Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3150,2,Mod(1151,3150)]
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, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3150.1151");
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.bf (of order \(6\), degree \(2\), 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 | 1601.7 | ||
Character | \(\chi\) | \(=\) | 3150.1601 |
Dual form | 3150.2.bf.e.1151.7 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | + | 0.500000i | 0.612372 | + | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.717905 | + | 2.54649i | −0.271343 | + | 0.962483i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.09272 | − | 2.94028i | 1.53551 | − | 0.886529i | 0.536419 | − | 0.843952i | \(-0.319777\pi\) |
0.999093 | − | 0.0425771i | \(-0.0135568\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.05674i | 1.12514i | 0.826751 | + | 0.562569i | \(0.190187\pi\) | ||||
−0.826751 | + | 0.562569i | \(0.809813\pi\) | |||||||
\(14\) | −1.89497 | + | 1.84637i | −0.506452 | + | 0.493464i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −0.214504 | − | 0.371532i | −0.0520249 | − | 0.0901098i | 0.838840 | − | 0.544378i | \(-0.183234\pi\) |
−0.890865 | + | 0.454268i | \(0.849901\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.30761 | + | 3.06435i | 1.21765 | + | 0.703010i | 0.964414 | − | 0.264395i | \(-0.0851723\pi\) |
0.253234 | + | 0.967405i | \(0.418506\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.88057 | 1.25374 | ||||||||
\(23\) | −1.51729 | − | 0.876005i | −0.316376 | − | 0.182660i | 0.333400 | − | 0.942785i | \(-0.391804\pi\) |
−0.649776 | + | 0.760126i | \(0.725137\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.02837 | + | 3.51324i | −0.397796 | + | 0.689003i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.56428 | + | 0.651521i | −0.484603 | + | 0.123126i | ||||
\(29\) | − | 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 | \(0.0263765\pi\) | |||||||
\(32\) | −0.866025 | + | 0.500000i | −0.153093 | + | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 0.429009i | − | 0.0735744i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.536089 | + | 0.928534i | −0.0881326 | + | 0.152650i | −0.906722 | − | 0.421729i | \(-0.861423\pi\) |
0.818589 | + | 0.574379i | \(0.194757\pi\) | |||||||
\(38\) | 3.06435 | + | 5.30761i | 0.497103 | + | 0.861008i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.61559 | −1.34553 | −0.672765 | − | 0.739856i | \(-0.734893\pi\) | ||||
−0.672765 | + | 0.739856i | \(0.734893\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.0724 | −1.68852 | −0.844259 | − | 0.535935i | \(-0.819959\pi\) | ||||
−0.844259 | + | 0.535935i | \(0.819959\pi\) | |||||||
\(44\) | 5.09272 | + | 2.94028i | 0.767756 | + | 0.443264i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.876005 | − | 1.51729i | −0.129160 | − | 0.223712i | ||||
\(47\) | −0.481567 | + | 0.834099i | −0.0702438 | + | 0.121666i | −0.899008 | − | 0.437932i | \(-0.855711\pi\) |
0.828764 | + | 0.559598i | \(0.189044\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.96922 | − | 3.65628i | −0.852746 | − | 0.522325i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.51324 | + | 2.02837i | −0.487199 | + | 0.281284i | ||||
\(53\) | 11.3848 | − | 6.57304i | 1.56383 | − | 0.902877i | 0.566965 | − | 0.823742i | \(-0.308117\pi\) |
0.996864 | − | 0.0791353i | \(-0.0252159\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.54649 | − | 0.717905i | −0.340289 | − | 0.0959341i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.0209532 | − | 0.0362921i | 0.00275129 | − | 0.00476538i | ||||
\(59\) | 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 | \(0.641785\pi\) | |||||||
\(62\) | 9.14972 | 1.16202 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.32352 | + | 10.9527i | 0.772541 | + | 1.33808i | 0.936166 | + | 0.351558i | \(0.114348\pi\) |
−0.163625 | + | 0.986523i | \(0.552319\pi\) | |||||||
\(68\) | 0.214504 | − | 0.371532i | 0.0260125 | − | 0.0450549i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.54990i | 0.302617i | 0.988487 | + | 0.151308i | \(0.0483487\pi\) | ||||
−0.988487 | + | 0.151308i | \(0.951651\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.08328 | + | 4.66689i | −0.946077 | + | 0.546218i | −0.891860 | − | 0.452311i | \(-0.850600\pi\) |
−0.0542168 | + | 0.998529i | \(0.517266\pi\) | |||||||
\(74\) | −0.928534 | + | 0.536089i | −0.107940 | + | 0.0623191i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.12870i | 0.703010i | ||||||||
\(77\) | 3.83131 | + | 15.0794i | 0.436619 | + | 1.71846i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.35961 | + | 9.28312i | −0.603003 | + | 1.04443i | 0.389360 | + | 0.921086i | \(0.372696\pi\) |
−0.992364 | + | 0.123347i | \(0.960637\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −7.46132 | − | 4.30780i | −0.823965 | − | 0.475717i | ||||
\(83\) | 10.1027 | 1.10891 | 0.554457 | − | 0.832212i | \(-0.312926\pi\) | ||||
0.554457 | + | 0.832212i | \(0.312926\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −9.58894 | − | 5.53618i | −1.03400 | − | 0.596981i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.94028 | + | 5.09272i | 0.313435 | + | 0.542886i | ||||
\(89\) | −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 | ||||
\(92\) | − | 1.75201i | − | 0.182660i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.834099 | + | 0.481567i | −0.0860307 | + | 0.0496698i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 2.59007i | − | 0.262982i | −0.991317 | − | 0.131491i | \(-0.958024\pi\) | ||
0.991317 | − | 0.131491i | \(-0.0419764\pi\) | |||||||
\(98\) | −3.34136 | − | 6.15104i | −0.337529 | − | 0.621349i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.21837 | + | 9.03849i | 0.519248 | + | 0.899363i | 0.999750 | + | 0.0223696i | \(0.00712105\pi\) |
−0.480502 | + | 0.876993i | \(0.659546\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.28191 | + | 2.47216i | 0.421909 | + | 0.243589i | 0.695894 | − | 0.718145i | \(-0.255008\pi\) |
−0.273985 | + | 0.961734i | \(0.588342\pi\) | |||||||
\(104\) | −4.05674 | −0.397796 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 13.1461 | 1.27686 | ||||||||
\(107\) | −0.602588 | − | 0.347904i | −0.0582544 | − | 0.0336332i | 0.470590 | − | 0.882352i | \(-0.344041\pi\) |
−0.528844 | + | 0.848719i | \(0.677374\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.98417 | − | 5.16874i | −0.285832 | − | 0.495076i | 0.686979 | − | 0.726678i | \(-0.258937\pi\) |
−0.972811 | + | 0.231602i | \(0.925603\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.84637 | − | 1.89497i | −0.174466 | − | 0.179058i | ||||
\(113\) | − | 0.809894i | − | 0.0761884i | −0.999274 | − | 0.0380942i | \(-0.987871\pi\) | ||
0.999274 | − | 0.0380942i | \(-0.0121287\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.0362921 | − | 0.0209532i | 0.00336963 | − | 0.00194546i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 13.5464i | 1.24704i | ||||||||
