Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2052,3,Mod(125,2052)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2052, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2052.125");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2052 = 2^{2} \cdot 3^{3} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2052.be (of order \(6\), degree \(2\), 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: | \(55.9129502467\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(40\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 684) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 125.8 | ||
Character | \(\chi\) | \(=\) | 2052.125 |
Dual form | 2052.3.be.a.197.8 |
$q$-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 \(\left(\mathbb{Z}/2052\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(1027\) | \(1217\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −5.40523 | + | 3.12071i | −1.08105 | + | 0.624143i | −0.931179 | − | 0.364563i | \(-0.881218\pi\) |
−0.149868 | + | 0.988706i | \(0.547885\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.14502 | + | 7.17938i | 0.592145 | + | 1.02563i | 0.993943 | + | 0.109897i | \(0.0350522\pi\) |
−0.401798 | + | 0.915729i | \(0.631614\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −16.6134 | + | 9.59174i | −1.51031 | + | 0.871976i | −0.510379 | + | 0.859950i | \(0.670495\pi\) |
−0.999928 | + | 0.0120264i | \(0.996172\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.01910 | 0.386085 | 0.193042 | − | 0.981190i | \(-0.438165\pi\) | ||||
0.193042 | + | 0.981190i | \(0.438165\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 25.7470 | + | 14.8650i | 1.51453 | + | 0.874414i | 0.999855 | + | 0.0170290i | \(0.00542075\pi\) |
0.514675 | + | 0.857385i | \(0.327913\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 17.0105 | + | 8.46421i | 0.895290 | + | 0.445485i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 10.5502i | 0.458703i | 0.973344 | + | 0.229351i | \(0.0736605\pi\) | ||||
−0.973344 | + | 0.229351i | \(0.926339\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.97770 | − | 12.0857i | 0.279108 | − | 0.483429i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 25.7875 | + | 14.8884i | 0.889225 | + | 0.513394i | 0.873689 | − | 0.486485i | \(-0.161721\pi\) |
0.0155362 | + | 0.999879i | \(0.495054\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.96277 | + | 5.13166i | −0.0955732 | + | 0.165538i | −0.909848 | − | 0.414942i | \(-0.863802\pi\) |
0.814275 | + | 0.580480i | \(0.197135\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −44.8096 | − | 25.8708i | −1.28027 | − | 0.739166i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 52.1430 | 1.40927 | 0.704635 | − | 0.709570i | \(-0.251111\pi\) | ||||
0.704635 | + | 0.709570i | \(0.251111\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 40.6831 | − | 23.4884i | 0.992271 | − | 0.572888i | 0.0863184 | − | 0.996268i | \(-0.472490\pi\) |
0.905952 | + | 0.423380i | \(0.139156\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −60.4290 | −1.40533 | −0.702663 | − | 0.711523i | \(-0.748006\pi\) | ||||
−0.702663 | + | 0.711523i | \(0.748006\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 25.9940 | + | 15.0076i | 0.553064 | + | 0.319311i | 0.750357 | − | 0.661033i | \(-0.229882\pi\) |
−0.197293 | + | 0.980345i | \(0.563215\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −9.86235 | + | 17.0821i | −0.201272 | + | 0.348614i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −42.0135 | + | 24.2565i | −0.792707 | + | 0.457670i | −0.840915 | − | 0.541167i | \(-0.817983\pi\) |
0.0482074 | + | 0.998837i | \(0.484649\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 59.8661 | − | 103.691i | 1.08847 | − | 1.88529i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −83.0645 | + | 47.9573i | −1.40787 | + | 0.812835i | −0.995183 | − | 0.0980364i | \(-0.968744\pi\) |
−0.412689 | + | 0.910872i | \(0.635411\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −46.3314 | + | 80.2483i | −0.759530 | + | 1.31555i | 0.183560 | + | 0.983009i | \(0.441238\pi\) |
−0.943090 | + | 0.332537i | \(0.892095\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −27.1294 | + | 15.6632i | −0.417375 | + | 0.240972i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 24.0870 | 0.359507 | 0.179753 | − | 0.983712i | \(-0.442470\pi\) | ||||
0.179753 | + | 0.983712i | \(0.442470\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.03023 | + | 0.594802i | 0.0145103 | + | 0.00837750i | 0.507238 | − | 0.861806i | \(-0.330667\pi\) |
−0.492727 | + | 0.870184i | \(0.664000\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −20.6395 | + | 35.7487i | −0.282733 | + | 0.489709i | −0.972057 | − | 0.234745i | \(-0.924574\pi\) |
0.689324 | + | 0.724454i | \(0.257908\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −137.725 | − | 79.5158i | −1.78864 | − | 1.03267i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.1846 | −0.154235 | −0.0771177 | − | 0.997022i | \(-0.524572\pi\) | ||||
−0.0771177 | + | 0.997022i | \(0.524572\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 124.538 | − | 71.9023i | 1.50046 | − | 0.866293i | 0.500463 | − | 0.865758i | \(-0.333163\pi\) |
1.00000 | 0.000535193i | \(-0.000170357\pi\) | ||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −185.558 | −2.18304 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −31.0467 | + | 17.9248i | −0.348839 | + | 0.201402i | −0.664174 | − | 0.747578i | \(-0.731217\pi\) |
0.315335 | + | 0.948981i | \(0.397883\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 20.8043 | + | 36.0340i | 0.228618 | + | 0.395978i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −118.360 | + | 7.33387i | −1.24590 | + | 0.0771986i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 86.6880 | 0.893691 | 0.446845 | − | 0.894611i | \(-0.352547\pi\) | ||||
0.446845 | + | 0.894611i | \(0.352547\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −120.418 | − | 69.5234i | −1.19226 | − | 0.688350i | −0.233440 | − | 0.972371i | \(-0.574998\pi\) |
