Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3150,2,Mod(899,3150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3150, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3150.899");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3150.bp (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(25.1528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1349.10 | ||
Character | \(\chi\) | \(=\) | 3150.1349 |
Dual form | 3150.2.bp.g.899.10 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(2801\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.54649 | + | 0.717905i | 0.962483 | + | 0.271343i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.09272 | + | 2.94028i | −1.53551 | + | 0.886529i | −0.536419 | + | 0.843952i | \(0.680223\pi\) |
−0.999093 | + | 0.0425771i | \(0.986443\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.05674 | −1.12514 | −0.562569 | − | 0.826751i | \(-0.690187\pi\) | ||||
−0.562569 | + | 0.826751i | \(0.690187\pi\) | |||||||
\(14\) | −1.89497 | + | 1.84637i | −0.506452 | + | 0.493464i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 0.371532 | − | 0.214504i | 0.0901098 | − | 0.0520249i | −0.454268 | − | 0.890865i | \(-0.650099\pi\) |
0.544378 | + | 0.838840i | \(0.316766\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.30761 | − | 3.06435i | −1.21765 | − | 0.703010i | −0.253234 | − | 0.967405i | \(-0.581494\pi\) |
−0.964414 | + | 0.264395i | \(0.914828\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 5.88057i | − | 1.25374i | ||||||
\(23\) | −0.876005 | + | 1.51729i | −0.182660 | + | 0.316376i | −0.942785 | − | 0.333400i | \(-0.891804\pi\) |
0.760126 | + | 0.649776i | \(0.225137\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.02837 | − | 3.51324i | 0.397796 | − | 0.689003i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.651521 | − | 2.56428i | −0.123126 | − | 0.484603i | ||||
\(29\) | − | 0.0419065i | − | 0.00778184i | −0.999992 | − | 0.00389092i | \(-0.998761\pi\) | ||
0.999992 | − | 0.00389092i | \(-0.00123852\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.92389 | − | 4.57486i | 1.42317 | − | 0.821669i | 0.426604 | − | 0.904439i | \(-0.359710\pi\) |
0.996569 | + | 0.0827694i | \(0.0263765\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.429009i | 0.0735744i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.928534 | + | 0.536089i | 0.152650 | + | 0.0881326i | 0.574379 | − | 0.818589i | \(-0.305243\pi\) |
−0.421729 | + | 0.906722i | \(0.638577\pi\) | |||||||
\(38\) | 5.30761 | − | 3.06435i | 0.861008 | − | 0.497103i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.61559 | 1.34553 | 0.672765 | − | 0.739856i | \(-0.265107\pi\) | ||||
0.672765 | + | 0.739856i | \(0.265107\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 11.0724i | − | 1.68852i | −0.535935 | − | 0.844259i | \(-0.680041\pi\) | ||
0.535935 | − | 0.844259i | \(-0.319959\pi\) | |||||||
\(44\) | 5.09272 | + | 2.94028i | 0.767756 | + | 0.443264i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.876005 | − | 1.51729i | −0.129160 | − | 0.223712i | ||||
\(47\) | −0.834099 | − | 0.481567i | −0.121666 | − | 0.0702438i | 0.437932 | − | 0.899008i | \(-0.355711\pi\) |
−0.559598 | + | 0.828764i | \(0.689044\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.96922 | + | 3.65628i | 0.852746 | + | 0.522325i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.02837 | + | 3.51324i | 0.281284 | + | 0.487199i | ||||
\(53\) | −6.57304 | − | 11.3848i | −0.902877 | − | 1.56383i | −0.823742 | − | 0.566965i | \(-0.808117\pi\) |
−0.0791353 | − | 0.996864i | \(-0.525216\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.54649 | + | 0.717905i | 0.340289 | + | 0.0959341i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.0362921 | + | 0.0209532i | 0.00476538 | + | 0.00275129i | ||||
\(59\) | 6.77318 | + | 11.7315i | 0.881793 | + | 1.52731i | 0.849345 | + | 0.527838i | \(0.176997\pi\) |
0.0324481 | + | 0.999473i | \(0.489670\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.05635 | + | 0.609885i | 0.135252 | + | 0.0780878i | 0.566099 | − | 0.824337i | \(-0.308452\pi\) |
−0.430847 | + | 0.902425i | \(0.641785\pi\) | |||||||
\(62\) | 9.14972i | 1.16202i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.9527 | − | 6.32352i | 1.33808 | − | 0.772541i | 0.351558 | − | 0.936166i | \(-0.385652\pi\) |
0.986523 | + | 0.163625i | \(0.0523186\pi\) | |||||||
\(68\) | −0.371532 | − | 0.214504i | −0.0450549 | − | 0.0260125i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 2.54990i | − | 0.302617i | −0.988487 | − | 0.151308i | \(-0.951651\pi\) | ||
0.988487 | − | 0.151308i | \(-0.0483487\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.66689 | − | 8.08328i | −0.546218 | − | 0.946077i | −0.998529 | − | 0.0542168i | \(-0.982734\pi\) |
0.452311 | − | 0.891860i | \(-0.350600\pi\) | |||||||
\(74\) | −0.928534 | + | 0.536089i | −0.107940 | + | 0.0623191i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.12870i | 0.703010i | ||||||||
\(77\) | −15.0794 | + | 3.83131i | −1.71846 | + | 0.436619i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.35961 | − | 9.28312i | 0.603003 | − | 1.04443i | −0.389360 | − | 0.921086i | \(-0.627304\pi\) |
0.992364 | − | 0.123347i | \(-0.0393628\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.30780 | + | 7.46132i | −0.475717 | + | 0.823965i | ||||
\(83\) | − | 10.1027i | − | 1.10891i | −0.832212 | − | 0.554457i | \(-0.812926\pi\) | ||
0.832212 | − | 0.554457i | \(-0.187074\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 9.58894 | + | 5.53618i | 1.03400 | + | 0.596981i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −5.09272 | + | 2.94028i | −0.542886 | + | 0.313435i | ||||
\(89\) | −3.15638 | + | 5.46700i | −0.334575 | + | 0.579501i | −0.983403 | − | 0.181434i | \(-0.941926\pi\) |
0.648828 | + | 0.760935i | \(0.275259\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.3304 | − | 2.91235i | −1.08293 | − | 0.305298i | ||||
\(92\) | 1.75201 | 0.182660 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.834099 | − | 0.481567i | 0.0860307 | − | 0.0496698i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.59007 | −0.262982 | −0.131491 | − | 0.991317i | \(-0.541976\pi\) | ||||
−0.131491 | + | 0.991317i | \(0.541976\pi\) | |||||||
\(98\) | −6.15104 | + | 3.34136i | −0.621349 | + | 0.337529i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.21837 | − | 9.03849i | −0.519248 | − | 0.899363i | −0.999750 | − | 0.0223696i | \(-0.992879\pi\) |
0.480502 | − | 0.876993i | \(-0.340454\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.47216 | + | 4.28191i | −0.243589 | + | 0.421909i | −0.961734 | − | 0.273985i | \(-0.911658\pi\) |
0.718145 | + | 0.695894i | \(0.244992\pi\) | |||||||
\(104\) | −4.05674 | −0.397796 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 13.1461 | 1.27686 | ||||||||
\(107\) | 0.347904 | − | 0.602588i | 0.0336332 | − | 0.0582544i | −0.848719 | − | 0.528844i | \(-0.822626\pi\) |
0.882352 | + | 0.470590i | \(0.155959\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.98417 | + | 5.16874i | 0.285832 | + | 0.495076i | 0.972811 | − | 0.231602i | \(-0.0743967\pi\) |
−0.686979 | + | 0.726678i | \(0.741063\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.89497 | + | 1.84637i | −0.179058 | + | 0.174466i | ||||
\(113\) | −0.809894 | −0.0761884 | −0.0380942 | − | 0.999274i | \(-0.512129\pi\) | ||||
−0.0380942 | + | 0.999274i | \(0.512129\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.0362921 | + | 0.0209532i | −0.00336963 | + | 0.00194546i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −13.5464 | −1.24704 | ||||||||
