Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4020,2,Mod(1609,4020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4020, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4020.1609");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4020.g (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(32.0998616126\) |
Analytic rank: | \(0\) |
Dimension: | \(38\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1609.16 | ||
Character | \(\chi\) | \(=\) | 4020.1609 |
Dual form | 4020.2.g.c.1609.35 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times\).
\(n\) | \(1141\) | \(2011\) | \(2681\) | \(3217\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.96624 | + | 1.06486i | 0.879327 | + | 0.476218i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.32230i | 1.63368i | 0.576867 | + | 0.816838i | \(0.304275\pi\) | ||||
−0.576867 | + | 0.816838i | \(0.695725\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.68751 | 1.11183 | 0.555913 | − | 0.831240i | \(-0.312369\pi\) | ||||
0.555913 | + | 0.831240i | \(0.312369\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 4.58547i | − | 1.27178i | −0.771780 | − | 0.635890i | \(-0.780633\pi\) | ||
0.771780 | − | 0.635890i | \(-0.219367\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.06486 | − | 1.96624i | 0.274945 | − | 0.507680i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 7.89141i | − | 1.91395i | −0.290172 | − | 0.956974i | \(-0.593713\pi\) | ||
0.290172 | − | 0.956974i | \(-0.406287\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.22571 | 0.969444 | 0.484722 | − | 0.874668i | \(-0.338921\pi\) | ||||
0.484722 | + | 0.874668i | \(0.338921\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.32230 | 0.943203 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 1.04462i | − | 0.217818i | −0.994052 | − | 0.108909i | \(-0.965264\pi\) | ||
0.994052 | − | 0.108909i | \(-0.0347357\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.73216 | + | 4.18752i | 0.546433 | + | 0.837503i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.93796 | −1.10265 | −0.551325 | − | 0.834290i | \(-0.685878\pi\) | ||||
−0.551325 | + | 0.834290i | \(0.685878\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.66037 | 1.01663 | 0.508316 | − | 0.861170i | \(-0.330268\pi\) | ||||
0.508316 | + | 0.861170i | \(0.330268\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 3.68751i | − | 0.641913i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.60263 | + | 8.49866i | −0.777986 | + | 1.43654i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 11.2388i | − | 1.84765i | −0.382810 | − | 0.923827i | \(-0.625044\pi\) | ||
0.382810 | − | 0.923827i | \(-0.374956\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.58547 | −0.734262 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.36096 | 0.212545 | 0.106273 | − | 0.994337i | \(-0.466108\pi\) | ||||
0.106273 | + | 0.994337i | \(0.466108\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 6.90749i | − | 1.05338i | −0.850057 | − | 0.526691i | \(-0.823433\pi\) | ||
0.850057 | − | 0.526691i | \(-0.176567\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.96624 | − | 1.06486i | −0.293109 | − | 0.158739i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 0.227862i | − | 0.0332371i | −0.999862 | − | 0.0166185i | \(-0.994710\pi\) | ||
0.999862 | − | 0.0166185i | \(-0.00529009\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −11.6823 | −1.66890 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.89141 | −1.10502 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.37470i | 0.600911i | 0.953796 | + | 0.300456i | \(0.0971387\pi\) | ||||
−0.953796 | + | 0.300456i | \(0.902861\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.25051 | + | 3.92667i | 0.977659 | + | 0.529472i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 4.22571i | − | 0.559709i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.83840 | 0.890284 | 0.445142 | − | 0.895460i | \(-0.353153\pi\) | ||||
0.445142 | + | 0.895460i | \(0.353153\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.41474 | 0.565249 | 0.282625 | − | 0.959231i | \(-0.408795\pi\) | ||||
0.282625 | + | 0.959231i | \(0.408795\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 4.32230i | − | 0.544559i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.88286 | − | 9.01611i | 0.605644 | − | 1.11831i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 1.00000i | − | 0.122169i | ||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.04462 | −0.125757 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.97099 | −0.827304 | −0.413652 | − | 0.910435i | \(-0.635747\pi\) | ||||
−0.413652 | + | 0.910435i | \(0.635747\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.49940i | 0.175491i | 0.996143 | + | 0.0877455i | \(0.0279662\pi\) | ||||
−0.996143 | + | 0.0877455i | \(0.972034\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.18752 | − | 2.73216i | 0.483533 | − | 0.315483i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 15.9385i | 1.81636i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.16488 | −0.581094 | −0.290547 | − | 0.956861i | \(-0.593837\pi\) | ||||
−0.290547 | + | 0.956861i | \(0.593837\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 10.3758i | − | 1.13889i | −0.822030 | − | 0.569444i | \(-0.807158\pi\) | ||
0.822030 | − | 0.569444i | \(-0.192842\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.40322 | − | 15.5164i | 0.911457 | − | 1.68299i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.93796i | 0.636616i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.71428 | 0.287713 | 0.143856 | − | 0.989599i | \(-0.454050\pi\) | ||||
0.143856 | + | 0.989599i | \(0.454050\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 19.8198 | 2.07768 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 5.66037i | − | 0.586953i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8.30873 | + | 4.49977i | 0.852458 | + | 0.461667i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.15818i | 0.828338i | 0.910200 | + | 0.414169i | \(0.135928\pi\) | ||||
−0.910200 | + | 0.414169i | \(0.864072\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.68751 | −0.370609 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.75538 | 0.274171 | 0.137085 | − | 0.990559i | \(-0.456227\pi\) | ||||
0.137085 | + | 0.990559i | \(0.456227\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 11.5307i | − | 1.13615i | −0.822975 | − | 0.568077i | \(-0.807688\pi\) | ||
0.822975 | − | 0.568077i | \(-0.192312\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 8.49866 | + | 4.60263i | 0.829384 | + | 0.449170i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.8485i | 1.24211i | 0.783767 | + | 0.621055i | \(0.213296\pi\) | ||||
−0.783767 | + | 0.621055i | \(0.786704\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.68327 | 0.352793 | 0.176397 | − | 0.984319i | \(-0.443556\pi\) | ||||
