Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1840,2,Mod(1839,1840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1840, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1840.1839");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1840 = 2^{4} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1840.m (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: | \(14.6924739719\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1839.10 | ||
Character | \(\chi\) | \(=\) | 1840.1839 |
Dual form | 1840.2.m.g.1839.11 |
$q$-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 \(\left(\mathbb{Z}/1840\mathbb{Z}\right)^\times\).
\(n\) | \(737\) | \(1151\) | \(1201\) | \(1381\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | −2.20329 | −1.27207 | −0.636034 | − | 0.771661i | \(-0.719426\pi\) | ||||
−0.636034 | + | 0.771661i | \(0.719426\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.71768 | + | 1.43163i | −0.768169 | + | 0.640247i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 0.642617i | − | 0.242886i | −0.992598 | − | 0.121443i | \(-0.961248\pi\) | ||
0.992598 | − | 0.121443i | \(-0.0387522\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.85447 | 0.618157 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.87003 | 0.865346 | 0.432673 | − | 0.901551i | \(-0.357571\pi\) | ||||
0.432673 | + | 0.901551i | \(0.357571\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.405025i | 0.112334i | 0.998421 | + | 0.0561668i | \(0.0178879\pi\) | ||||
−0.998421 | + | 0.0561668i | \(0.982112\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.78454 | − | 3.15430i | 0.977164 | − | 0.814437i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.93021 | −1.19575 | −0.597876 | − | 0.801589i | \(-0.703989\pi\) | ||||
−0.597876 | + | 0.801589i | \(0.703989\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.74284 | 0.629250 | 0.314625 | − | 0.949216i | \(-0.398121\pi\) | ||||
0.314625 | + | 0.949216i | \(0.398121\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.41587i | 0.308968i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.71132 | − | 0.896383i | 0.982377 | − | 0.186909i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.900844 | − | 4.91818i | 0.180169 | − | 0.983636i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.52393 | 0.485730 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.62882 | −0.302464 | −0.151232 | − | 0.988498i | \(-0.548324\pi\) | ||||
−0.151232 | + | 0.988498i | \(0.548324\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 4.55939i | − | 0.818890i | −0.912335 | − | 0.409445i | \(-0.865722\pi\) | ||
0.912335 | − | 0.409445i | \(-0.134278\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.32349 | −1.10078 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.919993 | + | 1.10381i | 0.155507 | + | 0.186578i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.00091 | 0.328947 | 0.164474 | − | 0.986381i | \(-0.447407\pi\) | ||||
0.164474 | + | 0.986381i | \(0.447407\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 0.892386i | − | 0.142896i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.79334 | −0.748593 | −0.374297 | − | 0.927309i | \(-0.622116\pi\) | ||||
−0.374297 | + | 0.927309i | \(0.622116\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.29086i | 0.501852i | 0.968006 | + | 0.250926i | \(0.0807351\pi\) | ||||
−0.968006 | + | 0.250926i | \(0.919265\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.18539 | + | 2.65493i | −0.474850 | + | 0.395773i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.58875 | −0.523473 | −0.261736 | − | 0.965139i | \(-0.584295\pi\) | ||||
−0.261736 | + | 0.965139i | \(0.584295\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.58704 | 0.941006 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 10.8627 | 1.52108 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.263678 | −0.0362190 | −0.0181095 | − | 0.999836i | \(-0.505765\pi\) | ||||
−0.0181095 | + | 0.999836i | \(0.505765\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.92979 | + | 4.10883i | −0.664732 | + | 0.554035i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.04326 | −0.800449 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.3753i | 1.35074i | 0.737478 | + | 0.675372i | \(0.236017\pi\) | ||||
−0.737478 | + | 0.675372i | \(0.763983\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.19418i | 1.17719i | 0.808427 | + | 0.588597i | \(0.200319\pi\) | ||||
−0.808427 | + | 0.588597i | \(0.799681\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 1.19172i | − | 0.150142i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.579847 | − | 0.695702i | −0.0719212 | − | 0.0862913i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 2.18044i | − | 0.266383i | −0.991090 | − | 0.133192i | \(-0.957477\pi\) | ||
