Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1512,2,Mod(757,1512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1512, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1512.757");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1512.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.0733807856\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 757.13 | ||
Character | \(\chi\) | \(=\) | 1512.757 |
Dual form | 1512.2.c.g.757.14 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1081\) | \(1135\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.417332 | − | 1.35123i | 0.295098 | − | 0.955467i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.65167 | − | 1.12783i | −0.825834 | − | 0.563913i | ||||
\(5\) | − | 3.04340i | − | 1.36105i | −0.732725 | − | 0.680525i | \(-0.761752\pi\) | ||
0.732725 | − | 0.680525i | \(-0.238248\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −2.21325 | + | 1.76111i | −0.782502 | + | 0.622648i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −4.11235 | − | 1.27011i | −1.30044 | − | 0.401643i | ||||
\(11\) | − | 0.128573i | − | 0.0387662i | −0.999812 | − | 0.0193831i | \(-0.993830\pi\) | ||
0.999812 | − | 0.0193831i | \(-0.00617022\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 6.30135i | − | 1.74768i | −0.486214 | − | 0.873840i | \(-0.661622\pi\) | ||
0.486214 | − | 0.873840i | \(-0.338378\pi\) | |||||||
\(14\) | 0.417332 | − | 1.35123i | 0.111537 | − | 0.361133i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.45602 | + | 3.72559i | 0.364005 | + | 0.931397i | ||||
\(17\) | −5.32168 | −1.29070 | −0.645348 | − | 0.763889i | \(-0.723288\pi\) | ||||
−0.645348 | + | 0.763889i | \(0.723288\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.68215i | 1.53299i | 0.642250 | + | 0.766495i | \(0.278001\pi\) | ||||
−0.642250 | + | 0.766495i | \(0.721999\pi\) | |||||||
\(20\) | −3.43243 | + | 5.02669i | −0.767514 | + | 1.12400i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.173732 | − | 0.0536575i | −0.0370398 | − | 0.0114398i | ||||
\(23\) | −5.18212 | −1.08055 | −0.540273 | − | 0.841490i | \(-0.681679\pi\) | ||||
−0.540273 | + | 0.841490i | \(0.681679\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.26229 | −0.852459 | ||||||||
\(26\) | −8.51460 | − | 2.62975i | −1.66985 | − | 0.515737i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.65167 | − | 1.12783i | −0.312136 | − | 0.213139i | ||||
\(29\) | − | 9.96821i | − | 1.85105i | −0.378686 | − | 0.925525i | \(-0.623624\pi\) | ||
0.378686 | − | 0.925525i | \(-0.376376\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.27122 | 0.587528 | 0.293764 | − | 0.955878i | \(-0.405092\pi\) | ||||
0.293764 | + | 0.955878i | \(0.405092\pi\) | |||||||
\(32\) | 5.64179 | − | 0.412618i | 0.997336 | − | 0.0729412i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.22090 | + | 7.19083i | −0.380882 | + | 1.23322i | ||||
\(35\) | − | 3.04340i | − | 0.514429i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.796970i | 0.131021i | 0.997852 | + | 0.0655106i | \(0.0208676\pi\) | ||||
−0.997852 | + | 0.0655106i | \(0.979132\pi\) | |||||||
\(38\) | 9.02915 | + | 2.78867i | 1.46472 | + | 0.452382i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 5.35978 | + | 6.73581i | 0.847455 | + | 1.06502i | ||||
\(41\) | 2.96782 | 0.463496 | 0.231748 | − | 0.972776i | \(-0.425556\pi\) | ||||
0.231748 | + | 0.972776i | \(0.425556\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 6.99100i | − | 1.06612i | −0.846078 | − | 0.533059i | \(-0.821042\pi\) | ||
0.846078 | − | 0.533059i | \(-0.178958\pi\) | |||||||
\(44\) | −0.145008 | + | 0.212360i | −0.0218607 | + | 0.0320145i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.16266 | + | 7.00226i | −0.318867 | + | 1.03243i | ||||
\(47\) | −4.76595 | −0.695186 | −0.347593 | − | 0.937646i | \(-0.613001\pi\) | ||||
−0.347593 | + | 0.937646i | \(0.613001\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.77879 | + | 5.75936i | −0.251559 | + | 0.814496i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −7.10682 | + | 10.4077i | −0.985539 | + | 1.44329i | ||||
\(53\) | 1.14264i | 0.156954i | 0.996916 | + | 0.0784772i | \(0.0250058\pi\) | ||||
−0.996916 | + | 0.0784772i | \(0.974994\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.391299 | −0.0527627 | ||||||||
\(56\) | −2.21325 | + | 1.76111i | −0.295758 | + | 0.235339i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −13.4694 | − | 4.16005i | −1.76862 | − | 0.546241i | ||||
\(59\) | 11.0999i | 1.44508i | 0.691329 | + | 0.722540i | \(0.257025\pi\) | ||||
−0.691329 | + | 0.722540i | \(0.742975\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.6662i | 1.87782i | 0.344165 | + | 0.938909i | \(0.388162\pi\) | ||||
−0.344165 | + | 0.938909i | \(0.611838\pi\) | |||||||
\(62\) | 1.36518 | − | 4.42018i | 0.173378 | − | 0.561364i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.79695 | − | 7.79557i | 0.224619 | − | 0.974447i | ||||
\(65\) | −19.1775 | −2.37868 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.05725i | 0.129163i | 0.997912 | + | 0.0645816i | \(0.0205713\pi\) | ||||
−0.997912 | + | 0.0645816i | \(0.979429\pi\) | |||||||
\(68\) | 8.78965 | + | 6.00192i | 1.06590 | + | 0.727840i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −4.11235 | − | 1.27011i | −0.491520 | − | 0.151807i | ||||
\(71\) | −1.10582 | −0.131237 | −0.0656185 | − | 0.997845i | \(-0.520902\pi\) | ||||
−0.0656185 | + | 0.997845i | \(0.520902\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.1019 | −1.41642 | −0.708212 | − | 0.706000i | \(-0.750498\pi\) | ||||
−0.708212 | + | 0.706000i | \(0.750498\pi\) | |||||||
\(74\) | 1.07689 | + | 0.332601i | 0.125186 | + | 0.0386641i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.53630 | − | 11.0367i | 0.864473 | − | 1.26600i | ||||
\(77\) | − | 0.128573i | − | 0.0146522i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.62426 | 0.295253 | 0.147626 | − | 0.989043i | \(-0.452837\pi\) | ||||
0.147626 | + | 0.989043i | \(0.452837\pi\) | |||||||
\(80\) | 11.3385 | − | 4.43125i | 1.26768 | − | 0.495429i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.23856 | − | 4.01022i | 0.136777 | − | 0.442855i | ||||
\(83\) | − | 6.46403i | − | 0.709520i | −0.934957 | − | 0.354760i | \(-0.884563\pi\) | ||
0.934957 | − | 0.354760i | \(-0.115437\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 16.1960i | 1.75670i | ||||||||
\(86\) | −9.44648 | − | 2.91757i | −1.01864 | − | 0.314609i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.226432 | + | 0.284564i | 0.0241377 | + | 0.0303346i | ||||
\(89\) | 2.23283 | 0.236680 | 0.118340 | − | 0.992973i | \(-0.462243\pi\) | ||||
0.118340 | + | 0.992973i | \(0.462243\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 6.30135i | − | 0.660561i | ||||||
\(92\) | 8.55915 | + | 5.84453i | 0.892353 | + | 0.609334i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.98898 | + | 6.43992i | −0.205148 | + | 0.664227i | ||||
\(95\) | 20.3365 | 2.08648 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.88097 | −0.800192 | −0.400096 | − | 0.916473i | \(-0.631023\pi\) | ||||
−0.400096 | + | 0.916473i | \(0.631023\pi\) | |||||||
\(98\) | 0.417332 | − | 1.35123i | 0.0421569 | − | 0.136495i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 7.03990 | + | 4.80712i | 0.703990 | + | 0.480712i | ||||
\(101\) | − | 16.9693i | − | 1.68851i | −0.535945 | − | 0.844253i | \(-0.680045\pi\) | ||
0.535945 | − | 0.844253i | \(-0.319955\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.7049 | −1.05479 | −0.527393 | − | 0.849621i | \(-0.676830\pi\) | ||||
−0.527393 | + | 0.849621i | \(0.676830\pi\) | |||||||
\(104\) | 11.0974 | + | 13.9465i | 1.08819 | + | 1.36756i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.54398 | + | 0.476862i | 0.149965 | + | 0.0463169i | ||||
\(107\) | − | 1.31462i | − | 0.127089i | −0.997979 | − | 0.0635445i | \(-0.979760\pi\) | ||
0.997979 | − | 0.0635445i | \(-0.0202405\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.2677i | 0.983465i | 0.870746 | + | 0.491732i | \(0.163636\pi\) | ||||
−0.870746 | + | 0.491732i | \(0.836364\pi\) | |||||||
