Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1089,3,Mod(604,1089)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1089, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1089.604");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1089 = 3^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1089.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(29.6731007888\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 3 x^{14} - 4 x^{13} + 77 x^{12} + 88 x^{11} - 577 x^{10} + 578 x^{9} + 1520 x^{8} + \cdots + 83521 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8}\cdot 11^{4} \) |
Twist minimal: | no (minimal twist has level 33) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 604.5 | ||
Root | \(1.60675 - 1.36085i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1089.604 |
Dual form | 1089.3.c.m.604.12 |
$q$-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 \(\left(\mathbb{Z}/1089\mathbb{Z}\right)^\times\).
\(n\) | \(244\) | \(848\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 2.21517i | − 1.10758i | −0.832655 | − | 0.553792i | \(-0.813180\pi\) | ||||
0.832655 | − | 0.553792i | \(-0.186820\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.906963 | −0.226741 | ||||||||
\(5\) | −8.69502 | −1.73900 | −0.869502 | − | 0.493929i | \(-0.835560\pi\) | ||||
−0.869502 | + | 0.493929i | \(0.835560\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 6.67189i | − 0.953127i | −0.879140 | − | 0.476564i | \(-0.841882\pi\) | ||||
0.879140 | − | 0.476564i | \(-0.158118\pi\) | |||||||
\(8\) | − 6.85159i | − 0.856449i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 19.2609i | 1.92609i | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 11.1547i | − 0.858051i | −0.903292 | − | 0.429026i | \(-0.858857\pi\) | ||||
0.903292 | − | 0.429026i | \(-0.141143\pi\) | |||||||
\(14\) | −14.7794 | −1.05567 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −18.8053 | −1.17533 | ||||||||
\(17\) | − 7.82687i | − 0.460404i | −0.973143 | − | 0.230202i | \(-0.926061\pi\) | ||||
0.973143 | − | 0.230202i | \(-0.0739387\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 8.44217i | − 0.444325i | −0.975010 | − | 0.222162i | \(-0.928688\pi\) | ||||
0.975010 | − | 0.222162i | \(-0.0713115\pi\) | |||||||
\(20\) | 7.88606 | 0.394303 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −9.30611 | −0.404613 | −0.202307 | − | 0.979322i | \(-0.564844\pi\) | ||||
−0.202307 | + | 0.979322i | \(0.564844\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 50.6034 | 2.02414 | ||||||||
\(26\) | −24.7094 | −0.950363 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 6.05116i | 0.216113i | ||||||||
\(29\) | 7.17852i | 0.247535i | 0.992311 | + | 0.123768i | \(0.0394978\pi\) | ||||
−0.992311 | + | 0.123768i | \(0.960502\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −27.4243 | −0.884655 | −0.442328 | − | 0.896854i | \(-0.645847\pi\) | ||||
−0.442328 | + | 0.896854i | \(0.645847\pi\) | |||||||
\(32\) | 14.2504i | 0.445326i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −17.3378 | −0.509936 | ||||||||
\(35\) | 58.0122i | 1.65749i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −52.9416 | −1.43085 | −0.715427 | − | 0.698688i | \(-0.753768\pi\) | ||||
−0.715427 | + | 0.698688i | \(0.753768\pi\) | |||||||
\(38\) | −18.7008 | −0.492127 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 59.5747i | 1.48937i | ||||||||
\(41\) | − 47.8535i | − 1.16716i | −0.812056 | − | 0.583580i | \(-0.801652\pi\) | ||||
0.812056 | − | 0.583580i | \(-0.198348\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 45.8381i | 1.06600i | 0.846114 | + | 0.533002i | \(0.178936\pi\) | ||||
−0.846114 | + | 0.533002i | \(0.821064\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 20.6146i | 0.448143i | ||||||||
\(47\) | 16.0778 | 0.342082 | 0.171041 | − | 0.985264i | \(-0.445287\pi\) | ||||
0.171041 | + | 0.985264i | \(0.445287\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.48587 | 0.0915484 | ||||||||
\(50\) | − 112.095i | − 2.24190i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 10.1169i | 0.194555i | ||||||||
\(53\) | 54.9322 | 1.03646 | 0.518228 | − | 0.855243i | \(-0.326592\pi\) | ||||
0.518228 | + | 0.855243i | \(0.326592\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −45.7131 | −0.816305 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 15.9016 | 0.274166 | ||||||||
\(59\) | 71.2113 | 1.20697 | 0.603486 | − | 0.797374i | \(-0.293778\pi\) | ||||
0.603486 | + | 0.797374i | \(0.293778\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.30131i | 0.0213330i | 0.999943 | + | 0.0106665i | \(0.00339531\pi\) | ||||
−0.999943 | + | 0.0106665i | \(0.996605\pi\) | |||||||
\(62\) | 60.7494i | 0.979830i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −43.6540 | −0.682094 | ||||||||
\(65\) | 96.9901i | 1.49216i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −28.9406 | −0.431949 | −0.215975 | − | 0.976399i | \(-0.569293\pi\) | ||||
−0.215975 | + | 0.976399i | \(0.569293\pi\) | |||||||
\(68\) | 7.09868i | 0.104392i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 128.507 | 1.83581 | ||||||||
\(71\) | −22.0521 | −0.310593 | −0.155296 | − | 0.987868i | \(-0.549633\pi\) | ||||
−0.155296 | + | 0.987868i | \(0.549633\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 125.227i | 1.71544i | 0.514120 | + | 0.857718i | \(0.328119\pi\) | ||||
−0.514120 | + | 0.857718i | \(0.671881\pi\) | |||||||
\(74\) | 117.274i | 1.58479i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.65674i | 0.100747i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 42.8764i | 0.542739i | 0.962475 | + | 0.271370i | \(0.0874765\pi\) | ||||
−0.962475 | + | 0.271370i | \(0.912523\pi\) | |||||||
\(80\) | 163.512 | 2.04390 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −106.004 | −1.29273 | ||||||||
\(83\) | 133.214i | 1.60499i | 0.596661 | + | 0.802493i | \(0.296494\pi\) | ||||
−0.596661 | + | 0.802493i | \(0.703506\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 68.0548i | 0.800645i | ||||||||
\(86\) | 101.539 | 1.18069 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.48441 | 0.106566 | 0.0532832 | − | 0.998579i | \(-0.483031\pi\) | ||||
0.0532832 | + | 0.998579i | \(0.483031\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −74.4227 | −0.817832 | ||||||||
\(92\) | 8.44030 | 0.0917423 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − 35.6151i | − 0.378884i | ||||||||
\(95\) | 73.4049i | 0.772683i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 156.020 | 1.60845 | 0.804226 | − | 0.594324i | \(-0.202580\pi\) | ||||
0.804226 | + | 0.594324i | \(0.202580\pi\) | |||||||
\(98\) | − 9.93695i | − 0.101397i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −45.8954 | −0.458954 | ||||||||
\(101\) | 55.0762i | 0.545309i | 0.962112 | + | 0.272655i | \(0.0879016\pi\) | ||||