0.991090 | − | 0.133192i | \(-0.0425225\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −10.3804 | + | 1.97499i | −1.24965 | + | 0.237761i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 10.3200i | − | 1.22475i | −0.790566 | − | 0.612376i | \(-0.790214\pi\) | ||
0.790566 | − | 0.612376i | \(-0.209786\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.43051i | 0.518552i | 0.965803 | + | 0.259276i | \(0.0834839\pi\) | ||||
−0.965803 | + | 0.259276i | \(0.916516\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.98482 | + | 10.8362i | −0.229187 | + | 1.25125i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 1.84433i | − | 0.210181i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.16051 | −0.355585 | −0.177792 | − | 0.984068i | \(-0.556896\pi\) | ||||
−0.177792 | + | 0.984068i | \(0.556896\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.1243 | −1.23604 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.14874i | 1.00420i | 0.864808 | + | 0.502102i | \(0.167440\pi\) | ||||
−0.864808 | + | 0.502102i | \(0.832560\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.46852 | − | 7.05826i | 0.918540 | − | 0.765576i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.58875 | 0.384754 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.0324i | 1.48744i | 0.668494 | + | 0.743718i | \(0.266939\pi\) | ||||
−0.668494 | + | 0.743718i | \(0.733061\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.260276 | 0.0272843 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 10.0456i | 1.04168i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.71132 | + | 3.92674i | −0.483371 | + | 0.402875i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.3665 | −1.05256 | −0.526278 | − | 0.850312i | \(-0.676413\pi\) | ||||
−0.526278 | + | 0.850312i | \(0.676413\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.32239 | 0.534920 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.2075 | −1.21469 | −0.607346 | − | 0.794437i | \(-0.707766\pi\) | ||||
−0.607346 | + | 0.794437i | \(0.707766\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.3098i | 1.11439i | 0.830382 | + | 0.557195i | \(0.188122\pi\) | ||||
−0.830382 | + | 0.557195i | \(0.811878\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.02701 | − | 2.43201i | −0.197816 | − | 0.237340i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.5211i | 1.50048i | 0.661167 | + | 0.750239i | \(0.270062\pi\) | ||||
−0.661167 | + | 0.750239i | \(0.729938\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.6376i | 1.30625i | 0.757251 | + | 0.653124i | \(0.226542\pi\) | ||||
−0.757251 | + | 0.653124i | \(0.773458\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.40857 | −0.418443 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.47503 | −0.703192 | −0.351596 | − | 0.936152i | \(-0.614361\pi\) | ||||
−0.351596 | + | 0.936152i | \(0.614361\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.80924 | + | 8.28458i | −0.634965 | + | 0.772541i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.751107i | 0.0694399i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.16824i | 0.290432i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.76295 | −0.251177 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 10.5611 | 0.952262 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.49368 | + | 9.73753i | 0.491369 | + | 0.870951i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.380884 | 0.0337980 | 0.0168990 | − | 0.999857i | \(-0.494621\pi\) | ||||
0.0168990 | + | 0.999857i | \(0.494621\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 7.25072i | − | 0.638390i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 14.8999i | − | 1.30181i | −0.759157 | − | 0.650907i | \(-0.774389\pi\) | ||
0.759157 | − | 0.650907i | \(-0.225611\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 1.76259i | − | 0.152836i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.33529 | + | 3.61334i | −0.373123 | + | 0.310987i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.37933 | 0.715894 | 0.357947 | − | 0.933742i | \(-0.383477\pi\) | ||||
0.357947 | + | 0.933742i | \(0.383477\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.37882i | 0.286588i | 0.989680 | + | 0.143294i | \(0.0457694\pi\) | ||||
−0.989680 | + | 0.143294i | \(0.954231\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.90704 | 0.665893 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.16243i | 0.0972074i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.79778 | − | 2.33187i | 0.232343 | − | 0.193651i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −14.5131 | −1.19702 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 17.7280i | 1.45233i | 0.687519 | + | 0.726167i | \(0.258700\pi\) | ||||
−0.687519 | + | 0.726167i | \(0.741300\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 16.9047i | − | 1.37568i | −0.725861 | − | 0.687841i | \(-0.758559\pi\) | ||