−0.958818 | + | 0.284021i | \(0.908331\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −49.7978 | + | 86.2523i | −0.483474 | + | 0.837401i | −0.999820 | − | 0.0189791i | \(-0.993958\pi\) |
0.516346 | + | 0.856380i | \(0.327292\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 160.156i | − | 1.49679i | −0.663254 | − | 0.748394i | \(-0.730825\pi\) | ||
0.663254 | − | 0.748394i | \(-0.269175\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −25.5188 | + | 44.1999i | −0.234117 | + | 0.405503i | −0.959016 | − | 0.283352i | \(-0.908553\pi\) |
0.724898 | + | 0.688856i | \(0.241887\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 137.055 | + | 79.1287i | 1.21288 | + | 0.700254i | 0.963385 | − | 0.268123i | \(-0.0864033\pi\) |
0.249491 | + | 0.968377i | \(0.419737\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −32.9240 | − | 57.0261i | −0.286296 | − | 0.495879i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 246.463i | 2.07112i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 123.503 | − | 213.913i | 1.02068 | − | 1.76788i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 68.9341i | − | 0.551473i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −102.738 | − | 177.947i | −0.808958 | − | 1.40116i | −0.913586 | − | 0.406646i | \(-0.866698\pi\) |
0.104628 | − | 0.994511i | \(-0.466635\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −80.9155 | + | 46.7166i | −0.617676 | + | 0.356615i | −0.775963 | − | 0.630778i | \(-0.782736\pi\) |
0.158288 | + | 0.987393i | \(0.449403\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.74105 | + | 157.209i | 0.0732410 | + | 1.18202i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.71952 | − | 3.87952i | −0.0490476 | − | 0.0283176i | 0.475276 | − | 0.879837i | \(-0.342348\pi\) |
−0.524323 | + | 0.851519i | \(0.675682\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 68.3785 | 0.491932 | 0.245966 | − | 0.969278i | \(-0.420895\pi\) | ||||
0.245966 | + | 0.969278i | \(0.420895\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −83.3842 | + | 48.1419i | −0.583106 | + | 0.336656i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −185.850 | −1.28173 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 43.0650 | − | 24.8636i | 0.289027 | − | 0.166870i | −0.348476 | − | 0.937318i | \(-0.613301\pi\) |
0.637503 | + | 0.770448i | \(0.279967\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −105.562 | − | 182.839i | −0.699088 | − | 1.21086i | −0.968783 | − | 0.247910i | \(-0.920256\pi\) |
0.269695 | − | 0.962946i | \(-0.413077\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 36.9838i | − | 0.238605i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.28248 | + | 10.8816i | 0.0400158 | + | 0.0693094i | 0.885340 | − | 0.464945i | \(-0.153926\pi\) |
−0.845324 | + | 0.534254i | \(0.820593\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −75.7437 | + | 43.7306i | −0.470458 | + | 0.271619i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 56.3032 | 0.345418 | 0.172709 | − | 0.984973i | \(-0.444748\pi\) | ||||
0.172709 | + | 0.984973i | \(0.444748\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 184.027i | 1.10196i | 0.834520 | + | 0.550978i | \(0.185745\pi\) | ||||
−0.834520 | + | 0.550978i | \(0.814255\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −143.809 | −0.850939 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 245.490i | 1.41902i | 0.704697 | + | 0.709508i | \(0.251083\pi\) | ||||
−0.704697 | + | 0.709508i | \(0.748917\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 115.691 | 0.661090 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 135.043i | 0.754431i | 0.926126 | + | 0.377215i | \(0.123118\pi\) | ||||
−0.926126 | + | 0.377215i | \(0.876882\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.36155 | + | 7.55442i | 0.0240970 | + | 0.0417372i | 0.877822 | − | 0.478986i | \(-0.158996\pi\) |
−0.853725 | + | 0.520723i | \(0.825662\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −281.845 | + | 162.723i | −1.52349 | + | 0.879586i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −570.326 | −3.04987 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 190.729 | − | 110.118i | 0.998582 | − | 0.576531i | 0.0907535 | − | 0.995873i | \(-0.471072\pi\) |
0.907828 | + | 0.419342i | \(0.137739\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −128.964 | − | 223.372i | −0.668207 | − | 1.15737i | −0.978405 | − | 0.206696i | \(-0.933729\pi\) |
0.310199 | − | 0.950672i | \(-0.399604\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 193.499i | − | 0.982229i | −0.871095 | − | 0.491114i | \(-0.836590\pi\) | ||
0.871095 | − | 0.491114i | \(-0.163410\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 34.0099 | + | 58.9068i | 0.170904 | + | 0.296014i | 0.938736 | − | 0.344637i | \(-0.111998\pi\) |
−0.767832 | + | 0.640651i | \(0.778665\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 246.851i | 1.21602i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −146.601 | + | 253.921i | −0.715127 | + | 1.23864i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −363.788 | + | 22.5412i | −1.74061 | + | 0.107853i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.4900 | + | 28.5616i | 0.0781518 | + | 0.135363i | 0.902453 | − | 0.430789i | \(-0.141765\pi\) |
−0.824301 | + | 0.566152i | \(0.808431\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 326.633 | − | 188.582i | 1.51922 | − | 0.877123i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −49.1229 | −0.226373 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 129.227 | + | 74.6091i | 0.584737 | + | 0.337598i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −301.114 | −1.35029 | −0.675143 | − | 0.737687i | \(-0.735918\pi\) | ||||
−0.675143 | + | 0.737687i | \(0.735918\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −250.357 | + | 144.544i | −1.10289 | + | 0.636756i | −0.936979 | − | 0.349385i | \(-0.886391\pi\) |
