Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1512,2,Mod(323,1512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1512, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1512.323");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1512.j (of order \(2\), degree \(1\), 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: | \(12.0733807856\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 323.20 | ||
Character | \(\chi\) | \(=\) | 1512.323 |
Dual form | 1512.2.j.c.323.19 |
$q$-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 \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1081\) | \(1135\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.481042 | + | 1.32989i | 0.340148 | + | 0.940372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.53720 | + | 1.27946i | −0.768599 | + | 0.639731i | ||||
\(5\) | 0.436221 | 0.195084 | 0.0975421 | − | 0.995231i | \(-0.468902\pi\) | ||||
0.0975421 | + | 0.995231i | \(0.468902\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | −2.44100 | − | 1.42882i | −0.863022 | − | 0.505166i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.209841 | + | 0.580125i | 0.0663575 | + | 0.183452i | ||||
\(11\) | − | 2.73863i | − | 0.825727i | −0.910793 | − | 0.412863i | \(-0.864529\pi\) | ||
0.910793 | − | 0.412863i | \(-0.135471\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.64657i | − | 0.456676i | −0.973582 | − | 0.228338i | \(-0.926671\pi\) | ||
0.973582 | − | 0.228338i | \(-0.0733291\pi\) | |||||||
\(14\) | −1.32989 | + | 0.481042i | −0.355427 | + | 0.128564i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.725955 | − | 3.93357i | 0.181489 | − | 0.983393i | ||||
\(17\) | 5.22231i | 1.26660i | 0.773908 | + | 0.633298i | \(0.218299\pi\) | ||||
−0.773908 | + | 0.633298i | \(0.781701\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.99963 | −1.37641 | −0.688204 | − | 0.725517i | \(-0.741601\pi\) | ||||
−0.688204 | + | 0.725517i | \(0.741601\pi\) | |||||||
\(20\) | −0.670559 | + | 0.558129i | −0.149942 | + | 0.124801i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.64206 | − | 1.31739i | 0.776490 | − | 0.280869i | ||||
\(23\) | −7.68296 | −1.60201 | −0.801004 | − | 0.598659i | \(-0.795700\pi\) | ||||
−0.801004 | + | 0.598659i | \(0.795700\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.80971 | −0.961942 | ||||||||
\(26\) | 2.18975 | − | 0.792068i | 0.429445 | − | 0.155337i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.27946 | − | 1.53720i | −0.241796 | − | 0.290503i | ||||
\(29\) | −4.94791 | −0.918804 | −0.459402 | − | 0.888228i | \(-0.651936\pi\) | ||||
−0.459402 | + | 0.888228i | \(0.651936\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.77950i | 1.75645i | 0.478248 | + | 0.878225i | \(0.341272\pi\) | ||||
−0.478248 | + | 0.878225i | \(0.658728\pi\) | |||||||
\(32\) | 5.58042 | − | 0.926774i | 0.986488 | − | 0.163832i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.94508 | + | 2.51215i | −1.19107 | + | 0.430830i | ||||
\(35\) | 0.436221i | 0.0737349i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.81676i | 0.627472i | 0.949510 | + | 0.313736i | \(0.101581\pi\) | ||||
−0.949510 | + | 0.313736i | \(0.898419\pi\) | |||||||
\(38\) | −2.88607 | − | 7.97883i | −0.468182 | − | 1.29434i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.06481 | − | 0.623284i | −0.168362 | − | 0.0985499i | ||||
\(41\) | − | 9.74668i | − | 1.52218i | −0.648649 | − | 0.761088i | \(-0.724666\pi\) | ||
0.648649 | − | 0.761088i | \(-0.275334\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.84195 | −1.34838 | −0.674192 | − | 0.738556i | \(-0.735508\pi\) | ||||
−0.674192 | + | 0.738556i | \(0.735508\pi\) | |||||||
\(44\) | 3.50397 | + | 4.20981i | 0.528243 | + | 0.634653i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.69582 | − | 10.2175i | −0.544919 | − | 1.50648i | ||||
\(47\) | 4.54668 | 0.663202 | 0.331601 | − | 0.943420i | \(-0.392411\pi\) | ||||
0.331601 | + | 0.943420i | \(0.392411\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | −2.31367 | − | 6.39637i | −0.327202 | − | 0.904583i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.10672 | + | 2.53110i | 0.292150 | + | 0.351001i | ||||
\(53\) | 9.94845 | 1.36652 | 0.683262 | − | 0.730173i | \(-0.260561\pi\) | ||||
0.683262 | + | 0.730173i | \(0.260561\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1.19465i | − | 0.161086i | ||||||
\(56\) | 1.42882 | − | 2.44100i | 0.190935 | − | 0.326192i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.38015 | − | 6.58016i | −0.312529 | − | 0.864018i | ||||
\(59\) | − | 13.2892i | − | 1.73011i | −0.501681 | − | 0.865053i | \(-0.667285\pi\) | ||
0.501681 | − | 0.865053i | \(-0.332715\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.26145i | 0.801696i | 0.916145 | + | 0.400848i | \(0.131284\pi\) | ||||
−0.916145 | + | 0.400848i | \(0.868716\pi\) | |||||||
\(62\) | −13.0056 | + | 4.70435i | −1.65172 | + | 0.597453i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 3.91692 | + | 6.97551i | 0.489615 | + | 0.871939i | ||||
\(65\) | − | 0.718269i | − | 0.0890903i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.42171 | 1.15104 | 0.575522 | − | 0.817786i | \(-0.304799\pi\) | ||||
0.575522 | + | 0.817786i | \(0.304799\pi\) | |||||||
\(68\) | −6.68175 | − | 8.02773i | −0.810281 | − | 0.973505i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.580125 | + | 0.209841i | −0.0693382 | + | 0.0250808i | ||||
\(71\) | −9.76751 | −1.15919 | −0.579595 | − | 0.814905i | \(-0.696789\pi\) | ||||
−0.579595 | + | 0.814905i | \(0.696789\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.14079 | −1.06985 | −0.534924 | − | 0.844900i | \(-0.679660\pi\) | ||||
−0.534924 | + | 0.844900i | \(0.679660\pi\) | |||||||
\(74\) | −5.07586 | + | 1.83602i | −0.590057 | + | 0.213433i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 9.22262 | − | 7.67629i | 1.05791 | − | 0.880531i | ||||
\(77\) | 2.73863 | 0.312095 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 5.19984i | − | 0.585028i | −0.956261 | − | 0.292514i | \(-0.905508\pi\) | ||
0.956261 | − | 0.292514i | \(-0.0944917\pi\) | |||||||
\(80\) | 0.316677 | − | 1.71591i | 0.0354056 | − | 0.191844i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 12.9620 | − | 4.68856i | 1.43141 | − | 0.517764i | ||||
\(83\) | 0.227071i | 0.0249243i | 0.999922 | + | 0.0124622i | \(0.00396693\pi\) | ||||
−0.999922 | + | 0.0124622i | \(0.996033\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.27808i | 0.247093i | ||||||||
\(86\) | −4.25335 | − | 11.7588i | −0.458650 | − | 1.26798i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.91302 | + | 6.68497i | −0.417129 | + | 0.712621i | ||||
\(89\) | − | 2.46567i | − | 0.261360i | −0.991425 | − | 0.130680i | \(-0.958284\pi\) | ||
0.991425 | − | 0.130680i | \(-0.0417161\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.64657 | 0.172607 | ||||||||
\(92\) | 11.8102 | − | 9.83005i | 1.23130 | − | 1.02485i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.18714 | + | 6.04657i | 0.225587 | + | 0.623657i | ||||
\(95\) | −2.61717 | −0.268516 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.37287 | −0.342463 | −0.171232 | − | 0.985231i | \(-0.554775\pi\) | ||||
−0.171232 | + | 0.985231i | \(0.554775\pi\) | |||||||
\(98\) | −0.481042 | − | 1.32989i | −0.0485925 | − | 0.134339i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 7.39348 | − | 6.15384i | 0.739348 | − | 0.615384i | ||||
\(101\) | −1.20021 | −0.119425 | −0.0597125 | − | 0.998216i | \(-0.519018\pi\) | ||||
−0.0597125 | + | 0.998216i | \(0.519018\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 10.7004i | − | 1.05434i | −0.849761 | − | 0.527169i | \(-0.823254\pi\) | ||
0.849761 | − | 0.527169i | \(-0.176746\pi\) | |||||||
\(104\) | −2.35266 | + | 4.01927i | −0.230697 | + | 0.394122i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.78562 | + | 13.2303i | 0.464820 | + | 1.28504i | ||||
\(107\) | − | 1.49655i | − | 0.144676i | −0.997380 | − | 0.0723382i | \(-0.976954\pi\) | ||
0.997380 | − | 0.0723382i | \(-0.0230461\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 18.4352i | 1.76578i | 0.469583 | + | 0.882888i | \(0.344404\pi\) | ||||
