Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [675,4,Mod(649,675)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(675, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("675.649");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 675 = 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 675.b (of order \(2\), degree \(1\), not 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: | \(39.8262892539\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.2033649216.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 47x^{4} + 541x^{2} + 36 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 135) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 649.5 | ||
Root | \(4.45938i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 675.649 |
Dual form | 675.4.b.l.649.2 |
$q$-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 \(\left(\mathbb{Z}/675\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.45938i | 1.57663i | 0.615272 | + | 0.788315i | \(0.289046\pi\) | ||||
−0.615272 | + | 0.788315i | \(0.710954\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −11.8861 | −1.48576 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.08123i | 0.274361i | 0.990546 | + | 0.137180i | \(0.0438040\pi\) | ||||
−0.990546 | + | 0.137180i | \(0.956196\pi\) | |||||||
\(8\) | − 17.3296i | − 0.765867i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 58.3007 | 1.59803 | 0.799014 | − | 0.601312i | \(-0.205355\pi\) | ||||
0.799014 | + | 0.601312i | \(0.205355\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 21.2119i | − 0.452548i | −0.974064 | − | 0.226274i | \(-0.927345\pi\) | ||||
0.974064 | − | 0.226274i | \(-0.0726545\pi\) | |||||||
\(14\) | −22.6592 | −0.432566 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −17.8095 | −0.278274 | ||||||||
\(17\) | − 68.8451i | − 0.982199i | −0.871104 | − | 0.491099i | \(-0.836595\pi\) | ||||
0.871104 | − | 0.491099i | \(-0.163405\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 40.8133 | 0.492800 | 0.246400 | − | 0.969168i | \(-0.420752\pi\) | ||||
0.246400 | + | 0.969168i | \(0.420752\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 259.985i | 2.51950i | ||||||||
\(23\) | 144.318i | 1.30837i | 0.756336 | + | 0.654184i | \(0.226988\pi\) | ||||
−0.756336 | + | 0.654184i | \(0.773012\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 94.5921 | 0.713501 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − 60.3960i | − 0.407635i | ||||||||
\(29\) | 220.058 | 1.40909 | 0.704547 | − | 0.709657i | \(-0.251150\pi\) | ||||
0.704547 | + | 0.709657i | \(0.251150\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 291.545 | 1.68913 | 0.844566 | − | 0.535452i | \(-0.179859\pi\) | ||||
0.844566 | + | 0.535452i | \(0.179859\pi\) | |||||||
\(32\) | − 218.056i | − 1.20460i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 307.006 | 1.54856 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 260.637i | 1.15807i | 0.815304 | + | 0.579033i | \(0.196570\pi\) | ||||
−0.815304 | + | 0.579033i | \(0.803430\pi\) | |||||||
\(38\) | 182.002i | 0.776964i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −169.766 | −0.646660 | −0.323330 | − | 0.946286i | \(-0.604802\pi\) | ||||
−0.323330 | + | 0.946286i | \(0.604802\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 438.596i | 1.55547i | 0.628592 | + | 0.777735i | \(0.283631\pi\) | ||||
−0.628592 | + | 0.777735i | \(0.716369\pi\) | |||||||
\(44\) | −692.967 | −2.37429 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −643.571 | −2.06281 | ||||||||
\(47\) | − 255.481i | − 0.792887i | −0.918059 | − | 0.396444i | \(-0.870244\pi\) | ||||
0.918059 | − | 0.396444i | \(-0.129756\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 317.181 | 0.924726 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 252.127i | 0.672379i | ||||||||
\(53\) | − 214.714i | − 0.556477i | −0.960512 | − | 0.278239i | \(-0.910249\pi\) | ||||
0.960512 | − | 0.278239i | \(-0.0897506\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 88.0557 | 0.210124 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 981.322i | 2.22162i | ||||||||
\(59\) | −331.524 | −0.731537 | −0.365769 | − | 0.930706i | \(-0.619194\pi\) | ||||
−0.365769 | + | 0.930706i | \(0.619194\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 54.9647 | 0.115369 | 0.0576845 | − | 0.998335i | \(-0.481628\pi\) | ||||
0.0576845 | + | 0.998335i | \(0.481628\pi\) | |||||||
\(62\) | 1300.11i | 2.66314i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 829.920 | 1.62094 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 758.179i | 1.38248i | 0.722624 | + | 0.691241i | \(0.242936\pi\) | ||||
−0.722624 | + | 0.691241i | \(0.757064\pi\) | |||||||
\(68\) | 818.299i | 1.45931i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −904.348 | −1.51164 | −0.755819 | − | 0.654780i | \(-0.772761\pi\) | ||||
−0.755819 | + | 0.654780i | \(0.772761\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 866.622i | − 1.38946i | −0.719271 | − | 0.694729i | \(-0.755524\pi\) | ||||
0.719271 | − | 0.694729i | \(-0.244476\pi\) | |||||||
\(74\) | −1162.28 | −1.82584 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −485.110 | −0.732184 | ||||||||
\(77\) | 296.239i | 0.438437i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −206.961 | −0.294746 | −0.147373 | − | 0.989081i | \(-0.547082\pi\) | ||||
−0.147373 | + | 0.989081i | \(0.547082\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − 757.054i | − 1.01954i | ||||||||
\(83\) | 463.397i | 0.612825i | 0.951899 | + | 0.306412i | \(0.0991287\pi\) | ||||
−0.951899 | + | 0.306412i | \(0.900871\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1955.87 | −2.45240 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − 1010.33i | − 1.22388i | ||||||||
\(89\) | −601.736 | −0.716673 | −0.358337 | − | 0.933592i | \(-0.616656\pi\) | ||||
−0.358337 | + | 0.933592i | \(0.616656\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 107.783 | 0.124162 | ||||||||
\(92\) | − 1715.38i | − 1.94392i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1139.29 | 1.25009 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 229.363i | 0.240086i | 0.992769 | + | 0.120043i | \(0.0383032\pi\) | ||||
−0.992769 | + | 0.120043i | \(0.961697\pi\) | |||||||
\(98\) | 1414.43i | 1.45795i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1345.66 | 1.32573 | 0.662863 | − | 0.748740i | \(-0.269341\pi\) | ||||