−0.962112 | + | 0.272655i | \(0.912098\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −81.0177 | −0.786579 | −0.393290 | − | 0.919415i | \(-0.628663\pi\) | ||||
−0.393290 | + | 0.919415i | \(0.628663\pi\) | |||||||
\(104\) | −76.4272 | −0.734877 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − 121.684i | − 1.14796i | ||||||||
\(107\) | 78.1987i | 0.730829i | 0.930845 | + | 0.365415i | \(0.119073\pi\) | ||||
−0.930845 | + | 0.365415i | \(0.880927\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 2.67841i | − 0.0245725i | −0.999925 | − | 0.0122863i | \(-0.996089\pi\) | ||||
0.999925 | − | 0.0122863i | \(-0.00391094\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 125.467i | 1.12024i | ||||||||
\(113\) | −184.206 | −1.63014 | −0.815069 | − | 0.579364i | \(-0.803301\pi\) | ||||
−0.815069 | + | 0.579364i | \(0.803301\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 80.9168 | 0.703624 | ||||||||
\(116\) | − 6.51066i | − 0.0561263i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − 157.745i | − 1.33682i | ||||||||
\(119\) | −52.2200 | −0.438824 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 2.88262 | 0.0236280 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 24.8728 | 0.200587 | ||||||||
\(125\) | −222.622 | −1.78098 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 119.107i | − 0.937849i | −0.883238 | − | 0.468924i | \(-0.844642\pi\) | ||||
0.883238 | − | 0.468924i | \(-0.155358\pi\) | |||||||
\(128\) | 153.703i | 1.20080i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 214.849 | 1.65269 | ||||||||
\(131\) | 17.9999i | 0.137403i | 0.997637 | + | 0.0687017i | \(0.0218857\pi\) | ||||
−0.997637 | + | 0.0687017i | \(0.978114\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −56.3253 | −0.423498 | ||||||||
\(134\) | 64.1083i | 0.478420i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −53.6265 | −0.394313 | ||||||||
\(137\) | −92.5606 | −0.675625 | −0.337812 | − | 0.941213i | \(-0.609687\pi\) | ||||
−0.337812 | + | 0.941213i | \(0.609687\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 216.817i | − 1.55983i | −0.625883 | − | 0.779917i | \(-0.715261\pi\) | ||||
0.625883 | − | 0.779917i | \(-0.284739\pi\) | |||||||
\(140\) | − 52.6150i | − 0.375821i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 48.8490i | 0.344007i | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − 62.4174i | − 0.430465i | ||||||||
\(146\) | 277.398 | 1.89999 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 48.0161 | 0.324433 | ||||||||
\(149\) | − 140.721i | − 0.944438i | −0.881481 | − | 0.472219i | \(-0.843453\pi\) | ||||
0.881481 | − | 0.472219i | \(-0.156547\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 11.5088i | − 0.0762172i | −0.999274 | − | 0.0381086i | \(-0.987867\pi\) | ||||
0.999274 | − | 0.0381086i | \(-0.0121333\pi\) | |||||||
\(152\) | −57.8423 | −0.380542 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 238.455 | 1.53842 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −149.729 | −0.953690 | −0.476845 | − | 0.878987i | \(-0.658220\pi\) | ||||
−0.476845 | + | 0.878987i | \(0.658220\pi\) | |||||||
\(158\) | 94.9783 | 0.601129 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − 123.908i | − 0.774424i | ||||||||
\(161\) | 62.0893i | 0.385648i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −54.8173 | −0.336302 | −0.168151 | − | 0.985761i | \(-0.553780\pi\) | ||||
−0.168151 | + | 0.985761i | \(0.553780\pi\) | |||||||
\(164\) | 43.4014i | 0.264643i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 295.091 | 1.77766 | ||||||||
\(167\) | 42.9417i | 0.257136i | 0.991701 | + | 0.128568i | \(0.0410381\pi\) | ||||
−0.991701 | + | 0.128568i | \(0.958962\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 44.5734 | 0.263748 | ||||||||
\(170\) | 150.753 | 0.886781 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − 41.5735i | − 0.241706i | ||||||||
\(173\) | 16.2431i | 0.0938907i | 0.998897 | + | 0.0469453i | \(0.0149487\pi\) | ||||
−0.998897 | + | 0.0469453i | \(0.985051\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 337.620i | − 1.92926i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 21.0095i | − 0.118031i | ||||||||
\(179\) | −130.353 | −0.728228 | −0.364114 | − | 0.931354i | \(-0.618628\pi\) | ||||
−0.364114 | + | 0.931354i | \(0.618628\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −101.541 | −0.560998 | −0.280499 | − | 0.959854i | \(-0.590500\pi\) | ||||
−0.280499 | + | 0.959854i | \(0.590500\pi\) | |||||||
\(182\) | 164.859i | 0.905817i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 63.7617i | 0.346531i | ||||||||
\(185\) | 460.328 | 2.48826 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −14.5820 | −0.0775639 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 162.604 | 0.855811 | ||||||||
\(191\) | 161.775 | 0.846987 | 0.423494 | − | 0.905899i | \(-0.360804\pi\) | ||||
0.423494 | + | 0.905899i | \(0.360804\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 34.1916i | 0.177159i | 0.996069 | + | 0.0885793i | \(0.0282327\pi\) | ||||
−0.996069 | + | 0.0885793i | \(0.971767\pi\) | |||||||
\(194\) | − 345.610i | − 1.78149i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.06852 | −0.0207577 | ||||||||
\(197\) | − 61.8792i | − 0.314107i | −0.987590 | − | 0.157054i | \(-0.949800\pi\) | ||||
0.987590 | − | 0.157054i | \(-0.0501996\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 238.301 | 1.19749 | 0.598747 | − | 0.800938i | \(-0.295666\pi\) | ||||
0.598747 | + | 0.800938i | \(0.295666\pi\) | |||||||
\(200\) | − 346.714i | − 1.73357i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 122.003 | 0.603975 | ||||||||
\(203\) | 47.8943 | 0.235933 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 416.087i | 2.02969i | ||||||||
\(206\) | 179.468i | 0.871202i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 209.767i | 1.00849i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 188.443i | − 0.893096i | −0.894760 | − | 0.446548i | \(-0.852653\pi\) | ||||
0.894760 | − | 0.446548i | \(-0.147347\pi\) | |||||||
\(212\) | −49.8214 | −0.235007 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 173.223 | 0.809454 | ||||||||
\(215\) | − 398.564i | − 1.85378i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 182.972i | 0.843189i | ||||||||
\(218\) | −5.93311 | −0.0272161 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −87.3062 | −0.395050 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −258.263 | −1.15813 | −0.579065 | − | 0.815281i | \(-0.696582\pi\) | ||||
−0.579065 | + | 0.815281i | \(0.696582\pi\) | |||||||
\(224\) | 95.0774 | 0.424453 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 408.046i | 1.80551i | ||||||||
\(227\) | − 44.3088i | − 0.195193i | −0.995226 | − | 0.0975965i | \(-0.968885\pi\) | ||||