−0.469583 | + | 0.882888i | \(0.655596\pi\) | |||||||
\(110\) | 1.58875 | − | 0.574675i | 0.151481 | − | 0.0547931i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.93357 | + | 0.725955i | 0.371688 | + | 0.0685963i | ||||
\(113\) | 5.25692i | 0.494529i | 0.968948 | + | 0.247265i | \(0.0795317\pi\) | ||||
−0.968948 | + | 0.247265i | \(0.920468\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.35147 | −0.312526 | ||||||||
\(116\) | 7.60592 | − | 6.33066i | 0.706192 | − | 0.587787i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 17.6731 | − | 6.39266i | 1.62694 | − | 0.588492i | ||||
\(119\) | −5.22231 | −0.478729 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.49993 | 0.318175 | ||||||||
\(122\) | −8.32702 | + | 3.01202i | −0.753893 | + | 0.272695i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −12.5125 | − | 15.0330i | −1.12366 | − | 1.35001i | ||||
\(125\) | −4.27921 | −0.382744 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.7677i | 1.75410i | 0.480396 | + | 0.877051i | \(0.340493\pi\) | ||||
−0.480396 | + | 0.877051i | \(0.659507\pi\) | |||||||
\(128\) | −7.39244 | + | 8.56457i | −0.653405 | + | 0.757008i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.955216 | − | 0.345517i | 0.0837780 | − | 0.0303039i | ||||
\(131\) | − | 9.25252i | − | 0.808397i | −0.914671 | − | 0.404198i | \(-0.867551\pi\) | ||
0.914671 | − | 0.404198i | \(-0.132449\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 5.99963i | − | 0.520234i | ||||||
\(134\) | 4.53223 | + | 12.5298i | 0.391525 | + | 1.08241i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.46177 | − | 12.7476i | 0.639842 | − | 1.09310i | ||||
\(137\) | − | 2.53255i | − | 0.216370i | −0.994131 | − | 0.108185i | \(-0.965496\pi\) | ||
0.994131 | − | 0.108185i | \(-0.0345039\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −19.7831 | −1.67798 | −0.838991 | − | 0.544146i | \(-0.816854\pi\) | ||||
−0.838991 | + | 0.544146i | \(0.816854\pi\) | |||||||
\(140\) | −0.558129 | − | 0.670559i | −0.0471705 | − | 0.0566726i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.69858 | − | 12.9897i | −0.394296 | − | 1.09007i | ||||
\(143\) | −4.50934 | −0.377090 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.15839 | −0.179244 | ||||||||
\(146\) | −4.39710 | − | 12.1562i | −0.363906 | − | 1.00606i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.88340 | − | 5.86712i | −0.401413 | − | 0.482274i | ||||
\(149\) | 8.16461 | 0.668871 | 0.334435 | − | 0.942419i | \(-0.391454\pi\) | ||||
0.334435 | + | 0.942419i | \(0.391454\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.8741i | 1.21044i | 0.796058 | + | 0.605220i | \(0.206915\pi\) | ||||
−0.796058 | + | 0.605220i | \(0.793085\pi\) | |||||||
\(152\) | 14.6451 | + | 8.57242i | 1.18787 | + | 0.695315i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.31739 | + | 3.64206i | 0.106159 | + | 0.293486i | ||||
\(155\) | 4.26603i | 0.342656i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.92207i | 0.392824i | 0.980521 | + | 0.196412i | \(0.0629290\pi\) | ||||
−0.980521 | + | 0.196412i | \(0.937071\pi\) | |||||||
\(158\) | 6.91520 | − | 2.50134i | 0.550144 | − | 0.198996i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.43430 | − | 0.404279i | 0.192448 | − | 0.0319610i | ||||
\(161\) | − | 7.68296i | − | 0.605502i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.87250 | −0.459970 | −0.229985 | − | 0.973194i | \(-0.573868\pi\) | ||||
−0.229985 | + | 0.973194i | \(0.573868\pi\) | |||||||
\(164\) | 12.4705 | + | 14.9826i | 0.973782 | + | 1.16994i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.301979 | + | 0.109231i | −0.0234381 | + | 0.00847795i | ||||
\(167\) | −22.1181 | −1.71155 | −0.855777 | − | 0.517345i | \(-0.826920\pi\) | ||||
−0.855777 | + | 0.517345i | \(0.826920\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.2888 | 0.791447 | ||||||||
\(170\) | −3.02960 | + | 1.09585i | −0.232359 | + | 0.0840481i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 13.5918 | − | 11.3129i | 1.03637 | − | 0.862603i | ||||
\(173\) | 24.1920 | 1.83928 | 0.919642 | − | 0.392758i | \(-0.128479\pi\) | ||||
0.919642 | + | 0.392758i | \(0.128479\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 4.80971i | − | 0.363580i | ||||||
\(176\) | −10.7726 | − | 1.98812i | −0.812014 | − | 0.149860i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.27906 | − | 1.18609i | 0.245776 | − | 0.0889010i | ||||
\(179\) | 5.41287i | 0.404577i | 0.979326 | + | 0.202288i | \(0.0648378\pi\) | ||||
−0.979326 | + | 0.202288i | \(0.935162\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 6.19672i | − | 0.460598i | −0.973120 | − | 0.230299i | \(-0.926030\pi\) | ||
0.973120 | − | 0.230299i | \(-0.0739705\pi\) | |||||||
\(182\) | 0.792068 | + | 2.18975i | 0.0587120 | + | 0.162315i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 18.7541 | + | 10.9776i | 1.38257 | + | 0.809280i | ||||
\(185\) | 1.66495i | 0.122410i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 14.3020 | 1.04586 | ||||||||
\(188\) | −6.98915 | + | 5.81731i | −0.509736 | + | 0.424271i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.25897 | − | 3.48054i | −0.0913350 | − | 0.252505i | ||||
\(191\) | −13.6191 | −0.985444 | −0.492722 | − | 0.870187i | \(-0.663998\pi\) | ||||
−0.492722 | + | 0.870187i | \(0.663998\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.89278 | 0.424172 | 0.212086 | − | 0.977251i | \(-0.431974\pi\) | ||||
0.212086 | + | 0.977251i | \(0.431974\pi\) | |||||||
\(194\) | −1.62249 | − | 4.48554i | −0.116488 | − | 0.322043i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.53720 | − | 1.27946i | 0.109800 | − | 0.0913901i | ||||
\(197\) | 19.0323 | 1.35600 | 0.677998 | − | 0.735064i | \(-0.262848\pi\) | ||||
0.677998 | + | 0.735064i | \(0.262848\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 5.91398i | − | 0.419231i | −0.977784 | − | 0.209616i | \(-0.932779\pi\) | ||
0.977784 | − | 0.209616i | \(-0.0672212\pi\) | |||||||
\(200\) | 11.7405 | + | 6.87223i | 0.830177 | + | 0.485940i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.577349 | − | 1.59614i | −0.0406221 | − | 0.112304i | ||||
\(203\) | − | 4.94791i | − | 0.347275i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 4.25171i | − | 0.296952i | ||||||
\(206\) | 14.2303 | − | 5.14732i | 0.991469 | − | 0.358631i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −6.47690 | − | 1.19534i | −0.449092 | − | 0.0828816i | ||||
\(209\) | 16.4307i | 1.13654i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.9334 | 0.890369 | 0.445185 | − | 0.895439i | \(-0.353138\pi\) | ||||
0.445185 | + | 0.895439i | \(0.353138\pi\) | |||||||
\(212\) | −15.2927 | + | 12.7287i | −1.05031 | + | 0.874208i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.99024 | − | 0.719901i | 0.136050 | − | 0.0492114i | ||||
\(215\) | −3.85705 | −0.263049 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.77950 | −0.663876 | ||||||||
\(218\) | −24.5168 | + | 8.86812i | −1.66049 | + | 0.600625i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.52851 | + | 1.83641i | 0.103052 | + | 0.123811i | ||||
\(221\) | 8.59890 | 0.578424 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 0.758557i | − | 0.0507967i | −0.999677 | − | 0.0253984i | \(-0.991915\pi\) | ||
0.999677 | − | 0.0253984i | \(-0.00808542\pi\) | |||||||
\(224\) | 0.926774 | + | 5.58042i | 0.0619227 | + | 0.372858i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.99111 | + | 2.52880i | −0.465042 | + | 0.168213i | ||||
\(227\) | − | 3.60986i | − | 0.239595i | −0.992798 | − | 0.119797i | \(-0.961776\pi\) | ||
0.992798 | − | 0.119797i | \(-0.0382245\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 3.47625i | − | 0.229717i | −0.993382 | − | 0.114859i | \(-0.963358\pi\) | ||
0.993382 | − | 0.114859i | \(-0.0366415\pi\) | |||||||
\(230\) | −1.61220 | − | 4.45708i | −0.106305 | − | 0.293891i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 12.0778 | + | 7.06970i | 0.792949 | + | 0.464149i | ||||
\(233\) | 22.9786i | 1.50538i | 0.658376 | + | 0.752689i | \(0.271244\pi\) | ||||