0.725861 | − | 0.687841i | \(-0.241441\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −9.14294 | −0.739163 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.52738 | + | 7.83157i | 0.524292 | + | 0.629046i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.1520 | 0.890027 | 0.445013 | − | 0.895524i | \(-0.353199\pi\) | ||||
0.445013 | + | 0.895524i | \(0.353199\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.580959 | 0.0460730 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.576031 | − | 3.02757i | −0.0453976 | − | 0.238606i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.50634 | −0.196312 | −0.0981559 | − | 0.995171i | \(-0.531294\pi\) | ||||
−0.0981559 | + | 0.995171i | \(0.531294\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 10.8617 | − | 9.05293i | 0.845585 | − | 0.704770i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.83999 | −0.142382 | −0.0711912 | − | 0.997463i | \(-0.522680\pi\) | ||||
−0.0711912 | + | 0.997463i | \(0.522680\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.8360 | 0.987381 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.08652 | 0.388976 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.2607i | 0.856136i | 0.903747 | + | 0.428068i | \(0.140806\pi\) | ||||
−0.903747 | + | 0.428068i | \(0.859194\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.16051 | − | 0.578898i | −0.238912 | − | 0.0437605i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 22.8597i | − | 1.71824i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 0.613572i | − | 0.0458605i | −0.999737 | − | 0.0229303i | \(-0.992700\pi\) | ||
0.999737 | − | 0.0229303i | \(-0.00729957\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 0.527590i | − | 0.0392154i | −0.999808 | − | 0.0196077i | \(-0.993758\pi\) | ||
0.999808 | − | 0.0196077i | \(-0.00624173\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 20.2574i | − | 1.49747i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.43692 | + | 2.86457i | −0.252687 | + | 0.210607i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −14.1498 | −1.03474 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 1.62192i | − | 0.117977i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.0548 | −0.944609 | −0.472304 | − | 0.881435i | \(-0.656578\pi\) | ||||
−0.472304 | + | 0.881435i | \(0.656578\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.3324i | 1.46356i | 0.681541 | + | 0.731780i | \(0.261310\pi\) | ||||
−0.681541 | + | 0.731780i | \(0.738690\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.27757 | + | 1.53283i | 0.0914887 | + | 0.109768i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 15.0465i | − | 1.07202i | −0.844213 | − | 0.536008i | \(-0.819932\pi\) | ||
0.844213 | − | 0.536008i | \(-0.180068\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.81716 | −0.483255 | −0.241628 | − | 0.970369i | \(-0.577681\pi\) | ||||
−0.241628 | + | 0.970369i | \(0.577681\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.80413i | 0.338857i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.04671i | 0.0734643i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.23341 | − | 6.86231i | 0.575047 | − | 0.479284i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.73701 | − | 1.66232i | 0.607264 | − | 0.115539i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.87202 | 0.544519 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 2.73591i | − | 0.188348i | −0.995556 | − | 0.0941739i | \(-0.969979\pi\) | ||
0.995556 | − | 0.0941739i | \(-0.0300210\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 22.7378i | 1.55797i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.71132 | − | 5.65265i | −0.321309 | − | 0.385507i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.92994 | −0.198897 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 9.76168i | − | 0.659633i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 1.99686i | − | 0.134323i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.6037 | 1.31276 | 0.656379 | − | 0.754431i | \(-0.272087\pi\) | ||||
0.656379 | + | 0.754431i | \(0.272087\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.67059 | − | 9.12063i | 0.111373 | − | 0.608042i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 18.0945i | 1.20097i | 0.799635 | + | 0.600487i | \(0.205026\pi\) | ||||
−0.799635 | + | 0.600487i | \(0.794974\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 27.1740i | − | 1.79571i | −0.440293 | − | 0.897854i | \(-0.645125\pi\) | ||
0.440293 | − | 0.897854i | \(-0.354875\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.06359i | 0.267364i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.25756i | 0.278922i | 0.990228 | + | 0.139461i | \(0.0445370\pi\) | ||||
