Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4012,2,Mod(237,4012)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4012, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4012.237");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4012 = 2^{2} \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4012.b (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: | \(32.0359812909\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 237.5 | ||
Character | \(\chi\) | \(=\) | 4012.237 |
Dual form | 4012.2.b.a.237.36 |
$q$-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 \(\left(\mathbb{Z}/4012\mathbb{Z}\right)^\times\).
\(n\) | \(2007\) | \(3129\) | \(3777\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − | 2.44713i | − | 1.41285i | −0.707789 | − | 0.706424i | \(-0.750307\pi\) | ||
0.707789 | − | 0.706424i | \(-0.249693\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 1.66009i | − | 0.742413i | −0.928550 | − | 0.371207i | \(-0.878944\pi\) | ||
0.928550 | − | 0.371207i | \(-0.121056\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.65944i | 1.38314i | 0.722311 | + | 0.691568i | \(0.243080\pi\) | ||||
−0.722311 | + | 0.691568i | \(0.756920\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.98842 | −0.996140 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.95066i | 0.588146i | 0.955783 | + | 0.294073i | \(0.0950109\pi\) | ||||
−0.955783 | + | 0.294073i | \(0.904989\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.88460 | −0.522694 | −0.261347 | − | 0.965245i | \(-0.584167\pi\) | ||||
−0.261347 | + | 0.965245i | \(0.584167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.06244 | −1.04892 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.75271 | − | 1.70796i | −0.910167 | − | 0.414242i | ||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.87170 | 1.11764 | 0.558822 | − | 0.829287i | \(-0.311253\pi\) | ||||
0.558822 | + | 0.829287i | \(0.311253\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 8.95510 | 1.95416 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 9.29998i | − | 1.93918i | −0.244733 | − | 0.969590i | \(-0.578700\pi\) | ||
0.244733 | − | 0.969590i | \(-0.421300\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.24411 | 0.448822 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 0.0283342i | − | 0.00545292i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.33623i | 0.619522i | 0.950814 | + | 0.309761i | \(0.100249\pi\) | ||||
−0.950814 | + | 0.309761i | \(0.899751\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 4.53272i | − | 0.814100i | −0.913406 | − | 0.407050i | \(-0.866558\pi\) | ||
0.913406 | − | 0.407050i | \(-0.133442\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.77351 | 0.830961 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.07498 | 1.02686 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 2.82715i | − | 0.464780i | −0.972623 | − | 0.232390i | \(-0.925345\pi\) | ||
0.972623 | − | 0.232390i | \(-0.0746546\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.61185i | 0.738487i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.268240i | 0.0418921i | 0.999781 | + | 0.0209460i | \(0.00666782\pi\) | ||||
−0.999781 | + | 0.0209460i | \(0.993332\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.42799 | −1.28526 | −0.642628 | − | 0.766178i | \(-0.722156\pi\) | ||||
−0.642628 | + | 0.766178i | \(0.722156\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.96104i | 0.739548i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.14320 | −1.18781 | −0.593904 | − | 0.804536i | \(-0.702414\pi\) | ||||
−0.593904 | + | 0.804536i | \(0.702414\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.39147 | −0.913067 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.17960 | + | 9.18336i | −0.585260 | + | 1.28593i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.67756 | 0.367792 | 0.183896 | − | 0.982946i | \(-0.441129\pi\) | ||||
0.183896 | + | 0.982946i | \(0.441129\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.23826 | 0.436647 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 11.9217i | − | 1.57906i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.00000 | −0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 2.27284i | − | 0.291007i | −0.989358 | − | 0.145504i | \(-0.953520\pi\) | ||
0.989358 | − | 0.145504i | \(-0.0464803\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 10.9359i | − | 1.37780i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.12860i | 0.388055i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −15.1523 | −1.85115 | −0.925574 | − | 0.378566i | \(-0.876417\pi\) | ||||
−0.925574 | + | 0.378566i | \(0.876417\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −22.7582 | −2.73977 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.53554i | 0.775626i | 0.921738 | + | 0.387813i | \(0.126769\pi\) | ||||
−0.921738 | + | 0.387813i | \(0.873231\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 6.29649i | − | 0.736948i | −0.929638 | − | 0.368474i | \(-0.879880\pi\) | ||
0.929638 | − | 0.368474i | \(-0.120120\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 5.49162i | − | 0.634118i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.13831 | −0.813486 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.53912i | 0.285673i | 0.989746 | + | 0.142837i | \(0.0456223\pi\) | ||||
−0.989746 | + | 0.142837i | \(0.954378\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.03460 | −1.00384 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.22158 | −0.243850 | −0.121925 | − | 0.992539i | \(-0.538907\pi\) | ||||
−0.121925 | + | 0.992539i | \(0.538907\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.83536 | + | 6.22983i | −0.307538 | + | 0.675720i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.16416 | 0.875290 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.3861 | −1.20693 | −0.603465 | − | 0.797390i | \(-0.706214\pi\) | ||||
−0.603465 | + | 0.797390i | \(0.706214\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 6.89657i | − | 0.722957i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −11.0921 | −1.15020 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 8.08745i | − | 0.829755i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.9275i | 1.51566i | 0.652452 | + | 0.757830i | \(0.273741\pi\) | ||||
−0.652452 | + | 0.757830i | \(0.726259\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 5.82939i | − | 0.585876i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.48872 | −0.446645 | −0.223322 | − | 0.974745i | \(-0.571690\pi\) | ||||
−0.223322 | + | 0.974745i | \(0.571690\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −17.6969 | −1.74373 | −0.871865 | − | 0.489747i | \(-0.837089\pi\) | ||||
