 0.414155i | 0.960460 | − | 0.278419i | \(-0.0898102\pi\) |
−0.721347 | + | 0.692573i | \(0.756477\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.14939 | − | 29.2686i | 0.210305 | − | 1.00097i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 17.5677 | 0.600102 | 0.300051 | − | 0.953923i | \(-0.402996\pi\) | ||||
0.300051 | + | 0.953923i | \(0.402996\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.84577 | −0.0970963 | −0.0485482 | − | 0.998821i | \(-0.515459\pi\) | ||||
−0.0485482 | + | 0.998821i | \(0.515459\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −22.1187 | + | 6.73024i | −0.753804 | + | 0.229366i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 27.7115 | + | 47.9977i | 0.943310 | + | 1.63386i | 0.759100 | + | 0.650974i | \(0.225639\pi\) |
0.184210 | + | 0.982887i | \(0.441027\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.99221 | − | 3.45061i | 0.0677372 | − | 0.117324i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.814721 | + | 5.10512i | 0.0276694 | + | 0.173379i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −22.2348 | + | 38.5119i | −0.754265 | + | 1.30643i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −69.5566 | −2.35684 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.28894 | − | 6.13483i | 0.0436240 | − | 0.207633i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −29.8263 | − | 12.1376i | −1.00831 | − | 0.410324i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 54.8689 | 1.85279 | 0.926396 | − | 0.376552i | \(-0.122890\pi\) | ||||
0.926396 | + | 0.376552i | \(0.122890\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.38654 | + | 1.93723i | −0.0804961 | + | 0.0653412i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −51.1572 | −1.72353 | −0.861765 | − | 0.507307i | \(-0.830641\pi\) | ||||
−0.861765 | + | 0.507307i | \(0.830641\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −38.6438 | −1.30047 | −0.650234 | − | 0.759734i | \(-0.725329\pi\) | ||||
−0.650234 | + | 0.759734i | \(0.725329\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.90625 | + | 18.2109i | 0.0976927 | + | 0.612152i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 17.8525 | 0.599429 | 0.299714 | − | 0.954029i | \(-0.403109\pi\) | ||||
0.299714 | + | 0.954029i | \(0.403109\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 26.6789 | + | 10.8568i | 0.894782 | + | 0.364124i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.04395 | + | 27.7080i | 0.101976 | + | 0.928254i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −25.0446 | −0.838087 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.98833 | + | 3.44388i | −0.0664624 | + | 0.115116i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 51.4182 | − | 41.7377i | 1.71680 | − | 1.39358i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.337199 | − | 0.584047i | 0.0112462 | − | 0.0194790i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −17.0369 | − | 29.5088i | −0.567581 | − | 0.983080i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 12.6415 | − | 54.4260i | 0.420681 | − | 1.81118i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.02451 | −0.0340559 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 36.4663 | 1.21084 | 0.605422 | − | 0.795905i | \(-0.293004\pi\) | ||||
0.605422 | + | 0.795905i | \(0.293004\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −36.7589 | − | 32.9418i | −1.21921 | − | 1.09261i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18.9847 | − | 32.8825i | −0.628993 | − | 1.08945i | −0.987754 | − | 0.156018i | \(-0.950134\pi\) |
0.358762 | − | 0.933429i | \(-0.383199\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.8666 | − | 20.5535i | −0.392726 | − | 0.680221i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −11.8857 | + | 9.64797i | −0.392928 | + | 0.318952i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −39.3465 | − | 16.0117i | −1.29934 | − | 0.528754i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.21770 | + | 2.10911i | 0.0401681 | + | 0.0695732i | 0.885411 | − | 0.464810i | \(-0.153877\pi\) |
−0.845242 | + | 0.534383i | \(0.820544\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −31.7586 | − | 12.1482i | −1.04648 | − | 0.400297i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 12.0284 | − | 20.8338i | 0.395919 | − | 0.685752i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.42153 | − | 2.46217i | −0.0467398 | − | 0.0809557i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 17.3077 | + | 15.5105i | 0.568461 | + | 0.509431i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 17.7404 | − | 30.7273i | 0.582044 | − | 1.00813i | −0.413193 | − | 0.910644i | \(-0.635586\pi\) |
0.995237 | − | 0.0974863i | \(-0.0310802\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.37687 | + | 36.8220i | −0.307314 | + | 1.20679i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3.63474 | − | 22.7756i | −0.118996 | − | 0.745640i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −10.6475 | + | 18.4420i | −0.348209 | + | 0.603116i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −30.0427 | −0.981452 | −0.490726 | − | 0.871314i | \(-0.663268\pi\) | ||||
−0.490726 | + | 0.871314i | \(0.663268\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.25698 | + | 5.07899i | −0.204189 | + | 0.165746i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.1250 | + | 26.1972i | 0.493060 | + | 0.854004i | 0.999968 | − | 0.00799565i | \(-0.00254512\pi\) |
