Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4028,2,Mod(3497,4028)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4028, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4028.3497");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4028 = 2^{2} \cdot 19 \cdot 53 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4028.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: | \(32.1637419342\) |
Analytic rank: | \(0\) |
Dimension: | \(82\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3497.5 | ||
Character | \(\chi\) | \(=\) | 4028.3497 |
Dual form | 4028.2.c.a.3497.78 |
$q$-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 \(\left(\mathbb{Z}/4028\mathbb{Z}\right)^\times\).
\(n\) | \(2015\) | \(2281\) | \(2757\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 3.07917i | − | 1.77776i | −0.458142 | − | 0.888879i | \(-0.651485\pi\) | ||
0.458142 | − | 0.888879i | \(-0.348515\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.328536i | 0.146926i | 0.997298 | + | 0.0734630i | \(0.0234051\pi\) | ||||
−0.997298 | + | 0.0734630i | \(0.976595\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.0673750 | −0.0254654 | −0.0127327 | − | 0.999919i | \(-0.504053\pi\) | ||||
−0.0127327 | + | 0.999919i | \(0.504053\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −6.48127 | −2.16042 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.92700 | 1.18403 | 0.592017 | − | 0.805925i | \(-0.298332\pi\) | ||||
0.592017 | + | 0.805925i | \(0.298332\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.28260 | −0.910431 | −0.455215 | − | 0.890381i | \(-0.650438\pi\) | ||||
−0.455215 | + | 0.890381i | \(0.650438\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.01162 | 0.261199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.87583 | 1.66763 | 0.833817 | − | 0.552040i | \(-0.186151\pi\) | ||||
0.833817 | + | 0.552040i | \(0.186151\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1.00000i | − | 0.229416i | ||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.207459i | 0.0452713i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 2.75415i | − | 0.574280i | −0.957889 | − | 0.287140i | \(-0.907296\pi\) | ||
0.957889 | − | 0.287140i | \(-0.0927045\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.89206 | 0.978413 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 10.7194i | 2.06295i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.62262 | 1.22979 | 0.614894 | − | 0.788609i | \(-0.289199\pi\) | ||||
0.614894 | + | 0.788609i | \(0.289199\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 8.36320i | − | 1.50207i | −0.660260 | − | 0.751037i | \(-0.729554\pi\) | ||
0.660260 | − | 0.751037i | \(-0.270446\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 12.0919i | − | 2.10493i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 0.0221352i | − | 0.00374152i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.84219 | 1.12485 | 0.562424 | − | 0.826849i | \(-0.309869\pi\) | ||||
0.562424 | + | 0.826849i | \(0.309869\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 10.1077i | 1.61853i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.14612i | 1.11604i | 0.829829 | + | 0.558018i | \(0.188438\pi\) | ||||
−0.829829 | + | 0.558018i | \(0.811562\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.6184 | −1.61929 | −0.809647 | − | 0.586918i | \(-0.800341\pi\) | ||||
−0.809647 | + | 0.586918i | \(0.800341\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 2.12933i | − | 0.317422i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.02840 | 0.879332 | 0.439666 | − | 0.898161i | \(-0.355097\pi\) | ||||
0.439666 | + | 0.898161i | \(0.355097\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.99546 | −0.999352 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 21.1718i | − | 2.96465i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.06972 | + | 5.22475i | 0.696379 | + | 0.717674i | ||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.29016i | 0.173965i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.07917 | −0.407846 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.4122 | 1.35556 | 0.677779 | − | 0.735266i | \(-0.262943\pi\) | ||||
0.677779 | + | 0.735266i | \(0.262943\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 9.76505i | − | 1.25029i | −0.780510 | − | 0.625144i | \(-0.785040\pi\) | ||
0.780510 | − | 0.625144i | \(-0.214960\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.436676 | 0.0550160 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 1.07845i | − | 0.133766i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.57441i | 0.314514i | 0.987558 | + | 0.157257i | \(0.0502652\pi\) | ||||
−0.987558 | + | 0.157257i | \(0.949735\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −8.48049 | −1.02093 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.31248i | 0.393119i | 0.980492 | + | 0.196559i | \(0.0629769\pi\) | ||||
−0.980492 | + | 0.196559i | \(0.937023\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.82088i | 0.330159i | 0.986280 | + | 0.165079i | \(0.0527881\pi\) | ||||
−0.986280 | + | 0.165079i | \(0.947212\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 15.0635i | − | 1.73938i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.264582 | −0.0301519 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 4.59891i | − | 0.517418i | −0.965955 | − | 0.258709i | \(-0.916703\pi\) | ||
0.965955 | − | 0.258709i | \(-0.0832971\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 13.5631 | 1.50701 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 14.3011i | − | 1.56976i | −0.619651 | − | 0.784878i | \(-0.712726\pi\) | ||
0.619651 | − | 0.784878i | \(-0.287274\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.25896i | 0.245019i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 20.3921i | − | 2.18627i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.42589 | −0.787143 | −0.393571 | − | 0.919294i | \(-0.628761\pi\) | ||||
−0.393571 | + | 0.919294i | \(0.628761\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.221166 | 0.0231845 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −25.7517 | −2.67033 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.328536 | 0.0337071 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.36020 | −0.848849 | −0.424425 | − | 0.905463i | \(-0.639524\pi\) | ||||
−0.424425 | + | 0.905463i | \(0.639524\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −25.4519 | −2.55802 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 6.72655i | − | 0.669316i | −0.942340 | − | 0.334658i | \(-0.891379\pi\) | ||
0.942340 | − | 0.334658i | \(-0.108621\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 12.1248i | − | 1.19469i | −0.801985 | − | 0.597344i | \(-0.796223\pi\) | ||