−0.871865 | + | 0.489747i | \(0.837089\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 14.8662i | − | 1.45080i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 14.0953i | − | 1.36265i | −0.731982 | − | 0.681324i | \(-0.761404\pi\) | ||
0.731982 | − | 0.681324i | \(-0.238596\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.55639i | 0.723770i | 0.932223 | + | 0.361885i | \(0.117867\pi\) | ||||
−0.932223 | + | 0.361885i | \(0.882133\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.91838 | −0.656664 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 11.8159i | − | 1.11155i | −0.831334 | − | 0.555773i | \(-0.812422\pi\) | ||
0.831334 | − | 0.555773i | \(-0.187578\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −15.4388 | −1.43967 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.63198 | 0.520676 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.25018 | − | 13.7328i | 0.572953 | − | 1.25889i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.19493 | 0.654084 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.656418 | 0.0591872 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 12.0259i | − | 1.07563i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.8742 | 1.67481 | 0.837407 | − | 0.546579i | \(-0.184070\pi\) | ||||
0.837407 | + | 0.546579i | \(0.184070\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 20.6243i | 1.81587i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.77368i | 0.766560i | 0.923632 | + | 0.383280i | \(0.125205\pi\) | ||||
−0.923632 | + | 0.383280i | \(0.874795\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 17.8277i | 1.54586i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.0470372 | −0.00404832 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.32087 | 0.796336 | 0.398168 | − | 0.917313i | \(-0.369646\pi\) | ||||
0.398168 | + | 0.917313i | \(0.369646\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.62901i | 0.647084i | 0.946214 | + | 0.323542i | \(0.104874\pi\) | ||||
−0.946214 | + | 0.323542i | \(0.895126\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 19.9274i | 1.67819i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 3.67621i | − | 0.307420i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.53843 | 0.459941 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 15.6407i | 1.29002i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −19.2065 | −1.57345 | −0.786727 | − | 0.617301i | \(-0.788226\pi\) | ||||
−0.786727 | + | 0.617301i | \(0.788226\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.62269 | 0.213431 | 0.106716 | − | 0.994290i | \(-0.465967\pi\) | ||||
0.106716 | + | 0.994290i | \(0.465967\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 11.2147 | + | 5.10411i | 0.906654 | + | 0.412643i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.52470 | −0.604399 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.77758 | 0.700528 | 0.350264 | − | 0.936651i | \(-0.386092\pi\) | ||||
0.350264 | + | 0.936651i | \(0.386092\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 6.55233i | − | 0.519634i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 34.0327 | 2.68215 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.56986i | 0.436265i | 0.975919 | + | 0.218133i | \(0.0699966\pi\) | ||||
−0.975919 | + | 0.218133i | \(0.930003\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 7.92444i | − | 0.616917i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 11.0444i | − | 0.854645i | −0.904099 | − | 0.427322i | \(-0.859457\pi\) | ||
0.904099 | − | 0.427322i | \(-0.140543\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.44829 | −0.726791 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −14.5587 | −1.11333 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 13.3496i | − | 1.01495i | −0.861666 | − | 0.507476i | \(-0.830579\pi\) | ||
0.861666 | − | 0.507476i | \(-0.169421\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.21218i | 0.620783i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.44713i | 0.183937i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.14078 | −0.0852657 | −0.0426328 | − | 0.999091i | \(-0.513575\pi\) | ||||
−0.0426328 | + | 0.999091i | \(0.513575\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 5.56258i | − | 0.413463i | −0.978398 | − | 0.206732i | \(-0.933717\pi\) | ||
0.978398 | − | 0.206732i | \(-0.0662827\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.56192 | −0.411149 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.69331 | −0.345059 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.33165 | − | 7.32027i | 0.243634 | − | 0.535311i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.103687 | 0.00754213 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.13657 | 0.226954 | 0.113477 | − | 0.993541i | \(-0.463801\pi\) | ||||
0.113477 | + | 0.993541i | \(0.463801\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 4.66615i | − | 0.335877i | −0.985798 | − | 0.167938i | \(-0.946289\pi\) | ||
0.985798 | − | 0.167938i | \(-0.0537109\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 7.65607 | 0.548263 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 12.7372i | − | 0.907485i | −0.891133 | − | 0.453743i | \(-0.850089\pi\) | ||
0.891133 | − | 0.453743i | \(-0.149911\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.3918i | 0.736653i | 0.929696 | + | 0.368327i | \(0.120069\pi\) | ||||
−0.929696 | + | 0.368327i | \(0.879931\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 37.0796i | 2.61539i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −12.2087 | −0.856883 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.445302 | 0.0311013 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 27.7923i | 1.93170i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.50303i | 0.657338i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.85042i | 0.471602i | 0.971801 | + | 0.235801i | \(0.0757714\pi\) | ||||
−0.971801 | + | 0.235801i | \(0.924229\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 15.9933 | 1.09584 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 13.9912i | 0.954192i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 16.5872 | 1.12601 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −15.4083 | −1.04120 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.07236 | + | 3.21882i | 0.475739 | + | 0.216521i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.3027 | −0.890817 | −0.445408 | − | 0.895328i | \(-0.646941\pi\) | ||||
−0.445408 | + | 0.895328i | \(0.646941\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.70635 | −0.447090 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 2.20817i | − | 0.146562i | −0.997311 | − | 0.0732808i | \(-0.976653\pi\) | ||