\(119\) | 1.10010 | − | 0.279508i | 0.100846 | − | 0.0256225i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.7905 | − | 20.4218i | 1.07187 | − | 1.85653i | ||||
\(122\) | 0.609885 | + | 1.05635i | 0.0552164 | + | 0.0956376i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7.92389 | + | 4.57486i | 0.711586 | + | 0.410835i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.0265 | −0.978442 | −0.489221 | − | 0.872160i | \(-0.662719\pi\) | ||||
−0.489221 | + | 0.872160i | \(0.662719\pi\) | |||||||
\(128\) | −0.866025 | − | 0.500000i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.44080 | − | 16.3520i | 0.824847 | − | 1.42868i | −0.0771893 | − | 0.997016i | \(-0.524595\pi\) |
0.902036 | − | 0.431660i | \(-0.142072\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −11.6137 | + | 11.3159i | −1.00704 | + | 0.981210i | ||||
\(134\) | 12.6470i | 1.09254i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.371532 | − | 0.214504i | 0.0318586 | − | 0.0183936i | ||||
\(137\) | −12.4458 | + | 7.18560i | −1.06332 | + | 0.613907i | −0.926348 | − | 0.376668i | \(-0.877070\pi\) |
−0.136970 | + | 0.990575i | \(0.543736\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.7650i | 1.42199i | 0.703198 | + | 0.710994i | \(0.251755\pi\) | ||||
−0.703198 | + | 0.710994i | \(0.748245\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.27495 | + | 2.20827i | −0.106991 | + | 0.185314i | ||||
\(143\) | 11.9280 | + | 20.6598i | 0.997466 | + | 1.72766i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −9.33377 | −0.772469 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.07218 | −0.0881326 | ||||||||
\(149\) | 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 | \(-0.366128\pi\) | |||||||
\(152\) | −3.06435 | + | 5.30761i | −0.248552 | + | 0.430504i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.22169 | + | 14.9748i | −0.340193 | + | 1.20670i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.41463 | − | 5.43554i | 0.751370 | − | 0.433803i | −0.0748190 | − | 0.997197i | \(-0.523838\pi\) |
0.826189 | + | 0.563394i | \(0.190505\pi\) | |||||||
\(158\) | −9.28312 | + | 5.35961i | −0.738525 | + | 0.426388i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.32001 | − | 3.23486i | 0.261653 | − | 0.254943i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.31125 | + | 9.19935i | −0.416009 | + | 0.720549i | −0.995534 | − | 0.0944058i | \(-0.969905\pi\) |
0.579525 | + | 0.814955i | \(0.303238\pi\) | |||||||
\(164\) | −4.30780 | − | 7.46132i | −0.336382 | − | 0.582631i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.74919 | + | 5.05134i | 0.679068 | + | 0.392060i | ||||
\(167\) | 3.45341 | 0.267233 | 0.133617 | − | 0.991033i | \(-0.457341\pi\) | ||||
0.133617 | + | 0.991033i | \(0.457341\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.45714 | −0.265934 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −5.53618 | − | 9.58894i | −0.422130 | − | 0.731150i | ||||
\(173\) | −3.97759 | + | 6.88939i | −0.302411 | + | 0.523790i | −0.976681 | − | 0.214694i | \(-0.931125\pi\) |
0.674271 | + | 0.738484i | \(0.264458\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.88057i | 0.443264i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5.46700 | + | 3.15638i | −0.409769 | + | 0.236580i | ||||
\(179\) | −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 | \(-0.0804943\pi\) | |||||||
\(182\) | −7.49025 | − | 7.68740i | −0.555215 | − | 0.569828i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.876005 | − | 1.51729i | 0.0645800 | − | 0.111856i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.18482 | − | 1.26141i | −0.159770 | − | 0.0922432i | ||||
\(188\) | −0.963134 | −0.0702438 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −21.3740 | − | 12.3403i | −1.54657 | − | 0.892911i | −0.998400 | − | 0.0565412i | \(-0.981993\pi\) |
−0.548166 | − | 0.836369i | \(-0.684674\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.343610 | + | 0.595151i | 0.0247336 | + | 0.0428399i | 0.878127 | − | 0.478427i | \(-0.158793\pi\) |
−0.853394 | + | 0.521267i | \(0.825460\pi\) | |||||||
\(194\) | 1.29503 | − | 2.24306i | 0.0929780 | − | 0.161043i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.181816 | − | 6.99764i | 0.0129868 | − | 0.499831i | ||||
\(197\) | 0.169154i | 0.0120517i | 0.999982 | + | 0.00602586i | \(0.00191810\pi\) | ||||
−0.999982 | + | 0.00602586i | \(0.998082\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.359798 | + | 0.207730i | −0.0255054 | + | 0.0147256i | −0.512699 | − | 0.858569i | \(-0.671354\pi\) |
0.487193 | + | 0.873294i | \(0.338021\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 10.4367i | 0.734327i | ||||||||
\(203\) | 0.106714 | + | 0.0300849i | 0.00748988 | + | 0.00211154i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2.47216 | + | 4.28191i | 0.172244 | + | 0.298335i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.51324 | − | 2.02837i | −0.243599 | − | 0.140642i | ||||
\(209\) | 36.0402 | 2.49295 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.10135 | −0.144663 | −0.0723313 | − | 0.997381i | \(-0.523044\pi\) | ||||
−0.0723313 | + | 0.997381i | \(0.523044\pi\) | |||||||
\(212\) | 11.3848 | + | 6.57304i | 0.781915 | + | 0.451439i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.347904 | − | 0.602588i | −0.0237823 | − | 0.0411921i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.96124 | + | 23.4624i | 0.404675 | + | 1.59273i | ||||
\(218\) | − | 5.96835i | − | 0.404227i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.50721 | − | 0.870188i | 0.101386 | − | 0.0585352i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 25.9946i | − | 1.74073i | −0.492409 | − | 0.870364i | \(-0.663883\pi\) | ||
0.492409 | − | 0.870364i | \(-0.336117\pi\) | |||||||
\(224\) | −0.651521 | − | 2.56428i | −0.0435316 | − | 0.171333i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.404947 | − | 0.701389i | 0.0269367 | − | 0.0466557i | ||||
\(227\) | −7.15363 | − | 12.3905i | −0.474803 | − | 0.822383i | 0.524781 | − | 0.851238i | \(-0.324147\pi\) |
−0.999584 | + | 0.0288545i | \(0.990814\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.36736 | − | 0.789445i | −0.0903576 | − | 0.0521680i | 0.454140 | − | 0.890930i | \(-0.349946\pi\) |
−0.544498 | + | 0.838762i | \(0.683280\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.0419065 | 0.00275129 | ||||||||
\(233\) | 15.8144 | + | 9.13044i | 1.03604 | + | 0.598155i | 0.918708 | − | 0.394938i | \(-0.129234\pi\) |
0.117327 | + | 0.993093i | \(0.462567\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −6.77318 | + | 11.7315i | −0.440897 | + | 0.763656i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.09247 | + | 0.307987i | 0.0708141 | + | 0.0199639i | ||||
\(239\) | − | 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 | \(0.470205\pi\) | |||||||
\(242\) | 20.4218 | − | 11.7905i | 1.31276 | − | 0.757924i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.21977i | 0.0780878i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −12.4313 | + | 21.5316i | −0.790983 | + | 1.37002i | ||||