0.801985 | − | 0.597344i | \(-0.203777\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.0681578 | −0.00665152 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.10962 | −0.783987 | −0.391993 | − | 0.919968i | \(-0.628214\pi\) | ||||
−0.391993 | + | 0.919968i | \(0.628214\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.3685i | 1.18469i | 0.805684 | + | 0.592346i | \(0.201798\pi\) | ||||
−0.805684 | + | 0.592346i | \(0.798202\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 21.0682i | − | 1.99971i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.22026 | 0.679225 | 0.339613 | − | 0.940565i | \(-0.389704\pi\) | ||||
0.339613 | + | 0.940565i | \(0.389704\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.904838 | 0.0843766 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 21.2754 | 1.96692 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.463260 | −0.0424669 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.42131 | 0.401937 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 22.0041 | 1.98404 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.24990i | 0.290680i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 11.2119i | − | 0.994893i | −0.867495 | − | 0.497447i | \(-0.834271\pi\) | ||
0.867495 | − | 0.497447i | \(-0.165729\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 32.6959i | 2.87871i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.97641 | −0.609532 | −0.304766 | − | 0.952427i | \(-0.598578\pi\) | ||||
−0.304766 | + | 0.952427i | \(0.598578\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.0673750i | 0.00584216i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.52172 | −0.303101 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 3.29776i | − | 0.281747i | −0.990028 | − | 0.140873i | \(-0.955009\pi\) | ||
0.990028 | − | 0.140873i | \(-0.0449911\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 5.00576i | − | 0.424583i | −0.977206 | − | 0.212291i | \(-0.931907\pi\) | ||
0.977206 | − | 0.212291i | \(-0.0680926\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 18.5624i | − | 1.56324i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −12.8908 | −1.07798 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.17577i | 0.180688i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 21.5402i | 1.77661i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.891002 | −0.0729937 | −0.0364968 | − | 0.999334i | \(-0.511620\pi\) | ||||
−0.0364968 | + | 0.999334i | \(0.511620\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 6.03360i | − | 0.491007i | −0.969396 | − | 0.245504i | \(-0.921047\pi\) | ||
0.969396 | − | 0.245504i | \(-0.0789534\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −44.5641 | −3.60280 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.74761 | 0.220694 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 7.68739i | − | 0.613520i | −0.951787 | − | 0.306760i | \(-0.900755\pi\) | ||
0.951787 | − | 0.306760i | \(-0.0992450\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 16.0879 | − | 15.6105i | 1.27585 | − | 1.23799i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.185561i | 0.0146242i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.0388 | −1.25626 | −0.628129 | − | 0.778109i | \(-0.716179\pi\) | ||||
−0.628129 | + | 0.778109i | \(0.716179\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.97262 | 0.309268 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.21312i | 0.248638i | 0.992242 | + | 0.124319i | \(0.0396747\pi\) | ||||
−0.992242 | + | 0.124319i | \(0.960325\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.22451 | −0.171116 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.48127i | 0.495635i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13.3330i | 1.01369i | 0.862038 | + | 0.506844i | \(0.169188\pi\) | ||||
−0.862038 | + | 0.506844i | \(0.830812\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.329603 | −0.0249156 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 32.0610i | − | 2.40985i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 17.7858i | − | 1.32937i | −0.747124 | − | 0.664685i | \(-0.768566\pi\) | ||
0.747124 | − | 0.664685i | \(-0.231434\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.8658i | 1.17929i | 0.807661 | + | 0.589647i | \(0.200733\pi\) | ||||
−0.807661 | + | 0.589647i | \(0.799267\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −30.0682 | −2.22271 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.24791i | 0.165269i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 27.0014 | 1.97454 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 0.722221i | − | 0.0525338i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 22.8865i | 1.65601i | 0.560719 | + | 0.828006i | \(0.310525\pi\) | ||||
−0.560719 | + | 0.828006i | \(0.689475\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.74851i | 0.413787i | 0.978364 | + | 0.206893i | \(0.0663353\pi\) | ||||
−0.978364 | + | 0.206893i | \(0.933665\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.32074 | −0.237803 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.31373 | −0.0935997 | −0.0467999 | − | 0.998904i | \(-0.514902\pi\) | ||||
−0.0467999 | + | 0.998904i | \(0.514902\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.356112 | 0.0252441 | 0.0126220 | − | 0.999920i | \(-0.495982\pi\) | ||||
0.0126220 | + | 0.999920i | \(0.495982\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.92704 | 0.559130 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.446199 | −0.0313170 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.34776 | −0.163975 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 17.8504i | 1.24069i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 3.92700i | − | 0.271636i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.6585 | 1.55987 | 0.779936 | − | 0.625859i | \(-0.215252\pi\) | ||||
0.779936 | + | 0.625859i | \(0.215252\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 10.1997 | 0.698870 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 3.48854i | − | 0.237916i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.563471i | 0.0382509i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.68596 | 0.586943 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −22.5706 | −1.51827 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.394431 | 0.0264131 | 0.0132065 | − | 0.999913i | \(-0.495796\pi\) | ||||
0.0132065 | + | 0.999913i | \(0.495796\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −31.7068 | −2.11379 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 24.4605 | 1.62350 | 0.811751 | − | 0.584003i | \(-0.198515\pi\) | ||||