0.997311 | − | 0.0732808i | \(-0.0233469\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −29.5080 | −1.94994 | −0.974971 | − | 0.222333i | \(-0.928633\pi\) | ||||
−0.974971 | + | 0.222333i | \(0.928633\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 17.4683i | 1.14933i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 21.0896i | − | 1.38163i | −0.723033 | − | 0.690813i | \(-0.757253\pi\) | ||
0.723033 | − | 0.690813i | \(-0.242747\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 13.5184i | 0.881845i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.21354 | 0.403613 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.1004 | 1.10613 | 0.553067 | − | 0.833137i | \(-0.313457\pi\) | ||||
0.553067 | + | 0.833137i | \(0.313457\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 5.72180i | − | 0.368573i | −0.982873 | − | 0.184287i | \(-0.941003\pi\) | ||
0.982873 | − | 0.184287i | \(-0.0589975\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 22.0238i | 1.41283i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 10.6104i | 0.677873i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.18120 | −0.584186 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.43649i | 0.344524i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −22.2638 | −1.40528 | −0.702641 | − | 0.711545i | \(-0.747996\pi\) | ||||
−0.702641 | + | 0.711545i | \(0.747996\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18.1411 | 1.14052 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 15.2452 | + | 6.93849i | 0.954690 | + | 0.434505i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −14.1030 | −0.879720 | −0.439860 | − | 0.898066i | \(-0.644972\pi\) | ||||
−0.439860 | + | 0.898066i | \(0.644972\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.3458 | 0.642855 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 9.97005i | − | 0.617131i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.0980 | 0.745994 | 0.372997 | − | 0.927833i | \(-0.378330\pi\) | ||||
0.372997 | + | 0.927833i | \(0.378330\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 4.44499i | − | 0.273054i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 27.8633i | 1.70521i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 27.1118i | − | 1.65303i | −0.562912 | − | 0.826517i | \(-0.690319\pi\) | ||
0.562912 | − | 0.826517i | \(-0.309681\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.82979 | 0.111152 | 0.0555760 | − | 0.998454i | \(-0.482300\pi\) | ||||
0.0555760 | + | 0.998454i | \(0.482300\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −16.8768 | −1.02143 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.37750i | 0.263973i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.9811i | 1.50097i | 0.660889 | + | 0.750484i | \(0.270179\pi\) | ||||
−0.660889 | + | 0.750484i | \(0.729821\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 13.5457i | 0.810958i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.89922 | 0.113298 | 0.0566490 | − | 0.998394i | \(-0.481958\pi\) | ||||
0.0566490 | + | 0.998394i | \(0.481958\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 23.7781i | − | 1.41346i | −0.707482 | − | 0.706731i | \(-0.750169\pi\) | ||
0.707482 | − | 0.706731i | \(-0.249831\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −19.7910 | −1.17232 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.981608 | −0.0579425 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.1657 | + | 12.8190i | 0.656808 | + | 0.754058i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 36.5295 | 2.14140 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.56125 | 0.324892 | 0.162446 | − | 0.986717i | \(-0.448062\pi\) | ||||
0.162446 | + | 0.986717i | \(0.448062\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.66009i | 0.0966540i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.0552703 | 0.00320711 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 17.5267i | 1.01360i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 30.8417i | − | 1.77769i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 10.9845i | 0.631041i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.77311 | −0.216048 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.01685 | −0.115108 | −0.0575539 | − | 0.998342i | \(-0.518330\pi\) | ||||
−0.0575539 | + | 0.998342i | \(0.518330\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 43.3066i | 2.46362i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 22.2487i | 1.26161i | 0.775942 | + | 0.630804i | \(0.217275\pi\) | ||||
−0.775942 | + | 0.630804i | \(0.782725\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 29.4934i | − | 1.66706i | −0.552472 | − | 0.833532i | \(-0.686315\pi\) | ||
0.552472 | − | 0.833532i | \(-0.313685\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −18.1546 | −1.02290 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.15858i | 0.345901i | 0.984931 | + | 0.172950i | \(0.0553300\pi\) | ||||
−0.984931 | + | 0.172950i | \(0.944670\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.50784 | −0.364369 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −34.4931 | −1.92522 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −18.2821 | − | 8.32068i | −1.01724 | − | 0.462975i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.22925 | −0.234597 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 18.4914 | 1.02258 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 29.7995i | − | 1.64290i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.6686 | −1.02612 | −0.513060 | − | 0.858353i | \(-0.671488\pi\) | ||||
−0.513060 | + | 0.858353i | \(0.671488\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.44871i | 0.462986i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 25.1541i | 1.37432i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 23.7041i | − | 1.29125i | −0.763656 | − | 0.645623i | \(-0.776598\pi\) | ||
0.763656 | − | 0.645623i | \(-0.223402\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −28.9150 | −1.57045 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.84178 | 0.478809 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.22688i | 0.120240i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 37.7806i | 2.03404i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 27.3088i | 1.46602i | 0.680220 | + | 0.733008i | \(0.261884\pi\) | ||||
−0.680220 | + | 0.733008i | \(0.738116\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −19.7076 | −1.05492 | −0.527462 | − | 0.849579i | \(-0.676856\pi\) | ||||
−0.527462 | + | 0.849579i | \(0.676856\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.0533986i | 0.00285020i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 27.1815 | 1.44673 | 0.723363 | − | 0.690468i | \(-0.242595\pi\) | ||||