0.176397 | + | 0.984319i | \(0.443556\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −11.2388 | −1.06674 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.93123i | 0.746108i | 0.927810 | + | 0.373054i | \(0.121689\pi\) | ||||
−0.927810 | + | 0.373054i | \(0.878311\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.11237 | − | 2.05396i | 0.103729 | − | 0.191533i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.58547i | 0.423926i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 34.1091 | 3.12677 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.59773 | 0.236157 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 1.36096i | − | 0.122713i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.912975 | + | 11.1430i | 0.0816590 | + | 0.996660i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.32450i | 0.561208i | 0.959824 | + | 0.280604i | \(0.0905348\pi\) | ||||
−0.959824 | + | 0.280604i | \(0.909465\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.90749 | −0.608170 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.81351 | 0.770040 | 0.385020 | − | 0.922908i | \(-0.374195\pi\) | ||||
0.385020 | + | 0.922908i | \(0.374195\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 18.2648i | 1.58376i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.06486 | + | 1.96624i | −0.0916482 | + | 0.169227i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.13167i | 0.694735i | 0.937729 | + | 0.347368i | \(0.112924\pi\) | ||||
−0.937729 | + | 0.347368i | \(0.887076\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.35176 | 0.369111 | 0.184556 | − | 0.982822i | \(-0.440915\pi\) | ||||
0.184556 | + | 0.982822i | \(0.440915\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.227862 | −0.0191894 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 16.9089i | − | 1.41400i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −11.6754 | − | 6.32307i | −0.969591 | − | 0.525102i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 11.6823i | 0.963538i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.32537 | 0.436271 | 0.218136 | − | 0.975918i | \(-0.430002\pi\) | ||||
0.218136 | + | 0.975918i | \(0.430002\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.9734 | 1.21852 | 0.609260 | − | 0.792970i | \(-0.291466\pi\) | ||||
0.609260 | + | 0.792970i | \(0.291466\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.89141i | 0.637983i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 11.1296 | + | 6.02748i | 0.893953 | + | 0.484139i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 23.0196i | 1.83717i | 0.395227 | + | 0.918583i | \(0.370666\pi\) | ||||
−0.395227 | + | 0.918583i | \(0.629334\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.37470 | 0.346936 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.51515 | 0.355844 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 19.1669i | 1.50127i | 0.660719 | + | 0.750633i | \(0.270251\pi\) | ||||
−0.660719 | + | 0.750633i | \(0.729749\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.92667 | − | 7.25051i | 0.305691 | − | 0.564452i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 14.7151i | 1.13869i | 0.822099 | + | 0.569345i | \(0.192803\pi\) | ||||
−0.822099 | + | 0.569345i | \(0.807197\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.02650 | −0.617423 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.22571 | −0.323148 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 14.7906i | − | 1.12451i | −0.826965 | − | 0.562253i | \(-0.809935\pi\) | ||
0.826965 | − | 0.562253i | \(-0.190065\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −18.0997 | + | 11.8092i | −1.36821 | + | 0.892694i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 6.83840i | − | 0.514006i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −16.7747 | −1.25380 | −0.626898 | − | 0.779101i | \(-0.715676\pi\) | ||||
−0.626898 | + | 0.779101i | \(0.715676\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.8727 | 1.40279 | 0.701397 | − | 0.712771i | \(-0.252560\pi\) | ||||
0.701397 | + | 0.712771i | \(0.252560\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 4.41474i | − | 0.326347i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 11.9677 | − | 22.0982i | 0.879886 | − | 1.62469i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 29.0997i | − | 2.12798i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.32230 | −0.314401 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.24583 | 0.307217 | 0.153609 | − | 0.988132i | \(-0.450910\pi\) | ||||
0.153609 | + | 0.988132i | \(0.450910\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.8178i | 1.28255i | 0.767311 | + | 0.641275i | \(0.221594\pi\) | ||||
−0.767311 | + | 0.641275i | \(0.778406\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −9.01611 | − | 4.88286i | −0.645657 | − | 0.349669i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 7.79528i | − | 0.555391i | −0.960669 | − | 0.277696i | \(-0.910429\pi\) | ||
0.960669 | − | 0.277696i | \(-0.0895706\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.01866 | 0.0722111 | 0.0361055 | − | 0.999348i | \(-0.488505\pi\) | ||||
0.0361055 | + | 0.999348i | \(0.488505\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.00000 | −0.0705346 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 25.6656i | − | 1.80137i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.67596 | + | 1.44922i | 0.186897 | + | 0.101218i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.04462i | 0.0726059i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 15.5823 | 1.07785 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.9281 | 1.16538 | 0.582689 | − | 0.812695i | \(-0.302001\pi\) | ||||
0.582689 | + | 0.812695i | \(0.302001\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.97099i | 0.477644i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.35548 | − | 13.5817i | 0.501640 | − | 0.926267i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 24.4658i | 1.66085i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.49940 | 0.101320 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −36.1858 | −2.43412 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 19.6720i | − | 1.31733i | −0.752435 | − | 0.658666i | \(-0.771121\pi\) | ||
0.752435 | − | 0.658666i | \(-0.228879\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.73216 | − | 4.18752i | −0.182144 | − | 0.279168i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 21.8906i | − | 1.45293i | −0.687203 | − | 0.726466i | \(-0.741162\pi\) | ||
0.687203 | − | 0.726466i | \(-0.258838\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.28727 | −0.217229 | −0.108614 | − | 0.994084i | \(-0.534641\pi\) | ||||
−0.108614 | + | 0.994084i | \(0.534641\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 15.9385 | 1.04868 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 10.4772i | − | 0.686382i | −0.939266 | − | 0.343191i | \(-0.888492\pi\) | ||
