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: | \(24\) |
Twist minimal: | no (minimal twist has level 95) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1084.8 | ||
Character | \(\chi\) | \(=\) | 1805.1084 |
Dual form | 1805.2.b.l.1084.17 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1805\mathbb{Z}\right)^\times\).
\(n\) | \(362\) | \(1446\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.22159i | − | 0.863792i | −0.901923 | − | 0.431896i | \(-0.857845\pi\) | ||
0.901923 | − | 0.431896i | \(-0.142155\pi\) | |||||||
\(3\) | 0.804421i | 0.464432i | 0.972664 | + | 0.232216i | \(0.0745977\pi\) | ||||
−0.972664 | + | 0.232216i | \(0.925402\pi\) | |||||||
\(4\) | 0.507728 | 0.253864 | ||||||||
\(5\) | −2.23387 | + | 0.0991400i | −0.999017 | + | 0.0443367i | ||||
\(6\) | 0.982669 | 0.401173 | ||||||||
\(7\) | − | 3.79180i | − | 1.43317i | −0.697502 | − | 0.716583i | \(-0.745705\pi\) | ||
0.697502 | − | 0.716583i | \(-0.254295\pi\) | |||||||
\(8\) | − | 3.06341i | − | 1.08308i | ||||||
\(9\) | 2.35291 | 0.784303 | ||||||||
\(10\) | 0.121108 | + | 2.72886i | 0.0382977 | + | 0.862942i | ||||
\(11\) | −1.23733 | −0.373068 | −0.186534 | − | 0.982449i | \(-0.559725\pi\) | ||||
−0.186534 | + | 0.982449i | \(0.559725\pi\) | |||||||
\(12\) | 0.408427i | 0.117903i | ||||||||
\(13\) | − | 3.45598i | − | 0.958517i | −0.877674 | − | 0.479259i | \(-0.840906\pi\) | ||
0.877674 | − | 0.479259i | \(-0.159094\pi\) | |||||||
\(14\) | −4.63201 | −1.23796 | ||||||||
\(15\) | −0.0797502 | − | 1.79697i | −0.0205914 | − | 0.463976i | ||||
\(16\) | −2.72676 | −0.681689 | ||||||||
\(17\) | − | 3.00695i | − | 0.729293i | −0.931146 | − | 0.364647i | \(-0.881190\pi\) | ||
0.931146 | − | 0.364647i | \(-0.118810\pi\) | |||||||
\(18\) | − | 2.87428i | − | 0.677474i | ||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −1.13420 | + | 0.0503361i | −0.253614 | + | 0.0112555i | ||||
\(21\) | 3.05020 | 0.665608 | ||||||||
\(22\) | 1.51150i | 0.322253i | ||||||||
\(23\) | 6.14780i | 1.28191i | 0.767580 | + | 0.640953i | \(0.221461\pi\) | ||||
−0.767580 | + | 0.640953i | \(0.778539\pi\) | |||||||
\(24\) | 2.46427 | 0.503016 | ||||||||
\(25\) | 4.98034 | − | 0.442931i | 0.996069 | − | 0.0885863i | ||||
\(26\) | −4.22178 | −0.827959 | ||||||||
\(27\) | 4.30599i | 0.828688i | ||||||||
\(28\) | − | 1.92520i | − | 0.363829i | ||||||
\(29\) | −4.28727 | −0.796126 | −0.398063 | − | 0.917358i | \(-0.630317\pi\) | ||||
−0.398063 | + | 0.917358i | \(0.630317\pi\) | |||||||
\(30\) | −2.19515 | + | 0.0974218i | −0.400778 | + | 0.0177867i | ||||
\(31\) | −5.10134 | −0.916227 | −0.458114 | − | 0.888894i | \(-0.651475\pi\) | ||||
−0.458114 | + | 0.888894i | \(0.651475\pi\) | |||||||
\(32\) | − | 2.79584i | − | 0.494240i | ||||||
\(33\) | − | 0.995330i | − | 0.173265i | ||||||
\(34\) | −3.67325 | −0.629958 | ||||||||
\(35\) | 0.375919 | + | 8.47038i | 0.0635419 | + | 1.43176i | ||||
\(36\) | 1.19464 | 0.199106 | ||||||||
\(37\) | 9.13084i | 1.50110i | 0.660813 | + | 0.750550i | \(0.270211\pi\) | ||||
−0.660813 | + | 0.750550i | \(0.729789\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.78006 | 0.445167 | ||||||||
\(40\) | 0.303706 | + | 6.84325i | 0.0480201 | + | 1.08201i | ||||
\(41\) | −5.33021 | −0.832440 | −0.416220 | − | 0.909264i | \(-0.636645\pi\) | ||||
−0.416220 | + | 0.909264i | \(0.636645\pi\) | |||||||
\(42\) | − | 3.72608i | − | 0.574947i | ||||||
\(43\) | − | 9.12495i | − | 1.39154i | −0.718264 | − | 0.695771i | \(-0.755063\pi\) | ||
0.718264 | − | 0.695771i | \(-0.244937\pi\) | |||||||
\(44\) | −0.628225 | −0.0947084 | ||||||||
\(45\) | −5.25609 | + | 0.233267i | −0.783531 | + | 0.0347734i | ||||
\(46\) | 7.51007 | 1.10730 | ||||||||
\(47\) | − | 7.30333i | − | 1.06530i | −0.846336 | − | 0.532650i | \(-0.821196\pi\) | ||
0.846336 | − | 0.532650i | \(-0.178804\pi\) | |||||||
\(48\) | − | 2.19346i | − | 0.316599i | ||||||
\(49\) | −7.37774 | −1.05396 | ||||||||
\(50\) | −0.541079 | − | 6.08392i | −0.0765201 | − | 0.860396i | ||||
\(51\) | 2.41886 | 0.338707 | ||||||||
\(52\) | − | 1.75470i | − | 0.243333i | ||||||
\(53\) | 3.33235i | 0.457734i | 0.973458 | + | 0.228867i | \(0.0735021\pi\) | ||||
−0.973458 | + | 0.228867i | \(0.926498\pi\) | |||||||
\(54\) | 5.26014 | 0.715814 | ||||||||
\(55\) | 2.76402 | − | 0.122668i | 0.372701 | − | 0.0165406i | ||||
\(56\) | −11.6158 | −1.55223 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.23727i | 0.687687i | ||||||||
\(59\) | −0.817318 | −0.106406 | −0.0532029 | − | 0.998584i | \(-0.516943\pi\) | ||||
−0.0532029 | + | 0.998584i | \(0.516943\pi\) | |||||||
\(60\) | −0.0404914 | − | 0.912372i | −0.00522742 | − | 0.117787i | ||||
\(61\) | 6.40201 | 0.819693 | 0.409847 | − | 0.912154i | \(-0.365582\pi\) | ||||
0.409847 | + | 0.912154i | \(0.365582\pi\) | |||||||
\(62\) | 6.23172i | 0.791430i | ||||||||
\(63\) | − | 8.92175i | − | 1.12404i | ||||||
\(64\) | −8.86888 | −1.10861 | ||||||||
\(65\) | 0.342626 | + | 7.72022i | 0.0424975 | + | 0.957575i | ||||
\(66\) | −1.21588 | −0.149665 | ||||||||
\(67\) | − | 1.01092i | − | 0.123504i | −0.998092 | − | 0.0617520i | \(-0.980331\pi\) | ||
0.998092 | − | 0.0617520i | \(-0.0196688\pi\) | |||||||
\(68\) | − | 1.52671i | − | 0.185141i | ||||||
\(69\) | −4.94542 | −0.595359 | ||||||||
\(70\) | 10.3473 | − | 0.459217i | 1.23674 | − | 0.0548869i | ||||
\(71\) | −13.6795 | −1.62346 | −0.811731 | − | 0.584032i | \(-0.801474\pi\) | ||||
−0.811731 | + | 0.584032i | \(0.801474\pi\) | |||||||
\(72\) | − | 7.20791i | − | 0.849460i | ||||||
\(73\) | − | 11.0627i | − | 1.29479i | −0.762155 | − | 0.647395i | \(-0.775858\pi\) | ||
0.762155 | − | 0.647395i | \(-0.224142\pi\) | |||||||
\(74\) | 11.1541 | 1.29664 | ||||||||
\(75\) | 0.356303 | + | 4.00629i | 0.0411423 | + | 0.462607i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.69169i | 0.534668i | ||||||||
\(78\) | − | 3.39609i | − | 0.384531i | ||||||
\(79\) | −1.38420 | −0.155735 | −0.0778673 | − | 0.996964i | \(-0.524811\pi\) | ||||
−0.0778673 | + | 0.996964i | \(0.524811\pi\) | |||||||
\(80\) | 6.09122 | − | 0.270331i | 0.681019 | − | 0.0302239i | ||||
\(81\) | 3.59490 | 0.399433 | ||||||||
\(82\) | 6.51132i | 0.719054i | ||||||||
\(83\) | − | 2.52052i | − | 0.276663i | −0.990386 | − | 0.138332i | \(-0.955826\pi\) | ||
0.990386 | − | 0.138332i | \(-0.0441740\pi\) | |||||||
\(84\) | 1.54867 | 0.168974 | ||||||||
\(85\) | 0.298109 | + | 6.71714i | 0.0323345 | + | 0.728576i | ||||
\(86\) | −11.1469 | −1.20200 | ||||||||
\(87\) | − | 3.44877i | − | 0.369747i | ||||||
\(88\) | 3.79043i | 0.404061i | ||||||||
\(89\) | 2.69842 | 0.286032 | 0.143016 | − | 0.989720i | \(-0.454320\pi\) | ||||
0.143016 | + | 0.989720i | \(0.454320\pi\) | |||||||
\(90\) | 0.284956 | + | 6.42076i | 0.0300370 | + | 0.676808i | ||||
\(91\) | −13.1044 | −1.37371 | ||||||||
\(92\) | 3.12141i | 0.325430i | ||||||||
\(93\) | − | 4.10362i | − | 0.425526i | ||||||
\(94\) | −8.92164 | −0.920197 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.24903 | 0.229541 | ||||||||
\(97\) | 3.06253i | 0.310953i | 0.987840 | + | 0.155476i | \(0.0496912\pi\) | ||||
−0.987840 | + | 0.155476i | \(0.950309\pi\) | |||||||
\(98\) | 9.01254i | 0.910404i | ||||||||
\(99\) | −2.91131 | −0.292598 | ||||||||
\(100\) | 2.52866 | − | 0.224889i | 0.252866 | − | 0.0224889i | ||||
\(101\) | 3.72705 | 0.370856 | 0.185428 | − | 0.982658i | \(-0.440633\pi\) | ||||
0.185428 | + | 0.982658i | \(0.440633\pi\) | |||||||
\(102\) | − | 2.95484i | − | 0.292573i | ||||||
\(103\) | − | 13.2086i | − | 1.30149i | −0.759298 | − | 0.650743i | \(-0.774457\pi\) | ||
0.759298 | − | 0.650743i | \(-0.225543\pi\) | |||||||
\(104\) | −10.5871 | −1.03815 | ||||||||
\(105\) | −6.81375 | + | 0.302397i | −0.664954 | + | 0.0295109i | ||||
\(106\) | 4.07076 | 0.395387 | ||||||||
\(107\) | 5.13305i | 0.496230i | 0.968731 | + | 0.248115i | \(0.0798112\pi\) | ||||
−0.968731 | + | 0.248115i | \(0.920189\pi\) | |||||||
\(108\) | 2.18627i | 0.210374i | ||||||||
\(109\) | −1.58777 | −0.152081 | −0.0760404 | − | 0.997105i | \(-0.524228\pi\) | ||||
−0.0760404 | + | 0.997105i | \(0.524228\pi\) | |||||||
\(110\) | −0.149850 | − | 3.37649i | −0.0142876 | − | 0.321936i | ||||
\(111\) | −7.34503 | −0.697160 | ||||||||