0.723363 | + | 0.690468i | \(0.242595\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.8496 | 0.575835 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −33.6059 | − | 15.2950i | −1.77861 | − | 0.809495i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −20.4096 | −1.07718 | −0.538588 | − | 0.842569i | \(-0.681042\pi\) | ||||
−0.538588 | + | 0.842569i | \(0.681042\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.73347 | 0.249130 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 17.6069i | − | 0.924122i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10.4527 | −0.547120 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22.9589i | 1.19845i | 0.800582 | + | 0.599224i | \(0.204524\pi\) | ||||
−0.800582 | + | 0.599224i | \(0.795476\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 0.801615i | − | 0.0417304i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.79837i | 0.508706i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 30.2437 | 1.56596 | 0.782979 | − | 0.622048i | \(-0.213699\pi\) | ||||
0.782979 | + | 0.622048i | \(0.213699\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −29.4288 | −1.51970 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 6.28745i | − | 0.323820i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 24.1637i | − | 1.24120i | −0.784126 | − | 0.620602i | \(-0.786888\pi\) | ||
0.784126 | − | 0.620602i | \(-0.213112\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 46.1875i | − | 2.36626i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.9208 | 0.558025 | 0.279012 | − | 0.960287i | \(-0.409993\pi\) | ||||
0.279012 | + | 0.960287i | \(0.409993\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 11.8502i | 0.603943i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 25.1864 | 1.28030 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 30.7751 | 1.56036 | 0.780181 | − | 0.625554i | \(-0.215127\pi\) | ||||
0.780181 | + | 0.625554i | \(0.215127\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −15.8840 | + | 34.9002i | −0.803289 | + | 1.76498i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 21.4703 | 1.08303 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.21516 | 0.212087 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 4.32581i | − | 0.217106i | −0.994091 | − | 0.108553i | \(-0.965378\pi\) | ||
0.994091 | − | 0.108553i | \(-0.0346217\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 43.6266 | 2.18406 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 14.1274i | − | 0.705488i | −0.935720 | − | 0.352744i | \(-0.885249\pi\) | ||
0.935720 | − | 0.352744i | \(-0.114751\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.54235i | 0.425525i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 14.9982i | 0.745268i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.51480 | 0.273359 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.8864 | 0.884427 | 0.442213 | − | 0.896910i | \(-0.354193\pi\) | ||||
0.442213 | + | 0.896910i | \(0.354193\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 22.8093i | − | 1.12510i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 3.65944i | − | 0.180069i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.68802i | 0.181038i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 18.6691 | 0.914232 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 21.8574i | − | 1.06780i | −0.845547 | − | 0.533901i | \(-0.820726\pi\) | ||
0.845547 | − | 0.533901i | \(-0.179274\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 35.8778 | 1.74858 | 0.874290 | − | 0.485405i | \(-0.161328\pi\) | ||||
0.874290 | + | 0.485405i | \(0.161328\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 24.3353 | 1.18322 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8.42151 | − | 3.83286i | −0.408503 | − | 0.185921i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.31731 | 0.402503 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −8.99615 | −0.434338 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 22.1694i | 1.06786i | 0.845528 | + | 0.533931i | \(0.179286\pi\) | ||||
−0.845528 | + | 0.533931i | \(0.820714\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.4783 | −0.791895 | −0.395948 | − | 0.918273i | \(-0.629584\pi\) | ||||
−0.395948 | + | 0.918273i | \(0.629584\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 13.5532i | − | 0.649827i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 45.3067i | − | 2.16732i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 19.0168i | 0.907621i | 0.891098 | + | 0.453810i | \(0.149936\pi\) | ||||
−0.891098 | + | 0.453810i | \(0.850064\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 19.1004 | 0.909543 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −18.7287 | −0.889829 | −0.444915 | − | 0.895573i | \(-0.646766\pi\) | ||||
−0.444915 | + | 0.895573i | \(0.646766\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 18.9020i | 0.896041i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 47.0006i | 2.22305i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 16.5835i | − | 0.782626i | −0.920258 | − | 0.391313i | \(-0.872021\pi\) | ||
0.920258 | − | 0.391313i | \(-0.127979\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.523245 | −0.0246387 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 6.41805i | − | 0.301546i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −11.4489 | −0.536733 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.6547 | 1.05974 | 0.529872 | − | 0.848078i | \(-0.322240\pi\) | ||||
0.529872 | + | 0.848078i | \(0.322240\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.0483937 | + | 0.106330i | −0.00225882 | + | 0.00496306i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.0852 | 0.702587 | 0.351294 | − | 0.936265i | \(-0.385742\pi\) | ||||
0.351294 | + | 0.936265i | \(0.385742\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.19632 | −0.334441 | −0.167221 | − | 0.985919i | \(-0.553479\pi\) | ||||
−0.167221 | + | 0.985919i | \(0.553479\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 18.4139i | 0.853924i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −36.1274 | −1.67178 | −0.835889 | − | 0.548899i | \(-0.815047\pi\) | ||||
−0.835889 | + | 0.548899i | \(0.815047\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 55.4489i | − | 2.56039i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 21.4798i | − | 0.989739i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 16.4401i | − | 0.755918i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10.9326 | 0.501624 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.00169 | −0.366372 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 24.4261i | − | 1.11606i | −0.829821 | − | 0.558029i | \(-0.811558\pi\) | ||
