Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1512,2,Mod(757,1512)]
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([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1512.757");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1512.c (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: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 757.18 | ||
Character | \(\chi\) | \(=\) | 1512.757 |
Dual form | 1512.2.c.g.757.17 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.10240 | + | 0.885841i | 0.779514 | + | 0.626384i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.430570 | + | 1.95310i | 0.215285 | + | 0.976551i | ||||
\(5\) | 2.99001i | 1.33717i | 0.743634 | + | 0.668587i | \(0.233100\pi\) | ||||
−0.743634 | + | 0.668587i | \(0.766900\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.25548 | + | 2.53452i | −0.443879 | + | 0.896087i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.64867 | + | 3.29619i | −0.837585 | + | 1.04235i | ||||
\(11\) | 2.13956i | 0.645101i | 0.946552 | + | 0.322550i | \(0.104540\pi\) | ||||
−0.946552 | + | 0.322550i | \(0.895460\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.665739i | 0.184643i | 0.995729 | + | 0.0923214i | \(0.0294287\pi\) | ||||
−0.995729 | + | 0.0923214i | \(0.970571\pi\) | |||||||
\(14\) | 1.10240 | + | 0.885841i | 0.294629 | + | 0.236751i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.62922 | + | 1.68190i | −0.907305 | + | 0.420474i | ||||
\(17\) | 7.04931 | 1.70971 | 0.854855 | − | 0.518867i | \(-0.173646\pi\) | ||||
0.854855 | + | 0.518867i | \(0.173646\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1.39525i | − | 0.320092i | −0.987110 | − | 0.160046i | \(-0.948836\pi\) | ||
0.987110 | − | 0.160046i | \(-0.0511642\pi\) | |||||||
\(20\) | −5.83980 | + | 1.28741i | −1.30582 | + | 0.287873i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.89531 | + | 2.35865i | −0.404081 | + | 0.502865i | ||||
\(23\) | 0.184371 | 0.0384439 | 0.0192220 | − | 0.999815i | \(-0.493881\pi\) | ||||
0.0192220 | + | 0.999815i | \(0.493881\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.94016 | −0.788032 | ||||||||
\(26\) | −0.589739 | + | 0.733911i | −0.115657 | + | 0.143932i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.430570 | + | 1.95310i | 0.0813701 | + | 0.369102i | ||||
\(29\) | 1.27564i | 0.236880i | 0.992961 | + | 0.118440i | \(0.0377893\pi\) | ||||
−0.992961 | + | 0.118440i | \(0.962211\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.62308 | −1.36915 | −0.684573 | − | 0.728944i | \(-0.740011\pi\) | ||||
−0.684573 | + | 0.728944i | \(0.740011\pi\) | |||||||
\(32\) | −5.49074 | − | 1.36079i | −0.970635 | − | 0.240556i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 7.77116 | + | 6.24457i | 1.33274 | + | 1.07094i | ||||
\(35\) | 2.99001i | 0.505404i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 6.69127i | − | 1.10004i | −0.835152 | − | 0.550019i | \(-0.814621\pi\) | ||
0.835152 | − | 0.550019i | \(-0.185379\pi\) | |||||||
\(38\) | 1.23597 | − | 1.53812i | 0.200500 | − | 0.249516i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −7.57823 | − | 3.75389i | −1.19822 | − | 0.593543i | ||||
\(41\) | −0.274106 | −0.0428081 | −0.0214041 | − | 0.999771i | \(-0.506814\pi\) | ||||
−0.0214041 | + | 0.999771i | \(0.506814\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.63971i | 0.402553i | 0.979535 | + | 0.201276i | \(0.0645089\pi\) | ||||
−0.979535 | + | 0.201276i | \(0.935491\pi\) | |||||||
\(44\) | −4.17877 | + | 0.921229i | −0.629974 | + | 0.138881i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.203250 | + | 0.163323i | 0.0299676 | + | 0.0240807i | ||||
\(47\) | −5.77739 | −0.842719 | −0.421359 | − | 0.906894i | \(-0.638447\pi\) | ||||
−0.421359 | + | 0.906894i | \(0.638447\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −4.34363 | − | 3.49036i | −0.614283 | − | 0.493611i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.30026 | + | 0.286647i | −0.180313 | + | 0.0397508i | ||||
\(53\) | − | 7.48353i | − | 1.02794i | −0.857808 | − | 0.513971i | \(-0.828174\pi\) | ||
0.857808 | − | 0.513971i | \(-0.171826\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.39730 | −0.862611 | ||||||||
\(56\) | −1.25548 | + | 2.53452i | −0.167770 | + | 0.338689i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.13001 | + | 1.40626i | −0.148378 | + | 0.184651i | ||||
\(59\) | 9.03787i | 1.17663i | 0.808632 | + | 0.588315i | \(0.200208\pi\) | ||||
−0.808632 | + | 0.588315i | \(0.799792\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.80298i | 1.25514i | 0.778559 | + | 0.627571i | \(0.215951\pi\) | ||||
−0.778559 | + | 0.627571i | \(0.784049\pi\) | |||||||
\(62\) | −8.40369 | − | 6.75284i | −1.06727 | − | 0.857612i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4.84755 | − | 6.36406i | −0.605943 | − | 0.795508i | ||||
\(65\) | −1.99057 | −0.246900 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 10.8191i | − | 1.32177i | −0.750488 | − | 0.660884i | \(-0.770181\pi\) | ||
0.750488 | − | 0.660884i | \(-0.229819\pi\) | |||||||
\(68\) | 3.03522 | + | 13.7680i | 0.368075 | + | 1.66962i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.64867 | + | 3.29619i | −0.316577 | + | 0.393970i | ||||
\(71\) | 7.93573 | 0.941798 | 0.470899 | − | 0.882187i | \(-0.343930\pi\) | ||||
0.470899 | + | 0.882187i | \(0.343930\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.80408 | −0.328193 | −0.164097 | − | 0.986444i | \(-0.552471\pi\) | ||||
−0.164097 | + | 0.986444i | \(0.552471\pi\) | |||||||
\(74\) | 5.92740 | − | 7.37645i | 0.689047 | − | 0.857495i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.72506 | − | 0.600752i | 0.312586 | − | 0.0689110i | ||||
\(77\) | 2.13956i | 0.243825i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.98350 | 0.898214 | 0.449107 | − | 0.893478i | \(-0.351742\pi\) | ||||
0.449107 | + | 0.893478i | \(0.351742\pi\) | |||||||
\(80\) | −5.02888 | − | 10.8514i | −0.562246 | − | 1.21322i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.302174 | − | 0.242814i | −0.0333695 | − | 0.0268143i | ||||
\(83\) | − | 6.76125i | − | 0.742143i | −0.928604 | − | 0.371072i | \(-0.878990\pi\) | ||
0.928604 | − | 0.371072i | \(-0.121010\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 21.0775i | 2.28618i | ||||||||
\(86\) | −2.33837 | + | 2.91002i | −0.252153 | + | 0.313795i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −5.42274 | − | 2.68617i | −0.578066 | − | 0.286346i | ||||
\(89\) | 16.7549 | 1.77602 | 0.888010 | − | 0.459825i | \(-0.152088\pi\) | ||||
0.888010 | + | 0.459825i | \(0.152088\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.665739i | 0.0697884i | ||||||||
\(92\) | 0.0793844 | + | 0.360095i | 0.00827640 | + | 0.0375425i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6.36899 | − | 5.11785i | −0.656911 | − | 0.527866i | ||||
\(95\) | 4.17180 | 0.428018 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.107694 | −0.0109346 | −0.00546732 | − | 0.999985i | \(-0.501740\pi\) | ||||
−0.00546732 | + | 0.999985i | \(0.501740\pi\) | |||||||
\(98\) | 1.10240 | + | 0.885841i | 0.111359 | + | 0.0894835i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.69652 | − | 7.69554i | −0.169652 | − | 0.769554i | ||||
\(101\) | − | 14.8524i | − | 1.47787i | −0.673775 | − | 0.738937i | \(-0.735328\pi\) | ||
0.673775 | − | 0.738937i | \(-0.264672\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.1461 | −1.59092 | −0.795459 | − | 0.606007i | \(-0.792770\pi\) | ||||
−0.795459 | + | 0.606007i | \(0.792770\pi\) | |||||||
\(104\) | −1.68733 | − | 0.835821i | −0.165456 | − | 0.0819590i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.62922 | − | 8.24984i | 0.643887 | − | 0.801295i | ||||
\(107\) | 15.6131i | 1.50937i | 0.656084 | + | 0.754687i | \(0.272211\pi\) | ||||
−0.656084 | + | 0.754687i | \(0.727789\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 4.15829i | − | 0.398292i | −0.979970 | − | 0.199146i | \(-0.936183\pi\) | ||
0.979970 | − | 0.199146i | \(-0.0638167\pi\) | |||||||
\(110\) | −7.05238 | − | 5.66699i | −0.672418 | − | 0.540326i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.62922 | + | 1.68190i | −0.342929 | + | 0.158924i | ||||