\(119\) | 1.10010 | − | 0.279508i | 0.100846 | − | 0.0256225i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.7905 | − | 20.4218i | 1.07187 | − | 1.85653i | ||||
\(122\) | −1.05635 | + | 0.609885i | −0.0956376 | + | 0.0552164i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7.92389 | − | 4.57486i | −0.711586 | − | 0.410835i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.0265i | 0.978442i | 0.872160 | + | 0.489221i | \(0.162719\pi\) | ||||
−0.872160 | + | 0.489221i | \(0.837281\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.44080 | + | 16.3520i | −0.824847 | + | 1.42868i | 0.0771893 | + | 0.997016i | \(0.475405\pi\) |
−0.902036 | + | 0.431660i | \(0.857928\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −11.3159 | − | 11.6137i | −0.981210 | − | 1.00704i | ||||
\(134\) | 12.6470i | 1.09254i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.371532 | − | 0.214504i | 0.0318586 | − | 0.0183936i | ||||
\(137\) | −7.18560 | − | 12.4458i | −0.613907 | − | 1.06332i | −0.990575 | − | 0.136970i | \(-0.956264\pi\) |
0.376668 | − | 0.926348i | \(-0.377070\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 16.7650i | − | 1.42199i | −0.703198 | − | 0.710994i | \(-0.748245\pi\) | ||
0.703198 | − | 0.710994i | \(-0.251755\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.20827 | + | 1.27495i | 0.185314 | + | 0.106991i | ||||
\(143\) | 20.6598 | − | 11.9280i | 1.72766 | − | 0.997466i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 9.33377 | 0.772469 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 1.07218i | − | 0.0881326i | ||||||
\(149\) | 8.67934 | + | 5.01102i | 0.711039 | + | 0.410519i | 0.811446 | − | 0.584428i | \(-0.198681\pi\) |
−0.100407 | + | 0.994946i | \(0.532014\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.20599 | − | 12.4811i | −0.586415 | − | 1.01570i | −0.994697 | − | 0.102845i | \(-0.967206\pi\) |
0.408283 | − | 0.912856i | \(-0.366128\pi\) | |||||||
\(152\) | −5.30761 | − | 3.06435i | −0.430504 | − | 0.248552i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 4.22169 | − | 14.9748i | 0.340193 | − | 1.20670i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.43554 | − | 9.41463i | −0.433803 | − | 0.751370i | 0.563394 | − | 0.826189i | \(-0.309495\pi\) |
−0.997197 | + | 0.0748190i | \(0.976162\pi\) | |||||||
\(158\) | 5.35961 | + | 9.28312i | 0.426388 | + | 0.738525i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.32001 | + | 3.23486i | −0.261653 | + | 0.254943i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.19935 | − | 5.31125i | −0.720549 | − | 0.416009i | 0.0944058 | − | 0.995534i | \(-0.469905\pi\) |
−0.814955 | + | 0.579525i | \(0.803238\pi\) | |||||||
\(164\) | −4.30780 | − | 7.46132i | −0.336382 | − | 0.582631i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.74919 | + | 5.05134i | 0.679068 | + | 0.392060i | ||||
\(167\) | 3.45341i | 0.267233i | 0.991033 | + | 0.133617i | \(0.0426591\pi\) | ||||
−0.991033 | + | 0.133617i | \(0.957341\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.45714 | 0.265934 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −9.58894 | + | 5.53618i | −0.731150 | + | 0.422130i | ||||
\(173\) | 6.88939 | + | 3.97759i | 0.523790 | + | 0.302411i | 0.738484 | − | 0.674271i | \(-0.235542\pi\) |
−0.214694 | + | 0.976681i | \(0.568875\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 5.88057i | − | 0.443264i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.15638 | − | 5.46700i | −0.236580 | − | 0.409769i | ||||
\(179\) | −2.38066 | + | 1.37447i | −0.177939 | + | 0.102733i | −0.586324 | − | 0.810077i | \(-0.699425\pi\) |
0.408385 | + | 0.912810i | \(0.366092\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 6.73202i | − | 0.500387i | −0.968196 | − | 0.250194i | \(-0.919506\pi\) | ||
0.968196 | − | 0.250194i | \(-0.0804943\pi\) | |||||||
\(182\) | 7.68740 | − | 7.49025i | 0.569828 | − | 0.555215i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.876005 | + | 1.51729i | −0.0645800 | + | 0.111856i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.26141 | + | 2.18482i | −0.0922432 | + | 0.159770i | ||||
\(188\) | 0.963134i | 0.0702438i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21.3740 | + | 12.3403i | 1.54657 | + | 0.892911i | 0.998400 | + | 0.0565412i | \(0.0180072\pi\) |
0.548166 | + | 0.836369i | \(0.315326\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.595151 | + | 0.343610i | −0.0428399 | + | 0.0247336i | −0.521267 | − | 0.853394i | \(-0.674540\pi\) |
0.478427 | + | 0.878127i | \(0.341207\pi\) | |||||||
\(194\) | 1.29503 | − | 2.24306i | 0.0929780 | − | 0.161043i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.181816 | − | 6.99764i | 0.0129868 | − | 0.499831i | ||||
\(197\) | −0.169154 | −0.0120517 | −0.00602586 | − | 0.999982i | \(-0.501918\pi\) | ||||
−0.00602586 | + | 0.999982i | \(0.501918\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.359798 | − | 0.207730i | 0.0255054 | − | 0.0147256i | −0.487193 | − | 0.873294i | \(-0.661979\pi\) |
0.512699 | + | 0.858569i | \(0.328646\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 10.4367 | 0.734327 | ||||||||
\(203\) | 0.0300849 | − | 0.106714i | 0.00211154 | − | 0.00748988i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.47216 | − | 4.28191i | −0.172244 | − | 0.298335i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.02837 | − | 3.51324i | 0.140642 | − | 0.243599i | ||||
\(209\) | 36.0402 | 2.49295 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.10135 | −0.144663 | −0.0723313 | − | 0.997381i | \(-0.523044\pi\) | ||||
−0.0723313 | + | 0.997381i | \(0.523044\pi\) | |||||||
\(212\) | −6.57304 | + | 11.3848i | −0.451439 | + | 0.781915i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.347904 | + | 0.602588i | 0.0237823 | + | 0.0411921i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 23.4624 | − | 5.96124i | 1.59273 | − | 0.404675i | ||||
\(218\) | −5.96835 | −0.404227 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.50721 | + | 0.870188i | −0.101386 | + | 0.0585352i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 25.9946 | 1.74073 | 0.870364 | − | 0.492409i | \(-0.163883\pi\) | ||||
0.870364 | + | 0.492409i | \(0.163883\pi\) | |||||||
\(224\) | −0.651521 | − | 2.56428i | −0.0435316 | − | 0.171333i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.404947 | − | 0.701389i | 0.0269367 | − | 0.0466557i | ||||
\(227\) | 12.3905 | − | 7.15363i | 0.822383 | − | 0.474803i | −0.0288545 | − | 0.999584i | \(-0.509186\pi\) |
0.851238 | + | 0.524781i | \(0.175853\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.36736 | + | 0.789445i | 0.0903576 | + | 0.0521680i | 0.544498 | − | 0.838762i | \(-0.316720\pi\) |
−0.454140 | + | 0.890930i | \(0.650054\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 0.0419065i | − | 0.00275129i | ||||||
\(233\) | 9.13044 | − | 15.8144i | 0.598155 | − | 1.03604i | −0.394938 | − | 0.918708i | \(-0.629234\pi\) |
0.993093 | − | 0.117327i | \(-0.0374327\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 6.77318 | − | 11.7315i | 0.440897 | − | 0.763656i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.307987 | + | 1.09247i | −0.0199639 | + | 0.0708141i | ||||
\(239\) | − | 23.1801i | − | 1.49940i | −0.661779 | − | 0.749699i | \(-0.730198\pi\) | ||
0.661779 | − | 0.749699i | \(-0.269802\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.2090 | + | 6.47152i | −0.722035 | + | 0.416867i | −0.815501 | − | 0.578755i | \(-0.803539\pi\) |
0.0934660 | + | 0.995622i | \(0.470205\pi\) | |||||||