0.829821 | − | 0.558029i | \(-0.188442\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.32804i | 0.242938i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 83.2823i | − | 3.78947i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 24.7810 | 1.12525 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 26.9195i | 1.21984i | 0.792463 | + | 0.609920i | \(0.208798\pi\) | ||||
−0.792463 | + | 0.609920i | \(0.791202\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 13.6302 | 0.616377 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −27.4229 | −1.23758 | −0.618789 | − | 0.785557i | \(-0.712377\pi\) | ||||
−0.618789 | + | 0.785557i | \(0.712377\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.69815 | − | 12.5199i | 0.256632 | − | 0.563868i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −9.67730 | −0.434962 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −23.9164 | −1.07280 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 39.6948i | − | 1.77698i | −0.458893 | − | 0.888492i | \(-0.651754\pi\) | ||
0.458893 | − | 0.888492i | \(-0.348246\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −27.0271 | −1.20748 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 11.1816i | 0.498562i | 0.968431 | + | 0.249281i | \(0.0801943\pi\) | ||||
−0.968431 | + | 0.249281i | \(0.919806\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.45167i | 0.331595i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 23.1211i | 1.02685i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.98016 | −0.220742 | −0.110371 | − | 0.993890i | \(-0.535204\pi\) | ||||
−0.110371 | + | 0.993890i | \(0.535204\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 23.0416 | 1.01930 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 0.138036i | − | 0.00609442i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 29.3784i | 1.29457i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 15.8846i | − | 0.698605i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −32.6682 | −1.43397 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.28507i | 0.231543i | 0.993276 | + | 0.115772i | \(0.0369341\pi\) | ||||
−0.993276 | + | 0.115772i | \(0.963066\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −21.1559 | −0.925082 | −0.462541 | − | 0.886598i | \(-0.653062\pi\) | ||||
−0.462541 | + | 0.886598i | \(0.653062\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 20.0962 | 0.877072 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.74171 | + | 17.0100i | −0.337234 | + | 0.740967i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −63.4897 | −2.76042 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.98842 | 0.129686 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 0.505525i | − | 0.0218967i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −23.3995 | −1.01165 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.79162i | 0.120467i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 12.4676i | − | 0.537017i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 3.17993i | − | 0.136716i | −0.997661 | − | 0.0683579i | \(-0.978224\pi\) | ||
0.997661 | − | 0.0683579i | \(-0.0217760\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −13.6123 | −0.584161 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12.5443 | 0.537337 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 7.26644i | − | 0.310690i | −0.987860 | − | 0.155345i | \(-0.950351\pi\) | ||
0.987860 | − | 0.155345i | \(-0.0496490\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.79220i | 0.289884i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16.2531i | 0.692405i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.29174 | −0.395125 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 11.4851i | 0.487516i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −30.7461 | −1.30275 | −0.651377 | − | 0.758754i | \(-0.725808\pi\) | ||||
−0.651377 | + | 0.758754i | \(0.725808\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15.8834 | 0.671795 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −17.9136 | − | 8.15297i | −0.756313 | − | 0.344219i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7.47020 | −0.314831 | −0.157416 | − | 0.987532i | \(-0.550316\pi\) | ||||
−0.157416 | + | 0.987532i | \(0.550316\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −19.6154 | −0.825227 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 33.0615i | − | 1.38845i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.66982 | 0.363458 | 0.181729 | − | 0.983349i | \(-0.441831\pi\) | ||||
0.181729 | + | 0.983349i | \(0.441831\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 14.6724i | − | 0.614021i | −0.951706 | − | 0.307010i | \(-0.900671\pi\) | ||
0.951706 | − | 0.307010i | \(-0.0993286\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 7.67558i | − | 0.320652i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 20.8702i | − | 0.870348i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.38842 | −0.307584 | −0.153792 | − | 0.988103i | \(-0.549149\pi\) | ||||
−0.153792 | + | 0.988103i | \(0.549149\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11.4186 | −0.474543 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 8.12974i | − | 0.337279i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.22302i | 0.216315i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 9.34957i | − | 0.386557i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 35.8463 | 1.47954 | 0.739768 | − | 0.672862i | \(-0.234935\pi\) | ||||
0.739768 | + | 0.672862i | \(0.234935\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 22.0820i | − | 0.909874i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −31.1694 | −1.28214 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −39.0091 | −1.60191 | −0.800957 | − | 0.598722i | \(-0.795675\pi\) | ||||
−0.800957 | + | 0.598722i | \(0.795675\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −22.7977 | − | 10.3758i | −0.934613 | − | 0.425368i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 25.4300 | 1.04078 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 31.2132 | 1.27533 | 0.637667 | − | 0.770312i | \(-0.279899\pi\) | ||||
0.637667 | + | 0.770312i | \(0.279899\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.1812i | 0.700838i | 0.936593 | + | 0.350419i | \(0.113961\pi\) | ||||
−0.936593 | + | 0.350419i | \(0.886039\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 45.2815 | 1.84400 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 11.9442i | − | 0.485601i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 42.2530i | 1.71500i | 0.514486 | + | 0.857499i | \(0.327983\pi\) | ||||
−0.514486 | + | 0.857499i | \(0.672017\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 29.8762i | 1.21065i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15.3467 | 0.620860 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.1640 | 0.774026 | 0.387013 | − | 0.922074i | \(-0.373507\pi\) | ||||