\(248\) | 4.57486 | + | 7.92389i | 0.290504 | + | 0.503168i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 22.7253 | 1.43441 | 0.717203 | − | 0.696865i | \(-0.245422\pi\) | ||||
0.717203 | + | 0.696865i | \(0.245422\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −10.3028 | −0.647732 | ||||||||
\(254\) | −9.54921 | − | 5.51324i | −0.599171 | − | 0.345931i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −3.50065 | + | 6.06331i | −0.218365 | + | 0.378219i | −0.954308 | − | 0.298824i | \(-0.903406\pi\) |
0.735943 | + | 0.677043i | \(0.236739\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.97964 | − | 2.03175i | −0.123009 | − | 0.126247i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 16.3520 | − | 9.44080i | 1.01023 | − | 0.583255i | ||||
\(263\) | 10.4091 | − | 6.00972i | 0.641855 | − | 0.370575i | −0.143473 | − | 0.989654i | \(-0.545827\pi\) |
0.785329 | + | 0.619079i | \(0.212494\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −15.7157 | + | 3.99298i | −0.963590 | + | 0.244825i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6.32352 | + | 10.9527i | −0.386271 | + | 0.669040i | ||||
\(269\) | −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 | \(0.500873\pi\) | |||||||
\(272\) | 0.429009 | 0.0260125 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −14.3712 | −0.868196 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.58712 | − | 11.4092i | −0.395781 | − | 0.685514i | 0.597419 | − | 0.801929i | \(-0.296193\pi\) |
−0.993201 | + | 0.116416i | \(0.962860\pi\) | |||||||
\(278\) | −8.38250 | + | 14.5189i | −0.502749 | + | 0.870786i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.72433i | 0.341485i | 0.985316 | + | 0.170742i | \(0.0546166\pi\) | ||||
−0.985316 | + | 0.170742i | \(0.945383\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.9838 | + | 8.07354i | −0.831249 | + | 0.479922i | −0.854280 | − | 0.519813i | \(-0.826002\pi\) |
0.0230311 | + | 0.999735i | \(0.492668\pi\) | |||||||
\(284\) | −2.20827 | + | 1.27495i | −0.131037 | + | 0.0756542i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 23.8559i | 1.41063i | ||||||||
\(287\) | 6.18518 | − | 21.9395i | 0.365100 | − | 1.29505i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.40798 | − | 14.5630i | 0.494587 | − | 0.856649i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −8.08328 | − | 4.66689i | −0.473038 | − | 0.273109i | ||||
\(293\) | 24.2757 | 1.41820 | 0.709100 | − | 0.705108i | \(-0.249102\pi\) | ||||
0.709100 | + | 0.705108i | \(0.249102\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.928534 | − | 0.536089i | −0.0539699 | − | 0.0311596i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5.01102 | + | 8.67934i | 0.290280 | + | 0.502780i | ||||
\(299\) | 3.55372 | − | 6.15523i | 0.205517 | − | 0.355966i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.94890 | − | 28.1956i | 0.458167 | − | 1.62517i | ||||
\(302\) | − | 14.4120i | − | 0.829316i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −5.30761 | + | 3.06435i | −0.304412 | + | 0.175752i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 19.1856i | − | 1.09498i | −0.836812 | − | 0.547490i | \(-0.815583\pi\) | ||
0.836812 | − | 0.547490i | \(-0.184417\pi\) | |||||||
\(308\) | −11.1435 | + | 10.8577i | −0.634959 | + | 0.618676i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.3473 | − | 28.3143i | −0.926969 | − | 1.60556i | −0.788363 | − | 0.615210i | \(-0.789071\pi\) |
−0.138606 | − | 0.990348i | \(-0.544262\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.9151 | + | 9.76593i | 0.956097 | + | 0.552003i | 0.894970 | − | 0.446127i | \(-0.147197\pi\) |
0.0611276 | + | 0.998130i | \(0.480530\pi\) | |||||||
\(314\) | 10.8711 | 0.613491 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −10.7192 | −0.603003 | ||||||||
\(317\) | 12.6110 | + | 7.28095i | 0.708303 | + | 0.408939i | 0.810432 | − | 0.585832i | \(-0.199232\pi\) |
−0.102129 | + | 0.994771i | \(0.532566\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.123217 | − | 0.213418i | −0.00689882 | − | 0.0119491i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 4.49264 | − | 1.14147i | 0.250365 | − | 0.0636117i | ||||
\(323\) | − | 2.62926i | − | 0.146296i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −9.19935 | + | 5.31125i | −0.509505 | + | 0.294163i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 8.61559i | − | 0.475717i | ||||||
\(329\) | −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 | \(0.0880422\pi\) | |||||||
\(332\) | 5.05134 | + | 8.74919i | 0.277229 | + | 0.480174i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2.99074 | + | 1.72671i | 0.163646 | + | 0.0944812i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.3636 | −0.564543 | −0.282271 | − | 0.959335i | \(-0.591088\pi\) | ||||
−0.282271 | + | 0.959335i | \(0.591088\pi\) | |||||||
\(338\) | −2.99397 | − | 1.72857i | −0.162850 | − | 0.0940217i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 26.9028 | − | 46.5970i | 1.45687 | − | 2.52337i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.5960 | − | 12.5757i | 0.734115 | − | 0.679025i | ||||
\(344\) | − | 11.0724i | − | 0.596981i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.88939 | + | 3.97759i | −0.370376 | + | 0.213837i | ||||
\(347\) | −25.5373 | + | 14.7440i | −1.37091 | + | 0.791497i | −0.991043 | − | 0.133542i | \(-0.957365\pi\) |
−0.379870 | + | 0.925040i | \(0.624031\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.85764i | 0.474138i | 0.971493 | + | 0.237069i | \(0.0761868\pi\) | ||||
−0.971493 | + | 0.237069i | \(0.923813\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.94028 | + | 5.09272i | −0.156718 | + | 0.271443i | ||||
\(353\) | −8.56472 | − | 14.8345i | −0.455854 | − | 0.789562i | 0.542883 | − | 0.839808i | \(-0.317333\pi\) |
−0.998737 | + | 0.0502461i | \(0.983999\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −6.31275 | −0.334575 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.74895 | −0.145286 | ||||||||
\(359\) | −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 | ||||
\(362\) | 3.36601 | − | 5.83010i | 0.176914 | − | 0.306423i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.64305 | − | 10.4026i | −0.138534 | − | 0.545245i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.83644 | + | 1.63762i | −0.148061 | + | 0.0854831i | −0.572200 | − | 0.820114i | \(-0.693910\pi\) |
0.424139 | + | 0.905597i | \(0.360577\pi\) | |||||||
\(368\) | 1.51729 | − | 0.876005i | 0.0790940 | − | 0.0456649i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.56495 | + | 33.7102i | 0.444670 | + | 1.75015i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.7209 | − | 32.4255i | 0.969331 | − | 1.67893i | 0.271834 | − | 0.962344i | \(-0.412370\pi\) |
0.697498 | − | 0.716587i | \(-0.254297\pi\) | |||||||
