Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1805,2,Mod(1084,1805)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1805, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1805.1084");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1805 = 5 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1805.b (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: | \(14.4129975648\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 22x^{14} + 190x^{12} + 820x^{10} + 1862x^{8} + 2154x^{6} + 1163x^{4} + 256x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1084.1 | ||
Root | \(-2.61137i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1805.1084 |
Dual form | 1805.2.b.j.1084.16 |
$q$-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 \(\left(\mathbb{Z}/1805\mathbb{Z}\right)^\times\).
\(n\) | \(362\) | \(1446\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.61137i | − | 1.84652i | −0.384180 | − | 0.923258i | \(-0.625516\pi\) | ||
0.384180 | − | 0.923258i | \(-0.374484\pi\) | |||||||
\(3\) | 0.146779i | 0.0847426i | 0.999102 | + | 0.0423713i | \(0.0134912\pi\) | ||||
−0.999102 | + | 0.0423713i | \(0.986509\pi\) | |||||||
\(4\) | −4.81924 | −2.40962 | ||||||||
\(5\) | 0.948930 | + | 2.02473i | 0.424375 | + | 0.905487i | ||||
\(6\) | 0.383293 | 0.156479 | ||||||||
\(7\) | − | 1.14057i | − | 0.431096i | −0.976493 | − | 0.215548i | \(-0.930846\pi\) | ||
0.976493 | − | 0.215548i | \(-0.0691538\pi\) | |||||||
\(8\) | 7.36208i | 2.60289i | ||||||||
\(9\) | 2.97846 | 0.992819 | ||||||||
\(10\) | 5.28732 | − | 2.47801i | 1.67200 | − | 0.783614i | ||||
\(11\) | −5.36995 | −1.61910 | −0.809550 | − | 0.587051i | \(-0.800289\pi\) | ||||
−0.809550 | + | 0.587051i | \(0.800289\pi\) | |||||||
\(12\) | − | 0.707361i | − | 0.204198i | ||||||
\(13\) | − | 2.41565i | − | 0.669980i | −0.942222 | − | 0.334990i | \(-0.891267\pi\) | ||
0.942222 | − | 0.334990i | \(-0.108733\pi\) | |||||||
\(14\) | −2.97846 | −0.796026 | ||||||||
\(15\) | −0.297187 | + | 0.139283i | −0.0767333 | + | 0.0359626i | ||||
\(16\) | 9.58662 | 2.39665 | ||||||||
\(17\) | 5.74451i | 1.39325i | 0.717436 | + | 0.696624i | \(0.245315\pi\) | ||||
−0.717436 | + | 0.696624i | \(0.754685\pi\) | |||||||
\(18\) | − | 7.77785i | − | 1.83326i | ||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −4.57313 | − | 9.75767i | −1.02258 | − | 2.18188i | ||||
\(21\) | 0.167412 | 0.0365322 | ||||||||
\(22\) | 14.0229i | 2.98969i | ||||||||
\(23\) | − | 1.23526i | − | 0.257570i | −0.991673 | − | 0.128785i | \(-0.958892\pi\) | ||
0.991673 | − | 0.128785i | \(-0.0411077\pi\) | |||||||
\(24\) | −1.08060 | −0.220576 | ||||||||
\(25\) | −3.19906 | + | 3.84266i | −0.639812 | + | 0.768531i | ||||
\(26\) | −6.30815 | −1.23713 | ||||||||
\(27\) | 0.877509i | 0.168877i | ||||||||
\(28\) | 5.49670i | 1.03878i | ||||||||
\(29\) | 3.91460 | 0.726923 | 0.363461 | − | 0.931609i | \(-0.381595\pi\) | ||||
0.363461 | + | 0.931609i | \(0.381595\pi\) | |||||||
\(30\) | 0.363718 | + | 0.776064i | 0.0664055 | + | 0.141689i | ||||
\(31\) | 6.48369 | 1.16450 | 0.582252 | − | 0.813008i | \(-0.302172\pi\) | ||||
0.582252 | + | 0.813008i | \(0.302172\pi\) | |||||||
\(32\) | − | 10.3100i | − | 1.82257i | ||||||
\(33\) | − | 0.788193i | − | 0.137207i | ||||||
\(34\) | 15.0010 | 2.57265 | ||||||||
\(35\) | 2.30935 | − | 1.08232i | 0.390352 | − | 0.182946i | ||||
\(36\) | −14.3539 | −2.39232 | ||||||||
\(37\) | 7.37637i | 1.21267i | 0.795210 | + | 0.606334i | \(0.207361\pi\) | ||||
−0.795210 | + | 0.606334i | \(0.792639\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.354565 | 0.0567759 | ||||||||
\(40\) | −14.9062 | + | 6.98610i | −2.35688 | + | 1.10460i | ||||
\(41\) | 4.86252 | 0.759398 | 0.379699 | − | 0.925110i | \(-0.376028\pi\) | ||||
0.379699 | + | 0.925110i | \(0.376028\pi\) | |||||||
\(42\) | − | 0.437173i | − | 0.0674573i | ||||||
\(43\) | 7.59744i | 1.15860i | 0.815115 | + | 0.579299i | \(0.196674\pi\) | ||||
−0.815115 | + | 0.579299i | \(0.803326\pi\) | |||||||
\(44\) | 25.8791 | 3.90142 | ||||||||
\(45\) | 2.82635 | + | 6.03057i | 0.421327 | + | 0.898984i | ||||
\(46\) | −3.22572 | −0.475607 | ||||||||
\(47\) | − | 7.85368i | − | 1.14558i | −0.819703 | − | 0.572788i | \(-0.805862\pi\) | ||
0.819703 | − | 0.572788i | \(-0.194138\pi\) | |||||||
\(48\) | 1.40711i | 0.203099i | ||||||||
\(49\) | 5.69909 | 0.814156 | ||||||||
\(50\) | 10.0346 | + | 8.35393i | 1.41910 | + | 1.18142i | ||||
\(51\) | −0.843170 | −0.118067 | ||||||||
\(52\) | 11.6416i | 1.61440i | ||||||||
\(53\) | 0.0179026i | 0.00245911i | 0.999999 | + | 0.00122955i | \(0.000391379\pi\) | ||||
−0.999999 | + | 0.00122955i | \(0.999609\pi\) | |||||||
\(54\) | 2.29150 | 0.311833 | ||||||||
\(55\) | −5.09571 | − | 10.8727i | −0.687105 | − | 1.46607i | ||||
\(56\) | 8.39699 | 1.12210 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 10.2225i | − | 1.34227i | ||||||
\(59\) | 13.0250 | 1.69571 | 0.847857 | − | 0.530225i | \(-0.177892\pi\) | ||||
0.847857 | + | 0.530225i | \(0.177892\pi\) | |||||||
\(60\) | 1.43222 | − | 0.671237i | 0.184898 | − | 0.0866563i | ||||
\(61\) | −0.0189653 | −0.00242826 | −0.00121413 | − | 0.999999i | \(-0.500386\pi\) | ||||
−0.00121413 | + | 0.999999i | \(0.500386\pi\) | |||||||
\(62\) | − | 16.9313i | − | 2.15028i | ||||||
\(63\) | − | 3.39715i | − | 0.428000i | ||||||
\(64\) | −7.75004 | −0.968754 | ||||||||
\(65\) | 4.89104 | − | 2.29228i | 0.606658 | − | 0.284323i | ||||
\(66\) | −2.05826 | −0.253355 | ||||||||
\(67\) | 7.07711i | 0.864606i | 0.901728 | + | 0.432303i | \(0.142299\pi\) | ||||
−0.901728 | + | 0.432303i | \(0.857701\pi\) | |||||||
\(68\) | − | 27.6842i | − | 3.35720i | ||||||
\(69\) | 0.181310 | 0.0218271 | ||||||||
\(70\) | −2.82635 | − | 6.03057i | −0.337813 | − | 0.720791i | ||||
\(71\) | −2.73751 | −0.324883 | −0.162442 | − | 0.986718i | \(-0.551937\pi\) | ||||
−0.162442 | + | 0.986718i | \(0.551937\pi\) | |||||||
\(72\) | 21.9276i | 2.58420i | ||||||||
\(73\) | 5.58836i | 0.654068i | 0.945013 | + | 0.327034i | \(0.106049\pi\) | ||||
−0.945013 | + | 0.327034i | \(0.893951\pi\) | |||||||
\(74\) | 19.2624 | 2.23921 | ||||||||
\(75\) | −0.564019 | − | 0.469554i | −0.0651273 | − | 0.0542194i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.12482i | 0.697988i | ||||||||
\(78\) | − | 0.925901i | − | 0.104838i | ||||||
\(79\) | 9.56774 | 1.07645 | 0.538227 | − | 0.842800i | \(-0.319094\pi\) | ||||
0.538227 | + | 0.842800i | \(0.319094\pi\) | |||||||
\(80\) | 9.09703 | + | 19.4103i | 1.01708 | + | 2.17014i | ||||
\(81\) | 8.80657 | 0.978508 | ||||||||
\(82\) | − | 12.6978i | − | 1.40224i | ||||||
\(83\) | − | 0.390810i | − | 0.0428970i | −0.999770 | − | 0.0214485i | \(-0.993172\pi\) | ||
0.999770 | − | 0.0214485i | \(-0.00682779\pi\) | |||||||
\(84\) | −0.806797 | −0.0880288 | ||||||||
\(85\) | −11.6311 | + | 5.45114i | −1.26157 | + | 0.591259i | ||||
\(86\) | 19.8397 | 2.13937 | ||||||||
\(87\) | 0.574579i | 0.0616014i | ||||||||
\(88\) | − | 39.5340i | − | 4.21434i | ||||||
\(89\) | 3.57717 | 0.379179 | 0.189590 | − | 0.981863i | \(-0.439284\pi\) | ||||
0.189590 | + | 0.981863i | \(0.439284\pi\) | |||||||
\(90\) | 15.7480 | − | 7.38063i | 1.65999 | − | 0.777987i | ||||
\(91\) | −2.75522 | −0.288826 | ||||||||
\(92\) | 5.95303i | 0.620646i | ||||||||
\(93\) | 0.951666i | 0.0986832i | ||||||||
\(94\) | −20.5088 | −2.11532 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.51329 | 0.154450 | ||||||||
\(97\) | 14.7430i | 1.49693i | 0.663176 | + | 0.748463i | \(0.269208\pi\) | ||||
−0.663176 | + | 0.748463i | \(0.730792\pi\) | |||||||
\(98\) | − | 14.8824i | − | 1.50335i | ||||||
\(99\) | −15.9942 | −1.60747 | ||||||||
\(100\) | 15.4171 | − | 18.5187i | 1.54171 | − | 1.85187i | ||||
\(101\) | −10.5437 | −1.04914 | −0.524569 | − | 0.851368i | \(-0.675774\pi\) | ||||
−0.524569 | + | 0.851368i | \(0.675774\pi\) | |||||||
\(102\) | 2.20183i | 0.218013i | ||||||||
\(103\) | − | 9.12063i | − | 0.898682i | −0.893360 | − | 0.449341i | \(-0.851659\pi\) | ||
0.893360 | − | 0.449341i | \(-0.148341\pi\) | |||||||
\(104\) | 17.7842 | 1.74388 | ||||||||
\(105\) | 0.158862 | + | 0.338963i | 0.0155033 | + | 0.0330794i | ||||
