Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4020,2,Mod(1609,4020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4020, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("4020.1609");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4020.g (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: | \(32.0998616126\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1609.6 | ||
Character | \(\chi\) | \(=\) | 4020.1609 |
Dual form | 4020.2.g.b.1609.18 |
$q$-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 \(\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times\).
\(n\) | \(1141\) | \(2011\) | \(2681\) | \(3217\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.880059 | − | 2.05560i | −0.393574 | − | 0.919293i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.30492i | 0.493213i | 0.969116 | + | 0.246607i | \(0.0793156\pi\) | ||||
−0.969116 | + | 0.246607i | \(0.920684\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.23619 | −0.372724 | −0.186362 | − | 0.982481i | \(-0.559670\pi\) | ||||
−0.186362 | + | 0.982481i | \(0.559670\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.57434i | − | 0.436642i | −0.975877 | − | 0.218321i | \(-0.929942\pi\) | ||
0.975877 | − | 0.218321i | \(-0.0700581\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.05560 | + | 0.880059i | −0.530754 | + | 0.227230i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.592305i | 0.143655i | 0.997417 | + | 0.0718275i | \(0.0228831\pi\) | ||||
−0.997417 | + | 0.0718275i | \(0.977117\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.53506 | 1.72866 | 0.864330 | − | 0.502924i | \(-0.167743\pi\) | ||||
0.864330 | + | 0.502924i | \(0.167743\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.30492 | 0.284757 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.48217i | 1.35163i | 0.737073 | + | 0.675813i | \(0.236207\pi\) | ||||
−0.737073 | + | 0.675813i | \(0.763793\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.45099 | + | 3.61810i | −0.690198 | + | 0.723620i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.11017 | 0.391849 | 0.195925 | − | 0.980619i | \(-0.437229\pi\) | ||||
0.195925 | + | 0.980619i | \(0.437229\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.06929 | 1.26968 | 0.634841 | − | 0.772643i | \(-0.281066\pi\) | ||||
0.634841 | + | 0.772643i | \(0.281066\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.23619i | 0.215192i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.68239 | − | 1.14841i | 0.453407 | − | 0.194116i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 0.162812i | − | 0.0267661i | −0.999910 | − | 0.0133830i | \(-0.995740\pi\) | ||
0.999910 | − | 0.0133830i | \(-0.00426008\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.57434 | −0.252096 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.68393 | 0.575334 | 0.287667 | − | 0.957731i | \(-0.407120\pi\) | ||||
0.287667 | + | 0.957731i | \(0.407120\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.0937305i | 0.0142938i | 0.999974 | + | 0.00714689i | \(0.00227494\pi\) | ||||
−0.999974 | + | 0.00714689i | \(0.997725\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.880059 | + | 2.05560i | 0.131191 | + | 0.306431i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 3.86807i | − | 0.564216i | −0.959383 | − | 0.282108i | \(-0.908966\pi\) | ||
0.959383 | − | 0.282108i | \(-0.0910337\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.29719 | 0.756741 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.592305 | 0.0829393 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 1.93402i | − | 0.265658i | −0.991139 | − | 0.132829i | \(-0.957594\pi\) | ||
0.991139 | − | 0.132829i | \(-0.0424061\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.08792 | + | 2.54111i | 0.146695 | + | 0.342643i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 7.53506i | − | 0.998043i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.34961 | −0.696460 | −0.348230 | − | 0.937409i | \(-0.613217\pi\) | ||||
−0.348230 | + | 0.937409i | \(0.613217\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.11784 | 0.271162 | 0.135581 | − | 0.990766i | \(-0.456710\pi\) | ||||
0.135581 | + | 0.990766i | \(0.456710\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 1.30492i | − | 0.164404i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.23621 | + | 1.38551i | −0.401402 | + | 0.171851i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.00000i | 0.122169i | ||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.48217 | 0.780361 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.62485 | 0.430191 | 0.215095 | − | 0.976593i | \(-0.430994\pi\) | ||||
0.215095 | + | 0.976593i | \(0.430994\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 11.0312i | − | 1.29110i | −0.763717 | − | 0.645551i | \(-0.776628\pi\) | ||
0.763717 | − | 0.645551i | \(-0.223372\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.61810 | + | 3.45099i | 0.417782 | + | 0.398486i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 1.61312i | − | 0.183832i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.58300 | 0.853155 | 0.426577 | − | 0.904451i | \(-0.359719\pi\) | ||||
0.426577 | + | 0.904451i | \(0.359719\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 5.94852i | − | 0.652935i | −0.945208 | − | 0.326467i | \(-0.894142\pi\) | ||
0.945208 | − | 0.326467i | \(-0.105858\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.21754 | − | 0.521263i | 0.132061 | − | 0.0565390i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 2.11017i | − | 0.226234i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.8934 | −1.26070 | −0.630350 | − | 0.776311i | \(-0.717089\pi\) | ||||
−0.630350 | + | 0.776311i | \(0.717089\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.05438 | 0.215358 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 7.06929i | − | 0.733051i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.63130 | − | 15.4891i | −0.680357 | − | 1.58915i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 18.6958i | − | 1.89827i | −0.314874 | − | 0.949133i | \(-0.601962\pi\) | ||
0.314874 | − | 0.949133i | \(-0.398038\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.23619 | 0.124241 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.56043 | −0.553284 | −0.276642 | − | 0.960973i | \(-0.589222\pi\) | ||||
−0.276642 | + | 0.960973i | \(0.589222\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.21921i | 0.218665i | 0.994005 | + | 0.109333i | \(0.0348714\pi\) | ||||
−0.994005 | + | 0.109333i | \(0.965129\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.14841 | − | 2.68239i | −0.112073 | − | 0.261775i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.31490i | 0.513810i | 0.966437 | + | 0.256905i | \(0.0827028\pi\) | ||||
−0.966437 | + | 0.256905i | \(0.917297\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.24639 | 0.215165 | 0.107582 | − | 0.994196i | \(-0.465689\pi\) | ||||