\(112\) | 10.3393i | 0.976973i | ||||||||
\(113\) | − | 20.0832i | − | 1.88927i | −0.328126 | − | 0.944634i | \(-0.606417\pi\) | ||
0.328126 | − | 0.944634i | \(-0.393583\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.609493 | − | 13.7334i | −0.0568355 | − | 1.28065i | ||||
\(116\) | −2.17676 | −0.202108 | ||||||||
\(117\) | − | 8.13161i | − | 0.751768i | ||||||
\(118\) | 0.998424i | 0.0919124i | ||||||||
\(119\) | −11.4018 | −1.04520 | ||||||||
\(120\) | −5.50485 | + | 0.244307i | −0.502522 | + | 0.0223021i | ||||
\(121\) | −9.46903 | −0.860821 | ||||||||
\(122\) | − | 7.82061i | − | 0.708044i | ||||||
\(123\) | − | 4.28773i | − | 0.386612i | ||||||
\(124\) | −2.59009 | −0.232597 | ||||||||
\(125\) | −11.0815 | + | 1.48320i | −0.991161 | + | 0.132662i | ||||
\(126\) | −10.8987 | −0.970932 | ||||||||
\(127\) | 3.45304i | 0.306408i | 0.988195 | + | 0.153204i | \(0.0489592\pi\) | ||||
−0.988195 | + | 0.153204i | \(0.951041\pi\) | |||||||
\(128\) | 5.24241i | 0.463368i | ||||||||
\(129\) | 7.34030 | 0.646277 | ||||||||
\(130\) | 9.43091 | − | 0.418547i | 0.827145 | − | 0.0367090i | ||||
\(131\) | −7.58746 | −0.662920 | −0.331460 | − | 0.943469i | \(-0.607541\pi\) | ||||
−0.331460 | + | 0.943469i | \(0.607541\pi\) | |||||||
\(132\) | − | 0.505357i | − | 0.0439857i | ||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1.23493 | −0.106682 | ||||||||
\(135\) | −0.426896 | − | 9.61902i | −0.0367413 | − | 0.827873i | ||||
\(136\) | −9.21152 | −0.789881 | ||||||||
\(137\) | 3.68633i | 0.314944i | 0.987523 | + | 0.157472i | \(0.0503344\pi\) | ||||
−0.987523 | + | 0.157472i | \(0.949666\pi\) | |||||||
\(138\) | 6.04126i | 0.514266i | ||||||||
\(139\) | 18.6273 | 1.57994 | 0.789972 | − | 0.613143i | \(-0.210095\pi\) | ||||
0.789972 | + | 0.613143i | \(0.210095\pi\) | |||||||
\(140\) | 0.190864 | + | 4.30065i | 0.0161310 | + | 0.363471i | ||||
\(141\) | 5.87494 | 0.494760 | ||||||||
\(142\) | 16.7107i | 1.40233i | ||||||||
\(143\) | 4.27618i | 0.357592i | ||||||||
\(144\) | −6.41581 | −0.534651 | ||||||||
\(145\) | 9.57719 | − | 0.425040i | 0.795343 | − | 0.0352976i | ||||
\(146\) | −13.5140 | −1.11843 | ||||||||
\(147\) | − | 5.93480i | − | 0.489494i | ||||||
\(148\) | 4.63598i | 0.381075i | ||||||||
\(149\) | −1.68785 | −0.138274 | −0.0691369 | − | 0.997607i | \(-0.522025\pi\) | ||||
−0.0691369 | + | 0.997607i | \(0.522025\pi\) | |||||||
\(150\) | 4.89403 | − | 0.435255i | 0.399596 | − | 0.0355384i | ||||
\(151\) | −1.33890 | −0.108958 | −0.0544791 | − | 0.998515i | \(-0.517350\pi\) | ||||
−0.0544791 | + | 0.998515i | \(0.517350\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 7.07508i | − | 0.571987i | ||||||
\(154\) | 5.73130 | 0.461841 | ||||||||
\(155\) | 11.3957 | − | 0.505746i | 0.915326 | − | 0.0406225i | ||||
\(156\) | 1.41152 | 0.113012 | ||||||||
\(157\) | − | 6.04267i | − | 0.482258i | −0.970493 | − | 0.241129i | \(-0.922482\pi\) | ||
0.970493 | − | 0.241129i | \(-0.0775176\pi\) | |||||||
\(158\) | 1.69092i | 0.134522i | ||||||||
\(159\) | −2.68061 | −0.212587 | ||||||||
\(160\) | 0.277180 | + | 6.24555i | 0.0219130 | + | 0.493754i | ||||
\(161\) | 23.3112 | 1.83718 | ||||||||
\(162\) | − | 4.39147i | − | 0.345027i | ||||||
\(163\) | − | 9.79728i | − | 0.767382i | −0.923462 | − | 0.383691i | \(-0.874653\pi\) | ||
0.923462 | − | 0.383691i | \(-0.125347\pi\) | |||||||
\(164\) | −2.70630 | −0.211326 | ||||||||
\(165\) | 0.0986770 | + | 2.22344i | 0.00768199 | + | 0.173094i | ||||
\(166\) | −3.07903 | −0.238979 | ||||||||
\(167\) | 3.87632i | 0.299959i | 0.988689 | + | 0.149979i | \(0.0479207\pi\) | ||||
−0.988689 | + | 0.149979i | \(0.952079\pi\) | |||||||
\(168\) | − | 9.34400i | − | 0.720905i | ||||||
\(169\) | 1.05618 | 0.0812444 | ||||||||
\(170\) | 8.20556 | − | 0.364166i | 0.629338 | − | 0.0279303i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 4.63299i | − | 0.353262i | ||||||
\(173\) | 4.73220i | 0.359782i | 0.983687 | + | 0.179891i | \(0.0575745\pi\) | ||||
−0.983687 | + | 0.179891i | \(0.942425\pi\) | |||||||
\(174\) | −4.21296 | −0.319384 | ||||||||
\(175\) | −1.67951 | − | 18.8845i | −0.126959 | − | 1.42753i | ||||
\(176\) | 3.37389 | 0.254316 | ||||||||
\(177\) | − | 0.657468i | − | 0.0494183i | ||||||
\(178\) | − | 3.29635i | − | 0.247072i | ||||||
\(179\) | −9.37815 | −0.700956 | −0.350478 | − | 0.936571i | \(-0.613981\pi\) | ||||
−0.350478 | + | 0.936571i | \(0.613981\pi\) | |||||||
\(180\) | −2.66866 | + | 0.118436i | −0.198910 | + | 0.00882772i | ||||
\(181\) | 19.5008 | 1.44948 | 0.724741 | − | 0.689022i | \(-0.241960\pi\) | ||||
0.724741 | + | 0.689022i | \(0.241960\pi\) | |||||||
\(182\) | 16.0081i | 1.18660i | ||||||||
\(183\) | 5.14991i | 0.380692i | ||||||||
\(184\) | 18.8332 | 1.38840 | ||||||||
\(185\) | −0.905231 | − | 20.3971i | −0.0665539 | − | 1.49962i | ||||
\(186\) | −5.01293 | −0.367566 | ||||||||
\(187\) | 3.72058i | 0.272076i | ||||||||
\(188\) | − | 3.70810i | − | 0.270441i | ||||||
\(189\) | 16.3274 | 1.18765 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.5024 | 1.12171 | 0.560857 | − | 0.827913i | \(-0.310472\pi\) | ||||
0.560857 | + | 0.827913i | \(0.310472\pi\) | |||||||
\(192\) | − | 7.13431i | − | 0.514874i | ||||||
\(193\) | − | 19.8432i | − | 1.42834i | −0.699970 | − | 0.714172i | \(-0.746804\pi\) | ||
0.699970 | − | 0.714172i | \(-0.253196\pi\) | |||||||
\(194\) | 3.74114 | 0.268598 | ||||||||
\(195\) | −6.21030 | + | 0.275615i | −0.444729 | + | 0.0197372i | ||||
\(196\) | −3.74588 | −0.267563 | ||||||||
\(197\) | 25.9708i | 1.85034i | 0.379553 | + | 0.925170i | \(0.376078\pi\) | ||||
−0.379553 | + | 0.925170i | \(0.623922\pi\) | |||||||
\(198\) | 3.55642i | 0.252744i | ||||||||
\(199\) | 5.41593 | 0.383925 | 0.191963 | − | 0.981402i | \(-0.438515\pi\) | ||||
0.191963 | + | 0.981402i | \(0.438515\pi\) | |||||||
\(200\) | −1.35688 | − | 15.2568i | −0.0959458 | − | 1.07882i | ||||
\(201\) | 0.813208 | 0.0573593 | ||||||||
\(202\) | − | 4.55291i | − | 0.320342i | ||||||
\(203\) | 16.2565i | 1.14098i | ||||||||
\(204\) | 1.22812 | 0.0859856 | ||||||||
\(205\) | 11.9070 | − | 0.528437i | 0.831621 | − | 0.0369077i | ||||
\(206\) | −16.1355 | −1.12421 | ||||||||
\(207\) | 14.4652i | 1.00540i | ||||||||
\(208\) | 9.42363i | 0.653411i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0.369404 | + | 8.32358i | 0.0254913 | + | 0.574382i | ||||
\(211\) | 20.1197 | 1.38510 | 0.692550 | − | 0.721370i | \(-0.256487\pi\) | ||||
0.692550 | + | 0.721370i | \(0.256487\pi\) | |||||||
\(212\) | 1.69193i | 0.116202i | ||||||||
\(213\) | − | 11.0041i | − | 0.753988i | ||||||
\(214\) | 6.27046 | 0.428640 | ||||||||
\(215\) | 0.904647 | + | 20.3839i | 0.0616964 | + | 1.39017i | ||||
\(216\) | 13.1910 | 0.897533 | ||||||||
\(217\) | 19.3432i | 1.31311i | ||||||||
\(218\) | 1.93960i | 0.131366i | ||||||||
\(219\) | 8.89905 | 0.601342 | ||||||||
\(220\) | 1.40337 | − | 0.0622822i | 0.0946153 | − | 0.00419906i | ||||
\(221\) | −10.3920 | −0.699040 | ||||||||
\(222\) | 8.97259i | 0.602201i | ||||||||
\(223\) | 10.8496i | 0.726546i | 0.931683 | + | 0.363273i | \(0.118341\pi\) | ||||
−0.931683 | + | 0.363273i | \(0.881659\pi\) | |||||||
\(224\) | −10.6013 | −0.708327 | ||||||||
\(225\) | 11.7183 | − | 1.04218i | 0.781219 | − | 0.0694784i | ||||
\(226\) | −24.5333 | −1.63193 | ||||||||
\(227\) | 8.78226i | 0.582899i | 0.956586 | + | 0.291449i | \(0.0941375\pi\) | ||||
−0.956586 | + | 0.291449i | \(0.905862\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.0824 | −1.19492 | −0.597459 | − | 0.801899i | \(-0.703823\pi\) | ||||
−0.597459 | + | 0.801899i | \(0.703823\pi\) | |||||||
\(230\) | −16.7765 | + | 0.744548i | −1.10621 | + | 0.0490941i | ||||
\(231\) | −3.77409 | −0.248317 | ||||||||
\(232\) | 13.1336i | 0.862265i | ||||||||
\(233\) | 26.3658i | 1.72728i | 0.504109 | + | 0.863640i | \(0.331821\pi\) | ||||
−0.504109 | + | 0.863640i | \(0.668179\pi\) | |||||||
\(234\) | −9.93346 | −0.649371 | ||||||||
\(235\) | 0.724051 | + | 16.3147i | 0.0472319 | + | 1.06425i | ||||
\(236\) | −0.414975 | −0.0270126 | ||||||||
\(237\) | − | 1.11348i | − | 0.0723282i | ||||||
\(238\) | 13.9282i | 0.902833i | ||||||||
\(239\) | 9.16897 | 0.593091 | 0.296546 | − | 0.955019i | \(-0.404165\pi\) | ||||
0.296546 | + | 0.955019i | \(0.404165\pi\) | |||||||