\(242\) | 11.7905 | + | 20.4218i | 0.757924 | + | 1.31276i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 1.21977i | − | 0.0780878i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 21.5316 | + | 12.4313i | 1.37002 | + | 0.790983i | ||||
\(248\) | 7.92389 | − | 4.57486i | 0.503168 | − | 0.290504i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −22.7253 | −1.43441 | −0.717203 | − | 0.696865i | \(-0.754578\pi\) | ||||
−0.717203 | + | 0.696865i | \(0.754578\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 10.3028i | − | 0.647732i | ||||||
\(254\) | −9.54921 | − | 5.51324i | −0.599171 | − | 0.345931i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −6.06331 | − | 3.50065i | −0.378219 | − | 0.218365i | 0.298824 | − | 0.954308i | \(-0.403406\pi\) |
−0.677043 | + | 0.735943i | \(0.736739\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.97964 | + | 2.03175i | 0.123009 | + | 0.126247i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −9.44080 | − | 16.3520i | −0.583255 | − | 1.01023i | ||||
\(263\) | −6.00972 | − | 10.4091i | −0.370575 | − | 0.641855i | 0.619079 | − | 0.785329i | \(-0.287506\pi\) |
−0.989654 | + | 0.143473i | \(0.954173\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 15.7157 | − | 3.99298i | 0.963590 | − | 0.244825i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −10.9527 | − | 6.32352i | −0.669040 | − | 0.386271i | ||||
\(269\) | −0.611792 | − | 1.05966i | −0.0373016 | − | 0.0646083i | 0.846772 | − | 0.531956i | \(-0.178543\pi\) |
−0.884074 | + | 0.467348i | \(0.845210\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.1888 | + | 8.19190i | 0.861908 | + | 0.497623i | 0.864651 | − | 0.502374i | \(-0.167540\pi\) |
−0.00274289 | + | 0.999996i | \(0.500873\pi\) | |||||||
\(272\) | 0.429009i | 0.0260125i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 14.3712 | 0.868196 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.4092 | + | 6.58712i | −0.685514 | + | 0.395781i | −0.801929 | − | 0.597419i | \(-0.796193\pi\) |
0.116416 | + | 0.993201i | \(0.462860\pi\) | |||||||
\(278\) | 14.5189 | + | 8.38250i | 0.870786 | + | 0.502749i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 5.72433i | − | 0.341485i | −0.985316 | − | 0.170742i | \(-0.945383\pi\) | ||
0.985316 | − | 0.170742i | \(-0.0546166\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.07354 | − | 13.9838i | −0.479922 | − | 0.831249i | 0.519813 | − | 0.854280i | \(-0.326002\pi\) |
−0.999735 | + | 0.0230311i | \(0.992668\pi\) | |||||||
\(284\) | −2.20827 | + | 1.27495i | −0.131037 | + | 0.0756542i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 23.8559i | 1.41063i | ||||||||
\(287\) | 21.9395 | + | 6.18518i | 1.29505 | + | 0.365100i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.40798 | + | 14.5630i | −0.494587 | + | 0.856649i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.66689 | + | 8.08328i | −0.273109 | + | 0.473038i | ||||
\(293\) | − | 24.2757i | − | 1.41820i | −0.705108 | − | 0.709100i | \(-0.749102\pi\) | ||
0.705108 | − | 0.709100i | \(-0.250898\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0.928534 | + | 0.536089i | 0.0539699 | + | 0.0311596i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −8.67934 | + | 5.01102i | −0.502780 | + | 0.290280i | ||||
\(299\) | 3.55372 | − | 6.15523i | 0.205517 | − | 0.355966i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.94890 | − | 28.1956i | 0.458167 | − | 1.62517i | ||||
\(302\) | 14.4120 | 0.829316 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5.30761 | − | 3.06435i | 0.304412 | − | 0.175752i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −19.1856 | −1.09498 | −0.547490 | − | 0.836812i | \(-0.684417\pi\) | ||||
−0.547490 | + | 0.836812i | \(0.684417\pi\) | |||||||
\(308\) | 10.8577 | + | 11.1435i | 0.618676 | + | 0.634959i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.3473 | + | 28.3143i | 0.926969 | + | 1.60556i | 0.788363 | + | 0.615210i | \(0.210929\pi\) |
0.138606 | + | 0.990348i | \(0.455738\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.76593 | + | 16.9151i | −0.552003 | + | 0.956097i | 0.446127 | + | 0.894970i | \(0.352803\pi\) |
−0.998130 | + | 0.0611276i | \(0.980530\pi\) | |||||||
\(314\) | 10.8711 | 0.613491 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −10.7192 | −0.603003 | ||||||||
\(317\) | −7.28095 | + | 12.6110i | −0.408939 | + | 0.708303i | −0.994771 | − | 0.102129i | \(-0.967434\pi\) |
0.585832 | + | 0.810432i | \(0.300768\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.123217 | + | 0.213418i | 0.00689882 | + | 0.0119491i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.14147 | − | 4.49264i | −0.0636117 | − | 0.250365i | ||||
\(323\) | −2.62926 | −0.146296 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 9.19935 | − | 5.31125i | 0.509505 | − | 0.294163i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 8.61559 | 0.475717 | ||||||||
\(329\) | −1.77830 | − | 1.82511i | −0.0980411 | − | 0.100622i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.44833 | − | 7.70473i | 0.244502 | − | 0.423490i | −0.717489 | − | 0.696569i | \(-0.754709\pi\) |
0.961992 | + | 0.273079i | \(0.0880422\pi\) | |||||||
\(332\) | −8.74919 | + | 5.05134i | −0.480174 | + | 0.277229i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.99074 | − | 1.72671i | −0.163646 | − | 0.0944812i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.3636i | 0.564543i | 0.959335 | + | 0.282271i | \(0.0910879\pi\) | ||||
−0.959335 | + | 0.282271i | \(0.908912\pi\) | |||||||
\(338\) | −1.72857 | + | 2.99397i | −0.0940217 | + | 0.162850i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −26.9028 | + | 46.5970i | −1.45687 | + | 2.52337i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.5757 | + | 13.5960i | 0.679025 | + | 0.734115i | ||||
\(344\) | − | 11.0724i | − | 0.596981i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.88939 | + | 3.97759i | −0.370376 | + | 0.213837i | ||||
\(347\) | −14.7440 | − | 25.5373i | −0.791497 | − | 1.37091i | −0.925040 | − | 0.379870i | \(-0.875969\pi\) |
0.133542 | − | 0.991043i | \(-0.457365\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 8.85764i | − | 0.474138i | −0.971493 | − | 0.237069i | \(-0.923813\pi\) | ||
0.971493 | − | 0.237069i | \(-0.0761868\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.09272 | + | 2.94028i | 0.271443 | + | 0.156718i | ||||
\(353\) | −14.8345 | + | 8.56472i | −0.789562 | + | 0.455854i | −0.839808 | − | 0.542883i | \(-0.817333\pi\) |
0.0502461 | + | 0.998737i | \(0.483999\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 6.31275 | 0.334575 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 2.74895i | − | 0.145286i | ||||||
\(359\) | −19.0997 | − | 11.0272i | −1.00804 | − | 0.581993i | −0.0974241 | − | 0.995243i | \(-0.531060\pi\) |
−0.910618 | + | 0.413250i | \(0.864394\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.28047 | + | 16.0743i | 0.488446 | + | 0.846013i | ||||
\(362\) | 5.83010 | + | 3.36601i | 0.306423 | + | 0.176914i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.64305 | + | 10.4026i | 0.138534 | + | 0.545245i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.63762 | + | 2.83644i | 0.0854831 | + | 0.148061i | 0.905597 | − | 0.424139i | \(-0.139423\pi\) |
−0.820114 | + | 0.572200i | \(0.806090\pi\) | |||||||
\(368\) | −0.876005 | − | 1.51729i | −0.0456649 | − | 0.0790940i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.56495 | − | 33.7102i | −0.444670 | − | 1.75015i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 32.4255 | + | 18.7209i | 1.67893 | + | 0.969331i | 0.962344 | + | 0.271834i | \(0.0876300\pi\) |
0.716587 | + | 0.697498i | \(0.245703\pi\) | |||||||