\(374\) | −1.26141 | − | 2.18482i | −0.0652258 | − | 0.112974i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.834099 | − | 0.481567i | −0.0430154 | − | 0.0248349i | ||||
\(377\) | 0.170004 | 0.00875563 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −37.2066 | −1.91117 | −0.955587 | − | 0.294708i | \(-0.904777\pi\) | ||||
−0.955587 | + | 0.294708i | \(0.904777\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −12.3403 | − | 21.3740i | −0.631383 | − | 1.09359i | ||||
\(383\) | 9.13135 | − | 15.8160i | 0.466590 | − | 0.808158i | −0.532682 | − | 0.846316i | \(-0.678816\pi\) |
0.999272 | + | 0.0381579i | \(0.0121490\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.687221i | 0.0349786i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.24306 | − | 1.29503i | 0.113874 | − | 0.0657454i | ||||
\(389\) | 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 | ||||||||
\(392\) | 3.65628 | − | 5.96922i | 0.184670 | − | 0.301491i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −0.0845770 | + | 0.146492i | −0.00426093 | + | 0.00738014i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.2994 | + | 9.98784i | 0.868234 | + | 0.501275i | 0.866761 | − | 0.498724i | \(-0.166198\pi\) |
0.00147306 | + | 0.999999i | \(0.499531\pi\) | |||||||
\(398\) | −0.415459 | −0.0208251 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 21.2087 | + | 12.2448i | 1.05911 | + | 0.611477i | 0.925186 | − | 0.379514i | \(-0.123909\pi\) |
0.133924 | + | 0.990992i | \(0.457242\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 18.5590 | + | 32.1452i | 0.924490 | + | 1.60126i | ||||
\(404\) | −5.21837 | + | 9.03849i | −0.259624 | + | 0.449682i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.0773750 | + | 0.0794115i | 0.00384006 | + | 0.00394113i | ||||
\(407\) | 6.30502i | 0.312528i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.0020 | − | 8.08403i | 0.692352 | − | 0.399730i | −0.112140 | − | 0.993692i | \(-0.535771\pi\) |
0.804493 | + | 0.593963i | \(0.202437\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 4.94432i | 0.243589i | ||||||||
\(413\) | −34.7366 | + | 8.82575i | −1.70928 | + | 0.434287i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.02837 | − | 3.51324i | −0.0994490 | − | 0.172251i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 31.2117 | + | 18.0201i | 1.52662 | + | 0.881392i | ||||
\(419\) | −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 | \(0.677444\pi\) | |||||||
\(422\) | −1.81982 | − | 1.05067i | −0.0885874 | − | 0.0511460i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6.57304 | + | 11.3848i | 0.319215 | + | 0.552897i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.31143 | + | 2.25215i | −0.111858 | + | 0.108989i | ||||
\(428\) | − | 0.695809i | − | 0.0336332i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.08126 | + | 1.77897i | −0.148419 | + | 0.0856899i | −0.572371 | − | 0.819995i | \(-0.693976\pi\) |
0.423951 | + | 0.905685i | \(0.360643\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.86329i | 0.473999i | 0.971510 | + | 0.237000i | \(0.0761641\pi\) | ||||
−0.971510 | + | 0.237000i | \(0.923836\pi\) | |||||||
\(434\) | −6.56863 | + | 23.2997i | −0.315304 | + | 1.11842i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.98417 | − | 5.16874i | 0.142916 | − | 0.247538i | ||||
\(437\) | −5.36877 | − | 9.29898i | −0.256823 | − | 0.444831i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.1701 | − | 7.02641i | −0.580847 | − | 0.335352i | 0.180623 | − | 0.983552i | \(-0.442189\pi\) |
−0.761470 | + | 0.648200i | \(0.775522\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.74038 | 0.0827812 | ||||||||
\(443\) | −13.3752 | − | 7.72219i | −0.635476 | − | 0.366892i | 0.147394 | − | 0.989078i | \(-0.452912\pi\) |
−0.782870 | + | 0.622186i | \(0.786245\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 12.9973 | − | 22.5120i | 0.615440 | − | 1.06597i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.717905 | − | 2.54649i | 0.0339178 | − | 0.120310i | ||||
\(449\) | 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 | ||||
\(452\) | 0.701389 | − | 0.404947i | 0.0329906 | − | 0.0190471i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 14.3073i | − | 0.671473i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.58150 | + | 11.3995i | −0.307870 | + | 0.533246i | −0.977896 | − | 0.209091i | \(-0.932949\pi\) |
0.670026 | + | 0.742337i | \(0.266283\pi\) | |||||||
\(458\) | −0.789445 | − | 1.36736i | −0.0368883 | − | 0.0638925i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 20.7565 | 0.966725 | 0.483363 | − | 0.875420i | \(-0.339415\pi\) | ||||
0.483363 | + | 0.875420i | \(0.339415\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.7932 | −0.826920 | −0.413460 | − | 0.910522i | \(-0.635680\pi\) | ||||
−0.413460 | + | 0.910522i | \(0.635680\pi\) | |||||||
\(464\) | 0.0362921 | + | 0.0209532i | 0.00168482 | + | 0.000972730i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9.13044 | + | 15.8144i | 0.422960 | + | 0.732587i | ||||
\(467\) | 1.08094 | − | 1.87225i | 0.0500201 | − | 0.0866373i | −0.839931 | − | 0.542693i | \(-0.817405\pi\) |
0.889951 | + | 0.456055i | \(0.150738\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −32.4305 | + | 8.23982i | −1.49750 | + | 0.380479i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −11.7315 | + | 6.77318i | −0.539986 | + | 0.311761i | ||||
\(473\) | −56.3884 | + | 32.5559i | −2.59274 | + | 1.49692i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.792110 | + | 0.812958i | 0.0363063 | + | 0.0372619i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 11.5901 | − | 20.0746i | 0.530117 | − | 0.918190i | ||||
\(479\) | −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 | ||||
\(482\) | −12.9430 | −0.589539 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 23.5811 | 1.07187 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.15363 | + | 5.46224i | 0.142904 | + | 0.247518i | 0.928589 | − | 0.371109i | \(-0.121022\pi\) |
−0.785685 | + | 0.618627i | \(0.787689\pi\) | |||||||
\(488\) | −0.609885 | + | 1.05635i | −0.0276082 | + | 0.0478188i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.6640i | 0.661776i | 0.943670 | + | 0.330888i | \(0.107348\pi\) | ||||
−0.943670 | + | 0.330888i | \(0.892652\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.0155696 | + | 0.00898912i | −0.000701220 | + | 0.000404849i | ||||
\(494\) | −21.5316 | + | 12.4313i | −0.968752 | + | 0.559309i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9.14972i | 0.410835i | ||||||||
\(497\) | −6.49328 | − | 1.83058i | −0.291264 | − | 0.0821129i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.1113 | − | 20.9774i | 0.542176 | − | 0.939076i | −0.456603 | − | 0.889670i | \(-0.650934\pi\) |
0.998779 | − | 0.0494053i | \(-0.0157326\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 19.6806 | + | 11.3626i | 0.878390 | + | 0.507139i | ||||
\(503\) | 34.9707 | 1.55927 | 0.779633 | − | 0.626237i | \(-0.215406\pi\) | ||||