\(113\) | 18.4682 | 1.73734 | 0.868672 | − | 0.495388i | \(-0.164974\pi\) | ||||
0.868672 | + | 0.495388i | \(0.164974\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.551270i | 0.0514062i | ||||||||
\(116\) | −2.49145 | + | 0.549250i | −0.231325 | + | 0.0509966i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −8.00612 | + | 9.96334i | −0.737023 | + | 0.917200i | ||||
\(119\) | 7.04931 | 0.646209 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.42230 | 0.583845 | ||||||||
\(122\) | −8.68388 | + | 10.8068i | −0.786202 | + | 0.978402i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.28227 | − | 14.8887i | −0.294757 | − | 1.33704i | ||||
\(125\) | 3.16893i | 0.283437i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.37444 | −0.388169 | −0.194084 | − | 0.980985i | \(-0.562174\pi\) | ||||
−0.194084 | + | 0.980985i | \(0.562174\pi\) | |||||||
\(128\) | 0.293616 | − | 11.3099i | 0.0259523 | − | 0.999663i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.19440 | − | 1.76333i | −0.192462 | − | 0.154654i | ||||
\(131\) | 5.76264i | 0.503484i | 0.967794 | + | 0.251742i | \(0.0810035\pi\) | ||||
−0.967794 | + | 0.251742i | \(0.918997\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 1.39525i | − | 0.120983i | ||||||
\(134\) | 9.58404 | − | 11.9270i | 0.827935 | − | 1.03034i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −8.85026 | + | 17.8666i | −0.758904 | + | 1.53205i | ||||
\(137\) | −10.5191 | −0.898704 | −0.449352 | − | 0.893355i | \(-0.648345\pi\) | ||||
−0.449352 | + | 0.893355i | \(0.648345\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.27000i | 0.616633i | 0.951284 | + | 0.308316i | \(0.0997656\pi\) | ||||
−0.951284 | + | 0.308316i | \(0.900234\pi\) | |||||||
\(140\) | −5.83980 | + | 1.28741i | −0.493553 | + | 0.108806i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 8.74835 | + | 7.02980i | 0.734145 | + | 0.589928i | ||||
\(143\) | −1.42439 | −0.119113 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.81416 | −0.316749 | ||||||||
\(146\) | −3.09122 | − | 2.48397i | −0.255831 | − | 0.205575i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 13.0687 | − | 2.88106i | 1.07424 | − | 0.236822i | ||||
\(149\) | 3.06625i | 0.251197i | 0.992081 | + | 0.125599i | \(0.0400851\pi\) | ||||
−0.992081 | + | 0.125599i | \(0.959915\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.8992 | −1.29386 | −0.646930 | − | 0.762549i | \(-0.723947\pi\) | ||||
−0.646930 | + | 0.762549i | \(0.723947\pi\) | |||||||
\(152\) | 3.53628 | + | 1.75170i | 0.286830 | + | 0.142082i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.89531 | + | 2.35865i | −0.152728 | + | 0.190065i | ||||
\(155\) | − | 22.7931i | − | 1.83079i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.3211i | 1.46219i | 0.682278 | + | 0.731093i | \(0.260989\pi\) | ||||
−0.682278 | + | 0.731093i | \(0.739011\pi\) | |||||||
\(158\) | 8.80101 | + | 7.07211i | 0.700171 | + | 0.562627i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 4.06878 | − | 16.4174i | 0.321665 | − | 1.29791i | ||||
\(161\) | 0.184371 | 0.0145304 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 22.0479i | − | 1.72692i | −0.504415 | − | 0.863462i | \(-0.668292\pi\) | ||
0.504415 | − | 0.863462i | \(-0.331708\pi\) | |||||||
\(164\) | −0.118022 | − | 0.535357i | −0.00921595 | − | 0.0418043i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.98939 | − | 7.45360i | 0.464867 | − | 0.578511i | ||||
\(167\) | 10.2650 | 0.794332 | 0.397166 | − | 0.917747i | \(-0.369994\pi\) | ||||
0.397166 | + | 0.917747i | \(0.369994\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.5568 | 0.965907 | ||||||||
\(170\) | −18.6713 | + | 23.2358i | −1.43203 | + | 1.78211i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −5.15563 | + | 1.13658i | −0.393113 | + | 0.0866636i | ||||
\(173\) | 15.5234i | 1.18022i | 0.807322 | + | 0.590111i | \(0.200916\pi\) | ||||
−0.807322 | + | 0.590111i | \(0.799084\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.94016 | −0.297848 | ||||||||
\(176\) | −3.59851 | − | 7.76492i | −0.271248 | − | 0.585303i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 18.4706 | + | 14.8422i | 1.38443 | + | 1.11247i | ||||
\(179\) | − | 17.2028i | − | 1.28580i | −0.765952 | − | 0.642898i | \(-0.777732\pi\) | ||
0.765952 | − | 0.642898i | \(-0.222268\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.5145i | 0.781538i | 0.920489 | + | 0.390769i | \(0.127791\pi\) | ||||
−0.920489 | + | 0.390769i | \(0.872209\pi\) | |||||||
\(182\) | −0.589739 | + | 0.733911i | −0.0437144 | + | 0.0544011i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.231473 | + | 0.467290i | −0.0170644 | + | 0.0344491i | ||||
\(185\) | 20.0070 | 1.47094 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.0824i | 1.10293i | ||||||||
\(188\) | −2.48757 | − | 11.2838i | −0.181425 | − | 0.822958i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.59900 | + | 3.69556i | 0.333646 | + | 0.268104i | ||||
\(191\) | 14.3893 | 1.04117 | 0.520587 | − | 0.853808i | \(-0.325713\pi\) | ||||
0.520587 | + | 0.853808i | \(0.325713\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.3579 | 0.817562 | 0.408781 | − | 0.912632i | \(-0.365954\pi\) | ||||
0.408781 | + | 0.912632i | \(0.365954\pi\) | |||||||
\(194\) | −0.118721 | − | 0.0953995i | −0.00852370 | − | 0.00684928i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.430570 | + | 1.95310i | 0.0307550 | + | 0.139507i | ||||
\(197\) | 6.44465i | 0.459163i | 0.973289 | + | 0.229581i | \(0.0737357\pi\) | ||||
−0.973289 | + | 0.229581i | \(0.926264\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.48055 | −0.459394 | −0.229697 | − | 0.973262i | \(-0.573774\pi\) | ||||
−0.229697 | + | 0.973262i | \(0.573774\pi\) | |||||||
\(200\) | 4.94679 | − | 9.98641i | 0.349791 | − | 0.706146i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 13.1569 | − | 16.3733i | 0.925717 | − | 1.15202i | ||||
\(203\) | 1.27564i | 0.0895321i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 0.819579i | − | 0.0572419i | ||||||
\(206\) | −17.7994 | − | 14.3028i | −1.24014 | − | 0.996527i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.11970 | − | 2.41611i | −0.0776375 | − | 0.167527i | ||||
\(209\) | 2.98521 | 0.206491 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 10.3150i | − | 0.710112i | −0.934845 | − | 0.355056i | \(-0.884462\pi\) | ||
0.934845 | − | 0.355056i | \(-0.115538\pi\) | |||||||
\(212\) | 14.6161 | − | 3.22218i | 1.00384 | − | 0.221300i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −13.8307 | + | 17.2119i | −0.945449 | + | 1.17658i | ||||
\(215\) | −7.89277 | −0.538283 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.62308 | −0.517489 | ||||||||
\(218\) | 3.68358 | − | 4.58409i | 0.249484 | − | 0.310474i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.75448 | − | 12.4946i | −0.185707 | − | 0.842384i | ||||
\(221\) | 4.69300i | 0.315686i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 23.8589 | 1.59771 | 0.798854 | − | 0.601526i | \(-0.205440\pi\) | ||||
0.798854 | + | 0.601526i | \(0.205440\pi\) | |||||||
\(224\) | −5.49074 | − | 1.36079i | −0.366866 | − | 0.0909217i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 20.3594 | + | 16.3599i | 1.35428 | + | 1.08825i | ||||
\(227\) | − | 1.88092i | − | 0.124841i | −0.998050 | − | 0.0624206i | \(-0.980118\pi\) | ||
0.998050 | − | 0.0624206i | \(-0.0198820\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.8128i | 1.24319i | 0.783340 | + | 0.621594i | \(0.213515\pi\) | ||||
−0.783340 | + | 0.621594i | \(0.786485\pi\) | |||||||
\(230\) | −0.488338 | + | 0.607720i | −0.0322000 | + | 0.0400719i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.23312 | − | 1.60153i | −0.212265 | − | 0.105146i | ||||
\(233\) | 9.18759 | 0.601899 | 0.300949 | − | 0.953640i | \(-0.402696\pi\) | ||||
0.300949 | + | 0.953640i | \(0.402696\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 17.2745i | − | 1.12686i | ||||||