0.939266 | − | 0.343191i | \(-0.111508\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.242640 | − | 0.448030i | 0.0158281 | − | 0.0292263i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.16488i | 0.335495i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −19.8748 | −1.28559 | −0.642796 | − | 0.766038i | \(-0.722226\pi\) | ||||
−0.642796 | + | 0.766038i | \(0.722226\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.2871 | −0.727065 | −0.363533 | − | 0.931581i | \(-0.618429\pi\) | ||||
−0.363533 | + | 0.931581i | \(0.618429\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −22.9701 | − | 12.4399i | −1.46751 | − | 0.794759i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 19.3768i | − | 1.23292i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −10.3758 | −0.657537 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −30.1154 | −1.90087 | −0.950434 | − | 0.310928i | \(-0.899360\pi\) | ||||
−0.950434 | + | 0.310928i | \(0.899360\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 3.85204i | − | 0.242175i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −15.5164 | − | 8.40322i | −0.971673 | − | 0.526230i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 26.5811i | − | 1.65808i | −0.559186 | − | 0.829042i | \(-0.688886\pi\) | ||
0.559186 | − | 0.829042i | \(-0.311114\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 48.5776 | 3.01847 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.93796 | 0.367550 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 10.5190i | − | 0.648629i | −0.945949 | − | 0.324315i | \(-0.894866\pi\) | ||
0.945949 | − | 0.324315i | \(-0.105134\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.65843 | + | 8.60169i | −0.286165 | + | 0.528398i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 2.71428i | − | 0.166111i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.906058 | 0.0552433 | 0.0276217 | − | 0.999618i | \(-0.491207\pi\) | ||||
0.0276217 | + | 0.999618i | \(0.491207\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.0749 | 0.672750 | 0.336375 | − | 0.941728i | \(-0.390799\pi\) | ||||
0.336375 | + | 0.941728i | \(0.390799\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 19.8198i | − | 1.19955i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10.0749 | + | 15.4415i | 0.607538 | + | 0.931158i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 3.74825i | − | 0.225211i | −0.993640 | − | 0.112605i | \(-0.964080\pi\) | ||
0.993640 | − | 0.112605i | \(-0.0359196\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.66037 | −0.338878 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −17.7546 | −1.05915 | −0.529576 | − | 0.848263i | \(-0.677649\pi\) | ||||
−0.529576 | + | 0.848263i | \(0.677649\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 19.6755i | − | 1.16959i | −0.811183 | − | 0.584793i | \(-0.801176\pi\) | ||
0.811183 | − | 0.584793i | \(-0.198824\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.49977 | − | 8.30873i | 0.266543 | − | 0.492167i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.88246i | 0.347230i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −45.2744 | −2.66320 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.15818 | 0.478241 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 16.3514i | 0.955259i | 0.878561 | + | 0.477629i | \(0.158504\pi\) | ||||
−0.878561 | + | 0.477629i | \(0.841496\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13.4459 | + | 7.28191i | 0.782851 | + | 0.423969i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.68751i | 0.213971i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.79006 | −0.277016 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 29.8562 | 1.72088 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 2.75538i | − | 0.158293i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.68042 | + | 4.70106i | 0.497039 | + | 0.269182i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.589802i | 0.0336618i | 0.999858 | + | 0.0168309i | \(0.00535770\pi\) | ||||
−0.999858 | + | 0.0168309i | \(0.994642\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.5307 | −0.655959 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.3850 | 0.758994 | 0.379497 | − | 0.925193i | \(-0.376097\pi\) | ||||
0.379497 | + | 0.925193i | \(0.376097\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.9356i | 0.900735i | 0.892843 | + | 0.450368i | \(0.148707\pi\) | ||||
−0.892843 | + | 0.450368i | \(0.851293\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.60263 | − | 8.49866i | 0.259329 | − | 0.478845i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 16.4627i | 0.924640i | 0.886713 | + | 0.462320i | \(0.152983\pi\) | ||||
−0.886713 | + | 0.462320i | \(0.847017\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −21.8963 | −1.22596 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.8485 | 0.717133 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 33.3468i | − | 1.85547i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 19.2017 | − | 12.5282i | 1.06512 | − | 0.694942i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 3.68327i | − | 0.203685i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.984887 | 0.0542986 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 32.0995 | 1.76435 | 0.882175 | − | 0.470923i | \(-0.156079\pi\) | ||||
0.882175 | + | 0.470923i | \(0.156079\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 11.2388i | 0.615885i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.06486 | − | 1.96624i | 0.0581793 | − | 0.107427i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.03842i | 0.111040i | 0.998458 | + | 0.0555198i | \(0.0176816\pi\) | ||||
−0.998458 | + | 0.0555198i | \(0.982318\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.93123 | 0.430766 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 20.8727 | 1.13032 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 20.2382i | − | 1.09276i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.05396 | − | 1.11237i | −0.110582 | − | 0.0598878i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 16.6466i | − | 0.893639i | −0.894624 | − | 0.446819i | \(-0.852557\pi\) | ||
0.894624 | − | 0.446819i | \(-0.147443\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.7609 | 1.16484 | 0.582418 | − | 0.812889i | \(-0.302107\pi\) | ||||
0.582418 | + | 0.812889i | \(0.302107\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.58547 | 0.244754 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 12.5331i | − | 0.667069i | −0.942738 | − | 0.333535i | \(-0.891759\pi\) | ||
0.942738 | − | 0.333535i | \(-0.108241\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13.7066 | − | 7.42310i | −0.727471 | − | 0.393977i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 34.1091i | − | 1.80524i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −21.5144 | −1.13549 | −0.567743 | − | 0.823206i | \(-0.692183\pi\) | ||||