\(374\) | −1.26141 | − | 2.18482i | −0.0652258 | − | 0.112974i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.834099 | − | 0.481567i | −0.0430154 | − | 0.0248349i | ||||
\(377\) | 0.170004i | 0.00875563i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 37.2066 | 1.91117 | 0.955587 | − | 0.294708i | \(-0.0952225\pi\) | ||||
0.955587 | + | 0.294708i | \(0.0952225\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −21.3740 | + | 12.3403i | −1.09359 | + | 0.631383i | ||||
\(383\) | −15.8160 | − | 9.13135i | −0.808158 | − | 0.466590i | 0.0381579 | − | 0.999272i | \(-0.487851\pi\) |
−0.846316 | + | 0.532682i | \(0.821184\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 0.687221i | − | 0.0349786i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.29503 | + | 2.24306i | 0.0657454 | + | 0.113874i | ||||
\(389\) | 2.21119 | − | 1.27663i | 0.112112 | − | 0.0647278i | −0.442896 | − | 0.896573i | \(-0.646049\pi\) |
0.555007 | + | 0.831845i | \(0.312715\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.751627i | 0.0380114i | ||||||||
\(392\) | 5.96922 | + | 3.65628i | 0.301491 | + | 0.184670i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.0845770 | − | 0.146492i | 0.00426093 | − | 0.00738014i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.98784 | − | 17.2994i | 0.501275 | − | 0.868234i | −0.498724 | − | 0.866761i | \(-0.666198\pi\) |
0.999999 | − | 0.00147306i | \(-0.000468889\pi\) | |||||||
\(398\) | 0.415459i | 0.0208251i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −21.2087 | − | 12.2448i | −1.05911 | − | 0.611477i | −0.133924 | − | 0.990992i | \(-0.542758\pi\) |
−0.925186 | + | 0.379514i | \(0.876091\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −32.1452 | + | 18.5590i | −1.60126 | + | 0.924490i | ||||
\(404\) | −5.21837 | + | 9.03849i | −0.259624 | + | 0.449682i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.0773750 | + | 0.0794115i | 0.00384006 | + | 0.00394113i | ||||
\(407\) | −6.30502 | −0.312528 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.0020 | + | 8.08403i | −0.692352 | + | 0.399730i | −0.804493 | − | 0.593963i | \(-0.797563\pi\) |
0.112140 | + | 0.993692i | \(0.464229\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 4.94432 | 0.243589 | ||||||||
\(413\) | 8.82575 | + | 34.7366i | 0.434287 | + | 1.70928i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.02837 | + | 3.51324i | 0.0994490 | + | 0.172251i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −18.0201 | + | 31.2117i | −0.881392 | + | 1.52662i | ||||
\(419\) | −14.1632 | −0.691920 | −0.345960 | − | 0.938249i | \(-0.612447\pi\) | ||||
−0.345960 | + | 0.938249i | \(0.612447\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −21.7096 | −1.05806 | −0.529031 | − | 0.848603i | \(-0.677444\pi\) | ||||
−0.529031 | + | 0.848603i | \(0.677444\pi\) | |||||||
\(422\) | 1.05067 | − | 1.81982i | 0.0511460 | − | 0.0885874i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.57304 | − | 11.3848i | −0.319215 | − | 0.552897i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.25215 | + | 2.31143i | 0.108989 | + | 0.111858i | ||||
\(428\) | −0.695809 | −0.0336332 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.08126 | − | 1.77897i | 0.148419 | − | 0.0856899i | −0.423951 | − | 0.905685i | \(-0.639357\pi\) |
0.572371 | + | 0.819995i | \(0.306024\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.86329 | −0.473999 | −0.237000 | − | 0.971510i | \(-0.576164\pi\) | ||||
−0.237000 | + | 0.971510i | \(0.576164\pi\) | |||||||
\(434\) | −6.56863 | + | 23.2997i | −0.315304 | + | 1.11842i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.98417 | − | 5.16874i | 0.142916 | − | 0.247538i | ||||
\(437\) | 9.29898 | − | 5.36877i | 0.444831 | − | 0.256823i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.1701 | + | 7.02641i | 0.580847 | + | 0.335352i | 0.761470 | − | 0.648200i | \(-0.224478\pi\) |
−0.180623 | + | 0.983552i | \(0.557811\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 1.74038i | − | 0.0827812i | ||||||
\(443\) | −7.72219 | + | 13.3752i | −0.366892 | + | 0.635476i | −0.989078 | − | 0.147394i | \(-0.952912\pi\) |
0.622186 | + | 0.782870i | \(0.286245\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −12.9973 | + | 22.5120i | −0.615440 | + | 1.06597i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.54649 | + | 0.717905i | 0.120310 | + | 0.0339178i | ||||
\(449\) | 0.159851i | 0.00754383i | 0.999993 | + | 0.00377192i | \(0.00120064\pi\) | ||||
−0.999993 | + | 0.00377192i | \(0.998799\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −43.8768 | + | 25.3323i | −2.06608 | + | 1.19285i | ||||
\(452\) | 0.404947 | + | 0.701389i | 0.0190471 | + | 0.0329906i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 14.3073i | 0.671473i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.3995 | + | 6.58150i | 0.533246 | + | 0.307870i | 0.742337 | − | 0.670026i | \(-0.233717\pi\) |
−0.209091 | + | 0.977896i | \(0.567051\pi\) | |||||||
\(458\) | −1.36736 | + | 0.789445i | −0.0638925 | + | 0.0368883i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −20.7565 | −0.966725 | −0.483363 | − | 0.875420i | \(-0.660585\pi\) | ||||
−0.483363 | + | 0.875420i | \(0.660585\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 17.7932i | − | 0.826920i | −0.910522 | − | 0.413460i | \(-0.864320\pi\) | ||
0.910522 | − | 0.413460i | \(-0.135680\pi\) | |||||||
\(464\) | 0.0362921 | + | 0.0209532i | 0.00168482 | + | 0.000972730i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9.13044 | + | 15.8144i | 0.422960 | + | 0.732587i | ||||
\(467\) | 1.87225 | + | 1.08094i | 0.0866373 | + | 0.0500201i | 0.542693 | − | 0.839931i | \(-0.317405\pi\) |
−0.456055 | + | 0.889951i | \(0.650738\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 32.4305 | − | 8.23982i | 1.49750 | − | 0.380479i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6.77318 | + | 11.7315i | 0.311761 | + | 0.539986i | ||||
\(473\) | 32.5559 | + | 56.3884i | 1.49692 | + | 2.59274i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −0.792110 | − | 0.812958i | −0.0363063 | − | 0.0372619i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 20.0746 | + | 11.5901i | 0.918190 | + | 0.530117i | ||||
\(479\) | −6.50176 | − | 11.2614i | −0.297073 | − | 0.514546i | 0.678392 | − | 0.734700i | \(-0.262677\pi\) |
−0.975465 | + | 0.220154i | \(0.929344\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.76682 | − | 2.17478i | −0.171752 | − | 0.0991612i | ||||
\(482\) | − | 12.9430i | − | 0.589539i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −23.5811 | −1.07187 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.46224 | − | 3.15363i | 0.247518 | − | 0.142904i | −0.371109 | − | 0.928589i | \(-0.621022\pi\) |
0.618627 | + | 0.785685i | \(0.287689\pi\) | |||||||
\(488\) | 1.05635 | + | 0.609885i | 0.0478188 | + | 0.0276082i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 14.6640i | − | 0.661776i | −0.943670 | − | 0.330888i | \(-0.892652\pi\) | ||
0.943670 | − | 0.330888i | \(-0.107348\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.00898912 | − | 0.0155696i | −0.000404849 | − | 0.000701220i | ||||
\(494\) | −21.5316 | + | 12.4313i | −0.968752 | + | 0.559309i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9.14972i | 0.410835i | ||||||||
\(497\) | 1.83058 | − | 6.49328i | 0.0821129 | − | 0.291264i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.1113 | + | 20.9774i | −0.542176 | + | 0.939076i | 0.456603 | + | 0.889670i | \(0.349066\pi\) |
−0.998779 | + | 0.0494053i | \(0.984267\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 11.3626 | − | 19.6806i | 0.507139 | − | 0.878390i | ||||