\(236\) | −17.6519 | + | 3.89144i | −1.14904 | + | 0.253311i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 7.77116 | + | 6.24457i | 0.503729 | + | 0.404776i | ||||
\(239\) | 29.1200 | 1.88362 | 0.941808 | − | 0.336152i | \(-0.109126\pi\) | ||||
0.941808 | + | 0.336152i | \(0.109126\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 25.4640 | 1.64028 | 0.820142 | − | 0.572160i | \(-0.193894\pi\) | ||||
0.820142 | + | 0.572160i | \(0.193894\pi\) | |||||||
\(242\) | 7.07994 | + | 5.68914i | 0.455116 | + | 0.365712i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −19.1462 | + | 4.22087i | −1.22571 | + | 0.270213i | ||||
\(245\) | 2.99001i | 0.191025i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.928871 | 0.0591027 | ||||||||
\(248\) | 9.57062 | − | 19.3208i | 0.607735 | − | 1.22687i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2.80717 | + | 3.49342i | −0.177541 | + | 0.220943i | ||||
\(251\) | 2.72427i | 0.171955i | 0.996297 | + | 0.0859773i | \(0.0274012\pi\) | ||||
−0.996297 | + | 0.0859773i | \(0.972599\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.394471i | 0.0248002i | ||||||||
\(254\) | −4.82238 | − | 3.87506i | −0.302583 | − | 0.243143i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 10.3425 | − | 12.2079i | 0.646404 | − | 0.762996i | ||||
\(257\) | −17.6181 | −1.09899 | −0.549494 | − | 0.835498i | \(-0.685179\pi\) | ||||
−0.549494 | + | 0.835498i | \(0.685179\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 6.69127i | − | 0.415775i | ||||||
\(260\) | −0.857079 | − | 3.88778i | −0.0531538 | − | 0.241110i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −5.10479 | + | 6.35273i | −0.315375 | + | 0.392473i | ||||
\(263\) | 5.42576 | 0.334567 | 0.167283 | − | 0.985909i | \(-0.446501\pi\) | ||||
0.167283 | + | 0.985909i | \(0.446501\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 22.3758 | 1.37454 | ||||||||
\(266\) | 1.23597 | − | 1.53812i | 0.0757821 | − | 0.0943082i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 21.1309 | − | 4.65840i | 1.29077 | − | 0.284557i | ||||
\(269\) | − | 17.6635i | − | 1.07696i | −0.842637 | − | 0.538482i | \(-0.818998\pi\) | ||
0.842637 | − | 0.538482i | \(-0.181002\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.5223 | 0.699929 | 0.349965 | − | 0.936763i | \(-0.386194\pi\) | ||||
0.349965 | + | 0.936763i | \(0.386194\pi\) | |||||||
\(272\) | −25.5835 | + | 11.8562i | −1.55123 | + | 0.718888i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −11.5962 | − | 9.31822i | −0.700553 | − | 0.562935i | ||||
\(275\) | − | 8.43020i | − | 0.508360i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 7.84872i | − | 0.471584i | −0.971804 | − | 0.235792i | \(-0.924232\pi\) | ||
0.971804 | − | 0.235792i | \(-0.0757684\pi\) | |||||||
\(278\) | −6.44006 | + | 8.01444i | −0.386249 | + | 0.480674i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −7.57823 | − | 3.75389i | −0.452886 | − | 0.224338i | ||||
\(281\) | −31.1308 | −1.85711 | −0.928555 | − | 0.371195i | \(-0.878948\pi\) | ||||
−0.928555 | + | 0.371195i | \(0.878948\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 24.7863i | − | 1.47339i | −0.676224 | − | 0.736696i | \(-0.736385\pi\) | ||
0.676224 | − | 0.736696i | \(-0.263615\pi\) | |||||||
\(284\) | 3.41689 | + | 15.4993i | 0.202755 | + | 0.919714i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.57024 | − | 1.26178i | −0.0928505 | − | 0.0746107i | ||||
\(287\) | −0.274106 | −0.0161800 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 32.6928 | 1.92311 | ||||||||
\(290\) | −4.20473 | − | 3.37874i | −0.246910 | − | 0.198407i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.20735 | − | 5.47666i | −0.0706551 | − | 0.320497i | ||||
\(293\) | 28.9898i | 1.69360i | 0.531909 | + | 0.846802i | \(0.321475\pi\) | ||||
−0.531909 | + | 0.846802i | \(0.678525\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −27.0233 | −1.57336 | ||||||||
\(296\) | 16.9591 | + | 8.40074i | 0.985729 | + | 0.488283i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.71621 | + | 3.38023i | −0.157346 | + | 0.195812i | ||||
\(299\) | 0.122743i | 0.00709839i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.63971i | 0.152151i | ||||||||
\(302\) | −17.5273 | − | 14.0842i | −1.00858 | − | 0.810454i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.34666 | + | 5.06366i | 0.134590 | + | 0.290421i | ||||
\(305\) | −29.3110 | −1.67834 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 18.8831i | − | 1.07772i | −0.842397 | − | 0.538858i | \(-0.818856\pi\) | ||
0.842397 | − | 0.538858i | \(-0.181144\pi\) | |||||||
\(308\) | −4.17877 | + | 0.921229i | −0.238108 | + | 0.0524919i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 20.1911 | − | 25.1271i | 1.14678 | − | 1.42712i | ||||
\(311\) | 0.147540 | 0.00836624 | 0.00418312 | − | 0.999991i | \(-0.498668\pi\) | ||||
0.00418312 | + | 0.999991i | \(0.498668\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −23.3154 | −1.31786 | −0.658932 | − | 0.752202i | \(-0.728992\pi\) | ||||
−0.658932 | + | 0.752202i | \(0.728992\pi\) | |||||||
\(314\) | −16.2296 | + | 20.1972i | −0.915890 | + | 1.13979i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.43746 | + | 15.5926i | 0.193372 | + | 0.877152i | ||||
\(317\) | − | 1.43318i | − | 0.0804954i | −0.999190 | − | 0.0402477i | \(-0.987185\pi\) | ||
0.999190 | − | 0.0402477i | \(-0.0128147\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.72929 | −0.152811 | ||||||||
\(320\) | 19.0286 | − | 14.4942i | 1.06373 | − | 0.810251i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.203250 | + | 0.163323i | 0.0113267 | + | 0.00910164i | ||||
\(323\) | − | 9.83554i | − | 0.547264i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 2.62312i | − | 0.145505i | ||||||
\(326\) | 19.5309 | − | 24.3056i | 1.08172 | − | 1.34616i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.344134 | − | 0.694726i | 0.0190016 | − | 0.0383598i | ||||
\(329\) | −5.77739 | −0.318518 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 23.3196i | − | 1.28176i | −0.767640 | − | 0.640882i | \(-0.778569\pi\) | ||
0.767640 | − | 0.640882i | \(-0.221431\pi\) | |||||||
\(332\) | 13.2054 | − | 2.91119i | 0.724741 | − | 0.159772i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 11.3162 | + | 9.09319i | 0.619193 | + | 0.497557i | ||||
\(335\) | 32.3493 | 1.76743 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.484629 | 0.0263994 | 0.0131997 | − | 0.999913i | \(-0.495798\pi\) | ||||
0.0131997 | + | 0.999913i | \(0.495798\pi\) | |||||||
\(338\) | 13.8426 | + | 11.1233i | 0.752938 | + | 0.605029i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −41.1666 | + | 9.07535i | −2.23257 | + | 0.492180i | ||||
\(341\) | − | 16.3100i | − | 0.883237i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −6.69040 | − | 3.31410i | −0.360722 | − | 0.178685i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −13.7513 | + | 17.1130i | −0.739272 | + | 0.919999i | ||||
\(347\) | 10.0395i | 0.538947i | 0.963008 | + | 0.269473i | \(0.0868496\pi\) | ||||
−0.963008 | + | 0.269473i | \(0.913150\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 9.55791i | − | 0.511623i | −0.966727 | − | 0.255812i | \(-0.917657\pi\) | ||
0.966727 | − | 0.255812i | \(-0.0823427\pi\) | |||||||
\(350\) | −4.34363 | − | 3.49036i | −0.232177 | − | 0.186568i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.91149 | − | 11.7478i | 0.155183 | − | 0.626157i | ||||
\(353\) | 28.2931 | 1.50589 | 0.752945 | − | 0.658083i | \(-0.228632\pi\) | ||||
0.752945 | + | 0.658083i | \(0.228632\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 23.7279i | 1.25935i | ||||||||
\(356\) | 7.21417 | + | 32.7241i | 0.382350 | + | 1.73437i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 15.2389 | − | 18.9643i | 0.805402 | − | 1.00230i | ||||
\(359\) | −25.8316 | −1.36334 | −0.681671 | − | 0.731659i | \(-0.738746\pi\) | ||||
−0.681671 | + | 0.731659i | \(0.738746\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.0533 | 0.897541 | ||||||||
\(362\) | −9.31419 | + | 11.5912i | −0.489543 | + | 0.609220i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.30026 | + | 0.286647i | −0.0681520 | + | 0.0150244i | ||||