0.779633 | + | 0.626237i | \(0.215406\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −8.92250 | − | 5.15141i | −0.396653 | − | 0.229008i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −5.51324 | − | 9.54921i | −0.244610 | − | 0.423678i | ||||
\(509\) | 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 | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −6.06331 | + | 3.50065i | −0.267441 | + | 0.154407i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.66377i | 0.249092i | ||||||||
\(518\) | −0.698547 | − | 2.74936i | −0.0306924 | − | 0.120800i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.0953 | + | 17.4855i | 0.442282 | + | 0.766054i | 0.997858 | − | 0.0654110i | \(-0.0208358\pi\) |
−0.555577 | + | 0.831465i | \(0.687503\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.69476 | + | 5.01992i | 0.380195 | + | 0.219506i | 0.677903 | − | 0.735151i | \(-0.262889\pi\) |
−0.297708 | + | 0.954657i | \(0.596222\pi\) | |||||||
\(524\) | 18.8816 | 0.824847 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 12.0194 | 0.524073 | ||||||||
\(527\) | −3.39942 | − | 1.96265i | −0.148081 | − | 0.0854946i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.96523 | − | 17.2603i | −0.433271 | − | 0.750447i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −15.6067 | − | 4.39982i | −0.676635 | − | 0.190757i | ||||
\(533\) | − | 34.9512i | − | 1.51391i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −10.9527 | + | 6.32352i | −0.473083 | + | 0.273135i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 1.22358i | − | 0.0527525i | ||||||
\(539\) | −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 | \(0.0447994\pi\) | |||||||
\(542\) | 8.19190 | + | 14.1888i | 0.351872 | + | 0.609461i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.371532 | + | 0.214504i | 0.0159293 | + | 0.00919679i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 32.6253 | 1.39496 | 0.697478 | − | 0.716606i | \(-0.254305\pi\) | ||||
0.697478 | + | 0.716606i | \(0.254305\pi\) | |||||||
\(548\) | −12.4458 | − | 7.18560i | −0.531659 | − | 0.306954i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.128416 | − | 0.222423i | 0.00547071 | − | 0.00947555i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −19.7917 | − | 20.3126i | −0.841628 | − | 0.863780i | ||||
\(554\) | − | 13.1742i | − | 0.559720i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −14.5189 | + | 8.38250i | −0.615739 | + | 0.355497i | ||||
\(557\) | 29.5585 | − | 17.0656i | 1.25243 | − | 0.723094i | 0.280842 | − | 0.959754i | \(-0.409386\pi\) |
0.971592 | + | 0.236660i | \(0.0760528\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 44.9177i | − | 1.89981i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.86216 | + | 4.95741i | −0.120733 | + | 0.209116i | ||||
\(563\) | 14.8964 | + | 25.8012i | 0.627806 | + | 1.08739i | 0.987991 | + | 0.154512i | \(0.0493804\pi\) |
−0.360185 | + | 0.932881i | \(0.617286\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −16.1471 | −0.678712 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.54990 | −0.106991 | ||||||||
\(569\) | 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 | \(0.820218\pi\) | |||||||
\(572\) | −11.9280 | + | 20.6598i | −0.498733 | + | 0.863831i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 16.3263 | − | 15.9076i | 0.681446 | − | 0.663970i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 34.6146 | − | 19.9848i | 1.44103 | − | 0.831977i | 0.443108 | − | 0.896468i | \(-0.353876\pi\) |
0.997918 | + | 0.0644912i | \(0.0205424\pi\) | |||||||
\(578\) | 14.5630 | − | 8.40798i | 0.605743 | − | 0.349726i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.25277 | + | 25.7264i | −0.300896 | + | 1.06731i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 38.6532 | − | 66.9493i | 1.60085 | − | 2.77276i | ||||
\(584\) | −4.66689 | − | 8.08328i | −0.193117 | − | 0.334489i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 21.0233 | + | 12.1378i | 0.868466 | + | 0.501409i | ||||
\(587\) | −25.5123 | −1.05300 | −0.526502 | − | 0.850174i | \(-0.676497\pi\) | ||||
−0.526502 | + | 0.850174i | \(0.676497\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 56.0759 | 2.31057 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.536089 | − | 0.928534i | −0.0220331 | − | 0.0381625i | ||||
\(593\) | 20.1656 | − | 34.9279i | 0.828103 | − | 1.43432i | −0.0714207 | − | 0.997446i | \(-0.522753\pi\) |
0.899524 | − | 0.436871i | \(-0.143913\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 10.0220i | 0.410519i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 6.15523 | − | 3.55372i | 0.251706 | − | 0.145323i | ||||
\(599\) | 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 | \(0.822513\pi\) | |||||||
\(602\) | 20.9818 | − | 20.4437i | 0.855153 | − | 0.833223i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 7.20599 | − | 12.4811i | 0.293207 | − | 0.507850i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −32.8311 | − | 18.9551i | −1.33257 | − | 0.769362i | −0.346881 | − | 0.937909i | \(-0.612759\pi\) |
−0.985694 | + | 0.168547i | \(0.946092\pi\) | |||||||
\(608\) | −6.12870 | −0.248552 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.38372 | − | 1.95359i | −0.136891 | − | 0.0790339i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.4012 | − | 18.0154i | −0.420101 | − | 0.727637i | 0.575848 | − | 0.817557i | \(-0.304672\pi\) |
−0.995949 | + | 0.0899202i | \(0.971339\pi\) | |||||||
\(614\) | 9.59280 | − | 16.6152i | 0.387134 | − | 0.670536i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −15.0794 | + | 3.83131i | −0.607566 | + | 0.154368i | ||||
\(617\) | − | 40.9298i | − | 1.64777i | −0.566755 | − | 0.823887i | \(-0.691801\pi\) | ||
0.566755 | − | 0.823887i | \(-0.308199\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −23.2122 | + | 13.4016i | −0.932976 | + | 0.538654i | −0.887752 | − | 0.460323i | \(-0.847734\pi\) |
−0.0452247 | + | 0.998977i | \(0.514400\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 32.6946i | − | 1.31093i | ||||||
\(623\) | −11.6557 | − | 11.9625i | −0.466975 | − | 0.479266i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 9.76593 | + | 16.9151i | 0.390325 | + | 0.676063i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 9.41463 | + | 5.43554i | 0.375685 | + | 0.216902i | ||||
\(629\) | 0.459974 | 0.0183404 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.28749 | −0.0910636 | −0.0455318 | − | 0.998963i | \(-0.514498\pi\) | ||||
−0.0455318 | + | 0.998963i | \(0.514498\pi\) | |||||||
\(632\) | −9.28312 | − | 5.35961i | −0.369263 | − | 0.213194i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 7.28095 | + | 12.6110i | 0.289164 | + | 0.500846i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 14.8326 | − | 24.2156i | 0.587687 | − | 0.959457i | ||||
\(638\) | − | 0.246434i | − | 0.00975641i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.82398 | − | 1.05307i | 0.0720428 | − | 0.0415939i | −0.463546 | − | 0.886073i | \(-0.653423\pi\) |