−0.165914 | + | 0.986140i | \(0.553057\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −135.468 | + | 234.637i | −0.591563 | + | 1.02462i | 0.402459 | + | 0.915438i | \(0.368156\pi\) |
−0.994022 | + | 0.109179i | \(0.965178\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −37.9517 | − | 21.9115i | −0.162883 | − | 0.0940406i | 0.416343 | − | 0.909208i | \(-0.363312\pi\) |
−0.579226 | + | 0.815167i | \(0.696645\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −187.338 | −0.797183 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 290.122 | + | 167.502i | 1.21390 | + | 0.700845i | 0.963606 | − | 0.267326i | \(-0.0861400\pi\) |
0.250292 | + | 0.968170i | \(0.419473\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −84.7677 | + | 146.822i | −0.351733 | + | 0.609220i | −0.986553 | − | 0.163440i | \(-0.947741\pi\) |
0.634820 | + | 0.772660i | \(0.281074\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 123.110i | − | 0.502491i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 85.3774 | + | 42.4827i | 0.345657 | + | 0.171995i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −140.235 | + | 80.9650i | −0.558707 | + | 0.322570i | −0.752626 | − | 0.658448i | \(-0.771213\pi\) |
0.193919 | + | 0.981017i | \(0.437880\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −101.194 | − | 175.274i | −0.399978 | − | 0.692782i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 59.0684i | 0.229838i | 0.993375 | + | 0.114919i | \(0.0366609\pi\) | ||||
−0.993375 | + | 0.114919i | \(0.963339\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 216.134 | + | 374.355i | 0.834493 | + | 1.44538i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 177.086i | − | 0.673329i | −0.941625 | − | 0.336665i | \(-0.890701\pi\) | ||
0.941625 | − | 0.336665i | \(-0.109299\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 151.395 | − | 262.224i | 0.571302 | − | 0.989525i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 111.617 | + | 64.4419i | 0.414932 | + | 0.239561i | 0.692907 | − | 0.721027i | \(-0.256330\pi\) |
−0.277975 | + | 0.960588i | \(0.589663\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 43.8719 | − | 75.9883i | 0.161889 | − | 0.280400i | −0.773657 | − | 0.633604i | \(-0.781575\pi\) |
0.935546 | + | 0.353205i | \(0.114908\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 267.713i | 0.973501i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −120.322 | − | 208.404i | −0.434375 | − | 0.752360i | 0.562869 | − | 0.826546i | \(-0.309698\pi\) |
−0.997244 | + | 0.0741858i | \(0.976364\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −72.5547 | − | 41.8895i | −0.258202 | − | 0.149073i | 0.365312 | − | 0.930885i | \(-0.380962\pi\) |
−0.623514 | + | 0.781812i | \(0.714296\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −185.400 | − | 321.122i | −0.655123 | − | 1.13471i | −0.981863 | − | 0.189592i | \(-0.939284\pi\) |
0.326740 | − | 0.945114i | \(-0.394050\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 337.264 | + | 194.720i | 1.17514 | + | 0.678466i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 297.439 | + | 515.180i | 1.02920 | + | 1.78263i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 119.643 | + | 69.0758i | 0.408337 | + | 0.235754i | 0.690075 | − | 0.723738i | \(-0.257577\pi\) |
−0.281738 | + | 0.959491i | \(0.590911\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 299.322 | − | 518.441i | 1.01465 | − | 1.75743i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 52.9523i | 0.177098i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −250.479 | − | 433.843i | −0.832157 | − | 1.44134i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 578.347i | − | 1.89622i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 231.124 | − | 400.319i | 0.752848 | − | 1.30397i | −0.193589 | − | 0.981083i | \(-0.562013\pi\) |
0.946437 | − | 0.322889i | \(-0.104654\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 336.644 | + | 194.362i | 1.08246 | + | 0.624957i | 0.931558 | − | 0.363592i | \(-0.118450\pi\) |
0.150899 | + | 0.988549i | \(0.451783\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 282.706 | − | 489.661i | 0.903213 | − | 1.56441i | 0.0799157 | − | 0.996802i | \(-0.474535\pi\) |
0.823298 | − | 0.567610i | \(-0.192132\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.1334 | + | 5.85051i | 0.0319665 | + | 0.0184559i | 0.515898 | − | 0.856650i | \(-0.327458\pi\) |
−0.483932 | + | 0.875106i | \(0.660792\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −571.224 | −1.79067 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 312.149 | + | 470.790i | 0.966405 | + | 1.45755i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 35.0217 | − | 60.6594i | 0.107759 | − | 0.186644i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 248.828i | 0.756315i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −36.1568 | − | 62.6255i | −0.109235 | − | 0.189201i | 0.806225 | − | 0.591608i | \(-0.201507\pi\) |
−0.915461 | + | 0.402408i | \(0.868173\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −130.196 | + | 75.1685i | −0.388644 | + | 0.224383i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 265.547 | + | 459.941i | 0.787973 | + | 1.36481i | 0.927207 | + | 0.374550i | \(0.122203\pi\) |
−0.139233 | + | 0.990260i | \(0.544464\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 113.672i | − | 0.333350i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 242.693 | 0.707561 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −274.157 | + | 158.284i | −0.790077 | + | 0.456151i | −0.839990 | − | 0.542602i | \(-0.817439\pi\) |
0.0499127 | + | 0.998754i | \(0.484106\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 331.633 | + | 574.406i | 0.950239 | + | 1.64586i | 0.744906 | + | 0.667169i | \(0.232494\pi\) |
0.205332 | + | 0.978692i | \(0.434172\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 396.651 | − | 229.006i | 1.12366 | − | 0.648743i | 0.181325 | − | 0.983423i | \(-0.441962\pi\) |