−0.658376 | + | 0.752689i | \(0.728756\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.98336 | 0.129380 | ||||||||
\(236\) | 17.0030 | + | 20.4281i | 1.10680 | + | 1.32976i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.51215 | − | 6.94508i | −0.162838 | − | 0.450183i | ||||
\(239\) | −10.4478 | −0.675813 | −0.337906 | − | 0.941180i | \(-0.609719\pi\) | ||||
−0.337906 | + | 0.941180i | \(0.609719\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.0939 | −0.650208 | −0.325104 | − | 0.945678i | \(-0.605399\pi\) | ||||
−0.325104 | + | 0.945678i | \(0.605399\pi\) | |||||||
\(242\) | 1.68361 | + | 4.65450i | 0.108227 | + | 0.299203i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −8.01128 | − | 9.62508i | −0.512870 | − | 0.616183i | ||||
\(245\) | −0.436221 | −0.0278692 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.87880i | 0.628573i | ||||||||
\(248\) | 13.9732 | − | 23.8717i | 0.887299 | − | 1.51586i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2.05848 | − | 5.69086i | −0.130189 | − | 0.359922i | ||||
\(251\) | 18.0568i | 1.13974i | 0.821736 | + | 0.569868i | \(0.193006\pi\) | ||||
−0.821736 | + | 0.569868i | \(0.806994\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 21.0408i | 1.32282i | ||||||||
\(254\) | −26.2889 | + | 9.50910i | −1.64951 | + | 0.596654i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −14.9460 | − | 5.71119i | −0.934124 | − | 0.356950i | ||||
\(257\) | 3.77643i | 0.235567i | 0.993039 | + | 0.117784i | \(0.0375789\pi\) | ||||
−0.993039 | + | 0.117784i | \(0.962421\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.81676 | −0.237162 | ||||||||
\(260\) | 0.918997 | + | 1.10412i | 0.0569938 | + | 0.0684747i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 12.3048 | − | 4.45085i | 0.760194 | − | 0.274974i | ||||
\(263\) | 19.1460 | 1.18060 | 0.590298 | − | 0.807185i | \(-0.299010\pi\) | ||||
0.590298 | + | 0.807185i | \(0.299010\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.33973 | 0.266587 | ||||||||
\(266\) | 7.97883 | − | 2.88607i | 0.489213 | − | 0.176956i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −14.4830 | + | 12.0547i | −0.884692 | + | 0.736359i | ||||
\(269\) | 11.9031 | 0.725747 | 0.362873 | − | 0.931838i | \(-0.381796\pi\) | ||||
0.362873 | + | 0.931838i | \(0.381796\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 26.4765i | 1.60833i | 0.594403 | + | 0.804167i | \(0.297388\pi\) | ||||
−0.594403 | + | 0.804167i | \(0.702612\pi\) | |||||||
\(272\) | 20.5423 | + | 3.79116i | 1.24556 | + | 0.229873i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.36800 | − | 1.21826i | 0.203469 | − | 0.0735979i | ||||
\(275\) | 13.1720i | 0.794302i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 9.49587i | − | 0.570552i | −0.958445 | − | 0.285276i | \(-0.907915\pi\) | ||
0.958445 | − | 0.285276i | \(-0.0920852\pi\) | |||||||
\(278\) | −9.51650 | − | 26.3093i | −0.570762 | − | 1.57793i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.623284 | − | 1.06481i | 0.0372484 | − | 0.0636349i | ||||
\(281\) | 16.7754i | 1.00073i | 0.865813 | + | 0.500367i | \(0.166802\pi\) | ||||
−0.865813 | + | 0.500367i | \(0.833198\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.6841 | 0.813437 | 0.406719 | − | 0.913554i | \(-0.366673\pi\) | ||||
0.406719 | + | 0.913554i | \(0.366673\pi\) | |||||||
\(284\) | 15.0146 | − | 12.4972i | 0.890952 | − | 0.741569i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.16918 | − | 5.99691i | −0.128266 | − | 0.354605i | ||||
\(287\) | 9.74668 | 0.575328 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.2725 | −0.604268 | ||||||||
\(290\) | −1.03827 | − | 2.87041i | −0.0609695 | − | 0.168556i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 14.0512 | − | 11.6953i | 0.822284 | − | 0.684415i | ||||
\(293\) | 9.46088 | 0.552710 | 0.276355 | − | 0.961056i | \(-0.410873\pi\) | ||||
0.276355 | + | 0.961056i | \(0.410873\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 5.79703i | − | 0.337516i | ||||||
\(296\) | 5.45348 | − | 9.31670i | 0.316977 | − | 0.541522i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.92752 | + | 10.8580i | 0.227515 | + | 0.628987i | ||||
\(299\) | 12.6505i | 0.731599i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 8.84195i | − | 0.509641i | ||||||
\(302\) | −19.7809 | + | 7.15508i | −1.13826 | + | 0.411728i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4.35546 | + | 23.6000i | −0.249803 | + | 1.35355i | ||||
\(305\) | 2.73138i | 0.156398i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.4055 | −0.708019 | −0.354009 | − | 0.935242i | \(-0.615182\pi\) | ||||
−0.354009 | + | 0.935242i | \(0.615182\pi\) | |||||||
\(308\) | −4.20981 | + | 3.50397i | −0.239876 | + | 0.199657i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −5.67333 | + | 2.05214i | −0.322224 | + | 0.116554i | ||||
\(311\) | 1.70862 | 0.0968870 | 0.0484435 | − | 0.998826i | \(-0.484574\pi\) | ||||
0.0484435 | + | 0.998826i | \(0.484574\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.9889 | 0.677652 | 0.338826 | − | 0.940849i | \(-0.389970\pi\) | ||||
0.338826 | + | 0.940849i | \(0.389970\pi\) | |||||||
\(314\) | −6.54580 | + | 2.36772i | −0.369401 | + | 0.133618i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.65300 | + | 7.99318i | 0.374260 | + | 0.449652i | ||||
\(317\) | −24.6470 | −1.38431 | −0.692155 | − | 0.721748i | \(-0.743339\pi\) | ||||
−0.692155 | + | 0.721748i | \(0.743339\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 13.5505i | 0.758681i | ||||||||
\(320\) | 1.70864 | + | 3.04287i | 0.0955161 | + | 0.170101i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 10.2175 | − | 3.69582i | 0.569397 | − | 0.205960i | ||||
\(323\) | − | 31.3319i | − | 1.74336i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.91952i | 0.439296i | ||||||||
\(326\) | −2.82492 | − | 7.80976i | −0.156458 | − | 0.432543i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −13.9263 | + | 23.7916i | −0.768951 | + | 1.31367i | ||||
\(329\) | 4.54668i | 0.250667i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.66221 | −0.311223 | −0.155612 | − | 0.987818i | \(-0.549735\pi\) | ||||
−0.155612 | + | 0.987818i | \(0.549735\pi\) | |||||||
\(332\) | −0.290529 | − | 0.349054i | −0.0159449 | − | 0.0191568i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −10.6397 | − | 29.4146i | −0.582181 | − | 1.60950i | ||||
\(335\) | 4.10995 | 0.224551 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −32.2480 | −1.75666 | −0.878331 | − | 0.478053i | \(-0.841343\pi\) | ||||
−0.878331 | + | 0.478053i | \(0.841343\pi\) | |||||||
\(338\) | 4.94935 | + | 13.6830i | 0.269209 | + | 0.744255i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.91472 | − | 3.50187i | −0.158073 | − | 0.189915i | ||||
\(341\) | 26.7824 | 1.45035 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 21.5832 | + | 12.6336i | 1.16369 | + | 0.681158i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 11.6374 | + | 32.1726i | 0.625628 | + | 1.72961i | ||||
\(347\) | − | 20.3357i | − | 1.09168i | −0.837889 | − | 0.545840i | \(-0.816211\pi\) | ||
0.837889 | − | 0.545840i | \(-0.183789\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 8.27539i | − | 0.442971i | −0.975164 | − | 0.221486i | \(-0.928909\pi\) | ||
0.975164 | − | 0.221486i | \(-0.0710906\pi\) | |||||||
\(350\) | 6.39637 | − | 2.31367i | 0.341900 | − | 0.123671i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.53809 | − | 15.2827i | −0.135280 | − | 0.814570i | ||||
\(353\) | − | 8.23298i | − | 0.438197i | −0.975703 | − | 0.219099i | \(-0.929688\pi\) | ||
0.975703 | − | 0.219099i | \(-0.0703117\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.26080 | −0.226140 | ||||||||
\(356\) | 3.15473 | + | 3.79022i | 0.167200 | + | 0.200881i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −7.19850 | + | 2.60381i | −0.380453 | + | 0.137616i | ||||
\(359\) | −10.5802 | −0.558403 | −0.279202 | − | 0.960232i | \(-0.590070\pi\) | ||||
−0.279202 | + | 0.960232i | \(0.590070\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.9955 | 0.894502 | ||||||||