0.535589 | + | 0.844479i | \(0.320090\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 44.2035i | − | 1.74322i | −0.490203 | − | 0.871608i | \(-0.663077\pi\) | ||
0.490203 | − | 0.871608i | \(-0.336923\pi\) | |||||||
\(644\) | 4.46148 | + | 1.25778i | 0.175807 | + | 0.0495634i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.31463 | − | 2.27701i | 0.0517235 | − | 0.0895877i | ||||
\(647\) | −10.3540 | − | 17.9336i | −0.407058 | − | 0.705044i | 0.587501 | − | 0.809223i | \(-0.300112\pi\) |
−0.994559 | + | 0.104179i | \(0.966779\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 68.9878 | + | 39.8302i | 2.70801 | + | 1.56347i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −10.6225 | −0.416009 | ||||||||
\(653\) | −23.3860 | − | 13.5019i | −0.915164 | − | 0.528370i | −0.0330748 | − | 0.999453i | \(-0.510530\pi\) |
−0.882089 | + | 0.471083i | \(0.843863\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 4.30780 | − | 7.46132i | 0.168191 | − | 0.291316i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.627502 | − | 2.46974i | −0.0244626 | − | 0.0962806i | ||||
\(659\) | − | 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 | \(0.631398\pi\) | |||||||
\(662\) | 7.70473 | − | 4.44833i | 0.299453 | − | 0.172889i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 10.1027i | 0.392060i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.0367103 | + | 0.0635841i | −0.00142143 | + | 0.00246199i | ||||
\(668\) | 1.72671 | + | 2.99074i | 0.0668083 | + | 0.115715i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.17294 | 0.276908 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15.2809 | −0.589037 | −0.294518 | − | 0.955646i | \(-0.595159\pi\) | ||||
−0.294518 | + | 0.955646i | \(0.595159\pi\) | |||||||
\(674\) | −8.97517 | − | 5.18182i | −0.345711 | − | 0.199596i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.72857 | − | 2.99397i | −0.0664834 | − | 0.115153i | ||||
\(677\) | −24.2831 | + | 42.0596i | −0.933277 | + | 1.61648i | −0.155598 | + | 0.987820i | \(0.549730\pi\) |
−0.777679 | + | 0.628662i | \(0.783603\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.59558 | + | 1.85942i | 0.253115 | + | 0.0713581i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 46.5970 | − | 26.9028i | 1.78429 | − | 1.03016i | ||||
\(683\) | 10.6643 | − | 6.15706i | 0.408059 | − | 0.235593i | −0.281896 | − | 0.959445i | \(-0.590963\pi\) |
0.689956 | + | 0.723852i | \(0.257630\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 18.0623 | − | 4.09288i | 0.689624 | − | 0.156267i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.53618 | − | 9.58894i | 0.211065 | − | 0.365575i | ||||
\(689\) | 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 | \(0.366747\pi\) | |||||||
\(692\) | −7.95518 | −0.302411 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −29.4879 | −1.11935 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.84808 | + | 3.20097i | 0.0700011 | + | 0.121245i | ||||
\(698\) | −4.42882 | + | 7.67094i | −0.167633 | + | 0.290349i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.16278i | 0.0816870i | 0.999166 | + | 0.0408435i | \(0.0130045\pi\) | ||||
−0.999166 | + | 0.0408435i | \(0.986995\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.69071 | + | 3.28553i | −0.214629 | + | 0.123916i | ||||
\(704\) | −5.09272 | + | 2.94028i | −0.191939 | + | 0.110816i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 17.1294i | − | 0.644675i | ||||||
\(707\) | −26.7627 | + | 6.79976i | −1.00652 | + | 0.255731i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.4912 | − | 18.1712i | 0.394004 | − | 0.682435i | −0.598969 | − | 0.800772i | \(-0.704423\pi\) |
0.992974 | + | 0.118337i | \(0.0377562\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −5.46700 | − | 3.15638i | −0.204885 | − | 0.118290i | ||||
\(713\) | −16.0304 | −0.600343 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.38066 | − | 1.37447i | −0.0889694 | − | 0.0513665i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −11.0272 | − | 19.0997i | −0.411531 | − | 0.712793i | ||||
\(719\) | −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 | ||||
\(722\) | 18.5609i | 0.690767i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5.83010 | − | 3.36601i | 0.216674 | − | 0.125097i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 12.4470i | − | 0.461633i | −0.972997 | − | 0.230816i | \(-0.925860\pi\) | ||
0.972997 | − | 0.230816i | \(-0.0741397\pi\) | |||||||
\(728\) | 2.91235 | − | 10.3304i | 0.107939 | − | 0.382872i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.37507 | + | 4.11374i | 0.0878450 | + | 0.152152i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.3654 | + | 11.1806i | 0.715279 | + | 0.412966i | 0.813012 | − | 0.582246i | \(-0.197826\pi\) |
−0.0977339 | + | 0.995213i | \(0.531159\pi\) | |||||||
\(734\) | −3.27524 | −0.120891 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.75201 | 0.0645800 | ||||||||
\(737\) | 64.4079 | + | 37.1859i | 2.37249 | + | 1.36976i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.9125 | + | 27.5613i | 0.585351 | + | 1.01386i | 0.994832 | + | 0.101539i | \(0.0323765\pi\) |
−0.409481 | + | 0.912319i | \(0.634290\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −9.43764 | + | 33.4764i | −0.346467 | + | 1.22896i | ||||
\(743\) | − | 15.1736i | − | 0.556667i | −0.960485 | − | 0.278333i | \(-0.910218\pi\) | ||
0.960485 | − | 0.278333i | \(-0.0897820\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 32.4255 | − | 18.7209i | 1.18718 | − | 0.685421i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 2.52281i | − | 0.0922432i | ||||||
\(749\) | 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 | \(0.0415607\pi\) | |||||||
\(752\) | −0.481567 | − | 0.834099i | −0.0175609 | − | 0.0304164i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.147227 | + | 0.0850018i | 0.00536171 | + | 0.00309558i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17.0421 | 0.619407 | 0.309704 | − | 0.950833i | \(-0.399770\pi\) | ||||
0.309704 | + | 0.950833i | \(0.399770\pi\) | |||||||
\(758\) | −32.2219 | − | 18.6033i | −1.17035 | − | 0.675702i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.13659 | − | 5.43274i | 0.113701 | − | 0.196937i | −0.803559 | − | 0.595226i | \(-0.797063\pi\) |
0.917260 | + | 0.398289i | \(0.130396\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15.3045 | − | 3.88850i | 0.554060 | − | 0.140773i | ||||
\(764\) | − | 24.6805i | − | 0.892911i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 15.8160 | − | 9.13135i | 0.571454 | − | 0.329929i | ||||
\(767\) | −47.5916 | + | 27.4770i | −1.71843 | + | 0.992139i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 20.7852i | − | 0.749534i | −0.927119 | − | 0.374767i | \(-0.877723\pi\) | ||
0.927119 | − | 0.374767i | \(-0.122277\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −0.343610 | + | 0.595151i | −0.0123668 | + | 0.0214199i | ||||