\(240\) | 0.217459 | + | 4.89990i | 0.0140369 | + | 0.316287i | ||||
\(241\) | −26.5167 | −1.70809 | −0.854045 | − | 0.520199i | \(-0.825858\pi\) | ||||
−0.854045 | + | 0.520199i | \(0.825858\pi\) | |||||||
\(242\) | 11.5672i | 0.743570i | ||||||||
\(243\) | 15.8098i | 1.01420i | ||||||||
\(244\) | 3.25048 | 0.208091 | ||||||||
\(245\) | 16.4809 | − | 0.731429i | 1.05293 | − | 0.0467293i | ||||
\(246\) | −5.23784 | −0.333952 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 15.6275i | 0.992345i | ||||||||
\(249\) | 2.02756 | 0.128491 | ||||||||
\(250\) | 1.81186 | + | 13.5370i | 0.114592 | + | 0.856157i | ||||
\(251\) | −14.9471 | −0.943451 | −0.471726 | − | 0.881745i | \(-0.656369\pi\) | ||||
−0.471726 | + | 0.881745i | \(0.656369\pi\) | |||||||
\(252\) | − | 4.52982i | − | 0.285352i | ||||||
\(253\) | − | 7.60684i | − | 0.478238i | ||||||
\(254\) | 4.21819 | 0.264673 | ||||||||
\(255\) | −5.40341 | + | 0.239805i | −0.338374 | + | 0.0150172i | ||||
\(256\) | −11.3337 | −0.708356 | ||||||||
\(257\) | − | 10.7988i | − | 0.673610i | −0.941574 | − | 0.336805i | \(-0.890654\pi\) | ||
0.941574 | − | 0.336805i | \(-0.109346\pi\) | |||||||
\(258\) | − | 8.96680i | − | 0.558249i | ||||||
\(259\) | 34.6223 | 2.15132 | ||||||||
\(260\) | 0.173961 | + | 3.91977i | 0.0107886 | + | 0.243094i | ||||
\(261\) | −10.0875 | −0.624403 | ||||||||
\(262\) | 9.26874i | 0.572624i | ||||||||
\(263\) | − | 0.549168i | − | 0.0338632i | −0.999857 | − | 0.0169316i | \(-0.994610\pi\) | ||
0.999857 | − | 0.0169316i | \(-0.00538975\pi\) | |||||||
\(264\) | −3.04910 | −0.187659 | ||||||||
\(265\) | −0.330370 | − | 7.44404i | −0.0202944 | − | 0.457284i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.17066i | 0.132842i | ||||||||
\(268\) | − | 0.513275i | − | 0.0313532i | ||||||
\(269\) | 21.9270 | 1.33691 | 0.668455 | − | 0.743752i | \(-0.266956\pi\) | ||||
0.668455 | + | 0.743752i | \(0.266956\pi\) | |||||||
\(270\) | −11.7505 | + | 0.521490i | −0.715110 | + | 0.0317369i | ||||
\(271\) | −5.28538 | −0.321064 | −0.160532 | − | 0.987031i | \(-0.551321\pi\) | ||||
−0.160532 | + | 0.987031i | \(0.551321\pi\) | |||||||
\(272\) | 8.19923i | 0.497151i | ||||||||
\(273\) | − | 10.5414i | − | 0.637997i | ||||||
\(274\) | 4.50316 | 0.272046 | ||||||||
\(275\) | −6.16230 | + | 0.548050i | −0.371601 | + | 0.0330487i | ||||
\(276\) | −2.51093 | −0.151140 | ||||||||
\(277\) | 17.4391i | 1.04781i | 0.851776 | + | 0.523906i | \(0.175526\pi\) | ||||
−0.851776 | + | 0.523906i | \(0.824474\pi\) | |||||||
\(278\) | − | 22.7548i | − | 1.36474i | ||||||
\(279\) | −12.0030 | −0.718599 | ||||||||
\(280\) | 25.9482 | − | 1.15159i | 1.55070 | − | 0.0688208i | ||||
\(281\) | 23.1841 | 1.38305 | 0.691524 | − | 0.722354i | \(-0.256940\pi\) | ||||
0.691524 | + | 0.722354i | \(0.256940\pi\) | |||||||
\(282\) | − | 7.17675i | − | 0.427369i | ||||||
\(283\) | − | 4.59388i | − | 0.273078i | −0.990635 | − | 0.136539i | \(-0.956402\pi\) | ||
0.990635 | − | 0.136539i | \(-0.0435979\pi\) | |||||||
\(284\) | −6.94548 | −0.412138 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.22372 | 0.308885 | ||||||||
\(287\) | 20.2111i | 1.19302i | ||||||||
\(288\) | − | 6.57836i | − | 0.387633i | ||||||
\(289\) | 7.95823 | 0.468131 | ||||||||
\(290\) | −0.519222 | − | 11.6994i | −0.0304898 | − | 0.687010i | ||||
\(291\) | −2.46356 | −0.144416 | ||||||||
\(292\) | − | 5.61684i | − | 0.328700i | ||||||
\(293\) | − | 18.1326i | − | 1.05932i | −0.848211 | − | 0.529659i | \(-0.822320\pi\) | ||
0.848211 | − | 0.529659i | \(-0.177680\pi\) | |||||||
\(294\) | −7.24987 | −0.422821 | ||||||||
\(295\) | 1.82578 | − | 0.0810289i | 0.106301 | − | 0.00471769i | ||||
\(296\) | 27.9715 | 1.62581 | ||||||||
\(297\) | − | 5.32791i | − | 0.309157i | ||||||
\(298\) | 2.06185i | 0.119440i | ||||||||
\(299\) | 21.2467 | 1.22873 | ||||||||
\(300\) | 0.180905 | + | 2.03410i | 0.0104446 | + | 0.117439i | ||||
\(301\) | −34.6000 | −1.99431 | ||||||||
\(302\) | 1.63558i | 0.0941171i | ||||||||
\(303\) | 2.99812i | 0.172237i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −14.3013 | + | 0.634695i | −0.818887 | + | 0.0363425i | ||||
\(306\) | −8.64282 | −0.494077 | ||||||||
\(307\) | − | 4.41407i | − | 0.251924i | −0.992035 | − | 0.125962i | \(-0.959798\pi\) | ||
0.992035 | − | 0.125962i | \(-0.0402018\pi\) | |||||||
\(308\) | 2.38210i | 0.135733i | ||||||||
\(309\) | 10.6253 | 0.604452 | ||||||||
\(310\) | −0.617813 | − | 13.9209i | −0.0350894 | − | 0.790651i | ||||
\(311\) | 15.0338 | 0.852487 | 0.426243 | − | 0.904609i | \(-0.359837\pi\) | ||||
0.426243 | + | 0.904609i | \(0.359837\pi\) | |||||||
\(312\) | − | 8.51646i | − | 0.482150i | ||||||
\(313\) | − | 7.80549i | − | 0.441193i | −0.975365 | − | 0.220596i | \(-0.929200\pi\) | ||
0.975365 | − | 0.220596i | \(-0.0708003\pi\) | |||||||
\(314\) | −7.38164 | −0.416570 | ||||||||
\(315\) | 0.884502 | + | 19.9300i | 0.0498361 | + | 1.12293i | ||||
\(316\) | −0.702796 | −0.0395354 | ||||||||
\(317\) | − | 27.2310i | − | 1.52944i | −0.644361 | − | 0.764722i | \(-0.722877\pi\) | ||
0.644361 | − | 0.764722i | \(-0.277123\pi\) | |||||||
\(318\) | 3.27460i | 0.183631i | ||||||||
\(319\) | 5.30474 | 0.297009 | ||||||||
\(320\) | 19.8119 | − | 0.879260i | 1.10752 | − | 0.0491521i | ||||
\(321\) | −4.12913 | −0.230466 | ||||||||
\(322\) | − | 28.4767i | − | 1.58694i | ||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 1.82523 | 0.101402 | ||||||||
\(325\) | −1.53076 | − | 17.2120i | −0.0849115 | − | 0.954749i | ||||
\(326\) | −11.9682 | −0.662858 | ||||||||
\(327\) | − | 1.27724i | − | 0.0706313i | ||||||
\(328\) | 16.3286i | 0.901596i | ||||||||
\(329\) | −27.6927 | −1.52675 | ||||||||
\(330\) | 2.71612 | − | 0.120542i | 0.149517 | − | 0.00663564i | ||||
\(331\) | 11.9800 | 0.658480 | 0.329240 | − | 0.944246i | \(-0.393208\pi\) | ||||
0.329240 | + | 0.944246i | \(0.393208\pi\) | |||||||
\(332\) | − | 1.27974i | − | 0.0702348i | ||||||
\(333\) | 21.4840i | 1.17732i | ||||||||
\(334\) | 4.73526 | 0.259102 | ||||||||
\(335\) | 0.100223 | + | 2.25827i | 0.00547577 | + | 0.123383i | ||||
\(336\) | −8.31716 | −0.453738 | ||||||||
\(337\) | − | 4.14343i | − | 0.225707i | −0.993612 | − | 0.112853i | \(-0.964001\pi\) | ||
0.993612 | − | 0.112853i | \(-0.0359991\pi\) | |||||||
\(338\) | − | 1.29021i | − | 0.0701782i | ||||||
\(339\) | 16.1553 | 0.877437 | ||||||||
\(340\) | 0.151358 | + | 3.41048i | 0.00820856 | + | 0.184959i | ||||
\(341\) | 6.31201 | 0.341815 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.43230i | 0.0773370i | ||||||||
\(344\) | −27.9534 | −1.50715 | ||||||||
\(345\) | 11.0474 | − | 0.490289i | 0.594773 | − | 0.0263963i | ||||
\(346\) | 5.78078 | 0.310777 | ||||||||
\(347\) | − | 9.16935i | − | 0.492237i | −0.969240 | − | 0.246118i | \(-0.920845\pi\) | ||
0.969240 | − | 0.246118i | \(-0.0791552\pi\) | |||||||
\(348\) | − | 1.75103i | − | 0.0938653i | ||||||
\(349\) | 32.6883 | 1.74976 | 0.874881 | − | 0.484337i | \(-0.160939\pi\) | ||||
0.874881 | + | 0.484337i | \(0.160939\pi\) | |||||||
\(350\) | −23.0690 | + | 2.05166i | −1.23309 | + | 0.109666i | ||||
\(351\) | 14.8814 | 0.794312 | ||||||||
\(352\) | 3.45937i | 0.184385i | ||||||||
\(353\) | − | 26.4701i | − | 1.40886i | −0.709773 | − | 0.704431i | \(-0.751202\pi\) | ||
0.709773 | − | 0.704431i | \(-0.248798\pi\) | |||||||
\(354\) | −0.803153 | −0.0426871 | ||||||||
\(355\) | 30.5583 | − | 1.35619i | 1.62187 | − | 0.0719790i | ||||
\(356\) | 1.37006 | 0.0726131 | ||||||||
\(357\) | − | 9.17181i | − | 0.485424i | ||||||
\(358\) | 11.4562i | 0.605480i | ||||||||
\(359\) | −12.4121 | −0.655083 | −0.327542 | − | 0.944837i | \(-0.606220\pi\) | ||||
−0.327542 | + | 0.944837i | \(0.606220\pi\) | |||||||
\(360\) | 0.714592 | + | 16.1015i | 0.0376623 | + | 0.848625i | ||||
\(361\) | 0 | 0 | ||||||||
\(362\) | − | 23.8219i | − | 1.25205i | ||||||
\(363\) | − | 7.61708i | − | 0.399793i | ||||||
\(364\) | −6.65347 | −0.348736 | ||||||||
\(365\) | 1.09675 | + | 24.7126i | 0.0574068 | + | 1.29352i | ||||
\(366\) | 6.29106 | 0.328839 | ||||||||
\(367\) | − | 5.32121i | − | 0.277765i | −0.990309 | − | 0.138882i | \(-0.955649\pi\) | ||
0.990309 | − | 0.138882i | \(-0.0443510\pi\) | |||||||
\(368\) | − | 16.7636i | − | 0.873861i | ||||||