\(503\) | − | 34.9707i | − | 1.55927i | −0.626237 | − | 0.779633i | \(-0.715406\pi\) | ||
0.626237 | − | 0.779633i | \(-0.284594\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 8.92250 | + | 5.15141i | 0.396653 | + | 0.229008i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9.54921 | − | 5.51324i | 0.423678 | − | 0.244610i | ||||
\(509\) | 9.58793 | − | 16.6068i | 0.424978 | − | 0.736083i | −0.571441 | − | 0.820643i | \(-0.693615\pi\) |
0.996418 | + | 0.0845605i | \(0.0269486\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.08115 | − | 23.9344i | −0.269014 | − | 1.05879i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6.06331 | − | 3.50065i | 0.267441 | − | 0.154407i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.66377 | 0.249092 | ||||||||
\(518\) | −2.74936 | + | 0.698547i | −0.120800 | + | 0.0306924i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.0953 | − | 17.4855i | −0.442282 | − | 0.766054i | 0.555577 | − | 0.831465i | \(-0.312497\pi\) |
−0.997858 | + | 0.0654110i | \(0.979164\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.01992 | + | 8.69476i | −0.219506 | + | 0.380195i | −0.954657 | − | 0.297708i | \(-0.903778\pi\) |
0.735151 | + | 0.677903i | \(0.237111\pi\) | |||||||
\(524\) | 18.8816 | 0.824847 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 12.0194 | 0.524073 | ||||||||
\(527\) | 1.96265 | − | 3.39942i | 0.0854946 | − | 0.148081i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.96523 | + | 17.2603i | 0.433271 | + | 0.750447i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4.39982 | + | 15.6067i | −0.190757 | + | 0.676635i | ||||
\(533\) | −34.9512 | −1.51391 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 10.9527 | − | 6.32352i | 0.473083 | − | 0.273135i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.22358 | 0.0527525 | ||||||||
\(539\) | −41.1501 | − | 1.06918i | −1.77246 | − | 0.0460528i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.68907 | − | 15.0499i | 0.373572 | − | 0.647046i | −0.616540 | − | 0.787324i | \(-0.711466\pi\) |
0.990112 | + | 0.140277i | \(0.0447994\pi\) | |||||||
\(542\) | −14.1888 | + | 8.19190i | −0.609461 | + | 0.351872i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.371532 | − | 0.214504i | −0.0159293 | − | 0.00919679i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 32.6253i | − | 1.39496i | −0.716606 | − | 0.697478i | \(-0.754305\pi\) | ||
0.716606 | − | 0.697478i | \(-0.245695\pi\) | |||||||
\(548\) | −7.18560 | + | 12.4458i | −0.306954 | + | 0.531659i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.128416 | + | 0.222423i | −0.00547071 | + | 0.00947555i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 20.3126 | − | 19.7917i | 0.863780 | − | 0.841628i | ||||
\(554\) | − | 13.1742i | − | 0.559720i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −14.5189 | + | 8.38250i | −0.615739 | + | 0.355497i | ||||
\(557\) | 17.0656 | + | 29.5585i | 0.723094 | + | 1.25243i | 0.959754 | + | 0.280842i | \(0.0906138\pi\) |
−0.236660 | + | 0.971592i | \(0.576053\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 44.9177i | 1.89981i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4.95741 | + | 2.86216i | 0.209116 | + | 0.120733i | ||||
\(563\) | 25.8012 | − | 14.8964i | 1.08739 | − | 0.627806i | 0.154512 | − | 0.987991i | \(-0.450620\pi\) |
0.932881 | + | 0.360185i | \(0.117286\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 16.1471 | 0.678712 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 2.54990i | − | 0.106991i | ||||||
\(569\) | 14.4586 | + | 8.34769i | 0.606137 | + | 0.349953i | 0.771452 | − | 0.636287i | \(-0.219531\pi\) |
−0.165315 | + | 0.986241i | \(0.552864\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.984264 | + | 1.70480i | 0.0411902 | + | 0.0713435i | 0.885886 | − | 0.463904i | \(-0.153552\pi\) |
−0.844695 | + | 0.535247i | \(0.820218\pi\) | |||||||
\(572\) | −20.6598 | − | 11.9280i | −0.863831 | − | 0.498733i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −16.3263 | + | 15.9076i | −0.681446 | + | 0.663970i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19.9848 | − | 34.6146i | −0.831977 | − | 1.44103i | −0.896468 | − | 0.443108i | \(-0.853876\pi\) |
0.0644912 | − | 0.997918i | \(-0.479458\pi\) | |||||||
\(578\) | −8.40798 | − | 14.5630i | −0.349726 | − | 0.605743i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.25277 | − | 25.7264i | 0.300896 | − | 1.06731i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 66.9493 | + | 38.6532i | 2.77276 | + | 1.60085i | ||||
\(584\) | −4.66689 | − | 8.08328i | −0.193117 | − | 0.334489i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 21.0233 | + | 12.1378i | 0.868466 | + | 0.501409i | ||||
\(587\) | − | 25.5123i | − | 1.05300i | −0.850174 | − | 0.526502i | \(-0.823503\pi\) | ||
0.850174 | − | 0.526502i | \(-0.176497\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −56.0759 | −2.31057 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.928534 | + | 0.536089i | −0.0381625 | + | 0.0220331i | ||||
\(593\) | −34.9279 | − | 20.1656i | −1.43432 | − | 0.828103i | −0.436871 | − | 0.899524i | \(-0.643913\pi\) |
−0.997446 | + | 0.0714207i | \(0.977247\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 10.0220i | − | 0.410519i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3.55372 | + | 6.15523i | 0.145323 | + | 0.251706i | ||||
\(599\) | 19.9124 | − | 11.4964i | 0.813600 | − | 0.469732i | −0.0346046 | − | 0.999401i | \(-0.511017\pi\) |
0.848204 | + | 0.529669i | \(0.177684\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.9443i | 1.05829i | 0.848532 | + | 0.529145i | \(0.177487\pi\) | ||||
−0.848532 | + | 0.529145i | \(0.822513\pi\) | |||||||
\(602\) | 20.4437 | + | 20.9818i | 0.833223 | + | 0.855153i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −7.20599 | + | 12.4811i | −0.293207 | + | 0.507850i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18.9551 | + | 32.8311i | −0.769362 | + | 1.33257i | 0.168547 | + | 0.985694i | \(0.446092\pi\) |
−0.937909 | + | 0.346881i | \(0.887241\pi\) | |||||||
\(608\) | 6.12870i | 0.248552i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.38372 | + | 1.95359i | 0.136891 | + | 0.0790339i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.0154 | − | 10.4012i | 0.727637 | − | 0.420101i | −0.0899202 | − | 0.995949i | \(-0.528661\pi\) |
0.817557 | + | 0.575848i | \(0.195328\pi\) | |||||||
\(614\) | 9.59280 | − | 16.6152i | 0.387134 | − | 0.670536i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −15.0794 | + | 3.83131i | −0.607566 | + | 0.154368i | ||||
\(617\) | 40.9298 | 1.64777 | 0.823887 | − | 0.566755i | \(-0.191801\pi\) | ||||
0.823887 | + | 0.566755i | \(0.191801\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23.2122 | − | 13.4016i | 0.932976 | − | 0.538654i | 0.0452247 | − | 0.998977i | \(-0.485600\pi\) |
0.887752 | + | 0.460323i | \(0.152266\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −32.6946 | −1.31093 | ||||||||
\(623\) | −11.9625 | + | 11.6557i | −0.479266 | + | 0.466975i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −9.76593 | − | 16.9151i | −0.390325 | − | 0.676063i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −5.43554 | + | 9.41463i | −0.216902 | + | 0.375685i | ||||
\(629\) | 0.459974 | 0.0183404 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.28749 | −0.0910636 | −0.0455318 | − | 0.998963i | \(-0.514498\pi\) | ||||
−0.0455318 | + | 0.998963i | \(0.514498\pi\) | |||||||