0.387013 | + | 0.922074i | \(0.373507\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 1.08971i | − | 0.0439414i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 7.69430i | − | 0.309761i | −0.987933 | − | 0.154880i | \(-0.950501\pi\) | ||
0.987933 | − | 0.154880i | \(-0.0494993\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25.9688i | 1.04377i | 0.853015 | + | 0.521887i | \(0.174772\pi\) | ||||
−0.853015 | + | 0.521887i | \(0.825228\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.263507 | −0.0105742 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 41.6669i | − | 1.66935i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.74341 | −0.349736 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 23.2551 | 0.928719 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.82866 | + | 10.6095i | −0.192531 | + | 0.423028i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.1095 | −0.641308 | −0.320654 | − | 0.947196i | \(-0.603903\pi\) | ||||
−0.320654 | + | 0.947196i | \(0.603903\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 16.7638 | 0.666302 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 31.3328i | − | 1.24341i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12.0454 | 0.477254 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 19.5310i | − | 0.772632i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 4.41509i | − | 0.174385i | −0.996191 | − | 0.0871927i | \(-0.972210\pi\) | ||
0.996191 | − | 0.0871927i | \(-0.0277896\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.71802i | 0.383241i | 0.981469 | + | 0.191621i | \(0.0613743\pi\) | ||||
−0.981469 | + | 0.191621i | \(0.938626\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 34.2382 | 1.34813 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.78118 | 0.148654 | 0.0743268 | − | 0.997234i | \(-0.476319\pi\) | ||||
0.0743268 | + | 0.997234i | \(0.476319\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 1.95066i | − | 0.0765701i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 40.5909i | − | 1.59088i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 28.3967i | − | 1.11125i | −0.831434 | − | 0.555624i | \(-0.812480\pi\) | ||
0.831434 | − | 0.555624i | \(-0.187520\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.5651 | 0.569104 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 18.8166i | 0.734104i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 28.8732 | 1.12474 | 0.562371 | − | 0.826885i | \(-0.309889\pi\) | ||||
0.562371 | + | 0.826885i | \(0.309889\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.4655 | 0.640434 | 0.320217 | − | 0.947344i | \(-0.396244\pi\) | ||||
0.320217 | + | 0.947344i | \(0.396244\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 7.87686 | − | 17.3070i | 0.305912 | − | 0.672146i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 29.5955 | 1.14766 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 31.0269 | 1.20136 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 32.5534i | 1.25859i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.43354 | 0.171155 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 21.8052i | − | 0.840530i | −0.907401 | − | 0.420265i | \(-0.861937\pi\) | ||
0.907401 | − | 0.420265i | \(-0.138063\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 0.0635851i | − | 0.00244739i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 42.5692i | 1.63607i | 0.575171 | + | 0.818033i | \(0.304936\pi\) | ||||
−0.575171 | + | 0.818033i | \(0.695064\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −54.6263 | −2.09637 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.40367 | −0.207069 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 10.3756i | − | 0.397013i | −0.980100 | − | 0.198507i | \(-0.936391\pi\) | ||
0.980100 | − | 0.198507i | \(-0.0636091\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 15.4735i | − | 0.591210i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 72.2097i | 2.75497i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.04613 | −0.192242 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 51.4201i | − | 1.95611i | −0.208341 | − | 0.978056i | \(-0.566806\pi\) | ||
0.208341 | − | 0.978056i | \(-0.433194\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 21.3323 | 0.810346 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 12.6648 | 0.480404 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.458144 | − | 1.00663i | 0.0173534 | − | 0.0381288i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −51.6089 | −1.95203 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 28.1674 | 1.06387 | 0.531934 | − | 0.846786i | \(-0.321465\pi\) | ||||
0.531934 | + | 0.846786i | \(0.321465\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 13.7730i | − | 0.519459i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 33.0813 | 1.24591 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 16.4262i | − | 0.617771i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.88214i | 0.145797i | 0.997339 | + | 0.0728985i | \(0.0232249\pi\) | ||||
−0.997339 | + | 0.0728985i | \(0.976775\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 7.58795i | − | 0.284570i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −42.1542 | −1.57869 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.10283 | −0.228233 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 41.8468i | − | 1.56280i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 14.1855i | 0.529031i | 0.964381 | + | 0.264516i | \(0.0852120\pi\) | ||||
−0.964381 | + | 0.264516i | \(0.914788\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 64.7607i | − | 2.41182i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −14.0020 | −0.520738 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.48687i | 0.278055i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16.3698 | −0.607123 | −0.303561 | − | 0.952812i | \(-0.598176\pi\) | ||||
−0.303561 | + | 0.952812i | \(0.598176\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.7912 | 0.992266 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 31.6278 | + | 14.3947i | 1.16980 | + | 0.532407i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −30.5715 | −1.12918 | −0.564591 | − | 0.825371i | \(-0.690966\pi\) | ||||
−0.564591 | + | 0.825371i | \(0.690966\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 25.9650 | 0.957732 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 29.5570i | − | 1.08875i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 34.7769 | 1.27929 | 0.639644 | − | 0.768671i | \(-0.279082\pi\) | ||||