\(106\) | 0.0467502 | 0.00454078 | ||||||||
\(107\) | − | 3.56368i | − | 0.344514i | −0.985052 | − | 0.172257i | \(-0.944894\pi\) | ||
0.985052 | − | 0.172257i | \(-0.0551060\pi\) | |||||||
\(108\) | − | 4.22893i | − | 0.406929i | ||||||
\(109\) | −10.6645 | −1.02147 | −0.510736 | − | 0.859737i | \(-0.670627\pi\) | ||||
−0.510736 | + | 0.859737i | \(0.670627\pi\) | |||||||
\(110\) | −28.3926 | + | 13.3068i | −2.70713 | + | 1.26875i | ||||
\(111\) | −1.08269 | −0.102765 | ||||||||
\(112\) | − | 10.9342i | − | 1.03319i | ||||||
\(113\) | − | 12.8769i | − | 1.21135i | −0.795711 | − | 0.605676i | \(-0.792903\pi\) | ||
0.795711 | − | 0.605676i | \(-0.207097\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.50107 | − | 1.17218i | 0.233226 | − | 0.109306i | ||||
\(116\) | −18.8654 | −1.75161 | ||||||||
\(117\) | − | 7.19490i | − | 0.665169i | ||||||
\(118\) | − | 34.0131i | − | 3.13116i | ||||||
\(119\) | 6.55203 | 0.600624 | ||||||||
\(120\) | −1.02541 | − | 2.18791i | −0.0936067 | − | 0.199728i | ||||
\(121\) | 17.8363 | 1.62149 | ||||||||
\(122\) | 0.0495254i | 0.00448382i | ||||||||
\(123\) | 0.713713i | 0.0643534i | ||||||||
\(124\) | −31.2465 | −2.80602 | ||||||||
\(125\) | −10.8160 | − | 2.83083i | −0.967415 | − | 0.253197i | ||||
\(126\) | −8.87120 | −0.790309 | ||||||||
\(127\) | 7.57260i | 0.671960i | 0.941869 | + | 0.335980i | \(0.109067\pi\) | ||||
−0.941869 | + | 0.335980i | \(0.890933\pi\) | |||||||
\(128\) | − | 0.381857i | − | 0.0337517i | ||||||
\(129\) | −1.11514 | −0.0981827 | ||||||||
\(130\) | −5.98599 | − | 12.7723i | −0.525006 | − | 1.12020i | ||||
\(131\) | 11.2785 | 0.985406 | 0.492703 | − | 0.870197i | \(-0.336009\pi\) | ||||
0.492703 | + | 0.870197i | \(0.336009\pi\) | |||||||
\(132\) | 3.79849i | 0.330616i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 18.4809 | 1.59651 | ||||||||
\(135\) | −1.77672 | + | 0.832695i | −0.152916 | + | 0.0716670i | ||||
\(136\) | −42.2915 | −3.62647 | ||||||||
\(137\) | 13.8445i | 1.18282i | 0.806373 | + | 0.591408i | \(0.201428\pi\) | ||||
−0.806373 | + | 0.591408i | \(0.798572\pi\) | |||||||
\(138\) | − | 0.473467i | − | 0.0403042i | ||||||
\(139\) | 1.97238 | 0.167295 | 0.0836475 | − | 0.996495i | \(-0.473343\pi\) | ||||
0.0836475 | + | 0.996495i | \(0.473343\pi\) | |||||||
\(140\) | −11.1293 | + | 5.21598i | −0.940600 | + | 0.440831i | ||||
\(141\) | 1.15275 | 0.0970791 | ||||||||
\(142\) | 7.14866i | 0.599902i | ||||||||
\(143\) | 12.9719i | 1.08477i | ||||||||
\(144\) | 28.5533 | 2.37944 | ||||||||
\(145\) | 3.71468 | + | 7.92601i | 0.308488 | + | 0.658219i | ||||
\(146\) | 14.5933 | 1.20775 | ||||||||
\(147\) | 0.836504i | 0.0689937i | ||||||||
\(148\) | − | 35.5485i | − | 2.92207i | ||||||
\(149\) | −11.1782 | −0.915753 | −0.457876 | − | 0.889016i | \(-0.651390\pi\) | ||||
−0.457876 | + | 0.889016i | \(0.651390\pi\) | |||||||
\(150\) | −1.22618 | + | 1.47286i | −0.100117 | + | 0.120259i | ||||
\(151\) | 10.4524 | 0.850603 | 0.425301 | − | 0.905052i | \(-0.360168\pi\) | ||||
0.425301 | + | 0.905052i | \(0.360168\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 17.1098i | 1.38324i | ||||||||
\(154\) | 15.9942 | 1.28885 | ||||||||
\(155\) | 6.15257 | + | 13.1277i | 0.494186 | + | 1.05444i | ||||
\(156\) | −1.70874 | −0.136808 | ||||||||
\(157\) | 5.62072i | 0.448583i | 0.974522 | + | 0.224291i | \(0.0720067\pi\) | ||||
−0.974522 | + | 0.224291i | \(0.927993\pi\) | |||||||
\(158\) | − | 24.9849i | − | 1.98769i | ||||||
\(159\) | −0.00262771 | −0.000208391 | ||||||||
\(160\) | 20.8750 | − | 9.78350i | 1.65032 | − | 0.773453i | ||||
\(161\) | −1.40891 | −0.111037 | ||||||||
\(162\) | − | 22.9972i | − | 1.80683i | ||||||
\(163\) | − | 5.97258i | − | 0.467808i | −0.972260 | − | 0.233904i | \(-0.924850\pi\) | ||
0.972260 | − | 0.233904i | \(-0.0751502\pi\) | |||||||
\(164\) | −23.4337 | −1.82986 | ||||||||
\(165\) | 1.59588 | − | 0.747940i | 0.124239 | − | 0.0582271i | ||||
\(166\) | −1.02055 | −0.0792100 | ||||||||
\(167\) | − | 10.2447i | − | 0.792756i | −0.918087 | − | 0.396378i | \(-0.870267\pi\) | ||
0.918087 | − | 0.396378i | \(-0.129733\pi\) | |||||||
\(168\) | 1.23250i | 0.0950893i | ||||||||
\(169\) | 7.16464 | 0.551126 | ||||||||
\(170\) | 14.2349 | + | 30.3730i | 1.09177 | + | 2.32950i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 36.6139i | − | 2.79178i | ||||||
\(173\) | 2.49506i | 0.189696i | 0.995492 | + | 0.0948479i | \(0.0302365\pi\) | ||||
−0.995492 | + | 0.0948479i | \(0.969764\pi\) | |||||||
\(174\) | 1.50044 | 0.113748 | ||||||||
\(175\) | 4.38283 | + | 3.64876i | 0.331311 | + | 0.275821i | ||||
\(176\) | −51.4796 | −3.88042 | ||||||||
\(177\) | 1.91179i | 0.143699i | ||||||||
\(178\) | − | 9.34131i | − | 0.700161i | ||||||
\(179\) | −22.5409 | −1.68478 | −0.842392 | − | 0.538865i | \(-0.818853\pi\) | ||||
−0.842392 | + | 0.538865i | \(0.818853\pi\) | |||||||
\(180\) | −13.6209 | − | 29.0628i | −1.01524 | − | 2.16621i | ||||
\(181\) | −6.81802 | −0.506779 | −0.253390 | − | 0.967364i | \(-0.581545\pi\) | ||||
−0.253390 | + | 0.967364i | \(0.581545\pi\) | |||||||
\(182\) | 7.19490i | 0.533322i | ||||||||
\(183\) | − | 0.00278370i | − | 0.000205777i | ||||||
\(184\) | 9.09410 | 0.670426 | ||||||||
\(185\) | −14.9352 | + | 6.99966i | −1.09805 | + | 0.514625i | ||||
\(186\) | 2.48515 | 0.182220 | ||||||||
\(187\) | − | 30.8477i | − | 2.25581i | ||||||
\(188\) | 37.8488i | 2.76041i | ||||||||
\(189\) | 1.00086 | 0.0728021 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.97452 | −0.359944 | −0.179972 | − | 0.983672i | \(-0.557601\pi\) | ||||
−0.179972 | + | 0.983672i | \(0.557601\pi\) | |||||||
\(192\) | − | 1.13754i | − | 0.0820948i | ||||||
\(193\) | 7.01693i | 0.505090i | 0.967585 | + | 0.252545i | \(0.0812675\pi\) | ||||
−0.967585 | + | 0.252545i | \(0.918733\pi\) | |||||||
\(194\) | 38.4995 | 2.76410 | ||||||||
\(195\) | 0.336458 | + | 0.717899i | 0.0240942 | + | 0.0514098i | ||||
\(196\) | −27.4653 | −1.96181 | ||||||||
\(197\) | 22.0852i | 1.57351i | 0.617266 | + | 0.786754i | \(0.288240\pi\) | ||||
−0.617266 | + | 0.786754i | \(0.711760\pi\) | |||||||
\(198\) | 41.7666i | 2.96822i | ||||||||
\(199\) | −2.40961 | −0.170812 | −0.0854062 | − | 0.996346i | \(-0.527219\pi\) | ||||
−0.0854062 | + | 0.996346i | \(0.527219\pi\) | |||||||
\(200\) | −28.2899 | − | 23.5518i | −2.00040 | − | 1.66536i | ||||
\(201\) | −1.03877 | −0.0732690 | ||||||||
\(202\) | 27.5335i | 1.93725i | ||||||||
\(203\) | − | 4.46489i | − | 0.313374i | ||||||
\(204\) | 4.06344 | 0.284498 | ||||||||
\(205\) | 4.61419 | + | 9.84529i | 0.322269 | + | 0.687625i | ||||
\(206\) | −23.8173 | −1.65943 | ||||||||
\(207\) | − | 3.67917i | − | 0.255720i | ||||||
\(208\) | − | 23.1579i | − | 1.60571i | ||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0.885158 | − | 0.414847i | 0.0610817 | − | 0.0286272i | ||||
\(211\) | 19.0046 | 1.30833 | 0.654166 | − | 0.756351i | \(-0.273020\pi\) | ||||
0.654166 | + | 0.756351i | \(0.273020\pi\) | |||||||
\(212\) | − | 0.0862768i | − | 0.00592552i | ||||||
\(213\) | − | 0.401808i | − | 0.0275315i | ||||||
\(214\) | −9.30609 | −0.636151 | ||||||||
\(215\) | −15.3828 | + | 7.20944i | −1.04910 | + | 0.491680i | ||||
\(216\) | −6.46029 | −0.439567 | ||||||||
\(217\) | − | 7.39512i | − | 0.502014i | ||||||
\(218\) | 27.8489i | 1.88617i | ||||||||
\(219\) | −0.820251 | −0.0554274 | ||||||||
\(220\) | 24.5574 | + | 52.3982i | 1.65566 | + | 3.53268i | ||||
\(221\) | 13.8767 | 0.933449 | ||||||||
\(222\) | 2.82731i | 0.189757i | ||||||||
\(223\) | 22.0446i | 1.47622i | 0.674683 | + | 0.738108i | \(0.264280\pi\) | ||||
−0.674683 | + | 0.738108i | \(0.735720\pi\) | |||||||
\(224\) | −11.7593 | −0.785704 | ||||||||
\(225\) | −9.52827 | + | 11.4452i | −0.635218 | + | 0.763012i | ||||
\(226\) | −33.6262 | −2.23678 | ||||||||
\(227\) | − | 11.7969i | − | 0.782990i | −0.920180 | − | 0.391495i | \(-0.871958\pi\) | ||
0.920180 | − | 0.391495i | \(-0.128042\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.19467 | 0.0789463 | 0.0394731 | − | 0.999221i | \(-0.487432\pi\) | ||||
0.0394731 | + | 0.999221i | \(0.487432\pi\) | |||||||
\(230\) | −3.06099 | − | 6.53122i | −0.201835 | − | 0.430656i | ||||