\(110\) | −0.163301 | + | 0.528737i | −0.0155702 | + | 0.0504131i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.45602 | + | 3.72559i | 0.137581 | + | 0.352035i | ||||
\(113\) | 13.1796 | 1.23983 | 0.619916 | − | 0.784668i | \(-0.287166\pi\) | ||||
0.619916 | + | 0.784668i | \(0.287166\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 15.7713i | 1.47068i | ||||||||
\(116\) | −11.2424 | + | 16.4642i | −1.04383 | + | 1.52866i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 14.9985 | + | 4.63232i | 1.38073 | + | 0.426440i | ||||
\(119\) | −5.32168 | −0.487837 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.9835 | 0.998497 | ||||||||
\(122\) | 19.8175 | + | 6.12068i | 1.79419 | + | 0.554140i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −5.40297 | − | 3.68936i | −0.485201 | − | 0.331315i | ||||
\(125\) | − | 2.24514i | − | 0.200811i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.840201 | −0.0745558 | −0.0372779 | − | 0.999305i | \(-0.511869\pi\) | ||||
−0.0372779 | + | 0.999305i | \(0.511869\pi\) | |||||||
\(128\) | −9.78372 | − | 5.68144i | −0.864767 | − | 0.502173i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −8.00339 | + | 25.9133i | −0.701944 | + | 2.27275i | ||||
\(131\) | − | 7.39979i | − | 0.646523i | −0.946310 | − | 0.323261i | \(-0.895221\pi\) | ||
0.946310 | − | 0.323261i | \(-0.104779\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.68215i | 0.579416i | ||||||||
\(134\) | 1.42859 | + | 0.441222i | 0.123411 | + | 0.0381158i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 11.7782 | − | 9.37208i | 1.00997 | − | 0.803649i | ||||
\(137\) | −5.61682 | −0.479877 | −0.239939 | − | 0.970788i | \(-0.577127\pi\) | ||||
−0.239939 | + | 0.970788i | \(0.577127\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.19553i | 0.440679i | 0.975423 | + | 0.220339i | \(0.0707165\pi\) | ||||
−0.975423 | + | 0.220339i | \(0.929284\pi\) | |||||||
\(140\) | −3.43243 | + | 5.02669i | −0.290093 | + | 0.424833i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.461495 | + | 1.49423i | −0.0387278 | + | 0.125393i | ||||
\(143\) | −0.810183 | −0.0677509 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −30.3373 | −2.51937 | ||||||||
\(146\) | −5.05052 | + | 16.3525i | −0.417984 | + | 1.35335i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.898844 | − | 1.31633i | 0.0738845 | − | 0.108202i | ||||
\(149\) | − | 11.6207i | − | 0.952009i | −0.879443 | − | 0.476004i | \(-0.842085\pi\) | ||
0.879443 | − | 0.476004i | \(-0.157915\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 21.5154 | 1.75090 | 0.875448 | − | 0.483313i | \(-0.160567\pi\) | ||||
0.875448 | + | 0.483313i | \(0.160567\pi\) | |||||||
\(152\) | −11.7680 | − | 14.7893i | −0.954514 | − | 1.19957i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.173732 | − | 0.0536575i | −0.0139997 | − | 0.00432385i | ||||
\(155\) | − | 9.95563i | − | 0.799655i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 18.3001i | − | 1.46050i | −0.683178 | − | 0.730252i | \(-0.739403\pi\) | ||
0.683178 | − | 0.730252i | \(-0.260597\pi\) | |||||||
\(158\) | 1.09519 | − | 3.54599i | 0.0871284 | − | 0.282104i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.25576 | − | 17.1702i | −0.0992767 | − | 1.35743i | ||||
\(161\) | −5.18212 | −0.408408 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 18.8550i | − | 1.47684i | −0.674344 | − | 0.738418i | \(-0.735573\pi\) | ||
0.674344 | − | 0.738418i | \(-0.264427\pi\) | |||||||
\(164\) | −4.90185 | − | 3.34718i | −0.382771 | − | 0.261371i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.73442 | − | 2.69764i | −0.677922 | − | 0.209378i | ||||
\(167\) | −20.8283 | −1.61174 | −0.805872 | − | 0.592089i | \(-0.798303\pi\) | ||||
−0.805872 | + | 0.592089i | \(0.798303\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −26.7070 | −2.05438 | ||||||||
\(170\) | 21.8846 | + | 6.75910i | 1.67847 | + | 0.518399i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −7.88463 | + | 11.5468i | −0.601198 | + | 0.880437i | ||||
\(173\) | − | 5.49174i | − | 0.417529i | −0.977966 | − | 0.208765i | \(-0.933056\pi\) | ||
0.977966 | − | 0.208765i | \(-0.0669443\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.26229 | −0.322199 | ||||||||
\(176\) | 0.479010 | − | 0.187205i | 0.0361067 | − | 0.0141111i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.931830 | − | 3.01708i | 0.0698436 | − | 0.226139i | ||||
\(179\) | − | 7.62941i | − | 0.570249i | −0.958491 | − | 0.285124i | \(-0.907965\pi\) | ||
0.958491 | − | 0.285124i | \(-0.0920349\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 10.0176i | − | 0.744600i | −0.928113 | − | 0.372300i | \(-0.878569\pi\) | ||
0.928113 | − | 0.372300i | \(-0.121431\pi\) | |||||||
\(182\) | −8.51460 | − | 2.62975i | −0.631144 | − | 0.194930i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 11.4693 | − | 9.12631i | 0.845530 | − | 0.672800i | ||||
\(185\) | 2.42550 | 0.178326 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.684223i | 0.0500354i | ||||||||
\(188\) | 7.87178 | + | 5.37516i | 0.574108 | + | 0.392024i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 8.48705 | − | 27.4793i | 0.615715 | − | 1.99356i | ||||
\(191\) | 6.25601 | 0.452669 | 0.226335 | − | 0.974050i | \(-0.427326\pi\) | ||||
0.226335 | + | 0.974050i | \(0.427326\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.46446 | 0.177396 | 0.0886980 | − | 0.996059i | \(-0.471729\pi\) | ||||
0.0886980 | + | 0.996059i | \(0.471729\pi\) | |||||||
\(194\) | −3.28898 | + | 10.6490i | −0.236135 | + | 0.764557i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.65167 | − | 1.12783i | −0.117976 | − | 0.0805590i | ||||
\(197\) | 23.8105i | 1.69643i | 0.529654 | + | 0.848214i | \(0.322322\pi\) | ||||
−0.529654 | + | 0.848214i | \(0.677678\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 24.1296 | 1.71050 | 0.855252 | − | 0.518212i | \(-0.173402\pi\) | ||||
0.855252 | + | 0.518212i | \(0.173402\pi\) | |||||||
\(200\) | 9.43352 | − | 7.50639i | 0.667051 | − | 0.530782i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −22.9295 | − | 7.08181i | −1.61331 | − | 0.498274i | ||||
\(203\) | − | 9.96821i | − | 0.699631i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 9.03227i | − | 0.630841i | ||||||
\(206\) | −4.46750 | + | 14.4648i | −0.311265 | + | 1.00781i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 23.4762 | − | 9.17488i | 1.62778 | − | 0.636164i | ||||
\(209\) | 0.859144 | 0.0594282 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 14.9668i | − | 1.03036i | −0.857083 | − | 0.515179i | \(-0.827726\pi\) | ||
0.857083 | − | 0.515179i | \(-0.172274\pi\) | |||||||
\(212\) | 1.28870 | − | 1.88727i | 0.0885085 | − | 0.129618i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.77636 | − | 0.548632i | −0.121429 | − | 0.0375037i | ||||
\(215\) | −21.2764 | −1.45104 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.27122 | 0.222065 | ||||||||
\(218\) | 13.8740 | + | 4.28502i | 0.939668 | + | 0.290218i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.646296 | + | 0.441317i | 0.0435733 | + | 0.0297536i | ||||
\(221\) | 33.5337i | 2.25572i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.6108 | 0.777518 | 0.388759 | − | 0.921340i | \(-0.372904\pi\) | ||||
0.388759 | + | 0.921340i | \(0.372904\pi\) | |||||||
\(224\) | 5.64179 | − | 0.412618i | 0.376958 | − | 0.0275692i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.50026 | − | 17.8087i | 0.365872 | − | 1.18462i | ||||
\(227\) | − | 0.939445i | − | 0.0623531i | −0.999514 | − | 0.0311766i | \(-0.990075\pi\) | ||
0.999514 | − | 0.0311766i | \(-0.00992542\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 0.0137124i | − | 0.000906143i | −1.00000 | 0.000453071i | \(-0.999856\pi\) | |||
1.00000 | 0.000453071i | \(-0.000144217\pi\) | ||||||||
\(230\) | 21.3107 | + | 6.58185i | 1.40519 | + | 0.433994i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 17.5552 | + | 22.0621i | 1.15255 | + | 1.44845i | ||||
\(233\) | 18.2195 | 1.19360 | 0.596800 | − | 0.802390i | \(-0.296439\pi\) | ||||
0.596800 | + | 0.802390i | \(0.296439\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 14.5047i | 0.946183i | ||||||||