0.811751 | + | 0.584003i | \(0.198515\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.12203 | 0.140228 | 0.0701139 | − | 0.997539i | \(-0.477664\pi\) | ||||
0.0701139 | + | 0.997539i | \(0.477664\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.814691i | 0.0536027i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.5633i | 1.08510i | 0.840024 | + | 0.542549i | \(0.182541\pi\) | ||||
−0.840024 | + | 0.542549i | \(0.817459\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.98055i | 0.129197i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −14.1608 | −0.919844 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 6.57821i | − | 0.425509i | −0.977106 | − | 0.212754i | \(-0.931757\pi\) | ||
0.977106 | − | 0.212754i | \(-0.0682434\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.0210 | 0.645511 | 0.322756 | − | 0.946482i | \(-0.395391\pi\) | ||||
0.322756 | + | 0.946482i | \(0.395391\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 9.60468i | − | 0.616141i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 2.29826i | − | 0.146831i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.28260i | 0.208867i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −44.0356 | −2.79064 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.17074i | 0.515732i | 0.966181 | + | 0.257866i | \(0.0830194\pi\) | ||||
−0.966181 | + | 0.257866i | \(0.916981\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 10.8155i | − | 0.679967i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.95572 | 0.435584 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 30.1648i | − | 1.88163i | −0.338926 | − | 0.940813i | \(-0.610064\pi\) | ||
0.338926 | − | 0.940813i | \(-0.389936\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.460993 | −0.0286447 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −42.9230 | −2.65686 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 25.2691i | 1.55816i | 0.626926 | + | 0.779079i | \(0.284313\pi\) | ||||
−0.626926 | + | 0.779079i | \(0.715687\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.71652 | + | 1.66559i | −0.105445 | + | 0.102316i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 22.8656i | 1.39935i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.13598 | −0.0692621 | −0.0346310 | − | 0.999400i | \(-0.511026\pi\) | ||||
−0.0346310 | + | 0.999400i | \(0.511026\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.38846 | −0.266580 | −0.133290 | − | 0.991077i | \(-0.542554\pi\) | ||||
−0.133290 | + | 0.991077i | \(0.542554\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 0.681006i | − | 0.0412163i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 19.2111 | 1.15847 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 8.36304i | − | 0.502486i | −0.967924 | − | 0.251243i | \(-0.919161\pi\) | ||
0.967924 | − | 0.251243i | \(-0.0808394\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 54.2042i | 3.24512i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.20514 | 0.131548 | 0.0657738 | − | 0.997835i | \(-0.479048\pi\) | ||||
0.0657738 | + | 0.997835i | \(0.479048\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.42637i | 0.144233i | 0.997396 | + | 0.0721165i | \(0.0229753\pi\) | ||||
−0.997396 | + | 0.0721165i | \(0.977025\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − | 1.01162i | − | 0.0599231i | ||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 0.481470i | − | 0.0284203i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 30.2771 | 1.78101 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 25.7424i | 1.50905i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.49769 | 0.145917 | 0.0729584 | − | 0.997335i | \(-0.476756\pi\) | ||||
0.0729584 | + | 0.997335i | \(0.476756\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.42080i | 0.199167i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 42.0951i | 2.44261i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.04078i | 0.522842i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.715416 | 0.0412359 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −20.7122 | −1.18988 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.20818 | 0.183700 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −21.8905 | −1.24935 | −0.624677 | − | 0.780883i | \(-0.714770\pi\) | ||||
−0.624677 | + | 0.780883i | \(0.714770\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −37.3342 | −2.12387 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.0040 | −0.680682 | −0.340341 | − | 0.940302i | \(-0.610543\pi\) | ||||
−0.340341 | + | 0.940302i | \(0.610543\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 19.1611i | − | 1.08305i | −0.840684 | − | 0.541525i | \(-0.817847\pi\) | ||
0.840684 | − | 0.541525i | \(-0.182153\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.143464i | 0.00808328i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 26.5137 | 1.48916 | 0.744580 | − | 0.667533i | \(-0.232650\pi\) | ||||
0.744580 | + | 0.667533i | \(0.232650\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 26.0070 | 1.45611 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 24.9709i | 1.39374i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 6.87583i | − | 0.382582i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −16.0587 | −0.890777 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 38.0848 | 2.10609 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.406164 | −0.0223925 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.1473 | −1.32726 | −0.663628 | − | 0.748063i | \(-0.730984\pi\) | ||||
−0.663628 | + | 0.748063i | \(0.730984\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −44.3461 | −2.43015 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.845788 | −0.0462103 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 8.69142i | − | 0.473452i | −0.971576 | − | 0.236726i | \(-0.923926\pi\) | ||
0.971576 | − | 0.236726i | \(-0.0760743\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 22.2324i | − | 1.20750i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 32.8423i | − | 1.77851i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.942945 | 0.0509142 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 2.78615i | − | 0.150001i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −21.6153 | −1.16037 | −0.580185 | − | 0.814485i | \(-0.697020\pi\) | ||||
−0.580185 | + | 0.814485i | \(0.697020\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 18.6583i | 0.998758i | 0.866384 | + | 0.499379i | \(0.166438\pi\) | ||||
−0.866384 | + | 0.499379i | \(0.833562\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 35.1876i | − | 1.87817i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 16.7132i | − | 0.889554i | −0.895641 | − | 0.444777i | \(-0.853283\pi\) | ||