−0.990228 | + | 0.139461i | \(0.955463\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.16432 | − | 5.13778i | 0.402116 | − | 0.335152i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.96350 | 0.452328 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.5247i | 1.19826i | 0.800651 | + | 0.599131i | \(0.204487\pi\) | ||||
−0.800651 | + | 0.599131i | \(0.795513\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.60856i | 0.232448i | 0.993223 | + | 0.116224i | \(0.0370790\pi\) | ||||
−0.993223 | + | 0.116224i | \(0.962921\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 16.9384 | 1.08660 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −11.3144 | + | 9.43024i | −0.722852 | + | 0.602476i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.11092i | 0.0706860i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 20.1573i | − | 1.27742i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.81994 | 0.241113 | 0.120556 | − | 0.992706i | \(-0.461532\pi\) | ||||
0.120556 | + | 0.992706i | \(0.461532\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 13.5216 | − | 2.57264i | 0.850096 | − | 0.161741i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −18.6586 | + | 15.5514i | −1.16845 | + | 0.973865i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 1.24356i | − | 0.0775712i | −0.999248 | − | 0.0387856i | \(-0.987651\pi\) | ||
0.999248 | − | 0.0387856i | \(-0.0123489\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 1.28582i | − | 0.0798968i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.02059 | −0.186970 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 10.0562i | − | 0.620094i | −0.950721 | − | 0.310047i | \(-0.899655\pi\) | ||
0.950721 | − | 0.310047i | \(-0.100345\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.452914 | − | 0.377491i | 0.0278223 | − | 0.0231891i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 30.9175i | − | 1.89212i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.19489 | −0.133825 | −0.0669125 | − | 0.997759i | \(-0.521315\pi\) | ||||
−0.0669125 | + | 0.997759i | \(0.521315\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.25997i | 0.258775i | 0.991594 | + | 0.129387i | \(0.0413010\pi\) | ||||
−0.991594 | + | 0.129387i | \(0.958699\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.573462 | −0.0347075 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.58545 | − | 14.1153i | 0.155908 | − | 0.851185i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.87597i | 0.533305i | 0.963793 | + | 0.266653i | \(0.0859176\pi\) | ||||
−0.963793 | + | 0.266653i | \(0.914082\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 8.45526i | − | 0.506203i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.57906i | 0.511784i | 0.966705 | + | 0.255892i | \(0.0823692\pi\) | ||||
−0.966705 | + | 0.255892i | \(0.917631\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.40195i | 0.202225i | 0.994875 | + | 0.101113i | \(0.0322402\pi\) | ||||
−0.994875 | + | 0.101113i | \(0.967760\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 10.3804 | − | 8.65174i | 0.614881 | − | 0.512485i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.08028i | 0.181823i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.30700 | 0.429824 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 22.8403 | 1.33892 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −28.9057 | −1.68869 | −0.844344 | − | 0.535801i | \(-0.820010\pi\) | ||||
−0.844344 | + | 0.535801i | \(0.820010\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.8536 | − | 17.8214i | −0.864809 | − | 1.03760i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 7.24374 | 0.420324 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.363057 | + | 1.90820i | 0.0209962 | + | 0.110354i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.11477 | 0.121893 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 26.8966 | 1.54517 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −13.1627 | − | 15.7926i | −0.753694 | − | 0.904284i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.66239 | 0.209024 | 0.104512 | − | 0.994524i | \(-0.466672\pi\) | ||||
0.104512 | + | 0.994524i | \(0.466672\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 24.9188i | − | 1.41758i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.46706i | 0.480123i | 0.970758 | + | 0.240061i | \(0.0771676\pi\) | ||||
−0.970758 | + | 0.240061i | \(0.922832\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18.5693 | 1.04960 | 0.524800 | − | 0.851226i | \(-0.324140\pi\) | ||||
0.524800 | + | 0.851226i | \(0.324140\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.70610 | + | 2.04699i | 0.0961280 | + | 0.115335i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 0.673248i | − | 0.0378134i | −0.999821 | − | 0.0189067i | \(-0.993981\pi\) | ||