\(369\) | −12.5415 | −0.652885 | ||||||||
\(370\) | −24.9168 | + | 1.10582i | −1.29536 | + | 0.0574887i | ||||
\(371\) | 12.6356 | 0.656009 | ||||||||
\(372\) | − | 2.08352i | − | 0.108026i | ||||||
\(373\) | 19.3050i | 0.999575i | 0.866148 | + | 0.499788i | \(0.166589\pi\) | ||||
−0.866148 | + | 0.499788i | \(0.833411\pi\) | |||||||
\(374\) | 4.54501 | 0.235017 | ||||||||
\(375\) | −1.19312 | − | 8.91420i | −0.0616124 | − | 0.460327i | ||||
\(376\) | −22.3730 | −1.15380 | ||||||||
\(377\) | 14.8167i | 0.763100i | ||||||||
\(378\) | − | 19.9454i | − | 1.02588i | ||||||
\(379\) | 20.5109 | 1.05357 | 0.526787 | − | 0.849997i | \(-0.323397\pi\) | ||||
0.526787 | + | 0.849997i | \(0.323397\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.77770 | −0.142306 | ||||||||
\(382\) | − | 18.9375i | − | 0.968927i | ||||||
\(383\) | 22.7253i | 1.16121i | 0.814186 | + | 0.580605i | \(0.197184\pi\) | ||||
−0.814186 | + | 0.580605i | \(0.802816\pi\) | |||||||
\(384\) | −4.21710 | −0.215203 | ||||||||
\(385\) | −0.465134 | − | 10.4806i | −0.0237054 | − | 0.534142i | ||||
\(386\) | −24.2402 | −1.23379 | ||||||||
\(387\) | − | 21.4702i | − | 1.09139i | ||||||
\(388\) | 1.55493i | 0.0789396i | ||||||||
\(389\) | −5.04493 | −0.255788 | −0.127894 | − | 0.991788i | \(-0.540822\pi\) | ||||
−0.127894 | + | 0.991788i | \(0.540822\pi\) | |||||||
\(390\) | 0.336688 | + | 7.58641i | 0.0170489 | + | 0.384153i | ||||
\(391\) | 18.4862 | 0.934885 | ||||||||
\(392\) | 22.6010i | 1.14152i | ||||||||
\(393\) | − | 6.10351i | − | 0.307881i | ||||||
\(394\) | 31.7255 | 1.59831 | ||||||||
\(395\) | 3.09212 | − | 0.137229i | 0.155581 | − | 0.00690476i | ||||
\(396\) | −1.47815 | −0.0742800 | ||||||||
\(397\) | − | 22.9429i | − | 1.15147i | −0.817636 | − | 0.575735i | \(-0.804716\pi\) | ||
0.817636 | − | 0.575735i | \(-0.195284\pi\) | |||||||
\(398\) | − | 6.61603i | − | 0.331632i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −13.5802 | + | 1.20777i | −0.679009 | + | 0.0603883i | ||||
\(401\) | 22.7649 | 1.13683 | 0.568413 | − | 0.822744i | \(-0.307558\pi\) | ||||
0.568413 | + | 0.822744i | \(0.307558\pi\) | |||||||
\(402\) | − | 0.993404i | − | 0.0495465i | ||||||
\(403\) | 17.6301i | 0.878220i | ||||||||
\(404\) | 1.89233 | 0.0941468 | ||||||||
\(405\) | −8.03053 | + | 0.356398i | −0.399040 | + | 0.0177096i | ||||
\(406\) | 19.8587 | 0.985568 | ||||||||
\(407\) | − | 11.2978i | − | 0.560012i | ||||||
\(408\) | − | 7.40993i | − | 0.366846i | ||||||
\(409\) | 23.8028 | 1.17697 | 0.588486 | − | 0.808507i | \(-0.299724\pi\) | ||||
0.588486 | + | 0.808507i | \(0.299724\pi\) | |||||||
\(410\) | −0.645532 | − | 14.5454i | −0.0318805 | − | 0.718347i | ||||
\(411\) | −2.96536 | −0.146270 | ||||||||
\(412\) | − | 6.70640i | − | 0.330400i | ||||||
\(413\) | 3.09911i | 0.152497i | ||||||||
\(414\) | 17.6705 | 0.868458 | ||||||||
\(415\) | 0.249884 | + | 5.63051i | 0.0122663 | + | 0.276391i | ||||
\(416\) | −9.66239 | −0.473737 | ||||||||
\(417\) | 14.9842i | 0.733777i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.9374 | 0.778593 | 0.389296 | − | 0.921113i | \(-0.372718\pi\) | ||||
0.389296 | + | 0.921113i | \(0.372718\pi\) | |||||||
\(420\) | −3.45953 | + | 0.153535i | −0.168808 | + | 0.00749175i | ||||
\(421\) | 2.65354 | 0.129326 | 0.0646629 | − | 0.997907i | \(-0.479403\pi\) | ||||
0.0646629 | + | 0.997907i | \(0.479403\pi\) | |||||||
\(422\) | − | 24.5780i | − | 1.19644i | ||||||
\(423\) | − | 17.1840i | − | 0.835517i | ||||||
\(424\) | 10.2084 | 0.495761 | ||||||||
\(425\) | −1.33187 | − | 14.9757i | −0.0646054 | − | 0.726426i | ||||
\(426\) | −13.4424 | −0.651289 | ||||||||
\(427\) | − | 24.2751i | − | 1.17476i | ||||||
\(428\) | 2.60619i | 0.125975i | ||||||||
\(429\) | −3.43984 | −0.166077 | ||||||||
\(430\) | 24.9007 | − | 1.10510i | 1.20082 | − | 0.0532929i | ||||
\(431\) | −33.3222 | −1.60507 | −0.802536 | − | 0.596604i | \(-0.796516\pi\) | ||||
−0.802536 | + | 0.596604i | \(0.796516\pi\) | |||||||
\(432\) | − | 11.7414i | − | 0.564908i | ||||||
\(433\) | − | 22.3800i | − | 1.07552i | −0.843099 | − | 0.537758i | \(-0.819272\pi\) | ||
0.843099 | − | 0.537758i | \(-0.180728\pi\) | |||||||
\(434\) | 23.6294 | 1.13425 | ||||||||
\(435\) | 0.341911 | + | 7.70409i | 0.0163934 | + | 0.369383i | ||||
\(436\) | −0.806155 | −0.0386078 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | − | 10.8710i | − | 0.519435i | ||||||
\(439\) | −17.4561 | −0.833132 | −0.416566 | − | 0.909105i | \(-0.636767\pi\) | ||||
−0.416566 | + | 0.909105i | \(0.636767\pi\) | |||||||
\(440\) | −0.375783 | − | 8.46732i | −0.0179148 | − | 0.403664i | ||||
\(441\) | −17.3591 | −0.826625 | ||||||||
\(442\) | 12.6947i | 0.603825i | ||||||||
\(443\) | 1.49859i | 0.0712001i | 0.999366 | + | 0.0356001i | \(0.0113342\pi\) | ||||
−0.999366 | + | 0.0356001i | \(0.988666\pi\) | |||||||
\(444\) | −3.72928 | −0.176984 | ||||||||
\(445\) | −6.02791 | + | 0.267521i | −0.285750 | + | 0.0126817i | ||||
\(446\) | 13.2538 | 0.627584 | ||||||||
\(447\) | − | 1.35774i | − | 0.0642189i | ||||||
\(448\) | 33.6290i | 1.58882i | ||||||||
\(449\) | 11.9911 | 0.565896 | 0.282948 | − | 0.959135i | \(-0.408688\pi\) | ||||
0.282948 | + | 0.959135i | \(0.408688\pi\) | |||||||
\(450\) | −1.27311 | − | 14.3149i | −0.0600149 | − | 0.674811i | ||||
\(451\) | 6.59521 | 0.310556 | ||||||||
\(452\) | − | 10.1968i | − | 0.479617i | ||||||
\(453\) | − | 1.07704i | − | 0.0506037i | ||||||
\(454\) | 10.7283 | 0.503503 | ||||||||
\(455\) | 29.2735 | − | 1.29917i | 1.37236 | − | 0.0609060i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.9472i | 0.605646i | 0.953047 | + | 0.302823i | \(0.0979291\pi\) | ||||
−0.953047 | + | 0.302823i | \(0.902071\pi\) | |||||||
\(458\) | 22.0892i | 1.03216i | ||||||||
\(459\) | 12.9479 | 0.604357 | ||||||||
\(460\) | −0.309457 | − | 6.97283i | −0.0144285 | − | 0.325110i | ||||
\(461\) | 13.8680 | 0.645899 | 0.322949 | − | 0.946416i | \(-0.395326\pi\) | ||||
0.322949 | + | 0.946416i | \(0.395326\pi\) | |||||||
\(462\) | 4.61038i | 0.214494i | ||||||||
\(463\) | − | 4.18473i | − | 0.194481i | −0.995261 | − | 0.0972405i | \(-0.968998\pi\) | ||
0.995261 | − | 0.0972405i | \(-0.0310016\pi\) | |||||||
\(464\) | 11.6903 | 0.542710 | ||||||||
\(465\) | 0.406833 | + | 9.16695i | 0.0188664 | + | 0.425107i | ||||
\(466\) | 32.2081 | 1.49201 | ||||||||
\(467\) | − | 23.3019i | − | 1.07828i | −0.842216 | − | 0.539141i | \(-0.818749\pi\) | ||
0.842216 | − | 0.539141i | \(-0.181251\pi\) | |||||||
\(468\) | − | 4.12864i | − | 0.190847i | ||||||
\(469\) | −3.83322 | −0.177002 | ||||||||
\(470\) | 19.9298 | − | 0.884491i | 0.919292 | − | 0.0407985i | ||||
\(471\) | 4.86085 | 0.223976 | ||||||||
\(472\) | 2.50378i | 0.115246i | ||||||||
\(473\) | 11.2905i | 0.519139i | ||||||||
\(474\) | −1.36021 | −0.0624765 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −5.78899 | −0.265338 | ||||||||
\(477\) | 7.84072i | 0.359002i | ||||||||
\(478\) | − | 11.2007i | − | 0.512307i | ||||||
\(479\) | −35.1170 | −1.60454 | −0.802268 | − | 0.596963i | \(-0.796374\pi\) | ||||
−0.802268 | + | 0.596963i | \(0.796374\pi\) | |||||||
\(480\) | −5.02405 | + | 0.222969i | −0.229315 | + | 0.0101771i | ||||
\(481\) | 31.5560 | 1.43883 | ||||||||
\(482\) | 32.3924i | 1.47543i | ||||||||
\(483\) | 18.7520i | 0.853247i | ||||||||
\(484\) | −4.80769 | −0.218531 | ||||||||
\(485\) | −0.303619 | − | 6.84128i | −0.0137866 | − | 0.310647i | ||||
\(486\) | 19.3130 | 0.876055 | ||||||||
\(487\) | − | 33.4209i | − | 1.51445i | −0.653156 | − | 0.757223i | \(-0.726556\pi\) | ||
0.653156 | − | 0.757223i | \(-0.273444\pi\) | |||||||
\(488\) | − | 19.6120i | − | 0.887791i | ||||||
\(489\) | 7.88113 | 0.356397 | ||||||||
\(490\) | −0.893503 | − | 20.1328i | −0.0403643 | − | 0.909509i | ||||
\(491\) | −17.5387 | −0.791511 | −0.395755 | − | 0.918356i | \(-0.629517\pi\) | ||||
−0.395755 | + | 0.918356i | \(0.629517\pi\) | |||||||
\(492\) | − | 2.17700i | − | 0.0981468i | ||||||
\(493\) | 12.8916i | 0.580609i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.50349 | − | 0.288627i | 0.292310 | − | 0.0129728i | ||||
\(496\) | 13.9101 | 0.624582 | ||||||||
\(497\) | 51.8700i | 2.32669i | ||||||||
\(498\) | − | 2.47684i | − | 0.110990i | ||||||