0.895641 | − | 0.444777i | \(-0.146717\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.08827 | −0.0577594 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.42645i | 0.0754959i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 14.7261i | − | 0.777216i | −0.921403 | − | 0.388608i | \(-0.872956\pi\) | ||
0.921403 | − | 0.388608i | \(-0.127044\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 13.6139i | − | 0.714547i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.926761 | −0.0485089 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.62402 | 0.0847731 | 0.0423865 | − | 0.999101i | \(-0.486504\pi\) | ||||
0.0423865 | + | 0.999101i | \(0.486504\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 46.3160i | − | 2.41111i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.341572 | − | 0.352018i | −0.0177335 | − | 0.0182758i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 35.9917i | − | 1.86358i | −0.363001 | − | 0.931789i | \(-0.618248\pi\) | ||
0.363001 | − | 0.931789i | \(-0.381752\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10.0070 | 0.516759 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −21.7394 | −1.11964 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 31.5284i | 1.61950i | 0.586772 | + | 0.809752i | \(0.300399\pi\) | ||||
−0.586772 | + | 0.809752i | \(0.699601\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −34.5232 | −1.76868 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.61481i | 0.286903i | 0.989657 | + | 0.143452i | \(0.0458202\pi\) | ||||
−0.989657 | + | 0.143452i | \(0.954180\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 0.0869247i | − | 0.00443009i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 68.8208 | 3.49836 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 32.5209i | − | 1.64887i | −0.565954 | − | 0.824437i | \(-0.691492\pi\) | ||
0.565954 | − | 0.824437i | \(-0.308508\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 18.9371i | − | 0.957689i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 21.4815i | 1.08360i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.51091 | 0.0760221 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.56480i | 0.229101i | 0.993417 | + | 0.114550i | \(0.0365427\pi\) | ||||
−0.993417 | + | 0.114550i | \(0.963457\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.207459 | 0.0103859 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.92403i | 0.0960813i | 0.998845 | + | 0.0480407i | \(0.0152977\pi\) | ||||
−0.998845 | + | 0.0480407i | \(0.984702\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 27.4531i | 1.36753i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.45596i | 0.221418i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 26.8692 | 1.33186 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −36.7067 | −1.81503 | −0.907514 | − | 0.420022i | \(-0.862022\pi\) | ||||
−0.907514 | + | 0.420022i | \(0.862022\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.1544 | −0.500878 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.701525 | −0.0345198 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.69845 | 0.230638 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −15.4136 | −0.754805 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 8.25974i | − | 0.403515i | −0.979436 | − | 0.201757i | \(-0.935335\pi\) | ||
0.979436 | − | 0.201757i | \(-0.0646652\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 1.85203i | − | 0.0902624i | −0.998981 | − | 0.0451312i | \(-0.985629\pi\) | ||
0.998981 | − | 0.0451312i | \(-0.0143706\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −39.0717 | −1.89973 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 33.6370 | 1.63163 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.657921i | 0.0318390i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 39.6929i | 1.91639i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 25.0919 | 1.20863 | 0.604316 | − | 0.796745i | \(-0.293446\pi\) | ||||
0.604316 | + | 0.796745i | \(0.293446\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −23.0086 | −1.10572 | −0.552862 | − | 0.833273i | \(-0.686464\pi\) | ||||
−0.552862 | + | 0.833273i | \(0.686464\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.69956 | 0.321219 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.75415 | −0.131749 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.79021 | 0.324079 | 0.162040 | − | 0.986784i | \(-0.448193\pi\) | ||||
0.162040 | + | 0.986784i | \(0.448193\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 45.3395 | 2.15902 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 29.5124i | 1.40218i | 0.713074 | + | 0.701088i | \(0.247302\pi\) | ||||
−0.713074 | + | 0.701088i | \(0.752698\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 2.43967i | − | 0.115652i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.74354i | 0.129765i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.80185 | 0.179421 | 0.0897103 | − | 0.995968i | \(-0.471406\pi\) | ||||
0.0897103 | + | 0.995968i | \(0.471406\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 28.0628i | 1.32143i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −18.5785 | −0.872892 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.0726609i | 0.00340640i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 23.5786i | 1.10296i | 0.834188 | + | 0.551480i | \(0.185937\pi\) | ||||
−0.834188 | + | 0.551480i | \(0.814063\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 73.7049i | 3.44025i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −33.2696 | −1.54952 | −0.774759 | − | 0.632256i | \(-0.782129\pi\) | ||||
−0.774759 | + | 0.632256i | \(0.782129\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 27.4818i | − | 1.27719i | −0.769545 | − | 0.638593i | \(-0.779517\pi\) | ||
0.769545 | − | 0.638593i | \(-0.220483\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 8.46037i | − | 0.392340i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −38.9537 | −1.80256 | −0.901282 | − | 0.433234i | \(-0.857372\pi\) | ||||
−0.901282 | + | 0.433234i | \(0.857372\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 0.173451i | − | 0.00800922i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −23.6708 | −1.09069 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −41.6985 | −1.91730 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 4.89206i | − | 0.224463i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −32.8582 | − | 33.8630i | −1.50447 | − | 1.55048i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 37.7395i | − | 1.72436i | −0.506601 | − | 0.862181i | \(-0.669098\pi\) | ||