\(773\) | −22.2466 | − | 38.5322i | −0.800153 | − | 1.38591i | −0.919515 | − | 0.393055i | \(-0.871418\pi\) |
0.119361 | − | 0.992851i | \(-0.461915\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2.59007 | 0.0929780 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.55326 | 0.0915390 | ||||||||
\(779\) | −45.7282 | − | 26.4012i | −1.63838 | − | 0.945921i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.49741 | + | 12.9859i | 0.268279 | + | 0.464672i | ||||
\(782\) | −0.375814 | + | 0.650928i | −0.0134391 | + | 0.0232771i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 6.15104 | − | 3.34136i | 0.219680 | − | 0.119334i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13.3112 | + | 7.68522i | −0.474493 | + | 0.273948i | −0.718118 | − | 0.695921i | \(-0.754996\pi\) |
0.243626 | + | 0.969869i | \(0.421663\pi\) | |||||||
\(788\) | −0.146492 | + | 0.0845770i | −0.00521855 | + | 0.00301293i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.06239 | + | 0.581427i | 0.0733301 | + | 0.0206732i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.47415 | + | 4.28535i | −0.0878595 | + | 0.152177i | ||||
\(794\) | 9.98784 | + | 17.2994i | 0.354455 | + | 0.613934i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.359798 | − | 0.207730i | −0.0127527 | − | 0.00736278i | ||||
\(797\) | 28.8285 | 1.02116 | 0.510580 | − | 0.859830i | \(-0.329431\pi\) | ||||
0.510580 | + | 0.859830i | \(0.329431\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.413193 | 0.0146177 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 12.2448 | + | 21.2087i | 0.432380 | + | 0.748904i | ||||
\(803\) | −27.4439 | + | 47.5343i | −0.968475 | + | 1.67745i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 37.1180i | 1.30743i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −9.03849 | + | 5.21837i | −0.317973 | + | 0.183582i | ||||
\(809\) | −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 | \(0.690965\pi\) | |||||||
\(812\) | 0.0273030 | + | 0.107460i | 0.000958146 | + | 0.00377110i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3.15251 | + | 5.46031i | −0.110495 | + | 0.191384i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −58.7677 | − | 33.9296i | −2.05602 | − | 1.18705i | ||||
\(818\) | 16.1681 | 0.565303 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −47.2833 | − | 27.2990i | −1.65020 | − | 0.952742i | −0.976989 | − | 0.213290i | \(-0.931582\pi\) |
−0.673209 | − | 0.739452i | \(-0.735085\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.358380 | + | 0.620733i | 0.0124924 | + | 0.0216374i | 0.872204 | − | 0.489142i | \(-0.162690\pi\) |
−0.859712 | + | 0.510780i | \(0.829357\pi\) | |||||||
\(824\) | −2.47216 | + | 4.28191i | −0.0861218 | + | 0.149167i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −34.4957 | − | 9.72501i | −1.20026 | − | 0.338376i | ||||
\(827\) | − | 32.8584i | − | 1.14260i | −0.820742 | − | 0.571299i | \(-0.806440\pi\) | ||
0.820742 | − | 0.571299i | \(-0.193560\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 43.6845 | − | 25.2212i | 1.51722 | − | 0.875970i | 0.517429 | − | 0.855726i | \(-0.326889\pi\) |
0.999795 | − | 0.0202442i | \(-0.00644436\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 4.05674i | − | 0.140642i | ||||||
\(833\) | −0.0780005 | + | 3.00205i | −0.00270256 | + | 0.104015i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 18.0201 | + | 31.2117i | 0.623238 | + | 1.07948i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −12.2657 | − | 7.08162i | −0.423713 | − | 0.244631i | ||||
\(839\) | −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 | ||||||||
\(842\) | −18.8011 | − | 10.8548i | −0.647928 | − | 0.374081i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.05067 | − | 1.81982i | −0.0361657 | − | 0.0626408i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 43.5394 | + | 44.6854i | 1.49603 | + | 1.53541i | ||||
\(848\) | 13.1461i | 0.451439i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.62680 | − | 0.939234i | 0.0557660 | − | 0.0321965i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 25.1282i | 0.860372i | 0.902740 | + | 0.430186i | \(0.141552\pi\) | ||||
−0.902740 | + | 0.430186i | \(0.858448\pi\) | |||||||
\(854\) | −3.12783 | + | 0.794706i | −0.107032 | + | 0.0271943i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.347904 | − | 0.602588i | 0.0118911 | − | 0.0205960i | ||||
\(857\) | −22.6085 | − | 39.1591i | −0.772293 | − | 1.33765i | −0.936304 | − | 0.351192i | \(-0.885777\pi\) |
0.164011 | − | 0.986459i | \(-0.447557\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.3260 | + | 14.0446i | 0.829992 | + | 0.479196i | 0.853850 | − | 0.520519i | \(-0.174262\pi\) |
−0.0238577 | + | 0.999715i | \(0.507595\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3.55794 | −0.121184 | ||||||||
\(863\) | −25.1390 | − | 14.5140i | −0.855740 | − | 0.494062i | 0.00684347 | − | 0.999977i | \(-0.497822\pi\) |
−0.862583 | + | 0.505915i | \(0.831155\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −4.93164 | + | 8.54186i | −0.167584 | + | 0.290264i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −17.3384 | + | 16.8938i | −0.588505 | + | 0.573413i | ||||
\(869\) | 63.0351i | 2.13832i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −44.4321 | + | 25.6529i | −1.50552 | + | 0.869215i | ||||
\(872\) | 5.16874 | − | 2.98417i | 0.175036 | − | 0.101057i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 10.7375i | − | 0.363203i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17.9210 | − | 31.0400i | 0.605148 | − | 1.04815i | −0.386880 | − | 0.922130i | \(-0.626447\pi\) |
0.992028 | − | 0.126017i | \(-0.0402195\pi\) | |||||||
\(878\) | −7.02641 | − | 12.1701i | −0.237130 | − | 0.410721i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16.4620 | 0.554619 | 0.277309 | − | 0.960781i | \(-0.410557\pi\) | ||||
0.277309 | + | 0.960781i | \(0.410557\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 43.5609 | 1.46594 | 0.732971 | − | 0.680260i | \(-0.238133\pi\) | ||||
0.732971 | + | 0.680260i | \(0.238133\pi\) | |||||||
\(884\) | 1.50721 | + | 0.870188i | 0.0506930 | + | 0.0292676i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −7.72219 | − | 13.3752i | −0.259432 | − | 0.449350i | ||||
\(887\) | −19.1749 | + | 33.2119i | −0.643831 | + | 1.11515i | 0.340739 | + | 0.940158i | \(0.389323\pi\) |
−0.984570 | + | 0.174990i | \(0.944011\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.91596 | − | 28.0788i | 0.265493 | − | 0.941733i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 22.5120 | − | 12.9973i | 0.753757 | − | 0.435182i | ||||
\(893\) | −5.11194 | + | 2.95138i | −0.171065 | + | 0.0987641i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.89497 | − | 1.84637i | 0.0633065 | − | 0.0616830i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −0.0799255 | + | 0.138435i | −0.00266715 | + | 0.00461964i | ||||
\(899\) | −0.191716 | − | 0.332062i | −0.00639409 | − | 0.0110749i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.88420 | − | 2.81989i | −0.162716 | − | 0.0939442i | ||||