0.107582 | + | 0.994196i | \(0.465689\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.162812 | −0.0154534 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 20.7190i | 1.94908i | 0.224223 | + | 0.974538i | \(0.428016\pi\) | ||||
−0.224223 | + | 0.974538i | \(0.571984\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 13.3248 | − | 5.70469i | 1.24254 | − | 0.531965i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.57434i | 0.145547i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.772910 | −0.0708526 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.47184 | −0.861077 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 3.68393i | − | 0.332169i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.4745 | + | 3.90972i | 0.936863 | + | 0.349696i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 16.1439i | − | 1.43254i | −0.697822 | − | 0.716271i | \(-0.745847\pi\) | ||
0.697822 | − | 0.716271i | \(-0.254153\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.0937305 | 0.00825251 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 19.2491 | 1.68180 | 0.840900 | − | 0.541191i | \(-0.182026\pi\) | ||||
0.840900 | + | 0.541191i | \(0.182026\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.83264i | 0.852598i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.05560 | − | 0.880059i | 0.176918 | − | 0.0757434i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 3.27970i | − | 0.280204i | −0.990137 | − | 0.140102i | \(-0.955257\pi\) | ||
0.990137 | − | 0.140102i | \(-0.0447430\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.38014 | 0.710794 | 0.355397 | − | 0.934715i | \(-0.384346\pi\) | ||||
0.355397 | + | 0.934715i | \(0.384346\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.86807 | −0.325750 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.94617i | 0.162747i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.85708 | − | 4.33767i | −0.154222 | − | 0.360224i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 5.29719i | − | 0.436904i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.27506 | 0.186380 | 0.0931901 | − | 0.995648i | \(-0.470294\pi\) | ||||
0.0931901 | + | 0.995648i | \(0.470294\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.289865 | −0.0235888 | −0.0117944 | − | 0.999930i | \(-0.503754\pi\) | ||||
−0.0117944 | + | 0.999930i | \(0.503754\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 0.592305i | − | 0.0478850i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.22139 | − | 14.5316i | −0.499714 | − | 1.16721i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 11.7437i | − | 0.937247i | −0.883398 | − | 0.468623i | \(-0.844750\pi\) | ||
0.883398 | − | 0.468623i | \(-0.155250\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.93402 | −0.153378 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.45871 | −0.666640 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.452956i | 0.0354783i | 0.999843 | + | 0.0177391i | \(0.00564684\pi\) | ||||
−0.999843 | + | 0.0177391i | \(0.994353\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.54111 | − | 1.08792i | 0.197825 | − | 0.0846942i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 8.10079i | − | 0.626858i | −0.949612 | − | 0.313429i | \(-0.898522\pi\) | ||
0.949612 | − | 0.313429i | \(-0.101478\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.5215 | 0.809343 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.53506 | −0.576220 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 4.88616i | − | 0.371488i | −0.982598 | − | 0.185744i | \(-0.940530\pi\) | ||
0.982598 | − | 0.185744i | \(-0.0594695\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.72133 | − | 4.50327i | −0.356899 | − | 0.340415i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.34961i | 0.402101i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.5004 | 0.934325 | 0.467162 | − | 0.884172i | \(-0.345276\pi\) | ||||
0.467162 | + | 0.884172i | \(0.345276\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.49590 | 0.557166 | 0.278583 | − | 0.960412i | \(-0.410135\pi\) | ||||
0.278583 | + | 0.960412i | \(0.410135\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 2.11784i | − | 0.156555i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.334676 | + | 0.143284i | −0.0246059 | + | 0.0105344i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 0.732199i | − | 0.0535437i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.30492 | −0.0949189 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −22.1237 | −1.60081 | −0.800406 | − | 0.599458i | \(-0.795383\pi\) | ||||
−0.800406 | + | 0.599458i | \(0.795383\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.6187i | 1.05227i | 0.850400 | + | 0.526137i | \(0.176360\pi\) | ||||
−0.850400 | + | 0.526137i | \(0.823640\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.38551 | + | 3.23621i | 0.0992184 | + | 0.231750i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.6226i | 0.899326i | 0.893198 | + | 0.449663i | \(0.148456\pi\) | ||||
−0.893198 | + | 0.449663i | \(0.851544\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.02683 | −0.427231 | −0.213615 | − | 0.976918i | \(-0.568524\pi\) | ||||
−0.213615 | + | 0.976918i | \(0.568524\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.00000 | 0.0705346 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.75361i | 0.193265i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.24208 | − | 7.57270i | −0.226437 | − | 0.528900i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 6.48217i | − | 0.450542i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9.31474 | −0.644314 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.4818 | 0.721599 | 0.360800 | − | 0.932643i | \(-0.382504\pi\) | ||||
0.360800 | + | 0.932643i | \(0.382504\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 3.62485i | − | 0.248371i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.192673 | − | 0.0824884i | 0.0131402 | − | 0.00562566i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.22485i | 0.626224i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −11.0312 | −0.745419 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.932487 | 0.0627259 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 12.2257i | − | 0.818693i | −0.912379 | − | 0.409346i | \(-0.865757\pi\) | ||
0.912379 | − | 0.409346i | \(-0.134243\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.45099 | − | 3.61810i | 0.230066 | − | 0.241207i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 1.01465i | − | 0.0673444i | −0.999433 | − | 0.0336722i | \(-0.989280\pi\) | ||
0.999433 | − | 0.0336722i | \(-0.0107202\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 28.3803 | 1.87542 | 0.937712 | − | 0.347412i | \(-0.112940\pi\) | ||||
0.937712 | + | 0.347412i | \(0.112940\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.61312 | −0.106136 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.93103i | 0.454067i | 0.973887 | + | 0.227033i | \(0.0729027\pi\) | ||||