\(231\) | −0.898992 | −0.0591493 | ||||||||
\(232\) | 28.8196i | 1.89210i | ||||||||
\(233\) | 15.6081i | 1.02252i | 0.859426 | + | 0.511260i | \(0.170821\pi\) | ||||
−0.859426 | + | 0.511260i | \(0.829179\pi\) | |||||||
\(234\) | −18.7885 | −1.22825 | ||||||||
\(235\) | 15.9016 | − | 7.45259i | 1.03730 | − | 0.486153i | ||||
\(236\) | −62.7708 | −4.08603 | ||||||||
\(237\) | 1.40434i | 0.0912216i | ||||||||
\(238\) | − | 17.1098i | − | 1.10906i | ||||||
\(239\) | −1.05474 | −0.0682255 | −0.0341128 | − | 0.999418i | \(-0.510861\pi\) | ||||
−0.0341128 | + | 0.999418i | \(0.510861\pi\) | |||||||
\(240\) | −2.84902 | + | 1.33525i | −0.183903 | + | 0.0861900i | ||||
\(241\) | 9.59410 | 0.618010 | 0.309005 | − | 0.951060i | \(-0.400004\pi\) | ||||
0.309005 | + | 0.951060i | \(0.400004\pi\) | |||||||
\(242\) | − | 46.5772i | − | 2.99410i | ||||||
\(243\) | 3.92514i | 0.251798i | ||||||||
\(244\) | 0.0913985 | 0.00585119 | ||||||||
\(245\) | 5.40804 | + | 11.5391i | 0.345507 | + | 0.737208i | ||||
\(246\) | 1.86377 | 0.118830 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 47.7334i | 3.03108i | ||||||||
\(249\) | 0.0573625 | 0.00363520 | ||||||||
\(250\) | −7.39233 | + | 28.2446i | −0.467532 | + | 1.78635i | ||||
\(251\) | −15.1640 | −0.957142 | −0.478571 | − | 0.878049i | \(-0.658845\pi\) | ||||
−0.478571 | + | 0.878049i | \(0.658845\pi\) | |||||||
\(252\) | 16.3717i | 1.03132i | ||||||||
\(253\) | 6.63329i | 0.417031i | ||||||||
\(254\) | 19.7748 | 1.24078 | ||||||||
\(255\) | −0.800110 | − | 1.70719i | −0.0501048 | − | 0.106909i | ||||
\(256\) | −16.4972 | −1.03108 | ||||||||
\(257\) | − | 23.0689i | − | 1.43900i | −0.694493 | − | 0.719499i | \(-0.744371\pi\) | ||
0.694493 | − | 0.719499i | \(-0.255629\pi\) | |||||||
\(258\) | 2.91204i | 0.181296i | ||||||||
\(259\) | 8.41329 | 0.522777 | ||||||||
\(260\) | −23.5711 | + | 11.0471i | −1.46182 | + | 0.685110i | ||||
\(261\) | 11.6595 | 0.721703 | ||||||||
\(262\) | − | 29.4523i | − | 1.81957i | ||||||
\(263\) | − | 3.05610i | − | 0.188447i | −0.995551 | − | 0.0942235i | \(-0.969963\pi\) | ||
0.995551 | − | 0.0942235i | \(-0.0300368\pi\) | |||||||
\(264\) | 5.80274 | 0.357134 | ||||||||
\(265\) | −0.0362479 | + | 0.0169883i | −0.00222669 | + | 0.00104358i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.525052i | 0.0321327i | ||||||||
\(268\) | − | 34.1063i | − | 2.08337i | ||||||
\(269\) | 1.05451 | 0.0642948 | 0.0321474 | − | 0.999483i | \(-0.489765\pi\) | ||||
0.0321474 | + | 0.999483i | \(0.489765\pi\) | |||||||
\(270\) | 2.17447 | + | 4.63967i | 0.132334 | + | 0.282361i | ||||
\(271\) | −1.67598 | −0.101809 | −0.0509043 | − | 0.998704i | \(-0.516210\pi\) | ||||
−0.0509043 | + | 0.998704i | \(0.516210\pi\) | |||||||
\(272\) | 55.0704i | 3.33913i | ||||||||
\(273\) | − | 0.404408i | − | 0.0244759i | ||||||
\(274\) | 36.1531 | 2.18409 | ||||||||
\(275\) | 17.1788 | − | 20.6349i | 1.03592 | − | 1.24433i | ||||
\(276\) | −0.873776 | −0.0525952 | ||||||||
\(277\) | 13.8944i | 0.834834i | 0.908715 | + | 0.417417i | \(0.137065\pi\) | ||||
−0.908715 | + | 0.417417i | \(0.862935\pi\) | |||||||
\(278\) | − | 5.15061i | − | 0.308913i | ||||||
\(279\) | 19.3114 | 1.15614 | ||||||||
\(280\) | 7.96816 | + | 17.0016i | 0.476189 | + | 1.01604i | ||||
\(281\) | 1.25004 | 0.0745713 | 0.0372856 | − | 0.999305i | \(-0.488129\pi\) | ||||
0.0372856 | + | 0.999305i | \(0.488129\pi\) | |||||||
\(282\) | − | 3.01026i | − | 0.179258i | ||||||
\(283\) | 15.7261i | 0.934819i | 0.884041 | + | 0.467409i | \(0.154813\pi\) | ||||
−0.884041 | + | 0.467409i | \(0.845187\pi\) | |||||||
\(284\) | 13.1927 | 0.782846 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 33.8744 | 2.00304 | ||||||||
\(287\) | − | 5.54606i | − | 0.327374i | ||||||
\(288\) | − | 30.7080i | − | 1.80948i | ||||||
\(289\) | −15.9994 | −0.941140 | ||||||||
\(290\) | 20.6977 | − | 9.70040i | 1.21541 | − | 0.569627i | ||||
\(291\) | −2.16396 | −0.126854 | ||||||||
\(292\) | − | 26.9316i | − | 1.57606i | ||||||
\(293\) | 11.9316i | 0.697051i | 0.937299 | + | 0.348526i | \(0.113318\pi\) | ||||
−0.937299 | + | 0.348526i | \(0.886682\pi\) | |||||||
\(294\) | 2.18442 | 0.127398 | ||||||||
\(295\) | 12.3598 | + | 26.3722i | 0.719618 | + | 1.53545i | ||||
\(296\) | −54.3055 | −3.15644 | ||||||||
\(297\) | − | 4.71218i | − | 0.273428i | ||||||
\(298\) | 29.1904i | 1.69095i | ||||||||
\(299\) | −2.98396 | −0.172567 | ||||||||
\(300\) | 2.71815 | + | 2.26289i | 0.156932 | + | 0.130648i | ||||
\(301\) | 8.66544 | 0.499467 | ||||||||
\(302\) | − | 27.2950i | − | 1.57065i | ||||||
\(303\) | − | 1.54759i | − | 0.0889067i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.0179968 | − | 0.0383996i | −0.00103049 | − | 0.00219876i | ||||
\(306\) | 44.6799 | 2.55418 | ||||||||
\(307\) | − | 24.3857i | − | 1.39176i | −0.718156 | − | 0.695882i | \(-0.755014\pi\) | ||
0.718156 | − | 0.695882i | \(-0.244986\pi\) | |||||||
\(308\) | − | 29.5170i | − | 1.68189i | ||||||
\(309\) | 1.33871 | 0.0761567 | ||||||||
\(310\) | 34.2813 | − | 16.0666i | 1.94705 | − | 0.912523i | ||||
\(311\) | −5.06773 | −0.287364 | −0.143682 | − | 0.989624i | \(-0.545894\pi\) | ||||
−0.143682 | + | 0.989624i | \(0.545894\pi\) | |||||||
\(312\) | 2.61034i | 0.147781i | ||||||||
\(313\) | − | 18.9537i | − | 1.07133i | −0.844431 | − | 0.535664i | \(-0.820061\pi\) | ||
0.844431 | − | 0.535664i | \(-0.179939\pi\) | |||||||
\(314\) | 14.6778 | 0.828315 | ||||||||
\(315\) | 6.87830 | − | 3.22366i | 0.387549 | − | 0.181632i | ||||
\(316\) | −46.1093 | −2.59385 | ||||||||
\(317\) | − | 12.1377i | − | 0.681720i | −0.940114 | − | 0.340860i | \(-0.889282\pi\) | ||
0.940114 | − | 0.340860i | \(-0.110718\pi\) | |||||||
\(318\) | 0.00686192i | 0.000384798i | ||||||||
\(319\) | −21.0212 | −1.17696 | ||||||||
\(320\) | −7.35424 | − | 15.6917i | −0.411115 | − | 0.877194i | ||||
\(321\) | 0.523072 | 0.0291950 | ||||||||
\(322\) | 3.67917i | 0.205032i | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −42.4410 | −2.35783 | ||||||||
\(325\) | 9.28251 | + | 7.72781i | 0.514901 | + | 0.428662i | ||||
\(326\) | −15.5966 | −0.863815 | ||||||||
\(327\) | − | 1.56532i | − | 0.0865623i | ||||||
\(328\) | 35.7983i | 1.97663i | ||||||||
\(329\) | −8.95769 | −0.493853 | ||||||||
\(330\) | −1.95315 | − | 4.16742i | −0.107517 | − | 0.229409i | ||||
\(331\) | 19.3649 | 1.06439 | 0.532197 | − | 0.846621i | \(-0.321367\pi\) | ||||
0.532197 | + | 0.846621i | \(0.321367\pi\) | |||||||
\(332\) | 1.88341i | 0.103366i | ||||||||
\(333\) | 21.9702i | 1.20396i | ||||||||
\(334\) | −26.7526 | −1.46384 | ||||||||
\(335\) | −14.3292 | + | 6.71568i | −0.782889 | + | 0.366917i | ||||
\(336\) | 1.60491 | 0.0875551 | ||||||||
\(337\) | 4.13312i | 0.225146i | 0.993643 | + | 0.112573i | \(0.0359091\pi\) | ||||
−0.993643 | + | 0.112573i | \(0.964091\pi\) | |||||||
\(338\) | − | 18.7095i | − | 1.01766i | ||||||
\(339\) | 1.89005 | 0.102653 | ||||||||
\(340\) | 56.0530 | − | 26.2704i | 3.03990 | − | 1.42471i | ||||
\(341\) | −34.8171 | −1.88545 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 14.4842i | − | 0.782076i | ||||||
\(344\) | −55.9330 | −3.01570 | ||||||||
\(345\) | 0.172050 | + | 0.367104i | 0.00926288 | + | 0.0197642i | ||||
\(346\) | 6.51552 | 0.350276 | ||||||||
\(347\) | 4.77587i | 0.256382i | 0.991749 | + | 0.128191i | \(0.0409171\pi\) | ||||
−0.991749 | + | 0.128191i | \(0.959083\pi\) | |||||||
\(348\) | − | 2.76904i | − | 0.148436i | ||||||
\(349\) | −0.557017 | −0.0298165 | −0.0149082 | − | 0.999889i | \(-0.504746\pi\) | ||||
−0.0149082 | + | 0.999889i | \(0.504746\pi\) | |||||||
\(350\) | 9.52827 | − | 11.4452i | 0.509307 | − | 0.611771i | ||||
\(351\) | 2.11975 | 0.113144 | ||||||||
\(352\) | 55.3643i | 2.95093i | ||||||||
\(353\) | − | 24.4841i | − | 1.30316i | −0.758580 | − | 0.651580i | \(-0.774107\pi\) | ||
0.758580 | − | 0.651580i | \(-0.225893\pi\) | |||||||
\(354\) | 4.99240 | 0.265343 | ||||||||
\(355\) | −2.59771 | − | 5.54273i | −0.137872 | − | 0.294177i | ||||
\(356\) | −17.2393 | −0.913679 | ||||||||
\(357\) | 0.961697i | 0.0508984i | ||||||||
\(358\) | 58.8625i | 3.11098i | ||||||||