0.995226 | − | 0.0975965i | \(-0.0311155\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.83877 | −0.0167632 | −0.00838160 | − | 0.999965i | \(-0.502668\pi\) | ||||
−0.00838160 | + | 0.999965i | \(0.502668\pi\) | |||||||
\(230\) | − 179.244i | − 0.779323i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 49.1843 | 0.212001 | ||||||||
\(233\) | 241.342i | 1.03580i | 0.855440 | + | 0.517902i | \(0.173287\pi\) | ||||
−0.855440 | + | 0.517902i | \(0.826713\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −139.797 | −0.594882 | ||||||||
\(236\) | −64.5860 | −0.273670 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 115.676i | 0.486034i | ||||||||
\(239\) | − 463.393i | − 1.93888i | −0.245323 | − | 0.969441i | \(-0.578894\pi\) | ||||
0.245323 | − | 0.969441i | \(-0.421106\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 447.213i | − 1.85565i | −0.373011 | − | 0.927827i | \(-0.621675\pi\) | ||||
0.373011 | − | 0.927827i | \(-0.378325\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − 1.18024i | − 0.00483705i | ||||||||
\(245\) | −39.0047 | −0.159203 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −94.1696 | −0.381254 | ||||||||
\(248\) | 187.900i | 0.757662i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 493.145i | 1.97258i | ||||||||
\(251\) | −380.631 | −1.51646 | −0.758230 | − | 0.651987i | \(-0.773936\pi\) | ||||
−0.758230 | + | 0.651987i | \(0.773936\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −263.841 | −1.03875 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 165.861 | 0.647894 | ||||||||
\(257\) | −3.33118 | −0.0129618 | −0.00648089 | − | 0.999979i | \(-0.502063\pi\) | ||||
−0.00648089 | + | 0.999979i | \(0.502063\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 353.220i | 1.36379i | ||||||||
\(260\) | − 87.9664i | − 0.338332i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 39.8727 | 0.152186 | ||||||||
\(263\) | − 379.793i | − 1.44408i | −0.691850 | − | 0.722041i | \(-0.743204\pi\) | ||||
0.691850 | − | 0.722041i | \(-0.256796\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −477.636 | −1.80240 | ||||||||
\(266\) | 124.770i | 0.469060i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 26.2481 | 0.0979405 | ||||||||
\(269\) | 187.216 | 0.695972 | 0.347986 | − | 0.937500i | \(-0.386866\pi\) | ||||
0.347986 | + | 0.937500i | \(0.386866\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 305.158i | − 1.12604i | −0.826442 | − | 0.563022i | \(-0.809639\pi\) | ||||
0.826442 | − | 0.563022i | \(-0.190361\pi\) | |||||||
\(272\) | 147.186i | 0.541127i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 205.037i | 0.748311i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 480.172i | 1.73347i | 0.498765 | + | 0.866737i | \(0.333787\pi\) | ||||
−0.498765 | + | 0.866737i | \(0.666213\pi\) | |||||||
\(278\) | −480.285 | −1.72765 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 397.476 | 1.41956 | ||||||||
\(281\) | − 9.05822i | − 0.0322357i | −0.999870 | − | 0.0161178i | \(-0.994869\pi\) | ||||
0.999870 | − | 0.0161178i | \(-0.00513069\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 266.704i | − 0.942416i | −0.882022 | − | 0.471208i | \(-0.843818\pi\) | ||||
0.882022 | − | 0.471208i | \(-0.156182\pi\) | |||||||
\(284\) | 20.0004 | 0.0704240 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −319.274 | −1.11245 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 227.740 | 0.788028 | ||||||||
\(290\) | −138.265 | −0.476776 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − 113.576i | − 0.388959i | ||||||||
\(293\) | − 170.234i | − 0.581004i | −0.956874 | − | 0.290502i | \(-0.906178\pi\) | ||||
0.956874 | − | 0.290502i | \(-0.0938223\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −619.184 | −2.09893 | ||||||||
\(296\) | 362.734i | 1.22545i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −311.721 | −1.04604 | ||||||||
\(299\) | 103.807i | 0.347179i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 305.827 | 1.01604 | ||||||||
\(302\) | −25.4939 | −0.0844169 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 158.757i | 0.522228i | ||||||||
\(305\) | − 11.3149i | − 0.0370981i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 228.869i | 0.745501i | 0.927932 | + | 0.372750i | \(0.121585\pi\) | ||||
−0.927932 | + | 0.372750i | \(0.878415\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | − 528.218i | − 1.70393i | ||||||||
\(311\) | −282.560 | −0.908555 | −0.454277 | − | 0.890860i | \(-0.650102\pi\) | ||||
−0.454277 | + | 0.890860i | \(0.650102\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −350.176 | −1.11877 | −0.559386 | − | 0.828907i | \(-0.688963\pi\) | ||||
−0.559386 | + | 0.828907i | \(0.688963\pi\) | |||||||
\(314\) | 331.675i | 1.05629i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − 38.8873i | − 0.123061i | ||||||||
\(317\) | −374.415 | −1.18112 | −0.590559 | − | 0.806994i | \(-0.701093\pi\) | ||||
−0.590559 | + | 0.806994i | \(0.701093\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 379.572 | 1.18616 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 137.538 | 0.427137 | ||||||||
\(323\) | −66.0758 | −0.204569 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 564.464i | − 1.73681i | ||||||||
\(326\) | 121.429i | 0.372483i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −327.873 | −0.999612 | ||||||||
\(329\) | − 107.270i | − 0.326048i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 262.925 | 0.794334 | 0.397167 | − | 0.917746i | \(-0.369993\pi\) | ||||
0.397167 | + | 0.917746i | \(0.369993\pi\) | |||||||
\(332\) | − 120.820i | − 0.363916i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 95.1230 | 0.284799 | ||||||||
\(335\) | 251.639 | 0.751162 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 31.6019i | − 0.0937743i | −0.998900 | − | 0.0468872i | \(-0.985070\pi\) | ||||
0.998900 | − | 0.0468872i | \(-0.0149301\pi\) | |||||||
\(338\) | − 98.7375i | − 0.292123i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | − 61.7232i | − 0.181539i | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 356.852i | − 1.04038i | ||||||||
\(344\) | 314.064 | 0.912977 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 35.9811 | 0.103992 | ||||||||
\(347\) | 413.522i | 1.19170i | 0.803094 | + | 0.595852i | \(0.203186\pi\) | ||||
−0.803094 | + | 0.595852i | \(0.796814\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 367.213i | − 1.05219i | −0.850427 | − | 0.526094i | \(-0.823656\pi\) | ||||
0.850427 | − | 0.526094i | \(-0.176344\pi\) | |||||||
\(350\) | −747.885 | −2.13682 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 415.577 | 1.17727 | 0.588636 | − | 0.808398i | \(-0.299665\pi\) | ||||
0.588636 | + | 0.808398i | \(0.299665\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 191.743 | 0.540122 | ||||||||
\(356\) | −8.60201 | −0.0241629 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 288.753i | 0.806574i | ||||||||