\(632\) | 5.35961 | − | 9.28312i | 0.213194 | − | 0.369263i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −7.28095 | − | 12.6110i | −0.289164 | − | 0.500846i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −24.2156 | − | 14.8326i | −0.959457 | − | 0.587687i | ||||
\(638\) | −0.246434 | −0.00975641 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.82398 | + | 1.05307i | −0.0720428 | + | 0.0415939i | −0.535589 | − | 0.844479i | \(-0.679910\pi\) |
0.463546 | + | 0.886073i | \(0.346577\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 44.2035 | 1.74322 | 0.871608 | − | 0.490203i | \(-0.163077\pi\) | ||||
0.871608 | + | 0.490203i | \(0.163077\pi\) | |||||||
\(644\) | 4.46148 | + | 1.25778i | 0.175807 | + | 0.0495634i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.31463 | − | 2.27701i | 0.0517235 | − | 0.0895877i | ||||
\(647\) | 17.9336 | − | 10.3540i | 0.705044 | − | 0.407058i | −0.104179 | − | 0.994559i | \(-0.533221\pi\) |
0.809223 | + | 0.587501i | \(0.199888\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −68.9878 | − | 39.8302i | −2.70801 | − | 1.56347i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 10.6225i | 0.416009i | ||||||||
\(653\) | −13.5019 | + | 23.3860i | −0.528370 | + | 0.915164i | 0.471083 | + | 0.882089i | \(0.343863\pi\) |
−0.999453 | + | 0.0330748i | \(0.989470\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −4.30780 | + | 7.46132i | −0.168191 | + | 0.291316i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.46974 | − | 0.627502i | 0.0962806 | − | 0.0244626i | ||||
\(659\) | − | 15.2065i | − | 0.592363i | −0.955132 | − | 0.296181i | \(-0.904287\pi\) | ||
0.955132 | − | 0.296181i | \(-0.0957133\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −35.8665 | + | 20.7075i | −1.39504 | + | 0.805429i | −0.993868 | − | 0.110572i | \(-0.964732\pi\) |
−0.401176 | + | 0.916001i | \(0.631398\pi\) | |||||||
\(662\) | 4.44833 | + | 7.70473i | 0.172889 | + | 0.299453i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 10.1027i | − | 0.392060i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.0635841 | + | 0.0367103i | 0.00246199 | + | 0.00142143i | ||||
\(668\) | 2.99074 | − | 1.72671i | 0.115715 | − | 0.0668083i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.17294 | −0.276908 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 15.2809i | − | 0.589037i | −0.955646 | − | 0.294518i | \(-0.904841\pi\) | ||
0.955646 | − | 0.294518i | \(-0.0951592\pi\) | |||||||
\(674\) | −8.97517 | − | 5.18182i | −0.345711 | − | 0.199596i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.72857 | − | 2.99397i | −0.0664834 | − | 0.115153i | ||||
\(677\) | −42.0596 | − | 24.2831i | −1.61648 | − | 0.933277i | −0.987820 | − | 0.155598i | \(-0.950270\pi\) |
−0.628662 | − | 0.777679i | \(-0.716397\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.59558 | − | 1.85942i | −0.253115 | − | 0.0713581i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −26.9028 | − | 46.5970i | −1.03016 | − | 1.78429i | ||||
\(683\) | −6.15706 | − | 10.6643i | −0.235593 | − | 0.408059i | 0.723852 | − | 0.689956i | \(-0.242370\pi\) |
−0.959445 | + | 0.281896i | \(0.909037\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −18.0623 | + | 4.09288i | −0.689624 | + | 0.156267i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 9.58894 | + | 5.53618i | 0.365575 | + | 0.211065i | ||||
\(689\) | 26.6651 | + | 46.1854i | 1.01586 | + | 1.75952i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 36.8280 | + | 21.2626i | 1.40100 | + | 0.808869i | 0.994496 | − | 0.104779i | \(-0.0334134\pi\) |
0.406507 | + | 0.913648i | \(0.366747\pi\) | |||||||
\(692\) | − | 7.95518i | − | 0.302411i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 29.4879 | 1.11935 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.20097 | − | 1.84808i | 0.121245 | − | 0.0700011i | ||||
\(698\) | 7.67094 | + | 4.42882i | 0.290349 | + | 0.167633i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 2.16278i | − | 0.0816870i | −0.999166 | − | 0.0408435i | \(-0.986995\pi\) | ||
0.999166 | − | 0.0408435i | \(-0.0130045\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.28553 | − | 5.69071i | −0.123916 | − | 0.214629i | ||||
\(704\) | −5.09272 | + | 2.94028i | −0.191939 | + | 0.110816i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 17.1294i | − | 0.644675i | ||||||
\(707\) | −6.79976 | − | 26.7627i | −0.255731 | − | 1.00652i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.4912 | + | 18.1712i | −0.394004 | + | 0.682435i | −0.992974 | − | 0.118337i | \(-0.962244\pi\) |
0.598969 | + | 0.800772i | \(0.295577\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.15638 | + | 5.46700i | −0.118290 | + | 0.204885i | ||||
\(713\) | 16.0304i | 0.600343i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.38066 | + | 1.37447i | 0.0889694 | + | 0.0513665i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 19.0997 | − | 11.0272i | 0.712793 | − | 0.411531i | ||||
\(719\) | −8.73253 | + | 15.1252i | −0.325668 | + | 0.564074i | −0.981647 | − | 0.190705i | \(-0.938923\pi\) |
0.655979 | + | 0.754779i | \(0.272256\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.36934 | + | 9.12906i | −0.348932 | + | 0.339984i | ||||
\(722\) | −18.5609 | −0.690767 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −5.83010 | + | 3.36601i | −0.216674 | + | 0.125097i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12.4470 | −0.461633 | −0.230816 | − | 0.972997i | \(-0.574140\pi\) | ||||
−0.230816 | + | 0.972997i | \(0.574140\pi\) | |||||||
\(728\) | −10.3304 | − | 2.91235i | −0.382872 | − | 0.107939i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.37507 | − | 4.11374i | −0.0878450 | − | 0.152152i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11.1806 | + | 19.3654i | −0.412966 | + | 0.715279i | −0.995213 | − | 0.0977339i | \(-0.968841\pi\) |
0.582246 | + | 0.813012i | \(0.302174\pi\) | |||||||
\(734\) | −3.27524 | −0.120891 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.75201 | 0.0645800 | ||||||||
\(737\) | −37.1859 | + | 64.4079i | −1.36976 | + | 2.37249i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.9125 | − | 27.5613i | −0.585351 | − | 1.01386i | −0.994832 | − | 0.101539i | \(-0.967623\pi\) |
0.409481 | − | 0.912319i | \(-0.365710\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 33.4764 | + | 9.43764i | 1.22896 | + | 0.346467i | ||||
\(743\) | −15.1736 | −0.556667 | −0.278333 | − | 0.960485i | \(-0.589782\pi\) | ||||
−0.278333 | + | 0.960485i | \(0.589782\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −32.4255 | + | 18.7209i | −1.18718 | + | 0.685421i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.52281 | 0.0922432 | ||||||||
\(749\) | 1.31854 | − | 1.28472i | 0.0481783 | − | 0.0469427i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.4956 | − | 18.1790i | 0.382991 | − | 0.663360i | −0.608497 | − | 0.793556i | \(-0.708227\pi\) |
0.991488 | + | 0.130196i | \(0.0415607\pi\) | |||||||
\(752\) | 0.834099 | − | 0.481567i | 0.0304164 | − | 0.0175609i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.147227 | − | 0.0850018i | −0.00536171 | − | 0.00309558i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 17.0421i | − | 0.619407i | −0.950833 | − | 0.309704i | \(-0.899770\pi\) | ||
0.950833 | − | 0.309704i | \(-0.100230\pi\) | |||||||
\(758\) | −18.6033 | + | 32.2219i | −0.675702 | + | 1.17035i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.13659 | + | 5.43274i | −0.113701 | + | 0.196937i | −0.917260 | − | 0.398289i | \(-0.869604\pi\) |
0.803559 | + | 0.595226i | \(0.202937\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.88850 | + | 15.3045i | 0.140773 | + | 0.554060i | ||||