\(359\) | −20.9706 | −1.10679 | −0.553393 | − | 0.832921i | \(-0.686667\pi\) | ||||
−0.553393 | + | 0.832921i | \(0.686667\pi\) | |||||||
\(360\) | −44.3975 | + | 20.8078i | −2.33996 | + | 1.09667i | ||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 17.8044i | 0.935776i | ||||||||
\(363\) | 2.61799i | 0.137409i | ||||||||
\(364\) | 13.2781 | 0.695961 | ||||||||
\(365\) | −11.3149 | + | 5.30296i | −0.592250 | + | 0.277570i | ||||
\(366\) | −0.00726927 | −0.000379971 | ||||||||
\(367\) | − | 21.4343i | − | 1.11886i | −0.828877 | − | 0.559431i | \(-0.811020\pi\) | ||
0.828877 | − | 0.559431i | \(-0.188980\pi\) | |||||||
\(368\) | − | 11.8420i | − | 0.617306i | ||||||
\(369\) | 14.4828 | 0.753945 | ||||||||
\(370\) | 18.2787 | + | 39.0012i | 0.950264 | + | 2.02758i | ||||
\(371\) | 0.0204192 | 0.00106011 | ||||||||
\(372\) | − | 4.58631i | − | 0.237789i | ||||||
\(373\) | − | 27.7981i | − | 1.43933i | −0.694321 | − | 0.719666i | \(-0.744295\pi\) | ||
0.694321 | − | 0.719666i | \(-0.255705\pi\) | |||||||
\(374\) | −80.5547 | −4.16539 | ||||||||
\(375\) | 0.415504 | − | 1.58756i | 0.0214566 | − | 0.0819813i | ||||
\(376\) | 57.8194 | 2.98181 | ||||||||
\(377\) | − | 9.45630i | − | 0.487024i | ||||||
\(378\) | − | 2.61362i | − | 0.134430i | ||||||
\(379\) | 1.97507 | 0.101452 | 0.0507261 | − | 0.998713i | \(-0.483846\pi\) | ||||
0.0507261 | + | 0.998713i | \(0.483846\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.11150 | −0.0569436 | ||||||||
\(382\) | 12.9903i | 0.664642i | ||||||||
\(383\) | − | 10.0103i | − | 0.511504i | −0.966742 | − | 0.255752i | \(-0.917677\pi\) | ||
0.966742 | − | 0.255752i | \(-0.0823231\pi\) | |||||||
\(384\) | 0.0560484 | 0.00286021 | ||||||||
\(385\) | −12.4011 | + | 5.81203i | −0.632019 | + | 0.296208i | ||||
\(386\) | 18.3238 | 0.932656 | ||||||||
\(387\) | 22.6286i | 1.15028i | ||||||||
\(388\) | − | 71.0502i | − | 3.60703i | ||||||
\(389\) | −12.0247 | −0.609678 | −0.304839 | − | 0.952404i | \(-0.598603\pi\) | ||||
−0.304839 | + | 0.952404i | \(0.598603\pi\) | |||||||
\(390\) | 1.87470 | − | 0.878615i | 0.0949291 | − | 0.0444904i | ||||
\(391\) | 7.09597 | 0.358859 | ||||||||
\(392\) | 41.9572i | 2.11916i | ||||||||
\(393\) | 1.65544i | 0.0835059i | ||||||||
\(394\) | 57.6727 | 2.90551 | ||||||||
\(395\) | 9.07912 | + | 19.3721i | 0.456820 | + | 0.974715i | ||||
\(396\) | 77.0797 | 3.87340 | ||||||||
\(397\) | − | 1.87227i | − | 0.0939666i | −0.998896 | − | 0.0469833i | \(-0.985039\pi\) | ||
0.998896 | − | 0.0469833i | \(-0.0149608\pi\) | |||||||
\(398\) | 6.29237i | 0.315408i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −30.6682 | + | 36.8381i | −1.53341 | + | 1.84190i | ||||
\(401\) | −23.5289 | −1.17498 | −0.587489 | − | 0.809232i | \(-0.699883\pi\) | ||||
−0.587489 | + | 0.809232i | \(0.699883\pi\) | |||||||
\(402\) | 2.71260i | 0.135292i | ||||||||
\(403\) | − | 15.6623i | − | 0.780196i | ||||||
\(404\) | 50.8127 | 2.52803 | ||||||||
\(405\) | 8.35682 | + | 17.8309i | 0.415254 | + | 0.886026i | ||||
\(406\) | −11.6595 | −0.578649 | ||||||||
\(407\) | − | 39.6107i | − | 1.96343i | ||||||
\(408\) | − | 6.20749i | − | 0.307316i | ||||||
\(409\) | 16.0211 | 0.792193 | 0.396097 | − | 0.918209i | \(-0.370364\pi\) | ||||
0.396097 | + | 0.918209i | \(0.370364\pi\) | |||||||
\(410\) | 25.7097 | − | 12.0494i | 1.26971 | − | 0.595075i | ||||
\(411\) | −2.03207 | −0.100235 | ||||||||
\(412\) | 43.9545i | 2.16548i | ||||||||
\(413\) | − | 14.8560i | − | 0.731016i | ||||||
\(414\) | −9.60767 | −0.472191 | ||||||||
\(415\) | 0.791285 | − | 0.370852i | 0.0388427 | − | 0.0182044i | ||||
\(416\) | −24.9054 | −1.22109 | ||||||||
\(417\) | 0.289503i | 0.0141770i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.2305 | 0.499794 | 0.249897 | − | 0.968272i | \(-0.419603\pi\) | ||||
0.249897 | + | 0.968272i | \(0.419603\pi\) | |||||||
\(420\) | −0.765594 | − | 1.63355i | −0.0373572 | − | 0.0797089i | ||||
\(421\) | 25.6300 | 1.24913 | 0.624565 | − | 0.780973i | \(-0.285276\pi\) | ||||
0.624565 | + | 0.780973i | \(0.285276\pi\) | |||||||
\(422\) | − | 49.6281i | − | 2.41586i | ||||||
\(423\) | − | 23.3918i | − | 1.13735i | ||||||
\(424\) | −0.131800 | −0.00640078 | ||||||||
\(425\) | −22.0742 | − | 18.3770i | −1.07075 | − | 0.891417i | ||||
\(426\) | −1.04927 | −0.0508373 | ||||||||
\(427\) | 0.0216313i | 0.00104681i | ||||||||
\(428\) | 17.1743i | 0.830149i | ||||||||
\(429\) | −1.90400 | −0.0919259 | ||||||||
\(430\) | 18.8265 | + | 40.1701i | 0.907895 | + | 1.93717i | ||||
\(431\) | −26.3929 | −1.27130 | −0.635650 | − | 0.771978i | \(-0.719268\pi\) | ||||
−0.635650 | + | 0.771978i | \(0.719268\pi\) | |||||||
\(432\) | 8.41234i | 0.404739i | ||||||||
\(433\) | 11.1339i | 0.535061i | 0.963549 | + | 0.267531i | \(0.0862077\pi\) | ||||
−0.963549 | + | 0.267531i | \(0.913792\pi\) | |||||||
\(434\) | −19.3114 | −0.926976 | ||||||||
\(435\) | −1.16337 | + | 0.545236i | −0.0557792 | + | 0.0261420i | ||||
\(436\) | 51.3948 | 2.46136 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 2.14198i | 0.102348i | ||||||||
\(439\) | −32.5878 | −1.55533 | −0.777666 | − | 0.628677i | \(-0.783597\pi\) | ||||
−0.777666 | + | 0.628677i | \(0.783597\pi\) | |||||||
\(440\) | 80.0457 | − | 37.5150i | 3.81603 | − | 1.78846i | ||||
\(441\) | 16.9745 | 0.808309 | ||||||||
\(442\) | − | 36.2372i | − | 1.72363i | ||||||
\(443\) | 41.7702i | 1.98456i | 0.124013 | + | 0.992281i | \(0.460424\pi\) | ||||
−0.124013 | + | 0.992281i | \(0.539576\pi\) | |||||||
\(444\) | 5.21776 | 0.247624 | ||||||||
\(445\) | 3.39449 | + | 7.24281i | 0.160914 | + | 0.343342i | ||||
\(446\) | 57.5666 | 2.72586 | ||||||||
\(447\) | − | 1.64072i | − | 0.0776033i | ||||||
\(448\) | 8.83948i | 0.417626i | ||||||||
\(449\) | 40.0139 | 1.88837 | 0.944187 | − | 0.329409i | \(-0.106849\pi\) | ||||
0.944187 | + | 0.329409i | \(0.106849\pi\) | |||||||
\(450\) | 29.8876 | + | 24.8818i | 1.40891 | + | 1.17294i | ||||
\(451\) | −26.1115 | −1.22954 | ||||||||
\(452\) | 62.0567i | 2.91890i | ||||||||
\(453\) | 1.53419i | 0.0720823i | ||||||||
\(454\) | −30.8061 | −1.44580 | ||||||||
\(455\) | −2.61452 | − | 5.57858i | −0.122570 | − | 0.261528i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 30.1103i | 1.40850i | 0.709953 | + | 0.704249i | \(0.248716\pi\) | ||||
−0.709953 | + | 0.704249i | \(0.751284\pi\) | |||||||
\(458\) | − | 3.11973i | − | 0.145776i | ||||||
\(459\) | −5.04086 | −0.235287 | ||||||||
\(460\) | −12.0533 | + | 5.64901i | −0.561987 | + | 0.263386i | ||||
\(461\) | −19.8065 | −0.922479 | −0.461239 | − | 0.887276i | \(-0.652595\pi\) | ||||
−0.461239 | + | 0.887276i | \(0.652595\pi\) | |||||||
\(462\) | 2.34760i | 0.109220i | ||||||||
\(463\) | 17.0673i | 0.793186i | 0.917994 | + | 0.396593i | \(0.129808\pi\) | ||||
−0.917994 | + | 0.396593i | \(0.870192\pi\) | |||||||
\(464\) | 37.5278 | 1.74218 | ||||||||
\(465\) | −1.92687 | + | 0.903065i | −0.0893563 | + | 0.0418786i | ||||
\(466\) | 40.7585 | 1.88810 | ||||||||
\(467\) | 24.1262i | 1.11643i | 0.829697 | + | 0.558214i | \(0.188513\pi\) | ||||
−0.829697 | + | 0.558214i | \(0.811487\pi\) | |||||||
\(468\) | 34.6740i | 1.60281i | ||||||||
\(469\) | 8.07196 | 0.372728 | ||||||||
\(470\) | −19.4615 | − | 41.5249i | −0.897690 | − | 1.91540i | ||||
\(471\) | −0.825001 | −0.0380141 | ||||||||
\(472\) | 95.8913i | 4.41376i | ||||||||
\(473\) | − | 40.7979i | − | 1.87589i | ||||||
\(474\) | 3.66724 | 0.168442 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −31.5758 | −1.44728 | ||||||||
\(477\) | 0.0533220i | 0.00244145i | ||||||||
\(478\) | 2.75432i | 0.125979i | ||||||||
\(479\) | 32.5068 | 1.48527 | 0.742637 | − | 0.669695i | \(-0.233575\pi\) | ||||
0.742637 | + | 0.669695i | \(0.233575\pi\) | |||||||
\(480\) | 1.43601 | + | 3.06400i | 0.0655445 | + | 0.139852i | ||||
\(481\) | 17.8187 | 0.812464 | ||||||||
\(482\) | − | 25.0537i | − | 1.14117i | ||||||
\(483\) | − | 0.206797i | − | 0.00940960i | ||||||
\(484\) | −85.9576 | −3.90717 | ||||||||
\(485\) | −29.8506 | + | 13.9901i | −1.35545 | + | 0.635258i | ||||
\(486\) | 10.2500 | 0.464949 | ||||||||
\(487\) | − | 30.4975i | − | 1.38197i | −0.722868 | − | 0.690986i | \(-0.757177\pi\) | ||