0.942332 | + | 0.334680i | \(0.108628\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.42483 | −0.0209150 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −116.361 | − | 67.1811i | −0.324125 | − | 0.187134i | 0.329104 | − | 0.944294i | \(-0.393253\pi\) |
−0.653230 | + | 0.757160i | \(0.726587\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 217.714 | + | 287.961i | 0.603087 | + | 0.797676i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 257.640i | − | 0.705864i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 49.6894 | − | 86.0646i | 0.135393 | − | 0.234508i | −0.790354 | − | 0.612650i | \(-0.790103\pi\) |
0.925748 | + | 0.378142i | \(0.123437\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −348.293 | − | 201.087i | −0.938796 | − | 0.542014i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 185.179 | − | 320.739i | 0.496457 | − | 0.859889i | −0.503534 | − | 0.863975i | \(-0.667967\pi\) |
0.999992 | + | 0.00408598i | \(0.00130061\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 129.430 | + | 74.7265i | 0.343316 | + | 0.198214i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −480.220 | −1.26707 | −0.633536 | − | 0.773713i | \(-0.718397\pi\) | ||||
−0.633536 | + | 0.773713i | \(0.718397\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −47.8137 | + | 27.6053i | −0.124840 | + | 0.0720764i | −0.561120 | − | 0.827735i | \(-0.689629\pi\) |
0.436280 | + | 0.899811i | \(0.356296\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 992.584 | 2.57814 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −247.457 | − | 142.869i | −0.636136 | − | 0.367273i | 0.146988 | − | 0.989138i | \(-0.453042\pi\) |
−0.783125 | + | 0.621865i | \(0.786375\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −156.829 | + | 271.635i | −0.401096 | + | 0.694719i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 65.8605 | − | 38.0246i | 0.166736 | − | 0.0962648i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 189.291 | − | 327.861i | 0.476802 | − | 0.825846i | −0.522844 | − | 0.852428i | \(-0.675129\pi\) |
0.999647 | + | 0.0265823i | \(0.00846239\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −142.320 | + | 82.1683i | −0.354912 | + | 0.204909i | −0.666847 | − | 0.745195i | \(-0.732356\pi\) |
0.311935 | + | 0.950104i | \(0.399023\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −14.8704 | + | 25.7563i | −0.0368993 | + | 0.0639115i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −866.271 | + | 500.142i | −2.12843 | + | 1.22885i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 211.156 | 0.516273 | 0.258136 | − | 0.966108i | \(-0.416892\pi\) | ||||
0.258136 | + | 0.966108i | \(0.416892\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −688.607 | − | 397.568i | −1.66733 | − | 0.962634i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −448.773 | + | 777.297i | −1.08138 | + | 1.87301i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −539.656 | − | 311.571i | −1.28796 | − | 0.743606i | −0.309672 | − | 0.950843i | \(-0.600219\pi\) |
−0.978291 | + | 0.207238i | \(0.933553\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 224.827 | 0.534032 | 0.267016 | − | 0.963692i | \(-0.413962\pi\) | ||||
0.267016 | + | 0.963692i | \(0.413962\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 359.310 | − | 207.447i | 0.845434 | − | 0.488112i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −768.177 | −1.79901 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 475.176 | − | 274.343i | 1.10250 | − | 0.636527i | 0.165621 | − | 0.986189i | \(-0.447037\pi\) |
0.936876 | + | 0.349663i | \(0.113704\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 78.5854 | + | 136.114i | 0.181491 | + | 0.314351i | 0.942388 | − | 0.334521i | \(-0.108574\pi\) |
−0.760898 | + | 0.648872i | \(0.775241\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −89.2988 | + | 179.464i | −0.204345 | + | 0.410672i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −210.141 | −0.478682 | −0.239341 | − | 0.970936i | \(-0.576931\pi\) | ||||
−0.239341 | + | 0.970936i | \(0.576931\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −221.312 | − | 127.774i | −0.499575 | − | 0.288430i | 0.228963 | − | 0.973435i | \(-0.426467\pi\) |
−0.728538 | + | 0.685005i | \(0.759800\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 111.876 | − | 193.776i | 0.251408 | − | 0.435451i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 499.573i | − | 1.11264i | −0.830970 | − | 0.556318i | \(-0.812214\pi\) | ||
0.830970 | − | 0.556318i | \(-0.187786\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −450.589 | + | 780.443i | −0.999089 | + | 1.73047i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −224.904 | − | 129.848i | −0.494294 | − | 0.285381i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −398.855 | − | 690.836i | −0.872767 | − | 1.51168i | −0.859123 | − | 0.511770i | \(-0.828990\pi\) |
−0.0136444 | − | 0.999907i | \(-0.504343\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 52.9853i | 0.114936i | 0.998347 | + | 0.0574678i | \(0.0183026\pi\) | ||||
−0.998347 | + | 0.0574678i | \(0.981697\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −95.1208 | + | 164.754i | −0.205445 | + | 0.355840i | −0.950274 | − | 0.311414i | \(-0.899197\pi\) |
0.744830 | + | 0.667255i | \(0.232531\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 316.369i | − | 0.677449i | −0.940886 | − | 0.338725i | \(-0.890004\pi\) | ||
0.940886 | − | 0.338725i | \(-0.109996\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 99.8409 | + | 172.929i | 0.212880 | + | 0.368719i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1003.93 | − | 579.619i | 2.12247 | − | 1.22541i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 220.990 | − | 146.524i | 0.465242 | − | 0.308471i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −380.884 | − | 219.904i | −0.795166 | − | 0.459089i | 0.0466123 | − | 0.998913i | \(-0.485157\pi\) |