\(499\) | −32.6830 | −1.46309 | −0.731545 | − | 0.681793i | \(-0.761201\pi\) | ||||
−0.731545 | + | 0.681793i | \(0.761201\pi\) | |||||||
\(500\) | −5.62640 | + | 0.753063i | −0.251620 | + | 0.0336780i | ||||
\(501\) | −3.11819 | −0.139310 | ||||||||
\(502\) | 18.2591i | 0.814946i | ||||||||
\(503\) | 17.5243i | 0.781370i | 0.920524 | + | 0.390685i | \(0.127762\pi\) | ||||
−0.920524 | + | 0.390685i | \(0.872238\pi\) | |||||||
\(504\) | −27.3309 | −1.21742 | ||||||||
\(505\) | −8.32575 | + | 0.369500i | −0.370491 | + | 0.0164425i | ||||
\(506\) | −9.29240 | −0.413098 | ||||||||
\(507\) | 0.849611i | 0.0377325i | ||||||||
\(508\) | 1.75321i | 0.0777860i | ||||||||
\(509\) | 29.9995 | 1.32970 | 0.664852 | − | 0.746975i | \(-0.268495\pi\) | ||||
0.664852 | + | 0.746975i | \(0.268495\pi\) | |||||||
\(510\) | 0.292943 | + | 6.60072i | 0.0129717 | + | 0.292285i | ||||
\(511\) | −41.9475 | −1.85565 | ||||||||
\(512\) | 24.3299i | 1.07524i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −13.1916 | −0.581858 | ||||||||
\(515\) | 1.30950 | + | 29.5064i | 0.0577037 | + | 1.30021i | ||||
\(516\) | 3.72687 | 0.164066 | ||||||||
\(517\) | 9.03659i | 0.397429i | ||||||||
\(518\) | − | 42.2941i | − | 1.85830i | ||||||
\(519\) | −3.80668 | −0.167094 | ||||||||
\(520\) | 23.6501 | − | 1.04960i | 1.03713 | − | 0.0460281i | ||||
\(521\) | 10.4875 | 0.459464 | 0.229732 | − | 0.973254i | \(-0.426215\pi\) | ||||
0.229732 | + | 0.973254i | \(0.426215\pi\) | |||||||
\(522\) | 12.3228i | 0.539354i | ||||||||
\(523\) | − | 32.7586i | − | 1.43244i | −0.697877 | − | 0.716218i | \(-0.745872\pi\) | ||
0.697877 | − | 0.716218i | \(-0.254128\pi\) | |||||||
\(524\) | −3.85237 | −0.168291 | ||||||||
\(525\) | 15.1910 | − | 1.35103i | 0.662992 | − | 0.0589638i | ||||
\(526\) | −0.670856 | −0.0292507 | ||||||||
\(527\) | 15.3395i | 0.668198i | ||||||||
\(528\) | 2.71402i | 0.118113i | ||||||||
\(529\) | −14.7955 | −0.643283 | ||||||||
\(530\) | −9.09354 | + | 0.403575i | −0.394998 | + | 0.0175302i | ||||
\(531\) | −1.92307 | −0.0834543 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 18.4211i | 0.797908i | ||||||||
\(534\) | 2.65165 | 0.114748 | ||||||||
\(535\) | −0.508890 | − | 11.4666i | −0.0220012 | − | 0.495743i | ||||
\(536\) | −3.09687 | −0.133764 | ||||||||
\(537\) | − | 7.54398i | − | 0.325547i | ||||||
\(538\) | − | 26.7857i | − | 1.15481i | ||||||
\(539\) | 9.12866 | 0.393199 | ||||||||
\(540\) | −0.216747 | − | 4.88384i | −0.00932730 | − | 0.210167i | ||||
\(541\) | 14.7958 | 0.636122 | 0.318061 | − | 0.948070i | \(-0.396968\pi\) | ||||
0.318061 | + | 0.948070i | \(0.396968\pi\) | |||||||
\(542\) | 6.45655i | 0.277333i | ||||||||
\(543\) | 15.6868i | 0.673186i | ||||||||
\(544\) | −8.40697 | −0.360446 | ||||||||
\(545\) | 3.54687 | − | 0.157411i | 0.151931 | − | 0.00674277i | ||||
\(546\) | −12.8773 | −0.551097 | ||||||||
\(547\) | − | 1.61001i | − | 0.0688390i | −0.999407 | − | 0.0344195i | \(-0.989042\pi\) | ||
0.999407 | − | 0.0344195i | \(-0.0109582\pi\) | |||||||
\(548\) | 1.87165i | 0.0799529i | ||||||||
\(549\) | 15.0633 | 0.642888 | ||||||||
\(550\) | 0.669491 | + | 7.52778i | 0.0285472 | + | 0.320986i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 15.1498i | 0.644819i | ||||||||
\(553\) | 5.24860i | 0.223193i | ||||||||
\(554\) | 21.3033 | 0.905092 | ||||||||
\(555\) | 16.4078 | − | 0.728186i | 0.696474 | − | 0.0309098i | ||||
\(556\) | 9.45758 | 0.401091 | ||||||||
\(557\) | − | 22.3165i | − | 0.945581i | −0.881175 | − | 0.472790i | \(-0.843247\pi\) | ||
0.881175 | − | 0.472790i | \(-0.156753\pi\) | |||||||
\(558\) | 14.6627i | 0.620720i | ||||||||
\(559\) | −31.5357 | −1.33382 | ||||||||
\(560\) | −1.02504 | − | 23.0967i | −0.0433158 | − | 0.976012i | ||||
\(561\) | −2.99291 | −0.126361 | ||||||||
\(562\) | − | 28.3214i | − | 1.19467i | ||||||
\(563\) | − | 2.42120i | − | 0.102042i | −0.998698 | − | 0.0510208i | \(-0.983753\pi\) | ||
0.998698 | − | 0.0510208i | \(-0.0162475\pi\) | |||||||
\(564\) | 2.98287 | 0.125602 | ||||||||
\(565\) | 1.99105 | + | 44.8632i | 0.0837640 | + | 1.88741i | ||||
\(566\) | −5.61182 | −0.235882 | ||||||||
\(567\) | − | 13.6311i | − | 0.572453i | ||||||
\(568\) | 41.9059i | 1.75833i | ||||||||
\(569\) | 25.3556 | 1.06296 | 0.531481 | − | 0.847070i | \(-0.321636\pi\) | ||||
0.531481 | + | 0.847070i | \(0.321636\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.79252 | 0.158712 | 0.0793561 | − | 0.996846i | \(-0.474714\pi\) | ||||
0.0793561 | + | 0.996846i | \(0.474714\pi\) | |||||||
\(572\) | 2.17113i | 0.0907797i | ||||||||
\(573\) | 12.4704i | 0.520960i | ||||||||
\(574\) | 24.6896 | 1.03052 | ||||||||
\(575\) | 2.72306 | + | 30.6182i | 0.113559 | + | 1.27687i | ||||
\(576\) | −20.8676 | −0.869485 | ||||||||
\(577\) | − | 36.8138i | − | 1.53258i | −0.642496 | − | 0.766289i | \(-0.722101\pi\) | ||
0.642496 | − | 0.766289i | \(-0.277899\pi\) | |||||||
\(578\) | − | 9.72166i | − | 0.404368i | ||||||
\(579\) | 15.9623 | 0.663369 | ||||||||
\(580\) | 4.86261 | − | 0.215804i | 0.201909 | − | 0.00896079i | ||||
\(581\) | −9.55731 | −0.396504 | ||||||||
\(582\) | 3.00945i | 0.124746i | ||||||||
\(583\) | − | 4.12321i | − | 0.170766i | ||||||
\(584\) | −33.8895 | −1.40236 | ||||||||
\(585\) | 0.806168 | + | 18.1650i | 0.0333309 | + | 0.751028i | ||||
\(586\) | −22.1505 | −0.915030 | ||||||||
\(587\) | − | 27.5764i | − | 1.13820i | −0.822268 | − | 0.569100i | \(-0.807292\pi\) | ||
0.822268 | − | 0.569100i | \(-0.192708\pi\) | |||||||
\(588\) | − | 3.01326i | − | 0.124265i | ||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −0.0989838 | − | 2.23035i | −0.00407510 | − | 0.0918220i | ||||
\(591\) | −20.8914 | −0.859358 | ||||||||
\(592\) | − | 24.8976i | − | 1.02328i | ||||||
\(593\) | − | 7.43391i | − | 0.305274i | −0.988282 | − | 0.152637i | \(-0.951223\pi\) | ||
0.988282 | − | 0.152637i | \(-0.0487766\pi\) | |||||||
\(594\) | −6.50850 | −0.267047 | ||||||||
\(595\) | 25.4700 | − | 1.13037i | 1.04417 | − | 0.0463407i | ||||
\(596\) | −0.856967 | −0.0351027 | ||||||||
\(597\) | 4.35669i | 0.178307i | ||||||||
\(598\) | − | 25.9547i | − | 1.06137i | ||||||
\(599\) | 7.48833 | 0.305965 | 0.152982 | − | 0.988229i | \(-0.451112\pi\) | ||||
0.152982 | + | 0.988229i | \(0.451112\pi\) | |||||||
\(600\) | 12.2729 | − | 1.09150i | 0.501039 | − | 0.0445603i | ||||
\(601\) | 24.9173 | 1.01640 | 0.508199 | − | 0.861240i | \(-0.330312\pi\) | ||||
0.508199 | + | 0.861240i | \(0.330312\pi\) | |||||||
\(602\) | 42.2668i | 1.72267i | ||||||||
\(603\) | − | 2.37861i | − | 0.0968646i | ||||||
\(604\) | −0.679797 | −0.0276605 | ||||||||
\(605\) | 21.1526 | − | 0.938759i | 0.859974 | − | 0.0381660i | ||||
\(606\) | 3.66246 | 0.148777 | ||||||||
\(607\) | − | 13.5201i | − | 0.548764i | −0.961621 | − | 0.274382i | \(-0.911527\pi\) | ||
0.961621 | − | 0.274382i | \(-0.0884733\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −13.0770 | −0.529908 | ||||||||
\(610\) | 0.775335 | + | 17.4702i | 0.0313924 | + | 0.707348i | ||||
\(611\) | −25.2402 | −1.02111 | ||||||||
\(612\) | − | 3.59222i | − | 0.145207i | ||||||
\(613\) | − | 5.65406i | − | 0.228365i | −0.993460 | − | 0.114183i | \(-0.963575\pi\) | ||
0.993460 | − | 0.114183i | \(-0.0364249\pi\) | |||||||
\(614\) | −5.39217 | −0.217610 | ||||||||
\(615\) | 0.425086 | + | 9.57824i | 0.0171411 | + | 0.386232i | ||||
\(616\) | 14.3725 | 0.579086 | ||||||||
\(617\) | 18.4368i | 0.742239i | 0.928585 | + | 0.371120i | \(0.121026\pi\) | ||||
−0.928585 | + | 0.371120i | \(0.878974\pi\) | |||||||
\(618\) | − | 12.9797i | − | 0.522121i | ||||||
\(619\) | 6.99902 | 0.281314 | 0.140657 | − | 0.990058i | \(-0.455078\pi\) | ||||
0.140657 | + | 0.990058i | \(0.455078\pi\) | |||||||
\(620\) | 5.78592 | − | 0.256782i | 0.232368 | − | 0.0103126i | ||||
\(621\) | −26.4724 | −1.06230 | ||||||||
\(622\) | − | 18.3650i | − | 0.736371i | ||||||
\(623\) | − | 10.2319i | − | 0.409931i | ||||||
\(624\) | −7.58056 | −0.303465 | ||||||||
\(625\) | 24.6076 | − | 4.41190i | 0.984305 | − | 0.176476i | ||||
\(626\) | −9.53508 | −0.381099 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 3.06803i | − | 0.122428i | ||||||
\(629\) | 27.4560 | 1.09474 | ||||||||
\(630\) | 24.3462 | − | 1.08050i | 0.969977 | − | 0.0430480i | ||||