−0.973887 | + | 0.227033i | \(0.927097\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.95121 | + | 3.40413i | −0.518680 | + | 0.222061i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 7.58300i | − | 0.492569i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.71985 | −0.499356 | −0.249678 | − | 0.968329i | \(-0.580325\pi\) | ||||
−0.249678 | + | 0.968329i | \(0.580325\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −29.7181 | −1.91431 | −0.957155 | − | 0.289576i | \(-0.906486\pi\) | ||||
−0.957155 | + | 0.289576i | \(0.906486\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.66184 | − | 10.8889i | −0.297834 | − | 0.695666i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 11.8627i | − | 0.754807i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.94852 | −0.376972 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.6919 | −0.674865 | −0.337432 | − | 0.941350i | \(-0.609558\pi\) | ||||
−0.337432 | + | 0.941350i | \(0.609558\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 8.01317i | − | 0.503784i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.521263 | − | 1.21754i | −0.0326428 | − | 0.0762455i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 25.4556i | − | 1.58788i | −0.607998 | − | 0.793939i | \(-0.708027\pi\) | ||
0.607998 | − | 0.793939i | \(-0.291973\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.212456 | 0.0132014 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.11017 | −0.130616 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 28.9432i | − | 1.78472i | −0.451328 | − | 0.892358i | \(-0.649049\pi\) | ||
0.451328 | − | 0.892358i | \(-0.350951\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.97557 | + | 1.70205i | −0.244217 | + | 0.104556i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 11.8934i | 0.727866i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 24.4214 | 1.48900 | 0.744499 | − | 0.667623i | \(-0.232688\pi\) | ||||
0.744499 | + | 0.667623i | \(0.232688\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.114801 | 0.00697369 | 0.00348685 | − | 0.999994i | \(-0.498890\pi\) | ||||
0.00348685 | + | 0.999994i | \(0.498890\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 2.05438i | − | 0.124337i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.26607 | − | 4.47265i | 0.257254 | − | 0.269711i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.1579i | 0.670415i | 0.942144 | + | 0.335207i | \(0.108806\pi\) | ||||
−0.942144 | + | 0.335207i | \(0.891194\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.06929 | −0.423227 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −28.9061 | −1.72439 | −0.862196 | − | 0.506576i | \(-0.830911\pi\) | ||||
−0.862196 | + | 0.506576i | \(0.830911\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 6.60958i | − | 0.392899i | −0.980514 | − | 0.196449i | \(-0.937059\pi\) | ||
0.980514 | − | 0.196449i | \(-0.0629412\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −15.4891 | + | 6.63130i | −0.917494 | + | 0.392804i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.80724i | 0.283762i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.6492 | 0.979363 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −18.6958 | −1.09596 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 16.4874i | − | 0.963204i | −0.876390 | − | 0.481602i | \(-0.840055\pi\) | ||
0.876390 | − | 0.481602i | \(-0.159945\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.70797 | + | 10.9967i | 0.274109 | + | 0.640250i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 1.23619i | − | 0.0717308i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 10.2051 | 0.590177 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.122311 | −0.00704988 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.56043i | 0.319438i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.86383 | − | 4.35344i | −0.106722 | − | 0.249277i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 14.7640i | − | 0.842625i | −0.906916 | − | 0.421312i | \(-0.861570\pi\) | ||
0.906916 | − | 0.421312i | \(-0.138430\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.21921 | 0.126247 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 18.9466 | 1.07437 | 0.537183 | − | 0.843466i | \(-0.319489\pi\) | ||||
0.537183 | + | 0.843466i | \(0.319489\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.12572i | 0.176676i | 0.996091 | + | 0.0883381i | \(0.0281556\pi\) | ||||
−0.996091 | + | 0.0883381i | \(0.971844\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.68239 | + | 1.14841i | −0.151136 | + | 0.0647054i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 25.8863i | − | 1.45392i | −0.686681 | − | 0.726959i | \(-0.740933\pi\) | ||
0.686681 | − | 0.726959i | \(-0.259067\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.60857 | −0.146052 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.31490 | 0.296649 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.46305i | 0.248331i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.69611 | + | 5.43302i | 0.315963 | + | 0.301370i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 2.24639i | − | 0.124225i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.04752 | 0.278279 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.97633 | 0.493384 | 0.246692 | − | 0.969094i | \(-0.420656\pi\) | ||||
0.246692 | + | 0.969094i | \(0.420656\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.162812i | 0.00892202i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.05560 | − | 0.880059i | 0.112309 | − | 0.0480828i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.7894i | 1.13247i | 0.824243 | + | 0.566236i | \(0.191601\pi\) | ||||
−0.824243 | + | 0.566236i | \(0.808399\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 20.7190 | 1.12530 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.73895 | −0.473241 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.0468i | 0.866448i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.70469 | − | 13.3248i | −0.307130 | − | 0.717381i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 7.71805i | − | 0.414327i | −0.978306 | − | 0.207163i | \(-0.933577\pi\) | ||
0.978306 | − | 0.207163i | \(-0.0664232\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 26.6170 | 1.42478 | 0.712388 | − | 0.701786i | \(-0.247614\pi\) | ||||
0.712388 | + | 0.701786i | \(0.247614\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.57434 | 0.0840319 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 4.27287i | − | 0.227422i | −0.993514 | − | 0.113711i | \(-0.963726\pi\) | ||
0.993514 | − | 0.113711i | \(-0.0362738\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.19009 | − | 7.45125i | −0.169312 | − | 0.395471i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.772910i | 0.0409067i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −30.2397 | −1.59599 | −0.797994 | − | 0.602665i | \(-0.794106\pi\) | ||||