\(764\) | − | 24.6805i | − | 0.892911i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 15.8160 | − | 9.13135i | 0.571454 | − | 0.329929i | ||||
\(767\) | −27.4770 | − | 47.5916i | −0.992139 | − | 1.71843i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.7852i | 0.749534i | 0.927119 | + | 0.374767i | \(0.122277\pi\) | ||||
−0.927119 | + | 0.374767i | \(0.877723\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0.595151 | + | 0.343610i | 0.0214199 | + | 0.0123668i | ||||
\(773\) | −38.5322 | + | 22.2466i | −1.38591 | + | 0.800153i | −0.992851 | − | 0.119361i | \(-0.961915\pi\) |
−0.393055 | + | 0.919515i | \(0.628582\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −2.59007 | −0.0929780 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.55326i | 0.0915390i | ||||||||
\(779\) | −45.7282 | − | 26.4012i | −1.63838 | − | 0.945921i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.49741 | + | 12.9859i | 0.268279 | + | 0.464672i | ||||
\(782\) | −0.650928 | − | 0.375814i | −0.0232771 | − | 0.0134391i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.15104 | + | 3.34136i | −0.219680 | + | 0.119334i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.68522 | + | 13.3112i | 0.273948 | + | 0.474493i | 0.969869 | − | 0.243626i | \(-0.0783369\pi\) |
−0.695921 | + | 0.718118i | \(0.745004\pi\) | |||||||
\(788\) | 0.0845770 | + | 0.146492i | 0.00301293 | + | 0.00521855i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.06239 | − | 0.581427i | −0.0733301 | − | 0.0206732i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.28535 | − | 2.47415i | −0.152177 | − | 0.0878595i | ||||
\(794\) | 9.98784 | + | 17.2994i | 0.354455 | + | 0.613934i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.359798 | − | 0.207730i | −0.0127527 | − | 0.00736278i | ||||
\(797\) | 28.8285i | 1.02116i | 0.859830 | + | 0.510580i | \(0.170569\pi\) | ||||
−0.859830 | + | 0.510580i | \(0.829431\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.413193 | −0.0146177 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 21.2087 | − | 12.2448i | 0.748904 | − | 0.432380i | ||||
\(803\) | 47.5343 | + | 27.4439i | 1.67745 | + | 0.968475i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 37.1180i | − | 1.30743i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −5.21837 | − | 9.03849i | −0.183582 | − | 0.317973i | ||||
\(809\) | −15.9209 | + | 9.19196i | −0.559751 | + | 0.323172i | −0.753045 | − | 0.657968i | \(-0.771416\pi\) |
0.193295 | + | 0.981141i | \(0.438083\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 47.0100i | 1.65074i | 0.564589 | + | 0.825372i | \(0.309035\pi\) | ||||
−0.564589 | + | 0.825372i | \(0.690965\pi\) | |||||||
\(812\) | −0.107460 | + | 0.0273030i | −0.00377110 | + | 0.000958146i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3.15251 | − | 5.46031i | 0.110495 | − | 0.191384i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −33.9296 | + | 58.7677i | −1.18705 | + | 2.05602i | ||||
\(818\) | − | 16.1681i | − | 0.565303i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 47.2833 | + | 27.2990i | 1.65020 | + | 0.952742i | 0.976989 | + | 0.213290i | \(0.0684180\pi\) |
0.673209 | + | 0.739452i | \(0.264915\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.620733 | + | 0.358380i | −0.0216374 | + | 0.0124924i | −0.510780 | − | 0.859712i | \(-0.670643\pi\) |
0.489142 | + | 0.872204i | \(0.337310\pi\) | |||||||
\(824\) | −2.47216 | + | 4.28191i | −0.0861218 | + | 0.149167i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −34.4957 | − | 9.72501i | −1.20026 | − | 0.338376i | ||||
\(827\) | 32.8584 | 1.14260 | 0.571299 | − | 0.820742i | \(-0.306440\pi\) | ||||
0.571299 | + | 0.820742i | \(0.306440\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −43.6845 | + | 25.2212i | −1.51722 | + | 0.875970i | −0.517429 | + | 0.855726i | \(0.673111\pi\) |
−0.999795 | + | 0.0202442i | \(0.993556\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4.05674 | −0.140642 | ||||||||
\(833\) | 3.00205 | + | 0.0780005i | 0.104015 | + | 0.00270256i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −18.0201 | − | 31.2117i | −0.623238 | − | 1.07948i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 7.08162 | − | 12.2657i | 0.244631 | − | 0.423713i | ||||
\(839\) | −21.6729 | −0.748233 | −0.374116 | − | 0.927382i | \(-0.622054\pi\) | ||||
−0.374116 | + | 0.927382i | \(0.622054\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.9982 | 0.999939 | ||||||||
\(842\) | 10.8548 | − | 18.8011i | 0.374081 | − | 0.647928i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.05067 | + | 1.81982i | 0.0361657 | + | 0.0626408i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 44.6854 | − | 43.5394i | 1.53541 | − | 1.49603i | ||||
\(848\) | 13.1461 | 0.451439 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.62680 | + | 0.939234i | −0.0557660 | + | 0.0321965i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −25.1282 | −0.860372 | −0.430186 | − | 0.902740i | \(-0.641552\pi\) | ||||
−0.430186 | + | 0.902740i | \(0.641552\pi\) | |||||||
\(854\) | −3.12783 | + | 0.794706i | −0.107032 | + | 0.0271943i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.347904 | − | 0.602588i | 0.0118911 | − | 0.0205960i | ||||
\(857\) | 39.1591 | − | 22.6085i | 1.33765 | − | 0.772293i | 0.351192 | − | 0.936304i | \(-0.385777\pi\) |
0.986459 | + | 0.164011i | \(0.0524433\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24.3260 | − | 14.0446i | −0.829992 | − | 0.479196i | 0.0238577 | − | 0.999715i | \(-0.492405\pi\) |
−0.853850 | + | 0.520519i | \(0.825738\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.55794i | 0.121184i | ||||||||
\(863\) | −14.5140 | + | 25.1390i | −0.494062 | + | 0.855740i | −0.999977 | − | 0.00684347i | \(-0.997822\pi\) |
0.505915 | + | 0.862583i | \(0.331155\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 4.93164 | − | 8.54186i | 0.167584 | − | 0.290264i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −16.8938 | − | 17.3384i | −0.573413 | − | 0.588505i | ||||
\(869\) | 63.0351i | 2.13832i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −44.4321 | + | 25.6529i | −1.50552 | + | 0.869215i | ||||
\(872\) | 2.98417 | + | 5.16874i | 0.101057 | + | 0.175036i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 10.7375i | 0.363203i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −31.0400 | − | 17.9210i | −1.04815 | − | 0.605148i | −0.126017 | − | 0.992028i | \(-0.540220\pi\) |
−0.922130 | + | 0.386880i | \(0.873553\pi\) | |||||||
\(878\) | −12.1701 | + | 7.02641i | −0.410721 | + | 0.237130i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −16.4620 | −0.554619 | −0.277309 | − | 0.960781i | \(-0.589443\pi\) | ||||
−0.277309 | + | 0.960781i | \(0.589443\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 43.5609i | 1.46594i | 0.680260 | + | 0.732971i | \(0.261867\pi\) | ||||
−0.680260 | + | 0.732971i | \(0.738133\pi\) | |||||||
\(884\) | 1.50721 | + | 0.870188i | 0.0506930 | + | 0.0292676i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −7.72219 | − | 13.3752i | −0.259432 | − | 0.449350i | ||||
\(887\) | −33.2119 | − | 19.1749i | −1.11515 | − | 0.643831i | −0.174990 | − | 0.984570i | \(-0.555989\pi\) |
−0.940158 | + | 0.340739i | \(0.889323\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.91596 | + | 28.0788i | −0.265493 | + | 0.941733i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −12.9973 | − | 22.5120i | −0.435182 | − | 0.753757i | ||||
\(893\) | 2.95138 | + | 5.11194i | 0.0987641 | + | 0.171065i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.89497 | + | 1.84637i | −0.0633065 | + | 0.0616830i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −0.138435 | − | 0.0799255i | −0.00461964 | − | 0.00266715i | ||||