0.722868 | − | 0.690986i | \(-0.242823\pi\) | |||||||
\(488\) | − | 0.139624i | − | 0.00632049i | ||||||
\(489\) | 0.876646 | 0.0396433 | ||||||||
\(490\) | 30.1329 | − | 14.1224i | 1.36127 | − | 0.637984i | ||||
\(491\) | −19.4673 | −0.878548 | −0.439274 | − | 0.898353i | \(-0.644764\pi\) | ||||
−0.439274 | + | 0.898353i | \(0.644764\pi\) | |||||||
\(492\) | − | 3.43956i | − | 0.155067i | ||||||
\(493\) | 22.4875i | 1.01278i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −15.1773 | − | 32.3838i | −0.682171 | − | 1.45555i | ||||
\(496\) | 62.1567 | 2.79092 | ||||||||
\(497\) | 3.12234i | 0.140056i | ||||||||
\(498\) | − | 0.149795i | − | 0.00671246i | ||||||
\(499\) | −1.81090 | −0.0810670 | −0.0405335 | − | 0.999178i | \(-0.512906\pi\) | ||||
−0.0405335 | + | 0.999178i | \(0.512906\pi\) | |||||||
\(500\) | 52.1251 | + | 13.6424i | 2.33110 | + | 0.610108i | ||||
\(501\) | 1.50370 | 0.0671802 | ||||||||
\(502\) | 39.5987i | 1.76738i | ||||||||
\(503\) | 26.5154i | 1.18226i | 0.806575 | + | 0.591132i | \(0.201319\pi\) | ||||
−0.806575 | + | 0.591132i | \(0.798681\pi\) | |||||||
\(504\) | 25.0101 | 1.11404 | ||||||||
\(505\) | −10.0052 | − | 21.3482i | −0.445228 | − | 0.949981i | ||||
\(506\) | 17.3220 | 0.770055 | ||||||||
\(507\) | 1.05162i | 0.0467039i | ||||||||
\(508\) | − | 36.4942i | − | 1.61917i | ||||||
\(509\) | 11.3299 | 0.502191 | 0.251095 | − | 0.967962i | \(-0.419209\pi\) | ||||
0.251095 | + | 0.967962i | \(0.419209\pi\) | |||||||
\(510\) | −4.45811 | + | 2.08938i | −0.197408 | + | 0.0925194i | ||||
\(511\) | 6.37393 | 0.281966 | ||||||||
\(512\) | 42.3167i | 1.87015i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −60.2414 | −2.65713 | ||||||||
\(515\) | 18.4668 | − | 8.65484i | 0.813745 | − | 0.381378i | ||||
\(516\) | 5.37414 | 0.236583 | ||||||||
\(517\) | 42.1738i | 1.85480i | ||||||||
\(518\) | − | 21.9702i | − | 0.965315i | ||||||
\(519\) | −0.366221 | −0.0160753 | ||||||||
\(520\) | 16.8760 | + | 36.0082i | 0.740060 | + | 1.57906i | ||||
\(521\) | −25.1821 | −1.10325 | −0.551624 | − | 0.834093i | \(-0.685992\pi\) | ||||
−0.551624 | + | 0.834093i | \(0.685992\pi\) | |||||||
\(522\) | − | 30.4472i | − | 1.33264i | ||||||
\(523\) | − | 2.56239i | − | 0.112045i | −0.998429 | − | 0.0560227i | \(-0.982158\pi\) | ||
0.998429 | − | 0.0560227i | \(-0.0178419\pi\) | |||||||
\(524\) | −54.3538 | −2.37446 | ||||||||
\(525\) | −0.535560 | + | 0.643305i | −0.0233738 | + | 0.0280761i | ||||
\(526\) | −7.98060 | −0.347971 | ||||||||
\(527\) | 37.2456i | 1.62244i | ||||||||
\(528\) | − | 7.55610i | − | 0.328837i | ||||||
\(529\) | 21.4741 | 0.933658 | ||||||||
\(530\) | 0.0443627 | + | 0.0946565i | 0.00192699 | + | 0.00411162i | ||||
\(531\) | 38.7945 | 1.68354 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 11.7461i | − | 0.508782i | ||||||
\(534\) | 1.37110 | 0.0593335 | ||||||||
\(535\) | 7.21550 | − | 3.38169i | 0.311953 | − | 0.146203i | ||||
\(536\) | −52.1022 | −2.25047 | ||||||||
\(537\) | − | 3.30852i | − | 0.142773i | ||||||
\(538\) | − | 2.75372i | − | 0.118721i | ||||||
\(539\) | −30.6038 | −1.31820 | ||||||||
\(540\) | 8.56244 | − | 4.01296i | 0.368469 | − | 0.172690i | ||||
\(541\) | 27.1770 | 1.16843 | 0.584215 | − | 0.811599i | \(-0.301402\pi\) | ||||
0.584215 | + | 0.811599i | \(0.301402\pi\) | |||||||
\(542\) | 4.37660i | 0.187991i | ||||||||
\(543\) | − | 1.00074i | − | 0.0429458i | ||||||
\(544\) | 59.2260 | 2.53929 | ||||||||
\(545\) | −10.1199 | − | 21.5927i | −0.433487 | − | 0.924930i | ||||
\(546\) | −1.05606 | −0.0451951 | ||||||||
\(547\) | − | 15.6526i | − | 0.669259i | −0.942350 | − | 0.334629i | \(-0.891389\pi\) | ||
0.942350 | − | 0.334629i | \(-0.108611\pi\) | |||||||
\(548\) | − | 66.7200i | − | 2.85014i | ||||||
\(549\) | −0.0564874 | −0.00241082 | ||||||||
\(550\) | −53.8852 | − | 44.8602i | −2.29767 | − | 1.91284i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 1.33482i | 0.0568136i | ||||||||
\(553\) | − | 10.9127i | − | 0.464055i | ||||||
\(554\) | 36.2834 | 1.54153 | ||||||||
\(555\) | −1.02740 | − | 2.19216i | −0.0436107 | − | 0.0930520i | ||||
\(556\) | −9.50537 | −0.403118 | ||||||||
\(557\) | − | 38.7469i | − | 1.64176i | −0.571101 | − | 0.820880i | \(-0.693484\pi\) | ||
0.571101 | − | 0.820880i | \(-0.306516\pi\) | |||||||
\(558\) | − | 50.4291i | − | 2.13484i | ||||||
\(559\) | 18.3528 | 0.776239 | ||||||||
\(560\) | 22.1389 | − | 10.3758i | 0.935538 | − | 0.438459i | ||||
\(561\) | 4.52778 | 0.191163 | ||||||||
\(562\) | − | 3.26432i | − | 0.137697i | ||||||
\(563\) | 38.8502i | 1.63734i | 0.574265 | + | 0.818670i | \(0.305288\pi\) | ||||
−0.574265 | + | 0.818670i | \(0.694712\pi\) | |||||||
\(564\) | −5.55539 | −0.233924 | ||||||||
\(565\) | 26.0722 | − | 12.2192i | 1.09686 | − | 0.514067i | ||||
\(566\) | 41.0666 | 1.72616 | ||||||||
\(567\) | − | 10.0445i | − | 0.421831i | ||||||
\(568\) | − | 20.1538i | − | 0.845635i | ||||||
\(569\) | 19.2093 | 0.805294 | 0.402647 | − | 0.915355i | \(-0.368090\pi\) | ||||
0.402647 | + | 0.915355i | \(0.368090\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.84542 | −0.370169 | −0.185085 | − | 0.982723i | \(-0.559256\pi\) | ||||
−0.185085 | + | 0.982723i | \(0.559256\pi\) | |||||||
\(572\) | − | 62.5148i | − | 2.61387i | ||||||
\(573\) | − | 0.730153i | − | 0.0305026i | ||||||
\(574\) | −14.4828 | −0.604500 | ||||||||
\(575\) | 4.74668 | + | 3.95168i | 0.197950 | + | 0.164796i | ||||
\(576\) | −23.0831 | −0.961797 | ||||||||
\(577\) | − | 15.0333i | − | 0.625845i | −0.949779 | − | 0.312922i | \(-0.898692\pi\) | ||
0.949779 | − | 0.312922i | \(-0.101308\pi\) | |||||||
\(578\) | 41.7802i | 1.73783i | ||||||||
\(579\) | −1.02993 | −0.0428026 | ||||||||
\(580\) | −17.9020 | − | 38.1974i | −0.743338 | − | 1.58606i | ||||
\(581\) | −0.445748 | −0.0184927 | ||||||||
\(582\) | 5.65089i | 0.234237i | ||||||||
\(583\) | − | 0.0961358i | − | 0.00398154i | ||||||
\(584\) | −41.1419 | −1.70247 | ||||||||
\(585\) | 14.5677 | − | 6.82746i | 0.602302 | − | 0.282281i | ||||
\(586\) | 31.1578 | 1.28712 | ||||||||
\(587\) | 42.7945i | 1.76632i | 0.469073 | + | 0.883159i | \(0.344588\pi\) | ||||
−0.469073 | + | 0.883159i | \(0.655412\pi\) | |||||||
\(588\) | − | 4.03132i | − | 0.166249i | ||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 68.8674 | − | 32.2761i | 2.83523 | − | 1.32879i | ||||
\(591\) | −3.24164 | −0.133343 | ||||||||
\(592\) | 70.7145i | 2.90635i | ||||||||
\(593\) | 30.9216i | 1.26980i | 0.772595 | + | 0.634900i | \(0.218959\pi\) | ||||
−0.772595 | + | 0.634900i | \(0.781041\pi\) | |||||||
\(594\) | −12.3052 | −0.504890 | ||||||||
\(595\) | 6.21742 | + | 13.2661i | 0.254889 | + | 0.543857i | ||||
\(596\) | 53.8704 | 2.20662 | ||||||||
\(597\) | − | 0.353678i | − | 0.0144751i | ||||||
\(598\) | 7.79221i | 0.318647i | ||||||||
\(599\) | −18.2839 | −0.747058 | −0.373529 | − | 0.927618i | \(-0.621852\pi\) | ||||
−0.373529 | + | 0.927618i | \(0.621852\pi\) | |||||||
\(600\) | 3.45689 | − | 4.15236i | 0.141127 | − | 0.169519i | ||||
\(601\) | −40.5660 | −1.65472 | −0.827361 | − | 0.561670i | \(-0.810159\pi\) | ||||
−0.827361 | + | 0.561670i | \(0.810159\pi\) | |||||||
\(602\) | − | 22.6286i | − | 0.922275i | ||||||
\(603\) | 21.0788i | 0.858397i | ||||||||
\(604\) | −50.3726 | −2.04963 | ||||||||
\(605\) | 16.9254 | + | 36.1138i | 0.688117 | + | 1.46823i | ||||
\(606\) | −4.04133 | −0.164168 | ||||||||
\(607\) | − | 9.33324i | − | 0.378825i | −0.981898 | − | 0.189412i | \(-0.939342\pi\) | ||
0.981898 | − | 0.189412i | \(-0.0606583\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.655350 | 0.0265561 | ||||||||
\(610\) | −0.100276 | + | 0.0469962i | −0.00406004 | + | 0.00190282i | ||||
\(611\) | −18.9717 | −0.767514 | ||||||||
\(612\) | − | 82.4561i | − | 3.33309i | ||||||
\(613\) | 40.6646i | 1.64243i | 0.570621 | + | 0.821213i | \(0.306702\pi\) | ||||
−0.570621 | + | 0.821213i | \(0.693298\pi\) | |||||||
\(614\) | −63.6800 | −2.56991 | ||||||||
\(615\) | −1.44508 | + | 0.677264i | −0.0582711 | + | 0.0273099i | ||||
\(616\) | −45.0914 | −1.81678 | ||||||||
\(617\) | − | 18.4246i | − | 0.741745i | −0.928684 | − | 0.370872i | \(-0.879059\pi\) | ||