−0.797994 | + | 0.602665i | \(0.794106\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 37.7771 | 1.98827 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9.47184i | 0.497143i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −22.6757 | + | 9.70810i | −1.18690 | + | 0.508145i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 12.4654i | − | 0.650688i | −0.945596 | − | 0.325344i | \(-0.894520\pi\) | ||
0.945596 | − | 0.325344i | \(-0.105480\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.68393 | −0.191778 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.52374 | 0.131026 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.5777i | 0.547691i | 0.961774 | + | 0.273846i | \(0.0882958\pi\) | ||||
−0.961774 | + | 0.273846i | \(0.911704\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.90972 | − | 10.4745i | 0.201897 | − | 0.540898i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 3.32212i | − | 0.171098i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.74645 | 0.141076 | 0.0705378 | − | 0.997509i | \(-0.477528\pi\) | ||||
0.0705378 | + | 0.997509i | \(0.477528\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −16.1439 | −0.827079 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.90931i | 0.353049i | 0.984296 | + | 0.176525i | \(0.0564855\pi\) | ||||
−0.984296 | + | 0.176525i | \(0.943515\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.31594 | + | 1.41964i | −0.168996 | + | 0.0723518i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 0.0937305i | − | 0.00476459i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.19305 | 0.314000 | 0.157000 | − | 0.987599i | \(-0.449818\pi\) | ||||
0.157000 | + | 0.987599i | \(0.449818\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.83942 | −0.194168 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 19.2491i | − | 0.970987i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.67349 | − | 15.5876i | −0.335780 | − | 0.784299i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.16458i | 0.359580i | 0.983705 | + | 0.179790i | \(0.0575418\pi\) | ||||
−0.983705 | + | 0.179790i | \(0.942458\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 9.83264 | 0.492248 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.8598 | 0.841936 | 0.420968 | − | 0.907076i | \(-0.361690\pi\) | ||||
0.420968 | + | 0.907076i | \(0.361690\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 11.1294i | − | 0.554397i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.880059 | − | 2.05560i | −0.0437305 | − | 0.102144i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.201266i | 0.00997636i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 22.4182 | 1.10851 | 0.554254 | − | 0.832347i | \(-0.313004\pi\) | ||||
0.554254 | + | 0.832347i | \(0.313004\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.27970 | −0.161776 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 6.98081i | − | 0.343503i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.2278 | + | 5.23505i | −0.600238 | + | 0.256979i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 8.38014i | − | 0.410377i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 30.7268 | 1.50110 | 0.750552 | − | 0.660812i | \(-0.229788\pi\) | ||||
0.750552 | + | 0.660812i | \(0.229788\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.28105 | 0.159909 | 0.0799544 | − | 0.996799i | \(-0.474523\pi\) | ||||
0.0799544 | + | 0.996799i | \(0.474523\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.86807i | 0.188072i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.14302 | − | 2.04404i | −0.103952 | − | 0.0991504i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.76361i | 0.133741i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.94617 | 0.0939621 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17.1165 | 0.824471 | 0.412235 | − | 0.911077i | \(-0.364748\pi\) | ||||
0.412235 | + | 0.911077i | \(0.364748\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 31.4276i | 1.51031i | 0.655545 | + | 0.755156i | \(0.272439\pi\) | ||||
−0.655545 | + | 0.755156i | \(0.727561\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.33767 | + | 1.85708i | −0.207976 | + | 0.0890401i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 48.8435i | 2.33650i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.6652 | 0.747658 | 0.373829 | − | 0.927498i | \(-0.378045\pi\) | ||||
0.373829 | + | 0.927498i | \(0.378045\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.29719 | −0.252247 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15.2049i | 0.722404i | 0.932488 | + | 0.361202i | \(0.117634\pi\) | ||||
−0.932488 | + | 0.361202i | \(0.882366\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.4669 | + | 24.4481i | 0.496180 | + | 1.15895i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 2.27506i | − | 0.107607i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −16.5501 | −0.781050 | −0.390525 | − | 0.920592i | \(-0.627706\pi\) | ||||
−0.390525 | + | 0.920592i | \(0.627706\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.55403 | −0.214441 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.289865i | 0.0136190i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.80798 | − | 4.22299i | −0.0847593 | − | 0.197977i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 38.5015i | 1.80103i | 0.434830 | + | 0.900513i | \(0.356808\pi\) | ||||
−0.434830 | + | 0.900513i | \(0.643192\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.592305 | −0.0276464 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.5513 | −0.584570 | −0.292285 | − | 0.956331i | \(-0.594416\pi\) | ||||
−0.292285 | + | 0.956331i | \(0.594416\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 12.1269i | − | 0.563586i | −0.959475 | − | 0.281793i | \(-0.909071\pi\) | ||
0.959475 | − | 0.281793i | \(-0.0909292\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −14.5316 | + | 6.22139i | −0.673888 | + | 0.288510i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.227492i | 0.0105271i | 0.999986 | + | 0.00526353i | \(0.00167544\pi\) | ||||
−0.999986 | + | 0.00526353i | \(0.998325\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.30492 | −0.0602556 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11.7437 | −0.541120 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 0.115868i | − | 0.00532763i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −26.0034 | + | 27.2626i | −1.19312 | + | 1.25089i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.93402i | 0.0885526i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14.1305 | 0.645641 | 0.322820 | − | 0.946460i | \(-0.395369\pi\) | ||||
0.322820 | + | 0.946460i | \(0.395369\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.256320 | −0.0116872 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 8.45871i | 0.384885i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −38.4310 | + | 16.4534i | −1.74506 | + | 0.747109i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 16.9555i | − | 0.768329i | −0.923265 | − | 0.384164i | \(-0.874490\pi\) | ||