0.999821 | − | 0.0189067i | \(-0.00601854\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.67475 | −0.261736 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 34.1974i | − | 1.90871i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −13.5228 | −0.752427 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.99198 | + | 0.364864i | 0.110495 | + | 0.0202390i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 30.0476i | − | 1.66164i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.30619i | 0.127144i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 11.3823i | − | 0.625630i | −0.949814 | − | 0.312815i | \(-0.898728\pi\) | ||
0.949814 | − | 0.312815i | \(-0.101272\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.71063 | 0.203341 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.12159 | + | 3.74530i | 0.170551 | + | 0.204627i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.41570 | −0.131592 | −0.0657959 | − | 0.997833i | \(-0.520959\pi\) | ||||
−0.0657959 | + | 0.997833i | \(0.520959\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 16.4696 | 0.894508 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 13.0856i | − | 0.708623i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 8.73127i | − | 0.471444i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 15.0027 | − | 18.2533i | 0.807718 | − | 0.982725i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −20.0264 | −1.07507 | −0.537536 | − | 0.843241i | \(-0.680645\pi\) | ||||
−0.537536 | + | 0.843241i | \(0.680645\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.9116 | −1.22643 | −0.613215 | − | 0.789916i | \(-0.710124\pi\) | ||||
−0.613215 | + | 0.789916i | \(0.710124\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.02225i | 0.0545638i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 28.3834i | 1.51070i | 0.655324 | + | 0.755348i | \(0.272532\pi\) | ||||
−0.655324 | + | 0.755348i | \(0.727468\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 14.7744 | + | 17.7264i | 0.784144 | + | 0.940818i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 6.98054i | − | 0.369449i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −13.5509 | −0.715189 | −0.357595 | − | 0.933877i | \(-0.616403\pi\) | ||||
−0.357595 | + | 0.933877i | \(0.616403\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.4768 | −0.604044 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.08756 | 0.319514 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.34287 | − | 7.61019i | −0.332001 | − | 0.398336i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 4.18607i | − | 0.218511i | −0.994014 | − | 0.109256i | \(-0.965153\pi\) | ||
0.994014 | − | 0.109256i | \(-0.0348467\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.88911 | −0.462749 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.169444i | 0.00879710i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.2025 | −0.683599 | −0.341799 | − | 0.939773i | \(-0.611036\pi\) | ||||
−0.341799 | + | 0.939773i | \(0.611036\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −12.1041 | − | 21.4546i | −0.625055 | − | 1.10791i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 0.659711i | − | 0.0339768i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.79915 | −0.400616 | −0.200308 | − | 0.979733i | \(-0.564194\pi\) | ||||
−0.200308 | + | 0.979733i | \(0.564194\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.839197 | −0.0429934 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 0.691775i | − | 0.0353480i | −0.999844 | − | 0.0176740i | \(-0.994374\pi\) | ||
0.999844 | − | 0.0176740i | \(-0.00562611\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.64041 | + | 3.16797i | 0.134568 | + | 0.161454i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.10282i | 0.310224i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 8.94180i | − | 0.453367i | −0.973968 | − | 0.226684i | \(-0.927212\pi\) | ||
0.973968 | − | 0.226684i | \(-0.0727883\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −23.2278 | + | 4.41936i | −1.17468 | + | 0.223497i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 32.8289i | 1.65600i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.42874 | − | 4.52469i | 0.273149 | − | 0.227662i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 7.00315i | − | 0.351478i | −0.984437 | − | 0.175739i | \(-0.943768\pi\) | ||
0.984437 | − | 0.175739i | \(-0.0562315\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.88350i | 0.194418i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 1.06280i | − | 0.0530736i | −0.999648 | − | 0.0265368i | \(-0.991552\pi\) | ||
0.999648 | − | 0.0265368i | \(-0.00844792\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.84666 | 0.0919889 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 19.1081 | − | 15.9260i | 0.949487 | − | 0.791370i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.74266 | 0.284653 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.85837 | 0.289678 | 0.144839 | − | 0.989455i | \(-0.453734\pi\) | ||||