0.928684 | − | 0.370872i | \(-0.120941\pi\) | |||||||
\(618\) | − | 3.49587i | − | 0.140625i | ||||||
\(619\) | 2.68372 | 0.107868 | 0.0539340 | − | 0.998545i | \(-0.482824\pi\) | ||||
0.0539340 | + | 0.998545i | \(0.482824\pi\) | |||||||
\(620\) | −29.6507 | − | 63.2657i | −1.19080 | − | 2.54081i | ||||
\(621\) | 1.08395 | 0.0434975 | ||||||||
\(622\) | 13.2337i | 0.530623i | ||||||||
\(623\) | − | 4.08003i | − | 0.163463i | ||||||
\(624\) | 3.39908 | 0.136072 | ||||||||
\(625\) | −4.53200 | − | 24.5858i | −0.181280 | − | 0.983432i | ||||
\(626\) | −49.4952 | −1.97823 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 27.0876i | − | 1.08091i | ||||||
\(629\) | −42.3736 | −1.68955 | ||||||||
\(630\) | −8.41815 | − | 17.9618i | −0.335387 | − | 0.715615i | ||||
\(631\) | −18.6512 | −0.742492 | −0.371246 | − | 0.928535i | \(-0.621069\pi\) | ||||
−0.371246 | + | 0.928535i | \(0.621069\pi\) | |||||||
\(632\) | 70.4385i | 2.80189i | ||||||||
\(633\) | 2.78947i | 0.110872i | ||||||||
\(634\) | −31.6959 | −1.25881 | ||||||||
\(635\) | −15.3325 | + | 7.18587i | −0.608451 | + | 0.285163i | ||||
\(636\) | 0.0126636 | 0.000502144 | ||||||||
\(637\) | − | 13.7670i | − | 0.545469i | ||||||
\(638\) | 54.8941i | 2.17328i | ||||||||
\(639\) | −8.15357 | −0.322550 | ||||||||
\(640\) | 0.773157 | − | 0.362356i | 0.0305617 | − | 0.0143234i | ||||
\(641\) | 4.88420 | 0.192914 | 0.0964572 | − | 0.995337i | \(-0.469249\pi\) | ||||
0.0964572 | + | 0.995337i | \(0.469249\pi\) | |||||||
\(642\) | − | 1.36593i | − | 0.0539091i | ||||||
\(643\) | 3.68757i | 0.145424i | 0.997353 | + | 0.0727118i | \(0.0231653\pi\) | ||||
−0.997353 | + | 0.0727118i | \(0.976835\pi\) | |||||||
\(644\) | 6.78986 | 0.267558 | ||||||||
\(645\) | −1.05819 | − | 2.25786i | −0.0416662 | − | 0.0889031i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 26.3559i | 1.03616i | 0.855333 | + | 0.518079i | \(0.173353\pi\) | ||||
−0.855333 | + | 0.518079i | \(0.826647\pi\) | |||||||
\(648\) | 64.8347i | 2.54695i | ||||||||
\(649\) | −69.9437 | −2.74553 | ||||||||
\(650\) | 20.1802 | − | 24.2400i | 0.791531 | − | 0.950773i | ||||
\(651\) | 1.08544 | 0.0425419 | ||||||||
\(652\) | 28.7833i | 1.12724i | ||||||||
\(653\) | − | 23.9281i | − | 0.936379i | −0.883628 | − | 0.468189i | \(-0.844907\pi\) | ||
0.883628 | − | 0.468189i | \(-0.155093\pi\) | |||||||
\(654\) | −4.08762 | −0.159839 | ||||||||
\(655\) | 10.7025 | + | 22.8359i | 0.418181 | + | 0.892272i | ||||
\(656\) | 46.6151 | 1.82001 | ||||||||
\(657\) | 16.6447i | 0.649371i | ||||||||
\(658\) | 23.3918i | 0.911908i | ||||||||
\(659\) | 5.97176 | 0.232627 | 0.116313 | − | 0.993213i | \(-0.462892\pi\) | ||||
0.116313 | + | 0.993213i | \(0.462892\pi\) | |||||||
\(660\) | −7.69092 | + | 3.60451i | −0.299369 | + | 0.140305i | ||||
\(661\) | −11.3007 | −0.439545 | −0.219773 | − | 0.975551i | \(-0.570532\pi\) | ||||
−0.219773 | + | 0.975551i | \(0.570532\pi\) | |||||||
\(662\) | − | 50.5690i | − | 1.96542i | ||||||
\(663\) | 2.03680i | 0.0791029i | ||||||||
\(664\) | 2.87718 | 0.111656 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 57.3723 | 2.22313 | ||||||||
\(667\) | − | 4.83555i | − | 0.187233i | ||||||
\(668\) | 49.3715i | 1.91024i | ||||||||
\(669\) | −3.23567 | −0.125098 | ||||||||
\(670\) | 17.5371 | + | 37.4189i | 0.677518 | + | 1.44562i | ||||
\(671\) | 0.101843 | 0.00393160 | ||||||||
\(672\) | − | 1.72602i | − | 0.0665826i | ||||||
\(673\) | 22.9796i | 0.885798i | 0.896571 | + | 0.442899i | \(0.146050\pi\) | ||||
−0.896571 | + | 0.442899i | \(0.853950\pi\) | |||||||
\(674\) | 10.7931 | 0.415735 | ||||||||
\(675\) | −3.37196 | − | 2.80721i | −0.129787 | − | 0.108049i | ||||
\(676\) | −34.5281 | −1.32801 | ||||||||
\(677\) | − | 30.2320i | − | 1.16191i | −0.813936 | − | 0.580955i | \(-0.802679\pi\) | ||
0.813936 | − | 0.580955i | \(-0.197321\pi\) | |||||||
\(678\) | − | 4.93561i | − | 0.189551i | ||||||
\(679\) | 16.8155 | 0.645319 | ||||||||
\(680\) | −40.1317 | − | 85.6289i | −1.53898 | − | 3.28372i | ||||
\(681\) | 1.73154 | 0.0663526 | ||||||||
\(682\) | 90.9202i | 3.48151i | ||||||||
\(683\) | − | 38.7762i | − | 1.48373i | −0.670549 | − | 0.741866i | \(-0.733941\pi\) | ||
0.670549 | − | 0.741866i | \(-0.266059\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −28.0314 | + | 13.1375i | −1.07102 | + | 0.501957i | ||||
\(686\) | −37.8237 | −1.44412 | ||||||||
\(687\) | 0.175352i | 0.00669011i | ||||||||
\(688\) | 72.8338i | 2.77676i | ||||||||
\(689\) | 0.0432463 | 0.00164755 | ||||||||
\(690\) | 0.958642 | − | 0.449287i | 0.0364949 | − | 0.0171041i | ||||
\(691\) | −34.4907 | −1.31209 | −0.656044 | − | 0.754723i | \(-0.727771\pi\) | ||||
−0.656044 | + | 0.754723i | \(0.727771\pi\) | |||||||
\(692\) | − | 12.0243i | − | 0.457095i | ||||||
\(693\) | 18.2425i | 0.692975i | ||||||||
\(694\) | 12.4716 | 0.473414 | ||||||||
\(695\) | 1.87165 | + | 3.99353i | 0.0709957 | + | 0.151483i | ||||
\(696\) | −4.23010 | −0.160341 | ||||||||
\(697\) | 27.9328i | 1.05803i | ||||||||
\(698\) | 1.45458i | 0.0550566i | ||||||||
\(699\) | −2.29093 | −0.0866511 | ||||||||
\(700\) | −21.1219 | − | 17.5843i | −0.798333 | − | 0.664623i | ||||
\(701\) | −2.43041 | −0.0917952 | −0.0458976 | − | 0.998946i | \(-0.514615\pi\) | ||||
−0.0458976 | + | 0.998946i | \(0.514615\pi\) | |||||||
\(702\) | − | 5.53546i | − | 0.208922i | ||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 41.6173 | 1.56851 | ||||||||
\(705\) | 1.09388 | + | 2.33401i | 0.0411979 | + | 0.0879039i | ||||
\(706\) | −63.9371 | −2.40630 | ||||||||
\(707\) | 12.0259i | 0.452279i | ||||||||
\(708\) | − | 9.21340i | − | 0.346261i | ||||||
\(709\) | 14.9095 | 0.559939 | 0.279969 | − | 0.960009i | \(-0.409676\pi\) | ||||
0.279969 | + | 0.960009i | \(0.409676\pi\) | |||||||
\(710\) | −14.4741 | + | 6.78358i | −0.543203 | + | 0.254583i | ||||
\(711\) | 28.4971 | 1.06872 | ||||||||
\(712\) | 26.3354i | 0.986962i | ||||||||
\(713\) | − | 8.00905i | − | 0.299941i | ||||||
\(714\) | 2.51135 | 0.0939848 | ||||||||
\(715\) | −26.2646 | + | 12.3094i | −0.982241 | + | 0.460347i | ||||
\(716\) | 108.630 | 4.05969 | ||||||||
\(717\) | − | 0.154813i | − | 0.00578161i | ||||||
\(718\) | 54.7619i | 2.04370i | ||||||||
\(719\) | 47.2596 | 1.76248 | 0.881242 | − | 0.472665i | \(-0.156708\pi\) | ||||
0.881242 | + | 0.472665i | \(0.156708\pi\) | |||||||
\(720\) | 27.0951 | + | 57.8128i | 1.00978 | + | 2.15455i | ||||
\(721\) | −10.4027 | −0.387419 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.40821i | 0.0523718i | ||||||||
\(724\) | 32.8577 | 1.22115 | ||||||||
\(725\) | −12.5230 | + | 15.0425i | −0.465094 | + | 0.558663i | ||||
\(726\) | 6.83654 | 0.253728 | ||||||||
\(727\) | − | 41.1123i | − | 1.52477i | −0.647123 | − | 0.762386i | \(-0.724028\pi\) | ||
0.647123 | − | 0.762386i | \(-0.275972\pi\) | |||||||
\(728\) | − | 20.2842i | − | 0.751782i | ||||||
\(729\) | 25.8436 | 0.957170 | ||||||||
\(730\) | 13.8480 | + | 29.5474i | 0.512537 | + | 1.09360i | ||||
\(731\) | −43.6436 | −1.61422 | ||||||||
\(732\) | 0.0134153i | 0.000495845i | ||||||||
\(733\) | 25.6070i | 0.945816i | 0.881112 | + | 0.472908i | \(0.156796\pi\) | ||||
−0.881112 | + | 0.472908i | \(0.843204\pi\) | |||||||
\(734\) | −55.9729 | −2.06600 | ||||||||
\(735\) | −1.69370 | + | 0.793784i | −0.0624729 | + | 0.0292792i | ||||
\(736\) | −12.7356 | −0.469440 | ||||||||
\(737\) | − | 38.0037i | − | 1.39988i | ||||||
\(738\) | − | 37.8199i | − | 1.39217i | ||||||
\(739\) | −10.4997 | −0.386237 | −0.193119 | − | 0.981175i | \(-0.561860\pi\) | ||||
−0.193119 | + | 0.981175i | \(0.561860\pi\) | |||||||
\(740\) | 71.9762 | − | 33.7331i | 2.64590 | − | 1.24005i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 0.0533220i | − | 0.00195751i | ||||||
\(743\) | 4.64951i | 0.170574i | 0.996356 | + | 0.0852871i | \(0.0271807\pi\) | ||||
−0.996356 | + | 0.0852871i | \(0.972819\pi\) | |||||||
\(744\) | −7.00624 | −0.256861 | ||||||||
\(745\) | −10.6073 | − | 22.6328i | −0.388622 | − | 0.829202i | ||||
\(746\) | −72.5911 | −2.65775 | ||||||||
\(747\) | − | 1.16401i | − | 0.0425889i | ||||||
\(748\) | 148.663i | 5.43564i | ||||||||