0.662863 | + | 0.748740i | \(0.269341\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1596.30i | 1.52707i | 0.645768 | + | 0.763534i | \(0.276537\pi\) | ||||
−0.645768 | + | 0.763534i | \(0.723463\pi\) | |||||||
\(104\) | −367.594 | −0.346592 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 957.494 | 0.877358 | ||||||||
\(107\) | 958.786i | 0.866256i | 0.901333 | + | 0.433128i | \(0.142590\pi\) | ||||
−0.901333 | + | 0.433128i | \(0.857410\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1690.23 | −1.48527 | −0.742635 | − | 0.669696i | \(-0.766424\pi\) | ||||
−0.742635 | + | 0.669696i | \(0.766424\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − 90.4943i | − 0.0763474i | ||||||||
\(113\) | 11.6211i | 0.00967456i | 0.999988 | + | 0.00483728i | \(0.00153976\pi\) | ||||
−0.999988 | + | 0.00483728i | \(0.998460\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2615.63 | −2.09358 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − 1478.39i | − 1.15336i | ||||||||
\(119\) | 349.818 | 0.269477 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2067.97 | 1.55370 | ||||||||
\(122\) | 245.109i | 0.181894i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3465.34 | −2.50965 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 309.141i | 0.215999i | 0.994151 | + | 0.107999i | \(0.0344444\pi\) | ||||
−0.994151 | + | 0.107999i | \(0.965556\pi\) | |||||||
\(128\) | 1956.48i | 1.35102i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2785.03 | 1.85747 | 0.928736 | − | 0.370742i | \(-0.120897\pi\) | ||||
0.928736 | + | 0.370742i | \(0.120897\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 207.382i | 0.135205i | ||||||||
\(134\) | −3381.01 | −2.17966 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1193.06 | −0.752233 | ||||||||
\(137\) | − 2489.41i | − 1.55244i | −0.630460 | − | 0.776222i | \(-0.717134\pi\) | ||||
0.630460 | − | 0.776222i | \(-0.282866\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1786.05 | −1.08986 | −0.544931 | − | 0.838481i | \(-0.683444\pi\) | ||||
−0.544931 | + | 0.838481i | \(0.683444\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − 4032.83i | − 2.38329i | ||||||||
\(143\) | − 1236.67i | − 0.723185i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 3864.60 | 2.19066 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − 3097.95i | − 1.72061i | ||||||||
\(149\) | −1568.83 | −0.862575 | −0.431288 | − | 0.902214i | \(-0.641941\pi\) | ||||
−0.431288 | + | 0.902214i | \(0.641941\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −438.327 | −0.236229 | −0.118114 | − | 0.993000i | \(-0.537685\pi\) | ||||
−0.118114 | + | 0.993000i | \(0.537685\pi\) | |||||||
\(152\) | − 707.277i | − 0.377419i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1321.04 | −0.691252 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 44.7479i | − 0.0227469i | −0.999935 | − | 0.0113735i | \(-0.996380\pi\) | ||||
0.999935 | − | 0.0113735i | \(-0.00362036\pi\) | |||||||
\(158\) | − 922.917i | − 0.464705i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −733.315 | −0.358965 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2611.84i | 1.25506i | 0.778591 | + | 0.627531i | \(0.215935\pi\) | ||||
−0.778591 | + | 0.627531i | \(0.784065\pi\) | |||||||
\(164\) | 2017.86 | 0.960783 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2066.47 | −0.966198 | ||||||||
\(167\) | − 188.947i | − 0.0875516i | −0.999041 | − | 0.0437758i | \(-0.986061\pi\) | ||||
0.999041 | − | 0.0437758i | \(-0.0139387\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1747.05 | 0.795200 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − 5213.19i | − 2.31106i | ||||||||
\(173\) | 1505.02i | 0.661413i | 0.943734 | + | 0.330707i | \(0.107287\pi\) | ||||
−0.943734 | + | 0.330707i | \(0.892713\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1038.31 | −0.444689 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 2683.37i | − 1.12993i | ||||||||
\(179\) | 3136.62 | 1.30973 | 0.654865 | − | 0.755746i | \(-0.272725\pi\) | ||||
0.654865 | + | 0.755746i | \(0.272725\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4512.67 | 1.85317 | 0.926586 | − | 0.376084i | \(-0.122730\pi\) | ||||
0.926586 | + | 0.376084i | \(0.122730\pi\) | |||||||
\(182\) | 480.644i | 0.195757i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2500.98 | 1.00204 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 4013.71i | − 1.56958i | ||||||||
\(188\) | 3036.67i | 1.17804i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1207.43 | 0.457418 | 0.228709 | − | 0.973495i | \(-0.426550\pi\) | ||||
0.228709 | + | 0.973495i | \(0.426550\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 923.164i | − 0.344305i | −0.985070 | − | 0.172152i | \(-0.944928\pi\) | ||||
0.985070 | − | 0.172152i | \(-0.0550721\pi\) | |||||||
\(194\) | −1022.82 | −0.378526 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3770.04 | −1.37392 | ||||||||
\(197\) | − 1180.87i | − 0.427075i | −0.976935 | − | 0.213537i | \(-0.931501\pi\) | ||||
0.976935 | − | 0.213537i | \(-0.0684985\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 839.805 | 0.299157 | 0.149578 | − | 0.988750i | \(-0.452208\pi\) | ||||
0.149578 | + | 0.988750i | \(0.452208\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 6000.82i | 2.09018i | ||||||||
\(203\) | 1118.17i | 0.386600i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −7118.51 | −2.40762 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 377.774i | 0.125932i | ||||||||
\(209\) | 2379.44 | 0.787509 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2589.65 | −0.844923 | −0.422461 | − | 0.906381i | \(-0.638834\pi\) | ||||
−0.422461 | + | 0.906381i | \(0.638834\pi\) | |||||||
\(212\) | 2552.12i | 0.826792i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4275.59 | −1.36576 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1481.41i | 0.463432i | ||||||||
\(218\) | − 7537.38i | − 2.34172i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1460.34 | −0.444492 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4180.76i | 1.25544i | 0.778437 | + | 0.627722i | \(0.216013\pi\) | ||||
−0.778437 | + | 0.627722i | \(0.783987\pi\) | |||||||
\(224\) | 1107.99 | 0.330495 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −51.8232 | −0.0152532 | ||||||||
\(227\) | − 2602.67i | − 0.760993i | −0.924782 | − | 0.380497i | \(-0.875753\pi\) | ||||