−0.841778 | + | 0.539824i | \(0.818491\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 261.711 | 0.544098 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −468.569 | + | 270.528i | −0.966121 | + | 0.557790i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 182.917 | 0.375600 | 0.187800 | − | 0.982207i | \(-0.439864\pi\) | ||||
0.187800 | + | 0.982207i | \(0.439864\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −399.817 | + | 230.834i | −0.814291 | + | 0.470131i | −0.848444 | − | 0.529286i | \(-0.822460\pi\) |
0.0341528 | + | 0.999417i | \(0.489127\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 442.635 | + | 766.665i | 0.897839 | + | 1.55510i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.86186i | 0.0198428i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 138.657 | + | 240.161i | 0.277870 | + | 0.481285i | 0.970855 | − | 0.239667i | \(-0.0770383\pi\) |
−0.692985 | + | 0.720952i | \(0.743705\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 735.341 | − | 424.549i | 1.46191 | − | 0.844034i | 0.462810 | − | 0.886458i | \(-0.346841\pi\) |
0.999100 | + | 0.0424236i | \(0.0135079\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 867.850 | 1.71851 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 66.3025i | 0.130260i | 0.997877 | + | 0.0651301i | \(0.0207462\pi\) | ||||
−0.997877 | + | 0.0651301i | \(0.979254\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −342.205 | −0.669677 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 621.618i | − | 1.20703i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −575.797 | −1.11373 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 92.5065i | 0.177556i | 0.996051 | + | 0.0887778i | \(0.0282961\pi\) | ||||
−0.996051 | + | 0.0887778i | \(0.971704\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 52.7222 | + | 91.3175i | 0.100807 | + | 0.174603i | 0.912017 | − | 0.410151i | \(-0.134524\pi\) |
−0.811210 | + | 0.584755i | \(0.801191\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −152.565 | + | 88.0833i | −0.289497 | + | 0.167141i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 417.694 | 0.789592 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 204.193 | − | 117.891i | 0.383100 | − | 0.221183i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 499.802 | + | 865.683i | 0.934209 | + | 1.61810i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 378.388i | − | 0.702019i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.28202 | − | 10.8808i | −0.0116119 | − | 0.0201124i | 0.860161 | − | 0.510022i | \(-0.170363\pi\) |
−0.871773 | + | 0.489910i | \(0.837030\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 318.547i | − | 0.584491i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 48.3736 | − | 83.7856i | 0.0884344 | − | 0.153173i | −0.818415 | − | 0.574627i | \(-0.805147\pi\) |
0.906850 | + | 0.421455i | \(0.138480\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 312.640 | + | 471.531i | 0.567405 | + | 0.855773i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −50.5053 | − | 87.4778i | −0.0913297 | − | 0.158188i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 429.405 | − | 247.917i | 0.770925 | − | 0.445094i | −0.0622792 | − | 0.998059i | \(-0.519837\pi\) |
0.833205 | + | 0.552965i | \(0.186504\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −303.299 | −0.542574 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −707.636 | − | 408.554i | −1.25690 | − | 0.725673i | −0.284431 | − | 0.958697i | \(-0.591805\pi\) |
−0.972471 | + | 0.233024i | \(0.925138\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −987.752 | −1.74823 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −369.359 | + | 213.249i | −0.649137 | + | 0.374779i | −0.788126 | − | 0.615515i | \(-0.788948\pi\) |
0.138988 | + | 0.990294i | \(0.455615\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 86.9476 | − | 150.598i | 0.152273 | − | 0.263744i | −0.779790 | − | 0.626041i | \(-0.784674\pi\) |
0.932063 | + | 0.362297i | \(0.118008\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 127.506 | + | 73.6158i | 0.221750 | + | 0.128028i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −291.789 | −0.505700 | −0.252850 | − | 0.967505i | \(-0.581368\pi\) | ||||
−0.252850 | + | 0.967505i | \(0.581368\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1032.43 | + | 596.073i | 1.77698 | + | 1.02594i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 465.324 | − | 805.965i | 0.798154 | − | 1.38244i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 203.125i | − | 0.346040i | −0.984918 | − | 0.173020i | \(-0.944647\pi\) | ||
0.984918 | − | 0.173020i | \(-0.0553525\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −93.8336 | + | 62.2147i | −0.159310 | + | 0.105628i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 256.281 | − | 147.964i | 0.432177 | − | 0.249517i | −0.268097 | − | 0.963392i | \(-0.586395\pi\) |
0.700274 | + | 0.713875i | \(0.253061\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −769.142 | − | 1332.19i | −1.29268 | − | 2.23898i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1082.64i | 1.80741i | 0.428160 | + | 0.903703i | \(0.359162\pi\) | ||||
−0.428160 | + | 0.903703i | \(0.640838\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 524.803 | + | 908.986i | 0.873217 | + | 1.51246i | 0.858650 | + | 0.512563i | \(0.171304\pi\) |
0.0145672 | + | 0.999894i | \(0.495363\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1541.67i | 2.54821i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 177.821 | − | 307.995i | 0.292951 | − | 0.507405i | −0.681556 | − | 0.731766i | \(-0.738696\pi\) |
0.974506 | + | 0.224361i | \(0.0720295\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 130.466 | + | 75.3248i | 0.213529 | + | 0.123281i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −279.541 | + | 484.179i | −0.456021 | + | 0.789852i | −0.998746 | − | 0.0500583i | \(-0.984059\pi\) |
0.542725 | + | 0.839911i | \(0.317393\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 393.300i | − | 0.637439i | −0.947849 | − | 0.318719i | \(-0.896747\pi\) | ||