0.923265 | − | 0.384164i | \(-0.125510\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.452956 | 0.0204834 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.8656 | 0.670877 | 0.335438 | − | 0.942062i | \(-0.391116\pi\) | ||||
0.335438 | + | 0.942062i | \(0.391116\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.24987i | 0.0562911i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.08792 | − | 2.54111i | −0.0488982 | − | 0.114214i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.73014i | 0.212176i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −34.9128 | −1.56291 | −0.781456 | − | 0.623960i | \(-0.785523\pi\) | ||||
−0.781456 | + | 0.623960i | \(0.785523\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.10079 | −0.361916 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 17.1124i | − | 0.763006i | −0.924368 | − | 0.381503i | \(-0.875407\pi\) | ||
0.924368 | − | 0.381503i | \(-0.124593\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.89351 | + | 11.4300i | 0.217758 | + | 0.508630i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 10.5215i | − | 0.467275i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 34.4109 | 1.52524 | 0.762618 | − | 0.646850i | \(-0.223914\pi\) | ||||
0.762618 | + | 0.646850i | \(0.223914\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.3948 | 0.636789 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.53506i | 0.332681i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.56181 | − | 1.95304i | 0.201017 | − | 0.0860611i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.78166i | 0.210297i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.88616 | −0.214479 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.6956 | 0.556205 | 0.278102 | − | 0.960551i | \(-0.410295\pi\) | ||||
0.278102 | + | 0.960551i | \(0.410295\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19.7757i | 0.864733i | 0.901698 | + | 0.432367i | \(0.142321\pi\) | ||||
−0.901698 | + | 0.432367i | \(0.857679\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.50327 | + | 4.72133i | −0.196539 | + | 0.206056i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.18717i | 0.182396i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.0185 | −0.826892 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.34961 | 0.232153 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 5.79975i | − | 0.251215i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.9253 | − | 4.67742i | 0.472342 | − | 0.202223i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 12.5004i | − | 0.539433i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.54831 | −0.282056 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −26.7233 | −1.14893 | −0.574463 | − | 0.818531i | \(-0.694789\pi\) | ||||
−0.574463 | + | 0.818531i | \(0.694789\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 7.49590i | − | 0.321680i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.97695 | − | 4.61768i | −0.0846834 | − | 0.197799i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 30.0531i | 1.28498i | 0.766295 | + | 0.642489i | \(0.222098\pi\) | ||||
−0.766295 | + | 0.642489i | \(0.777902\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.11784 | −0.0903873 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15.9003 | 0.677375 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.89521i | 0.420787i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.143284 | + | 0.334676i | 0.00608206 | + | 0.0142062i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 30.5660i | 1.29512i | 0.762014 | + | 0.647561i | \(0.224211\pi\) | ||||
−0.762014 | + | 0.647561i | \(0.775789\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.147563 | 0.00624127 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.732199 | −0.0309135 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 13.9746i | − | 0.588959i | −0.955658 | − | 0.294479i | \(-0.904854\pi\) | ||
0.955658 | − | 0.294479i | \(-0.0951462\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 42.5899 | − | 18.2339i | 1.79177 | − | 0.767106i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.30492i | 0.0548015i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −16.3060 | −0.683583 | −0.341791 | − | 0.939776i | \(-0.611034\pi\) | ||||
−0.341791 | + | 0.939776i | \(0.611034\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.9588 | 1.00265 | 0.501323 | − | 0.865260i | \(-0.332847\pi\) | ||||
0.501323 | + | 0.865260i | \(0.332847\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 22.1237i | 0.924229i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −23.4531 | − | 22.3699i | −0.978064 | − | 0.932890i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19.5651i | 0.814507i | 0.913315 | + | 0.407254i | \(0.133514\pi\) | ||||
−0.913315 | + | 0.407254i | \(0.866486\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 14.6187 | 0.607531 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.76234 | 0.322036 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.39081i | 0.0990171i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.23621 | − | 1.38551i | 0.133801 | − | 0.0572838i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 19.9745i | − | 0.824435i | −0.911085 | − | 0.412218i | \(-0.864754\pi\) | ||
0.911085 | − | 0.412218i | \(-0.135246\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 53.2675 | 2.19485 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 12.6226 | 0.519226 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 34.2195i | − | 1.40523i | −0.711572 | − | 0.702613i | \(-0.752016\pi\) | ||
0.711572 | − | 0.702613i | \(-0.247984\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.680207 | + | 1.58879i | 0.0278858 | + | 0.0651342i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.02683i | 0.246662i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.75053 | 0.398396 | 0.199198 | − | 0.979959i | \(-0.436166\pi\) | ||||
0.199198 | + | 0.979959i | \(0.436166\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 28.8348 | 1.17620 | 0.588098 | − | 0.808790i | \(-0.299877\pi\) | ||||
0.588098 | + | 0.808790i | \(0.299877\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 1.00000i | − | 0.0407231i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.33578 | + | 19.4703i | 0.338898 | + | 0.791582i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 32.8932i | − | 1.33509i | −0.744567 | − | 0.667547i | \(-0.767344\pi\) | ||
0.744567 | − | 0.667547i | \(-0.232656\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.75361 | 0.111582 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.08965 | −0.246361 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 32.5057i | 1.31289i | 0.754373 | + | 0.656446i | \(0.227941\pi\) | ||||