\(362\) | 8.24093 | − | 2.98088i | 0.433134 | − | 0.156672i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.53110 | + | 2.10672i | −0.132666 | + | 0.110422i | ||||
\(365\) | −3.98741 | −0.208710 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 23.7595i | − | 1.24023i | −0.784509 | − | 0.620117i | \(-0.787085\pi\) | ||
0.784509 | − | 0.620117i | \(-0.212915\pi\) | |||||||
\(368\) | −5.57748 | + | 30.2215i | −0.290746 | + | 1.57540i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2.21420 | + | 0.800912i | −0.115111 | + | 0.0416374i | ||||
\(371\) | 9.94845i | 0.516498i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.1442i | 0.628802i | 0.949290 | + | 0.314401i | \(0.101804\pi\) | ||||
−0.949290 | + | 0.314401i | \(0.898196\pi\) | |||||||
\(374\) | 6.87984 | + | 19.0200i | 0.355748 | + | 0.983500i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −11.0984 | − | 6.49642i | −0.572358 | − | 0.335027i | ||||
\(377\) | 8.14708i | 0.419596i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −32.1386 | −1.65085 | −0.825426 | − | 0.564511i | \(-0.809065\pi\) | ||||
−0.825426 | + | 0.564511i | \(0.809065\pi\) | |||||||
\(380\) | 4.02310 | − | 3.34856i | 0.206381 | − | 0.171778i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −6.55136 | − | 18.1119i | −0.335197 | − | 0.926684i | ||||
\(383\) | −30.0530 | −1.53564 | −0.767819 | − | 0.640667i | \(-0.778658\pi\) | ||||
−0.767819 | + | 0.640667i | \(0.778658\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.19465 | 0.0608849 | ||||||||
\(386\) | 2.83467 | + | 7.83673i | 0.144281 | + | 0.398879i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 5.18477 | − | 4.31546i | 0.263217 | − | 0.219084i | ||||
\(389\) | −12.8723 | −0.652652 | −0.326326 | − | 0.945257i | \(-0.605811\pi\) | ||||
−0.326326 | + | 0.945257i | \(0.605811\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 40.1228i | − | 2.02910i | ||||||
\(392\) | 2.44100 | + | 1.42882i | 0.123289 | + | 0.0721666i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 9.15533 | + | 25.3108i | 0.461239 | + | 1.27514i | ||||
\(395\) | − | 2.26828i | − | 0.114130i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 20.8323i | − | 1.04554i | −0.852473 | − | 0.522771i | \(-0.824898\pi\) | ||
0.852473 | − | 0.522771i | \(-0.175102\pi\) | |||||||
\(398\) | 7.86493 | − | 2.84487i | 0.394233 | − | 0.142601i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.49163 | + | 18.9193i | −0.174582 | + | 0.945967i | ||||
\(401\) | − | 15.8270i | − | 0.790361i | −0.918604 | − | 0.395180i | \(-0.870682\pi\) | ||
0.918604 | − | 0.395180i | \(-0.129318\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16.1026 | 0.802129 | ||||||||
\(404\) | 1.84495 | − | 1.53562i | 0.0917899 | − | 0.0763998i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.58016 | − | 2.38015i | 0.326568 | − | 0.118125i | ||||
\(407\) | 10.4527 | 0.518120 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.95136 | −0.195382 | −0.0976910 | − | 0.995217i | \(-0.531146\pi\) | ||||
−0.0976910 | + | 0.995217i | \(0.531146\pi\) | |||||||
\(410\) | 5.65429 | − | 2.04525i | 0.279246 | − | 0.101008i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 13.6907 | + | 16.4486i | 0.674492 | + | 0.810363i | ||||
\(413\) | 13.2892 | 0.653919 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.0990534i | 0.00486234i | ||||||||
\(416\) | −1.52600 | − | 9.18855i | −0.0748181 | − | 0.450506i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −21.8510 | + | 7.90387i | −1.06877 | + | 0.386591i | ||||
\(419\) | 3.56977i | 0.174395i | 0.996191 | + | 0.0871974i | \(0.0277911\pi\) | ||||
−0.996191 | + | 0.0871974i | \(0.972209\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.3767i | 0.798152i | 0.916918 | + | 0.399076i | \(0.130669\pi\) | ||||
−0.916918 | + | 0.399076i | \(0.869331\pi\) | |||||||
\(422\) | 6.22148 | + | 17.1999i | 0.302857 | + | 0.837278i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −24.2841 | − | 14.2146i | −1.17934 | − | 0.690321i | ||||
\(425\) | − | 25.1178i | − | 1.21839i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.26145 | −0.303013 | ||||||||
\(428\) | 1.91477 | + | 2.30049i | 0.0925540 | + | 0.111198i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.85540 | − | 5.12944i | −0.0894754 | − | 0.247363i | ||||
\(431\) | −28.7503 | −1.38485 | −0.692426 | − | 0.721489i | \(-0.743458\pi\) | ||||
−0.692426 | + | 0.721489i | \(0.743458\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −23.6276 | −1.13547 | −0.567735 | − | 0.823212i | \(-0.692180\pi\) | ||||
−0.567735 | + | 0.823212i | \(0.692180\pi\) | |||||||
\(434\) | −4.70435 | − | 13.0056i | −0.225816 | − | 0.624290i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −23.5872 | − | 28.3386i | −1.12962 | − | 1.35717i | ||||
\(437\) | 46.0949 | 2.20502 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 15.4891i | − | 0.739255i | −0.929180 | − | 0.369628i | \(-0.879485\pi\) | ||
0.929180 | − | 0.369628i | \(-0.120515\pi\) | |||||||
\(440\) | −1.70694 | + | 2.91613i | −0.0813753 | + | 0.139021i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.13643 | + | 11.4356i | 0.196750 | + | 0.543934i | ||||
\(443\) | 21.7640i | 1.03404i | 0.855974 | + | 0.517019i | \(0.172958\pi\) | ||||
−0.855974 | + | 0.517019i | \(0.827042\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 1.07558i | − | 0.0509872i | ||||||
\(446\) | 1.00879 | − | 0.364897i | 0.0477678 | − | 0.0172784i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −6.97551 | + | 3.91692i | −0.329562 | + | 0.185057i | ||||
\(449\) | 28.9358i | 1.36557i | 0.730621 | + | 0.682783i | \(0.239231\pi\) | ||||
−0.730621 | + | 0.682783i | \(0.760769\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −26.6925 | −1.25690 | ||||||||
\(452\) | −6.72603 | − | 8.08093i | −0.316366 | − | 0.380095i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4.80070 | − | 1.73649i | 0.225308 | − | 0.0814976i | ||||
\(455\) | 0.718269 | 0.0336730 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.2466 | 1.22776 | 0.613882 | − | 0.789397i | \(-0.289607\pi\) | ||||
0.613882 | + | 0.789397i | \(0.289607\pi\) | |||||||
\(458\) | 4.62302 | − | 1.67222i | 0.216020 | − | 0.0781378i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 5.15188 | − | 4.28808i | 0.240207 | − | 0.199933i | ||||
\(461\) | 7.47471 | 0.348132 | 0.174066 | − | 0.984734i | \(-0.444309\pi\) | ||||
0.174066 | + | 0.984734i | \(0.444309\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 8.09410i | − | 0.376165i | −0.982153 | − | 0.188082i | \(-0.939773\pi\) | ||
0.982153 | − | 0.188082i | \(-0.0602272\pi\) | |||||||
\(464\) | −3.59196 | + | 19.4630i | −0.166753 | + | 0.903546i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −30.5590 | + | 11.0537i | −1.41562 | + | 0.512051i | ||||
\(467\) | 16.0617i | 0.743246i | 0.928384 | + | 0.371623i | \(0.121199\pi\) | ||||
−0.928384 | + | 0.371623i | \(0.878801\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.42171i | 0.435054i | ||||||||
\(470\) | 0.954079 | + | 2.63765i | 0.0440084 | + | 0.121666i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −18.9879 | + | 32.4389i | −0.873991 | + | 1.49312i | ||||
\(473\) | 24.2148i | 1.11340i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 28.8565 | 1.32403 | ||||||||
\(476\) | 8.02773 | − | 6.68175i | 0.367950 | − | 0.306257i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −5.02583 | − | 13.8944i | −0.229876 | − | 0.635515i | ||||
\(479\) | 31.6989 | 1.44836 | 0.724181 | − | 0.689610i | \(-0.242218\pi\) | ||||
0.724181 | + | 0.689610i | \(0.242218\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.28456 | 0.286551 | ||||||||
\(482\) | −4.85561 | − | 13.4238i | −0.221167 | − | 0.611437i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.38008 | + | 4.47802i | −0.244549 | + | 0.203546i | ||||
\(485\) | −1.47132 | −0.0668092 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 30.5363i | 1.38373i | 0.722025 | + | 0.691867i | \(0.243211\pi\) | ||||
−0.722025 | + | 0.691867i | \(0.756789\pi\) | |||||||
\(488\) | 8.94651 | − | 15.2842i | 0.404990 | − | 0.691882i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.209841 | − | 0.580125i | −0.00947964 | − | 0.0262074i | ||||