−0.567743 | + | 0.823206i | \(0.692183\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.14340 | −0.0601789 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 2.59773i | − | 0.136345i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.59664 | + | 2.94816i | −0.0835720 | + | 0.154314i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.6410i | 0.712052i | 0.934476 | + | 0.356026i | \(0.115869\pi\) | ||||
−0.934476 | + | 0.356026i | \(0.884131\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.36096 | −0.0708485 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −18.9088 | −0.981694 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 29.8002i | 1.54300i | 0.636231 | + | 0.771498i | \(0.280492\pi\) | ||||
−0.636231 | + | 0.771498i | \(0.719508\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 11.1430 | − | 0.912975i | 0.575422 | − | 0.0471458i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 27.2283i | 1.40233i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −30.1563 | −1.54902 | −0.774512 | − | 0.632559i | \(-0.782005\pi\) | ||||
−0.774512 | + | 0.632559i | \(0.782005\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.32450 | 0.324014 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.16543i | 0.263941i | 0.991254 | + | 0.131971i | \(0.0421305\pi\) | ||||
−0.991254 | + | 0.131971i | \(0.957870\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −16.9722 | + | 31.3389i | −0.864985 | + | 1.59718i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.90749i | 0.351127i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 24.9691 | 1.26598 | 0.632992 | − | 0.774159i | \(-0.281827\pi\) | ||||
0.632992 | + | 0.774159i | \(0.281827\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.24351 | −0.416892 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 8.81351i | − | 0.444583i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10.1554 | − | 5.49985i | −0.510972 | − | 0.276727i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 33.8747i | 1.70012i | 0.526685 | + | 0.850060i | \(0.323435\pi\) | ||||
−0.526685 | + | 0.850060i | \(0.676565\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 18.2648 | 0.914382 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −37.5275 | −1.87403 | −0.937016 | − | 0.349286i | \(-0.886424\pi\) | ||||
−0.937016 | + | 0.349286i | \(0.886424\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 25.9554i | − | 1.29293i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.96624 | + | 1.06486i | 0.0977030 | + | 0.0529131i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 41.4433i | − | 2.05427i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −38.5255 | −1.90496 | −0.952481 | − | 0.304597i | \(-0.901478\pi\) | ||||
−0.952481 | + | 0.304597i | \(0.901478\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.13167 | 0.401106 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 29.5576i | 1.45444i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.0487 | − | 20.4012i | 0.542359 | − | 1.00146i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 4.35176i | − | 0.213107i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.95992 | −0.193455 | −0.0967274 | − | 0.995311i | \(-0.530837\pi\) | ||||
−0.0967274 | + | 0.995311i | \(0.530837\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −24.5101 | −1.19455 | −0.597274 | − | 0.802038i | \(-0.703749\pi\) | ||||
−0.597274 | + | 0.802038i | \(0.703749\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.227862i | 0.0110790i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 33.0454 | − | 21.5606i | 1.60294 | − | 1.04584i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 19.0818i | 0.923434i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −16.9089 | −0.816372 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −37.0414 | −1.78422 | −0.892110 | − | 0.451819i | \(-0.850775\pi\) | ||||
−0.892110 | + | 0.451819i | \(0.850775\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.3638i | 0.594164i | 0.954852 | + | 0.297082i | \(0.0960136\pi\) | ||||
−0.954852 | + | 0.297082i | \(0.903986\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.32307 | + | 11.6754i | −0.303168 | + | 0.559794i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 4.41425i | − | 0.211162i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.0541 | 0.718492 | 0.359246 | − | 0.933243i | \(-0.383034\pi\) | ||||
0.359246 | + | 0.933243i | \(0.383034\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 11.6823 | 0.556299 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.4444i | 1.16139i | 0.814122 | + | 0.580694i | \(0.197219\pi\) | ||||
−0.814122 | + | 0.580694i | \(0.802781\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.33691 | + | 2.89032i | 0.252994 | + | 0.137014i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 5.32537i | − | 0.251881i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.53808 | −0.0725864 | −0.0362932 | − | 0.999341i | \(-0.511555\pi\) | ||||
−0.0362932 | + | 0.999341i | \(0.511555\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.01854 | 0.236314 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 14.9734i | − | 0.703513i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 38.9703 | + | 21.1052i | 1.82696 | + | 0.989427i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 17.2881i | − | 0.808705i | −0.914603 | − | 0.404353i | \(-0.867497\pi\) | ||
0.914603 | − | 0.404353i | \(-0.132503\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.89141 | 0.368340 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 39.7237 | 1.85012 | 0.925058 | − | 0.379826i | \(-0.124016\pi\) | ||||
0.925058 | + | 0.379826i | \(0.124016\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.7437i | 1.01051i | 0.862969 | + | 0.505257i | \(0.168602\pi\) | ||||
−0.862969 | + | 0.505257i | \(0.831398\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.02748 | − | 11.1296i | 0.279518 | − | 0.516124i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 17.1176i | − | 0.792108i | −0.918227 | − | 0.396054i | \(-0.870379\pi\) | ||
0.918227 | − | 0.396054i | \(-0.129621\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.32230 | 0.199585 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 23.0196 | 1.06069 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 25.4714i | − | 1.17118i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 11.5453 | + | 17.6952i | 0.529736 | + | 0.811912i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 4.37470i | − | 0.200304i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 33.0239 | 1.50890 | 0.754449 | − | 0.656358i | \(-0.227904\pi\) | ||||
0.754449 | + | 0.656358i | \(0.227904\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −51.5353 | −2.34981 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 4.51515i | − | 0.205446i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.68729 | + | 16.0409i | −0.394470 | + | 0.728380i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 26.9318i | 1.22040i | 0.792249 | + | 0.610198i | \(0.208910\pi\) | ||||