\(365\) | − | 8.38424i | − | 0.438851i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.78123 | −0.0929793 | −0.0464896 | − | 0.998919i | \(-0.514803\pi\) | ||||
−0.0464896 | + | 0.998919i | \(0.514803\pi\) | |||||||
\(368\) | −0.669121 | + | 0.310092i | −0.0348803 | + | 0.0161647i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 22.0557 | + | 17.7230i | 1.14662 | + | 0.921375i | ||||
\(371\) | − | 7.48353i | − | 0.388525i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 22.1074i | − | 1.14468i | −0.820017 | − | 0.572340i | \(-0.806036\pi\) | ||
0.820017 | − | 0.572340i | \(-0.193964\pi\) | |||||||
\(374\) | −13.3606 | + | 16.6268i | −0.690861 | + | 0.859753i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.25339 | − | 14.6429i | 0.374065 | − | 0.755149i | ||||
\(377\) | −0.849241 | −0.0437381 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 35.4109i | − | 1.81893i | −0.415776 | − | 0.909467i | \(-0.636490\pi\) | ||
0.415776 | − | 0.909467i | \(-0.363510\pi\) | |||||||
\(380\) | 1.79625 | + | 8.14796i | 0.0921459 | + | 0.417982i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 15.8628 | + | 12.7467i | 0.811611 | + | 0.652176i | ||||
\(383\) | −24.1927 | −1.23619 | −0.618095 | − | 0.786104i | \(-0.712095\pi\) | ||||
−0.618095 | + | 0.786104i | \(0.712095\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.39730 | −0.326036 | ||||||||
\(386\) | 12.5210 | + | 10.0613i | 0.637302 | + | 0.512108i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.0463697 | − | 0.210337i | −0.00235406 | − | 0.0106782i | ||||
\(389\) | 13.0465i | 0.661483i | 0.943721 | + | 0.330741i | \(0.107299\pi\) | ||||
−0.943721 | + | 0.330741i | \(0.892701\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.29969 | 0.0657279 | ||||||||
\(392\) | −1.25548 | + | 2.53452i | −0.0634113 | + | 0.128012i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −5.70894 | + | 7.10458i | −0.287612 | + | 0.357924i | ||||
\(395\) | 23.8707i | 1.20107i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 36.0707i | − | 1.81034i | −0.425053 | − | 0.905168i | \(-0.639745\pi\) | ||
0.425053 | − | 0.905168i | \(-0.360255\pi\) | |||||||
\(398\) | −7.14416 | − | 5.74074i | −0.358104 | − | 0.287757i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 14.2997 | − | 6.62694i | 0.714986 | − | 0.331347i | ||||
\(401\) | −15.5149 | −0.774778 | −0.387389 | − | 0.921916i | \(-0.626623\pi\) | ||||
−0.387389 | + | 0.921916i | \(0.626623\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 5.07499i | − | 0.252803i | ||||||
\(404\) | 29.0083 | − | 6.39502i | 1.44322 | − | 0.318164i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.13001 | + | 1.40626i | −0.0560815 | + | 0.0697915i | ||||
\(407\) | 14.3163 | 0.709635 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −28.6937 | −1.41881 | −0.709406 | − | 0.704800i | \(-0.751037\pi\) | ||||
−0.709406 | + | 0.704800i | \(0.751037\pi\) | |||||||
\(410\) | 0.726017 | − | 0.903504i | 0.0358554 | − | 0.0446209i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −6.95201 | − | 31.5349i | −0.342501 | − | 1.55361i | ||||
\(413\) | 9.03787i | 0.444724i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 20.2162 | 0.992374 | ||||||||
\(416\) | 0.905932 | − | 3.65540i | 0.0444170 | − | 0.179221i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.29090 | + | 2.64442i | 0.160963 | + | 0.129343i | ||||
\(419\) | 22.9355i | 1.12047i | 0.828333 | + | 0.560236i | \(0.189290\pi\) | ||||
−0.828333 | + | 0.560236i | \(0.810710\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.1562i | 0.641193i | 0.947216 | + | 0.320596i | \(0.103883\pi\) | ||||
−0.947216 | + | 0.320596i | \(0.896117\pi\) | |||||||
\(422\) | 9.13743 | − | 11.3712i | 0.444803 | − | 0.553543i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 18.9671 | + | 9.39541i | 0.921125 | + | 0.456281i | ||||
\(425\) | −27.7754 | −1.34731 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.80298i | 0.474399i | ||||||||
\(428\) | −30.4940 | + | 6.72253i | −1.47398 | + | 0.324946i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8.70099 | − | 6.99174i | −0.419599 | − | 0.337172i | ||||
\(431\) | −39.6373 | −1.90926 | −0.954631 | − | 0.297792i | \(-0.903750\pi\) | ||||
−0.954631 | + | 0.297792i | \(0.903750\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.5906 | 0.557010 | 0.278505 | − | 0.960435i | \(-0.410161\pi\) | ||||
0.278505 | + | 0.960435i | \(0.410161\pi\) | |||||||
\(434\) | −8.40369 | − | 6.75284i | −0.403390 | − | 0.324147i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.12156 | − | 1.79043i | 0.388952 | − | 0.0857462i | ||||
\(437\) | − | 0.257243i | − | 0.0123056i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.88971 | −0.472010 | −0.236005 | − | 0.971752i | \(-0.575838\pi\) | ||||
−0.236005 | + | 0.971752i | \(0.575838\pi\) | |||||||
\(440\) | 8.03167 | − | 16.2141i | 0.382895 | − | 0.772975i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.15726 | + | 5.17357i | −0.197741 | + | 0.246081i | ||||
\(443\) | − | 2.14448i | − | 0.101888i | −0.998702 | − | 0.0509438i | \(-0.983777\pi\) | ||
0.998702 | − | 0.0509438i | \(-0.0162229\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 50.0974i | 2.37485i | ||||||||
\(446\) | 26.3020 | + | 21.1352i | 1.24544 | + | 1.00078i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −4.84755 | − | 6.36406i | −0.229025 | − | 0.300674i | ||||
\(449\) | 4.65352 | 0.219613 | 0.109807 | − | 0.993953i | \(-0.464977\pi\) | ||||
0.109807 | + | 0.993953i | \(0.464977\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 0.586465i | − | 0.0276156i | ||||||
\(452\) | 7.95186 | + | 36.0703i | 0.374024 | + | 1.69661i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.66620 | − | 2.07353i | 0.0781986 | − | 0.0973155i | ||||
\(455\) | −1.99057 | −0.0933192 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.0517 | 0.891203 | 0.445601 | − | 0.895232i | \(-0.352990\pi\) | ||||
0.445601 | + | 0.895232i | \(0.352990\pi\) | |||||||
\(458\) | −16.6652 | + | 20.7393i | −0.778713 | + | 0.969083i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.07669 | + | 0.237360i | −0.0502008 | + | 0.0110670i | ||||
\(461\) | 26.0354i | 1.21259i | 0.795240 | + | 0.606294i | \(0.207345\pi\) | ||||
−0.795240 | + | 0.606294i | \(0.792655\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 29.6096 | 1.37607 | 0.688036 | − | 0.725676i | \(-0.258473\pi\) | ||||
0.688036 | + | 0.725676i | \(0.258473\pi\) | |||||||
\(464\) | −2.14548 | − | 4.62956i | −0.0996016 | − | 0.214922i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 10.1284 | + | 8.13875i | 0.469189 | + | 0.377020i | ||||
\(467\) | 25.8983i | 1.19843i | 0.800588 | + | 0.599216i | \(0.204521\pi\) | ||||
−0.800588 | + | 0.599216i | \(0.795479\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 10.8191i | − | 0.499581i | ||||||
\(470\) | 15.3024 | − | 19.0434i | 0.705848 | − | 0.878404i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −22.9066 | − | 11.3468i | −1.05436 | − | 0.522281i | ||||
\(473\) | −5.64782 | −0.259687 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.49750i | 0.252243i | ||||||||
\(476\) | 3.03522 | + | 13.7680i | 0.139119 | + | 0.631057i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 32.1019 | + | 25.7957i | 1.46830 | + | 1.17987i | ||||
\(479\) | −19.2498 | −0.879544 | −0.439772 | − | 0.898109i | \(-0.644941\pi\) | ||||
−0.439772 | + | 0.898109i | \(0.644941\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.45464 | 0.203114 | ||||||||
\(482\) | 28.0716 | + | 22.5571i | 1.27862 | + | 1.02745i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.76525 | + | 12.5434i | 0.125693 | + | 0.570155i | ||||
\(485\) | − | 0.322005i | − | 0.0146215i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.32047 | 0.105150 | 0.0525752 | − | 0.998617i | \(-0.483257\pi\) | ||||
0.0525752 | + | 0.998617i | \(0.483257\pi\) | |||||||
\(488\) | −24.8458 | − | 12.3074i | −1.12472 | − | 0.557131i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.64867 | + | 3.29619i | −0.119655 | + | 0.148907i | ||||
\(491\) | − | 0.578109i | − | 0.0260897i | −0.999915 | − | 0.0130449i | \(-0.995848\pi\) | ||