\(491\) | − | 41.2201i | − | 1.86024i | −0.367259 | − | 0.930119i | \(-0.619704\pi\) | ||
0.367259 | − | 0.930119i | \(-0.380296\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 25.8395i | − | 1.16375i | ||||||
\(494\) | −13.1377 | + | 4.75211i | −0.591092 | + | 0.213808i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 38.4684 | + | 7.09948i | 1.72728 | + | 0.318776i | ||||
\(497\) | − | 9.76751i | − | 0.438133i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.03676 | 0.180710 | 0.0903552 | − | 0.995910i | \(-0.471200\pi\) | ||||
0.0903552 | + | 0.995910i | \(0.471200\pi\) | |||||||
\(500\) | 6.57799 | − | 5.47508i | 0.294177 | − | 0.244853i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −24.0135 | + | 8.68608i | −1.07178 | + | 0.387679i | ||||
\(503\) | −40.2393 | −1.79418 | −0.897092 | − | 0.441845i | \(-0.854324\pi\) | ||||
−0.897092 | + | 0.441845i | \(0.854324\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.523556 | −0.0232979 | ||||||||
\(506\) | −27.9818 | + | 10.1215i | −1.24394 | + | 0.449955i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −25.2921 | − | 30.3869i | −1.12215 | − | 1.34820i | ||||
\(509\) | 9.68050 | 0.429081 | 0.214540 | − | 0.976715i | \(-0.431175\pi\) | ||||
0.214540 | + | 0.976715i | \(0.431175\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 9.14079i | − | 0.404365i | ||||||
\(512\) | 0.405604 | − | 22.6238i | 0.0179253 | − | 0.999839i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −5.02222 | + | 1.81662i | −0.221521 | + | 0.0801276i | ||||
\(515\) | − | 4.66773i | − | 0.205685i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 12.4517i | − | 0.547624i | ||||||
\(518\) | −1.83602 | − | 5.07586i | −0.0806701 | − | 0.223020i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.02628 | + | 1.75329i | −0.0450054 | + | 0.0768869i | ||||
\(521\) | 3.92629i | 0.172014i | 0.996295 | + | 0.0860069i | \(0.0274107\pi\) | ||||
−0.996295 | + | 0.0860069i | \(0.972589\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.8709 | 0.912623 | 0.456311 | − | 0.889820i | \(-0.349170\pi\) | ||||
0.456311 | + | 0.889820i | \(0.349170\pi\) | |||||||
\(524\) | 11.8382 | + | 14.2230i | 0.517156 | + | 0.621333i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.21005 | + | 25.4621i | 0.401577 | + | 1.11020i | ||||
\(527\) | −51.0716 | −2.22471 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 36.0279 | 1.56643 | ||||||||
\(530\) | 2.08759 | + | 5.77134i | 0.0906791 | + | 0.250691i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 7.67629 | + | 9.22262i | 0.332810 | + | 0.399851i | ||||
\(533\) | −16.0486 | −0.695141 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 0.652825i | − | 0.0282241i | ||||||
\(536\) | −22.9983 | − | 13.4620i | −0.993377 | − | 0.581469i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 5.72590 | + | 15.8298i | 0.246861 | + | 0.682472i | ||||
\(539\) | 2.73863i | 0.117961i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 3.18975i | − | 0.137138i | −0.997646 | − | 0.0685691i | \(-0.978157\pi\) | ||
0.997646 | − | 0.0685691i | \(-0.0218434\pi\) | |||||||
\(542\) | −35.2108 | + | 12.7363i | −1.51243 | + | 0.547071i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.83990 | + | 29.1427i | 0.207509 | + | 1.24948i | ||||
\(545\) | 8.04185i | 0.344475i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 27.9137 | 1.19350 | 0.596751 | − | 0.802426i | \(-0.296458\pi\) | ||||
0.596751 | + | 0.802426i | \(0.296458\pi\) | |||||||
\(548\) | 3.24030 | + | 3.89303i | 0.138419 | + | 0.166302i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −17.5173 | + | 6.33628i | −0.746939 | + | 0.270180i | ||||
\(551\) | 29.6856 | 1.26465 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.19984 | 0.221120 | ||||||||
\(554\) | 12.6284 | − | 4.56791i | 0.536531 | − | 0.194072i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 30.4106 | − | 25.3117i | 1.28970 | − | 1.07346i | ||||
\(557\) | 14.0025 | 0.593304 | 0.296652 | − | 0.954986i | \(-0.404130\pi\) | ||||
0.296652 | + | 0.954986i | \(0.404130\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14.5589i | 0.615775i | ||||||||
\(560\) | 1.71591 | + | 0.316677i | 0.0725104 | + | 0.0133821i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −22.3093 | + | 8.06965i | −0.941063 | + | 0.340398i | ||||
\(563\) | 13.8839i | 0.585137i | 0.956245 | + | 0.292569i | \(0.0945100\pi\) | ||||
−0.956245 | + | 0.292569i | \(0.905490\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.29318i | 0.0964749i | ||||||||
\(566\) | 6.58264 | + | 18.1983i | 0.276689 | + | 0.764933i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 23.8424 | + | 13.9561i | 1.00041 | + | 0.585583i | ||||
\(569\) | 14.7512i | 0.618401i | 0.950997 | + | 0.309200i | \(0.100061\pi\) | ||||
−0.950997 | + | 0.309200i | \(0.899939\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.28135 | 0.179169 | 0.0895845 | − | 0.995979i | \(-0.471446\pi\) | ||||
0.0895845 | + | 0.995979i | \(0.471446\pi\) | |||||||
\(572\) | 6.93174 | − | 5.76952i | 0.289831 | − | 0.241236i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4.68856 | + | 12.9620i | 0.195697 | + | 0.541022i | ||||
\(575\) | 36.9528 | 1.54104 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.1951 | 0.466059 | 0.233030 | − | 0.972470i | \(-0.425136\pi\) | ||||
0.233030 | + | 0.972470i | \(0.425136\pi\) | |||||||
\(578\) | −4.94152 | − | 13.6613i | −0.205540 | − | 0.568236i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3.31787 | − | 2.76157i | 0.137767 | − | 0.114668i | ||||
\(581\) | −0.227071 | −0.00942051 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 27.2451i | − | 1.12838i | ||||||
\(584\) | 22.3126 | + | 13.0606i | 0.923303 | + | 0.540451i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.55107 | + | 12.5819i | 0.188003 | + | 0.519753i | ||||
\(587\) | 1.45377i | 0.0600035i | 0.999550 | + | 0.0300018i | \(0.00955129\pi\) | ||||
−0.999550 | + | 0.0300018i | \(0.990449\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 58.6733i | − | 2.41759i | ||||||
\(590\) | 7.70940 | − | 2.78861i | 0.317391 | − | 0.114805i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 15.0135 | + | 2.77080i | 0.617051 | + | 0.113879i | ||||
\(593\) | − | 13.1827i | − | 0.541347i | −0.962671 | − | 0.270674i | \(-0.912754\pi\) | ||
0.962671 | − | 0.270674i | \(-0.0872464\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.27808 | −0.0933924 | ||||||||
\(596\) | −12.5506 | + | 10.4463i | −0.514093 | + | 0.427897i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −16.8238 | + | 6.08543i | −0.687975 | + | 0.248852i | ||||
\(599\) | 14.4852 | 0.591848 | 0.295924 | − | 0.955211i | \(-0.404372\pi\) | ||||
0.295924 | + | 0.955211i | \(0.404372\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −27.7364 | −1.13139 | −0.565695 | − | 0.824614i | \(-0.691392\pi\) | ||||
−0.565695 | + | 0.824614i | \(0.691392\pi\) | |||||||
\(602\) | 11.7588 | − | 4.25335i | 0.479253 | − | 0.173353i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −19.0309 | − | 22.8645i | −0.774356 | − | 0.930343i | ||||
\(605\) | 1.52674 | 0.0620709 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18.5137i | 0.751447i | 0.926732 | + | 0.375723i | \(0.122606\pi\) | ||||
−0.926732 | + | 0.375723i | \(0.877394\pi\) | |||||||
\(608\) | −33.4804 | + | 5.56030i | −1.35781 | + | 0.225500i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.63242 | + | 1.31391i | −0.147073 | + | 0.0531985i | ||||
\(611\) | − | 7.48643i | − | 0.302868i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 25.3069i | 1.02213i | 0.859541 | + | 0.511067i | \(0.170750\pi\) | ||||
−0.859541 | + | 0.511067i | \(0.829250\pi\) | |||||||
\(614\) | −5.96756 | − | 16.4979i | −0.240831 | − | 0.665801i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −6.68497 | − | 3.91302i | −0.269345 | − | 0.157660i | ||||
\(617\) | 47.8249i | 1.92536i | 0.270647 | + | 0.962679i | \(0.412762\pi\) | ||||
−0.270647 | + | 0.962679i | \(0.587238\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.22411 | 0.129588 | 0.0647939 | − | 0.997899i | \(-0.479361\pi\) | ||||