−0.792249 | + | 0.610198i | \(0.791090\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 19.1669 | 0.866756 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 26.7624 | 1.20777 | 0.603886 | − | 0.797071i | \(-0.293618\pi\) | ||||
0.603886 | + | 0.797071i | \(0.293618\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 46.8589i | 2.11042i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7.25051 | − | 3.92667i | −0.325886 | − | 0.176491i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 30.1307i | − | 1.35155i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.7069 | 0.837435 | 0.418717 | − | 0.908117i | \(-0.362480\pi\) | ||||
0.418717 | + | 0.908117i | \(0.362480\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 14.7151 | 0.657423 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 37.1869i | 1.65808i | 0.559189 | + | 0.829040i | \(0.311113\pi\) | ||||
−0.559189 | + | 0.829040i | \(0.688887\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.41773 | + | 2.93409i | 0.241086 | + | 0.130565i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.02650i | 0.356469i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.39023 | −0.238918 | −0.119459 | − | 0.992839i | \(-0.538116\pi\) | ||||
−0.119459 | + | 0.992839i | \(0.538116\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.48084 | −0.286695 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.22571i | 0.186570i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 12.2785 | − | 22.6721i | 0.541057 | − | 0.999051i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 0.840243i | − | 0.0369538i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −14.7906 | −0.649234 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.7511 | −0.821500 | −0.410750 | − | 0.911748i | \(-0.634733\pi\) | ||||
−0.410750 | + | 0.911748i | \(0.634733\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.43214i | 0.0626230i | 0.999510 | + | 0.0313115i | \(0.00996839\pi\) | ||||
−0.999510 | + | 0.0313115i | \(0.990032\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 11.8092 | + | 18.0997i | 0.515397 | + | 0.789936i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 44.6683i | − | 1.94578i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.9088 | 0.952555 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.83840 | −0.296761 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 6.24061i | − | 0.270311i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13.6818 | + | 25.2631i | −0.591515 | + | 1.09222i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 16.7747i | 0.723880i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −43.0785 | −1.85552 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.35121 | 0.101087 | 0.0505433 | − | 0.998722i | \(-0.483905\pi\) | ||||
0.0505433 | + | 0.998722i | \(0.483905\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 18.8727i | − | 0.809904i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.24218 | + | 3.92215i | 0.310221 | + | 0.168007i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 41.0405i | − | 1.75476i | −0.479793 | − | 0.877382i | \(-0.659288\pi\) | ||
0.479793 | − | 0.877382i | \(-0.340712\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.41474 | −0.188416 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −25.0921 | −1.06896 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 22.3241i | − | 0.949319i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −22.0982 | − | 11.9677i | −0.938017 | − | 0.508003i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 3.09843i | − | 0.131285i | −0.997843 | − | 0.0656424i | \(-0.979090\pi\) | ||
0.997843 | − | 0.0656424i | \(-0.0209097\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −31.6740 | −1.33967 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −29.0997 | −1.22859 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15.9187i | 0.670891i | 0.942060 | + | 0.335446i | \(0.108887\pi\) | ||||
−0.942060 | + | 0.335446i | \(0.891113\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.44562 | + | 15.5947i | −0.355310 | + | 0.656073i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.32230i | 0.181520i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 28.1166 | 1.17871 | 0.589355 | − | 0.807874i | \(-0.299382\pi\) | ||||
0.589355 | + | 0.807874i | \(0.299382\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.2535 | −0.889431 | −0.444716 | − | 0.895672i | \(-0.646695\pi\) | ||||
−0.444716 | + | 0.895672i | \(0.646695\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 4.24583i | − | 0.177372i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.37435 | − | 2.85406i | 0.182423 | − | 0.119023i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 44.9336i | − | 1.87061i | −0.353842 | − | 0.935305i | \(-0.615125\pi\) | ||
0.353842 | − | 0.935305i | \(-0.384875\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 17.8178 | 0.740480 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 44.8472 | 1.86057 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 16.1317i | 0.668109i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.88286 | + | 9.01611i | −0.201881 | + | 0.372770i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 14.3953i | − | 0.594157i | −0.954853 | − | 0.297078i | \(-0.903988\pi\) | ||
0.954853 | − | 0.297078i | \(-0.0960123\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 23.9191 | 0.985568 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.79528 | −0.320655 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15.5990i | 0.640576i | 0.947320 | + | 0.320288i | \(0.103780\pi\) | ||||
−0.947320 | + | 0.320288i | \(0.896220\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 67.0664 | + | 36.3212i | 2.74946 | + | 1.48903i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 1.01866i | − | 0.0416911i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.80305 | −0.359683 | −0.179841 | − | 0.983696i | \(-0.557558\pi\) | ||||
−0.179841 | + | 0.983696i | \(0.557558\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.90124 | −0.240717 | −0.120358 | − | 0.992731i | \(-0.538404\pi\) | ||||
−0.120358 | + | 0.992731i | \(0.538404\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.00000i | 0.0407231i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.10774 | + | 2.76621i | 0.207659 | + | 0.112462i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 42.2861i | 1.71634i | 0.513367 | + | 0.858169i | \(0.328398\pi\) | ||||
−0.513367 | + | 0.858169i | \(0.671602\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −25.6656 | −1.04002 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.04485 | −0.0422702 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.3331i | 0.740469i | 0.928938 | + | 0.370234i | \(0.120723\pi\) | ||||