0.999915 | − | 0.0130449i | \(-0.00415242\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.99235i | 0.404995i | ||||||||
\(494\) | 1.02399 | + | 0.822833i | 0.0460714 | + | 0.0370210i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 27.6658 | − | 12.8212i | 1.24223 | − | 0.575690i | ||||
\(497\) | 7.93573 | 0.355966 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 26.3969i | 1.18169i | 0.806785 | + | 0.590845i | \(0.201205\pi\) | ||||
−0.806785 | + | 0.590845i | \(0.798795\pi\) | |||||||
\(500\) | −6.18924 | + | 1.36444i | −0.276791 | + | 0.0610198i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2.41327 | + | 3.00324i | −0.107710 | + | 0.134041i | ||||
\(503\) | 8.40780 | 0.374885 | 0.187443 | − | 0.982276i | \(-0.439980\pi\) | ||||
0.187443 | + | 0.982276i | \(0.439980\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 44.4090 | 1.97617 | ||||||||
\(506\) | −0.349439 | + | 0.434865i | −0.0155345 | + | 0.0193321i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.88350 | − | 8.54373i | −0.0835669 | − | 0.379067i | ||||
\(509\) | − | 32.9679i | − | 1.46128i | −0.682764 | − | 0.730639i | \(-0.739222\pi\) | ||
0.682764 | − | 0.730639i | \(-0.260778\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.80408 | −0.124045 | ||||||||
\(512\) | 22.2158 | − | 4.29624i | 0.981809 | − | 0.189869i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −19.4222 | − | 15.6069i | −0.856676 | − | 0.688389i | ||||
\(515\) | − | 48.2769i | − | 2.12733i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 12.3611i | − | 0.543638i | ||||||
\(518\) | 5.92740 | − | 7.37645i | 0.260435 | − | 0.324103i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.49911 | − | 5.04513i | 0.109593 | − | 0.221243i | ||||
\(521\) | 30.9299 | 1.35506 | 0.677531 | − | 0.735494i | \(-0.263050\pi\) | ||||
0.677531 | + | 0.735494i | \(0.263050\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.73852i | 0.119747i | 0.998206 | + | 0.0598735i | \(0.0190697\pi\) | ||||
−0.998206 | + | 0.0598735i | \(0.980930\pi\) | |||||||
\(524\) | −11.2550 | + | 2.48122i | −0.491678 | + | 0.108393i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.98136 | + | 4.80636i | 0.260799 | + | 0.209567i | ||||
\(527\) | −53.7375 | −2.34084 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9660 | −0.998522 | ||||||||
\(530\) | 24.6671 | + | 19.8214i | 1.07147 | + | 0.860988i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.72506 | − | 0.600752i | 0.118146 | − | 0.0260459i | ||||
\(533\) | − | 0.182483i | − | 0.00790421i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −46.6833 | −2.01830 | ||||||||
\(536\) | 27.4213 | + | 13.5832i | 1.18442 | + | 0.586705i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 15.6471 | − | 19.4723i | 0.674594 | − | 0.839509i | ||||
\(539\) | 2.13956i | 0.0921572i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 32.3372i | 1.39029i | 0.718872 | + | 0.695143i | \(0.244659\pi\) | ||||
−0.718872 | + | 0.695143i | \(0.755341\pi\) | |||||||
\(542\) | 12.7022 | + | 10.2069i | 0.545605 | + | 0.438425i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −38.7060 | − | 9.59265i | −1.65950 | − | 0.411281i | ||||
\(545\) | 12.4333 | 0.532585 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 20.4045i | − | 0.872434i | −0.899842 | − | 0.436217i | \(-0.856318\pi\) | ||
0.899842 | − | 0.436217i | \(-0.143682\pi\) | |||||||
\(548\) | −4.52920 | − | 20.5448i | −0.193478 | − | 0.877631i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 7.46782 | − | 9.29345i | 0.318429 | − | 0.396274i | ||||
\(551\) | 1.77983 | 0.0758232 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.98350 | 0.339493 | ||||||||
\(554\) | 6.95272 | − | 8.65243i | 0.295393 | − | 0.367606i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −14.1990 | + | 3.13024i | −0.602174 | + | 0.132752i | ||||
\(557\) | 4.16560i | 0.176502i | 0.996098 | + | 0.0882510i | \(0.0281278\pi\) | ||||
−0.996098 | + | 0.0882510i | \(0.971872\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.75736 | −0.0743285 | ||||||||
\(560\) | −5.02888 | − | 10.8514i | −0.212509 | − | 0.458555i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −34.3186 | − | 27.5770i | −1.44764 | − | 1.16326i | ||||
\(563\) | − | 4.37435i | − | 0.184357i | −0.995743 | − | 0.0921784i | \(-0.970617\pi\) | ||
0.995743 | − | 0.0921784i | \(-0.0293830\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 55.2202i | 2.32313i | ||||||||
\(566\) | 21.9567 | − | 27.3244i | 0.922910 | − | 1.14853i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9.96315 | + | 20.1132i | −0.418044 | + | 0.843933i | ||||
\(569\) | 4.59520 | 0.192641 | 0.0963204 | − | 0.995350i | \(-0.469293\pi\) | ||||
0.0963204 | + | 0.995350i | \(0.469293\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 30.6111i | 1.28103i | 0.767944 | + | 0.640517i | \(0.221280\pi\) | ||||
−0.767944 | + | 0.640517i | \(0.778720\pi\) | |||||||
\(572\) | −0.613298 | − | 2.78197i | −0.0256433 | − | 0.116320i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.302174 | − | 0.242814i | −0.0126125 | − | 0.0101349i | ||||
\(575\) | −0.726450 | −0.0302951 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.32558 | −0.346598 | −0.173299 | − | 0.984869i | \(-0.555443\pi\) | ||||
−0.173299 | + | 0.984869i | \(0.555443\pi\) | |||||||
\(578\) | 36.0405 | + | 28.9606i | 1.49909 | + | 1.20460i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.64226 | − | 7.44945i | −0.0681913 | − | 0.309322i | ||||
\(581\) | − | 6.76125i | − | 0.280504i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 16.0114 | 0.663126 | ||||||||
\(584\) | 3.52047 | − | 7.10700i | 0.145678 | − | 0.294090i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −25.6804 | + | 31.9584i | −1.06085 | + | 1.32019i | ||||
\(587\) | 24.4147i | 1.00770i | 0.863791 | + | 0.503851i | \(0.168084\pi\) | ||||
−0.863791 | + | 0.503851i | \(0.831916\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.6361i | 0.438252i | ||||||||
\(590\) | −29.7905 | − | 23.9384i | −1.22646 | − | 0.985527i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 11.2540 | + | 24.2841i | 0.462537 | + | 0.998069i | ||||
\(593\) | −5.57185 | −0.228809 | −0.114404 | − | 0.993434i | \(-0.536496\pi\) | ||||
−0.114404 | + | 0.993434i | \(0.536496\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 21.0775i | 0.864094i | ||||||||
\(596\) | −5.98870 | + | 1.32024i | −0.245307 | + | 0.0540790i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.108731 | + | 0.135312i | −0.00444632 | + | 0.00553330i | ||||
\(599\) | −28.6835 | −1.17198 | −0.585988 | − | 0.810319i | \(-0.699294\pi\) | ||||
−0.585988 | + | 0.810319i | \(0.699294\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −28.9086 | −1.17921 | −0.589603 | − | 0.807693i | \(-0.700716\pi\) | ||||
−0.589603 | + | 0.807693i | \(0.700716\pi\) | |||||||
\(602\) | −2.33837 | + | 2.91002i | −0.0953048 | + | 0.118604i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −6.84573 | − | 31.0528i | −0.278549 | − | 1.26352i | ||||
\(605\) | 19.2027i | 0.780702i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.3353 | −0.419498 | −0.209749 | − | 0.977755i | \(-0.567265\pi\) | ||||
−0.209749 | + | 0.977755i | \(0.567265\pi\) | |||||||
\(608\) | −1.89864 | + | 7.66094i | −0.0770001 | + | 0.310692i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −32.3124 | − | 25.9649i | −1.30829 | − | 1.05129i | ||||
\(611\) | − | 3.84624i | − | 0.155602i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.77963i | 0.112268i | 0.998423 | + | 0.0561341i | \(0.0178774\pi\) | ||||
−0.998423 | + | 0.0561341i | \(0.982123\pi\) | |||||||
\(614\) | 16.7274 | − | 20.8167i | 0.675064 | − | 0.840094i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5.42274 | − | 2.68617i | −0.218488 | − | 0.108229i | ||||
\(617\) | 22.1145 | 0.890296 | 0.445148 | − | 0.895457i | \(-0.353151\pi\) | ||||
0.445148 | + | 0.895457i | \(0.353151\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 8.20284i | − | 0.329700i | −0.986319 | − | 0.164850i | \(-0.947286\pi\) | ||
0.986319 | − | 0.164850i | \(-0.0527140\pi\) | |||||||