0.506601 | − | 0.862181i | \(-0.330902\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −22.4602 | −1.02410 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.571373 | 0.0259984 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 2.74663i | − | 0.124718i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 37.8215 | 1.71386 | 0.856928 | − | 0.515436i | \(-0.172370\pi\) | ||||
0.856928 | + | 0.515436i | \(0.172370\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 49.3862i | 2.23332i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 13.2598i | − | 0.598407i | −0.954189 | − | 0.299204i | \(-0.903279\pi\) | ||
0.954189 | − | 0.299204i | \(-0.0967210\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 45.5360 | 2.05084 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 8.36189i | − | 0.375839i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 0.223178i | − | 0.0100109i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.5189i | 0.560423i | 0.959938 | + | 0.280212i | \(0.0904047\pi\) | ||||
−0.959938 | + | 0.280212i | \(0.909595\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.89372 | 0.442019 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 32.5534i | − | 1.45149i | −0.687966 | − | 0.725743i | \(-0.741496\pi\) | ||
0.687966 | − | 0.725743i | \(-0.258504\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.20991 | 0.0983399 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.84964i | 0.304203i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 41.4168i | 1.83577i | 0.396847 | + | 0.917885i | \(0.370104\pi\) | ||||
−0.396847 | + | 0.917885i | \(0.629896\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 0.190057i | − | 0.00840762i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 10.7194 | 0.473274 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.98343 | 0.175531 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 23.6735 | 1.04116 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 41.0545 | 1.80209 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.40801 | 0.0616860 | 0.0308430 | − | 0.999524i | \(-0.490181\pi\) | ||||
0.0308430 | + | 0.999524i | \(0.490181\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.4483 | 0.456872 | 0.228436 | − | 0.973559i | \(-0.426639\pi\) | ||||
0.228436 | + | 0.973559i | \(0.426639\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.01490i | 0.0442940i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 57.5040i | − | 2.50491i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.4147 | 0.670203 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −67.4845 | −2.92858 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 23.4579i | − | 1.01607i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 2.66431i | − | 0.115188i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −54.7653 | −2.36330 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −27.4712 | −1.18327 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.09242 | −0.175947 | −0.0879734 | − | 0.996123i | \(-0.528039\pi\) | ||||
−0.0879734 | + | 0.996123i | \(0.528039\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 48.8534 | 2.09650 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.06351 | −0.174062 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.2792 | 0.738805 | 0.369402 | − | 0.929270i | \(-0.379562\pi\) | ||||
0.369402 | + | 0.929270i | \(0.379562\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 63.2900i | 2.70115i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 6.62262i | − | 0.282133i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.309852i | 0.0131762i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.92168 | 0.293809 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 28.2663i | − | 1.19768i | −0.800868 | − | 0.598841i | \(-0.795628\pi\) | ||
0.800868 | − | 0.598841i | \(-0.204372\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 34.8561 | 1.47425 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 83.1418i | − | 3.51025i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12.0007i | 0.505768i | 0.967497 | + | 0.252884i | \(0.0813791\pi\) | ||||
−0.967497 | + | 0.252884i | \(0.918621\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.37212i | 0.0997958i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.913812 | −0.0383765 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 27.0926i | 1.13578i | 0.823105 | + | 0.567889i | \(0.192240\pi\) | ||||
−0.823105 | + | 0.567889i | \(0.807760\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 40.6812i | 1.70245i | 0.524797 | + | 0.851227i | \(0.324141\pi\) | ||||
−0.524797 | + | 0.851227i | \(0.675859\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 70.4715 | 2.94399 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 13.4735i | − | 0.561883i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 29.8641 | 1.24326 | 0.621629 | − | 0.783312i | \(-0.286471\pi\) | ||||
0.621629 | + | 0.783312i | \(0.286471\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 17.7006 | 0.735612 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.963540i | 0.0399744i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 19.9088 | + | 20.5176i | 0.824537 | + | 0.849751i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.98976i | 0.288991i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22.7113 | 0.937397 | 0.468698 | − | 0.883358i | \(-0.344723\pi\) | ||||
0.468698 | + | 0.883358i | \(0.344723\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.36320 | −0.344600 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.04521i | 0.166398i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 17.4158 | 0.715183 | 0.357591 | − | 0.933878i | \(-0.383598\pi\) | ||||
0.357591 | + | 0.933878i | \(0.383598\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 0.152198i | − | 0.00623949i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 1.09653i | − | 0.0448779i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 47.3331 | 1.93398 | 0.966989 | − | 0.254819i | \(-0.0820158\pi\) | ||||
0.966989 | + | 0.254819i | \(0.0820158\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 8.11541i | − | 0.331035i | −0.986207 | − | 0.165517i | \(-0.947071\pi\) | ||
0.986207 | − | 0.165517i | \(-0.0529294\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 16.6855i | − | 0.679484i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.45256i | 0.0590550i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.8574 | 0.684219 | 0.342109 | − | 0.939660i | \(-0.388859\pi\) | ||||
0.342109 | + | 0.939660i | \(0.388859\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.37392i | 0.0556741i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −19.7888 | −0.800571 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 22.4407i | − | 0.906371i | −0.891416 | − | 0.453186i | \(-0.850287\pi\) | ||