\(359\) | − 154.752i | − 0.431065i | −0.976497 | − | 0.215532i | \(-0.930851\pi\) | ||||
0.976497 | − | 0.215532i | \(-0.0691487\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 289.730 | 0.802575 | ||||||||
\(362\) | 224.929i | 0.621352i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 67.4987 | 0.185436 | ||||||||
\(365\) | − 1088.85i | − 2.98315i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −108.936 | −0.296829 | −0.148414 | − | 0.988925i | \(-0.547417\pi\) | ||||
−0.148414 | + | 0.988925i | \(0.547417\pi\) | |||||||
\(368\) | 175.004 | 0.475554 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − 1019.70i | − 2.75596i | ||||||||
\(371\) | − 366.501i | − 0.987875i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 721.229i | 1.93359i | 0.255555 | + | 0.966795i | \(0.417742\pi\) | ||||
−0.255555 | + | 0.966795i | \(0.582258\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − 110.159i | − 0.292976i | ||||||||
\(377\) | 80.0741 | 0.212398 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.9375 | −0.0341358 | −0.0170679 | − | 0.999854i | \(-0.505433\pi\) | ||||
−0.0170679 | + | 0.999854i | \(0.505433\pi\) | |||||||
\(380\) | − 66.5755i | − 0.175199i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − 358.358i | − 0.938109i | ||||||||
\(383\) | 99.6126 | 0.260085 | 0.130043 | − | 0.991508i | \(-0.458489\pi\) | ||||
0.130043 | + | 0.991508i | \(0.458489\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 75.7401 | 0.196218 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −141.504 | −0.364701 | ||||||||
\(389\) | −202.122 | −0.519595 | −0.259797 | − | 0.965663i | \(-0.583656\pi\) | ||||
−0.259797 | + | 0.965663i | \(0.583656\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 72.8377i | 0.186286i | ||||||||
\(392\) | − 30.7353i | − 0.0784065i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −137.073 | −0.347900 | ||||||||
\(395\) | − 372.811i | − 0.943826i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 332.729 | 0.838108 | 0.419054 | − | 0.907961i | \(-0.362362\pi\) | ||||
0.419054 | + | 0.907961i | \(0.362362\pi\) | |||||||
\(398\) | − 527.877i | − 1.32632i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −951.611 | −2.37903 | ||||||||
\(401\) | −656.880 | −1.63811 | −0.819053 | − | 0.573718i | \(-0.805500\pi\) | ||||
−0.819053 | + | 0.573718i | \(0.805500\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 305.909i | 0.759080i | ||||||||
\(404\) | − 49.9521i | − 0.123644i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | − 106.094i | − 0.261315i | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 469.056i | 1.14684i | 0.819263 | + | 0.573418i | \(0.194383\pi\) | ||||
−0.819263 | + | 0.573418i | \(0.805617\pi\) | |||||||
\(410\) | 921.703 | 2.24806 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 73.4800 | 0.178350 | ||||||||
\(413\) | − 475.114i | − 1.15040i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 1158.30i | − 2.79108i | ||||||||
\(416\) | 158.959 | 0.382113 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −242.229 | −0.578112 | −0.289056 | − | 0.957312i | \(-0.593341\pi\) | ||||
−0.289056 | + | 0.957312i | \(0.593341\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −737.569 | −1.75195 | −0.875973 | − | 0.482360i | \(-0.839780\pi\) | ||||
−0.875973 | + | 0.482360i | \(0.839780\pi\) | |||||||
\(422\) | −417.433 | −0.989178 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − 376.373i | − 0.887672i | ||||||||
\(425\) | − 396.066i | − 0.931921i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.68220 | 0.0203330 | ||||||||
\(428\) | − 70.9233i | − 0.165709i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −882.885 | −2.05322 | ||||||||
\(431\) | 491.440i | 1.14023i | 0.821564 | + | 0.570116i | \(0.193102\pi\) | ||||
−0.821564 | + | 0.570116i | \(0.806898\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −402.664 | −0.929939 | −0.464970 | − | 0.885327i | \(-0.653935\pi\) | ||||
−0.464970 | + | 0.885327i | \(0.653935\pi\) | |||||||
\(434\) | 405.314 | 0.933902 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.42921i | 0.00557159i | ||||||||
\(437\) | 78.5638i | 0.179780i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 68.4030i | 0.155815i | 0.996961 | + | 0.0779077i | \(0.0248240\pi\) | ||||
−0.996961 | + | 0.0779077i | \(0.975176\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 193.398i | 0.437551i | ||||||||
\(443\) | −313.441 | −0.707542 | −0.353771 | − | 0.935332i | \(-0.615101\pi\) | ||||
−0.353771 | + | 0.935332i | \(0.615101\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −82.4671 | −0.185319 | ||||||||
\(446\) | 572.096i | 1.28273i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 291.255i | 0.650122i | ||||||||
\(449\) | −329.111 | −0.732987 | −0.366494 | − | 0.930421i | \(-0.619442\pi\) | ||||
−0.366494 | + | 0.930421i | \(0.619442\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 167.068 | 0.369619 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −98.1514 | −0.216193 | ||||||||
\(455\) | 647.107 | 1.42221 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 88.5487i | − 0.193761i | −0.995296 | − | 0.0968804i | \(-0.969114\pi\) | ||||
0.995296 | − | 0.0968804i | \(-0.0308864\pi\) | |||||||
\(458\) | 8.50352i | 0.0185666i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −73.3886 | −0.159540 | ||||||||
\(461\) | 607.310i | 1.31737i | 0.752417 | + | 0.658687i | \(0.228888\pi\) | ||||
−0.752417 | + | 0.658687i | \(0.771112\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −40.7126 | −0.0879321 | −0.0439660 | − | 0.999033i | \(-0.513999\pi\) | ||||
−0.0439660 | + | 0.999033i | \(0.513999\pi\) | |||||||
\(464\) | − 134.994i | − 0.290936i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 534.614 | 1.14724 | ||||||||
\(467\) | 447.800 | 0.958887 | 0.479443 | − | 0.877573i | \(-0.340839\pi\) | ||||
0.479443 | + | 0.877573i | \(0.340839\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 193.089i | 0.411703i | ||||||||
\(470\) | 309.674i | 0.658881i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − 487.911i | − 1.03371i | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 427.203i | − 0.899374i | ||||||||
\(476\) | 47.3616 | 0.0994992 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1026.49 | −2.14747 | ||||||||
\(479\) | 58.4924i | 0.122114i | 0.998134 | + | 0.0610568i | \(0.0194471\pi\) | ||||
−0.998134 | + | 0.0610568i | \(0.980553\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 590.546i | 1.22775i | ||||||||
\(482\) | −990.650 | −2.05529 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1356.60 | −2.79710 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −653.283 | −1.34144 | −0.670722 | − | 0.741709i | \(-0.734015\pi\) | ||||
−0.670722 | + | 0.741709i | \(0.734015\pi\) | |||||||