0.924782 | − | 0.380497i | \(-0.124247\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1845.35 | 0.532508 | 0.266254 | − | 0.963903i | \(-0.414214\pi\) | ||||
0.266254 | + | 0.963903i | \(0.414214\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − 3813.51i | − 1.07918i | ||||||||
\(233\) | − 240.637i | − 0.0676594i | −0.999428 | − | 0.0338297i | \(-0.989230\pi\) | ||||
0.999428 | − | 0.0338297i | \(-0.0107704\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3940.52 | 1.08689 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1559.97i | 0.424865i | ||||||||
\(239\) | −2567.64 | −0.694924 | −0.347462 | − | 0.937694i | \(-0.612956\pi\) | ||||
−0.347462 | + | 0.937694i | \(0.612956\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3987.99 | 1.06593 | 0.532965 | − | 0.846137i | \(-0.321078\pi\) | ||||
0.532965 | + | 0.846137i | \(0.321078\pi\) | |||||||
\(242\) | 9221.86i | 2.44960i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −653.315 | −0.171411 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 865.728i | − 0.223016i | ||||||||
\(248\) | − 5052.36i | − 1.29365i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 967.393 | 0.243272 | 0.121636 | − | 0.992575i | \(-0.461186\pi\) | ||||
0.121636 | + | 0.992575i | \(0.461186\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8413.86i | 2.09081i | ||||||||
\(254\) | −1378.58 | −0.340550 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2085.34 | −0.509116 | ||||||||
\(257\) | 3743.03i | 0.908498i | 0.890875 | + | 0.454249i | \(0.150092\pi\) | ||||
−0.890875 | + | 0.454249i | \(0.849908\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1324.36 | −0.317728 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 12419.5i | 2.92855i | ||||||||
\(263\) | 2497.47i | 0.585554i | 0.956181 | + | 0.292777i | \(0.0945794\pi\) | ||||
−0.956181 | + | 0.292777i | \(0.905421\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −924.795 | −0.213168 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − 9011.79i | − 2.05404i | ||||||||
\(269\) | 2142.91 | 0.485709 | 0.242855 | − | 0.970063i | \(-0.421916\pi\) | ||||
0.242855 | + | 0.970063i | \(0.421916\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1540.64 | 0.345341 | 0.172671 | − | 0.984980i | \(-0.444760\pi\) | ||||
0.172671 | + | 0.984980i | \(0.444760\pi\) | |||||||
\(272\) | 1226.10i | 0.273320i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11101.2 | 2.44763 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6777.80i | 1.47018i | 0.677972 | + | 0.735088i | \(0.262859\pi\) | ||||
−0.677972 | + | 0.735088i | \(0.737141\pi\) | |||||||
\(278\) | − 7964.69i | − 1.71831i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 827.653 | 0.175707 | 0.0878535 | − | 0.996133i | \(-0.471999\pi\) | ||||
0.0878535 | + | 0.996133i | \(0.471999\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3171.98i | 0.666270i | 0.942879 | + | 0.333135i | \(0.108106\pi\) | ||||
−0.942879 | + | 0.333135i | \(0.891894\pi\) | |||||||
\(284\) | 10749.2 | 2.24593 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5514.78 | 1.14020 | ||||||||
\(287\) | − 862.623i | − 0.177418i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 173.358 | 0.0352856 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 10300.8i | 2.06440i | ||||||||
\(293\) | − 1376.02i | − 0.274362i | −0.990546 | − | 0.137181i | \(-0.956196\pi\) | ||||
0.990546 | − | 0.137181i | \(-0.0438043\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 4516.73 | 0.886923 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − 6996.02i | − 1.35996i | ||||||||
\(299\) | 3061.27 | 0.592099 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2228.61 | −0.426760 | ||||||||
\(302\) | − 1954.67i | − 0.372445i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −726.864 | −0.137133 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 119.504i | − 0.0222165i | −0.999938 | − | 0.0111083i | \(-0.996464\pi\) | ||||
0.999938 | − | 0.0111083i | \(-0.00353594\pi\) | |||||||
\(308\) | − 3521.13i | − 0.651412i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2139.35 | 0.390069 | 0.195035 | − | 0.980796i | \(-0.437518\pi\) | ||||
0.195035 | + | 0.980796i | \(0.437518\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 5163.50i | − 0.932455i | −0.884665 | − | 0.466227i | \(-0.845613\pi\) | ||||
0.884665 | − | 0.466227i | \(-0.154387\pi\) | |||||||
\(314\) | 199.548 | 0.0358635 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2459.95 | 0.437922 | ||||||||
\(317\) | − 8631.69i | − 1.52935i | −0.644416 | − | 0.764675i | \(-0.722899\pi\) | ||||
0.644416 | − | 0.764675i | \(-0.277101\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12829.5 | 2.25177 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − 3270.13i | − 0.565955i | ||||||||
\(323\) | − 2809.79i | − 0.484028i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −11647.2 | −1.97877 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2941.98i | 0.495255i | ||||||||
\(329\) | 1298.16 | 0.217537 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2942.34 | −0.488597 | −0.244298 | − | 0.969700i | \(-0.578558\pi\) | ||||
−0.244298 | + | 0.969700i | \(0.578558\pi\) | |||||||
\(332\) | − 5507.98i | − 0.910512i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 842.585 | 0.138037 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9897.46i | 1.59985i | 0.600101 | + | 0.799924i | \(0.295127\pi\) | ||||
−0.600101 | + | 0.799924i | \(0.704873\pi\) | |||||||
\(338\) | 7790.79i | 1.25374i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16997.3 | 2.69928 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3354.53i | 0.528070i | ||||||||
\(344\) | 7600.68 | 1.19128 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6711.46 | −1.04280 | ||||||||
\(347\) | − 12015.7i | − 1.85890i | −0.368947 | − | 0.929451i | \(-0.620282\pi\) | ||||
0.368947 | − | 0.929451i | \(-0.379718\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7894.62 | −1.21086 | −0.605428 | − | 0.795900i | \(-0.706998\pi\) | ||||
−0.605428 | + | 0.795900i | \(0.706998\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − 12712.8i | − 1.92499i | ||||||||
\(353\) | − 741.154i | − 0.111750i | −0.998438 | − | 0.0558748i | \(-0.982205\pi\) | ||||