\(620\) | 44.5173 | − | 9.81403i | 1.78786 | − | 0.394141i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0.162648 | + | 0.130697i | 0.00652160 | + | 0.00524048i | ||||
\(623\) | 16.7549 | 0.671272 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.1759 | −1.16704 | ||||||||
\(626\) | −25.7029 | − | 20.6537i | −1.02729 | − | 0.825490i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −35.7830 | + | 7.88853i | −1.42790 | + | 0.314787i | ||||
\(629\) | − | 47.1688i | − | 1.88074i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28.2572 | −1.12490 | −0.562450 | − | 0.826831i | \(-0.690141\pi\) | ||||
−0.562450 | + | 0.826831i | \(0.690141\pi\) | |||||||
\(632\) | −10.0231 | + | 20.2343i | −0.398698 | + | 0.804878i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.26957 | − | 1.57994i | 0.0504211 | − | 0.0627473i | ||||
\(635\) | − | 13.0796i | − | 0.519049i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.665739i | 0.0263776i | ||||||||
\(638\) | −3.00877 | − | 2.41772i | −0.119118 | − | 0.0957185i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 33.8167 | + | 0.877916i | 1.33672 | + | 0.0347027i | ||||
\(641\) | −48.7144 | −1.92410 | −0.962051 | − | 0.272870i | \(-0.912027\pi\) | ||||
−0.962051 | + | 0.272870i | \(0.912027\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.8806i | 0.941757i | 0.882198 | + | 0.470879i | \(0.156063\pi\) | ||||
−0.882198 | + | 0.470879i | \(0.843937\pi\) | |||||||
\(644\) | 0.0793844 | + | 0.360095i | 0.00312819 | + | 0.0141897i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 8.71273 | − | 10.8427i | 0.342798 | − | 0.426600i | ||||
\(647\) | −33.9383 | −1.33425 | −0.667127 | − | 0.744944i | \(-0.732476\pi\) | ||||
−0.667127 | + | 0.744944i | \(0.732476\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −19.3370 | −0.759045 | ||||||||
\(650\) | 2.32367 | − | 2.89173i | 0.0911418 | − | 0.113423i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 43.0618 | − | 9.49316i | 1.68643 | − | 0.371781i | ||||
\(653\) | − | 35.4564i | − | 1.38752i | −0.720208 | − | 0.693759i | \(-0.755953\pi\) | ||
0.720208 | − | 0.693759i | \(-0.244047\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −17.2304 | −0.673246 | ||||||||
\(656\) | 0.994790 | − | 0.461017i | 0.0388400 | − | 0.0179997i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −6.36899 | − | 5.11785i | −0.248289 | − | 0.199515i | ||||
\(659\) | − | 4.40093i | − | 0.171436i | −0.996319 | − | 0.0857179i | \(-0.972682\pi\) | ||
0.996319 | − | 0.0857179i | \(-0.0273184\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.8183i | 0.537470i | 0.963214 | + | 0.268735i | \(0.0866056\pi\) | ||||
−0.963214 | + | 0.268735i | \(0.913394\pi\) | |||||||
\(662\) | 20.6575 | − | 25.7076i | 0.802876 | − | 0.999153i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 17.1365 | + | 8.48860i | 0.665025 | + | 0.329422i | ||||
\(665\) | 4.17180 | 0.161776 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.235190i | 0.00910658i | ||||||||
\(668\) | 4.41982 | + | 20.0487i | 0.171008 | + | 0.775706i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 35.6619 | + | 28.6564i | 1.37774 | + | 1.10709i | ||||
\(671\) | −20.9740 | −0.809693 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28.7125 | 1.10679 | 0.553393 | − | 0.832921i | \(-0.313333\pi\) | ||||
0.553393 | + | 0.832921i | \(0.313333\pi\) | |||||||
\(674\) | 0.534255 | + | 0.429304i | 0.0205787 | + | 0.0165362i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.40658 | + | 24.5247i | 0.207945 | + | 0.943258i | ||||
\(677\) | − | 30.5789i | − | 1.17524i | −0.809136 | − | 0.587621i | \(-0.800064\pi\) | ||
0.809136 | − | 0.587621i | \(-0.199936\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.107694 | −0.00413290 | ||||||||
\(680\) | −53.4213 | − | 26.4624i | −2.04861 | − | 1.01479i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 14.4481 | − | 17.9802i | 0.553246 | − | 0.688496i | ||||
\(683\) | 10.0994i | 0.386443i | 0.981155 | + | 0.193221i | \(0.0618936\pi\) | ||||
−0.981155 | + | 0.193221i | \(0.938106\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 31.4521i | − | 1.20172i | ||||||
\(686\) | 1.10240 | + | 0.885841i | 0.0420898 | + | 0.0338216i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4.43972 | − | 9.58010i | −0.169263 | − | 0.365238i | ||||
\(689\) | 4.98208 | 0.189802 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.93187i | 0.0734916i | 0.999325 | + | 0.0367458i | \(0.0116992\pi\) | ||||
−0.999325 | + | 0.0367458i | \(0.988301\pi\) | |||||||
\(692\) | −30.3188 | + | 6.68391i | −1.15255 | + | 0.254084i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8.89338 | + | 11.0675i | −0.337588 | + | 0.420117i | ||||
\(695\) | −21.7374 | −0.824545 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.93226 | −0.0731895 | ||||||||
\(698\) | 8.46679 | − | 10.5366i | 0.320473 | − | 0.398818i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.69652 | − | 7.69554i | −0.0641223 | − | 0.290864i | ||||
\(701\) | − | 23.6511i | − | 0.893288i | −0.894712 | − | 0.446644i | \(-0.852619\pi\) | ||
0.894712 | − | 0.446644i | \(-0.147381\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.33598 | −0.352113 | ||||||||
\(704\) | 13.6163 | − | 10.3716i | 0.513183 | − | 0.390894i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 31.1903 | + | 25.0632i | 1.17386 | + | 0.943267i | ||||
\(707\) | − | 14.8524i | − | 0.558584i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 20.8417i | − | 0.782728i | −0.920236 | − | 0.391364i | \(-0.872003\pi\) | ||
0.920236 | − | 0.391364i | \(-0.127997\pi\) | |||||||
\(710\) | −21.0192 | + | 26.1577i | −0.788836 | + | 0.981680i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −21.0355 | + | 42.4656i | −0.788337 | + | 1.59147i | ||||
\(713\) | −1.40547 | −0.0526354 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 4.25893i | − | 0.159275i | ||||||
\(716\) | 33.5988 | − | 7.40700i | 1.25565 | − | 0.276813i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −28.4768 | − | 22.8827i | −1.06274 | − | 0.853976i | ||||
\(719\) | 2.81902 | 0.105132 | 0.0525658 | − | 0.998617i | \(-0.483260\pi\) | ||||
0.0525658 | + | 0.998617i | \(0.483260\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.1461 | −0.601311 | ||||||||
\(722\) | 18.7995 | + | 15.1065i | 0.699646 | + | 0.562206i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −20.5359 | + | 4.52724i | −0.763212 | + | 0.168253i | ||||
\(725\) | − | 5.02621i | − | 0.186669i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14.6918 | −0.544887 | −0.272444 | − | 0.962172i | \(-0.587832\pi\) | ||||
−0.272444 | + | 0.962172i | \(0.587832\pi\) | |||||||
\(728\) | −1.68733 | − | 0.835821i | −0.0625365 | − | 0.0309776i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 7.42711 | − | 9.24278i | 0.274890 | − | 0.342091i | ||||
\(731\) | 18.6082i | 0.688248i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 45.7679i | − | 1.69048i | −0.534389 | − | 0.845239i | \(-0.679458\pi\) | ||
0.534389 | − | 0.845239i | \(-0.320542\pi\) | |||||||
\(734\) | −1.96362 | − | 1.57788i | −0.0724787 | − | 0.0582408i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.01233 | − | 0.250890i | −0.0373150 | − | 0.00924792i | ||||
\(737\) | 23.1482 | 0.852673 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 37.7771i | 1.38965i | 0.719178 | + | 0.694826i | \(0.244519\pi\) | ||||
−0.719178 | + | 0.694826i | \(0.755481\pi\) | |||||||
\(740\) | 8.61440 | + | 39.0756i | 0.316672 | + | 1.43645i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 6.62922 | − | 8.24984i | 0.243366 | − | 0.302861i | ||||
\(743\) | −6.38675 | −0.234307 | −0.117154 | − | 0.993114i | \(-0.537377\pi\) | ||||
−0.117154 | + | 0.993114i | \(0.537377\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.16812 | −0.335894 | ||||||||
\(746\) | 19.5837 | − | 24.3712i | 0.717009 | − | 0.892294i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −29.4575 | + | 6.49403i | −1.07707 | + | 0.237445i | ||||
\(749\) | 15.6131i | 0.570490i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 52.5372 | 1.91711 | 0.958554 | − | 0.284910i | \(-0.0919639\pi\) | ||||