−0.506908 | + | 0.862000i | \(0.669212\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 20.0756 | − | 34.7719i | 0.653750 | − | 1.13233i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.22624 | + | 25.1503i | 0.0724196 | + | 0.818141i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 16.9944 | − | 29.4352i | 0.552245 | − | 0.956516i | −0.445868 | − | 0.895099i | \(-0.647105\pi\) |
0.998112 | − | 0.0614168i | \(-0.0195619\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.71360 | + | 15.0924i | 0.282855 | + | 0.489920i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.54790 | − | 4.50340i | 0.179903 | − | 0.146033i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −21.4324 | −0.694265 | −0.347132 | − | 0.937816i | \(-0.612845\pi\) | ||||
−0.347132 | + | 0.937816i | \(0.612845\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 22.0385 | − | 38.1719i | 0.713151 | − | 1.23521i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.549972 | − | 3.44618i | −0.0177781 | − | 0.111399i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −32.9377 | − | 13.4037i | −1.06361 | − | 0.432829i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.9626 | − | 25.9161i | 0.482666 | − | 0.836002i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.62316 | − | 22.0044i | 0.148979 | − | 0.709081i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −19.5406 | − | 33.8452i | −0.629033 | − | 1.08952i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.4095 | + | 21.4938i | −0.399061 | + | 0.691194i | −0.993610 | − | 0.112865i | \(-0.963997\pi\) |
0.594549 | + | 0.804059i | \(0.297331\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 32.8747 | + | 12.5751i | 1.05609 | + | 0.403971i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 13.9437 | + | 24.1512i | 0.447475 | + | 0.775050i | 0.998221 | − | 0.0596234i | \(-0.0189900\pi\) |
−0.550746 | + | 0.834673i | \(0.685657\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −17.0021 | + | 13.2151i | −0.545062 | + | 0.423656i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −10.5120 | + | 8.53294i | −0.336654 | + | 0.273273i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −13.6237 | − | 23.5969i | −0.435859 | − | 0.754930i | 0.561506 | − | 0.827473i | \(-0.310222\pi\) |
−0.997365 | + | 0.0725422i | \(0.976889\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −17.8645 | − | 30.9423i | −0.570953 | − | 0.988920i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −24.5552 | + | 8.04230i | −0.783986 | + | 0.256771i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 13.8908 | 0.443047 | 0.221523 | − | 0.975155i | \(-0.428897\pi\) | ||||
0.221523 | + | 0.975155i | \(0.428897\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 27.3223 | 0.870561 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 20.2276 | − | 6.15480i | 0.643850 | − | 0.195909i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 48.5173 | + | 84.0344i | 1.54276 | + | 2.67214i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21.3271 | + | 36.9397i | −0.677479 | + | 1.17343i | 0.298259 | + | 0.954485i | \(0.403594\pi\) |
−0.975738 | + | 0.218942i | \(0.929739\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.0592500 | − | 0.0480950i | 0.00188024 | − | 0.00152625i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11.3479 | − | 19.6551i | 0.359752 | − | 0.623108i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 43.1810 | 1.36756 | 0.683779 | − | 0.729690i | \(-0.260335\pi\) | ||||
0.683779 | + | 0.729690i | \(0.260335\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.91839 | + | 7.63241i | −0.155611 | + | 0.241479i |
(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.193.11 | 22 | ||
3.2 | odd | 2 | 3024.2.t.l.1873.8 | 22 | |||
4.3 | odd | 2 | 504.2.t.d.193.1 | yes | 22 | ||
7.2 | even | 3 | 1008.2.q.k.625.3 | 22 | |||
9.2 | odd | 6 | 3024.2.q.k.2881.4 | 22 | |||
9.7 | even | 3 | 1008.2.q.k.529.3 | 22 | |||
12.11 | even | 2 | 1512.2.t.d.361.8 | 22 | |||
21.2 | odd | 6 | 3024.2.q.k.2305.4 | 22 | |||
28.23 | odd | 6 | 504.2.q.d.121.9 | yes | 22 | ||
36.7 | odd | 6 | 504.2.q.d.25.9 | ✓ | 22 | ||
36.11 | even | 6 | 1512.2.q.c.1369.4 | 22 | |||
63.2 | odd | 6 | 3024.2.t.l.289.8 | 22 | |||
63.16 | even | 3 | inner | 1008.2.t.k.961.11 | 22 | ||
84.23 | even | 6 | 1512.2.q.c.793.4 | 22 | |||
252.79 | odd | 6 | 504.2.t.d.457.1 | yes | 22 | ||
252.191 | even | 6 | 1512.2.t.d.289.8 | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.q.d.25.9 | ✓ | 22 | 36.7 | odd | 6 | ||
504.2.q.d.121.9 | yes | 22 | 28.23 | odd | 6 | ||
504.2.t.d.193.1 | yes | 22 | 4.3 | odd | 2 | ||
504.2.t.d.457.1 | yes | 22 | 252.79 | odd | 6 | ||
1008.2.q.k.529.3 | 22 | 9.7 | even | 3 | |||
1008.2.q.k.625.3 | 22 | 7.2 | even | 3 | |||
1008.2.t.k.193.11 | 22 | 1.1 | even | 1 | trivial | ||
1008.2.t.k.961.11 | 22 | 63.16 | even | 3 | inner | ||
1512.2.q.c.793.4 | 22 | 84.23 | even | 6 | |||
1512.2.q.c.1369.4 | 22 | 36.11 | even | 6 | |||
1512.2.t.d.289.8 | 22 | 252.191 | even | 6 | |||
1512.2.t.d.361.8 | 22 | 12.11 | even | 2 | |||
3024.2.q.k.2305.4 | 22 | 21.2 | odd | 6 | |||
3024.2.q.k.2881.4 | 22 | 9.2 | odd | 6 | |||
3024.2.t.l.289.8 | 22 | 63.2 | odd | 6 | |||
3024.2.t.l.1873.8 | 22 | 3.2 | odd | 2 |