0.0647939 | + | 0.997899i | \(0.479361\pi\) | |||||||
\(620\) | −5.45822 | − | 6.55773i | −0.219207 | − | 0.263365i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0.821918 | + | 2.27227i | 0.0329559 | + | 0.0911098i | ||||
\(623\) | 2.46567 | 0.0987848 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22.1819 | 0.887275 | ||||||||
\(626\) | 5.76715 | + | 15.9439i | 0.230502 | + | 0.637245i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −6.29760 | − | 7.56620i | −0.251302 | − | 0.301924i | ||||
\(629\) | −19.9323 | −0.794754 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 22.6025i | − | 0.899791i | −0.893081 | − | 0.449896i | \(-0.851461\pi\) | ||
0.893081 | − | 0.449896i | \(-0.148539\pi\) | |||||||
\(632\) | −7.42966 | + | 12.6928i | −0.295536 | + | 0.504892i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −11.8562 | − | 32.7777i | −0.470870 | − | 1.30177i | ||||
\(635\) | 8.62311i | 0.342198i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.64657i | 0.0652394i | ||||||||
\(638\) | −18.0206 | + | 6.51835i | −0.713443 | + | 0.258064i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3.22474 | + | 3.73605i | −0.127469 | + | 0.147680i | ||||
\(641\) | − | 15.4383i | − | 0.609775i | −0.952388 | − | 0.304888i | \(-0.901381\pi\) | ||
0.952388 | − | 0.304888i | \(-0.0986189\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.41036 | 0.0556191 | 0.0278095 | − | 0.999613i | \(-0.491147\pi\) | ||||
0.0278095 | + | 0.999613i | \(0.491147\pi\) | |||||||
\(644\) | 9.83005 | + | 11.8102i | 0.387358 | + | 0.465388i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 41.6679 | − | 15.0720i | 1.63940 | − | 0.592998i | ||||
\(647\) | 0.811574 | 0.0319063 | 0.0159531 | − | 0.999873i | \(-0.494922\pi\) | ||||
0.0159531 | + | 0.999873i | \(0.494922\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −36.3941 | −1.42860 | ||||||||
\(650\) | −10.5321 | + | 3.80962i | −0.413102 | + | 0.149426i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9.02719 | − | 7.51364i | 0.353532 | − | 0.294257i | ||||
\(653\) | −9.82168 | −0.384352 | −0.192176 | − | 0.981360i | \(-0.561554\pi\) | ||||
−0.192176 | + | 0.981360i | \(0.561554\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 4.03615i | − | 0.157705i | ||||||
\(656\) | −38.3393 | − | 7.07565i | −1.49690 | − | 0.276258i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −6.04657 | + | 2.18714i | −0.235720 | + | 0.0852637i | ||||
\(659\) | − | 11.1456i | − | 0.434170i | −0.976153 | − | 0.217085i | \(-0.930345\pi\) | ||
0.976153 | − | 0.217085i | \(-0.0696548\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.3989i | 0.598947i | 0.954105 | + | 0.299474i | \(0.0968111\pi\) | ||||
−0.954105 | + | 0.299474i | \(0.903189\pi\) | |||||||
\(662\) | −2.72376 | − | 7.53010i | −0.105862 | − | 0.292666i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.324445 | − | 0.554280i | 0.0125909 | − | 0.0215102i | ||||
\(665\) | − | 2.61717i | − | 0.101489i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 38.0146 | 1.47193 | ||||||||
\(668\) | 34.0000 | − | 28.2993i | 1.31550 | − | 1.09493i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.97706 | + | 5.46577i | 0.0763804 | + | 0.211161i | ||||
\(671\) | 17.1478 | 0.661982 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.4112 | 0.786795 | 0.393398 | − | 0.919368i | \(-0.371300\pi\) | ||||
0.393398 | + | 0.919368i | \(0.371300\pi\) | |||||||
\(674\) | −15.5126 | − | 42.8862i | −0.597525 | − | 1.65192i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −15.8159 | + | 13.1641i | −0.608305 | + | 0.506313i | ||||
\(677\) | −50.5124 | −1.94135 | −0.970674 | − | 0.240401i | \(-0.922721\pi\) | ||||
−0.970674 | + | 0.240401i | \(0.922721\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 3.37287i | − | 0.129439i | ||||||
\(680\) | 3.25498 | − | 5.56080i | 0.124823 | − | 0.213247i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 12.8834 | + | 35.6176i | 0.493333 | + | 1.36387i | ||||
\(683\) | − | 33.3625i | − | 1.27658i | −0.769796 | − | 0.638291i | \(-0.779642\pi\) | ||
0.769796 | − | 0.638291i | \(-0.220358\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 1.10475i | − | 0.0422104i | ||||||
\(686\) | 1.32989 | − | 0.481042i | 0.0507753 | − | 0.0183663i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6.41886 | + | 34.7804i | −0.244717 | + | 1.32599i | ||||
\(689\) | − | 16.3808i | − | 0.624059i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24.3714 | 0.927133 | 0.463567 | − | 0.886062i | \(-0.346569\pi\) | ||||
0.463567 | + | 0.886062i | \(0.346569\pi\) | |||||||
\(692\) | −37.1879 | + | 30.9527i | −1.41367 | + | 1.17665i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 27.0442 | − | 9.78234i | 1.02659 | − | 0.371333i | ||||
\(695\) | −8.62982 | −0.327348 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 50.9002 | 1.92798 | ||||||||
\(698\) | 11.0053 | − | 3.98081i | 0.416558 | − | 0.150676i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 6.15384 | + | 7.39348i | 0.232593 | + | 0.279447i | ||||
\(701\) | −34.1271 | −1.28896 | −0.644481 | − | 0.764620i | \(-0.722927\pi\) | ||||
−0.644481 | + | 0.764620i | \(0.722927\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 22.8991i | − | 0.863658i | ||||||
\(704\) | 19.1033 | − | 10.7270i | 0.719983 | − | 0.404288i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 10.9489 | − | 3.96041i | 0.412069 | − | 0.149052i | ||||
\(707\) | − | 1.20021i | − | 0.0451384i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 22.8145i | − | 0.856818i | −0.903585 | − | 0.428409i | \(-0.859074\pi\) | ||
0.903585 | − | 0.428409i | \(-0.140926\pi\) | |||||||
\(710\) | −2.04962 | − | 5.66638i | −0.0769209 | − | 0.212655i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.52300 | + | 6.01868i | −0.132030 | + | 0.225560i | ||||
\(713\) | − | 75.1355i | − | 2.81385i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.96707 | −0.0735642 | ||||||||
\(716\) | −6.92556 | − | 8.32065i | −0.258820 | − | 0.310957i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −5.08953 | − | 14.0705i | −0.189940 | − | 0.525107i | ||||
\(719\) | −2.18175 | −0.0813654 | −0.0406827 | − | 0.999172i | \(-0.512953\pi\) | ||||
−0.0406827 | + | 0.999172i | \(0.512953\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.7004 | 0.398502 | ||||||||
\(722\) | 8.17556 | + | 22.6021i | 0.304263 | + | 0.841164i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 7.92846 | + | 9.52558i | 0.294659 | + | 0.354015i | ||||
\(725\) | 23.7980 | 0.883837 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 15.3017i | − | 0.567507i | −0.958897 | − | 0.283754i | \(-0.908420\pi\) | ||
0.958897 | − | 0.283754i | \(-0.0915798\pi\) | |||||||
\(728\) | −4.01927 | − | 2.35266i | −0.148964 | − | 0.0871953i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.91811 | − | 5.30280i | −0.0709924 | − | 0.196265i | ||||
\(731\) | − | 46.1754i | − | 1.70786i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.8711i | 0.586213i | 0.956080 | + | 0.293106i | \(0.0946890\pi\) | ||||
−0.956080 | + | 0.293106i | \(0.905311\pi\) | |||||||
\(734\) | 31.5974 | − | 11.4293i | 1.16628 | − | 0.421863i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −42.8741 | + | 7.12036i | −1.58036 | + | 0.262460i | ||||
\(737\) | − | 25.8025i | − | 0.950449i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 31.1319 | 1.14521 | 0.572603 | − | 0.819833i | \(-0.305934\pi\) | ||||
0.572603 | + | 0.819833i | \(0.305934\pi\) | |||||||
\(740\) | −2.13024 | − | 2.55936i | −0.0783093 | − | 0.0940840i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −13.2303 | + | 4.78562i | −0.485700 | + | 0.175686i | ||||
\(743\) | −14.6629 | −0.537930 | −0.268965 | − | 0.963150i | \(-0.586682\pi\) | ||||
−0.268965 | + | 0.963150i | \(0.586682\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.56158 | 0.130486 | ||||||||
\(746\) | −16.1504 | + | 5.84186i | −0.591308 | + | 0.213886i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −21.9849 | + | 18.2988i | −0.803849 | + | 0.669071i | ||||
\(749\) | 1.49655 | 0.0546826 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.46100i | 0.308746i | 0.988013 | + | 0.154373i | \(0.0493358\pi\) | ||||