\(902\) | −50.6646 | −1.68695 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.809894 | 0.0269367 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.4865 | + | 21.6272i | 0.414607 | + | 0.718120i | 0.995387 | − | 0.0959402i | \(-0.0305858\pi\) |
−0.580780 | + | 0.814060i | \(0.697252\pi\) | |||||||
\(908\) | 7.15363 | − | 12.3905i | 0.237402 | − | 0.411192i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.02786i | 0.166580i | 0.996525 | + | 0.0832902i | \(0.0265428\pi\) | ||||
−0.996525 | + | 0.0832902i | \(0.973457\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 51.4502 | − | 29.7048i | 1.70275 | − | 0.983084i | ||||
\(914\) | −11.3995 | + | 6.58150i | −0.377062 | + | 0.217697i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 1.57889i | − | 0.0521680i | ||||||
\(917\) | 34.8625 | + | 35.7801i | 1.15126 | + | 1.18156i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.76087 | + | 9.97811i | −0.190033 | + | 0.329148i | −0.945261 | − | 0.326315i | \(-0.894193\pi\) |
0.755228 | + | 0.655463i | \(0.227526\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 17.9756 | + | 10.3782i | 0.591996 | + | 0.341789i | ||||
\(923\) | −10.3443 | −0.340486 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −15.4094 | − | 8.89659i | −0.506383 | − | 0.292360i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0.0209532 | + | 0.0362921i | 0.000687824 | + | 0.00119135i | ||||
\(929\) | −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 | ||||
\(932\) | 18.2609i | 0.598155i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.87225 | − | 1.08094i | 0.0612618 | − | 0.0353695i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 49.5320i | − | 1.61814i | −0.587713 | − | 0.809070i | \(-0.699972\pi\) | ||
0.587713 | − | 0.809070i | \(-0.300028\pi\) | |||||||
\(938\) | −32.2056 | − | 9.07938i | −1.05155 | − | 0.296452i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 22.4564 | + | 38.8957i | 0.732059 | + | 1.26796i | 0.956002 | + | 0.293361i | \(0.0947739\pi\) |
−0.223942 | + | 0.974602i | \(0.571893\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.0723 | + | 7.54730i | 0.425693 | + | 0.245774i | ||||
\(944\) | −13.5464 | −0.440897 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −65.1117 | −2.11696 | ||||||||
\(947\) | −2.29992 | − | 1.32786i | −0.0747373 | − | 0.0431496i | 0.462166 | − | 0.886794i | \(-0.347073\pi\) |
−0.536903 | + | 0.843644i | \(0.680406\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −18.9323 | − | 32.7918i | −0.614570 | − | 1.06447i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.279508 | + | 1.10010i | 0.00905891 | + | 0.0356543i | ||||
\(953\) | − | 36.5346i | − | 1.18347i | −0.806132 | − | 0.591735i | \(-0.798443\pi\) | ||
0.806132 | − | 0.591735i | \(-0.201557\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 20.0746 | − | 11.5901i | 0.649258 | − | 0.374850i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 13.0035i | − | 0.420125i | ||||||
\(959\) | −9.36314 | − | 36.8517i | −0.302351 | − | 1.19000i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 26.3587 | − | 45.6546i | 0.850280 | − | 1.47273i | ||||
\(962\) | −2.17478 | − | 3.76682i | −0.0701176 | − | 0.121447i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −11.2090 | − | 6.47152i | −0.361018 | − | 0.208434i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 22.6175 | 0.727330 | 0.363665 | − | 0.931530i | \(-0.381525\pi\) | ||||
0.363665 | + | 0.931530i | \(0.381525\pi\) | |||||||
\(968\) | 20.4218 | + | 11.7905i | 0.656381 | + | 0.378962i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.86871 | + | 8.43286i | −0.156244 | + | 0.270623i | −0.933511 | − | 0.358548i | \(-0.883272\pi\) |
0.777267 | + | 0.629171i | \(0.216605\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −42.6919 | − | 12.0357i | −1.36864 | − | 0.385846i | ||||
\(974\) | 6.30725i | 0.202097i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.05635 | + | 0.609885i | −0.0338130 | + | 0.0195220i | ||||
\(977\) | −37.4682 | + | 21.6323i | −1.19871 | + | 0.692078i | −0.960269 | − | 0.279077i | \(-0.909971\pi\) |
−0.238446 | + | 0.971156i | \(0.576638\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 37.1225i | 1.18644i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −7.33199 | + | 12.6994i | −0.233973 | + | 0.405253i | ||||
\(983\) | 17.9821 | + | 31.1460i | 0.573541 | + | 0.993402i | 0.996198 | + | 0.0871125i | \(0.0277640\pi\) |
−0.422658 | + | 0.906289i | \(0.638903\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −0.0179782 | −0.000572544 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −24.8625 | −0.790983 | ||||||||
\(989\) | 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 | \(0.707212\pi\) | |||||||
\(992\) | −4.57486 | + | 7.92389i | −0.145252 | + | 0.251584i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −4.70806 | − | 4.83197i | −0.149331 | − | 0.153261i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −46.5513 | + | 26.8764i | −1.47429 | + | 0.851184i | −0.999581 | − | 0.0289572i | \(-0.990781\pi\) |
−0.474713 | + | 0.880141i | \(0.657448\pi\) | |||||||
\(998\) | 20.9774 | − | 12.1113i | 0.664027 | − | 0.383376i | ||||
\(999\) | 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.bf.e.1601.7 | yes | 24 | |
3.2 | odd | 2 | inner | 3150.2.bf.e.1601.6 | yes | 24 | |
5.2 | odd | 4 | 3150.2.bp.g.1349.3 | 24 | |||
5.3 | odd | 4 | 3150.2.bp.h.1349.10 | 24 | |||
5.4 | even | 2 | 3150.2.bf.d.1601.6 | yes | 24 | ||
7.3 | odd | 6 | inner | 3150.2.bf.e.1151.6 | yes | 24 | |
15.2 | even | 4 | 3150.2.bp.h.1349.3 | 24 | |||
15.8 | even | 4 | 3150.2.bp.g.1349.10 | 24 | |||
15.14 | odd | 2 | 3150.2.bf.d.1601.7 | yes | 24 | ||
21.17 | even | 6 | inner | 3150.2.bf.e.1151.7 | yes | 24 | |
35.3 | even | 12 | 3150.2.bp.h.899.3 | 24 | |||
35.17 | even | 12 | 3150.2.bp.g.899.10 | 24 | |||
35.24 | odd | 6 | 3150.2.bf.d.1151.7 | yes | 24 | ||
105.17 | odd | 12 | 3150.2.bp.h.899.10 | 24 | |||
105.38 | odd | 12 | 3150.2.bp.g.899.3 | 24 | |||
105.59 | even | 6 | 3150.2.bf.d.1151.6 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3150.2.bf.d.1151.6 | ✓ | 24 | 105.59 | even | 6 | ||
3150.2.bf.d.1151.7 | yes | 24 | 35.24 | odd | 6 | ||
3150.2.bf.d.1601.6 | yes | 24 | 5.4 | even | 2 | ||
3150.2.bf.d.1601.7 | yes | 24 | 15.14 | odd | 2 | ||
3150.2.bf.e.1151.6 | yes | 24 | 7.3 | odd | 6 | inner | |
3150.2.bf.e.1151.7 | yes | 24 | 21.17 | even | 6 | inner | |
3150.2.bf.e.1601.6 | yes | 24 | 3.2 | odd | 2 | inner | |
3150.2.bf.e.1601.7 | yes | 24 | 1.1 | even | 1 | trivial | |
3150.2.bp.g.899.3 | 24 | 105.38 | odd | 12 | |||
3150.2.bp.g.899.10 | 24 | 35.17 | even | 12 | |||
3150.2.bp.g.1349.3 | 24 | 5.2 | odd | 4 | |||
3150.2.bp.g.1349.10 | 24 | 15.8 | even | 4 | |||
3150.2.bp.h.899.3 | 24 | 35.3 | even | 12 | |||
3150.2.bp.h.899.10 | 24 | 105.17 | odd | 12 | |||
3150.2.bp.h.1349.3 | 24 | 15.2 | even | 4 | |||
3150.2.bp.h.1349.10 | 24 | 5.3 | odd | 4 |