0.947849 | − | 0.318719i | \(-0.103253\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 315.129 | + | 545.820i | 0.509094 | + | 0.881777i | 0.999945 | + | 0.0105328i | \(0.00335277\pi\) |
−0.490851 | + | 0.871244i | \(0.663314\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −257.378 | − | 148.597i | −0.413127 | − | 0.238519i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 389.566 | + | 674.748i | 0.623305 | + | 1.07960i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1342.53 | + | 775.108i | 2.13438 | + | 1.23229i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −436.567 | − | 756.155i | −0.691865 | − | 1.19834i | −0.971226 | − | 0.238159i | \(-0.923456\pi\) |
0.279362 | − | 0.960186i | \(-0.409877\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1110.64 | + | 641.230i | 1.74904 | + | 1.00981i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −49.5001 | + | 85.7367i | −0.0777082 | + | 0.134594i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 1027.74i | − | 1.60335i | −0.597763 | − | 0.801673i | \(-0.703943\pi\) | ||
0.597763 | − | 0.801673i | \(-0.296057\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 237.714 | + | 411.733i | 0.369695 | + | 0.640331i | 0.989518 | − | 0.144411i | \(-0.0461288\pi\) |
−0.619823 | + | 0.784742i | \(0.712795\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 80.3000i | 0.124111i | 0.998073 | + | 0.0620557i | \(0.0197656\pi\) | ||||
−0.998073 | + | 0.0620557i | \(0.980234\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 919.987 | − | 1593.46i | 1.41755 | − | 2.45526i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 666.603 | + | 384.863i | 1.02083 | + | 0.589377i | 0.914345 | − | 0.404937i | \(-0.132706\pi\) |
0.106487 | + | 0.994314i | \(0.466040\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 291.578 | − | 505.028i | 0.445157 | − | 0.771035i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −370.850 | − | 214.111i | −0.562747 | − | 0.324902i | 0.191500 | − | 0.981493i | \(-0.438665\pi\) |
−0.754247 | + | 0.656590i | \(0.771998\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 996.915 | 1.50819 | 0.754096 | − | 0.656764i | \(-0.228075\pi\) | ||||
0.754096 | + | 0.656764i | \(0.228075\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −543.257 | − | 819.353i | −0.816928 | − | 1.23211i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −157.075 | + | 272.063i | −0.235495 | + | 0.407890i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 1777.59i | − | 2.64917i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 431.710 | + | 747.743i | 0.641470 | + | 1.11106i | 0.985105 | + | 0.171956i | \(0.0550086\pi\) |
−0.343634 | + | 0.939104i | \(0.611658\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 914.184 | − | 527.804i | 1.35035 | − | 0.779622i | 0.362048 | − | 0.932160i | \(-0.382078\pi\) |
0.988298 | + | 0.152537i | \(0.0487445\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 359.323 | + | 622.366i | 0.529195 | + | 0.916592i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 828.737i | 1.21338i | 0.794939 | + | 0.606689i | \(0.207503\pi\) | ||||
−0.794939 | + | 0.606689i | \(0.792497\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 48.4274 | 0.0706970 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −210.870 | + | 121.746i | −0.306052 | + | 0.176699i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 118.397 | + | 205.070i | 0.171342 | + | 0.296773i | 0.938889 | − | 0.344219i | \(-0.111856\pi\) |
−0.767547 | + | 0.640993i | \(0.778523\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −369.602 | + | 213.390i | −0.531801 | + | 0.307036i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1396.62 | 2.00377 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 664.672 | + | 383.748i | 0.948177 | + | 0.547430i | 0.892514 | − | 0.451020i | \(-0.148940\pi\) |
0.0556627 | + | 0.998450i | \(0.482273\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 886.979 | + | 441.349i | 1.26171 | + | 0.627808i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 1152.70i | − | 1.63041i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 498.446 | − | 863.333i | 0.703026 | − | 1.21768i | −0.264373 | − | 0.964421i | \(-0.585165\pi\) |
0.967399 | − | 0.253257i | \(-0.0815017\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −54.1399 | − | 31.2577i | −0.0759326 | − | 0.0438397i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 300.474 | − | 520.436i | 0.420243 | − | 0.727883i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −858.980 | − | 495.932i | −1.19469 | − | 0.689753i | −0.235321 | − | 0.971918i | \(-0.575614\pi\) |
−0.959366 | + | 0.282165i | \(0.908947\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −825.651 | −1.14515 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 359.875 | − | 207.774i | 0.496379 | − | 0.286585i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −226.650 | −0.311761 | −0.155881 | − | 0.987776i | \(-0.549822\pi\) | ||||
−0.155881 | + | 0.987776i | \(0.549822\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1555.87 | − | 898.280i | −2.12841 | − | 1.22884i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −394.329 | + | 682.998i | −0.537966 | + | 0.931785i | 0.461047 | + | 0.887376i | \(0.347474\pi\) |
−0.999013 | + | 0.0444091i | \(0.985859\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −400.166 | + | 231.036i | −0.542965 | + | 0.313481i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 83.0957 | − | 143.926i | 0.112443 | − | 0.194758i | −0.804311 | − | 0.594208i | \(-0.797466\pi\) |
0.916755 | + | 0.399450i | \(0.130799\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 838.921 | − | 484.351i | 1.12910 | − | 0.651886i | 0.185391 | − | 0.982665i | \(-0.440645\pi\) |
0.943708 | + | 0.330779i | \(0.107311\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −155.184 | + | 268.787i | −0.208301 | + | 0.360788i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1149.82 | − | 663.851i | 1.53515 | − | 0.886316i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1252.30 | 1.66750 | 0.833752 | − | 0.552139i | \(-0.186188\pi\) | ||||