\(236\) | 12.5187 | − | 18.3333i | 0.814899 | − | 1.19340i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.22090 | + | 7.19083i | −0.143960 | + | 0.466112i | ||||
\(239\) | −1.37153 | −0.0887169 | −0.0443585 | − | 0.999016i | \(-0.514124\pi\) | ||||
−0.0443585 | + | 0.999016i | \(0.514124\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.5054 | −0.676711 | −0.338355 | − | 0.941018i | \(-0.609871\pi\) | ||||
−0.338355 | + | 0.941018i | \(0.609871\pi\) | |||||||
\(242\) | 4.58375 | − | 14.8412i | 0.294654 | − | 0.954031i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 16.5409 | − | 24.2238i | 1.05893 | − | 1.55077i | ||||
\(245\) | − | 3.04340i | − | 0.194436i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 42.1066 | 2.67918 | ||||||||
\(248\) | −7.24002 | + | 5.76099i | −0.459742 | + | 0.365823i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −3.03371 | − | 0.936967i | −0.191869 | − | 0.0592590i | ||||
\(251\) | − | 20.0556i | − | 1.26590i | −0.774192 | − | 0.632950i | \(-0.781844\pi\) | ||
0.774192 | − | 0.632950i | \(-0.218156\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.666280i | 0.0418887i | ||||||||
\(254\) | −0.350643 | + | 1.13531i | −0.0220013 | + | 0.0712356i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −11.7600 | + | 10.8491i | −0.735001 | + | 0.678066i | ||||
\(257\) | −24.6631 | −1.53844 | −0.769220 | − | 0.638984i | \(-0.779355\pi\) | ||||
−0.769220 | + | 0.638984i | \(0.779355\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.796970i | 0.0495213i | ||||||||
\(260\) | 31.6749 | + | 21.6289i | 1.96440 | + | 1.34137i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −9.99885 | − | 3.08817i | −0.617731 | − | 0.190788i | ||||
\(263\) | −14.0542 | −0.866616 | −0.433308 | − | 0.901246i | \(-0.642654\pi\) | ||||
−0.433308 | + | 0.901246i | \(0.642654\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.47753 | 0.213623 | ||||||||
\(266\) | 9.02915 | + | 2.78867i | 0.553613 | + | 0.170984i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.19239 | − | 1.74622i | 0.0728368 | − | 0.106667i | ||||
\(269\) | − | 13.1276i | − | 0.800404i | −0.916427 | − | 0.400202i | \(-0.868940\pi\) | ||
0.916427 | − | 0.400202i | \(-0.131060\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.4626 | −0.939285 | −0.469642 | − | 0.882857i | \(-0.655617\pi\) | ||||
−0.469642 | + | 0.882857i | \(0.655617\pi\) | |||||||
\(272\) | −7.74846 | − | 19.8264i | −0.469820 | − | 1.20215i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.34407 | + | 7.58964i | −0.141611 | + | 0.458507i | ||||
\(275\) | 0.548015i | 0.0330466i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 11.1880i | − | 0.672223i | −0.941822 | − | 0.336112i | \(-0.890888\pi\) | ||
0.941822 | − | 0.336112i | \(-0.109112\pi\) | |||||||
\(278\) | 7.02037 | + | 2.16826i | 0.421054 | + | 0.130043i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 5.35978 | + | 6.73581i | 0.320308 | + | 0.402542i | ||||
\(281\) | 0.179766 | 0.0107240 | 0.00536198 | − | 0.999986i | \(-0.498293\pi\) | ||||
0.00536198 | + | 0.999986i | \(0.498293\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 29.0480i | − | 1.72673i | −0.504583 | − | 0.863363i | \(-0.668354\pi\) | ||
0.504583 | − | 0.863363i | \(-0.331646\pi\) | |||||||
\(284\) | 1.82645 | + | 1.24717i | 0.108380 | + | 0.0740062i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.338115 | + | 1.09475i | −0.0199931 | + | 0.0647337i | ||||
\(287\) | 2.96782 | 0.175185 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.3202 | 0.665897 | ||||||||
\(290\) | −12.6607 | + | 40.9928i | −0.743462 | + | 2.40718i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 19.9884 | + | 13.6489i | 1.16973 | + | 0.798739i | ||||
\(293\) | − | 4.42498i | − | 0.258510i | −0.991611 | − | 0.129255i | \(-0.958741\pi\) | ||
0.991611 | − | 0.129255i | \(-0.0412586\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 33.7813 | 1.96683 | ||||||||
\(296\) | −1.40356 | − | 1.76389i | −0.0815800 | − | 0.102524i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −15.7024 | − | 4.84970i | −0.909613 | − | 0.280936i | ||||
\(299\) | 32.6543i | 1.88845i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 6.99100i | − | 0.402955i | ||||||
\(302\) | 8.97904 | − | 29.0723i | 0.516686 | − | 1.67292i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −24.8949 | + | 9.72934i | −1.42782 | + | 0.558016i | ||||
\(305\) | 44.6352 | 2.55581 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.36831i | 0.477605i | 0.971068 | + | 0.238802i | \(0.0767548\pi\) | ||||
−0.971068 | + | 0.238802i | \(0.923245\pi\) | |||||||
\(308\) | −0.145008 | + | 0.212360i | −0.00826259 | + | 0.0121003i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −13.4524 | − | 4.15480i | −0.764044 | − | 0.235977i | ||||
\(311\) | 28.1701 | 1.59738 | 0.798690 | − | 0.601743i | \(-0.205527\pi\) | ||||
0.798690 | + | 0.601743i | \(0.205527\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.0081 | 0.791784 | 0.395892 | − | 0.918297i | \(-0.370435\pi\) | ||||
0.395892 | + | 0.918297i | \(0.370435\pi\) | |||||||
\(314\) | −24.7277 | − | 7.63719i | −1.39546 | − | 0.430992i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.33441 | − | 2.95971i | −0.243830 | − | 0.166497i | ||||
\(317\) | − | 14.4390i | − | 0.810974i | −0.914101 | − | 0.405487i | \(-0.867102\pi\) | ||
0.914101 | − | 0.405487i | \(-0.132898\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.28164 | −0.0717582 | ||||||||
\(320\) | −23.7251 | − | 5.46885i | −1.32627 | − | 0.305718i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.16266 | + | 7.00226i | −0.120520 | + | 0.390221i | ||||
\(323\) | − | 35.5603i | − | 1.97863i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 26.8582i | 1.48982i | ||||||||
\(326\) | −25.4775 | − | 7.86877i | −1.41107 | − | 0.435811i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −6.56853 | + | 5.22667i | −0.362686 | + | 0.288595i | ||||
\(329\) | −4.76595 | −0.262756 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 32.5738i | − | 1.79042i | −0.445648 | − | 0.895208i | \(-0.647027\pi\) | ||
0.445648 | − | 0.895208i | \(-0.352973\pi\) | |||||||
\(332\) | −7.29030 | + | 10.6764i | −0.400107 | + | 0.585946i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −8.69232 | + | 28.1440i | −0.475623 | + | 1.53997i | ||||
\(335\) | 3.21762 | 0.175798 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.17181 | −0.118306 | −0.0591529 | − | 0.998249i | \(-0.518840\pi\) | ||||
−0.0591529 | + | 0.998249i | \(0.518840\pi\) | |||||||
\(338\) | −11.1457 | + | 36.0874i | −0.606244 | + | 1.96290i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 18.2663 | − | 26.7504i | 0.990627 | − | 1.45075i | ||||
\(341\) | − | 0.420590i | − | 0.0227762i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 12.3120 | + | 15.4728i | 0.663816 | + | 0.834240i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.42063 | − | 2.29188i | −0.398935 | − | 0.123212i | ||||
\(347\) | 2.79477i | 0.150031i | 0.997182 | + | 0.0750157i | \(0.0239007\pi\) | ||||
−0.997182 | + | 0.0750157i | \(0.976099\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 3.19085i | − | 0.170802i | −0.996347 | − | 0.0854011i | \(-0.972783\pi\) | ||
0.996347 | − | 0.0854011i | \(-0.0272172\pi\) | |||||||
\(350\) | −1.77879 | + | 5.75936i | −0.0950803 | + | 0.307851i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.0530515 | − | 0.725381i | −0.00282765 | − | 0.0386629i | ||||
\(353\) | −8.10245 | −0.431250 | −0.215625 | − | 0.976476i | \(-0.569179\pi\) | ||||
−0.215625 | + | 0.976476i | \(0.569179\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.36546i | 0.178620i | ||||||||
\(356\) | −3.68790 | − | 2.51824i | −0.195458 | − | 0.133467i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −10.3091 | − | 3.18399i | −0.544854 | − | 0.168279i | ||||
\(359\) | 17.2635 | 0.911134 | 0.455567 | − | 0.890202i | \(-0.349437\pi\) | ||||
0.455567 | + | 0.890202i | \(0.349437\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −25.6511 | −1.35006 | ||||||||