0.958554 | + | 0.284910i | \(0.0919639\pi\) | |||||||
\(752\) | 20.9674 | − | 9.71696i | 0.764603 | − | 0.354341i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.936203 | − | 0.752292i | −0.0340945 | − | 0.0273969i | ||||
\(755\) | − | 47.5388i | − | 1.73012i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.80676i | 0.138359i | 0.997604 | + | 0.0691794i | \(0.0220381\pi\) | ||||
−0.997604 | + | 0.0691794i | \(0.977962\pi\) | |||||||
\(758\) | 31.3684 | − | 39.0369i | 1.13935 | − | 1.41788i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5.23761 | + | 10.5735i | −0.189988 | + | 0.383541i | ||||
\(761\) | −25.9307 | −0.939986 | −0.469993 | − | 0.882670i | \(-0.655744\pi\) | ||||
−0.469993 | + | 0.882670i | \(0.655744\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 4.15829i | − | 0.150540i | ||||||
\(764\) | 6.19561 | + | 28.1038i | 0.224149 | + | 1.01676i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −26.6700 | − | 21.4309i | −0.963627 | − | 0.774330i | ||||
\(767\) | −6.01686 | −0.217256 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −42.2680 | −1.52422 | −0.762112 | − | 0.647445i | \(-0.775838\pi\) | ||||
−0.762112 | + | 0.647445i | \(0.775838\pi\) | |||||||
\(770\) | −7.05238 | − | 5.66699i | −0.254150 | − | 0.204224i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4.89039 | + | 22.1832i | 0.176009 | + | 0.798392i | ||||
\(773\) | − | 13.4481i | − | 0.483696i | −0.970314 | − | 0.241848i | \(-0.922246\pi\) | ||
0.970314 | − | 0.241848i | \(-0.0777536\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 30.0362 | 1.07893 | ||||||||
\(776\) | 0.135207 | − | 0.272951i | 0.00485365 | − | 0.00979838i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −11.5571 | + | 14.3824i | −0.414343 | + | 0.515635i | ||||
\(779\) | 0.382445i | 0.0137025i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.9790i | 0.607555i | ||||||||
\(782\) | 1.43277 | + | 1.15132i | 0.0512359 | + | 0.0411710i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.62922 | + | 1.68190i | −0.129615 | + | 0.0600677i | ||||
\(785\) | −54.7804 | −1.95520 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 1.40104i | − | 0.0499418i | −0.999688 | − | 0.0249709i | \(-0.992051\pi\) | ||
0.999688 | − | 0.0249709i | \(-0.00794932\pi\) | |||||||
\(788\) | −12.5871 | + | 2.77487i | −0.448396 | + | 0.0988508i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −21.1457 | + | 26.3151i | −0.752330 | + | 0.936249i | ||||
\(791\) | 18.4682 | 0.656654 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.52623 | −0.231753 | ||||||||
\(794\) | 31.9529 | − | 39.7643i | 1.13397 | − | 1.41118i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.79033 | − | 12.6572i | −0.0989007 | − | 0.448622i | ||||
\(797\) | − | 19.3605i | − | 0.685783i | −0.939375 | − | 0.342891i | \(-0.888594\pi\) | ||
0.939375 | − | 0.342891i | \(-0.111406\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −40.7266 | −1.44080 | ||||||||
\(800\) | 21.6344 | + | 5.36174i | 0.764892 | + | 0.189566i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −17.1036 | − | 13.7438i | −0.603950 | − | 0.485309i | ||||
\(803\) | − | 5.99950i | − | 0.211718i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.551270i | 0.0194297i | ||||||||
\(806\) | 4.49563 | − | 5.59466i | 0.158352 | − | 0.197064i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 37.6438 | + | 18.6469i | 1.32430 | + | 0.655996i | ||||
\(809\) | −14.4386 | −0.507633 | −0.253816 | − | 0.967252i | \(-0.581686\pi\) | ||||
−0.253816 | + | 0.967252i | \(0.581686\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 42.1307i | − | 1.47941i | −0.672932 | − | 0.739705i | \(-0.734965\pi\) | ||
0.672932 | − | 0.739705i | \(-0.265035\pi\) | |||||||
\(812\) | −2.49145 | + | 0.549250i | −0.0874326 | + | 0.0192749i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 15.7823 | + | 12.6820i | 0.553171 | + | 0.444504i | ||||
\(815\) | 65.9234 | 2.30920 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.68305 | 0.128854 | ||||||||
\(818\) | −31.6319 | − | 25.4181i | −1.10598 | − | 0.888722i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.60072 | − | 0.352886i | 0.0558996 | − | 0.0123233i | ||||
\(821\) | − | 7.21315i | − | 0.251741i | −0.992047 | − | 0.125870i | \(-0.959828\pi\) | ||
0.992047 | − | 0.125870i | \(-0.0401723\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.47104 | −0.225566 | −0.112783 | − | 0.993620i | \(-0.535977\pi\) | ||||
−0.112783 | + | 0.993620i | \(0.535977\pi\) | |||||||
\(824\) | 20.2710 | − | 40.9225i | 0.706175 | − | 1.42560i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.00612 | + | 9.96334i | −0.278568 | + | 0.346669i | ||||
\(827\) | 55.8363i | 1.94162i | 0.239850 | + | 0.970810i | \(0.422902\pi\) | ||||
−0.239850 | + | 0.970810i | \(0.577098\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.1807i | 0.492517i | 0.969204 | + | 0.246258i | \(0.0792011\pi\) | ||||
−0.969204 | + | 0.246258i | \(0.920799\pi\) | |||||||
\(830\) | 22.2863 | + | 17.9083i | 0.773570 | + | 0.621608i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4.23681 | − | 3.22720i | 0.146885 | − | 0.111883i | ||||
\(833\) | 7.04931 | 0.244244 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 30.6925i | 1.06216i | ||||||||
\(836\) | 1.28534 | + | 5.83042i | 0.0444545 | + | 0.201649i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −20.3172 | + | 25.2841i | −0.701847 | + | 0.873425i | ||||
\(839\) | 31.4229 | 1.08484 | 0.542420 | − | 0.840108i | \(-0.317508\pi\) | ||||
0.542420 | + | 0.840108i | \(0.317508\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.3728 | 0.943888 | ||||||||
\(842\) | −11.6543 | + | 14.5034i | −0.401633 | + | 0.499819i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 20.1462 | − | 4.44132i | 0.693461 | − | 0.152877i | ||||
\(845\) | 37.5449i | 1.29159i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.42230 | 0.220673 | ||||||||
\(848\) | 12.5865 | + | 27.1594i | 0.432222 | + | 0.932656i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −30.6196 | − | 24.6046i | −1.05024 | − | 0.843932i | ||||
\(851\) | − | 1.23367i | − | 0.0422898i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 23.3929i | − | 0.800957i | −0.916306 | − | 0.400479i | \(-0.868844\pi\) | ||
0.916306 | − | 0.400479i | \(-0.131156\pi\) | |||||||
\(854\) | −8.68388 | + | 10.8068i | −0.297156 | + | 0.369801i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −39.5716 | − | 19.6019i | −1.35253 | − | 0.669979i | ||||
\(857\) | −24.0033 | −0.819936 | −0.409968 | − | 0.912100i | \(-0.634460\pi\) | ||||
−0.409968 | + | 0.912100i | \(0.634460\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 41.5626i | − | 1.41810i | −0.705160 | − | 0.709048i | \(-0.749125\pi\) | ||
0.705160 | − | 0.709048i | \(-0.250875\pi\) | |||||||
\(860\) | −3.39839 | − | 15.4154i | −0.115884 | − | 0.525661i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −43.6961 | − | 35.1124i | −1.48830 | − | 1.19593i | ||||
\(863\) | 3.43323 | 0.116868 | 0.0584342 | − | 0.998291i | \(-0.481389\pi\) | ||||
0.0584342 | + | 0.998291i | \(0.481389\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −46.4151 | −1.57816 | ||||||||
\(866\) | 12.7775 | + | 10.2675i | 0.434197 | + | 0.348902i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −3.28227 | − | 14.8887i | −0.111408 | − | 0.505354i | ||||
\(869\) | 17.0812i | 0.579438i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.20273 | 0.244055 | ||||||||
\(872\) | 10.5392 | + | 5.22064i | 0.356904 | + | 0.176793i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.227876 | − | 0.283584i | 0.00770802 | − | 0.00959238i | ||||
\(875\) | 3.16893i | 0.107129i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 47.9141i | − | 1.61794i | −0.587847 | − | 0.808972i | \(-0.700024\pi\) | ||
0.587847 | − | 0.808972i | \(-0.299976\pi\) | |||||||
\(878\) | −10.9024 | − | 8.76072i | −0.367939 | − | 0.295660i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 23.2172 | − | 10.7596i | 0.782651 | − | 0.362705i | ||||
\(881\) | 25.7071 | 0.866095 | 0.433047 | − | 0.901371i | \(-0.357438\pi\) | ||||