\(749\) | −4.06464 | −0.148519 | ||||||||
\(750\) | −4.14570 | − | 1.08503i | −0.151380 | − | 0.0396199i | ||||
\(751\) | −52.7364 | −1.92438 | −0.962190 | − | 0.272381i | \(-0.912189\pi\) | ||||
−0.962190 | + | 0.272381i | \(0.912189\pi\) | |||||||
\(752\) | − | 75.2902i | − | 2.74555i | ||||||
\(753\) | − | 2.22575i | − | 0.0811107i | ||||||
\(754\) | −24.6939 | −0.899298 | ||||||||
\(755\) | 9.91858 | + | 21.1633i | 0.360974 | + | 0.770210i | ||||
\(756\) | −4.82340 | −0.175425 | ||||||||
\(757\) | − | 13.3049i | − | 0.483575i | −0.970329 | − | 0.241788i | \(-0.922266\pi\) | ||
0.970329 | − | 0.241788i | \(-0.0777337\pi\) | |||||||
\(758\) | − | 5.15762i | − | 0.187333i | ||||||
\(759\) | −0.973624 | −0.0353403 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −20.3115 | −0.736292 | −0.368146 | − | 0.929768i | \(-0.620007\pi\) | ||||
−0.368146 | + | 0.929768i | \(0.620007\pi\) | |||||||
\(762\) | 2.90252i | 0.105147i | ||||||||
\(763\) | 12.1636i | 0.440353i | ||||||||
\(764\) | 23.9734 | 0.867328 | ||||||||
\(765\) | −34.6427 | + | 16.2360i | −1.25251 | + | 0.587013i | ||||
\(766\) | −26.1407 | −0.944501 | ||||||||
\(767\) | − | 31.4639i | − | 1.13610i | ||||||
\(768\) | − | 2.42144i | − | 0.0873762i | ||||||
\(769\) | 21.2618 | 0.766721 | 0.383360 | − | 0.923599i | \(-0.374767\pi\) | ||||
0.383360 | + | 0.923599i | \(0.374767\pi\) | |||||||
\(770\) | 15.1773 | + | 32.3838i | 0.546953 | + | 1.16703i | ||||
\(771\) | 3.38602 | 0.121945 | ||||||||
\(772\) | − | 33.8163i | − | 1.21707i | ||||||
\(773\) | − | 36.0232i | − | 1.29566i | −0.761783 | − | 0.647832i | \(-0.775676\pi\) | ||
0.761783 | − | 0.647832i | \(-0.224324\pi\) | |||||||
\(774\) | 59.0917 | 2.12401 | ||||||||
\(775\) | −20.7417 | + | 24.9146i | −0.745065 | + | 0.894958i | ||||
\(776\) | −108.539 | −3.89633 | ||||||||
\(777\) | 1.23489i | 0.0443014i | ||||||||
\(778\) | 31.4010i | 1.12578i | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −1.62147 | − | 3.45973i | −0.0580580 | − | 0.123878i | ||||
\(781\) | 14.7003 | 0.526018 | ||||||||
\(782\) | − | 18.5302i | − | 0.662638i | ||||||
\(783\) | 3.43510i | 0.122760i | ||||||||
\(784\) | 54.6350 | 1.95125 | ||||||||
\(785\) | −11.3804 | + | 5.33368i | −0.406186 | + | 0.190367i | ||||
\(786\) | 4.32296 | 0.154195 | ||||||||
\(787\) | 41.0609i | 1.46366i | 0.681486 | + | 0.731831i | \(0.261334\pi\) | ||||
−0.681486 | + | 0.731831i | \(0.738666\pi\) | |||||||
\(788\) | − | 106.434i | − | 3.79156i | ||||||
\(789\) | 0.448570 | 0.0159695 | ||||||||
\(790\) | 50.5876 | − | 23.7089i | 1.79983 | − | 0.843525i | ||||
\(791\) | −14.6870 | −0.522210 | ||||||||
\(792\) | − | 117.750i | − | 4.18407i | ||||||
\(793\) | 0.0458135i | 0.00162689i | ||||||||
\(794\) | −4.88919 | −0.173511 | ||||||||
\(795\) | −0.00249352 | − | 0.00532041i | −8.84359e−5 | − | 0.000188695i | ||||
\(796\) | 11.6125 | 0.411593 | ||||||||
\(797\) | 33.9392i | 1.20219i | 0.799179 | + | 0.601093i | \(0.205268\pi\) | ||||
−0.799179 | + | 0.601093i | \(0.794732\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 45.1155 | 1.59607 | ||||||||
\(800\) | 39.6179 | + | 32.9824i | 1.40070 | + | 1.16610i | ||||
\(801\) | 10.6545 | 0.376456 | ||||||||
\(802\) | 61.4426i | 2.16961i | ||||||||
\(803\) | − | 30.0092i | − | 1.05900i | ||||||
\(804\) | 5.00607 | 0.176551 | ||||||||
\(805\) | −1.33695 | − | 2.85265i | −0.0471214 | − | 0.100543i | ||||
\(806\) | −40.9001 | −1.44064 | ||||||||
\(807\) | 0.154780i | 0.00544851i | ||||||||
\(808\) | − | 77.6237i | − | 2.73079i | ||||||
\(809\) | 51.3707 | 1.80610 | 0.903048 | − | 0.429539i | \(-0.141324\pi\) | ||||
0.903048 | + | 0.429539i | \(0.141324\pi\) | |||||||
\(810\) | 46.5631 | − | 21.8227i | 1.63606 | − | 0.766773i | ||||
\(811\) | −20.6118 | −0.723779 | −0.361890 | − | 0.932221i | \(-0.617868\pi\) | ||||
−0.361890 | + | 0.932221i | \(0.617868\pi\) | |||||||
\(812\) | 21.5174i | 0.755112i | ||||||||
\(813\) | − | 0.245998i | − | 0.00862752i | ||||||
\(814\) | −103.438 | −3.62551 | ||||||||
\(815\) | 12.0929 | − | 5.66756i | 0.423594 | − | 0.198526i | ||||
\(816\) | −8.08315 | −0.282967 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | − | 41.8370i | − | 1.46280i | ||||||
\(819\) | −8.20631 | −0.286752 | ||||||||
\(820\) | −22.2369 | − | 47.4468i | −0.776547 | − | 1.65692i | ||||
\(821\) | 38.7002 | 1.35065 | 0.675323 | − | 0.737522i | \(-0.264004\pi\) | ||||
0.675323 | + | 0.737522i | \(0.264004\pi\) | |||||||
\(822\) | 5.30650i | 0.185085i | ||||||||
\(823\) | 18.7887i | 0.654932i | 0.944863 | + | 0.327466i | \(0.106195\pi\) | ||||
−0.944863 | + | 0.327466i | \(0.893805\pi\) | |||||||
\(824\) | 67.1468 | 2.33917 | ||||||||
\(825\) | 3.02875 | + | 2.52148i | 0.105448 | + | 0.0877866i | ||||
\(826\) | −38.7945 | −1.34983 | ||||||||
\(827\) | − | 36.8031i | − | 1.27977i | −0.768471 | − | 0.639885i | \(-0.778982\pi\) | ||
0.768471 | − | 0.639885i | \(-0.221018\pi\) | |||||||
\(828\) | 17.7308i | 0.616189i | ||||||||
\(829\) | −22.6730 | −0.787466 | −0.393733 | − | 0.919225i | \(-0.628816\pi\) | ||||
−0.393733 | + | 0.919225i | \(0.628816\pi\) | |||||||
\(830\) | −0.968430 | − | 2.06634i | −0.0336147 | − | 0.0717236i | ||||
\(831\) | −2.03940 | −0.0707460 | ||||||||
\(832\) | 18.7214i | 0.649047i | ||||||||
\(833\) | 32.7385i | 1.13432i | ||||||||
\(834\) | 0.755998 | 0.0261781 | ||||||||
\(835\) | 20.7427 | − | 9.72147i | 0.717830 | − | 0.336425i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.68950i | 0.196658i | ||||||||
\(838\) | − | 26.7157i | − | 0.922878i | ||||||
\(839\) | −2.70578 | −0.0934139 | −0.0467070 | − | 0.998909i | \(-0.514873\pi\) | ||||
−0.0467070 | + | 0.998909i | \(0.514873\pi\) | |||||||
\(840\) | −2.49548 | + | 1.16955i | −0.0861021 | + | 0.0403535i | ||||
\(841\) | −13.6759 | −0.471583 | ||||||||
\(842\) | − | 66.9293i | − | 2.30654i | ||||||
\(843\) | 0.183479i | 0.00631937i | ||||||||
\(844\) | −91.5879 | −3.15259 | ||||||||
\(845\) | 6.79874 | + | 14.5065i | 0.233884 | + | 0.499037i | ||||
\(846\) | −61.0847 | −2.10013 | ||||||||
\(847\) | − | 20.3436i | − | 0.699016i | ||||||
\(848\) | 0.171625i | 0.00589363i | ||||||||
\(849\) | −2.30825 | −0.0792190 | ||||||||
\(850\) | −47.9892 | + | 57.6438i | −1.64602 | + | 1.97716i | ||||
\(851\) | 9.11175 | 0.312347 | ||||||||
\(852\) | 1.93641i | 0.0663404i | ||||||||
\(853\) | − | 28.0139i | − | 0.959178i | −0.877493 | − | 0.479589i | \(-0.840786\pi\) | ||
0.877493 | − | 0.479589i | \(-0.159214\pi\) | |||||||
\(854\) | 0.0564874 | 0.00193296 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 26.2361 | 0.896732 | ||||||||
\(857\) | 37.9069i | 1.29487i | 0.762119 | + | 0.647437i | \(0.224159\pi\) | ||||
−0.762119 | + | 0.647437i | \(0.775841\pi\) | |||||||
\(858\) | 4.97204i | 0.169743i | ||||||||
\(859\) | 25.5377 | 0.871336 | 0.435668 | − | 0.900107i | \(-0.356512\pi\) | ||||
0.435668 | + | 0.900107i | \(0.356512\pi\) | |||||||
\(860\) | 74.1333 | − | 34.7441i | 2.52792 | − | 1.18476i | ||||
\(861\) | 0.814042 | 0.0277425 | ||||||||
\(862\) | 68.9215i | 2.34747i | ||||||||
\(863\) | − | 46.3212i | − | 1.57679i | −0.615169 | − | 0.788395i | \(-0.710912\pi\) | ||
0.615169 | − | 0.788395i | \(-0.289088\pi\) | |||||||
\(864\) | 9.04714 | 0.307790 | ||||||||
\(865\) | −5.05182 | + | 2.36764i | −0.171767 | + | 0.0805021i | ||||
\(866\) | 29.0747 | 0.987999 | ||||||||
\(867\) | − | 2.34836i | − | 0.0797546i | ||||||
\(868\) | 35.6389i | 1.20966i | ||||||||
\(869\) | −51.3783 | −1.74289 | ||||||||
\(870\) | 1.42381 | + | 3.03798i | 0.0482717 | + | 0.102997i | ||||
\(871\) | 17.0958 | 0.579269 | ||||||||
\(872\) | − | 78.5128i | − | 2.65878i | ||||||
\(873\) | 43.9114i | 1.48618i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.22876 | + | 12.3365i | −0.109152 | + | 0.417049i | ||||
\(876\) | 3.95299 | 0.133559 | ||||||||
\(877\) | − | 43.7693i | − | 1.47798i | −0.673715 | − | 0.738992i | \(-0.735302\pi\) | ||
0.673715 | − | 0.738992i | \(-0.264698\pi\) | |||||||
\(878\) | 85.0988i | 2.87195i | ||||||||
\(879\) | −1.75130 | −0.0590700 | ||||||||
\(880\) | −48.8506 | − | 104.232i | −1.64675 | − | 3.51367i | ||||
\(881\) | −34.6665 | −1.16795 | −0.583973 | − | 0.811773i | \(-0.698503\pi\) | ||||