−0.754373 | + | 0.656446i | \(0.772059\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7.57270 | + | 3.24208i | −0.305361 | + | 0.130733i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13.6881i | 0.551063i | 0.961292 | + | 0.275531i | \(0.0888538\pi\) | ||||
−0.961292 | + | 0.275531i | \(0.911146\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −27.9120 | −1.12188 | −0.560940 | − | 0.827857i | \(-0.689560\pi\) | ||||
−0.560940 | + | 0.827857i | \(0.689560\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.48217 | −0.260120 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 15.5200i | − | 0.621794i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.18132 | − | 24.9721i | −0.0472527 | − | 0.998883i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 9.31474i | 0.371995i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.0964341 | 0.00384508 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.0300462 | −0.00119612 | −0.000598060 | − | 1.00000i | \(-0.500190\pi\) | ||||
−0.000598060 | 1.00000i | \(0.500190\pi\) | ||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 10.4818i | − | 0.416615i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −33.1855 | + | 14.2076i | −1.31693 | + | 0.563812i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 8.33955i | − | 0.330425i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.62485 | −0.143397 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.76797 | −0.385812 | −0.192906 | − | 0.981217i | \(-0.561791\pi\) | ||||
−0.192906 | + | 0.981217i | \(0.561791\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 23.3098i | − | 0.919250i | −0.888113 | − | 0.459625i | \(-0.847984\pi\) | ||
0.888113 | − | 0.459625i | \(-0.152016\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.0824884 | − | 0.192673i | −0.00324798 | − | 0.00758647i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16.8313i | 0.661705i | 0.943682 | + | 0.330852i | \(0.107336\pi\) | ||||
−0.943682 | + | 0.330852i | \(0.892664\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.61311 | 0.259587 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.22485 | 0.361550 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 12.0118i | 0.470057i | 0.971988 | + | 0.235029i | \(0.0755184\pi\) | ||||
−0.971988 | + | 0.235029i | \(0.924482\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −16.9403 | − | 39.5684i | −0.661913 | − | 1.54607i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11.0312i | 0.430368i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.52770 | 0.0595107 | 0.0297553 | − | 0.999557i | \(-0.490527\pi\) | ||||
0.0297553 | + | 0.999557i | \(0.490527\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −32.5270 | −1.26516 | −0.632578 | − | 0.774497i | \(-0.718003\pi\) | ||||
−0.632578 | + | 0.774497i | \(0.718003\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 0.932487i | − | 0.0362148i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 20.2120 | − | 8.65331i | 0.783788 | − | 0.335561i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 13.6785i | 0.529634i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −12.2257 | −0.472673 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.61805 | −0.101069 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 0.0149889i | − | 0.000577778i | −1.00000 | 0.000288889i | \(-0.999908\pi\) | |||
1.00000 | 0.000288889i | \(-9.19562e-5\pi\) | ||||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.61810 | − | 3.45099i | −0.139261 | − | 0.132829i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 1.93040i | − | 0.0741914i | −0.999312 | − | 0.0370957i | \(-0.988189\pi\) | ||
0.999312 | − | 0.0370957i | \(-0.0118106\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 24.3965 | 0.936250 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.01465 | −0.0388813 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.0554i | 0.461287i | 0.973038 | + | 0.230643i | \(0.0740831\pi\) | ||||
−0.973038 | + | 0.230643i | \(0.925917\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.74176 | + | 2.88633i | −0.257589 | + | 0.110281i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 28.3803i | − | 1.08278i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.04480 | −0.115997 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.226926 | 0.00863269 | 0.00431634 | − | 0.999991i | \(-0.498626\pi\) | ||||
0.00431634 | + | 0.999991i | \(0.498626\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.61312i | 0.0612775i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.37502 | − | 17.2262i | −0.279750 | − | 0.653428i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.18201i | 0.0826496i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.93103 | 0.262156 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17.2451 | −0.651340 | −0.325670 | − | 0.945484i | \(-0.605590\pi\) | ||||
−0.325670 | + | 0.945484i | \(0.605590\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1.22680i | − | 0.0462695i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.40413 | + | 7.95121i | 0.128207 | + | 0.299460i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 7.25592i | − | 0.272887i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.2177 | 0.421289 | 0.210644 | − | 0.977563i | \(-0.432444\pi\) | ||||
0.210644 | + | 0.977563i | \(0.432444\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.58300 | −0.284385 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 45.8243i | 1.71613i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.00056 | − | 1.71275i | 0.149612 | − | 0.0640531i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.71985i | 0.288303i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 41.0928 | 1.53250 | 0.766251 | − | 0.642541i | \(-0.222120\pi\) | ||||
0.766251 | + | 0.642541i | \(0.222120\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.89589 | −0.107849 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 29.7181i | 1.10523i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.28219 | + | 7.63482i | −0.270454 | + | 0.283550i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 27.0300i | 1.00249i | 0.865307 | + | 0.501243i | \(0.167124\pi\) | ||||
−0.865307 | + | 0.501243i | \(0.832876\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.0555170 | −0.00205337 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 44.1973i | 1.63247i | 0.577723 | + | 0.816233i | \(0.303941\pi\) | ||||
−0.577723 | + | 0.816233i | \(0.696059\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −10.8889 | + | 4.66184i | −0.401643 | + | 0.171954i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 1.23619i | − | 0.0455355i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.33310 | −0.269753 | −0.134876 | − | 0.990862i | \(-0.543064\pi\) | ||||
−0.134876 | + | 0.990862i | \(0.543064\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −11.8627 | −0.435788 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 9.52091i | − | 0.349288i | −0.984632 | − | 0.174644i | \(-0.944122\pi\) | ||