\(488\) | 8.91605 | 0.0182706 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 86.4020i | 0.176331i | ||||||||
\(491\) | 294.767i | 0.600339i | 0.953886 | + | 0.300170i | \(0.0970433\pi\) | ||||
−0.953886 | + | 0.300170i | \(0.902957\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 56.1854 | 0.113966 | ||||||||
\(494\) | 208.601i | 0.422270i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 515.722 | 1.03976 | ||||||||
\(497\) | 147.129i | 0.296034i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 41.3213 | 0.0828083 | 0.0414042 | − | 0.999142i | \(-0.486817\pi\) | ||||
0.0414042 | + | 0.999142i | \(0.486817\pi\) | |||||||
\(500\) | 201.910 | 0.403820 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 843.162i | 1.67961i | ||||||||
\(503\) | 612.314i | 1.21733i | 0.793429 | + | 0.608663i | \(0.208294\pi\) | ||||
−0.793429 | + | 0.608663i | \(0.791706\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − 478.889i | − 0.948295i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 108.025i | 0.212648i | ||||||||
\(509\) | 299.983 | 0.589358 | 0.294679 | − | 0.955596i | \(-0.404787\pi\) | ||||
0.294679 | + | 0.955596i | \(0.404787\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 835.500 | 1.63503 | ||||||||
\(512\) | 247.401i | 0.483205i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 7.37911i | 0.0143562i | ||||||||
\(515\) | 704.450 | 1.36786 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 782.442 | 1.51051 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 664.537 | 1.27795 | ||||||||
\(521\) | −635.801 | −1.22035 | −0.610174 | − | 0.792268i | \(-0.708900\pi\) | ||||
−0.610174 | + | 0.792268i | \(0.708900\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 8.23200i | − 0.0157400i | −0.999969 | − | 0.00786998i | \(-0.997495\pi\) | ||||
0.999969 | − | 0.00786998i | \(-0.00250512\pi\) | |||||||
\(524\) | − 16.3252i | − 0.0311550i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −841.306 | −1.59944 | ||||||||
\(527\) | 214.647i | 0.407299i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −442.396 | −0.836288 | ||||||||
\(530\) | 1058.04i | 1.99631i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 51.0849 | 0.0960243 | ||||||||
\(533\) | −533.790 | −1.00148 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 679.939i | − 1.27091i | ||||||||
\(536\) | 198.289i | 0.369943i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 414.716i | − 0.770847i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 205.864i | − 0.380526i | −0.981733 | − | 0.190263i | \(-0.939066\pi\) | ||||
0.981733 | − | 0.190263i | \(-0.0609340\pi\) | |||||||
\(542\) | −675.975 | −1.24719 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 111.536 | 0.205030 | ||||||||
\(545\) | 23.2888i | 0.0427317i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 932.049i | 1.70393i | 0.523600 | + | 0.851964i | \(0.324589\pi\) | ||||
−0.523600 | + | 0.851964i | \(0.675411\pi\) | |||||||
\(548\) | 83.9491 | 0.153192 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 60.6023 | 0.109986 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 286.067 | 0.517299 | ||||||||
\(554\) | 1063.66 | 1.91997 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 196.645i | 0.353678i | ||||||||
\(557\) | − 745.673i | − 1.33873i | −0.742933 | − | 0.669366i | \(-0.766566\pi\) | ||||
0.742933 | − | 0.669366i | \(-0.233434\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 511.309 | 0.914686 | ||||||||
\(560\) | − 1090.94i | − 1.94810i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −20.0655 | −0.0357037 | ||||||||
\(563\) | − 766.304i | − 1.36111i | −0.732698 | − | 0.680554i | \(-0.761739\pi\) | ||||
0.732698 | − | 0.680554i | \(-0.238261\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1601.67 | 2.83482 | ||||||||
\(566\) | −590.793 | −1.04380 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 151.092i | 0.266007i | ||||||||
\(569\) | − 886.251i | − 1.55756i | −0.627297 | − | 0.778780i | \(-0.715839\pi\) | ||||
0.627297 | − | 0.778780i | \(-0.284161\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 504.852i | 0.884154i | 0.896977 | + | 0.442077i | \(0.145758\pi\) | ||||
−0.896977 | + | 0.442077i | \(0.854242\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 707.244i | 1.23213i | ||||||||
\(575\) | −470.921 | −0.818993 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 865.114 | 1.49933 | 0.749666 | − | 0.661817i | \(-0.230214\pi\) | ||||
0.749666 | + | 0.661817i | \(0.230214\pi\) | |||||||
\(578\) | − 504.482i | − 0.872807i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 56.6103i | 0.0976040i | ||||||||
\(581\) | 888.788 | 1.52976 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 858.004 | 1.46918 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −377.097 | −0.643511 | ||||||||
\(587\) | 733.629 | 1.24979 | 0.624897 | − | 0.780708i | \(-0.285141\pi\) | ||||
0.624897 | + | 0.780708i | \(0.285141\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 231.521i | 0.393074i | ||||||||
\(590\) | 1371.60i | 2.32474i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 995.581 | 1.68172 | ||||||||
\(593\) | − 1126.19i | − 1.89915i | −0.313544 | − | 0.949574i | \(-0.601516\pi\) | ||||
0.313544 | − | 0.949574i | \(-0.398484\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 454.054 | 0.763117 | ||||||||
\(596\) | 127.629i | 0.214143i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 229.949 | 0.384530 | ||||||||
\(599\) | 36.7240 | 0.0613089 | 0.0306545 | − | 0.999530i | \(-0.490241\pi\) | ||||
0.0306545 | + | 0.999530i | \(0.490241\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − 642.204i | − 1.06856i | −0.845308 | − | 0.534279i | \(-0.820583\pi\) | ||||
0.845308 | − | 0.534279i | \(-0.179417\pi\) | |||||||
\(602\) | − 677.458i | − 1.12535i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 10.4381i | 0.0172815i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 660.993i | 1.08895i | 0.838777 | + | 0.544475i | \(0.183271\pi\) | ||||
−0.838777 | + | 0.544475i | \(0.816729\pi\) | |||||||
\(608\) | 120.305 | 0.197869 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −25.0644 | −0.0410892 | ||||||||
\(611\) | − 179.343i | − 0.293524i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 729.719i | 1.19041i | 0.803575 | + | 0.595203i | \(0.202928\pi\) | ||||
−0.803575 | + | 0.595203i | \(0.797072\pi\) | |||||||
\(614\) | 506.982 | 0.825704 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 329.848 | 0.534600 | 0.267300 | − | 0.963613i | \(-0.413868\pi\) | ||||
0.267300 | + | 0.963613i | \(0.413868\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1033.26 | 1.66924 | 0.834620 | − | 0.550826i | \(-0.185687\pi\) | ||||
0.834620 | + | 0.550826i | \(0.185687\pi\) | |||||||