−0.583973 | + | 0.811773i | \(0.698503\pi\) | |||||||
\(882\) | − | 44.3267i | − | 1.49256i | ||||||
\(883\) | − | 43.5573i | − | 1.46582i | −0.680325 | − | 0.732910i | \(-0.738161\pi\) | ||
0.680325 | − | 0.732910i | \(-0.261839\pi\) | |||||||
\(884\) | −66.8753 | −2.24926 | ||||||||
\(885\) | −3.87087 | + | 1.81416i | −0.130118 | + | 0.0609823i | ||||
\(886\) | 109.077 | 3.66452 | ||||||||
\(887\) | 48.2351i | 1.61957i | 0.586723 | + | 0.809787i | \(0.300418\pi\) | ||||
−0.586723 | + | 0.809787i | \(0.699582\pi\) | |||||||
\(888\) | − | 7.97087i | − | 0.267485i | ||||||
\(889\) | 8.63710 | 0.289679 | ||||||||
\(890\) | 18.9136 | − | 8.86426i | 0.633987 | − | 0.297131i | ||||
\(891\) | −47.2908 | −1.58430 | ||||||||
\(892\) | − | 106.238i | − | 3.55712i | ||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −4.28452 | −0.143296 | ||||||||
\(895\) | −21.3897 | − | 45.6392i | −0.714979 | − | 1.52555i | ||||
\(896\) | −0.435536 | −0.0145502 | ||||||||
\(897\) | − | 0.437981i | − | 0.0146238i | ||||||
\(898\) | − | 104.491i | − | 3.48691i | ||||||
\(899\) | 25.3810 | 0.846505 | ||||||||
\(900\) | 45.9190 | − | 55.1571i | 1.53063 | − | 1.83857i | ||||
\(901\) | −0.102841 | −0.00342615 | ||||||||
\(902\) | 68.1867i | 2.27037i | ||||||||
\(903\) | 1.27190i | 0.0423262i | ||||||||
\(904\) | 94.8005 | 3.15302 | ||||||||
\(905\) | −6.46982 | − | 13.8046i | −0.215064 | − | 0.458882i | ||||
\(906\) | 4.00632 | 0.133101 | ||||||||
\(907\) | − | 44.1877i | − | 1.46723i | −0.679567 | − | 0.733613i | \(-0.737832\pi\) | ||
0.679567 | − | 0.733613i | \(-0.262168\pi\) | |||||||
\(908\) | 56.8523i | 1.88671i | ||||||||
\(909\) | −31.4040 | −1.04160 | ||||||||
\(910\) | −14.5677 | + | 6.82746i | −0.482916 | + | 0.226328i | ||||
\(911\) | −33.6536 | −1.11499 | −0.557496 | − | 0.830180i | \(-0.688238\pi\) | ||||
−0.557496 | + | 0.830180i | \(0.688238\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.09863i | 0.0694545i | ||||||||
\(914\) | 78.6290 | 2.60082 | ||||||||
\(915\) | 0.00563624 | − | 0.00264154i | 0.000186328 | − | 8.73266e-5i | ||||
\(916\) | −5.75742 | −0.190231 | ||||||||
\(917\) | − | 12.8639i | − | 0.424805i | ||||||
\(918\) | 13.1635i | 0.434461i | ||||||||
\(919\) | −4.04484 | −0.133427 | −0.0667134 | − | 0.997772i | \(-0.521251\pi\) | ||||
−0.0667134 | + | 0.997772i | \(0.521251\pi\) | |||||||
\(920\) | 8.62966 | + | 18.4131i | 0.284512 | + | 0.607062i | ||||
\(921\) | 3.57929 | 0.117942 | ||||||||
\(922\) | 51.7220i | 1.70337i | ||||||||
\(923\) | 6.61287i | 0.217665i | ||||||||
\(924\) | 4.33246 | 0.142527 | ||||||||
\(925\) | −28.3449 | − | 23.5975i | −0.931973 | − | 0.775880i | ||||
\(926\) | 44.5691 | 1.46463 | ||||||||
\(927\) | − | 27.1654i | − | 0.892229i | ||||||
\(928\) | − | 40.3596i | − | 1.32487i | ||||||
\(929\) | 40.2101 | 1.31925 | 0.659625 | − | 0.751594i | \(-0.270715\pi\) | ||||
0.659625 | + | 0.751594i | \(0.270715\pi\) | |||||||
\(930\) | 2.35824 | + | 5.03176i | 0.0773296 | + | 0.164998i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 75.2192i | − | 2.46389i | ||||||
\(933\) | − | 0.743833i | − | 0.0243520i | ||||||
\(934\) | 63.0024 | 2.06150 | ||||||||
\(935\) | 62.4583 | − | 29.2723i | 2.04260 | − | 0.957307i | ||||
\(936\) | 52.9695 | 1.73136 | ||||||||
\(937\) | 13.1716i | 0.430297i | 0.976581 | + | 0.215149i | \(0.0690236\pi\) | ||||
−0.976581 | + | 0.215149i | \(0.930976\pi\) | |||||||
\(938\) | − | 21.0788i | − | 0.688249i | ||||||
\(939\) | 2.78200 | 0.0907872 | ||||||||
\(940\) | −76.6335 | + | 35.9158i | −2.49951 | + | 1.17145i | ||||
\(941\) | 33.9107 | 1.10546 | 0.552729 | − | 0.833361i | \(-0.313586\pi\) | ||||
0.552729 | + | 0.833361i | \(0.313586\pi\) | |||||||
\(942\) | 2.15438i | 0.0701936i | ||||||||
\(943\) | − | 6.00648i | − | 0.195598i | ||||||
\(944\) | 124.866 | 4.06404 | ||||||||
\(945\) | 0.949749 | + | 2.02648i | 0.0308953 | + | 0.0659213i | ||||
\(946\) | −106.538 | −3.46386 | ||||||||
\(947\) | − | 34.4561i | − | 1.11967i | −0.828603 | − | 0.559836i | \(-0.810864\pi\) | ||
0.828603 | − | 0.559836i | \(-0.189136\pi\) | |||||||
\(948\) | − | 6.76785i | − | 0.219810i | ||||||
\(949\) | 13.4995 | 0.438213 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.78155 | 0.0577707 | ||||||||
\(952\) | 48.2366i | 1.56336i | ||||||||
\(953\) | − | 6.03770i | − | 0.195580i | −0.995207 | − | 0.0977902i | \(-0.968823\pi\) | ||
0.995207 | − | 0.0977902i | \(-0.0311774\pi\) | |||||||
\(954\) | 0.139243 | 0.00450817 | ||||||||
\(955\) | −4.72047 | − | 10.0721i | −0.152751 | − | 0.325924i | ||||
\(956\) | 5.08305 | 0.164398 | ||||||||
\(957\) | − | 3.08546i | − | 0.0997388i | ||||||
\(958\) | − | 84.8872i | − | 2.74258i | ||||||
\(959\) | 15.7907 | 0.509907 | ||||||||
\(960\) | 2.30321 | − | 1.07944i | 0.0743357 | − | 0.0348389i | ||||
\(961\) | 11.0382 | 0.356072 | ||||||||
\(962\) | − | 46.5313i | − | 1.50023i | ||||||
\(963\) | − | 10.6143i | − | 0.342040i | ||||||
\(964\) | −46.2363 | −1.48917 | ||||||||
\(965\) | −14.2074 | + | 6.65858i | −0.457352 | + | 0.214347i | ||||
\(966\) | −0.540023 | −0.0173750 | ||||||||
\(967\) | 12.5734i | 0.404334i | 0.979351 | + | 0.202167i | \(0.0647983\pi\) | ||||
−0.979351 | + | 0.202167i | \(0.935202\pi\) | |||||||
\(968\) | 131.313i | 4.22055i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 36.5333 | + | 77.9510i | 1.17301 | + | 2.50286i | ||||
\(971\) | −20.5595 | −0.659787 | −0.329894 | − | 0.944018i | \(-0.607013\pi\) | ||||
−0.329894 | + | 0.944018i | \(0.607013\pi\) | |||||||
\(972\) | − | 18.9162i | − | 0.606738i | ||||||
\(973\) | − | 2.24964i | − | 0.0721202i | ||||||
\(974\) | −79.6401 | −2.55183 | ||||||||
\(975\) | −1.13428 | + | 1.36247i | −0.0363259 | + | 0.0436340i | ||||
\(976\) | −0.181813 | −0.00581970 | ||||||||
\(977\) | − | 1.26370i | − | 0.0404295i | −0.999796 | − | 0.0202147i | \(-0.993565\pi\) | ||
0.999796 | − | 0.0202147i | \(-0.00643499\pi\) | |||||||
\(978\) | − | 2.28924i | − | 0.0732020i | ||||||
\(979\) | −19.2092 | −0.613930 | ||||||||
\(980\) | −26.0627 | − | 55.6098i | −0.832541 | − | 1.77639i | ||||
\(981\) | −31.7637 | −1.01414 | ||||||||
\(982\) | 50.8364i | 1.62225i | ||||||||
\(983\) | − | 35.5329i | − | 1.13332i | −0.823950 | − | 0.566662i | \(-0.808235\pi\) | ||
0.823950 | − | 0.566662i | \(-0.191765\pi\) | |||||||
\(984\) | −5.25442 | −0.167505 | ||||||||
\(985\) | −44.7166 | + | 20.9574i | −1.42479 | + | 0.667757i | ||||
\(986\) | 58.7230 | 1.87012 | ||||||||
\(987\) | − | 1.31480i | − | 0.0418504i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.38483 | 0.298420 | ||||||||
\(990\) | −84.5661 | + | 39.6336i | −2.68769 | + | 1.25964i | ||||
\(991\) | 4.48854 | 0.142583 | 0.0712916 | − | 0.997456i | \(-0.477288\pi\) | ||||
0.0712916 | + | 0.997456i | \(0.477288\pi\) | |||||||
\(992\) | − | 66.8470i | − | 2.12239i | ||||||
\(993\) | 2.84236i | 0.0901995i | ||||||||
\(994\) | 8.15357 | 0.258615 | ||||||||
\(995\) | −2.28655 | − | 4.87880i | −0.0724885 | − | 0.154668i | ||||
\(996\) | −0.276444 | −0.00875946 | ||||||||
\(997\) | − | 8.36943i | − | 0.265063i | −0.991179 | − | 0.132531i | \(-0.957690\pi\) | ||
0.991179 | − | 0.132531i | \(-0.0423105\pi\) | |||||||
\(998\) | 4.72892i | 0.149691i | ||||||||
\(999\) | −6.47283 | −0.204791 |
(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 | 1805.2.b.j.1084.1 | yes | 16 | |
5.2 | odd | 4 | 9025.2.a.ck.1.16 | 16 | |||
5.3 | odd | 4 | 9025.2.a.ck.1.1 | 16 | |||
5.4 | even | 2 | inner | 1805.2.b.j.1084.16 | yes | 16 | |
19.18 | odd | 2 | 1805.2.b.i.1084.16 | yes | 16 | ||
95.18 | even | 4 | 9025.2.a.cl.1.16 | 16 | |||
95.37 | even | 4 | 9025.2.a.cl.1.1 | 16 | |||
95.94 | odd | 2 | 1805.2.b.i.1084.1 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1805.2.b.i.1084.1 | ✓ | 16 | 95.94 | odd | 2 | ||
1805.2.b.i.1084.16 | yes | 16 | 19.18 | odd | 2 | ||
1805.2.b.j.1084.1 | yes | 16 | 1.1 | even | 1 | trivial | |
1805.2.b.j.1084.16 | yes | 16 | 5.4 | even | 2 | inner | |
9025.2.a.ck.1.1 | 16 | 5.3 | odd | 4 | |||
9025.2.a.ck.1.16 | 16 | 5.2 | odd | 4 | |||
9025.2.a.cl.1.1 | 16 | 95.37 | even | 4 | |||
9025.2.a.cl.1.16 | 16 | 95.18 | even | 4 |