0.433047 | + | 0.901371i | \(0.357438\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 41.7112i | − | 1.40369i | −0.712328 | − | 0.701847i | \(-0.752359\pi\) | ||
0.712328 | − | 0.701847i | \(-0.247641\pi\) | |||||||
\(884\) | −9.16592 | + | 2.02067i | −0.308283 | + | 0.0679624i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.89967 | − | 2.36408i | 0.0638208 | − | 0.0794228i | ||||
\(887\) | −32.6475 | −1.09620 | −0.548099 | − | 0.836414i | \(-0.684648\pi\) | ||||
−0.548099 | + | 0.836414i | \(0.684648\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.37444 | −0.146714 | ||||||||
\(890\) | −44.3784 | + | 55.2274i | −1.48757 | + | 1.85123i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 10.2729 | + | 46.5988i | 0.343962 | + | 1.56024i | ||||
\(893\) | 8.06089i | 0.269747i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 51.4365 | 1.71933 | ||||||||
\(896\) | 0.293616 | − | 11.3099i | 0.00980903 | − | 0.377837i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 5.13004 | + | 4.12228i | 0.171192 | + | 0.137562i | ||||
\(899\) | − | 9.72428i | − | 0.324323i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 52.7537i | − | 1.75748i | ||||||
\(902\) | 0.519515 | − | 0.646519i | 0.0172980 | − | 0.0215267i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −23.1865 | + | 46.8080i | −0.771170 | + | 1.55681i | ||||
\(905\) | −31.4385 | −1.04505 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 22.4610i | − | 0.745804i | −0.927871 | − | 0.372902i | \(-0.878363\pi\) | ||
0.927871 | − | 0.372902i | \(-0.121637\pi\) | |||||||
\(908\) | 3.67363 | − | 0.809869i | 0.121914 | − | 0.0268764i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.19440 | − | 1.76333i | −0.0727437 | − | 0.0584537i | ||||
\(911\) | −20.7360 | −0.687015 | −0.343507 | − | 0.939150i | \(-0.611615\pi\) | ||||
−0.343507 | + | 0.939150i | \(0.611615\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.4661 | 0.478757 | ||||||||
\(914\) | 21.0026 | + | 16.8768i | 0.694705 | + | 0.558236i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −36.7434 | + | 8.10025i | −1.21404 | + | 0.267640i | ||||
\(917\) | 5.76264i | 0.190299i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −42.9827 | −1.41787 | −0.708935 | − | 0.705274i | \(-0.750824\pi\) | ||||
−0.708935 | + | 0.705274i | \(0.750824\pi\) | |||||||
\(920\) | −1.39720 | − | 0.692108i | −0.0460644 | − | 0.0228181i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −23.0632 | + | 28.7014i | −0.759547 | + | 0.945230i | ||||
\(923\) | 5.28313i | 0.173896i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 26.3647i | 0.866865i | ||||||||
\(926\) | 32.6416 | + | 26.2294i | 1.07267 | + | 0.861951i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.73587 | − | 7.00418i | 0.0569829 | − | 0.229924i | ||||
\(929\) | 3.62200 | 0.118834 | 0.0594170 | − | 0.998233i | \(-0.481076\pi\) | ||||
0.0594170 | + | 0.998233i | \(0.481076\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 1.39525i | − | 0.0457274i | ||||||
\(932\) | 3.95590 | + | 17.9443i | 0.129580 | + | 0.587785i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −22.9418 | + | 28.5503i | −0.750679 | + | 0.934194i | ||||
\(935\) | −45.0965 | −1.47481 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21.8189 | 0.712793 | 0.356396 | − | 0.934335i | \(-0.384005\pi\) | ||||
0.356396 | + | 0.934335i | \(0.384005\pi\) | |||||||
\(938\) | 9.58404 | − | 11.9270i | 0.312930 | − | 0.389431i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 33.7388 | − | 7.43786i | 1.10044 | − | 0.242596i | ||||
\(941\) | 16.8639i | 0.549747i | 0.961480 | + | 0.274873i | \(0.0886359\pi\) | ||||
−0.961480 | + | 0.274873i | \(0.911364\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.0505370 | −0.00164571 | ||||||||
\(944\) | −15.2007 | − | 32.8004i | −0.494742 | − | 1.06756i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.22615 | − | 5.00307i | −0.202430 | − | 0.162664i | ||||
\(947\) | − | 18.5568i | − | 0.603016i | −0.953464 | − | 0.301508i | \(-0.902510\pi\) | ||
0.953464 | − | 0.301508i | \(-0.0974900\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 1.86679i | − | 0.0605985i | ||||||
\(950\) | −4.86992 | + | 6.06044i | −0.158001 | + | 0.196627i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −8.85026 | + | 17.8666i | −0.286839 | + | 0.579060i | ||||
\(953\) | 36.6643 | 1.18767 | 0.593836 | − | 0.804586i | \(-0.297613\pi\) | ||||
0.593836 | + | 0.804586i | \(0.297613\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 43.0242i | 1.39223i | ||||||||
\(956\) | 12.5382 | + | 56.8743i | 0.405514 | + | 1.83945i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −21.2209 | − | 17.0522i | −0.685617 | − | 0.550933i | ||||
\(959\) | −10.5191 | −0.339678 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27.1114 | 0.874562 | ||||||||
\(962\) | 4.91079 | + | 3.94610i | 0.158330 | + | 0.127228i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 10.9641 | + | 49.7339i | 0.353129 | + | 1.60182i | ||||
\(965\) | 33.9604i | 1.09322i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11.1440 | −0.358367 | −0.179184 | − | 0.983816i | \(-0.557346\pi\) | ||||
−0.179184 | + | 0.983816i | \(0.557346\pi\) | |||||||
\(968\) | −8.06306 | + | 16.2774i | −0.259156 | + | 0.523176i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.285245 | − | 0.354978i | 0.00915868 | − | 0.0113977i | ||||
\(971\) | 3.98773i | 0.127972i | 0.997951 | + | 0.0639862i | \(0.0203814\pi\) | ||||
−0.997951 | + | 0.0639862i | \(0.979619\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.27000i | 0.233065i | ||||||||
\(974\) | 2.55808 | + | 2.05556i | 0.0819662 | + | 0.0658645i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −16.4876 | − | 35.5772i | −0.527755 | − | 1.13880i | ||||
\(977\) | −32.7959 | −1.04923 | −0.524617 | − | 0.851338i | \(-0.675791\pi\) | ||||
−0.524617 | + | 0.851338i | \(0.675791\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 35.8481i | 1.14571i | ||||||||
\(980\) | −5.83980 | + | 1.28741i | −0.186545 | + | 0.0411248i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0.512113 | − | 0.637308i | 0.0163422 | − | 0.0203373i | ||||
\(983\) | 26.0499 | 0.830864 | 0.415432 | − | 0.909624i | \(-0.363630\pi\) | ||||
0.415432 | + | 0.909624i | \(0.363630\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −19.2696 | −0.613980 | ||||||||
\(986\) | −7.96580 | + | 9.91317i | −0.253683 | + | 0.315700i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.399944 | + | 1.81418i | 0.0127239 | + | 0.0577168i | ||||
\(989\) | 0.486686i | 0.0154757i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17.5053 | −0.556075 | −0.278037 | − | 0.960570i | \(-0.589684\pi\) | ||||
−0.278037 | + | 0.960570i | \(0.589684\pi\) | |||||||
\(992\) | 41.8564 | + | 10.3734i | 1.32894 | + | 0.329357i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 8.74835 | + | 7.02980i | 0.277481 | + | 0.222972i | ||||
\(995\) | − | 19.3769i | − | 0.614289i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 29.5008i | 0.934300i | 0.884178 | + | 0.467150i | \(0.154719\pi\) | ||||
−0.884178 | + | 0.467150i | \(0.845281\pi\) | |||||||
\(998\) | −23.3835 | + | 29.1000i | −0.740192 | + | 0.921144i | ||||
\(999\) | 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.c.g.757.18 | yes | 24 | |
3.2 | odd | 2 | inner | 1512.2.c.g.757.7 | ✓ | 24 | |
4.3 | odd | 2 | 6048.2.c.f.3025.20 | 24 | |||
8.3 | odd | 2 | 6048.2.c.f.3025.5 | 24 | |||
8.5 | even | 2 | inner | 1512.2.c.g.757.17 | yes | 24 | |
12.11 | even | 2 | 6048.2.c.f.3025.6 | 24 | |||
24.5 | odd | 2 | inner | 1512.2.c.g.757.8 | yes | 24 | |
24.11 | even | 2 | 6048.2.c.f.3025.19 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.c.g.757.7 | ✓ | 24 | 3.2 | odd | 2 | inner | |
1512.2.c.g.757.8 | yes | 24 | 24.5 | odd | 2 | inner | |
1512.2.c.g.757.17 | yes | 24 | 8.5 | even | 2 | inner | |
1512.2.c.g.757.18 | yes | 24 | 1.1 | even | 1 | trivial | |
6048.2.c.f.3025.5 | 24 | 8.3 | odd | 2 | |||
6048.2.c.f.3025.6 | 24 | 12.11 | even | 2 | |||
6048.2.c.f.3025.19 | 24 | 24.11 | even | 2 | |||
6048.2.c.f.3025.20 | 24 | 4.3 | odd | 2 |