0.998438 | − | 0.0558748i | \(-0.0177948\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 7152.30 | 1.06481 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 13987.4i | 2.06496i | ||||||||
\(359\) | 11564.4 | 1.70012 | 0.850060 | − | 0.526685i | \(-0.176565\pi\) | ||||
0.850060 | + | 0.526685i | \(0.176565\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5193.28 | −0.757148 | ||||||||
\(362\) | 20123.7i | 2.92177i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1281.12 | −0.184474 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 1148.57i | − 0.163365i | −0.996658 | − | 0.0816823i | \(-0.973971\pi\) | ||||
0.996658 | − | 0.0816823i | \(-0.0260293\pi\) | |||||||
\(368\) | − 2570.24i | − 0.364084i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1091.01 | 0.152676 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4602.98i | 0.638963i | 0.947593 | + | 0.319481i | \(0.103509\pi\) | ||||
−0.947593 | + | 0.319481i | \(0.896491\pi\) | |||||||
\(374\) | 17898.7 | 2.47465 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4427.38 | −0.607246 | ||||||||
\(377\) | − 4667.85i | − 0.637683i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3988.46 | 0.540563 | 0.270282 | − | 0.962781i | \(-0.412883\pi\) | ||||
0.270282 | + | 0.962781i | \(0.412883\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 5384.41i | 0.721179i | ||||||||
\(383\) | − 7788.20i | − 1.03906i | −0.854454 | − | 0.519528i | \(-0.826108\pi\) | ||||
0.854454 | − | 0.519528i | \(-0.173892\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4116.74 | 0.542841 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − 2726.23i | − 0.356710i | ||||||||
\(389\) | −8524.87 | −1.11113 | −0.555563 | − | 0.831474i | \(-0.687497\pi\) | ||||
−0.555563 | + | 0.831474i | \(0.687497\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9935.60 | 1.28508 | ||||||||
\(392\) | − 5496.62i | − 0.708217i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5265.97 | 0.673339 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 155.729i | − 0.0196872i | −0.999952 | − | 0.00984361i | \(-0.996867\pi\) | ||||
0.999952 | − | 0.00984361i | \(-0.00313337\pi\) | |||||||
\(398\) | 3745.01i | 0.471659i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5933.96 | 0.738972 | 0.369486 | − | 0.929236i | \(-0.379534\pi\) | ||||
0.369486 | + | 0.929236i | \(0.379534\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 6184.23i | − 0.764414i | ||||||||
\(404\) | −15994.7 | −1.96971 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4986.33 | −0.609526 | ||||||||
\(407\) | 15195.3i | 1.85062i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14161.4 | −1.71207 | −0.856035 | − | 0.516917i | \(-0.827079\pi\) | ||||
−0.856035 | + | 0.516917i | \(0.827079\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − 18973.8i | − 2.26886i | ||||||||
\(413\) | − 1684.55i | − 0.200705i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −4625.39 | −0.545140 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 10610.8i | 1.24161i | ||||||||
\(419\) | −9624.24 | −1.12214 | −0.561068 | − | 0.827770i | \(-0.689609\pi\) | ||||
−0.561068 | + | 0.827770i | \(0.689609\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1536.26 | −0.177845 | −0.0889223 | − | 0.996039i | \(-0.528342\pi\) | ||||
−0.0889223 | + | 0.996039i | \(0.528342\pi\) | |||||||
\(422\) | − 11548.2i | − 1.33213i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3720.91 | −0.426187 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 279.288i | 0.0316527i | ||||||||
\(428\) | − 11396.2i | − 1.28705i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11582.2 | 1.29441 | 0.647207 | − | 0.762314i | \(-0.275937\pi\) | ||||
0.647207 | + | 0.762314i | \(0.275937\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 14892.6i | − 1.65287i | −0.563029 | − | 0.826437i | \(-0.690364\pi\) | ||||
0.563029 | − | 0.826437i | \(-0.309636\pi\) | |||||||
\(434\) | −6606.17 | −0.730660 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 20090.2 | 2.20676 | ||||||||
\(437\) | 5890.10i | 0.644764i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1642.51 | 0.178571 | 0.0892853 | − | 0.996006i | \(-0.471542\pi\) | ||||
0.0892853 | + | 0.996006i | \(0.471542\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − 6512.20i | − 0.700800i | ||||||||
\(443\) | − 3916.31i | − 0.420021i | −0.977699 | − | 0.210011i | \(-0.932650\pi\) | ||||
0.977699 | − | 0.210011i | \(-0.0673499\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −18643.6 | −1.97937 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 4217.02i | 0.444722i | ||||||||
\(449\) | 3985.25 | 0.418876 | 0.209438 | − | 0.977822i | \(-0.432837\pi\) | ||||
0.209438 | + | 0.977822i | \(0.432837\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9897.50 | −1.03338 | ||||||||
\(452\) | − 138.130i | − 0.0143741i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 11606.3 | 1.19980 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 14177.8i | − 1.45122i | −0.688105 | − | 0.725611i | \(-0.741557\pi\) | ||||
0.688105 | − | 0.725611i | \(-0.258443\pi\) | |||||||
\(458\) | 8229.13i | 0.839567i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16394.3 | −1.65631 | −0.828154 | − | 0.560500i | \(-0.810609\pi\) | ||||
−0.828154 | + | 0.560500i | \(0.810609\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 3319.60i | − 0.333207i | −0.986024 | − | 0.166603i | \(-0.946720\pi\) | ||||
0.986024 | − | 0.166603i | \(-0.0532800\pi\) | |||||||
\(464\) | −3919.12 | −0.392114 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1073.09 | 0.106674 | ||||||||
\(467\) | − 2529.79i | − 0.250674i | −0.992114 | − | 0.125337i | \(-0.959999\pi\) | ||||
0.992114 | − | 0.125337i | \(-0.0400012\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3852.49 | −0.379299 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5745.17i | 0.560260i | ||||||||
\(473\) | 25570.4i | 2.48569i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −4157.97 | −0.400379 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − 11450.1i | − 1.09564i | ||||||||
\(479\) | 8646.75 | 0.824802 | 0.412401 | − | 0.911002i | \(-0.364690\pi\) | ||||
0.412401 | + | 0.911002i | \(0.364690\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5528.60 | 0.524080 | ||||||||
\(482\) | 17784.0i | 1.68058i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −24580.1 | −2.30842 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 15251.7i | − 1.41914i | −0.704636 | − | 0.709569i | \(-0.748890\pi\) | ||||