0.984632 | − | 0.174644i | \(-0.0558775\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.00219 | − | 4.67661i | −0.0733545 | − | 0.171338i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.94852i | 0.217645i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.93551 | −0.253418 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 28.3616 | 1.03493 | 0.517464 | − | 0.855705i | \(-0.326876\pi\) | ||||
0.517464 | + | 0.855705i | \(0.326876\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 10.6919i | 0.389633i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.255098 | + | 0.595846i | 0.00928397 | + | 0.0216851i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28.3033i | 1.02870i | 0.857580 | + | 0.514350i | \(0.171967\pi\) | ||||
−0.857580 | + | 0.514350i | \(0.828033\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −8.01317 | −0.290860 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.8758 | −0.901747 | −0.450873 | − | 0.892588i | \(-0.648887\pi\) | ||||
−0.450873 | + | 0.892588i | \(0.648887\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.93135i | 0.106122i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.21754 | + | 0.521263i | −0.0440203 | + | 0.0188463i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.42208i | 0.304104i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.54759 | 0.200051 | 0.100026 | − | 0.994985i | \(-0.468108\pi\) | ||||
0.100026 | + | 0.994985i | \(0.468108\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −25.4556 | −0.916762 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 3.11314i | − | 0.111972i | −0.998432 | − | 0.0559858i | \(-0.982170\pi\) | ||
0.998432 | − | 0.0559858i | \(-0.0178302\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −24.3960 | + | 25.5774i | −0.876332 | + | 0.918767i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 0.212456i | − | 0.00762182i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 27.7586 | 0.994557 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.48099 | −0.160343 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.11017i | 0.0754114i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −24.1403 | + | 10.3351i | −0.861604 | + | 0.368876i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 42.4624i | − | 1.51362i | −0.653634 | − | 0.756811i | \(-0.726756\pi\) | ||
0.653634 | − | 0.756811i | \(-0.273244\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −28.9432 | −1.03041 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −27.0366 | −0.961310 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 3.33420i | − | 0.118401i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.70205 | + | 3.97557i | 0.0603655 | + | 0.140999i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 10.5642i | − | 0.374202i | −0.982341 | − | 0.187101i | \(-0.940091\pi\) | ||
0.982341 | − | 0.187101i | \(-0.0599091\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.29108 | 0.0810525 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11.8934 | 0.420234 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 13.6366i | 0.481225i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.44417 | + | 17.3877i | 0.262372 | + | 0.612837i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 24.4214i | − | 0.859673i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −34.5813 | −1.21581 | −0.607906 | − | 0.794009i | \(-0.707990\pi\) | ||||
−0.607906 | + | 0.794009i | \(0.707990\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −48.9854 | −1.72011 | −0.860055 | − | 0.510201i | \(-0.829571\pi\) | ||||
−0.860055 | + | 0.510201i | \(0.829571\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 0.114801i | − | 0.00402626i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.931098 | − | 0.398629i | 0.0326149 | − | 0.0139633i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.706265i | 0.0247091i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.05438 | −0.0717859 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.4895 | −0.540587 | −0.270294 | − | 0.962778i | \(-0.587121\pi\) | ||||
−0.270294 | + | 0.962778i | \(0.587121\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 25.8631i | 0.901532i | 0.892642 | + | 0.450766i | \(0.148849\pi\) | ||||
−0.892642 | + | 0.450766i | \(0.851151\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.47265 | − | 4.26607i | −0.155718 | − | 0.148525i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16.9253i | 0.588550i | 0.955721 | + | 0.294275i | \(0.0950782\pi\) | ||||
−0.955721 | + | 0.294275i | \(0.904922\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13.1239 | −0.455811 | −0.227906 | − | 0.973683i | \(-0.573188\pi\) | ||||
−0.227906 | + | 0.973683i | \(0.573188\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11.1579 | 0.387064 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.13755i | 0.108710i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −16.6520 | + | 7.12917i | −0.576266 | + | 0.246715i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.06929i | 0.244350i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.22286 | 0.214837 | 0.107419 | − | 0.994214i | \(-0.465742\pi\) | ||||
0.107419 | + | 0.994214i | \(0.465742\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.5472 | −0.846454 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 28.9061i | 0.995578i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9.25951 | − | 21.6279i | −0.318537 | − | 0.744023i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 12.3600i | − | 0.424694i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.60958 | −0.226840 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.05537 | 0.0361777 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 13.4403i | − | 0.460186i | −0.973169 | − | 0.230093i | \(-0.926097\pi\) | ||
0.973169 | − | 0.230093i | \(-0.0739030\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.63130 | + | 15.4891i | 0.226786 | + | 0.529715i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 51.3309i | 1.75343i | 0.481011 | + | 0.876715i | \(0.340270\pi\) | ||||
−0.481011 | + | 0.876715i | \(0.659730\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.4338 | 0.390116 | 0.195058 | − | 0.980792i | \(-0.437510\pi\) | ||||
0.195058 | + | 0.980792i | \(0.437510\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.80724 | 0.163830 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 32.8696i | − | 1.11889i | −0.828866 | − | 0.559447i | \(-0.811014\pi\) | ||
0.828866 | − | 0.559447i | \(-0.188986\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10.0440 | + | 4.30011i | −0.341506 | + | 0.146208i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 16.6492i | − | 0.565436i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.37400 | −0.317991 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.57434 | 0.0533444 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 18.6958i | 0.632756i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.10187 | + | 13.6683i | −0.172475 | + | 0.462073i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27.7686i | 0.937678i | 0.883284 | + | 0.468839i | \(0.155328\pi\) | ||||