−0.928938 | + | 0.370234i | \(0.879277\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.44922 | − | 2.67596i | 0.0584382 | − | 0.107905i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 21.0364i | − | 0.846892i | −0.905921 | − | 0.423446i | \(-0.860820\pi\) | ||
0.905921 | − | 0.423446i | \(-0.139180\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.00519 | −0.321756 | −0.160878 | − | 0.986974i | \(-0.551433\pi\) | ||||
−0.160878 | + | 0.986974i | \(0.551433\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.04462 | 0.0419190 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 11.7319i | 0.470030i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −10.0706 | + | 22.8820i | −0.402823 | + | 0.915278i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 15.5823i | − | 0.622299i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −88.6903 | −3.53632 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 38.5012 | 1.53271 | 0.766354 | − | 0.642418i | \(-0.222069\pi\) | ||||
0.766354 | + | 0.642418i | \(0.222069\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 16.9281i | − | 0.672831i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.73468 | + | 12.4355i | −0.267258 | + | 0.493486i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 53.5687i | 2.12247i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.97099 | 0.275768 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −36.6360 | −1.44703 | −0.723517 | − | 0.690307i | \(-0.757476\pi\) | ||||
−0.723517 | + | 0.690307i | \(0.757476\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.482014i | 0.0190088i | 0.999955 | + | 0.00950439i | \(0.00302539\pi\) | ||||
−0.999955 | + | 0.00950439i | \(0.996975\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −13.5817 | − | 7.35548i | −0.534781 | − | 0.289622i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 42.4176i | 1.66761i | 0.552060 | + | 0.833804i | \(0.313842\pi\) | ||||
−0.552060 | + | 0.833804i | \(0.686158\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 25.2167 | 0.989841 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 24.4658 | 0.958891 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.57080i | 0.0614703i | 0.999528 | + | 0.0307352i | \(0.00978485\pi\) | ||||
−0.999528 | + | 0.0307352i | \(0.990215\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 17.3294 | + | 9.38512i | 0.677117 | + | 0.366707i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 1.49940i | − | 0.0584970i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.85440 | 0.0722370 | 0.0361185 | − | 0.999348i | \(-0.488501\pi\) | ||||
0.0361185 | + | 0.999348i | \(0.488501\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.8088 | 0.692683 | 0.346342 | − | 0.938108i | \(-0.387424\pi\) | ||||
0.346342 | + | 0.938108i | \(0.387424\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 36.1858i | 1.40534i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −19.4494 | + | 35.9128i | −0.754214 | + | 1.39264i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.20289i | 0.240177i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −19.6720 | −0.760562 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 16.2794 | 0.628459 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 8.76791i | − | 0.337978i | −0.985618 | − | 0.168989i | \(-0.945950\pi\) | ||
0.985618 | − | 0.168989i | \(-0.0540502\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.18752 | + | 2.73216i | −0.161178 | + | 0.105161i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 14.2467i | − | 0.547547i | −0.961794 | − | 0.273773i | \(-0.911728\pi\) | ||
0.961794 | − | 0.273773i | \(-0.0882718\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −35.2621 | −1.35324 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −21.8906 | −0.838850 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.19495i | 0.275307i | 0.990480 | + | 0.137654i | \(0.0439561\pi\) | ||||
−0.990480 | + | 0.137654i | \(0.956044\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.65905 | + | 15.9888i | −0.330845 | + | 0.610899i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.28727i | 0.125417i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 20.0600 | 0.764227 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.2758 | 0.390911 | 0.195455 | − | 0.980713i | \(-0.437382\pi\) | ||||
0.195455 | + | 0.980713i | \(0.437382\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 15.9385i | − | 0.605454i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.55658 | + | 4.63400i | 0.324570 | + | 0.175778i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 10.7399i | − | 0.406801i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −10.4772 | −0.396283 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.73210 | 0.178729 | 0.0893644 | − | 0.995999i | \(-0.471516\pi\) | ||||
0.0893644 | + | 0.995999i | \(0.471516\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 47.4920i | − | 1.79120i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.448030 | − | 0.242640i | −0.0168738 | − | 0.00913835i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11.9096i | 0.447906i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −23.8274 | −0.894858 | −0.447429 | − | 0.894319i | \(-0.647660\pi\) | ||||
−0.447429 | + | 0.894319i | \(0.647660\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.16488 | 0.193698 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 5.91292i | − | 0.221441i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 18.0056 | − | 33.2470i | 0.673371 | − | 1.24337i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 19.8748i | 0.742236i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.11082 | 0.190601 | 0.0953007 | − | 0.995449i | \(-0.469619\pi\) | ||||
0.0953007 | + | 0.995449i | \(0.469619\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 49.8391 | 1.85611 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 11.2871i | 0.419771i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −16.2235 | − | 24.8653i | −0.602524 | − | 0.923474i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 30.2795i | 1.12300i | 0.827475 | + | 0.561502i | \(0.189776\pi\) | ||||
−0.827475 | + | 0.561502i | \(0.810224\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −54.5098 | −2.01612 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21.5837i | 0.797213i | 0.917122 | + | 0.398607i | \(0.130506\pi\) | ||||
−0.917122 | + | 0.398607i | \(0.869494\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −12.4399 | + | 22.9701i | −0.458854 | + | 0.847265i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 3.68751i | − | 0.135831i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −51.2289 | −1.88449 | −0.942243 | − | 0.334929i | \(-0.891288\pi\) | ||||
−0.942243 | + | 0.334929i | \(0.891288\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −19.3768 | −0.711826 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 42.0409i | 1.54233i | 0.636634 | + | 0.771166i | \(0.280326\pi\) | ||||