\(631\) | 28.0613 | 1.11710 | 0.558551 | − | 0.829470i | \(-0.311358\pi\) | ||||
0.558551 | + | 0.829470i | \(0.311358\pi\) | |||||||
\(632\) | 4.24036i | 0.168672i | ||||||||
\(633\) | 16.1847i | 0.643285i | ||||||||
\(634\) | −33.2650 | −1.32112 | ||||||||
\(635\) | −0.342335 | − | 7.71365i | −0.0135851 | − | 0.306107i | ||||
\(636\) | −1.36102 | −0.0539681 | ||||||||
\(637\) | 25.4973i | 1.01024i | ||||||||
\(638\) | − | 6.48020i | − | 0.256554i | ||||||
\(639\) | −32.1867 | −1.27328 | ||||||||
\(640\) | −0.519732 | − | 11.7109i | −0.0205442 | − | 0.462912i | ||||
\(641\) | −26.8330 | −1.05984 | −0.529921 | − | 0.848047i | \(-0.677778\pi\) | ||||
−0.529921 | + | 0.848047i | \(0.677778\pi\) | |||||||
\(642\) | 5.04409i | 0.199074i | ||||||||
\(643\) | − | 26.8783i | − | 1.05998i | −0.848005 | − | 0.529988i | \(-0.822196\pi\) | ||
0.848005 | − | 0.529988i | \(-0.177804\pi\) | |||||||
\(644\) | 11.8358 | 0.466394 | ||||||||
\(645\) | −16.3973 | + | 0.727717i | −0.645642 | + | 0.0286538i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.88424i | 0.349275i | 0.984633 | + | 0.174638i | \(0.0558754\pi\) | ||||
−0.984633 | + | 0.174638i | \(0.944125\pi\) | |||||||
\(648\) | − | 11.0126i | − | 0.432617i | ||||||
\(649\) | 1.01129 | 0.0396965 | ||||||||
\(650\) | −21.0259 | + | 1.86996i | −0.824704 | + | 0.0733458i | ||||
\(651\) | −15.5601 | −0.609849 | ||||||||
\(652\) | − | 4.97435i | − | 0.194811i | ||||||
\(653\) | 39.4102i | 1.54224i | 0.636689 | + | 0.771121i | \(0.280303\pi\) | ||||
−0.636689 | + | 0.771121i | \(0.719697\pi\) | |||||||
\(654\) | −1.56025 | −0.0610107 | ||||||||
\(655\) | 16.9494 | − | 0.752221i | 0.662268 | − | 0.0293917i | ||||
\(656\) | 14.5342 | 0.567465 | ||||||||
\(657\) | − | 26.0295i | − | 1.01551i | ||||||
\(658\) | 33.8291i | 1.31879i | ||||||||
\(659\) | 17.3119 | 0.674377 | 0.337189 | − | 0.941437i | \(-0.390524\pi\) | ||||
0.337189 | + | 0.941437i | \(0.390524\pi\) | |||||||
\(660\) | 0.0501011 | + | 1.12890i | 0.00195018 | + | 0.0439424i | ||||
\(661\) | −14.2421 | −0.553952 | −0.276976 | − | 0.960877i | \(-0.589332\pi\) | ||||
−0.276976 | + | 0.960877i | \(0.589332\pi\) | |||||||
\(662\) | − | 14.6346i | − | 0.568789i | ||||||
\(663\) | − | 8.35952i | − | 0.324657i | ||||||
\(664\) | −7.72138 | −0.299647 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 26.2446 | 1.01696 | ||||||||
\(667\) | − | 26.3573i | − | 1.02056i | ||||||
\(668\) | 1.96811i | 0.0761486i | ||||||||
\(669\) | −8.72768 | −0.337431 | ||||||||
\(670\) | 2.75867 | − | 0.122431i | 0.106577 | − | 0.00472992i | ||||
\(671\) | −7.92137 | −0.305801 | ||||||||
\(672\) | − | 8.52788i | − | 0.328970i | ||||||
\(673\) | − | 3.86700i | − | 0.149062i | −0.997219 | − | 0.0745310i | \(-0.976254\pi\) | ||
0.997219 | − | 0.0745310i | \(-0.0237460\pi\) | |||||||
\(674\) | −5.06155 | −0.194964 | ||||||||
\(675\) | 1.90726 | + | 21.4453i | 0.0734104 | + | 0.825430i | ||||
\(676\) | 0.536250 | 0.0206250 | ||||||||
\(677\) | 15.7102i | 0.603790i | 0.953341 | + | 0.301895i | \(0.0976193\pi\) | ||||
−0.953341 | + | 0.301895i | \(0.902381\pi\) | |||||||
\(678\) | − | 19.7351i | − | 0.757923i | ||||||
\(679\) | 11.6125 | 0.445646 | ||||||||
\(680\) | 20.5773 | − | 0.913229i | 0.789104 | − | 0.0350208i | ||||
\(681\) | −7.06463 | −0.270717 | ||||||||
\(682\) | − | 7.71067i | − | 0.295257i | ||||||
\(683\) | − | 11.3613i | − | 0.434727i | −0.976091 | − | 0.217364i | \(-0.930254\pi\) | ||
0.976091 | − | 0.217364i | \(-0.0697458\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.365462 | − | 8.23477i | −0.0139636 | − | 0.314634i | ||||
\(686\) | 1.74968 | 0.0668031 | ||||||||
\(687\) | − | 14.5458i | − | 0.554959i | ||||||
\(688\) | 24.8815i | 0.948599i | ||||||||
\(689\) | 11.5166 | 0.438746 | ||||||||
\(690\) | −0.598930 | − | 13.4954i | −0.0228009 | − | 0.513760i | ||||
\(691\) | −2.01088 | −0.0764974 | −0.0382487 | − | 0.999268i | \(-0.512178\pi\) | ||||
−0.0382487 | + | 0.999268i | \(0.512178\pi\) | |||||||
\(692\) | 2.40267i | 0.0913357i | ||||||||
\(693\) | 11.0391i | 0.419341i | ||||||||
\(694\) | −11.2012 | −0.425190 | ||||||||
\(695\) | −41.6109 | + | 1.84671i | −1.57839 | + | 0.0700496i | ||||
\(696\) | −10.5650 | −0.400464 | ||||||||
\(697\) | 16.0277i | 0.607093i | ||||||||
\(698\) | − | 39.9315i | − | 1.51143i | ||||||
\(699\) | −21.2092 | −0.802205 | ||||||||
\(700\) | −0.852732 | − | 9.58816i | −0.0322303 | − | 0.362399i | ||||
\(701\) | 12.4628 | 0.470713 | 0.235357 | − | 0.971909i | \(-0.424374\pi\) | ||||
0.235357 | + | 0.971909i | \(0.424374\pi\) | |||||||
\(702\) | − | 18.1789i | − | 0.686120i | ||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 10.9737 | 0.413586 | ||||||||
\(705\) | −13.1239 | + | 0.582442i | −0.494273 | + | 0.0219360i | ||||
\(706\) | −32.3355 | −1.21696 | ||||||||
\(707\) | − | 14.1322i | − | 0.531497i | ||||||
\(708\) | − | 0.333815i | − | 0.0125455i | ||||||
\(709\) | 3.52250 | 0.132290 | 0.0661452 | − | 0.997810i | \(-0.478930\pi\) | ||||
0.0661452 | + | 0.997810i | \(0.478930\pi\) | |||||||
\(710\) | −1.65670 | − | 37.3296i | −0.0621749 | − | 1.40095i | ||||
\(711\) | −3.25689 | −0.122143 | ||||||||
\(712\) | − | 8.26634i | − | 0.309794i | ||||||
\(713\) | − | 31.3620i | − | 1.17452i | ||||||
\(714\) | −11.2042 | −0.419305 | ||||||||
\(715\) | −0.423940 | − | 9.55242i | −0.0158545 | − | 0.357240i | ||||
\(716\) | −4.76155 | −0.177947 | ||||||||
\(717\) | 7.37571i | 0.275451i | ||||||||
\(718\) | 15.1624i | 0.565855i | ||||||||
\(719\) | 23.9065 | 0.891563 | 0.445781 | − | 0.895142i | \(-0.352926\pi\) | ||||
0.445781 | + | 0.895142i | \(0.352926\pi\) | |||||||
\(720\) | 14.3321 | − | 0.636063i | 0.534125 | − | 0.0237047i | ||||
\(721\) | −50.0845 | −1.86524 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 21.3306i | − | 0.793293i | ||||||
\(724\) | 9.90109 | 0.367971 | ||||||||
\(725\) | −21.3521 | + | 1.89897i | −0.792996 | + | 0.0705258i | ||||
\(726\) | −9.30492 | −0.345338 | ||||||||
\(727\) | 5.47926i | 0.203214i | 0.994825 | + | 0.101607i | \(0.0323985\pi\) | ||||
−0.994825 | + | 0.101607i | \(0.967602\pi\) | |||||||
\(728\) | 40.1441i | 1.48784i | ||||||||
\(729\) | −1.93302 | −0.0715933 | ||||||||
\(730\) | 30.1886 | − | 1.33978i | 1.11733 | − | 0.0495875i | ||||
\(731\) | −27.4383 | −1.01484 | ||||||||
\(732\) | 2.61475i | 0.0966440i | ||||||||
\(733\) | 18.8893i | 0.697691i | 0.937180 | + | 0.348846i | \(0.113426\pi\) | ||||
−0.937180 | + | 0.348846i | \(0.886574\pi\) | |||||||
\(734\) | −6.50031 | −0.239931 | ||||||||
\(735\) | 0.588376 | + | 13.2576i | 0.0217026 | + | 0.489013i | ||||
\(736\) | 17.1883 | 0.633569 | ||||||||
\(737\) | 1.25084i | 0.0460754i | ||||||||
\(738\) | 15.3205i | 0.563956i | ||||||||
\(739\) | −34.9585 | −1.28597 | −0.642985 | − | 0.765879i | \(-0.722304\pi\) | ||||
−0.642985 | + | 0.765879i | \(0.722304\pi\) | |||||||
\(740\) | −0.459611 | − | 10.3562i | −0.0168956 | − | 0.380700i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 15.4355i | − | 0.566655i | ||||||
\(743\) | − | 27.6384i | − | 1.01395i | −0.861960 | − | 0.506976i | \(-0.830763\pi\) | ||
0.861960 | − | 0.506976i | \(-0.169237\pi\) | |||||||
\(744\) | −12.5711 | −0.460877 | ||||||||
\(745\) | 3.77043 | − | 0.167333i | 0.138138 | − | 0.00613061i | ||||
\(746\) | 23.5827 | 0.863425 | ||||||||
\(747\) | − | 5.93055i | − | 0.216988i | ||||||
\(748\) | 1.88904i | 0.0690702i | ||||||||
\(749\) | 19.4635 | 0.711180 | ||||||||
\(750\) | −10.8895 | + | 1.45750i | −0.397627 | + | 0.0532202i | ||||
\(751\) | −53.7087 | −1.95986 | −0.979929 | − | 0.199348i | \(-0.936118\pi\) | ||||
−0.979929 | + | 0.199348i | \(0.936118\pi\) | |||||||
\(752\) | 19.9144i | 0.726203i | ||||||||
\(753\) | − | 12.0237i | − | 0.438169i | ||||||
\(754\) | 18.0999 | 0.659160 | ||||||||
\(755\) | 2.99093 | − | 0.132738i | 0.108851 | − | 0.00483085i | ||||
\(756\) | 8.28990 | 0.301501 | ||||||||
\(757\) | 24.5798i | 0.893368i | 0.894692 | + | 0.446684i | \(0.147395\pi\) | ||||
−0.894692 | + | 0.446684i | \(0.852605\pi\) | |||||||
\(758\) | − | 25.0558i | − | 0.910068i | ||||||
\(759\) | 6.11909 | 0.222109 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −0.906887 | −0.0328746 | −0.0164373 | − | 0.999865i | \(-0.505232\pi\) | ||||