0.891416 | − | 0.453186i | \(-0.149713\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7.22915i | 0.291507i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 31.7241i | − | 1.27716i | −0.769554 | − | 0.638582i | \(-0.779521\pi\) | ||
0.769554 | − | 0.638582i | \(-0.220479\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13.2692 | 0.533334 | 0.266667 | − | 0.963789i | \(-0.414078\pi\) | ||||
0.266667 | + | 0.963789i | \(0.414078\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 29.5229 | 1.18471 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.500320 | 0.0200449 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.3926 | 0.935704 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −12.0919 | −0.482903 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 47.0457 | 1.87584 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 1.02862i | − | 0.0409487i | −0.999790 | − | 0.0204744i | \(-0.993482\pi\) | ||
0.999790 | − | 0.0204744i | \(-0.00651765\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 69.7692i | − | 2.77308i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.68351 | 0.146176 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 22.9633 | 0.909840 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 21.4691i | − | 0.849303i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 20.3773i | 0.804857i | 0.915452 | + | 0.402428i | \(0.131834\pi\) | ||||
−0.915452 | + | 0.402428i | \(0.868166\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.0328109 | 0.00129393 | 0.000646967 | − | 1.00000i | \(-0.499794\pi\) | ||||
0.000646967 | 1.00000i | \(0.499794\pi\) | ||||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −10.7418 | −0.422957 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 31.7936 | 1.24994 | 0.624968 | − | 0.780650i | \(-0.285112\pi\) | ||||
0.624968 | + | 0.780650i | \(0.285112\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 40.8888 | 1.60503 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.73502 | 0.0680008 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −32.7316 | −1.28089 | −0.640443 | − | 0.768006i | \(-0.721249\pi\) | ||||
−0.640443 | + | 0.768006i | \(0.721249\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 2.29201i | − | 0.0895561i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 18.2829i | − | 0.713283i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 26.4997i | − | 1.03228i | −0.856503 | − | 0.516142i | \(-0.827368\pi\) | ||
0.856503 | − | 0.516142i | \(-0.172632\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.7653 | −0.652093 | −0.326047 | − | 0.945354i | \(-0.605717\pi\) | ||||
−0.326047 | + | 0.945354i | \(0.605717\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 69.4988i | 2.69911i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.0221352 | −0.000858364 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 18.2397i | − | 0.706243i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 1.21452i | − | 0.0469560i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 38.3473i | − | 1.48038i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.66250 | 0.372462 | 0.186231 | − | 0.982506i | \(-0.440373\pi\) | ||||
0.186231 | + | 0.982506i | \(0.440373\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 52.4401i | 2.01842i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 29.5959i | 1.13746i | 0.822524 | + | 0.568731i | \(0.192565\pi\) | ||||
−0.822524 | + | 0.568731i | \(0.807435\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.563269 | 0.0216163 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 75.3181i | − | 2.88619i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −23.6867 | −0.906346 | −0.453173 | − | 0.891422i | \(-0.649708\pi\) | ||||
−0.453173 | + | 0.891422i | \(0.649708\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.08344 | 0.0413959 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 6.53409i | − | 0.249291i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −16.6419 | − | 17.1508i | −0.634005 | − | 0.653393i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26.5901i | 1.01153i | 0.862670 | + | 0.505767i | \(0.168790\pi\) | ||||
−0.862670 | + | 0.505767i | \(0.831210\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.71482 | 0.0651408 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.64457 | 0.0623822 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 49.1356i | 1.86114i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 51.0012 | 1.92904 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 33.1360i | 1.25153i | 0.780012 | + | 0.625764i | \(0.215213\pi\) | ||||
−0.780012 | + | 0.625764i | \(0.784787\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 6.84219i | − | 0.258058i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.09844 | 0.229681 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.453201i | 0.0170444i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 51.5212i | 1.93492i | 0.253024 | + | 0.967460i | \(0.418575\pi\) | ||||
−0.253024 | + | 0.967460i | \(0.581425\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 29.8068i | 1.11784i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −23.0335 | −0.862611 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 4.23509i | − | 0.158383i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −20.2554 | −0.756452 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 19.4058i | − | 0.723713i | −0.932234 | − | 0.361857i | \(-0.882143\pi\) | ||
0.932234 | − | 0.361857i | \(-0.117857\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.816907i | 0.0304232i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 30.8564i | − | 1.14756i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 32.3983 | 1.20324 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 39.2039 | 1.45399 | 0.726996 | − | 0.686642i | \(-0.240916\pi\) | ||||
0.726996 | + | 0.686642i | \(0.240916\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 11.1148 | 0.411658 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −73.0105 | −2.70039 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.0741 | 0.445967 | 0.222984 | − | 0.974822i | \(-0.428420\pi\) | ||||
0.222984 | + | 0.974822i | \(0.428420\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −7.07674 | −0.261029 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10.1097i | 0.372396i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.42296i | 0.273058i | 0.990636 | + | 0.136529i | \(0.0435947\pi\) | ||||