−0.988013 | + | 0.154373i | \(0.950664\pi\) | |||||||
\(752\) | 3.30069 | − | 17.8847i | 0.120364 | − | 0.652188i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −10.8347 | + | 3.91908i | −0.394576 | + | 0.142725i | ||||
\(755\) | 6.48842i | 0.236138i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 39.6473i | − | 1.44101i | −0.693451 | − | 0.720504i | \(-0.743911\pi\) | ||
0.693451 | − | 0.720504i | \(-0.256089\pi\) | |||||||
\(758\) | −15.4600 | − | 42.7408i | −0.561533 | − | 1.55241i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6.38849 | + | 3.73947i | 0.231735 | + | 0.135645i | ||||
\(761\) | − | 49.7301i | − | 1.80271i | −0.433076 | − | 0.901357i | \(-0.642572\pi\) | ||
0.433076 | − | 0.901357i | \(-0.357428\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −18.4352 | −0.667401 | ||||||||
\(764\) | 20.9353 | − | 17.4251i | 0.757411 | − | 0.630419i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −14.4568 | − | 39.9671i | −0.522344 | − | 1.44407i | ||||
\(767\) | −21.8816 | −0.790098 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.62877 | 0.202979 | 0.101489 | − | 0.994837i | \(-0.467639\pi\) | ||||
0.101489 | + | 0.994837i | \(0.467639\pi\) | |||||||
\(770\) | 0.574675 | + | 1.58875i | 0.0207099 | + | 0.0572544i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −9.05837 | + | 7.53959i | −0.326018 | + | 0.271356i | ||||
\(773\) | −25.3999 | −0.913570 | −0.456785 | − | 0.889577i | \(-0.650999\pi\) | ||||
−0.456785 | + | 0.889577i | \(0.650999\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 47.0366i | − | 1.68960i | ||||||
\(776\) | 8.23317 | + | 4.81924i | 0.295553 | + | 0.173001i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −6.19211 | − | 17.1187i | −0.221998 | − | 0.613736i | ||||
\(779\) | 58.4764i | 2.09514i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 26.7495i | 0.957174i | ||||||||
\(782\) | 53.3588 | − | 19.3007i | 1.90811 | − | 0.690193i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.725955 | + | 3.93357i | −0.0259270 | + | 0.140485i | ||||
\(785\) | 2.14711i | 0.0766338i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −31.5311 | −1.12396 | −0.561982 | − | 0.827150i | \(-0.689961\pi\) | ||||
−0.561982 | + | 0.827150i | \(0.689961\pi\) | |||||||
\(788\) | −29.2564 | + | 24.3511i | −1.04222 | + | 0.867472i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3.01656 | − | 1.09114i | 0.107324 | − | 0.0388209i | ||||
\(791\) | −5.25692 | −0.186915 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10.3099 | 0.366115 | ||||||||
\(794\) | 27.7046 | − | 10.0212i | 0.983199 | − | 0.355639i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.56671 | + | 9.09096i | 0.268195 | + | 0.322221i | ||||
\(797\) | 37.3724 | 1.32380 | 0.661899 | − | 0.749593i | \(-0.269751\pi\) | ||||
0.661899 | + | 0.749593i | \(0.269751\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 23.7442i | 0.840010i | ||||||||
\(800\) | −26.8402 | + | 4.45751i | −0.948945 | + | 0.157597i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 21.0481 | − | 7.61343i | 0.743233 | − | 0.268840i | ||||
\(803\) | 25.0332i | 0.883402i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 3.35147i | − | 0.118124i | ||||||
\(806\) | 7.74603 | + | 21.4147i | 0.272842 | + | 0.754299i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2.92970 | + | 1.71488i | 0.103066 | + | 0.0603294i | ||||
\(809\) | 4.37230i | 0.153722i | 0.997042 | + | 0.0768610i | \(0.0244898\pi\) | ||||
−0.997042 | + | 0.0768610i | \(0.975510\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −29.1067 | −1.02208 | −0.511038 | − | 0.859558i | \(-0.670739\pi\) | ||||
−0.511038 | + | 0.859558i | \(0.670739\pi\) | |||||||
\(812\) | 6.33066 | + | 7.60592i | 0.222163 | + | 0.266915i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 5.02817 | + | 13.9009i | 0.176237 | + | 0.487226i | ||||
\(815\) | −2.56171 | −0.0897328 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 53.0484 | 1.85593 | ||||||||
\(818\) | −1.90077 | − | 5.25486i | −0.0664587 | − | 0.183732i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5.43990 | + | 6.53572i | 0.189970 | + | 0.228237i | ||||
\(821\) | −45.1785 | −1.57674 | −0.788370 | − | 0.615201i | \(-0.789075\pi\) | ||||
−0.788370 | + | 0.615201i | \(0.789075\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 30.6242i | − | 1.06749i | −0.845644 | − | 0.533747i | \(-0.820783\pi\) | ||
0.845644 | − | 0.533747i | \(-0.179217\pi\) | |||||||
\(824\) | −15.2889 | + | 26.1195i | −0.532615 | + | 0.909917i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.39266 | + | 17.6731i | 0.222429 | + | 0.614927i | ||||
\(827\) | 12.0993i | 0.420734i | 0.977623 | + | 0.210367i | \(0.0674658\pi\) | ||||
−0.977623 | + | 0.210367i | \(0.932534\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 15.2105i | − | 0.528283i | −0.964484 | − | 0.264142i | \(-0.914911\pi\) | ||
0.964484 | − | 0.264142i | \(-0.0850886\pi\) | |||||||
\(830\) | −0.131730 | + | 0.0476488i | −0.00457241 | + | 0.00165391i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 11.4857 | − | 6.44948i | 0.398194 | − | 0.223595i | ||||
\(833\) | − | 5.22231i | − | 0.180942i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.64841 | −0.333897 | ||||||||
\(836\) | −21.0225 | − | 25.2573i | −0.727078 | − | 0.873542i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −4.74739 | + | 1.71721i | −0.163996 | + | 0.0593200i | ||||
\(839\) | 42.2155 | 1.45744 | 0.728721 | − | 0.684811i | \(-0.240115\pi\) | ||||
0.728721 | + | 0.684811i | \(0.240115\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.51816 | −0.155799 | ||||||||
\(842\) | −21.7792 | + | 7.87788i | −0.750560 | + | 0.271490i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −19.8811 | + | 16.5477i | −0.684337 | + | 0.569597i | ||||
\(845\) | 4.48820 | 0.154399 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.49993i | 0.120259i | ||||||||
\(848\) | 7.22213 | − | 39.1329i | 0.248009 | − | 1.34383i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 33.4038 | − | 12.0827i | 1.14574 | − | 0.414434i | ||||
\(851\) | − | 29.3240i | − | 1.00521i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 49.2536i | − | 1.68641i | −0.537592 | − | 0.843205i | \(-0.680666\pi\) | ||
0.537592 | − | 0.843205i | \(-0.319334\pi\) | |||||||
\(854\) | −3.01202 | − | 8.32702i | −0.103069 | − | 0.284945i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.13830 | + | 3.65306i | −0.0730856 | + | 0.124859i | ||||
\(857\) | 25.9243i | 0.885557i | 0.896631 | + | 0.442779i | \(0.146007\pi\) | ||||
−0.896631 | + | 0.442779i | \(0.853993\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.25940 | 0.315927 | 0.157963 | − | 0.987445i | \(-0.449507\pi\) | ||||
0.157963 | + | 0.987445i | \(0.449507\pi\) | |||||||
\(860\) | 5.92905 | − | 4.93495i | 0.202179 | − | 0.168280i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −13.8301 | − | 38.2346i | −0.471055 | − | 1.30228i | ||||
\(863\) | 6.21443 | 0.211542 | 0.105771 | − | 0.994391i | \(-0.466269\pi\) | ||||
0.105771 | + | 0.994391i | \(0.466269\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.5531 | 0.358815 | ||||||||
\(866\) | −11.3659 | − | 31.4220i | −0.386227 | − | 1.06776i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 15.0330 | − | 12.5125i | 0.510254 | − | 0.424702i | ||||
\(869\) | −14.2404 | −0.483073 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 15.5135i | − | 0.525655i | ||||||
\(872\) | 26.3407 | − | 45.0004i | 0.892010 | − | 1.52390i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 22.1736 | + | 61.3010i | 0.750032 | + | 2.07354i | ||||
\(875\) | − | 4.27921i | − | 0.144664i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.1038i | 0.510020i | 0.966938 | + | 0.255010i | \(0.0820787\pi\) | ||||
−0.966938 | + | 0.255010i | \(0.917921\pi\) | |||||||
\(878\) | 20.5988 | − | 7.45091i | 0.695175 | − | 0.251456i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −4.69923 | − | 0.867261i | −0.158411 | − | 0.0292354i | ||||
\(881\) | − | 2.59677i | − | 0.0874874i | −0.999043 | − | 0.0437437i | \(-0.986072\pi\) | ||