0.639644 | + | 0.768671i | \(0.279082\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 22.4676i | 0.825366i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 42.2206i | − | 1.54892i | −0.632621 | − | 0.774461i | \(-0.718021\pi\) | ||
0.632621 | − | 0.774461i | \(-0.281979\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 31.8844i | 1.16815i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.63903 | 0.242909 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 51.5810 | 1.88473 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 42.3310i | 1.54468i | 0.635210 | + | 0.772340i | \(0.280914\pi\) | ||||
−0.635210 | + | 0.772340i | \(0.719086\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 54.4824i | 1.98545i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 4.35389i | − | 0.158454i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 40.5379 | 1.47337 | 0.736687 | − | 0.676234i | \(-0.236389\pi\) | ||||
0.736687 | + | 0.676234i | \(0.236389\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 44.3935i | − | 1.61138i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 48.5505 | 1.75995 | 0.879977 | − | 0.475016i | \(-0.157558\pi\) | ||||
0.879977 | + | 0.475016i | \(0.157558\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −27.6521 | −1.00107 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 8.47326 | − | 18.6174i | 0.306352 | − | 0.673112i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.88460 | 0.0680489 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.93593 | 0.141933 | 0.0709666 | − | 0.997479i | \(-0.477392\pi\) | ||||
0.0709666 | + | 0.997479i | \(0.477392\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 34.5117i | 1.24291i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 25.6453 | 0.922396 | 0.461198 | − | 0.887297i | \(-0.347420\pi\) | ||||
0.461198 | + | 0.887297i | \(0.347420\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 10.1719i | − | 0.365386i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 25.3174i | − | 0.908256i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.30679i | 0.0468205i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.7486 | −0.456181 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.0945293 | 0.00337820 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 14.5716i | − | 0.520081i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.3766i | 0.548117i | 0.961713 | + | 0.274059i | \(0.0883662\pi\) | ||||
−0.961713 | + | 0.274059i | \(0.911634\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 29.6053i | − | 1.05398i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 43.2395 | 1.53742 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.28339i | 0.152108i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −10.8774 | −0.385783 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −19.0948 | −0.676371 | −0.338185 | − | 0.941079i | \(-0.609813\pi\) | ||||
−0.338185 | + | 0.941079i | \(0.609813\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 30.5591 | + | 13.9083i | 1.08110 | + | 0.492040i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 34.0266 | 1.20227 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 12.2823 | 0.433433 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 56.4972i | − | 1.99127i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −66.3459 | −2.33549 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 19.6778i | 0.691836i | 0.938265 | + | 0.345918i | \(0.112432\pi\) | ||||
−0.938265 | + | 0.345918i | \(0.887568\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 33.1887i | − | 1.16541i | −0.812683 | − | 0.582706i | \(-0.801994\pi\) | ||
0.812683 | − | 0.582706i | \(-0.198006\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 4.47773i | − | 0.157041i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9.24646 | 0.323889 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −41.0586 | −1.43646 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 20.6099i | 0.720167i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.75011i | 0.305381i | 0.988274 | + | 0.152691i | \(0.0487938\pi\) | ||||
−0.988274 | + | 0.152691i | \(0.951206\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21.5943i | 0.752730i | 0.926471 | + | 0.376365i | \(0.122826\pi\) | ||||
−0.926471 | + | 0.376365i | \(0.877174\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 10.7123 | 0.372954 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 42.6129i | − | 1.48180i | −0.671617 | − | 0.740899i | \(-0.734400\pi\) | ||
0.671617 | − | 0.740899i | \(-0.265600\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17.2293 | 0.598399 | 0.299199 | − | 0.954191i | \(-0.403280\pi\) | ||||
0.299199 | + | 0.954191i | \(0.403280\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 61.1318 | 2.12064 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 23.9854 | + | 10.9164i | 0.831043 | + | 0.378230i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −18.3347 | −0.634500 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.128431 | −0.00443922 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 3.47333i | − | 0.119913i | −0.998201 | − | 0.0599564i | \(-0.980904\pi\) | ||
0.998201 | − | 0.0599564i | \(-0.0190962\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17.8696 | 0.616193 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 4.64763i | − | 0.160073i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 15.6850i | 0.539580i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 26.3294i | 0.904688i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −58.1880 | −1.99701 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −26.2924 | −0.901293 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 0.242761i | − | 0.00831199i | −0.999991 | − | 0.00415600i | \(-0.998677\pi\) | ||
0.999991 | − | 0.00415600i | \(-0.00132290\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 24.1687i | 0.826552i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 40.7514i | 1.39204i | 0.718022 | + | 0.696021i | \(0.245048\pi\) | ||||
−0.718022 | + | 0.696021i | \(0.754952\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 34.1939 | 1.16668 | 0.583340 | − | 0.812228i | \(-0.301746\pi\) | ||||
0.583340 | + | 0.812228i | \(0.301746\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.40212i | 0.0818639i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 23.8791 | 0.812853 | 0.406426 | − | 0.913684i | \(-0.366775\pi\) | ||||
0.406426 | + | 0.913684i | \(0.366775\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −22.1615 | −0.753514 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 31.3697 | − | 27.3239i | 1.06537 | − | 0.927970i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.95295 | −0.168017 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 28.5560 | 0.967584 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 44.6097i | − | 1.50981i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 44.0078 | 1.48774 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.3774i | 0.890701i | 0.895356 | + | 0.445350i | \(0.146921\pi\) | ||||