0.704636 | − | 0.709569i | \(-0.251110\pi\) | |||||||
\(488\) | − 952.515i | − 0.0883572i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1766.87 | −0.162398 | −0.0811992 | − | 0.996698i | \(-0.525875\pi\) | ||||
−0.0811992 | + | 0.996698i | \(0.525875\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 15149.9i | − 1.38401i | ||||||||
\(494\) | 3860.61 | 0.351614 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5192.28 | −0.470041 | ||||||||
\(497\) | − 4595.20i | − 0.414734i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11733.8 | −1.05266 | −0.526332 | − | 0.850279i | \(-0.676433\pi\) | ||||
−0.526332 | + | 0.850279i | \(0.676433\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 4313.98i | 0.383550i | ||||||||
\(503\) | 977.608i | 0.0866589i | 0.999061 | + | 0.0433294i | \(0.0137965\pi\) | ||||
−0.999061 | + | 0.0433294i | \(0.986203\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −37520.6 | −3.29643 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − 3674.48i | − 0.320923i | ||||||||
\(509\) | −9674.72 | −0.842484 | −0.421242 | − | 0.906948i | \(-0.638406\pi\) | ||||
−0.421242 | + | 0.906948i | \(0.638406\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4403.51 | 0.381213 | ||||||||
\(512\) | 6352.52i | 0.548329i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −16691.6 | −1.43237 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 14894.7i | − 1.26706i | ||||||||
\(518\) | − 5905.81i | − 0.500939i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5178.95 | 0.435497 | 0.217748 | − | 0.976005i | \(-0.430129\pi\) | ||||
0.217748 | + | 0.976005i | \(0.430129\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 14280.7i | − 1.19398i | −0.802248 | − | 0.596992i | \(-0.796363\pi\) | ||||
0.802248 | − | 0.596992i | \(-0.203637\pi\) | |||||||
\(524\) | −33103.1 | −2.75976 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11137.2 | −0.923203 | ||||||||
\(527\) | − 20071.5i | − 1.65906i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8660.78 | −0.711826 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − 2464.96i | − 0.200883i | ||||||||
\(533\) | 3601.07i | 0.292645i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 13138.9 | 1.05880 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 9556.08i | 0.765784i | ||||||||
\(539\) | 18491.9 | 1.47774 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12923.8 | 1.02706 | 0.513529 | − | 0.858072i | \(-0.328338\pi\) | ||||
0.513529 | + | 0.858072i | \(0.328338\pi\) | |||||||
\(542\) | 6870.32i | 0.544475i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −15012.1 | −1.18316 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13653.3i | 1.06723i | 0.845728 | + | 0.533614i | \(0.179166\pi\) | ||||
−0.845728 | + | 0.533614i | \(0.820834\pi\) | |||||||
\(548\) | 29589.4i | 2.30656i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8981.28 | 0.694402 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 1051.62i | − 0.0808666i | ||||||||
\(554\) | −30224.8 | −2.31792 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 21229.2 | 1.61928 | ||||||||
\(557\) | − 9313.63i | − 0.708494i | −0.935152 | − | 0.354247i | \(-0.884737\pi\) | ||||
0.935152 | − | 0.354247i | \(-0.115263\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9303.46 | 0.703925 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3690.82i | 0.277025i | ||||||||
\(563\) | 10625.4i | 0.795394i | 0.917517 | + | 0.397697i | \(0.130190\pi\) | ||||
−0.917517 | + | 0.397697i | \(0.869810\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −14145.1 | −1.05046 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 15672.0i | 1.15771i | ||||||||
\(569\) | −9060.50 | −0.667550 | −0.333775 | − | 0.942653i | \(-0.608323\pi\) | ||||
−0.333775 | + | 0.942653i | \(0.608323\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21379.1 | −1.56688 | −0.783440 | − | 0.621467i | \(-0.786537\pi\) | ||||
−0.783440 | + | 0.621467i | \(0.786537\pi\) | |||||||
\(572\) | 14699.2i | 1.07448i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3846.77 | 0.279723 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6347.76i | 0.457991i | 0.973427 | + | 0.228996i | \(0.0735441\pi\) | ||||
−0.973427 | + | 0.228996i | \(0.926456\pi\) | |||||||
\(578\) | 773.071i | 0.0556324i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2354.63 | −0.168135 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 12518.0i | − 0.889266i | ||||||||
\(584\) | −15018.2 | −1.06414 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6136.22 | 0.432568 | ||||||||
\(587\) | 14773.7i | 1.03880i | 0.854531 | + | 0.519401i | \(0.173845\pi\) | ||||
−0.854531 | + | 0.519401i | \(0.826155\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11898.9 | 0.832405 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − 4641.81i | − 0.322259i | ||||||||
\(593\) | − 26868.1i | − 1.86061i | −0.366790 | − | 0.930304i | \(-0.619543\pi\) | ||||
0.366790 | − | 0.930304i | \(-0.380457\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 18647.3 | 1.28158 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 13651.4i | 0.933522i | ||||||||
\(599\) | 1749.83 | 0.119359 | 0.0596794 | − | 0.998218i | \(-0.480992\pi\) | ||||
0.0596794 | + | 0.998218i | \(0.480992\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17964.0 | −1.21924 | −0.609622 | − | 0.792692i | \(-0.708679\pi\) | ||||
−0.609622 | + | 0.792692i | \(0.708679\pi\) | |||||||
\(602\) | − 9938.21i | − 0.672843i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 5209.99 | 0.350979 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 4418.22i | − 0.295437i | −0.989029 | − | 0.147718i | \(-0.952807\pi\) | ||||
0.989029 | − | 0.147718i | \(-0.0471929\pi\) | |||||||
\(608\) | − 8899.58i | − 0.593628i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5419.24 | −0.358820 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20179.7i | 1.32961i | 0.747018 | + | 0.664804i | \(0.231485\pi\) | ||||
−0.747018 | + | 0.664804i | \(0.768515\pi\) | |||||||
\(614\) | 532.915 | 0.0350272 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5133.71 | 0.335784 | ||||||||
\(617\) | − 4673.01i | − 0.304908i | −0.988311 | − | 0.152454i | \(-0.951282\pi\) | ||||
0.988311 | − | 0.152454i | \(-0.0487176\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19976.8 | 1.29715 | 0.648574 | − | 0.761151i | \(-0.275366\pi\) | ||||