\(620\) | −216.270 | −0.348822 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 625.919i | 1.00630i | ||||||||
\(623\) | − 63.2789i | − 0.101571i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 670.620 | 1.07299 | ||||||||
\(626\) | 775.697i | 1.23913i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 135.799 | 0.216240 | ||||||||
\(629\) | 414.367i | 0.658771i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −854.749 | −1.35459 | −0.677297 | − | 0.735709i | \(-0.736849\pi\) | ||||
−0.677297 | + | 0.735709i | \(0.736849\pi\) | |||||||
\(632\) | 293.771 | 0.464828 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 829.391i | 1.30819i | ||||||||
\(635\) | 1035.64i | 1.63092i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 50.0384i | − 0.0785532i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − 1336.45i | − 2.08820i | ||||||||
\(641\) | −452.979 | −0.706676 | −0.353338 | − | 0.935496i | \(-0.614953\pi\) | ||||
−0.353338 | + | 0.935496i | \(0.614953\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −265.255 | −0.412527 | −0.206264 | − | 0.978496i | \(-0.566130\pi\) | ||||
−0.206264 | + | 0.978496i | \(0.566130\pi\) | |||||||
\(644\) | − 56.3127i | − 0.0874421i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 146.369i | 0.226577i | ||||||||
\(647\) | 342.818 | 0.529859 | 0.264929 | − | 0.964268i | \(-0.414651\pi\) | ||||
0.264929 | + | 0.964268i | \(0.414651\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −1250.38 | −1.92366 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 49.7172 | 0.0762534 | ||||||||
\(653\) | −543.167 | −0.831802 | −0.415901 | − | 0.909410i | \(-0.636534\pi\) | ||||
−0.415901 | + | 0.909410i | \(0.636534\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 156.509i | − 0.238945i | ||||||||
\(656\) | 899.899i | 1.37180i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −237.620 | −0.361125 | ||||||||
\(659\) | 309.878i | 0.470224i | 0.971968 | + | 0.235112i | \(0.0755457\pi\) | ||||
−0.971968 | + | 0.235112i | \(0.924454\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 389.483 | 0.589234 | 0.294617 | − | 0.955615i | \(-0.404808\pi\) | ||||
0.294617 | + | 0.955615i | \(0.404808\pi\) | |||||||
\(662\) | − 582.422i | − 0.879791i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 912.727 | 1.37459 | ||||||||
\(665\) | 489.749 | 0.736465 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 66.8041i | − 0.100156i | ||||||||
\(668\) | − 38.9465i | − 0.0583032i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − 557.423i | − 0.831974i | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 721.948i | 1.07273i | 0.843986 | + | 0.536365i | \(0.180203\pi\) | ||||
−0.843986 | + | 0.536365i | \(0.819797\pi\) | |||||||
\(674\) | −70.0036 | −0.103863 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −40.4264 | −0.0598024 | ||||||||
\(677\) | − 846.044i | − 1.24970i | −0.780746 | − | 0.624848i | \(-0.785161\pi\) | ||||
0.780746 | − | 0.624848i | \(-0.214839\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 1040.95i | − 1.53306i | ||||||||
\(680\) | 466.284 | 0.685712 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −49.2192 | −0.0720632 | −0.0360316 | − | 0.999351i | \(-0.511472\pi\) | ||||
−0.0360316 | + | 0.999351i | \(0.511472\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 804.817 | 1.17491 | ||||||||
\(686\) | −790.486 | −1.15231 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − 861.999i | − 1.25290i | ||||||||
\(689\) | − 612.750i | − 0.889333i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 705.693 | 1.02126 | 0.510632 | − | 0.859799i | \(-0.329411\pi\) | ||||
0.510632 | + | 0.859799i | \(0.329411\pi\) | |||||||
\(692\) | − 14.7319i | − 0.0212888i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 916.019 | 1.31991 | ||||||||
\(695\) | 1885.23i | 2.71256i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −374.543 | −0.537365 | ||||||||
\(698\) | −813.439 | −1.16538 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 306.209i | 0.437442i | ||||||||
\(701\) | 56.9789i | 0.0812823i | 0.999174 | + | 0.0406412i | \(0.0129400\pi\) | ||||
−0.999174 | + | 0.0406412i | \(0.987060\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 446.942i | 0.635764i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − 920.573i | − 1.30393i | ||||||||
\(707\) | 367.463 | 0.519749 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 481.533 | 0.679172 | 0.339586 | − | 0.940575i | \(-0.389713\pi\) | ||||
0.339586 | + | 0.940575i | \(0.389713\pi\) | |||||||
\(710\) | − 424.743i | − 0.598230i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 64.9833i | − 0.0912687i | ||||||||
\(713\) | 255.214 | 0.357943 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 118.225 | 0.165119 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −342.802 | −0.477440 | ||||||||
\(719\) | −987.683 | −1.37369 | −0.686845 | − | 0.726804i | \(-0.741005\pi\) | ||||
−0.686845 | + | 0.726804i | \(0.741005\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 540.541i | 0.749710i | ||||||||
\(722\) | − 641.800i | − 0.888919i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 92.0936 | 0.127201 | ||||||||
\(725\) | 363.258i | 0.501045i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −146.472 | −0.201474 | −0.100737 | − | 0.994913i | \(-0.532120\pi\) | ||||
−0.100737 | + | 0.994913i | \(0.532120\pi\) | |||||||
\(728\) | 509.914i | 0.700432i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2411.99 | −3.30409 | ||||||||
\(731\) | 358.769 | 0.490792 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 140.454i | − 0.191615i | −0.995400 | − | 0.0958076i | \(-0.969457\pi\) | ||||
0.995400 | − | 0.0958076i | \(-0.0305433\pi\) | |||||||
\(734\) | 241.312i | 0.328763i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − 132.616i | − 0.180185i | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 662.223i | 0.896107i | 0.894007 | + | 0.448053i | \(0.147883\pi\) | ||||
−0.894007 | + | 0.448053i | \(0.852117\pi\) | |||||||
\(740\) | −417.501 | −0.564190 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −811.862 | −1.09415 | ||||||||
\(743\) | 191.960i | 0.258358i | 0.991621 | + | 0.129179i | \(0.0412341\pi\) | ||||
−0.991621 | + | 0.129179i | \(0.958766\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1223.57i | 1.64238i | ||||||||
\(746\) | 1597.64 | 2.14161 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 521.733 | 0.696573 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1199.85 | −1.59767 | −0.798833 | − | 0.601552i | \(-0.794549\pi\) | ||||
−0.798833 | + | 0.601552i | \(0.794549\pi\) | |||||||
\(752\) | −302.348 | −0.402059 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − 177.377i | − 0.235249i | ||||||||
\(755\) | 100.069i | 0.132542i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −572.112 | −0.755762 | −0.377881 | − | 0.925854i | \(-0.623347\pi\) | ||||