\(899\) | −0.191716 | − | 0.332062i | −0.00639409 | − | 0.0110749i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.88420 | − | 2.81989i | −0.162716 | − | 0.0939442i | ||||
\(902\) | − | 50.6646i | − | 1.68695i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.809894 | −0.0269367 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21.6272 | − | 12.4865i | 0.718120 | − | 0.414607i | −0.0959402 | − | 0.995387i | \(-0.530586\pi\) |
0.814060 | + | 0.580780i | \(0.197252\pi\) | |||||||
\(908\) | −12.3905 | − | 7.15363i | −0.411192 | − | 0.237402i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 5.02786i | − | 0.166580i | −0.996525 | − | 0.0832902i | \(-0.973457\pi\) | ||
0.996525 | − | 0.0832902i | \(-0.0265428\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 29.7048 | + | 51.4502i | 0.983084 | + | 1.70275i | ||||
\(914\) | −11.3995 | + | 6.58150i | −0.377062 | + | 0.217697i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 1.57889i | − | 0.0521680i | ||||||
\(917\) | −35.7801 | + | 34.8625i | −1.18156 | + | 1.15126i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.76087 | − | 9.97811i | 0.190033 | − | 0.329148i | −0.755228 | − | 0.655463i | \(-0.772474\pi\) |
0.945261 | + | 0.326315i | \(0.105807\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 10.3782 | − | 17.9756i | 0.341789 | − | 0.591996i | ||||
\(923\) | 10.3443i | 0.340486i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 15.4094 | + | 8.89659i | 0.506383 | + | 0.292360i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.0362921 | + | 0.0209532i | −0.00119135 | + | 0.000687824i | ||||
\(929\) | −9.55386 | + | 16.5478i | −0.313452 | + | 0.542915i | −0.979107 | − | 0.203345i | \(-0.934819\pi\) |
0.665655 | + | 0.746259i | \(0.268152\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −20.4782 | − | 37.6979i | −0.671146 | − | 1.23550i | ||||
\(932\) | −18.2609 | −0.598155 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.87225 | + | 1.08094i | −0.0612618 | + | 0.0353695i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −49.5320 | −1.61814 | −0.809070 | − | 0.587713i | \(-0.800028\pi\) | ||||
−0.809070 | + | 0.587713i | \(0.800028\pi\) | |||||||
\(938\) | −9.07938 | + | 32.2056i | −0.296452 | + | 1.05155i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −22.4564 | − | 38.8957i | −0.732059 | − | 1.26796i | −0.956002 | − | 0.293361i | \(-0.905226\pi\) |
0.223942 | − | 0.974602i | \(-0.428107\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.54730 | + | 13.0723i | −0.245774 | + | 0.425693i | ||||
\(944\) | −13.5464 | −0.440897 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −65.1117 | −2.11696 | ||||||||
\(947\) | 1.32786 | − | 2.29992i | 0.0431496 | − | 0.0747373i | −0.843644 | − | 0.536903i | \(-0.819594\pi\) |
0.886794 | + | 0.462166i | \(0.152927\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18.9323 | + | 32.7918i | 0.614570 | + | 1.06447i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.10010 | − | 0.279508i | 0.0356543 | − | 0.00905891i | ||||
\(953\) | −36.5346 | −1.18347 | −0.591735 | − | 0.806132i | \(-0.701557\pi\) | ||||
−0.591735 | + | 0.806132i | \(0.701557\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −20.0746 | + | 11.5901i | −0.649258 | + | 0.374850i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 13.0035 | 0.420125 | ||||||||
\(959\) | −9.36314 | − | 36.8517i | −0.302351 | − | 1.19000i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 26.3587 | − | 45.6546i | 0.850280 | − | 1.47273i | ||||
\(962\) | 3.76682 | − | 2.17478i | 0.121447 | − | 0.0701176i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 11.2090 | + | 6.47152i | 0.361018 | + | 0.208434i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 22.6175i | − | 0.727330i | −0.931530 | − | 0.363665i | \(-0.881525\pi\) | ||
0.931530 | − | 0.363665i | \(-0.118475\pi\) | |||||||
\(968\) | 11.7905 | − | 20.4218i | 0.378962 | − | 0.656381i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.86871 | − | 8.43286i | 0.156244 | − | 0.270623i | −0.777267 | − | 0.629171i | \(-0.783395\pi\) |
0.933511 | + | 0.358548i | \(0.116728\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.0357 | − | 42.6919i | 0.385846 | − | 1.36864i | ||||
\(974\) | 6.30725i | 0.202097i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.05635 | + | 0.609885i | −0.0338130 | + | 0.0195220i | ||||
\(977\) | −21.6323 | − | 37.4682i | −0.692078 | − | 1.19871i | −0.971156 | − | 0.238446i | \(-0.923362\pi\) |
0.279077 | − | 0.960269i | \(-0.409971\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 37.1225i | − | 1.18644i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 12.6994 | + | 7.33199i | 0.405253 | + | 0.233973i | ||||
\(983\) | 31.1460 | − | 17.9821i | 0.993402 | − | 0.573541i | 0.0871125 | − | 0.996198i | \(-0.472236\pi\) |
0.906289 | + | 0.422658i | \(0.138903\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0.0179782 | 0.000572544 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 24.8625i | − | 0.790983i | ||||||
\(989\) | 16.7999 | + | 9.69944i | 0.534206 | + | 0.308424i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.1494 | + | 21.0433i | 0.385937 | + | 0.668463i | 0.991899 | − | 0.127031i | \(-0.0405448\pi\) |
−0.605962 | + | 0.795494i | \(0.707212\pi\) | |||||||
\(992\) | −7.92389 | − | 4.57486i | −0.251584 | − | 0.145252i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 4.70806 | + | 4.83197i | 0.149331 | + | 0.153261i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26.8764 | + | 46.5513i | 0.851184 | + | 1.47429i | 0.880141 | + | 0.474713i | \(0.157448\pi\) |
−0.0289572 | + | 0.999581i | \(0.509219\pi\) | |||||||
\(998\) | −12.1113 | − | 20.9774i | −0.383376 | − | 0.664027i | ||||
\(999\) | 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 | 3150.2.bp.g.1349.10 | 24 | ||
3.2 | odd | 2 | 3150.2.bp.h.1349.10 | 24 | |||
5.2 | odd | 4 | 3150.2.bf.e.1601.6 | yes | 24 | ||
5.3 | odd | 4 | 3150.2.bf.d.1601.7 | yes | 24 | ||
5.4 | even | 2 | 3150.2.bp.h.1349.3 | 24 | |||
7.3 | odd | 6 | inner | 3150.2.bp.g.899.3 | 24 | ||
15.2 | even | 4 | 3150.2.bf.e.1601.7 | yes | 24 | ||
15.8 | even | 4 | 3150.2.bf.d.1601.6 | yes | 24 | ||
15.14 | odd | 2 | inner | 3150.2.bp.g.1349.3 | 24 | ||
21.17 | even | 6 | 3150.2.bp.h.899.3 | 24 | |||
35.3 | even | 12 | 3150.2.bf.d.1151.6 | ✓ | 24 | ||
35.17 | even | 12 | 3150.2.bf.e.1151.7 | yes | 24 | ||
35.24 | odd | 6 | 3150.2.bp.h.899.10 | 24 | |||
105.17 | odd | 12 | 3150.2.bf.e.1151.6 | yes | 24 | ||
105.38 | odd | 12 | 3150.2.bf.d.1151.7 | yes | 24 | ||
105.59 | even | 6 | inner | 3150.2.bp.g.899.10 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3150.2.bf.d.1151.6 | ✓ | 24 | 35.3 | even | 12 | ||
3150.2.bf.d.1151.7 | yes | 24 | 105.38 | odd | 12 | ||
3150.2.bf.d.1601.6 | yes | 24 | 15.8 | even | 4 | ||
3150.2.bf.d.1601.7 | yes | 24 | 5.3 | odd | 4 | ||
3150.2.bf.e.1151.6 | yes | 24 | 105.17 | odd | 12 | ||
3150.2.bf.e.1151.7 | yes | 24 | 35.17 | even | 12 | ||
3150.2.bf.e.1601.6 | yes | 24 | 5.2 | odd | 4 | ||
3150.2.bf.e.1601.7 | yes | 24 | 15.2 | even | 4 | ||
3150.2.bp.g.899.3 | 24 | 7.3 | odd | 6 | inner | ||
3150.2.bp.g.899.10 | 24 | 105.59 | even | 6 | inner | ||
3150.2.bp.g.1349.3 | 24 | 15.14 | odd | 2 | inner | ||
3150.2.bp.g.1349.10 | 24 | 1.1 | even | 1 | trivial | ||
3150.2.bp.h.899.3 | 24 | 21.17 | even | 6 | |||
3150.2.bp.h.899.10 | 24 | 35.24 | odd | 6 | |||
3150.2.bp.h.1349.3 | 24 | 5.4 | even | 2 | |||
3150.2.bp.h.1349.10 | 24 | 3.2 | odd | 2 |