−0.990636 | + | 0.136529i | \(0.956405\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 10.1077 | 0.371315 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −17.8249 | −0.653931 | −0.326965 | − | 0.945036i | \(-0.606026\pi\) | ||||
−0.326965 | + | 0.945036i | \(0.606026\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 0.292726i | − | 0.0107247i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 92.6896i | 3.39134i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.546386 | 0.0199645 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −48.9104 | −1.78476 | −0.892382 | − | 0.451280i | \(-0.850968\pi\) | ||||
−0.892382 | + | 0.451280i | \(0.850968\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 25.1591 | 0.916847 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.98226 | 0.0721417 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 40.5789 | 1.47487 | 0.737433 | − | 0.675420i | \(-0.236038\pi\) | ||||
0.737433 | + | 0.675420i | \(0.236038\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −33.3028 | −1.20882 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.68772i | 0.242430i | 0.992626 | + | 0.121215i | \(0.0386790\pi\) | ||||
−0.992626 | + | 0.121215i | \(0.961321\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 0.833331i | − | 0.0301686i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − | 14.6409i | − | 0.529344i | ||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −34.1792 | −1.23414 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 5.62446i | − | 0.202823i | −0.994845 | − | 0.101412i | \(-0.967664\pi\) | ||
0.994845 | − | 0.101412i | \(-0.0323359\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −92.8823 | −3.34508 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 14.6890i | − | 0.528328i | −0.964478 | − | 0.264164i | \(-0.914904\pi\) | ||
0.964478 | − | 0.264164i | \(-0.0850961\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 40.9133i | − | 1.46965i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.41947i | 0.0509233i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.14612 | 0.256036 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.0081i | 0.465466i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 70.9906i | 2.53700i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.52559 | 0.0901421 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 38.7538i | 1.38142i | 0.723130 | + | 0.690712i | \(0.242703\pi\) | ||||
−0.723130 | + | 0.690712i | \(0.757297\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 77.8077 | 2.77003 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.486466 | −0.0172967 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 32.0548i | 1.13830i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5.12862 | + | 5.28545i | 0.181893 | + | 0.187456i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 26.2079i | − | 0.928332i | −0.885748 | − | 0.464166i | \(-0.846354\pi\) | ||
0.885748 | − | 0.464166i | \(-0.153646\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 41.4503 | 1.46641 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 48.1292 | 1.70056 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 11.0776i | 0.390919i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.0609635 | −0.00214868 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.49788i | 0.123131i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 31.0360i | − | 1.09117i | −0.838056 | − | 0.545584i | \(-0.816308\pi\) | ||
0.838056 | − | 0.545584i | \(-0.183692\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22.1708 | 0.778523 | 0.389262 | − | 0.921127i | \(-0.372730\pi\) | ||||
0.389262 | + | 0.921127i | \(0.372730\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 13.5128i | 0.473914i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 5.26934i | − | 0.184577i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.6184i | 0.371491i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.43343 | −0.0500882 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.77096i | 0.201408i | 0.994916 | + | 0.100704i | \(0.0321095\pi\) | ||||
−0.994916 | + | 0.100704i | \(0.967891\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.4344 | −0.572869 | −0.286434 | − | 0.958100i | \(-0.592470\pi\) | ||||
−0.286434 | + | 0.958100i | \(0.592470\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 59.1543i | − | 2.05949i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 22.9599i | 0.798395i | 0.916865 | + | 0.399198i | \(0.130711\pi\) | ||||
−0.916865 | + | 0.399198i | \(0.869289\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.23901i | 0.320884i | 0.987045 | + | 0.160442i | \(0.0512920\pi\) | ||||
−0.987045 | + | 0.160442i | \(0.948708\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −25.7512 | −0.893299 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −48.0996 | −1.66655 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.05563 | −0.0365314 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 89.6486 | 3.09871 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 41.8408 | 1.44451 | 0.722253 | − | 0.691629i | \(-0.243107\pi\) | ||||
0.722253 | + | 0.691629i | \(0.243107\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.8590 | 0.512381 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 6.78999i | − | 0.233860i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 0.730833i | − | 0.0251414i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.297886 | −0.0102355 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7.47121 | 0.256411 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 18.8444i | − | 0.645978i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 8.39209i | − | 0.287340i | −0.989626 | − | 0.143670i | \(-0.954110\pi\) | ||
0.989626 | − | 0.143670i | \(-0.0458903\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.12933 | −0.0728217 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 27.0489 | 0.923974 | 0.461987 | − | 0.886887i | \(-0.347137\pi\) | ||||
0.461987 | + | 0.886887i | \(0.347137\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −33.4374 | −1.14087 | −0.570434 | − | 0.821343i | \(-0.693225\pi\) | ||||
−0.570434 | + | 0.821343i | \(0.693225\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.48253 | −0.0505244 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 34.5370 | 1.17565 | 0.587826 | − | 0.808987i | \(-0.299984\pi\) | ||||
0.587826 | + | 0.808987i | \(0.299984\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.38037 | −0.148937 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 93.2282i | − | 3.16620i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 18.0599i | − | 0.612641i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 8.45077i | − | 0.286343i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 54.1847 | 1.83387 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 0.218962i | − | 0.00740228i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −36.4836 | −1.23196 | −0.615981 | − | 0.787761i | \(-0.711240\pi\) | ||||