−0.895356 | + | 0.445350i | \(0.853079\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 13.6091i | − | 0.459022i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 39.7274i | − | 1.33845i | −0.743059 | − | 0.669226i | \(-0.766626\pi\) | ||
0.743059 | − | 0.669226i | \(-0.233374\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −32.4719 | −1.09277 | −0.546383 | − | 0.837535i | \(-0.683996\pi\) | ||||
−0.546383 | + | 0.837535i | \(0.683996\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.06244 | 0.136557 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 24.3417i | 0.817313i | 0.912688 | + | 0.408657i | \(0.134003\pi\) | ||||
−0.912688 | + | 0.408657i | \(0.865997\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 69.0689i | 2.31650i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 17.6234i | − | 0.590407i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −39.6712 | −1.32755 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.89379i | 0.0633024i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 42.8901 | 1.43206 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 15.1222 | 0.504353 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.0481 | − | 4.57318i | −0.334752 | − | 0.152355i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −75.4735 | −2.51160 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9.23436 | −0.306961 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 18.1651i | − | 0.603163i | −0.953440 | − | 0.301581i | \(-0.902485\pi\) | ||
0.953440 | − | 0.301581i | \(-0.0975145\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 13.4142 | 0.444921 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.77676i | 0.0919981i | 0.998941 | + | 0.0459991i | \(0.0146471\pi\) | ||||
−0.998941 | + | 0.0459991i | \(0.985353\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 4.33355i | − | 0.143420i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 9.23328i | 0.305243i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −32.1067 | −1.06026 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −35.7442 | −1.17909 | −0.589546 | − | 0.807735i | \(-0.700693\pi\) | ||||
−0.589546 | + | 0.807735i | \(0.700693\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.93549i | 0.162630i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 12.3169i | − | 0.405415i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 6.34443i | − | 0.208604i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 52.8858 | 1.73700 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 30.3989i | − | 0.997355i | −0.866788 | − | 0.498677i | \(-0.833819\pi\) | ||
0.866788 | − | 0.498677i | \(-0.166181\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −31.1373 | −1.02048 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 54.4453 | 1.78246 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −12.1523 | − | 5.53083i | −0.397422 | − | 0.180878i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −42.7091 | −1.39524 | −0.697622 | − | 0.716466i | \(-0.745759\pi\) | ||||
−0.697622 | + | 0.716466i | \(0.745759\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −72.1739 | −2.35531 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 31.3912i | − | 1.02332i | −0.859187 | − | 0.511662i | \(-0.829030\pi\) | ||
0.859187 | − | 0.511662i | \(-0.170970\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.49463 | 0.0812363 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 0.172130i | − | 0.00559938i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 48.4051i | − | 1.57295i | −0.617620 | − | 0.786477i | \(-0.711903\pi\) | ||
0.617620 | − | 0.786477i | \(-0.288097\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11.8664i | 0.385198i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 15.0708 | 0.488705 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −12.7349 | −0.412524 | −0.206262 | − | 0.978497i | \(-0.566130\pi\) | ||||
−0.206262 | + | 0.978497i | \(0.566130\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 5.20698i | − | 0.168494i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 15.9255i | 0.514798i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 34.1091i | 1.10144i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.4545 | 0.337241 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 42.1228i | 1.35739i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7.74621 | −0.249359 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.7652 | 0.796395 | 0.398197 | − | 0.917300i | \(-0.369636\pi\) | ||||
0.398197 | + | 0.917300i | \(0.369636\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −20.3617 | + | 44.7386i | −0.654113 | + | 1.43721i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.97708 | −0.0955389 | −0.0477694 | − | 0.998858i | \(-0.515211\pi\) | ||||
−0.0477694 | + | 0.998858i | \(0.515211\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −27.9179 | −0.895006 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 10.3495i | 0.331449i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 37.1271 | 1.18780 | 0.593901 | − | 0.804538i | \(-0.297587\pi\) | ||||
0.593901 | + | 0.804538i | \(0.297587\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 22.2105i | − | 0.709851i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 22.5817i | − | 0.720977i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 13.2382i | − | 0.422234i | −0.977461 | − | 0.211117i | \(-0.932290\pi\) | ||
0.977461 | − | 0.211117i | \(-0.0677101\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −21.1448 | −0.673729 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −72.9232 | −2.32117 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 78.3802i | 2.49234i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23.6257i | 0.750496i | 0.926924 | + | 0.375248i | \(0.122443\pi\) | ||||
−0.926924 | + | 0.375248i | \(0.877557\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 45.6845i | 1.44975i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 17.2512 | 0.546901 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 22.6973i | − | 0.718830i | −0.933178 | − | 0.359415i | \(-0.882976\pi\) | ||
0.933178 | − | 0.359415i | \(-0.117024\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.0801049 | −0.00253441 |
(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 | 4012.2.b.a.237.5 | ✓ | 40 | |
17.16 | even | 2 | inner | 4012.2.b.a.237.36 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4012.2.b.a.237.5 | ✓ | 40 | 1.1 | even | 1 | trivial | |
4012.2.b.a.237.36 | yes | 40 | 17.16 | even | 2 | inner |