−0.0164373 | + | 0.999865i | \(0.505232\pi\) | |||||||
\(762\) | 3.39320i | 0.122923i | ||||||||
\(763\) | 6.02051i | 0.217957i | ||||||||
\(764\) | 7.87099 | 0.284763 | ||||||||
\(765\) | 0.701424 | + | 15.8048i | 0.0253600 | + | 0.571424i | ||||
\(766\) | 27.7609 | 1.00304 | ||||||||
\(767\) | 2.82464i | 0.101992i | ||||||||
\(768\) | − | 9.11706i | − | 0.328984i | ||||||
\(769\) | −21.3193 | −0.768792 | −0.384396 | − | 0.923168i | \(-0.625590\pi\) | ||||
−0.384396 | + | 0.923168i | \(0.625590\pi\) | |||||||
\(770\) | −12.8030 | + | 0.568201i | −0.461387 | + | 0.0204765i | ||||
\(771\) | 8.68676 | 0.312846 | ||||||||
\(772\) | − | 10.0749i | − | 0.362605i | ||||||
\(773\) | 16.6037i | 0.597192i | 0.954380 | + | 0.298596i | \(0.0965184\pi\) | ||||
−0.954380 | + | 0.298596i | \(0.903482\pi\) | |||||||
\(774\) | −26.2277 | −0.942733 | ||||||||
\(775\) | −25.4064 | + | 2.25954i | −0.912625 | + | 0.0811652i | ||||
\(776\) | 9.38176 | 0.336786 | ||||||||
\(777\) | 27.8509i | 0.999145i | ||||||||
\(778\) | 6.16282i | 0.220948i | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −3.15314 | + | 0.139938i | −0.112901 | + | 0.00501057i | ||||
\(781\) | 16.9260 | 0.605661 | ||||||||
\(782\) | − | 22.5824i | − | 0.807546i | ||||||
\(783\) | − | 18.4609i | − | 0.659740i | ||||||
\(784\) | 20.1173 | 0.718475 | ||||||||
\(785\) | 0.599070 | + | 13.4985i | 0.0213817 | + | 0.481783i | ||||
\(786\) | −7.45596 | −0.265945 | ||||||||
\(787\) | − | 41.3474i | − | 1.47388i | −0.675960 | − | 0.736938i | \(-0.736271\pi\) | ||
0.675960 | − | 0.736938i | \(-0.263729\pi\) | |||||||
\(788\) | 13.1861i | 0.469735i | ||||||||
\(789\) | 0.441762 | 0.0157271 | ||||||||
\(790\) | −0.167637 | − | 3.77729i | −0.00596427 | − | 0.134390i | ||||
\(791\) | −76.1514 | −2.70763 | ||||||||
\(792\) | 8.91853i | 0.316906i | ||||||||
\(793\) | − | 22.1252i | − | 0.785690i | ||||||
\(794\) | −28.0267 | −0.994631 | ||||||||
\(795\) | 5.98814 | − | 0.265756i | 0.212378 | − | 0.00942540i | ||||
\(796\) | 2.74982 | 0.0974648 | ||||||||
\(797\) | − | 22.7002i | − | 0.804083i | −0.915621 | − | 0.402042i | \(-0.868301\pi\) | ||
0.915621 | − | 0.402042i | \(-0.131699\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −21.9608 | −0.776916 | ||||||||
\(800\) | −1.23837 | − | 13.9243i | −0.0437829 | − | 0.492297i | ||||
\(801\) | 6.34913 | 0.224335 | ||||||||
\(802\) | − | 27.8093i | − | 0.981980i | ||||||
\(803\) | 13.6881i | 0.483044i | ||||||||
\(804\) | 0.412889 | 0.0145615 | ||||||||
\(805\) | −52.0743 | + | 2.31108i | −1.83538 | + | 0.0814547i | ||||
\(806\) | 21.5367 | 0.758599 | ||||||||
\(807\) | 17.6385i | 0.620905i | ||||||||
\(808\) | − | 11.4175i | − | 0.401665i | ||||||
\(809\) | 27.1508 | 0.954571 | 0.477285 | − | 0.878748i | \(-0.341621\pi\) | ||||
0.477285 | + | 0.878748i | \(0.341621\pi\) | |||||||
\(810\) | 0.435371 | + | 9.80998i | 0.0152974 | + | 0.344688i | ||||
\(811\) | 45.2598 | 1.58929 | 0.794644 | − | 0.607076i | \(-0.207658\pi\) | ||||
0.794644 | + | 0.607076i | \(0.207658\pi\) | |||||||
\(812\) | 8.25385i | 0.289653i | ||||||||
\(813\) | − | 4.25167i | − | 0.149113i | ||||||
\(814\) | −13.8013 | −0.483734 | ||||||||
\(815\) | 0.971302 | + | 21.8858i | 0.0340232 | + | 0.766627i | ||||
\(816\) | −6.59563 | −0.230893 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | − | 29.0771i | − | 1.01666i | ||||||
\(819\) | −30.8334 | −1.07741 | ||||||||
\(820\) | 6.04552 | − | 0.268302i | 0.211119 | − | 0.00936952i | ||||
\(821\) | 14.7796 | 0.515813 | 0.257907 | − | 0.966170i | \(-0.416967\pi\) | ||||
0.257907 | + | 0.966170i | \(0.416967\pi\) | |||||||
\(822\) | 3.62244i | 0.126347i | ||||||||
\(823\) | 38.1769i | 1.33076i | 0.746504 | + | 0.665381i | \(0.231731\pi\) | ||||
−0.746504 | + | 0.665381i | \(0.768269\pi\) | |||||||
\(824\) | −40.4634 | −1.40961 | ||||||||
\(825\) | −0.440863 | − | 4.95708i | −0.0153489 | − | 0.172584i | ||||
\(826\) | 3.78582 | 0.131726 | ||||||||
\(827\) | 45.3277i | 1.57620i | 0.615548 | + | 0.788099i | \(0.288935\pi\) | ||||
−0.615548 | + | 0.788099i | \(0.711065\pi\) | |||||||
\(828\) | 7.34439i | 0.255235i | ||||||||
\(829\) | 37.9276 | 1.31728 | 0.658640 | − | 0.752458i | \(-0.271132\pi\) | ||||
0.658640 | + | 0.752458i | \(0.271132\pi\) | |||||||
\(830\) | 6.87816 | − | 0.305255i | 0.238744 | − | 0.0105956i | ||||
\(831\) | −14.0284 | −0.486638 | ||||||||
\(832\) | 30.6507i | 1.06262i | ||||||||
\(833\) | 22.1845i | 0.768648i | ||||||||
\(834\) | 18.3044 | 0.633831 | ||||||||
\(835\) | −0.384298 | − | 8.65919i | −0.0132992 | − | 0.299664i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 21.9663i | − | 0.759267i | ||||||
\(838\) | − | 19.4689i | − | 0.672542i | ||||||
\(839\) | −7.14266 | −0.246592 | −0.123296 | − | 0.992370i | \(-0.539346\pi\) | ||||
−0.123296 | + | 0.992370i | \(0.539346\pi\) | |||||||
\(840\) | 0.926364 | + | 20.8733i | 0.0319626 | + | 0.720196i | ||||
\(841\) | −10.6193 | −0.366184 | ||||||||
\(842\) | − | 3.24153i | − | 0.111710i | ||||||
\(843\) | 18.6498i | 0.642332i | ||||||||
\(844\) | 10.2153 | 0.351627 | ||||||||
\(845\) | −2.35936 | + | 0.104709i | −0.0811645 | + | 0.00360211i | ||||
\(846\) | −20.9918 | −0.721713 | ||||||||
\(847\) | 35.9046i | 1.23370i | ||||||||
\(848\) | − | 9.08652i | − | 0.312032i | ||||||
\(849\) | 3.69541 | 0.126826 | ||||||||
\(850\) | −18.2941 | + | 1.62700i | −0.627481 | + | 0.0558056i | ||||
\(851\) | −56.1346 | −1.92427 | ||||||||
\(852\) | − | 5.58709i | − | 0.191410i | ||||||
\(853\) | 51.0391i | 1.74755i | 0.486335 | + | 0.873773i | \(0.338334\pi\) | ||||
−0.486335 | + | 0.873773i | \(0.661666\pi\) | |||||||
\(854\) | −29.6542 | −1.01474 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 15.7246 | 0.537456 | ||||||||
\(857\) | − | 13.6042i | − | 0.464710i | −0.972631 | − | 0.232355i | \(-0.925357\pi\) | ||
0.972631 | − | 0.232355i | \(-0.0746431\pi\) | |||||||
\(858\) | 4.20207i | 0.143456i | ||||||||
\(859\) | 38.4375 | 1.31147 | 0.655735 | − | 0.754991i | \(-0.272359\pi\) | ||||
0.655735 | + | 0.754991i | \(0.272359\pi\) | |||||||
\(860\) | 0.459315 | + | 10.3495i | 0.0156625 | + | 0.352915i | ||||
\(861\) | −16.2582 | −0.554079 | ||||||||
\(862\) | 40.7059i | 1.38645i | ||||||||
\(863\) | 54.3455i | 1.84994i | 0.380039 | + | 0.924970i | \(0.375910\pi\) | ||||
−0.380039 | + | 0.924970i | \(0.624090\pi\) | |||||||
\(864\) | 12.0389 | 0.409571 | ||||||||
\(865\) | −0.469150 | − | 10.5711i | −0.0159516 | − | 0.359428i | ||||
\(866\) | −27.3391 | −0.929021 | ||||||||
\(867\) | 6.40176i | 0.217415i | ||||||||
\(868\) | 9.82110i | 0.333350i | ||||||||
\(869\) | 1.71270 | 0.0580995 | ||||||||
\(870\) | 9.41121 | − | 0.417673i | 0.319070 | − | 0.0141604i | ||||
\(871\) | −3.49374 | −0.118381 | ||||||||
\(872\) | 4.86398i | 0.164715i | ||||||||
\(873\) | 7.20584i | 0.243881i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.62400 | + | 42.0189i | 0.190126 | + | 1.42050i | ||||
\(876\) | 4.51830 | 0.152659 | ||||||||
\(877\) | 13.5325i | 0.456961i | 0.973548 | + | 0.228481i | \(0.0733758\pi\) | ||||
−0.973548 | + | 0.228481i | \(0.926624\pi\) | |||||||
\(878\) | 21.3241i | 0.719653i | ||||||||
\(879\) | 14.5862 | 0.491982 | ||||||||
\(880\) | −7.53682 | + | 0.334487i | −0.254066 | + | 0.0112756i | ||||
\(881\) | −27.9577 | −0.941920 | −0.470960 | − | 0.882155i | \(-0.656092\pi\) | ||||
−0.470960 | + | 0.882155i | \(0.656092\pi\) | |||||||
\(882\) | 21.2057i | 0.714032i | ||||||||
\(883\) | 54.5487i | 1.83571i | 0.396915 | + | 0.917855i | \(0.370081\pi\) | ||||
−0.396915 | + | 0.917855i | \(0.629919\pi\) | |||||||
\(884\) | −5.27630 | −0.177461 | ||||||||
\(885\) | 0.0651813 | + | 1.46870i | 0.00219105 | + | 0.0493697i | ||||
\(886\) | 1.83066 | 0.0615021 | ||||||||
\(887\) | − | 35.9778i | − | 1.20802i | −0.796979 | − | 0.604008i | \(-0.793570\pi\) | ||
0.796979 | − | 0.604008i | \(-0.206430\pi\) | |||||||
\(888\) | 22.5008i | 0.755078i | ||||||||
\(889\) | 13.0932 | 0.439133 | ||||||||
\(890\) | 0.326800 | + | 7.36361i | 0.0109544 | + | 0.246829i | ||||
\(891\) | −4.44806 | −0.149016 | ||||||||
\(892\) | 5.50867i | 0.184444i | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −1.65860 | −0.0554717 | ||||||||
\(895\) | 20.9496 | − | 0.929749i | 0.700266 | − | 0.0310781i | ||||