−0.377881 | + | 0.925854i | \(0.623347\pi\) | |||||||
\(758\) | 28.6586i | 0.0378082i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 502.940 | 0.661764 | ||||||||
\(761\) | 71.9549i | 0.0945531i | 0.998882 | + | 0.0472765i | \(0.0150542\pi\) | ||||
−0.998882 | + | 0.0472765i | \(0.984946\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −17.8700 | −0.0234207 | ||||||||
\(764\) | −146.724 | −0.192047 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − 220.658i | − 0.288066i | ||||||||
\(767\) | − 794.338i | − 1.03564i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 87.6070i | 0.113923i | 0.998376 | + | 0.0569616i | \(0.0181413\pi\) | ||||
−0.998376 | + | 0.0569616i | \(0.981859\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − 31.0105i | − 0.0401691i | ||||||||
\(773\) | 767.814 | 0.993291 | 0.496646 | − | 0.867953i | \(-0.334565\pi\) | ||||
0.496646 | + | 0.867953i | \(0.334565\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1387.76 | −1.79066 | ||||||||
\(776\) | − 1068.98i | − 1.37756i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 447.735i | 0.575495i | ||||||||
\(779\) | −403.988 | −0.518598 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 161.348 | 0.206327 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −84.3580 | −0.107599 | ||||||||
\(785\) | 1301.90 | 1.65847 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 313.510i | − 0.398361i | −0.979963 | − | 0.199181i | \(-0.936172\pi\) | ||||
0.979963 | − | 0.199181i | \(-0.0638280\pi\) | |||||||
\(788\) | 56.1221i | 0.0712210i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −825.839 | −1.04537 | ||||||||
\(791\) | 1229.00i | 1.55373i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14.5157 | 0.0183048 | ||||||||
\(794\) | − 737.050i | − 0.928274i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −216.130 | −0.271521 | ||||||||
\(797\) | 671.426 | 0.842442 | 0.421221 | − | 0.906958i | \(-0.361602\pi\) | ||||
0.421221 | + | 0.906958i | \(0.361602\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 125.839i | − 0.157496i | ||||||||
\(800\) | 721.121i | 0.901401i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1455.10i | 1.81434i | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 539.868i | − 0.670644i | ||||||||
\(806\) | 677.640 | 0.840744 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 377.360 | 0.467029 | ||||||||
\(809\) | − 1059.92i | − 1.31016i | −0.755562 | − | 0.655078i | \(-0.772636\pi\) | ||||
0.755562 | − | 0.655078i | \(-0.227364\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 868.931i | − 1.07143i | −0.844398 | − | 0.535716i | \(-0.820042\pi\) | ||||
0.844398 | − | 0.535716i | \(-0.179958\pi\) | |||||||
\(812\) | −43.4384 | −0.0534956 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 476.637 | 0.584831 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 386.974 | 0.473652 | ||||||||
\(818\) | 1039.04 | 1.27022 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − 377.376i | − 0.460215i | ||||||||
\(821\) | 749.652i | 0.913096i | 0.889699 | + | 0.456548i | \(0.150914\pi\) | ||||
−0.889699 | + | 0.456548i | \(0.849086\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1184.79 | 1.43960 | 0.719800 | − | 0.694182i | \(-0.244234\pi\) | ||||
0.719800 | + | 0.694182i | \(0.244234\pi\) | |||||||
\(824\) | 555.100i | 0.673665i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1052.46 | −1.27416 | ||||||||
\(827\) | − 100.344i | − 0.121335i | −0.998158 | − | 0.0606674i | \(-0.980677\pi\) | ||||
0.998158 | − | 0.0606674i | \(-0.0193229\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 249.143 | 0.300535 | 0.150267 | − | 0.988645i | \(-0.451987\pi\) | ||||
0.150267 | + | 0.988645i | \(0.451987\pi\) | |||||||
\(830\) | −2565.82 | −3.09135 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 486.946i | 0.585271i | ||||||||
\(833\) | − 35.1103i | − 0.0421492i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 373.379i | − 0.447161i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 536.577i | 0.640307i | ||||||||
\(839\) | 121.681 | 0.145030 | 0.0725152 | − | 0.997367i | \(-0.476897\pi\) | ||||
0.0725152 | + | 0.997367i | \(0.476897\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 789.469 | 0.938726 | ||||||||
\(842\) | 1633.84i | 1.94043i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 170.911i | 0.202501i | ||||||||
\(845\) | −387.567 | −0.458659 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −1033.01 | −1.21818 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −877.353 | −1.03218 | ||||||||
\(851\) | 492.680 | 0.578942 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 144.122i | − 0.168959i | −0.996425 | − | 0.0844795i | \(-0.973077\pi\) | ||||
0.996425 | − | 0.0844795i | \(-0.0269228\pi\) | |||||||
\(854\) | − 19.2325i | − 0.0225205i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 535.786 | 0.625918 | ||||||||
\(857\) | − 527.163i | − 0.615126i | −0.951528 | − | 0.307563i | \(-0.900487\pi\) | ||||
0.951528 | − | 0.307563i | \(-0.0995134\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 122.027 | 0.142057 | 0.0710284 | − | 0.997474i | \(-0.477372\pi\) | ||||
0.0710284 | + | 0.997474i | \(0.477372\pi\) | |||||||
\(860\) | 361.482i | 0.420328i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1088.62 | 1.26290 | ||||||||
\(863\) | −845.250 | −0.979432 | −0.489716 | − | 0.871882i | \(-0.662900\pi\) | ||||
−0.489716 | + | 0.871882i | \(0.662900\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − 141.234i | − 0.163276i | ||||||||
\(866\) | 891.967i | 1.02998i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − 165.949i | − 0.191185i | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 322.823i | 0.370635i | ||||||||
\(872\) | −18.3513 | −0.0210451 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 174.032 | 0.199121 | ||||||||
\(875\) | 1485.31i | 1.69750i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 914.615i | − 1.04289i | −0.853285 | − | 0.521445i | \(-0.825393\pi\) | ||||
0.853285 | − | 0.521445i | \(-0.174607\pi\) | |||||||
\(878\) | 151.524 | 0.172579 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −618.978 | −0.702586 | −0.351293 | − | 0.936266i | \(-0.614258\pi\) | ||||
−0.351293 | + | 0.936266i | \(0.614258\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −58.5805 | −0.0663425 | −0.0331713 | − | 0.999450i | \(-0.510561\pi\) | ||||
−0.0331713 | + | 0.999450i | \(0.510561\pi\) | |||||||
\(884\) | 79.1835 | 0.0895740 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 694.324i | 0.783661i | ||||||||
\(887\) | 1060.58i | 1.19569i | 0.801612 | + | 0.597845i | \(0.203976\pi\) | ||||
−0.801612 | + | 0.597845i | \(0.796024\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −794.667 | −0.893889 | ||||||||
\(890\) | 182.678i | 0.205257i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 234.235 | 0.262595 | ||||||||