−0.883284 | + | 0.468839i | \(0.844672\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −16.4874 | −0.556106 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.19038 | 0.107487 | 0.0537434 | − | 0.998555i | \(-0.482885\pi\) | ||||
0.0537434 | + | 0.998555i | \(0.482885\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.0164i | 0.673605i | 0.941575 | + | 0.336802i | \(0.109345\pi\) | ||||
−0.941575 | + | 0.336802i | \(0.890655\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 10.9967 | − | 4.70797i | 0.369649 | − | 0.158257i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 0.490396i | − | 0.0164659i | −0.999966 | − | 0.00823295i | \(-0.997379\pi\) | ||
0.999966 | − | 0.00823295i | \(-0.00262066\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 21.0665 | 0.706549 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.23619 | −0.0414138 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 29.1461i | − | 0.975338i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −11.0011 | − | 25.6959i | −0.367726 | − | 0.858918i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 10.2051i | − | 0.340739i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 14.9174 | 0.497524 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.14553 | 0.0381631 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.122311i | 0.00407025i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6.59683 | − | 15.4086i | −0.219286 | − | 0.512198i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 9.67301i | − | 0.321187i | −0.987021 | − | 0.160593i | \(-0.948659\pi\) | ||
0.987021 | − | 0.160593i | \(-0.0513408\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.56043 | 0.184428 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22.4548 | −0.743962 | −0.371981 | − | 0.928240i | \(-0.621321\pi\) | ||||
−0.371981 | + | 0.928240i | \(0.621321\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.35348i | 0.243365i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4.35344 | + | 1.86383i | −0.143920 | + | 0.0616162i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 25.1185i | 0.829486i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 43.3615 | 1.43037 | 0.715183 | − | 0.698938i | \(-0.246344\pi\) | ||||
0.715183 | + | 0.698938i | \(0.246344\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −14.7640 | −0.486490 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 5.70674i | − | 0.187840i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.589069 | + | 0.561862i | 0.0193685 | + | 0.0184739i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 2.21921i | − | 0.0728885i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 16.1920 | 0.531242 | 0.265621 | − | 0.964078i | \(-0.414423\pi\) | ||||
0.265621 | + | 0.964078i | \(0.414423\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 39.9146 | 1.30815 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 18.9466i | − | 0.620285i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.50511 | + | 0.644379i | −0.0492223 | + | 0.0210734i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 20.9083i | − | 0.683044i | −0.939874 | − | 0.341522i | \(-0.889058\pi\) | ||
0.939874 | − | 0.341522i | \(-0.110942\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.12572 | 0.102004 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.92418 | −0.258321 | −0.129160 | − | 0.991624i | \(-0.541228\pi\) | ||||
−0.129160 | + | 0.991624i | \(0.541228\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 23.8799i | 0.777636i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.14841 | + | 2.68239i | 0.0373577 | + | 0.0872583i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 36.1312i | 1.17411i | 0.809549 | + | 0.587053i | \(0.199712\pi\) | ||||
−0.809549 | + | 0.587053i | \(0.800288\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −17.3668 | −0.563750 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −25.8863 | −0.839420 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 18.0300i | 0.584049i | 0.956411 | + | 0.292025i | \(0.0943289\pi\) | ||||
−0.956411 | + | 0.292025i | \(0.905671\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 19.4701 | + | 45.4774i | 0.630039 | + | 1.47161i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.60857i | 0.0843230i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.27975 | 0.138200 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18.9748 | 0.612090 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 5.31490i | − | 0.171270i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 30.0501 | − | 12.8653i | 0.967348 | − | 0.414148i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 57.0853i | − | 1.83574i | −0.396881 | − | 0.917870i | \(-0.629908\pi\) | ||
0.396881 | − | 0.917870i | \(-0.370092\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.46305 | 0.143374 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −52.7922 | −1.69418 | −0.847091 | − | 0.531448i | \(-0.821648\pi\) | ||||
−0.847091 | + | 0.531448i | \(0.821648\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10.9354i | 0.350573i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.43302 | − | 5.69611i | 0.173996 | − | 0.182422i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 40.3290i | 1.29024i | 0.764082 | + | 0.645119i | \(0.223192\pi\) | ||||
−0.764082 | + | 0.645119i | \(0.776808\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14.7025 | 0.469894 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.24639 | −0.0717216 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 51.8308i | − | 1.65315i | −0.562830 | − | 0.826573i | \(-0.690287\pi\) | ||
0.562830 | − | 0.826573i | \(-0.309713\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 25.9471 | − | 11.1087i | 0.826744 | − | 0.353952i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 5.04752i | − | 0.160664i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.607577 | −0.0193198 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26.5090 | −0.842087 | −0.421044 | − | 0.907040i | \(-0.638336\pi\) | ||||
−0.421044 | + | 0.907040i | \(0.638336\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 8.97633i | − | 0.284855i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.30397 | + | 12.3888i | 0.168147 | + | 0.392750i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 4.65120i | − | 0.147305i | −0.997284 | − | 0.0736525i | \(-0.976534\pi\) | ||
0.997284 | − | 0.0736525i | \(-0.0234656\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.162812 | 0.00515113 |
(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 | 4020.2.g.b.1609.6 | ✓ | 24 | |
5.4 | even | 2 | inner | 4020.2.g.b.1609.18 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4020.2.g.b.1609.6 | ✓ | 24 | 1.1 | even | 1 | trivial | |
4020.2.g.b.1609.18 | yes | 24 | 5.4 | even | 2 | inner |