−0.636634 | + | 0.771166i | \(0.719674\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.4709 | + | 5.67075i | 0.383625 | + | 0.207760i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 10.3758i | 0.379629i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −55.5350 | −2.02921 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15.1306 | −0.552125 | −0.276062 | − | 0.961140i | \(-0.589030\pi\) | ||||
−0.276062 | + | 0.961140i | \(0.589030\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 30.1154i | 1.09747i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 29.4413 | + | 15.9446i | 1.07148 | + | 0.580282i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 46.7505i | − | 1.69918i | −0.527447 | − | 0.849588i | \(-0.676851\pi\) | ||
0.527447 | − | 0.849588i | \(-0.323149\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.85204 | −0.139820 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 27.2113 | 0.986410 | 0.493205 | − | 0.869913i | \(-0.335825\pi\) | ||||
0.493205 | + | 0.869913i | \(0.335825\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15.9202i | 0.576350i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −8.40322 | + | 15.5164i | −0.303819 | + | 0.560996i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 31.3573i | − | 1.13224i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.97578 | −0.323675 | −0.161838 | − | 0.986817i | \(-0.551742\pi\) | ||||
−0.161838 | + | 0.986817i | \(0.551742\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −26.5811 | −0.957295 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 29.6344i | − | 1.06587i | −0.846155 | − | 0.532937i | \(-0.821088\pi\) | ||
0.846155 | − | 0.532937i | \(-0.178912\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 15.4651 | + | 23.7029i | 0.555521 | + | 0.851433i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 48.5776i | − | 1.74271i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.75100 | 0.206051 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −25.7056 | −0.919819 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 5.93796i | − | 0.212205i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −24.5126 | + | 45.2620i | −0.874892 | + | 1.61547i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.6729i | 0.594325i | 0.954827 | + | 0.297162i | \(0.0960403\pi\) | ||||
−0.954827 | + | 0.297162i | \(0.903960\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −10.5190 | −0.374486 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −34.2812 | −1.21890 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 20.2436i | − | 0.718872i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 8.60169 | + | 4.65843i | 0.305070 | + | 0.165217i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.25284i | 0.150643i | 0.997159 | + | 0.0753216i | \(0.0239983\pi\) | ||||
−0.997159 | + | 0.0753216i | \(0.976002\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.79815 | −0.0636141 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.71428 | −0.0959043 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.52903i | 0.195115i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.87784 | + | 4.80798i | 0.312903 | + | 0.169459i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 0.906058i | − | 0.0318948i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −15.7772 | −0.554696 | −0.277348 | − | 0.960770i | \(-0.589455\pi\) | ||||
−0.277348 | + | 0.960770i | \(0.589455\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −39.9011 | −1.40112 | −0.700559 | − | 0.713594i | \(-0.747066\pi\) | ||||
−0.700559 | + | 0.713594i | \(0.747066\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 11.0749i | − | 0.388412i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −20.4100 | + | 37.6866i | −0.714930 | + | 1.32010i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 29.1890i | − | 1.02119i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −19.8198 | −0.692558 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.842179 | 0.0293923 | 0.0146961 | − | 0.999892i | \(-0.495322\pi\) | ||||
0.0146961 | + | 0.999892i | \(0.495322\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 51.5407i | − | 1.79660i | −0.439388 | − | 0.898298i | \(-0.644805\pi\) | ||
0.439388 | − | 0.898298i | \(-0.355195\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 15.4415 | − | 10.0749i | 0.537604 | − | 0.350762i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 0.433745i | − | 0.0150828i | −0.999972 | − | 0.00754140i | \(-0.997599\pi\) | ||
0.999972 | − | 0.00754140i | \(-0.00240052\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −24.8652 | −0.863604 | −0.431802 | − | 0.901968i | \(-0.642122\pi\) | ||||
−0.431802 | + | 0.901968i | \(0.642122\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.74825 | −0.130025 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 92.1897i | 3.19418i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −15.6695 | + | 28.9334i | −0.542265 | + | 1.00128i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.66037i | 0.195651i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −43.0915 | −1.48768 | −0.743842 | − | 0.668355i | \(-0.766999\pi\) | ||||
−0.743842 | + | 0.668355i | \(0.766999\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.25933 | 0.215839 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 17.7546i | 0.611501i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −15.7820 | − | 8.54706i | −0.542917 | − | 0.294028i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11.2282i | 0.385804i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −19.6755 | −0.675260 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11.7403 | −0.402452 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 45.0330i | 1.54190i | 0.636895 | + | 0.770951i | \(0.280219\pi\) | ||||
−0.636895 | + | 0.770951i | \(0.719781\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.30873 | − | 4.49977i | −0.284153 | − | 0.153889i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 45.9359i | − | 1.56914i | −0.620039 | − | 0.784571i | \(-0.712883\pi\) | ||
0.620039 | − | 0.784571i | \(-0.287117\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 47.9577 | 1.63629 | 0.818147 | − | 0.575009i | \(-0.195002\pi\) | ||||
0.818147 | + | 0.575009i | \(0.195002\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.88246 | 0.200474 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 47.8219i | − | 1.62788i | −0.580952 | − | 0.813938i | \(-0.697319\pi\) | ||
0.580952 | − | 0.813938i | \(-0.302681\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15.7498 | − | 29.0818i | 0.535510 | − | 0.988809i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 45.2744i | 1.53760i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −19.0455 | −0.646075 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.58547 | −0.155373 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 8.15818i | − | 0.276113i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −48.1634 | + | 3.94615i | −1.62822 | + | 0.133404i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 56.1039i | 1.89449i | 0.320505 | + | 0.947247i | \(0.396147\pi\) | ||||