0.999043 | − | 0.0437437i | \(-0.0139285\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.0661 | 0.372404 | 0.186202 | − | 0.982511i | \(-0.440382\pi\) | ||||
0.186202 | + | 0.982511i | \(0.440382\pi\) | |||||||
\(884\) | −13.2182 | + | 11.0020i | −0.444576 | + | 0.370036i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −28.9436 | + | 10.4694i | −0.972380 | + | 0.351726i | ||||
\(887\) | 7.38595 | 0.247996 | 0.123998 | − | 0.992282i | \(-0.460428\pi\) | ||||
0.123998 | + | 0.992282i | \(0.460428\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −19.7677 | −0.662989 | ||||||||
\(890\) | 1.43039 | − | 0.517397i | 0.0479469 | − | 0.0173432i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0.970544 | + | 1.16605i | 0.0324962 | + | 0.0390423i | ||||
\(893\) | −27.2784 | −0.912837 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.36121i | 0.0789265i | ||||||||
\(896\) | −8.56457 | − | 7.39244i | −0.286122 | − | 0.246964i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −38.4814 | + | 13.9193i | −1.28414 | + | 0.464494i | ||||
\(899\) | − | 48.3881i | − | 1.61383i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 51.9539i | 1.73084i | ||||||||
\(902\) | −12.8402 | − | 35.4980i | −0.427532 | − | 1.18195i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.51122 | − | 12.8321i | 0.249819 | − | 0.426790i | ||||
\(905\) | − | 2.70314i | − | 0.0898555i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.58114 | 0.185319 | 0.0926594 | − | 0.995698i | \(-0.470463\pi\) | ||||
0.0926594 | + | 0.995698i | \(0.470463\pi\) | |||||||
\(908\) | 4.61867 | + | 5.54906i | 0.153276 | + | 0.184152i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0.345517 | + | 0.955216i | 0.0114538 | + | 0.0316651i | ||||
\(911\) | 7.02450 | 0.232732 | 0.116366 | − | 0.993206i | \(-0.462875\pi\) | ||||
0.116366 | + | 0.993206i | \(0.462875\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.621864 | 0.0205807 | ||||||||
\(914\) | 12.6257 | + | 34.9050i | 0.417622 | + | 1.15456i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.44773 | + | 5.34369i | 0.146957 | + | 0.176560i | ||||
\(917\) | 9.25252 | 0.305545 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25.7961i | 0.850935i | 0.904974 | + | 0.425468i | \(0.139890\pi\) | ||||
−0.904974 | + | 0.425468i | \(0.860110\pi\) | |||||||
\(920\) | 8.18093 | + | 4.78867i | 0.269717 | + | 0.157878i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 3.59564 | + | 9.94051i | 0.118416 | + | 0.327373i | ||||
\(923\) | 16.0829i | 0.529374i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 18.3575i | − | 0.603591i | ||||||
\(926\) | 10.7642 | − | 3.89360i | 0.353735 | − | 0.127952i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −27.6114 | + | 4.58559i | −0.906390 | + | 0.150530i | ||||
\(929\) | 10.1558i | 0.333201i | 0.986024 | + | 0.166600i | \(0.0532790\pi\) | ||||
−0.986024 | + | 0.166600i | \(0.946721\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.99963 | 0.196630 | ||||||||
\(932\) | −29.4003 | − | 35.3227i | −0.963037 | − | 1.15703i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −21.3602 | + | 7.72633i | −0.698927 | + | 0.252813i | ||||
\(935\) | 6.23882 | 0.204031 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19.1504 | 0.625616 | 0.312808 | − | 0.949816i | \(-0.398730\pi\) | ||||
0.312808 | + | 0.949816i | \(0.398730\pi\) | |||||||
\(938\) | −12.5298 | + | 4.53223i | −0.409113 | + | 0.147983i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3.04882 | + | 2.53763i | −0.0994415 | + | 0.0827685i | ||||
\(941\) | −14.3260 | −0.467016 | −0.233508 | − | 0.972355i | \(-0.575020\pi\) | ||||
−0.233508 | + | 0.972355i | \(0.575020\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 74.8833i | 2.43854i | ||||||||
\(944\) | −52.2740 | − | 9.64736i | −1.70137 | − | 0.313995i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −32.2029 | + | 11.6483i | −1.04701 | + | 0.378720i | ||||
\(947\) | 7.67662i | 0.249456i | 0.992191 | + | 0.124728i | \(0.0398059\pi\) | ||||
−0.992191 | + | 0.124728i | \(0.960194\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 15.0509i | 0.488574i | ||||||||
\(950\) | 13.8812 | + | 38.3758i | 0.450364 | + | 1.24508i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 12.7476 | + | 7.46177i | 0.413153 | + | 0.241837i | ||||
\(953\) | − | 52.6546i | − | 1.70565i | −0.522197 | − | 0.852825i | \(-0.674887\pi\) | ||
0.522197 | − | 0.852825i | \(-0.325113\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.94095 | −0.192245 | ||||||||
\(956\) | 16.0604 | − | 13.3676i | 0.519429 | − | 0.432338i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 15.2485 | + | 42.1560i | 0.492657 | + | 1.36200i | ||||
\(959\) | 2.53255 | 0.0817803 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −64.6386 | −2.08512 | ||||||||
\(962\) | 3.02313 | + | 8.35775i | 0.0974698 | + | 0.269465i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 15.5164 | − | 12.9148i | 0.499749 | − | 0.415958i | ||||
\(965\) | 2.57056 | 0.0827492 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 50.1578i | − | 1.61297i | −0.591257 | − | 0.806483i | \(-0.701368\pi\) | ||
0.591257 | − | 0.806483i | \(-0.298632\pi\) | |||||||
\(968\) | −8.54330 | − | 5.00078i | −0.274592 | − | 0.160731i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −0.707766 | − | 1.95669i | −0.0227250 | − | 0.0628255i | ||||
\(971\) | − | 54.8144i | − | 1.75908i | −0.475828 | − | 0.879538i | \(-0.657852\pi\) | ||
0.475828 | − | 0.879538i | \(-0.342148\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 19.7831i | − | 0.634217i | ||||||
\(974\) | −40.6099 | + | 14.6892i | −1.30122 | + | 0.470674i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 24.6299 | + | 4.54553i | 0.788382 | + | 0.145499i | ||||
\(977\) | 0.0603583i | 0.00193103i | 1.00000 | 0.000965516i | \(0.000307333\pi\) | |||||
−1.00000 | 0.000965516i | \(0.999693\pi\) | ||||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.75254 | −0.215812 | ||||||||
\(980\) | 0.670559 | − | 0.558129i | 0.0214202 | − | 0.0178288i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 54.8181 | − | 19.8286i | 1.74932 | − | 0.632756i | ||||
\(983\) | 7.40354 | 0.236136 | 0.118068 | − | 0.993005i | \(-0.462330\pi\) | ||||
0.118068 | + | 0.993005i | \(0.462330\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.30230 | 0.264533 | ||||||||
\(986\) | 34.3637 | − | 12.4299i | 1.09436 | − | 0.395849i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −12.6395 | − | 15.1857i | −0.402118 | − | 0.483121i | ||||
\(989\) | 67.9323 | 2.16012 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 35.6861i | 1.13361i | 0.823853 | + | 0.566803i | \(0.191820\pi\) | ||||
−0.823853 | + | 0.566803i | \(0.808180\pi\) | |||||||
\(992\) | 9.06338 | + | 54.5737i | 0.287763 | + | 1.73272i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 12.9897 | − | 4.69858i | 0.412008 | − | 0.149030i | ||||
\(995\) | − | 2.57981i | − | 0.0817853i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 52.4345i | − | 1.66062i | −0.557304 | − | 0.830308i | \(-0.688164\pi\) | ||
0.557304 | − | 0.830308i | \(-0.311836\pi\) | |||||||
\(998\) | 1.94185 | + | 5.36844i | 0.0614682 | + | 0.169935i | ||||
\(999\) | 0 | 0 |
(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 | 1512.2.j.c.323.20 | yes | 32 | |
3.2 | odd | 2 | inner | 1512.2.j.c.323.13 | ✓ | 32 | |
4.3 | odd | 2 | 6048.2.j.c.5615.21 | 32 | |||
8.3 | odd | 2 | inner | 1512.2.j.c.323.14 | yes | 32 | |
8.5 | even | 2 | 6048.2.j.c.5615.11 | 32 | |||
12.11 | even | 2 | 6048.2.j.c.5615.12 | 32 | |||
24.5 | odd | 2 | 6048.2.j.c.5615.22 | 32 | |||
24.11 | even | 2 | inner | 1512.2.j.c.323.19 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.j.c.323.13 | ✓ | 32 | 3.2 | odd | 2 | inner | |
1512.2.j.c.323.14 | yes | 32 | 8.3 | odd | 2 | inner | |
1512.2.j.c.323.19 | yes | 32 | 24.11 | even | 2 | inner | |
1512.2.j.c.323.20 | yes | 32 | 1.1 | even | 1 | trivial | |
6048.2.j.c.5615.11 | 32 | 8.5 | even | 2 | |||
6048.2.j.c.5615.12 | 32 | 12.11 | even | 2 | |||
6048.2.j.c.5615.21 | 32 | 4.3 | odd | 2 | |||
6048.2.j.c.5615.22 | 32 | 24.5 | odd | 2 |