\(893\) | − 135.732i | − 0.151995i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1133.42 | 1.26639 | ||||||||
\(896\) | 1025.49 | 1.14452 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 729.036i | 0.811845i | ||||||||
\(899\) | − 196.866i | − 0.218983i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 429.947i | − 0.477189i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1262.10i | 1.39613i | ||||||||
\(905\) | 882.898 | 0.975578 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1248.22 | −1.37621 | −0.688105 | − | 0.725611i | \(-0.741557\pi\) | ||||
−0.688105 | + | 0.725611i | \(0.741557\pi\) | |||||||
\(908\) | 40.1865i | 0.0442582i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | − 1433.45i | − 1.57522i | ||||||||
\(911\) | 619.331 | 0.679837 | 0.339918 | − | 0.940455i | \(-0.389601\pi\) | ||||
0.339918 | + | 0.940455i | \(0.389601\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −196.150 | −0.214606 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.48162 | 0.00380090 | ||||||||
\(917\) | 120.093 | 0.130963 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 1704.20i | − 1.85441i | −0.374558 | − | 0.927204i | \(-0.622205\pi\) | ||||
0.374558 | − | 0.927204i | \(-0.377795\pi\) | |||||||
\(920\) | − 554.409i | − 0.602618i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1345.29 | 1.45910 | ||||||||
\(923\) | 245.984i | 0.266504i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2679.02 | −2.89624 | ||||||||
\(926\) | 90.1851i | 0.0973921i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −102.297 | −0.110234 | ||||||||
\(929\) | 505.092 | 0.543694 | 0.271847 | − | 0.962340i | \(-0.412365\pi\) | ||||
0.271847 | + | 0.962340i | \(0.412365\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 37.8705i | − 0.0406772i | ||||||||
\(932\) | − 218.889i | − 0.234859i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − 991.952i | − 1.06205i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 1305.95i | − 1.39376i | −0.717189 | − | 0.696878i | \(-0.754572\pi\) | ||||
0.717189 | − | 0.696878i | \(-0.245428\pi\) | |||||||
\(938\) | 427.723 | 0.455995 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 126.791 | 0.134884 | ||||||||
\(941\) | − 31.8347i | − 0.0338307i | −0.999857 | − | 0.0169154i | \(-0.994615\pi\) | ||||
0.999857 | − | 0.0169154i | \(-0.00538459\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 445.330i | 0.472248i | ||||||||
\(944\) | −1339.15 | −1.41859 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 749.175 | 0.791103 | 0.395552 | − | 0.918444i | \(-0.370553\pi\) | ||||
0.395552 | + | 0.918444i | \(0.370553\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1396.86 | 1.47193 | ||||||||
\(950\) | −946.325 | −0.996132 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 357.790i | 0.375830i | ||||||||
\(953\) | 1452.72i | 1.52437i | 0.647361 | + | 0.762183i | \(0.275873\pi\) | ||||
−0.647361 | + | 0.762183i | \(0.724127\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1406.63 | −1.47291 | ||||||||
\(956\) | 420.280i | 0.439624i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 129.571 | 0.135251 | ||||||||
\(959\) | 617.554i | 0.643957i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −208.907 | −0.217385 | ||||||||
\(962\) | 1308.16 | 1.35983 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 405.605i | 0.420752i | ||||||||
\(965\) | − 297.297i | − 0.308079i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 950.193i | 0.982619i | 0.870985 | + | 0.491310i | \(0.163482\pi\) | ||||
−0.870985 | + | 0.491310i | \(0.836518\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3005.09i | 3.09803i | ||||||||
\(971\) | 659.055 | 0.678738 | 0.339369 | − | 0.940653i | \(-0.389786\pi\) | ||||
0.339369 | + | 0.940653i | \(0.389786\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1446.58 | −1.48672 | ||||||||
\(974\) | 1447.13i | 1.48576i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − 24.4715i | − 0.0250733i | ||||||||
\(977\) | −206.627 | −0.211491 | −0.105746 | − | 0.994393i | \(-0.533723\pi\) | ||||
−0.105746 | + | 0.994393i | \(0.533723\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 35.3758 | 0.0360978 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 652.957 | 0.664926 | ||||||||
\(983\) | −228.441 | −0.232391 | −0.116196 | − | 0.993226i | \(-0.537070\pi\) | ||||
−0.116196 | + | 0.993226i | \(0.537070\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 538.041i | 0.546234i | ||||||||
\(986\) | − 124.460i | − 0.126227i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 85.4084 | 0.0864457 | ||||||||
\(989\) | − 426.575i | − 0.431319i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1872.78 | −1.88979 | −0.944895 | − | 0.327373i | \(-0.893837\pi\) | ||||
−0.944895 | + | 0.327373i | \(0.893837\pi\) | |||||||
\(992\) | − 390.809i | − 0.393960i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 325.915 | 0.327883 | ||||||||
\(995\) | −2072.03 | −2.08245 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1536.35i | 1.54097i | 0.637459 | + | 0.770484i | \(0.279985\pi\) | ||||
−0.637459 | + | 0.770484i | \(0.720015\pi\) | |||||||
\(998\) | − 91.5337i | − 0.0917171i | ||||||||
\(999\) | 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 | 1089.3.c.m.604.5 | 16 | ||
3.2 | odd | 2 | 363.3.c.e.241.12 | 16 | |||
11.6 | odd | 10 | 99.3.k.c.19.2 | 16 | |||
11.9 | even | 5 | 99.3.k.c.73.2 | 16 | |||
11.10 | odd | 2 | inner | 1089.3.c.m.604.12 | 16 | ||
33.2 | even | 10 | 363.3.g.f.40.2 | 16 | |||
33.5 | odd | 10 | 363.3.g.f.118.2 | 16 | |||
33.8 | even | 10 | 363.3.g.a.112.2 | 16 | |||
33.14 | odd | 10 | 363.3.g.g.112.3 | 16 | |||
33.17 | even | 10 | 33.3.g.a.19.3 | yes | 16 | ||
33.20 | odd | 10 | 33.3.g.a.7.3 | ✓ | 16 | ||
33.26 | odd | 10 | 363.3.g.a.94.2 | 16 | |||
33.29 | even | 10 | 363.3.g.g.94.3 | 16 | |||
33.32 | even | 2 | 363.3.c.e.241.5 | 16 | |||
132.83 | odd | 10 | 528.3.bf.b.481.1 | 16 | |||
132.119 | even | 10 | 528.3.bf.b.337.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.3.g.a.7.3 | ✓ | 16 | 33.20 | odd | 10 | ||
33.3.g.a.19.3 | yes | 16 | 33.17 | even | 10 | ||
99.3.k.c.19.2 | 16 | 11.6 | odd | 10 | |||
99.3.k.c.73.2 | 16 | 11.9 | even | 5 | |||
363.3.c.e.241.5 | 16 | 33.32 | even | 2 | |||
363.3.c.e.241.12 | 16 | 3.2 | odd | 2 | |||
363.3.g.a.94.2 | 16 | 33.26 | odd | 10 | |||
363.3.g.a.112.2 | 16 | 33.8 | even | 10 | |||
363.3.g.f.40.2 | 16 | 33.2 | even | 10 | |||
363.3.g.f.118.2 | 16 | 33.5 | odd | 10 | |||
363.3.g.g.94.3 | 16 | 33.29 | even | 10 | |||
363.3.g.g.112.3 | 16 | 33.14 | odd | 10 | |||
528.3.bf.b.337.1 | 16 | 132.119 | even | 10 | |||
528.3.bf.b.481.1 | 16 | 132.83 | odd | 10 | |||
1089.3.c.m.604.5 | 16 | 1.1 | even | 1 | trivial | ||
1089.3.c.m.604.12 | 16 | 11.10 | odd | 2 | inner |