−0.320505 | + | 0.947247i | \(0.603853\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 16.3514 | 0.551519 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27.8879 | 0.939567 | 0.469784 | − | 0.882782i | \(-0.344332\pi\) | ||||
0.469784 | + | 0.882782i | \(0.344332\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 48.5203i | 1.63284i | 0.577459 | + | 0.816419i | \(0.304044\pi\) | ||||
−0.577459 | + | 0.816419i | \(0.695956\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.28191 | − | 13.4459i | 0.244779 | − | 0.451979i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 42.3930i | − | 1.42342i | −0.702475 | − | 0.711708i | \(-0.747922\pi\) | ||
0.702475 | − | 0.711708i | \(-0.252078\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −27.3364 | −0.916833 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.68751 | 0.123536 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 0.962878i | − | 0.0322215i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −32.9829 | − | 17.8626i | −1.10250 | − | 0.597081i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.79006i | 0.159935i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −33.6111 | −1.12099 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 34.5226 | 1.15011 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 29.8562i | − | 0.993553i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 37.1081 | + | 20.0967i | 1.23352 | + | 0.668036i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 27.2037i | − | 0.903283i | −0.892200 | − | 0.451641i | \(-0.850839\pi\) | ||
0.892200 | − | 0.451641i | \(-0.149161\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.75538 | −0.0913903 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 38.6906 | 1.28188 | 0.640938 | − | 0.767592i | \(-0.278545\pi\) | ||||
0.640938 | + | 0.767592i | \(0.278545\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 38.2607i | − | 1.26625i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.70106 | − | 8.68042i | 0.155412 | − | 0.286966i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 38.0946i | 1.25800i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 38.3399 | 1.26472 | 0.632359 | − | 0.774676i | \(-0.282087\pi\) | ||||
0.632359 | + | 0.774676i | \(0.282087\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.589802 | 0.0194347 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 31.9652i | 1.05215i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 47.0628 | − | 30.7063i | 1.54742 | − | 1.00962i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 11.5307i | 0.378718i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −39.2640 | −1.28821 | −0.644105 | − | 0.764937i | \(-0.722770\pi\) | ||||
−0.644105 | + | 0.764937i | \(0.722770\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −49.3659 | −1.61790 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 13.3850i | − | 0.438206i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 30.9870 | − | 57.2168i | 1.01338 | − | 1.87119i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18.8708i | 0.616483i | 0.951308 | + | 0.308242i | \(0.0997405\pi\) | ||||
−0.951308 | + | 0.308242i | \(0.900259\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 15.9356 | 0.520040 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −33.8851 | −1.10462 | −0.552311 | − | 0.833638i | \(-0.686254\pi\) | ||||
−0.552311 | + | 0.833638i | \(0.686254\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 1.42168i | − | 0.0462962i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −8.49866 | − | 4.60263i | −0.276461 | − | 0.149723i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 24.6489i | 0.800980i | 0.916301 | + | 0.400490i | \(0.131160\pi\) | ||||
−0.916301 | + | 0.400490i | \(0.868840\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.87543 | 0.223186 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 16.4627 | 0.533841 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 44.0917i | − | 1.42827i | −0.700007 | − | 0.714136i | \(-0.746820\pi\) | ||
0.700007 | − | 0.714136i | \(-0.253180\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.34830 | + | 4.52120i | 0.270145 | + | 0.146303i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 21.8963i | 0.707806i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −35.1475 | −1.13497 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.03982 | 0.0335426 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 12.8485i | − | 0.414037i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −18.9733 | + | 35.0339i | −0.610773 | + | 1.12778i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.29052i | 0.298763i | 0.988780 | + | 0.149381i | \(0.0477282\pi\) | ||||
−0.988780 | + | 0.149381i | \(0.952272\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −33.3468 | −1.07125 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.6614 | 0.695147 | 0.347574 | − | 0.937653i | \(-0.387006\pi\) | ||||
0.347574 | + | 0.937653i | \(0.387006\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 18.8096i | 0.603008i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −12.5282 | − | 19.2017i | −0.401225 | − | 0.614947i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 60.2392i | − | 1.92722i | −0.267308 | − | 0.963611i | \(-0.586134\pi\) | ||
0.267308 | − | 0.963611i | \(-0.413866\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.0089 | 0.319887 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.68327 | −0.117598 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 41.4407i | − | 1.32175i | −0.750495 | − | 0.660877i | \(-0.770185\pi\) | ||
0.750495 | − | 0.660877i | \(-0.229815\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.30086 | − | 15.3274i | 0.264487 | − | 0.488370i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 0.984887i | − | 0.0313493i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.21568 | −0.229445 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.3043 | 0.581454 | 0.290727 | − | 0.956806i | \(-0.406103\pi\) | ||||
0.290727 | + | 0.956806i | \(0.406103\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 32.0995i | − | 1.01865i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.00293 | + | 1.08473i | 0.0634972 | + | 0.0343882i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 18.1938i | − | 0.576204i | −0.957600 | − | 0.288102i | \(-0.906976\pi\) | ||
0.957600 | − | 0.288102i | \(-0.0930242\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 11.2388 | 0.355581 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4020.2.g.c.1609.16 | ✓ | 38 | |
5.4 | even | 2 | inner | 4020.2.g.c.1609.35 | yes | 38 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4020.2.g.c.1609.16 | ✓ | 38 | 1.1 | even | 1 | trivial | |
4020.2.g.c.1609.35 | yes | 38 | 5.4 | even | 2 | inner |