0.648574 | + | 0.761151i | \(0.275366\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 9540.19i | 0.614994i | ||||||||
\(623\) | − 3057.56i | − 0.196627i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 23026.0 | 1.47014 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 531.877i | 0.0337965i | ||||||||
\(629\) | 17943.5 | 1.13745 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10457.5 | 0.659757 | 0.329879 | − | 0.944023i | \(-0.392992\pi\) | ||||
0.329879 | + | 0.944023i | \(0.392992\pi\) | |||||||
\(632\) | 3586.54i | 0.225736i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 38492.0 | 2.41122 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 6728.02i | − 0.418483i | ||||||||
\(638\) | 57211.8i | 3.55021i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4395.86 | 0.270867 | 0.135434 | − | 0.990786i | \(-0.456757\pi\) | ||||
0.135434 | + | 0.990786i | \(0.456757\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 5786.36i | − 0.354886i | −0.984131 | − | 0.177443i | \(-0.943217\pi\) | ||||
0.984131 | − | 0.177443i | \(-0.0567825\pi\) | |||||||
\(644\) | 8716.26 | 0.533336 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 12529.9 | 0.763133 | ||||||||
\(647\) | − 25367.7i | − 1.54143i | −0.637178 | − | 0.770717i | \(-0.719898\pi\) | ||||
0.637178 | − | 0.770717i | \(-0.280102\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −19328.1 | −1.16902 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − 31044.6i | − 1.86472i | ||||||||
\(653\) | 21633.2i | 1.29644i | 0.761454 | + | 0.648218i | \(0.224486\pi\) | ||||
−0.761454 | + | 0.648218i | \(0.775514\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3023.46 | 0.179948 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 5788.98i | 0.342976i | ||||||||
\(659\) | −18312.4 | −1.08248 | −0.541238 | − | 0.840870i | \(-0.682044\pi\) | ||||
−0.541238 | + | 0.840870i | \(0.682044\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5526.08 | −0.325174 | −0.162587 | − | 0.986694i | \(-0.551984\pi\) | ||||
−0.162587 | + | 0.986694i | \(0.551984\pi\) | |||||||
\(662\) | − 13121.0i | − 0.770337i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 8030.48 | 0.469342 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 31758.4i | 1.84361i | ||||||||
\(668\) | 2245.84i | 0.130081i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3204.48 | 0.184363 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 1437.24i | − 0.0823204i | −0.999153 | − | 0.0411602i | \(-0.986895\pi\) | ||||
0.999153 | − | 0.0411602i | \(-0.0131054\pi\) | |||||||
\(674\) | −44136.6 | −2.52237 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −20765.7 | −1.18148 | ||||||||
\(677\) | − 23405.9i | − 1.32875i | −0.747401 | − | 0.664373i | \(-0.768699\pi\) | ||||
0.747401 | − | 0.664373i | \(-0.231301\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1165.45 | −0.0658701 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 75797.4i | 4.25577i | ||||||||
\(683\) | − 19227.4i | − 1.07719i | −0.842566 | − | 0.538593i | \(-0.818956\pi\) | ||||
0.842566 | − | 0.538593i | \(-0.181044\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −14959.2 | −0.832570 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − 7811.17i | − 0.432846i | ||||||||
\(689\) | −4554.50 | −0.251833 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −35284.8 | −1.94254 | −0.971271 | − | 0.237975i | \(-0.923516\pi\) | ||||
−0.971271 | + | 0.237975i | \(0.923516\pi\) | |||||||
\(692\) | − 17888.8i | − 0.982703i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 53582.8 | 2.93080 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11687.6i | 0.635149i | ||||||||
\(698\) | − 35205.1i | − 1.90907i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9173.00 | 0.494236 | 0.247118 | − | 0.968985i | \(-0.420516\pi\) | ||||
0.247118 | + | 0.968985i | \(0.420516\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10637.4i | 0.570695i | ||||||||
\(704\) | 48384.9 | 2.59030 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3305.09 | 0.176188 | ||||||||
\(707\) | 6837.63i | 0.363728i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 33951.6 | 1.79842 | 0.899210 | − | 0.437517i | \(-0.144142\pi\) | ||||
0.899210 | + | 0.437517i | \(0.144142\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 10427.8i | 0.548876i | ||||||||
\(713\) | 42075.3i | 2.21001i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −37282.1 | −1.94595 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 51569.9i | 2.68046i | ||||||||
\(719\) | 6727.90 | 0.348968 | 0.174484 | − | 0.984660i | \(-0.444174\pi\) | ||||
0.174484 | + | 0.984660i | \(0.444174\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8111.17 | −0.418968 | ||||||||
\(722\) | − 23158.8i | − 1.19374i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −53638.0 | −2.75337 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 36726.1i | − 1.87359i | −0.349885 | − | 0.936793i | \(-0.613779\pi\) | ||||
0.349885 | − | 0.936793i | \(-0.386221\pi\) | |||||||
\(728\) | − 1867.83i | − 0.0950912i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 30195.1 | 1.52778 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 26691.4i | − 1.34498i | −0.740108 | − | 0.672489i | \(-0.765225\pi\) | ||||
0.740108 | − | 0.672489i | \(-0.234775\pi\) | |||||||
\(734\) | 5121.91 | 0.257566 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 31469.5 | 1.57606 | ||||||||
\(737\) | 44202.4i | 2.20925i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12207.0 | −0.607634 | −0.303817 | − | 0.952730i | \(-0.598261\pi\) | ||||
−0.303817 | + | 0.952730i | \(0.598261\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4865.25i | 0.240713i | ||||||||
\(743\) | 12473.3i | 0.615882i | 0.951405 | + | 0.307941i | \(0.0996400\pi\) | ||||
−0.951405 | + | 0.307941i | \(0.900360\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −20526.4 | −1.00741 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 47707.4i | 2.33202i | ||||||||
\(749\) | −4871.82 | −0.237667 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15102.6 | −0.733825 | −0.366913 | − | 0.930255i | \(-0.619585\pi\) | ||||
−0.366913 | + | 0.930255i | \(0.619585\pi\) | |||||||