\(362\) | −13.5361 | − | 4.18064i | −0.711440 | − | 0.219730i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −7.10682 | + | 10.4077i | −0.372499 | + | 0.545514i | ||||
\(365\) | 36.8310i | 1.92782i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.5508 | −0.707348 | −0.353674 | − | 0.935369i | \(-0.615068\pi\) | ||||
−0.353674 | + | 0.935369i | \(0.615068\pi\) | |||||||
\(368\) | −7.54527 | − | 19.3064i | −0.393324 | − | 1.00642i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.01224 | − | 3.27742i | 0.0526238 | − | 0.170385i | ||||
\(371\) | 1.14264i | 0.0593232i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 16.3399i | − | 0.846048i | −0.906118 | − | 0.423024i | \(-0.860969\pi\) | ||
0.906118 | − | 0.423024i | \(-0.139031\pi\) | |||||||
\(374\) | 0.924546 | + | 0.285548i | 0.0478072 | + | 0.0147653i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.5482 | − | 8.39339i | 0.543984 | − | 0.432856i | ||||
\(377\) | −62.8132 | −3.23504 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.37754i | 0.122126i | 0.998134 | + | 0.0610630i | \(0.0194491\pi\) | ||||
−0.998134 | + | 0.0610630i | \(0.980551\pi\) | |||||||
\(380\) | −33.5891 | − | 22.9360i | −1.72309 | − | 1.17659i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.61083 | − | 8.45334i | 0.133582 | − | 0.432511i | ||||
\(383\) | 17.6210 | 0.900389 | 0.450194 | − | 0.892931i | \(-0.351355\pi\) | ||||
0.450194 | + | 0.892931i | \(0.351355\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.391299 | −0.0199424 | ||||||||
\(386\) | 1.02850 | − | 3.33007i | 0.0523492 | − | 0.169496i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 13.0168 | + | 8.88836i | 0.660826 | + | 0.451238i | ||||
\(389\) | 12.6831i | 0.643058i | 0.946900 | + | 0.321529i | \(0.104197\pi\) | ||||
−0.946900 | + | 0.321529i | \(0.895803\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 27.5776 | 1.39466 | ||||||||
\(392\) | −2.21325 | + | 1.76111i | −0.111786 | + | 0.0889497i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 32.1736 | + | 9.93687i | 1.62088 | + | 0.500612i | ||||
\(395\) | − | 7.98668i | − | 0.401854i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 34.3856i | 1.72576i | 0.505405 | + | 0.862882i | \(0.331343\pi\) | ||||
−0.505405 | + | 0.862882i | \(0.668657\pi\) | |||||||
\(398\) | 10.0701 | − | 32.6048i | 0.504767 | − | 1.63433i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −6.20598 | − | 15.8795i | −0.310299 | − | 0.793977i | ||||
\(401\) | 3.75947 | 0.187739 | 0.0938696 | − | 0.995585i | \(-0.470076\pi\) | ||||
0.0938696 | + | 0.995585i | \(0.470076\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 20.6131i | − | 1.02681i | ||||||
\(404\) | −19.1384 | + | 28.0276i | −0.952170 | + | 1.39443i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −13.4694 | − | 4.16005i | −0.668475 | − | 0.206460i | ||||
\(407\) | 0.102469 | 0.00507919 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.0996 | 0.647731 | 0.323866 | − | 0.946103i | \(-0.395017\pi\) | ||||
0.323866 | + | 0.946103i | \(0.395017\pi\) | |||||||
\(410\) | −12.2047 | − | 3.76945i | −0.602748 | − | 0.186160i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 17.6810 | + | 12.0733i | 0.871079 | + | 0.594807i | ||||
\(413\) | 11.0999i | 0.546189i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −19.6726 | −0.965692 | ||||||||
\(416\) | −2.60005 | − | 35.5509i | −0.127478 | − | 1.74302i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.358548 | − | 1.16090i | 0.0175371 | − | 0.0567817i | ||||
\(419\) | − | 24.4344i | − | 1.19370i | −0.802353 | − | 0.596849i | \(-0.796419\pi\) | ||
0.802353 | − | 0.596849i | \(-0.203581\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 26.3907i | − | 1.28620i | −0.765781 | − | 0.643101i | \(-0.777647\pi\) | ||
0.765781 | − | 0.643101i | \(-0.222353\pi\) | |||||||
\(422\) | −20.2237 | − | 6.24612i | −0.984472 | − | 0.304056i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.01233 | − | 2.52896i | −0.0977273 | − | 0.122817i | ||||
\(425\) | 22.6825 | 1.10027 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 14.6662i | 0.709749i | ||||||||
\(428\) | −1.48266 | + | 2.17132i | −0.0716671 | + | 0.104954i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8.87933 | + | 28.7494i | −0.428199 | + | 1.38642i | ||||
\(431\) | −32.7161 | −1.57588 | −0.787940 | − | 0.615751i | \(-0.788853\pi\) | ||||
−0.787940 | + | 0.615751i | \(0.788853\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.3235 | 0.592228 | 0.296114 | − | 0.955153i | \(-0.404309\pi\) | ||||
0.296114 | + | 0.955153i | \(0.404309\pi\) | |||||||
\(434\) | 1.36518 | − | 4.42018i | 0.0655308 | − | 0.212176i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 11.5801 | − | 16.9588i | 0.554588 | − | 0.812179i | ||||
\(437\) | − | 34.6277i | − | 1.65647i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.67878 | 0.223306 | 0.111653 | − | 0.993747i | \(-0.464385\pi\) | ||||
0.111653 | + | 0.993747i | \(0.464385\pi\) | |||||||
\(440\) | 0.866043 | − | 0.689122i | 0.0412870 | − | 0.0328526i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 45.3119 | + | 13.9947i | 2.15527 | + | 0.665659i | ||||
\(443\) | 35.6471i | 1.69364i | 0.531877 | + | 0.846821i | \(0.321487\pi\) | ||||
−0.531877 | + | 0.846821i | \(0.678513\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 6.79540i | − | 0.322133i | ||||||
\(446\) | 4.84556 | − | 15.6889i | 0.229444 | − | 0.742892i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.79695 | − | 7.79557i | 0.0848980 | − | 0.368306i | ||||
\(449\) | −6.02786 | −0.284472 | −0.142236 | − | 0.989833i | \(-0.545429\pi\) | ||||
−0.142236 | + | 0.989833i | \(0.545429\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 0.381581i | − | 0.0179680i | ||||||
\(452\) | −21.7683 | − | 14.8643i | −1.02390 | − | 0.699158i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.26941 | − | 0.392060i | −0.0595764 | − | 0.0184003i | ||||
\(455\) | −19.1775 | −0.899057 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.88761 | 0.228633 | 0.114316 | − | 0.993444i | \(-0.463532\pi\) | ||||
0.114316 | + | 0.993444i | \(0.463532\pi\) | |||||||
\(458\) | −0.0185287 | − | 0.00572263i | −0.000865789 | − | 0.000267401i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 17.7872 | − | 26.0489i | 0.829335 | − | 1.21454i | ||||
\(461\) | − | 9.16306i | − | 0.426766i | −0.976969 | − | 0.213383i | \(-0.931552\pi\) | ||
0.976969 | − | 0.213383i | \(-0.0684483\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 32.8412 | 1.52626 | 0.763130 | − | 0.646245i | \(-0.223662\pi\) | ||||
0.763130 | + | 0.646245i | \(0.223662\pi\) | |||||||
\(464\) | 37.1374 | − | 14.5139i | 1.72406 | − | 0.673791i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.60358 | − | 24.6188i | 0.352229 | − | 1.14045i | ||||
\(467\) | 6.40559i | 0.296415i | 0.988956 | + | 0.148208i | \(0.0473504\pi\) | ||||
−0.988956 | + | 0.148208i | \(0.952650\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.05725i | 0.0488191i | ||||||||
\(470\) | 19.5993 | + | 6.05327i | 0.904047 | + | 0.279217i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −19.5481 | − | 24.5668i | −0.899776 | − | 1.13078i | ||||
\(473\) | −0.898854 | −0.0413293 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 28.4813i | − | 1.30681i | ||||||
\(476\) | 8.78965 | + | 6.00192i | 0.402873 | + | 0.275098i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −0.572383 | + | 1.85326i | −0.0261802 | + | 0.0847661i | ||||
\(479\) | −27.3218 | −1.24837 | −0.624184 | − | 0.781278i | \(-0.714568\pi\) | ||||
−0.624184 | + | 0.781278i | \(0.714568\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.02199 | 0.228983 | ||||||||
\(482\) | −4.38423 | + | 14.1952i | −0.199696 | + | 0.646575i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −18.1411 | − | 12.3874i | −0.824593 | − | 0.563065i | ||||
\(485\) | 23.9850i | 1.08910i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.05264 | 0.410214 | 0.205107 | − | 0.978740i | \(-0.434246\pi\) | ||||
0.205107 | + | 0.978740i | \(0.434246\pi\) | |||||||
\(488\) | −25.8289 | − | 32.4600i | −1.16922 | − | 1.46940i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −4.11235 | − | 1.27011i | −0.185777 | − | 0.0573776i | ||||