−0.615981 | + | 0.787761i | \(0.711240\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 7.69081i | − | 0.259405i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14.4788i | 0.487803i | 0.969800 | + | 0.243902i | \(0.0784274\pi\) | ||||
−0.969800 | + | 0.243902i | \(0.921573\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 7.25178i | − | 0.244042i | −0.992528 | − | 0.122021i | \(-0.961062\pi\) | ||
0.992528 | − | 0.122021i | \(-0.0389375\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 10.5332 | 0.354070 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 26.4542i | 0.888244i | 0.895966 | + | 0.444122i | \(0.146484\pi\) | ||||
−0.895966 | + | 0.444122i | \(0.853516\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.755401i | 0.0253353i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 53.2621 | 1.78435 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 6.02840i | − | 0.201733i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.84327 | 0.195319 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 27.8381 | 0.929486 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 55.3862i | − | 1.84723i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 34.8585 | + | 35.9245i | 1.16131 | + | 1.19682i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 2.20289i | − | 0.0733075i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.21249 | −0.173269 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 29.6638 | 0.984972 | 0.492486 | − | 0.870320i | \(-0.336088\pi\) | ||||
0.492486 | + | 0.870320i | \(0.336088\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 43.5966i | 1.44601i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 33.5901 | 1.11289 | 0.556444 | − | 0.830885i | \(-0.312165\pi\) | ||||
0.556444 | + | 0.830885i | \(0.312165\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 56.1606i | − | 1.85864i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 9.87851i | − | 0.326573i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.470036 | 0.0155220 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 56.2845i | − | 1.85665i | −0.371763 | − | 0.928327i | \(-0.621247\pi\) | ||
0.371763 | − | 0.928327i | \(-0.378753\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 67.4044i | 2.22105i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 10.8736i | − | 0.357907i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 33.4724 | 1.10057 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 78.5839i | 2.58103i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −20.8349 | −0.683571 | −0.341785 | − | 0.939778i | \(-0.611032\pi\) | ||||
−0.341785 | + | 0.939778i | \(0.611032\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.99546i | 0.229267i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 36.9622i | 1.21009i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8.87094i | 0.290111i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.666786 | 0.0217829 | 0.0108915 | − | 0.999941i | \(-0.496533\pi\) | ||||
0.0108915 | + | 0.999941i | \(0.496533\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −59.0003 | −1.92540 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.15647 | 0.102898 | 0.0514491 | − | 0.998676i | \(-0.483616\pi\) | ||||
0.0514491 | + | 0.998676i | \(0.483616\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 19.6815 | 0.640917 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.237276 | 0.00771858 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −37.4996 | −1.21857 | −0.609286 | − | 0.792951i | \(-0.708544\pi\) | ||||
−0.609286 | + | 0.792951i | \(0.708544\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 9.25983i | − | 0.300587i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 81.6402i | − | 2.64737i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.98085 | 0.0641661 | 0.0320830 | − | 0.999485i | \(-0.489786\pi\) | ||||
0.0320830 | + | 0.999485i | \(0.489786\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.51906 | −0.243311 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 80.0799i | − | 2.58861i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.222187i | 0.00717479i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −38.9431 | −1.25623 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 52.5607 | 1.69374 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.88859 | −0.0607960 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.3735 | 0.526538 | 0.263269 | − | 0.964723i | \(-0.415199\pi\) | ||||
0.263269 | + | 0.964723i | \(0.415199\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −21.1718 | −0.680138 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 52.8833 | 1.69710 | 0.848552 | − | 0.529111i | \(-0.177475\pi\) | ||||
0.848552 | + | 0.529111i | \(0.177475\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.337263i | 0.0108122i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 49.4474i | 1.58359i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 49.3272i | 1.57812i | 0.614318 | + | 0.789058i | \(0.289431\pi\) | ||||
−0.614318 | + | 0.789058i | \(0.710569\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −29.1614 | −0.932004 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 80.1638i | − | 2.55943i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 43.4940 | 1.38724 | 0.693622 | − | 0.720339i | \(-0.256014\pi\) | ||||
0.693622 | + | 0.720339i | \(0.256014\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 0.431610i | − | 0.0137522i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.25065i | 0.0398085i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 29.2447i | 0.929927i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22.7711 | 0.723348 | 0.361674 | − | 0.932305i | \(-0.382205\pi\) | ||||
0.361674 | + | 0.932305i | \(0.382205\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 74.3536i | 2.35954i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.116996i | 0.00370901i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −36.6175 | −1.15969 | −0.579844 | − | 0.814728i | \(-0.696886\pi\) | ||||
−0.579844 | + | 0.814728i | \(0.696886\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 73.3442i | 2.32051i |
(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 | 4028.2.c.a.3497.5 | ✓ | 82 | |
53.52 | even | 2 | inner | 4028.2.c.a.3497.78 | yes | 82 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4028.2.c.a.3497.5 | ✓ | 82 | 1.1 | even | 1 | trivial | |
4028.2.c.a.3497.78 | yes | 82 | 53.52 | even | 2 | inner |