\(752\) | 4549.99i | 0.220640i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 20815.7 | 1.00539 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 3418.34i | − 0.164124i | −0.996627 | − | 0.0820618i | \(-0.973850\pi\) | ||||
0.996627 | − | 0.0820618i | \(-0.0261505\pi\) | |||||||
\(758\) | 17786.1i | 0.852268i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12684.5 | −0.604224 | −0.302112 | − | 0.953272i | \(-0.597692\pi\) | ||||
−0.302112 | + | 0.953272i | \(0.597692\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 8588.45i | − 0.407500i | ||||||||
\(764\) | −14351.7 | −0.679614 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 34730.6 | 1.63821 | ||||||||
\(767\) | 7032.25i | 0.331056i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27580.2 | 1.29333 | 0.646663 | − | 0.762776i | \(-0.276164\pi\) | ||||
0.646663 | + | 0.762776i | \(0.276164\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 10972.8i | 0.511555i | ||||||||
\(773\) | − 17386.0i | − 0.808966i | −0.914546 | − | 0.404483i | \(-0.867452\pi\) | ||||
0.914546 | − | 0.404483i | \(-0.132548\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 3974.77 | 0.183874 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − 38015.7i | − 1.75183i | ||||||||
\(779\) | −6928.72 | −0.318674 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −52724.1 | −2.41564 | ||||||||
\(782\) | 44306.7i | 2.02609i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5648.84 | −0.257327 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4680.29i | 0.211988i | 0.994367 | + | 0.105994i | \(0.0338024\pi\) | ||||
−0.994367 | + | 0.105994i | \(0.966198\pi\) | |||||||
\(788\) | 14036.0i | 0.634531i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −59.0498 | −0.00265432 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 1165.91i | − 0.0522100i | ||||||||
\(794\) | 694.456 | 0.0310395 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9982.00 | −0.444476 | ||||||||
\(797\) | 7278.62i | 0.323490i | 0.986833 | + | 0.161745i | \(0.0517123\pi\) | ||||
−0.986833 | + | 0.161745i | \(0.948288\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −17588.6 | −0.778773 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 26461.8i | 1.16508i | ||||||||
\(803\) | − 50524.7i | − 2.22039i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 27577.9 | 1.20520 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − 23319.8i | − 1.01533i | ||||||||
\(809\) | −29212.5 | −1.26954 | −0.634770 | − | 0.772701i | \(-0.718905\pi\) | ||||
−0.634770 | + | 0.772701i | \(0.718905\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 41992.4 | 1.81819 | 0.909094 | − | 0.416590i | \(-0.136775\pi\) | ||||
0.909094 | + | 0.416590i | \(0.136775\pi\) | |||||||
\(812\) | − 13290.6i | − 0.574396i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −67761.6 | −2.91774 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 17900.5i | 0.766536i | ||||||||
\(818\) | − 63151.2i | − 2.69930i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8722.99 | −0.370809 | −0.185405 | − | 0.982662i | \(-0.559360\pi\) | ||||
−0.185405 | + | 0.982662i | \(0.559360\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 13584.8i | − 0.575379i | −0.957724 | − | 0.287690i | \(-0.907113\pi\) | ||||
0.957724 | − | 0.287690i | \(-0.0928871\pi\) | |||||||
\(824\) | 27663.2 | 1.16953 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 7512.05 | 0.316438 | ||||||||
\(827\) | 26573.6i | 1.11736i | 0.829384 | + | 0.558679i | \(0.188692\pi\) | ||||
−0.829384 | + | 0.558679i | \(0.811308\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 43238.4 | 1.81150 | 0.905748 | − | 0.423816i | \(-0.139310\pi\) | ||||
0.905748 | + | 0.423816i | \(0.139310\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − 17604.2i | − 0.733552i | ||||||||
\(833\) | − 21836.3i | − 0.908265i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −28282.3 | −1.17005 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − 42918.2i | − 1.76919i | ||||||||
\(839\) | 4093.21 | 0.168431 | 0.0842154 | − | 0.996448i | \(-0.473162\pi\) | ||||
0.0842154 | + | 0.996448i | \(0.473162\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24036.5 | 0.985546 | ||||||||
\(842\) | − 6850.75i | − 0.280395i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 30780.8 | 1.25535 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10507.8i | 0.426273i | ||||||||
\(848\) | 3823.96i | 0.154853i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −37614.7 | −1.51517 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20201.5i | 0.810886i | 0.914120 | + | 0.405443i | \(0.132883\pi\) | ||||
−0.914120 | + | 0.405443i | \(0.867117\pi\) | |||||||
\(854\) | −1245.45 | −0.0499046 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 16615.4 | 0.663436 | ||||||||
\(857\) | 4551.65i | 0.181425i | 0.995877 | + | 0.0907126i | \(0.0289145\pi\) | ||||
−0.995877 | + | 0.0907126i | \(0.971086\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11962.6 | −0.475154 | −0.237577 | − | 0.971369i | \(-0.576353\pi\) | ||||
−0.237577 | + | 0.971369i | \(0.576353\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 51649.3i | 2.04081i | ||||||||
\(863\) | 7164.61i | 0.282603i | 0.989967 | + | 0.141301i | \(0.0451287\pi\) | ||||
−0.989967 | + | 0.141301i | \(0.954871\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 66412.0 | 2.60597 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − 17608.2i | − 0.688549i | ||||||||
\(869\) | −12065.9 | −0.471012 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16082.4 | 0.625640 | ||||||||
\(872\) | 29291.0i | 1.13752i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −26266.2 | −1.01655 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 19218.7i | − 0.739987i | −0.929034 | − | 0.369994i | \(-0.879360\pi\) | ||||
0.929034 | − | 0.369994i | \(-0.120640\pi\) | |||||||
\(878\) | 7324.56i | 0.281540i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −45914.5 | −1.75585 | −0.877923 | − | 0.478802i | \(-0.841071\pi\) | ||||
−0.877923 | + | 0.478802i | \(0.841071\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 44656.7i | 1.70194i | 0.525211 | + | 0.850972i | \(0.323986\pi\) | ||||
−0.525211 | + | 0.850972i | \(0.676014\pi\) | |||||||
\(884\) | 17357.7 | 0.660410 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 17464.3 | 0.662218 | ||||||||
\(887\) | 14975.2i | 0.566873i | 0.958991 | + | 0.283437i | \(0.0914745\pi\) | ||||