\(491\) | 10.1183i | 0.456632i | 0.973587 | + | 0.228316i | \(0.0733219\pi\) | ||||
−0.973587 | + | 0.228316i | \(0.926678\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 53.0476i | 2.38914i | ||||||||
\(494\) | 17.5724 | − | 56.8958i | 0.790619 | − | 2.55986i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.76296 | + | 12.1872i | 0.213863 | + | 0.547222i | ||||
\(497\) | −1.10582 | −0.0496029 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 19.9396i | − | 0.892621i | −0.894878 | − | 0.446310i | \(-0.852738\pi\) | ||
0.894878 | − | 0.446310i | \(-0.147262\pi\) | |||||||
\(500\) | −2.53212 | + | 3.70823i | −0.113240 | + | 0.165837i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −27.0999 | − | 8.36985i | −1.20953 | − | 0.373565i | ||||
\(503\) | −24.3936 | −1.08766 | −0.543828 | − | 0.839197i | \(-0.683026\pi\) | ||||
−0.543828 | + | 0.839197i | \(0.683026\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −51.6443 | −2.29814 | ||||||||
\(506\) | 0.900301 | + | 0.278060i | 0.0400233 | + | 0.0123613i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.38773 | + | 0.947601i | 0.0615708 | + | 0.0420430i | ||||
\(509\) | 7.20394i | 0.319309i | 0.987173 | + | 0.159655i | \(0.0510381\pi\) | ||||
−0.987173 | + | 0.159655i | \(0.948962\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.1019 | −0.535358 | ||||||||
\(512\) | 9.75179 | + | 20.4182i | 0.430972 | + | 0.902365i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −10.2927 | + | 33.3256i | −0.453991 | + | 1.46993i | ||||
\(515\) | 32.5793i | 1.43562i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.612773i | 0.0269497i | ||||||||
\(518\) | 1.07689 | + | 0.332601i | 0.0473160 | + | 0.0146136i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 42.4447 | − | 33.7738i | 1.86132 | − | 1.48108i | ||||
\(521\) | −14.8648 | −0.651240 | −0.325620 | − | 0.945501i | \(-0.605573\pi\) | ||||
−0.325620 | + | 0.945501i | \(0.605573\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 32.1286i | 1.40489i | 0.711740 | + | 0.702443i | \(0.247907\pi\) | ||||
−0.711740 | + | 0.702443i | \(0.752093\pi\) | |||||||
\(524\) | −8.34567 | + | 12.2220i | −0.364582 | + | 0.533921i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.86524 | + | 18.9905i | −0.255737 | + | 0.828023i | ||||
\(527\) | −17.4084 | −0.758320 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.85438 | 0.167582 | ||||||||
\(530\) | 1.45128 | − | 4.69895i | 0.0630396 | − | 0.204109i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 7.53630 | − | 11.0367i | 0.326740 | − | 0.478502i | ||||
\(533\) | − | 18.7013i | − | 0.810042i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.00091 | −0.172975 | ||||||||
\(536\) | −1.86193 | − | 2.33995i | −0.0804232 | − | 0.101070i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −17.7385 | − | 5.47856i | −0.764760 | − | 0.236198i | ||||
\(539\) | − | 0.128573i | − | 0.00553803i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 30.6123i | − | 1.31612i | −0.752964 | − | 0.658062i | \(-0.771376\pi\) | ||
0.752964 | − | 0.658062i | \(-0.228624\pi\) | |||||||
\(542\) | −6.45302 | + | 20.8936i | −0.277181 | + | 0.897456i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −30.0238 | + | 2.19582i | −1.28726 | + | 0.0941449i | ||||
\(545\) | 31.2487 | 1.33855 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.64518i | 0.326884i | 0.986553 | + | 0.163442i | \(0.0522597\pi\) | ||||
−0.986553 | + | 0.163442i | \(0.947740\pi\) | |||||||
\(548\) | 9.27712 | + | 6.33479i | 0.396299 | + | 0.270609i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.740497 | + | 0.228704i | 0.0315749 | + | 0.00975198i | ||||
\(551\) | 66.6091 | 2.83764 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.62426 | 0.111595 | ||||||||
\(554\) | −15.1176 | − | 4.66911i | −0.642287 | − | 0.198372i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.85965 | − | 8.58129i | 0.248504 | − | 0.363928i | ||||
\(557\) | 24.9682i | 1.05794i | 0.848641 | + | 0.528969i | \(0.177421\pi\) | ||||
−0.848641 | + | 0.528969i | \(0.822579\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −44.0527 | −1.86323 | ||||||||
\(560\) | 11.3385 | − | 4.43125i | 0.479137 | − | 0.187255i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.0750222 | − | 0.242907i | 0.00316462 | − | 0.0102464i | ||||
\(563\) | 33.1836i | 1.39852i | 0.714865 | + | 0.699262i | \(0.246488\pi\) | ||||
−0.714865 | + | 0.699262i | \(0.753512\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 40.1108i | − | 1.68748i | ||||||
\(566\) | −39.2507 | − | 12.1227i | −1.64983 | − | 0.509553i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.44746 | − | 1.94748i | 0.102693 | − | 0.0817144i | ||||
\(569\) | 17.0679 | 0.715523 | 0.357761 | − | 0.933813i | \(-0.383540\pi\) | ||||
0.357761 | + | 0.933813i | \(0.383540\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.13058i | 0.214708i | 0.994221 | + | 0.107354i | \(0.0342378\pi\) | ||||
−0.994221 | + | 0.107354i | \(0.965762\pi\) | |||||||
\(572\) | 1.33815 | + | 0.913745i | 0.0559510 | + | 0.0382056i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.23856 | − | 4.01022i | 0.0516967 | − | 0.167383i | ||||
\(575\) | 22.0877 | 0.921121 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −47.5819 | −1.98086 | −0.990429 | − | 0.138021i | \(-0.955926\pi\) | ||||
−0.990429 | + | 0.138021i | \(0.955926\pi\) | |||||||
\(578\) | 4.72430 | − | 15.2963i | 0.196505 | − | 0.636242i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 50.1071 | + | 34.2151i | 2.08058 | + | 1.42071i | ||||
\(581\) | − | 6.46403i | − | 0.268173i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.146913 | 0.00608452 | ||||||||
\(584\) | 26.7846 | − | 21.3129i | 1.10835 | − | 0.881933i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5.97919 | − | 1.84668i | −0.246998 | − | 0.0762858i | ||||
\(587\) | 23.6803i | 0.977390i | 0.872455 | + | 0.488695i | \(0.162527\pi\) | ||||
−0.872455 | + | 0.488695i | \(0.837473\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 21.8588i | 0.900675i | ||||||||
\(590\) | 14.0980 | − | 45.6465i | 0.580406 | − | 1.87924i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.96918 | + | 1.16040i | −0.122033 | + | 0.0476923i | ||||
\(593\) | 17.8919 | 0.734734 | 0.367367 | − | 0.930076i | \(-0.380259\pi\) | ||||
0.367367 | + | 0.930076i | \(0.380259\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 16.1960i | 0.663971i | ||||||||
\(596\) | −13.1062 | + | 19.1936i | −0.536850 | + | 0.786201i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 44.1237 | + | 13.6277i | 1.80435 | + | 0.557278i | ||||
\(599\) | 32.0167 | 1.30817 | 0.654083 | − | 0.756423i | \(-0.273055\pi\) | ||||
0.654083 | + | 0.756423i | \(0.273055\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.7187 | 0.967507 | 0.483754 | − | 0.875204i | \(-0.339273\pi\) | ||||
0.483754 | + | 0.875204i | \(0.339273\pi\) | |||||||
\(602\) | −9.44648 | − | 2.91757i | −0.385010 | − | 0.118911i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −35.5362 | − | 24.2656i | −1.44595 | − | 0.987352i | ||||
\(605\) | − | 33.4271i | − | 1.35901i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.4444 | −0.586281 | −0.293141 | − | 0.956069i | \(-0.594700\pi\) | ||||
−0.293141 | + | 0.956069i | \(0.594700\pi\) | |||||||
\(608\) | 2.75717 | + | 37.6993i | 0.111818 | + | 1.52891i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 18.6277 | − | 60.3127i | 0.754213 | − | 2.44199i | ||||
\(611\) | 30.0319i | 1.21496i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.2817i | 0.657610i | 0.944398 | + | 0.328805i | \(0.106646\pi\) | ||||
−0.944398 | + | 0.328805i | \(0.893354\pi\) | |||||||
\(614\) | 11.3076 | + | 3.49236i | 0.456336 | + | 0.140940i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.226432 | + | 0.284564i | 0.00912319 | + | 0.0114654i | ||||
\(617\) | 28.7753 | 1.15845 | 0.579225 | − | 0.815167i | \(-0.303355\pi\) | ||||
0.579225 | + | 0.815167i | \(0.303355\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 36.0871i | 1.45046i | 0.688506 | + | 0.725231i | \(0.258267\pi\) | ||||