0.833752 | + | 0.552139i | \(0.186188\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1141.18 | + | 658.859i | 1.51149 | + | 0.872661i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 592.866 | − | 1026.87i | 0.783179 | − | 1.35651i | −0.146902 | − | 0.989151i | \(-0.546930\pi\) |
0.930081 | − | 0.367355i | \(-0.119736\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 643.588 | + | 371.576i | 0.845714 | + | 0.488273i | 0.859202 | − | 0.511636i | \(-0.170960\pi\) |
−0.0134887 | + | 0.999909i | \(0.504294\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −423.104 | −0.554526 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −416.909 | + | 240.702i | −0.543558 | + | 0.313823i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −962.692 | −1.25187 | −0.625937 | − | 0.779873i | \(-0.715283\pi\) | ||||
−0.625937 | + | 0.779873i | \(0.715283\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −34.6745 | + | 20.0193i | −0.0448570 | + | 0.0258982i | −0.522261 | − | 0.852786i | \(-0.674911\pi\) |
0.477404 | + | 0.878684i | \(0.341578\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 41.3466 | + | 71.6144i | 0.0533504 | + | 0.0924057i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 890.851 | − | 55.1992i | 1.14358 | − | 0.0708590i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −22.8207 | −0.0292199 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −67.9166 | − | 39.2117i | −0.0865179 | − | 0.0499511i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 718.501 | − | 1244.48i | 0.912961 | − | 1.58130i | 0.103102 | − | 0.994671i | \(-0.467123\pi\) |
0.809859 | − | 0.586625i | \(-0.199544\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1311.96i | 1.65861i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −232.542 | + | 402.774i | −0.293243 | + | 0.507912i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 772.318 | + | 445.898i | 0.969031 | + | 0.559470i | 0.898941 | − | 0.438070i | \(-0.144338\pi\) |
0.0700902 | + | 0.997541i | \(0.477671\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 446.178 | + | 772.804i | 0.558421 | + | 0.967214i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 791.876i | − | 0.986147i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 272.941 | − | 472.748i | 0.339058 | − | 0.587265i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 14.9006i | − | 0.0184186i | −0.999958 | − | 0.00920928i | \(-0.997069\pi\) | ||
0.999958 | − | 0.00920928i | \(-0.00293145\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 741.642 | + | 1284.56i | 0.914478 | + | 1.58392i | 0.807663 | + | 0.589644i | \(0.200732\pi\) |
0.106815 | + | 0.994279i | \(0.465935\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −304.332 | + | 175.706i | −0.373413 | + | 0.215590i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1027.93 | − | 511.484i | −1.25817 | − | 0.626051i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1155.51 | − | 667.132i | −1.40744 | − | 0.812585i | −0.412298 | − | 0.911049i | \(-0.635274\pi\) |
−0.995141 | + | 0.0984639i | \(0.968607\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −940.461 | −1.14272 | −0.571362 | − | 0.820698i | \(-0.693585\pi\) | ||||
−0.571362 | + | 0.820698i | \(0.693585\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1348.77 | + | 778.714i | −1.63092 | + | 0.941613i | −0.647112 | + | 0.762395i | \(0.724024\pi\) |
−0.983809 | + | 0.179218i | \(0.942643\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −215.811 | −0.260327 | −0.130163 | − | 0.991493i | \(-0.541550\pi\) | ||||
−0.130163 | + | 0.991493i | \(0.541550\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −507.852 | + | 293.208i | −0.609666 | + | 0.351991i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −574.294 | − | 994.707i | −0.687778 | − | 1.19127i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 304.380i | 0.362789i | 0.983410 | + | 0.181394i | \(0.0580610\pi\) | ||||
−0.983410 | + | 0.181394i | \(0.941939\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.8311 | + | 39.5446i | 0.0271476 | + | 0.0470209i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 777.319 | − | 448.785i | 0.919904 | − | 0.531107i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2047.68 | 2.41757 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 550.117i | 0.646437i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1090.96 | −1.27897 | −0.639487 | − | 0.768802i | \(-0.720853\pi\) | ||||
−0.639487 | + | 0.768802i | \(0.720853\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 1057.91i | − | 1.23443i | −0.786793 | − | 0.617217i | \(-0.788260\pi\) | ||
0.786793 | − | 0.617217i | \(-0.211740\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 658.540 | 0.766635 | 0.383318 | − | 0.923617i | \(-0.374781\pi\) | ||||
0.383318 | + | 0.923617i | \(0.374781\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 611.208i | − | 0.708236i | −0.935201 | − | 0.354118i | \(-0.884781\pi\) | ||
0.935201 | − | 0.354118i | \(-0.115219\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −766.103 | − | 1326.93i | −0.885668 | − | 1.53402i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 202.427 | − | 116.871i | 0.232943 | − | 0.134489i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 120.895 | 0.138800 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 494.904 | − | 285.733i | 0.565605 | − | 0.326552i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 66.2995 | + | 114.834i | 0.0755980 | + | 0.130940i | 0.901346 | − | 0.433099i | \(-0.142580\pi\) |
−0.825748 | + | 0.564039i | \(0.809247\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 75.4585i | − | 0.0856510i | −0.999083 | − | 0.0428255i | \(-0.986364\pi\) | ||
0.999083 | − | 0.0428255i | \(-0.0136360\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −374.686 | − | 648.975i | −0.424333 | − | 0.734966i | 0.572025 | − | 0.820236i | \(-0.306158\pi\) |