−0.958991 | + | 0.283437i | \(0.908525\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1570.82 | −0.0592616 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − 49692.9i | − 1.86529i | ||||||||
\(893\) | − 10427.0i | − 0.390735i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −9941.33 | −0.370666 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 17771.7i | 0.660413i | ||||||||
\(899\) | 64156.8 | 2.38015 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14782.0 | −0.546571 | ||||||||
\(902\) | − 44136.7i | − 1.62926i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 201.390 | 0.00740943 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 14818.1i | − 0.542479i | −0.962512 | − | 0.271240i | \(-0.912566\pi\) | ||||
0.962512 | − | 0.271240i | \(-0.0874336\pi\) | |||||||
\(908\) | 30935.6i | 1.13065i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21846.5 | 0.794518 | 0.397259 | − | 0.917707i | \(-0.369961\pi\) | ||||
0.397259 | + | 0.917707i | \(0.369961\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 27016.4i | 0.979312i | ||||||||
\(914\) | 63224.2 | 2.28804 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −21934.0 | −0.791179 | ||||||||
\(917\) | 14151.4i | 0.509618i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −28878.9 | −1.03659 | −0.518296 | − | 0.855201i | \(-0.673434\pi\) | ||||
−0.518296 | + | 0.855201i | \(0.673434\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − 73108.4i | − 2.61139i | ||||||||
\(923\) | 19182.9i | 0.684089i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 14803.4 | 0.525344 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − 47985.0i | − 1.69740i | ||||||||
\(929\) | −4608.79 | −0.162766 | −0.0813829 | − | 0.996683i | \(-0.525934\pi\) | ||||
−0.0813829 | + | 0.996683i | \(0.525934\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12945.2 | 0.455705 | ||||||||
\(932\) | 2860.23i | 0.100526i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 11281.3 | 0.395220 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 21063.8i | − 0.734391i | −0.930144 | − | 0.367195i | \(-0.880318\pi\) | ||||
0.930144 | − | 0.367195i | \(-0.119682\pi\) | |||||||
\(938\) | − 17179.7i | − 0.598014i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20244.8 | −0.701339 | −0.350670 | − | 0.936499i | \(-0.614046\pi\) | ||||
−0.350670 | + | 0.936499i | \(0.614046\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 24500.4i | − 0.846069i | ||||||||
\(944\) | 5904.27 | 0.203567 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −114028. | −3.91901 | ||||||||
\(947\) | − 29978.3i | − 1.02868i | −0.857585 | − | 0.514342i | \(-0.828036\pi\) | ||||
0.857585 | − | 0.514342i | \(-0.171964\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −18382.7 | −0.628797 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − 6062.20i | − 0.206383i | ||||||||
\(953\) | − 5782.65i | − 0.196556i | −0.995159 | − | 0.0982782i | \(-0.968666\pi\) | ||||
0.995159 | − | 0.0982782i | \(-0.0313335\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 30519.2 | 1.03249 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 38559.2i | 1.30041i | ||||||||
\(959\) | 12649.3 | 0.425930 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 55207.7 | 1.85317 | ||||||||
\(962\) | 24654.2i | 0.826281i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −47401.6 | −1.58372 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 26119.2i | − 0.868600i | −0.900768 | − | 0.434300i | \(-0.856996\pi\) | ||||
0.900768 | − | 0.434300i | \(-0.143004\pi\) | |||||||
\(968\) | − 35837.0i | − 1.18992i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5101.93 | 0.168619 | 0.0843093 | − | 0.996440i | \(-0.473132\pi\) | ||||
0.0843093 | + | 0.996440i | \(0.473132\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 9075.34i | − 0.299016i | ||||||||
\(974\) | 68013.1 | 2.23746 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −978.894 | −0.0321041 | ||||||||
\(977\) | − 45902.4i | − 1.50312i | −0.659666 | − | 0.751559i | \(-0.729302\pi\) | ||||
0.659666 | − | 0.751559i | \(-0.270698\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −35081.6 | −1.14526 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − 7879.14i | − 0.256042i | ||||||||
\(983\) | − 13416.5i | − 0.435321i | −0.976025 | − | 0.217661i | \(-0.930157\pi\) | ||||
0.976025 | − | 0.217661i | \(-0.0698426\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 67559.2 | 2.18207 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 10290.1i | 0.331349i | ||||||||
\(989\) | −63297.4 | −2.03513 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3806.66 | 0.122021 | 0.0610104 | − | 0.998137i | \(-0.480568\pi\) | ||||
0.0610104 | + | 0.998137i | \(0.480568\pi\) | |||||||
\(992\) | − 63573.2i | − 2.03473i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 20491.8 | 0.653883 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 22523.8i | − 0.715483i | −0.933821 | − | 0.357742i | \(-0.883547\pi\) | ||||
0.933821 | − | 0.357742i | \(-0.116453\pi\) | |||||||
\(998\) | − 52325.7i | − 1.65966i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 675.4.b.l.649.5 | 6 | ||
3.2 | odd | 2 | 675.4.b.k.649.2 | 6 | |||
5.2 | odd | 4 | 675.4.a.r.1.1 | 3 | |||
5.3 | odd | 4 | 135.4.a.f.1.3 | ✓ | 3 | ||
5.4 | even | 2 | inner | 675.4.b.l.649.2 | 6 | ||
15.2 | even | 4 | 675.4.a.q.1.3 | 3 | |||
15.8 | even | 4 | 135.4.a.g.1.1 | yes | 3 | ||
15.14 | odd | 2 | 675.4.b.k.649.5 | 6 | |||
20.3 | even | 4 | 2160.4.a.bm.1.3 | 3 | |||
45.13 | odd | 12 | 405.4.e.t.136.1 | 6 | |||
45.23 | even | 12 | 405.4.e.r.136.3 | 6 | |||
45.38 | even | 12 | 405.4.e.r.271.3 | 6 | |||
45.43 | odd | 12 | 405.4.e.t.271.1 | 6 | |||
60.23 | odd | 4 | 2160.4.a.be.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
135.4.a.f.1.3 | ✓ | 3 | 5.3 | odd | 4 | ||
135.4.a.g.1.1 | yes | 3 | 15.8 | even | 4 | ||
405.4.e.r.136.3 | 6 | 45.23 | even | 12 | |||
405.4.e.r.271.3 | 6 | 45.38 | even | 12 | |||
405.4.e.t.136.1 | 6 | 45.13 | odd | 12 | |||
405.4.e.t.271.1 | 6 | 45.43 | odd | 12 | |||
675.4.a.q.1.3 | 3 | 15.2 | even | 4 | |||
675.4.a.r.1.1 | 3 | 5.2 | odd | 4 | |||
675.4.b.k.649.2 | 6 | 3.2 | odd | 2 | |||
675.4.b.k.649.5 | 6 | 15.14 | odd | 2 | |||
675.4.b.l.649.2 | 6 | 5.4 | even | 2 | inner | ||
675.4.b.l.649.5 | 6 | 1.1 | even | 1 | trivial | ||
2160.4.a.be.1.3 | 3 | 60.23 | odd | 4 | |||
2160.4.a.bm.1.3 | 3 | 20.3 | even | 4 |