−0.688506 | + | 0.725231i | \(0.741733\pi\) | |||||||
\(620\) | −11.2282 | + | 16.4434i | −0.450936 | + | 0.660383i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 11.7563 | − | 38.0644i | 0.471383 | − | 1.52624i | ||||
\(623\) | 2.23283 | 0.0894564 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −28.1443 | −1.12577 | ||||||||
\(626\) | 5.84602 | − | 18.9282i | 0.233654 | − | 0.756524i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −20.6393 | + | 30.2256i | −0.823596 | + | 1.20613i | ||||
\(629\) | − | 4.24122i | − | 0.169108i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.0509 | 0.718595 | 0.359297 | − | 0.933223i | \(-0.383016\pi\) | ||||
0.359297 | + | 0.933223i | \(0.383016\pi\) | |||||||
\(632\) | −5.80815 | + | 4.62163i | −0.231036 | + | 0.183838i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −19.5104 | − | 6.02584i | −0.774859 | − | 0.239317i | ||||
\(635\) | 2.55707i | 0.101474i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 6.30135i | − | 0.249668i | ||||||
\(638\) | −0.534870 | + | 1.73180i | −0.0211757 | + | 0.0685626i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −17.2909 | + | 29.7758i | −0.683483 | + | 1.17699i | ||||
\(641\) | 12.0253 | 0.474971 | 0.237486 | − | 0.971391i | \(-0.423677\pi\) | ||||
0.237486 | + | 0.971391i | \(0.423677\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 9.54316i | − | 0.376345i | −0.982136 | − | 0.188173i | \(-0.939744\pi\) | ||
0.982136 | − | 0.188173i | \(-0.0602565\pi\) | |||||||
\(644\) | 8.55915 | + | 5.84453i | 0.337278 | + | 0.230307i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −48.0502 | − | 14.8404i | −1.89051 | − | 0.583888i | ||||
\(647\) | 32.2201 | 1.26670 | 0.633351 | − | 0.773865i | \(-0.281679\pi\) | ||||
0.633351 | + | 0.773865i | \(0.281679\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.42714 | 0.0560202 | ||||||||
\(650\) | 36.2917 | + | 11.2088i | 1.42348 | + | 0.439644i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −21.2651 | + | 31.1422i | −0.832806 | + | 1.21962i | ||||
\(653\) | − | 14.5245i | − | 0.568388i | −0.958767 | − | 0.284194i | \(-0.908274\pi\) | ||
0.958767 | − | 0.284194i | \(-0.0917259\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −22.5205 | −0.879950 | ||||||||
\(656\) | 4.32120 | + | 11.0569i | 0.168715 | + | 0.431698i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1.98898 | + | 6.43992i | −0.0775386 | + | 0.251054i | ||||
\(659\) | 10.5726i | 0.411849i | 0.978568 | + | 0.205924i | \(0.0660201\pi\) | ||||
−0.978568 | + | 0.205924i | \(0.933980\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27.0965i | 1.05393i | 0.849887 | + | 0.526965i | \(0.176670\pi\) | ||||
−0.849887 | + | 0.526965i | \(0.823330\pi\) | |||||||
\(662\) | −44.0148 | − | 13.5941i | −1.71068 | − | 0.528348i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 11.3839 | + | 14.3065i | 0.441781 | + | 0.555200i | ||||
\(665\) | 20.3365 | 0.788614 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 51.6565i | 2.00015i | ||||||||
\(668\) | 34.4015 | + | 23.4907i | 1.33103 | + | 0.908883i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.34282 | − | 4.34777i | 0.0518775 | − | 0.167969i | ||||
\(671\) | 1.88568 | 0.0727959 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 38.2417 | 1.47411 | 0.737055 | − | 0.675833i | \(-0.236216\pi\) | ||||
0.737055 | + | 0.675833i | \(0.236216\pi\) | |||||||
\(674\) | −0.906363 | + | 2.93462i | −0.0349118 | + | 0.113037i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 44.1111 | + | 30.1208i | 1.69658 | + | 1.15849i | ||||
\(677\) | 14.2289i | 0.546860i | 0.961892 | + | 0.273430i | \(0.0881582\pi\) | ||||
−0.961892 | + | 0.273430i | \(0.911842\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.88097 | −0.302444 | ||||||||
\(680\) | −28.5230 | − | 35.8458i | −1.09381 | − | 1.37462i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.568316 | − | 0.175525i | −0.0217619 | − | 0.00672122i | ||||
\(683\) | 39.0552i | 1.49441i | 0.664596 | + | 0.747203i | \(0.268603\pi\) | ||||
−0.664596 | + | 0.747203i | \(0.731397\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 17.0942i | 0.653137i | ||||||||
\(686\) | 0.417332 | − | 1.35123i | 0.0159338 | − | 0.0515904i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 26.0456 | − | 10.1790i | 0.992979 | − | 0.388072i | ||||
\(689\) | 7.20020 | 0.274306 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 20.1602i | − | 0.766929i | −0.923556 | − | 0.383464i | \(-0.874731\pi\) | ||
0.923556 | − | 0.383464i | \(-0.125269\pi\) | |||||||
\(692\) | −6.19373 | + | 9.07054i | −0.235450 | + | 0.344810i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.77639 | + | 1.16635i | 0.143350 | + | 0.0442739i | ||||
\(695\) | 15.8121 | 0.599786 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −15.7938 | −0.598232 | ||||||||
\(698\) | −4.31159 | − | 1.33164i | −0.163196 | − | 0.0504034i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 7.03990 | + | 4.80712i | 0.266083 | + | 0.181692i | ||||
\(701\) | − | 22.4760i | − | 0.848908i | −0.905449 | − | 0.424454i | \(-0.860466\pi\) | ||
0.905449 | − | 0.424454i | \(-0.139534\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.32548 | −0.200854 | ||||||||
\(704\) | −1.00230 | − | 0.231039i | −0.0377756 | − | 0.00870762i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.38141 | + | 10.9483i | −0.127261 | + | 0.412045i | ||||
\(707\) | − | 16.9693i | − | 0.638195i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20.2609i | 0.760915i | 0.924798 | + | 0.380458i | \(0.124233\pi\) | ||||
−0.924798 | + | 0.380458i | \(0.875767\pi\) | |||||||
\(710\) | 4.54753 | + | 1.40451i | 0.170666 | + | 0.0527104i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −4.94181 | + | 3.93227i | −0.185202 | + | 0.147368i | ||||
\(713\) | −16.9518 | −0.634852 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.46571i | 0.0922124i | ||||||||
\(716\) | −8.60464 | + | 12.6013i | −0.321571 | + | 0.470931i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 7.20461 | − | 23.3271i | 0.268874 | − | 0.870558i | ||||
\(719\) | 21.2440 | 0.792269 | 0.396134 | − | 0.918193i | \(-0.370351\pi\) | ||||
0.396134 | + | 0.918193i | \(0.370351\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.7049 | −0.398672 | ||||||||
\(722\) | −10.7050 | + | 34.6607i | −0.398400 | + | 1.28994i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −11.2981 | + | 16.5457i | −0.419889 | + | 0.614916i | ||||
\(725\) | 42.4874i | 1.57794i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −32.9048 | −1.22037 | −0.610185 | − | 0.792259i | \(-0.708905\pi\) | ||||
−0.610185 | + | 0.792259i | \(0.708905\pi\) | |||||||
\(728\) | 11.0974 | + | 13.9465i | 0.411297 | + | 0.516890i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 49.7674 | + | 15.3708i | 1.84197 | + | 0.568897i | ||||
\(731\) | 37.2039i | 1.37603i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 32.0598i | − | 1.18415i | −0.805881 | − | 0.592077i | \(-0.798308\pi\) | ||
0.805881 | − | 0.592077i | \(-0.201692\pi\) | |||||||
\(734\) | −5.65519 | + | 18.3104i | −0.208737 | + | 0.675847i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −29.2364 | + | 2.13823i | −1.07767 | + | 0.0788164i | ||||
\(737\) | 0.135933 | 0.00500716 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 46.3826i | − | 1.70621i | −0.521738 | − | 0.853106i | \(-0.674716\pi\) | ||
0.521738 | − | 0.853106i | \(-0.325284\pi\) | |||||||
\(740\) | −4.00612 | − | 2.73554i | −0.147268 | − | 0.100561i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.54398 | + | 0.476862i | 0.0566813 | + | 0.0175061i | ||||
\(743\) | −12.1782 | −0.446777 | −0.223388 | − | 0.974730i | \(-0.571712\pi\) | ||||
−0.223388 | + | 0.974730i | \(0.571712\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −35.3666 | −1.29573 | ||||||||
\(746\) | −22.0790 | − | 6.81916i | −0.808371 | − | 0.249667i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.771685 | − | 1.13011i | 0.0282156 | − | 0.0413209i | ||||
\(749\) | − | 1.31462i | − | 0.0480351i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.4371 | 0.891723 | 0.445862 | − | 0.895102i | \(-0.352897\pi\) | ||||