\(896\) | 19.8782 | 0.664083 | ||||||||
\(897\) | 17.0913i | 0.570662i | ||||||||
\(898\) | − | 14.6482i | − | 0.488817i | ||||||
\(899\) | 21.8708 | 0.729432 | ||||||||
\(900\) | 5.94970 | − | 0.529142i | 0.198323 | − | 0.0176381i | ||||
\(901\) | 10.0202 | 0.333822 | ||||||||
\(902\) | − | 8.05662i | − | 0.268256i | ||||||
\(903\) | − | 27.8329i | − | 0.926222i | ||||||
\(904\) | −61.5230 | −2.04622 | ||||||||
\(905\) | −43.5622 | + | 1.93331i | −1.44806 | + | 0.0642653i | ||||
\(906\) | −1.31570 | −0.0437110 | ||||||||
\(907\) | − | 4.40371i | − | 0.146223i | −0.997324 | − | 0.0731114i | \(-0.976707\pi\) | ||
0.997324 | − | 0.0731114i | \(-0.0232929\pi\) | |||||||
\(908\) | 4.45900i | 0.147977i | ||||||||
\(909\) | 8.76941 | 0.290863 | ||||||||
\(910\) | −1.58705 | − | 35.7601i | −0.0526101 | − | 1.18544i | ||||
\(911\) | 14.2563 | 0.472333 | 0.236166 | − | 0.971713i | \(-0.424109\pi\) | ||||
0.236166 | + | 0.971713i | \(0.424109\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.11870i | 0.103214i | ||||||||
\(914\) | 15.8162 | 0.523152 | ||||||||
\(915\) | −0.510562 | − | 11.5042i | −0.0168787 | − | 0.380318i | ||||
\(916\) | −9.18093 | −0.303347 | ||||||||
\(917\) | 28.7701i | 0.950073i | ||||||||
\(918\) | − | 15.8170i | − | 0.522038i | ||||||
\(919\) | 28.7276 | 0.947637 | 0.473819 | − | 0.880622i | \(-0.342875\pi\) | ||||
0.473819 | + | 0.880622i | \(0.342875\pi\) | |||||||
\(920\) | −42.0709 | + | 1.86712i | −1.38704 | + | 0.0615573i | ||||
\(921\) | 3.55077 | 0.117002 | ||||||||
\(922\) | − | 16.9410i | − | 0.557922i | ||||||
\(923\) | 47.2762i | 1.55612i | ||||||||
\(924\) | −1.91621 | −0.0630387 | ||||||||
\(925\) | 4.04433 | + | 45.4747i | 0.132977 | + | 1.49520i | ||||
\(926\) | −5.11201 | −0.167991 | ||||||||
\(927\) | − | 31.0787i | − | 1.02076i | ||||||
\(928\) | 11.9865i | 0.393477i | ||||||||
\(929\) | 30.6928 | 1.00700 | 0.503499 | − | 0.863996i | \(-0.332046\pi\) | ||||
0.503499 | + | 0.863996i | \(0.332046\pi\) | |||||||
\(930\) | 11.1982 | − | 0.496981i | 0.367204 | − | 0.0162967i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 13.3866i | 0.438494i | ||||||||
\(933\) | 12.0935i | 0.395923i | ||||||||
\(934\) | −28.4652 | −0.931411 | ||||||||
\(935\) | −0.368858 | − | 8.31129i | −0.0120630 | − | 0.271808i | ||||
\(936\) | −24.9104 | −0.814222 | ||||||||
\(937\) | 50.4315i | 1.64752i | 0.566936 | + | 0.823762i | \(0.308129\pi\) | ||||
−0.566936 | + | 0.823762i | \(0.691871\pi\) | |||||||
\(938\) | 4.68261i | 0.152893i | ||||||||
\(939\) | 6.27890 | 0.204904 | ||||||||
\(940\) | 0.367621 | + | 8.28341i | 0.0119905 | + | 0.270175i | ||||
\(941\) | −8.54594 | −0.278590 | −0.139295 | − | 0.990251i | \(-0.544484\pi\) | ||||
−0.139295 | + | 0.990251i | \(0.544484\pi\) | |||||||
\(942\) | − | 5.93795i | − | 0.193469i | ||||||
\(943\) | − | 32.7691i | − | 1.06711i | ||||||
\(944\) | 2.22863 | 0.0725357 | ||||||||
\(945\) | −36.4734 | + | 1.61870i | −1.18648 | + | 0.0526564i | ||||
\(946\) | 13.7924 | 0.448428 | ||||||||
\(947\) | − | 20.5825i | − | 0.668841i | −0.942424 | − | 0.334421i | \(-0.891459\pi\) | ||
0.942424 | − | 0.334421i | \(-0.108541\pi\) | |||||||
\(948\) | − | 0.565344i | − | 0.0183615i | ||||||
\(949\) | −38.2325 | −1.24108 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 21.9051 | 0.710323 | ||||||||
\(952\) | 34.9282i | 1.13203i | ||||||||
\(953\) | − | 59.1921i | − | 1.91742i | −0.284384 | − | 0.958711i | \(-0.591789\pi\) | ||
0.284384 | − | 0.958711i | \(-0.408211\pi\) | |||||||
\(954\) | 9.57812 | 0.310103 | ||||||||
\(955\) | −34.6303 | + | 1.53691i | −1.12061 | + | 0.0497331i | ||||
\(956\) | 4.65534 | 0.150564 | ||||||||
\(957\) | 4.26725i | 0.137940i | ||||||||
\(958\) | 42.8984i | 1.38599i | ||||||||
\(959\) | 13.9778 | 0.451367 | ||||||||
\(960\) | 0.707295 | + | 15.9371i | 0.0228278 | + | 0.514368i | ||||
\(961\) | −4.97635 | −0.160528 | ||||||||
\(962\) | − | 38.5484i | − | 1.24285i | ||||||
\(963\) | 12.0776i | 0.389195i | ||||||||
\(964\) | −13.4633 | −0.433623 | ||||||||
\(965\) | 1.96725 | + | 44.3271i | 0.0633281 | + | 1.42694i | ||||
\(966\) | 22.9072 | 0.737028 | ||||||||
\(967\) | − | 10.9970i | − | 0.353639i | −0.984243 | − | 0.176819i | \(-0.943419\pi\) | ||
0.984243 | − | 0.176819i | \(-0.0565808\pi\) | |||||||
\(968\) | 29.0075i | 0.932335i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −8.35722 | + | 0.370897i | −0.268334 | + | 0.0119088i | ||||
\(971\) | −32.3692 | −1.03878 | −0.519389 | − | 0.854538i | \(-0.673840\pi\) | ||||
−0.519389 | + | 0.854538i | \(0.673840\pi\) | |||||||
\(972\) | 8.02706i | 0.257468i | ||||||||
\(973\) | − | 70.6309i | − | 2.26432i | ||||||
\(974\) | −40.8265 | −1.30817 | ||||||||
\(975\) | 13.8457 | − | 1.23138i | 0.443416 | − | 0.0394357i | ||||
\(976\) | −17.4567 | −0.558776 | ||||||||
\(977\) | − | 11.1038i | − | 0.355241i | −0.984099 | − | 0.177621i | \(-0.943160\pi\) | ||
0.984099 | − | 0.177621i | \(-0.0568400\pi\) | |||||||
\(978\) | − | 9.62748i | − | 0.307853i | ||||||
\(979\) | −3.33882 | −0.106709 | ||||||||
\(980\) | 8.36781 | − | 0.371367i | 0.267300 | − | 0.0118629i | ||||
\(981\) | −3.73588 | −0.119277 | ||||||||
\(982\) | 21.4250i | 0.683701i | ||||||||
\(983\) | − | 12.5322i | − | 0.399716i | −0.979825 | − | 0.199858i | \(-0.935952\pi\) | ||
0.979825 | − | 0.199858i | \(-0.0640481\pi\) | |||||||
\(984\) | −13.1351 | −0.418731 | ||||||||
\(985\) | −2.57474 | − | 58.0153i | −0.0820380 | − | 1.84852i | ||||
\(986\) | 15.7482 | 0.501525 | ||||||||
\(987\) | − | 22.2766i | − | 0.709072i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 56.0984 | 1.78383 | ||||||||
\(990\) | −0.352583 | − | 7.94457i | −0.0112058 | − | 0.252495i | ||||
\(991\) | −36.7597 | −1.16771 | −0.583856 | − | 0.811857i | \(-0.698457\pi\) | ||||
−0.583856 | + | 0.811857i | \(0.698457\pi\) | |||||||
\(992\) | 14.2625i | 0.452836i | ||||||||
\(993\) | 9.63695i | 0.305819i | ||||||||
\(994\) | 63.3637 | 2.00977 | ||||||||
\(995\) | −12.0985 | + | 0.536936i | −0.383548 | + | 0.0170220i | ||||
\(996\) | 1.02945 | 0.0326193 | ||||||||
\(997\) | − | 24.4801i | − | 0.775291i | −0.921808 | − | 0.387646i | \(-0.873288\pi\) | ||
0.921808 | − | 0.387646i | \(-0.126712\pi\) | |||||||
\(998\) | 39.9251i | 1.26381i | ||||||||
\(999\) | −39.3173 | −1.24394 |
(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.l.1084.8 | 24 | ||
5.2 | odd | 4 | 9025.2.a.ct.1.17 | 24 | |||
5.3 | odd | 4 | 9025.2.a.ct.1.8 | 24 | |||
5.4 | even | 2 | inner | 1805.2.b.l.1084.17 | 24 | ||
19.3 | odd | 18 | 95.2.p.a.9.3 | ✓ | 48 | ||
19.13 | odd | 18 | 95.2.p.a.74.6 | yes | 48 | ||
19.18 | odd | 2 | 1805.2.b.k.1084.17 | 24 | |||
57.32 | even | 18 | 855.2.da.b.739.3 | 48 | |||
57.41 | even | 18 | 855.2.da.b.199.6 | 48 | |||
95.3 | even | 36 | 475.2.l.f.351.6 | 48 | |||
95.13 | even | 36 | 475.2.l.f.226.6 | 48 | |||
95.18 | even | 4 | 9025.2.a.cu.1.17 | 24 | |||
95.22 | even | 36 | 475.2.l.f.351.3 | 48 | |||
95.32 | even | 36 | 475.2.l.f.226.3 | 48 | |||
95.37 | even | 4 | 9025.2.a.cu.1.8 | 24 | |||
95.79 | odd | 18 | 95.2.p.a.9.6 | yes | 48 | ||
95.89 | odd | 18 | 95.2.p.a.74.3 | yes | 48 | ||
95.94 | odd | 2 | 1805.2.b.k.1084.8 | 24 | |||
285.89 | even | 18 | 855.2.da.b.739.6 | 48 | |||
285.269 | even | 18 | 855.2.da.b.199.3 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.p.a.9.3 | ✓ | 48 | 19.3 | odd | 18 | ||
95.2.p.a.9.6 | yes | 48 | 95.79 | odd | 18 | ||
95.2.p.a.74.3 | yes | 48 | 95.89 | odd | 18 | ||
95.2.p.a.74.6 | yes | 48 | 19.13 | odd | 18 | ||
475.2.l.f.226.3 | 48 | 95.32 | even | 36 | |||
475.2.l.f.226.6 | 48 | 95.13 | even | 36 | |||
475.2.l.f.351.3 | 48 | 95.22 | even | 36 | |||
475.2.l.f.351.6 | 48 | 95.3 | even | 36 | |||
855.2.da.b.199.3 | 48 | 285.269 | even | 18 | |||
855.2.da.b.199.6 | 48 | 57.41 | even | 18 | |||
855.2.da.b.739.3 | 48 | 57.32 | even | 18 | |||
855.2.da.b.739.6 | 48 | 285.89 | even | 18 | |||
1805.2.b.k.1084.8 | 24 | 95.94 | odd | 2 | |||
1805.2.b.k.1084.17 | 24 | 19.18 | odd | 2 | |||
1805.2.b.l.1084.8 | 24 | 1.1 | even | 1 | trivial | ||
1805.2.b.l.1084.17 | 24 | 5.4 | even | 2 | inner | ||
9025.2.a.ct.1.8 | 24 | 5.3 | odd | 4 | |||
9025.2.a.ct.1.17 | 24 | 5.2 | odd | 4 | |||
9025.2.a.cu.1.8 | 24 | 95.37 | even | 4 | |||
9025.2.a.cu.1.17 | 24 | 95.18 | even | 4 |