−0.996358 | + | 0.0852698i | \(0.972825\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1377.75i | 1.55327i | 0.629949 | + | 0.776636i | \(0.283076\pi\) | ||||
−0.629949 | + | 0.776636i | \(0.716924\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 851.699 | − | 1475.19i | 0.958042 | − | 1.65938i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 315.143 | + | 475.306i | 0.352904 | + | 0.532258i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −421.431 | − | 729.940i | −0.470872 | − | 0.815575i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −152.805 | + | 88.2220i | −0.169972 | + | 0.0981334i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1442.30 | −1.60077 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −47.1504 | − | 27.2223i | −0.0520999 | − | 0.0300799i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −564.480 | −0.622359 | −0.311179 | − | 0.950351i | \(-0.600724\pi\) | ||||
−0.311179 | + | 0.950351i | \(0.600724\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −100.741 | + | 58.1627i | −0.110583 | + | 0.0638450i | −0.554271 | − | 0.832336i | \(-0.687003\pi\) |
0.443689 | + | 0.896181i | \(0.353670\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1379.34 | + | 2389.08i | −1.51077 | + | 2.61674i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −670.792 | − | 387.282i | −0.731507 | − | 0.422336i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −806.769 | −0.877877 | −0.438939 | − | 0.898517i | \(-0.644645\pi\) | ||||
−0.438939 | + | 0.898517i | \(0.644645\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.17082 | + | 2.98537i | 0.00560218 | + | 0.00323442i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 363.838 | − | 630.186i | 0.393338 | − | 0.681282i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 403.812i | − | 0.434674i | −0.976097 | − | 0.217337i | \(-0.930263\pi\) | ||
0.976097 | − | 0.217337i | \(-0.0697371\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −312.350 | + | 207.098i | −0.335499 | + | 0.222447i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3082.75 | − | 1779.82i | 3.29705 | − | 1.90356i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 119.261 | + | 206.566i | 0.127279 | + | 0.220454i | 0.922622 | − | 0.385706i | \(-0.126042\pi\) |
−0.795342 | + | 0.606161i | \(0.792709\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 773.528i | 0.822027i | 0.911629 | + | 0.411014i | \(0.134825\pi\) | ||||
−0.911629 | + | 0.411014i | \(0.865175\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 247.807 | + | 429.214i | 0.262785 | + | 0.455157i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 801.869i | 0.846747i | 0.905955 | + | 0.423373i | \(0.139154\pi\) | ||||
−0.905955 | + | 0.423373i | \(0.860846\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −103.592 | + | 179.426i | −0.109159 | + | 0.189069i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1027.59 | + | 593.282i | 1.07827 | + | 0.622542i | 0.930430 | − | 0.366469i | \(-0.119433\pi\) |
0.147843 | + | 0.989011i | \(0.452767\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −687.290 | + | 1190.42i | −0.719676 | + | 1.24651i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 64.3227i | − | 0.0670726i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 462.944 | + | 801.843i | 0.481732 | + | 0.834384i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1394.16 | + | 804.918i | 1.44472 | + | 0.834112i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 546.727 | + | 946.959i | 0.565385 | + | 0.979275i | 0.997014 | + | 0.0772241i | \(0.0246057\pi\) |
−0.431629 | + | 0.902051i | \(0.642061\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −184.215 | − | 106.357i | −0.189717 | − | 0.109533i | 0.402133 | − | 0.915581i | \(-0.368269\pi\) |
−0.591850 | + | 0.806048i | \(0.701602\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 283.430 | + | 490.915i | 0.291295 | + | 0.504538i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −639.024 | − | 368.941i | −0.654068 | − | 0.377626i | 0.135945 | − | 0.990716i | \(-0.456593\pi\) |
−0.790013 | + | 0.613090i | \(0.789926\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 343.860 | − | 595.583i | 0.351236 | − | 0.608359i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1508.76i | 1.53485i | 0.641136 | + | 0.767427i | \(0.278464\pi\) | ||||
−0.641136 | + | 0.767427i | \(0.721536\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 603.855 | + | 1045.91i | 0.613051 | + | 1.06183i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 637.536i | − | 0.644627i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −751.118 | + | 1300.97i | −0.757939 | + | 1.31279i | 0.185960 | + | 0.982557i | \(0.440460\pi\) |
−0.943900 | + | 0.330232i | \(0.892873\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −367.662 | − | 212.270i | −0.369510 | − | 0.213337i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −269.965 | + | 467.594i | −0.270778 | + | 0.469001i | −0.969061 | − | 0.246821i | \(-0.920614\pi\) |
0.698283 | + | 0.715821i | \(0.253948\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 2052.3.be.a.125.8 | 80 | ||
3.2 | odd | 2 | 684.3.be.a.581.32 | yes | 80 | ||
9.2 | odd | 6 | 2052.3.m.a.1493.33 | 80 | |||
9.7 | even | 3 | 684.3.m.a.353.4 | ✓ | 80 | ||
19.7 | even | 3 | 2052.3.m.a.881.8 | 80 | |||
57.26 | odd | 6 | 684.3.m.a.653.4 | yes | 80 | ||
171.7 | even | 3 | 684.3.be.a.425.32 | yes | 80 | ||
171.83 | odd | 6 | inner | 2052.3.be.a.197.8 | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
684.3.m.a.353.4 | ✓ | 80 | 9.7 | even | 3 | ||
684.3.m.a.653.4 | yes | 80 | 57.26 | odd | 6 | ||
684.3.be.a.425.32 | yes | 80 | 171.7 | even | 3 | ||
684.3.be.a.581.32 | yes | 80 | 3.2 | odd | 2 | ||
2052.3.m.a.881.8 | 80 | 19.7 | even | 3 | |||
2052.3.m.a.1493.33 | 80 | 9.2 | odd | 6 | |||
2052.3.be.a.125.8 | 80 | 1.1 | even | 1 | trivial | ||
2052.3.be.a.197.8 | 80 | 171.83 | odd | 6 | inner |