0.445862 | + | 0.895102i | \(0.352897\pi\) | |||||||
\(752\) | −6.93932 | − | 17.7560i | −0.253051 | − | 0.647494i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −26.2139 | + | 84.8753i | −0.954655 | + | 3.09098i | ||||
\(755\) | − | 65.4799i | − | 2.38306i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 7.15224i | − | 0.259953i | −0.991517 | − | 0.129976i | \(-0.958510\pi\) | ||
0.991517 | − | 0.129976i | \(-0.0414902\pi\) | |||||||
\(758\) | 3.21261 | + | 0.992223i | 0.116687 | + | 0.0360391i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −45.0097 | + | 35.8148i | −1.63267 | + | 1.29914i | ||||
\(761\) | −14.7809 | −0.535806 | −0.267903 | − | 0.963446i | \(-0.586331\pi\) | ||||
−0.267903 | + | 0.963446i | \(0.586331\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.2677i | 0.371715i | ||||||||
\(764\) | −10.3329 | − | 7.05569i | −0.373830 | − | 0.255266i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.35378 | − | 23.8100i | 0.265703 | − | 0.860292i | ||||
\(767\) | 69.9441 | 2.52554 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.90576 | −0.0687235 | −0.0343618 | − | 0.999409i | \(-0.510940\pi\) | ||||
−0.0343618 | + | 0.999409i | \(0.510940\pi\) | |||||||
\(770\) | −0.163301 | + | 0.528737i | −0.00588497 | + | 0.0190543i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −4.07048 | − | 2.77948i | −0.146500 | − | 0.100036i | ||||
\(773\) | 6.63435i | 0.238621i | 0.992857 | + | 0.119310i | \(0.0380684\pi\) | ||||
−0.992857 | + | 0.119310i | \(0.961932\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −13.9429 | −0.500843 | ||||||||
\(776\) | 17.4426 | − | 13.8793i | 0.626152 | − | 0.498238i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 17.1378 | + | 5.29305i | 0.614421 | + | 0.189765i | ||||
\(779\) | 19.8314i | 0.710534i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.142179i | 0.00508756i | ||||||||
\(782\) | 11.5090 | − | 37.2638i | 0.411561 | − | 1.33255i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.45602 | + | 3.72559i | 0.0520007 | + | 0.133057i | ||||
\(785\) | −55.6944 | −1.98782 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.91096i | 0.103765i | 0.998653 | + | 0.0518823i | \(0.0165221\pi\) | ||||
−0.998653 | + | 0.0518823i | \(0.983478\pi\) | |||||||
\(788\) | 26.8541 | − | 39.3271i | 0.956637 | − | 1.40097i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −10.7919 | − | 3.33309i | −0.383958 | − | 0.118586i | ||||
\(791\) | 13.1796 | 0.468613 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 92.4170 | 3.28182 | ||||||||
\(794\) | 46.4630 | + | 14.3502i | 1.64891 | + | 0.509270i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −39.8542 | − | 27.2140i | −1.41259 | − | 0.964576i | ||||
\(797\) | 6.96910i | 0.246858i | 0.992353 | + | 0.123429i | \(0.0393891\pi\) | ||||
−0.992353 | + | 0.123429i | \(0.960611\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 25.3629 | 0.897274 | ||||||||
\(800\) | −24.0469 | + | 1.75870i | −0.850188 | + | 0.0621793i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.56895 | − | 5.07993i | 0.0554014 | − | 0.179379i | ||||
\(803\) | 1.55598i | 0.0549094i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 15.7713i | 0.555864i | ||||||||
\(806\) | −27.8531 | − | 8.60249i | −0.981084 | − | 0.303010i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 29.8848 | + | 37.5572i | 1.05134 | + | 1.32126i | ||||
\(809\) | 21.3012 | 0.748909 | 0.374454 | − | 0.927245i | \(-0.377830\pi\) | ||||
0.374454 | + | 0.927245i | \(0.377830\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 18.1357i | − | 0.636832i | −0.947951 | − | 0.318416i | \(-0.896849\pi\) | ||
0.947951 | − | 0.318416i | \(-0.103151\pi\) | |||||||
\(812\) | −11.2424 | + | 16.4642i | −0.394531 | + | 0.577780i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.0427635 | − | 0.138459i | 0.00149886 | − | 0.00485300i | ||||
\(815\) | −57.3832 | −2.01005 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 46.7149 | 1.63435 | ||||||||
\(818\) | 5.46686 | − | 17.7006i | 0.191144 | − | 0.618886i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −10.1868 | + | 14.9183i | −0.355739 | + | 0.520970i | ||||
\(821\) | 24.3030i | 0.848180i | 0.905620 | + | 0.424090i | \(0.139406\pi\) | ||||
−0.905620 | + | 0.424090i | \(0.860594\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.29306 | 0.0450734 | 0.0225367 | − | 0.999746i | \(-0.492826\pi\) | ||||
0.0225367 | + | 0.999746i | \(0.492826\pi\) | |||||||
\(824\) | 23.6926 | − | 18.8526i | 0.825372 | − | 0.656760i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 14.9985 | + | 4.63232i | 0.521865 | + | 0.161179i | ||||
\(827\) | 23.6268i | 0.821585i | 0.911729 | + | 0.410792i | \(0.134748\pi\) | ||||
−0.911729 | + | 0.410792i | \(0.865252\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 5.66492i | − | 0.196751i | −0.995149 | − | 0.0983754i | \(-0.968635\pi\) | ||
0.995149 | − | 0.0983754i | \(-0.0313646\pi\) | |||||||
\(830\) | −8.21001 | + | 26.5823i | −0.284974 | + | 0.922687i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −49.1226 | − | 11.3232i | −1.70302 | − | 0.392562i | ||||
\(833\) | −5.32168 | −0.184385 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 63.3890i | 2.19367i | ||||||||
\(836\) | −1.41902 | − | 0.968964i | −0.0490779 | − | 0.0335123i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −33.0166 | − | 10.1972i | −1.14054 | − | 0.352258i | ||||
\(839\) | 21.1554 | 0.730366 | 0.365183 | − | 0.930936i | \(-0.381006\pi\) | ||||
0.365183 | + | 0.930936i | \(0.381006\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −70.3652 | −2.42639 | ||||||||
\(842\) | −35.6600 | − | 11.0137i | −1.22892 | − | 0.379556i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −16.8799 | + | 24.7202i | −0.581032 | + | 0.850904i | ||||
\(845\) | 81.2801i | 2.79612i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.9835 | 0.377396 | ||||||||
\(848\) | −4.25702 | + | 1.66371i | −0.146187 | + | 0.0571321i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 9.46614 | − | 30.6494i | 0.324686 | − | 1.05127i | ||||
\(851\) | − | 4.13000i | − | 0.141574i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 4.41255i | − | 0.151083i | −0.997143 | − | 0.0755413i | \(-0.975932\pi\) | ||
0.997143 | − | 0.0755413i | \(-0.0240685\pi\) | |||||||
\(854\) | 19.8175 | + | 6.12068i | 0.678141 | + | 0.209445i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.31519 | + | 2.90958i | 0.0791317 | + | 0.0994474i | ||||
\(857\) | −20.9783 | −0.716606 | −0.358303 | − | 0.933605i | \(-0.616644\pi\) | ||||
−0.358303 | + | 0.933605i | \(0.616644\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.6318i | 0.533351i | 0.963786 | + | 0.266676i | \(0.0859253\pi\) | ||||
−0.963786 | + | 0.266676i | \(0.914075\pi\) | |||||||
\(860\) | 35.1416 | + | 23.9961i | 1.19832 | + | 0.818260i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −13.6535 | + | 44.2072i | −0.465039 | + | 1.50570i | ||||
\(863\) | −16.1880 | −0.551047 | −0.275523 | − | 0.961294i | \(-0.588851\pi\) | ||||
−0.275523 | + | 0.961294i | \(0.588851\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −16.7136 | −0.568278 | ||||||||
\(866\) | 5.14297 | − | 16.6519i | 0.174765 | − | 0.565855i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −5.40297 | − | 3.68936i | −0.183389 | − | 0.125225i | ||||
\(869\) | − | 0.337409i | − | 0.0114458i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.66208 | 0.225736 | ||||||||
\(872\) | −18.0826 | − | 22.7249i | −0.612352 | − | 0.769563i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −46.7902 | − | 14.4512i | −1.58270 | − | 0.488820i | ||||
\(875\) | − | 2.24514i | − | 0.0758995i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 38.1001i | − | 1.28655i | −0.765636 | − | 0.643274i | \(-0.777576\pi\) | ||
0.765636 | − | 0.643274i | \(-0.222424\pi\) | |||||||
\(878\) | 1.95260 | − | 6.32213i | 0.0658972 | − | 0.213362i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.569739 | − | 1.45782i | −0.0192059 | − | 0.0491431i | ||||
\(881\) | 46.4289 | 1.56423 | 0.782114 | − | 0.623135i | \(-0.214141\pi\) | ||||
0.782114 | + | 0.623135i | \(0.214141\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17.8873i | 0.601956i | 0.953631 | + | 0.300978i | \(0.0973131\pi\) | ||||
−0.953631 | + | 0.300978i | \(0.902687\pi\) | |||||||
\(884\) | 37.8202 | − | 55.3866i | 1.27203 | − | 1.86285i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 48.1675 | + | 14.8766i | 1.61822 | + | 0.499791i | ||||
\(887\) | −35.5228 | −1.19274 | −0.596369 | − | 0.802711i | \(-0.703390\pi\) | ||||
−0.596369 | + | 0.802711i | \(0.703390\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.840201 | −0.0281795 | ||||||||
\(890\) | −9.18218 | − | 2.83593i | −0.307787 | − | 0.0950607i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −19.1772 | − | 13.0950i | −0.642101 | − | 0.438452i | ||||
\(893\) | − | 31.8468i | − | 1.06571i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −23.2194 | −0.776137 | ||||||||
\(896\) | −9.78372 | − | 5.68144i | −0.326851 | − | 0.189804i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2.51562 | + | 8.14505i | −0.0839472 | + | 0.271804i | ||||
\(899\) | − | 32.6082i | − | 1.08754i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 6.08079i | − | 0.202580i | ||||||
\(902\) | −0.515606 | − | 0.159246i | −0.0171678 | − | 0.00530231i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −29.1698 | + | 23.2108i | −0.970172 | + | 0.771979i | ||||
\(905\) | −30.4875 | −1.01344 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 41.8996i | 1.39125i | 0.718404 | + | 0.695627i | \(0.244873\pi\) | ||||
−0.718404 | + | 0.695627i | \(0.755127\pi\) | |||||||
\(908\) | −1.05953 | + | 1.55165i | −0.0351617 | + | 0.0514934i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −8.00339 | + | 25.9133i | −0.265310 | + | 0.859019i | ||||
\(911\) | −5.35427 | −0.177395 | −0.0886974 | − | 0.996059i | \(-0.528270\pi\) | ||||
−0.0886974 | + | 0.996059i | \(0.528270\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.831099 | −0.0275054 | ||||||||
\(914\) | 2.03975 | − | 6.60431i | 0.0674691 | − | 0.218451i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.0154652 | + | 0.0226484i | −0.000510985 | + | 0.000748324i | ||||
\(917\) | − | 7.39979i | − | 0.244363i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −54.8843 | −1.81047 | −0.905234 | − | 0.424914i | \(-0.860304\pi\) | ||||
−0.905234 | + | 0.424914i | \(0.860304\pi\) | |||||||
\(920\) | −27.7750 | − | 34.9058i | −0.915715 | − | 1.15081i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −12.3814 | − | 3.82403i | −0.407761 | − | 0.125938i | ||||
\(923\) | 6.96817i | 0.229360i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 3.39692i | − | 0.111690i | ||||||
\(926\) | 13.7057 | − | 44.3761i | 0.450396 | − | 1.45829i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.11306 | − | 56.2385i | −0.135018 | − | 1.84612i | ||||
\(929\) | 10.4091 | 0.341512 | 0.170756 | − | 0.985313i | \(-0.445379\pi\) | ||||
0.170756 | + | 0.985313i | \(0.445379\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.68215i | 0.218999i | ||||||||
\(932\) | −30.0926 | − | 20.5484i | −0.985716 | − | 0.673086i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 8.65545 | + | 2.67325i | 0.283215 | + | 0.0874715i | ||||
\(935\) | 2.08237 | 0.0681007 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 49.8177 | 1.62747 | 0.813737 | − | 0.581233i | \(-0.197430\pi\) | ||||
0.813737 | + | 0.581233i | \(0.197430\pi\) | |||||||
\(938\) | 1.42859 | + | 0.441222i | 0.0466450 | + | 0.0144064i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 16.3588 | − | 23.9570i | 0.533565 | − | 0.781390i | ||||
\(941\) | 5.61503i | 0.183045i | 0.995803 | + | 0.0915224i | \(0.0291733\pi\) | ||||
−0.995803 | + | 0.0915224i | \(0.970827\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −15.3796 | −0.500829 | ||||||||
\(944\) | −41.3535 | + | 16.1616i | −1.34594 | + | 0.526016i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.375120 | + | 1.21456i | −0.0121962 | + | 0.0394888i | ||||
\(947\) | − | 22.3495i | − | 0.726262i | −0.931738 | − | 0.363131i | \(-0.881708\pi\) | ||
0.931738 | − | 0.363131i | \(-0.118292\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 76.2585i | 2.47545i | ||||||||
\(950\) | −38.4849 | − | 11.8861i | −1.24861 | − | 0.385637i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 11.7782 | − | 9.37208i | 0.381734 | − | 0.303751i | ||||
\(953\) | 19.9449 | 0.646080 | 0.323040 | − | 0.946385i | \(-0.395295\pi\) | ||||
0.323040 | + | 0.946385i | \(0.395295\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 19.0396i | − | 0.616106i | ||||||
\(956\) | 2.26531 | + | 1.54685i | 0.0732655 | + | 0.0500286i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −11.4023 | + | 36.9182i | −0.368391 | + | 1.19277i | ||||
\(959\) | −5.61682 | −0.181376 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.2991 | −0.654811 | ||||||||
\(962\) | 2.09583 | − | 6.78588i | 0.0675724 | − | 0.218786i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 17.3514 | + | 11.8482i | 0.558851 | + | 0.381606i | ||||
\(965\) | − | 7.50035i | − | 0.241445i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.6951 | 1.05140 | 0.525702 | − | 0.850669i | \(-0.323803\pi\) | ||||
0.525702 | + | 0.850669i | \(0.323803\pi\) | |||||||
\(968\) | −24.3092 | + | 19.3431i | −0.781326 | + | 0.621712i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 32.4093 | + | 10.0097i | 1.04060 | + | 0.321392i | ||||
\(971\) | 33.7391i | 1.08274i | 0.840785 | + | 0.541369i | \(0.182094\pi\) | ||||
−0.840785 | + | 0.541369i | \(0.817906\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.19553i | 0.166561i | ||||||||
\(974\) | 3.77795 | − | 12.2322i | 0.121053 | − | 0.391946i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −54.6403 | + | 21.3543i | −1.74899 | + | 0.683535i | ||||
\(977\) | 45.8374 | 1.46647 | 0.733235 | − | 0.679976i | \(-0.238010\pi\) | ||||
0.733235 | + | 0.679976i | \(0.238010\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 0.287081i | − | 0.00917516i | ||||||
\(980\) | −3.43243 | + | 5.02669i | −0.109645 | + | 0.160572i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 13.6722 | + | 4.22268i | 0.436296 | + | 0.134751i | ||||
\(983\) | −14.0557 | −0.448307 | −0.224154 | − | 0.974554i | \(-0.571962\pi\) | ||||
−0.224154 | + | 0.974554i | \(0.571962\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 72.4649 | 2.30892 | ||||||||
\(986\) | 71.6797 | + | 22.1384i | 2.28275 | + | 0.705031i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −69.5461 | − | 47.4889i | −2.21256 | − | 1.51082i | ||||
\(989\) | 36.2282i | 1.15199i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.3875 | 0.584099 | 0.292050 | − | 0.956403i | \(-0.405663\pi\) | ||||
0.292050 | + | 0.956403i | \(0.405663\pi\) | |||||||
\(992\) | 18.4555 | − | 1.34976i | 0.585963 | − | 0.0428550i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −0.461495 | + | 1.49423i | −0.0146377 | + | 0.0473939i | ||||
\(995\) | − | 73.4362i | − | 2.32808i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 20.8011i | − | 0.658776i | −0.944195 | − | 0.329388i | \(-0.893158\pi\) | ||
0.944195 | − | 0.329388i | \(-0.106842\pi\) | |||||||
\(998\) | −26.9431 | − | 8.32144i | −0.852870 | − | 0.263411i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1512.2.c.g.757.13 | yes | 24 | |
3.2 | odd | 2 | inner | 1512.2.c.g.757.12 | yes | 24 | |
4.3 | odd | 2 | 6048.2.c.f.3025.3 | 24 | |||
8.3 | odd | 2 | 6048.2.c.f.3025.22 | 24 | |||
8.5 | even | 2 | inner | 1512.2.c.g.757.14 | yes | 24 | |
12.11 | even | 2 | 6048.2.c.f.3025.21 | 24 | |||
24.5 | odd | 2 | inner | 1512.2.c.g.757.11 | ✓ | 24 | |
24.11 | even | 2 | 6048.2.c.f.3025.4 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.c.g.757.11 | ✓ | 24 | 24.5 | odd | 2 | inner | |
1512.2.c.g.757.12 | yes | 24 | 3.2 | odd | 2 | inner | |
1512.2.c.g.757.13 | yes | 24 | 1.1 | even | 1 | trivial | |
1512.2.c.g.757.14 | yes | 24 | 8.5 | even | 2 | inner | |
6048.2.c.f.3025.3 | 24 | 4.3 | odd | 2 | |||
6048.2.c.f.3025.4 | 24 | 24.11 | even | 2 | |||
6048.2.c.f.3025.21 | 24 | 12.11 | even | 2 | |||
6048.2.c.f.3025.22 | 24 | 8.3 | odd | 2 |