0.144839 | + | 0.989455i | \(0.453734\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −18.4621 | −0.910666 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.66732 | 0.328077 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.0977 | − | 15.7146i | −0.642939 | − | 0.771399i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 7.44451i | − | 0.364559i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 30.7667 | 1.50305 | 0.751525 | − | 0.659705i | \(-0.229319\pi\) | ||||
0.751525 | + | 0.659705i | \(0.229319\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 37.3043i | − | 1.81810i | −0.416687 | − | 0.909050i | \(-0.636809\pi\) | ||
0.416687 | − | 0.909050i | \(-0.363191\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.65524 | −0.323589 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.44135 | + | 24.2477i | −0.215437 | + | 1.17618i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.90834 | 0.285924 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 2.56117i | − | 0.123654i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.2987 | 0.881416 | 0.440708 | − | 0.897651i | \(-0.354727\pi\) | ||||
0.440708 | + | 0.897651i | \(0.354727\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 31.1511 | 1.49702 | 0.748512 | − | 0.663121i | \(-0.230769\pi\) | ||||
0.748512 | + | 0.663121i | \(0.230769\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.16432 | + | 5.13778i | −0.295557 | + | 0.246338i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 12.9224 | − | 2.45863i | 0.618161 | − | 0.117612i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 8.87110i | − | 0.423394i | −0.977335 | − | 0.211697i | \(-0.932101\pi\) | ||
0.977335 | − | 0.211697i | \(-0.0678991\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 12.2155 | 0.581690 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 34.1696 | 1.62344 | 0.811722 | − | 0.584044i | \(-0.198530\pi\) | ||||
0.811722 | + | 0.584044i | \(0.198530\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −20.0893 | − | 24.1032i | −0.952325 | − | 1.14260i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 39.0598i | − | 1.84747i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.3702 | 0.772558 | 0.386279 | − | 0.922382i | \(-0.373760\pi\) | ||||
0.386279 | + | 0.922382i | \(0.373760\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.7570 | −0.647792 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 37.2458i | 1.74996i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.447070 | + | 0.372620i | −0.0209590 | + | 0.0174687i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 34.4242 | 1.61030 | 0.805148 | − | 0.593074i | \(-0.202086\pi\) | ||||
0.805148 | + | 0.593074i | \(0.202086\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −12.4435 | −0.580812 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19.6000 | 0.912861 | 0.456430 | − | 0.889759i | \(-0.349128\pi\) | ||||
0.456430 | + | 0.889759i | \(0.349128\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.4580 | −0.578970 | −0.289485 | − | 0.957183i | \(-0.593484\pi\) | ||||
−0.289485 | + | 0.957183i | \(0.593484\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −14.3817 | − | 17.2552i | −0.666935 | − | 0.800190i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.93867i | 0.459907i | 0.973202 | + | 0.229953i | \(0.0738574\pi\) | ||||
−0.973202 | + | 0.229953i | \(0.926143\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.40119 | −0.0647008 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −24.5711 | −1.13217 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.44487i | 0.434276i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.47087 | − | 13.4898i | 0.113371 | − | 0.618953i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.488984 | −0.0223890 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −39.2013 | −1.79115 | −0.895576 | − | 0.444908i | \(-0.853236\pi\) | ||||
−0.895576 | + | 0.444908i | \(0.853236\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.810417i | 0.0369518i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.26916 | + | 6.67061i | 0.0577489 | + | 0.303523i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 17.8063 | − | 14.8410i | 0.808542 | − | 0.673896i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 31.2472 | 1.41594 | 0.707972 | − | 0.706241i | \(-0.249610\pi\) | ||||
0.707972 | + | 0.706241i | \(0.249610\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.52219 | 0.249722 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 28.2058i | 1.27291i | 0.771313 | + | 0.636456i | \(0.219600\pi\) | ||||
−0.771313 | + | 0.636456i | \(0.780400\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.03041 | 0.361672 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −9.14215 | + | 7.61971i | −0.410909 | + | 0.342481i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.63178 | −0.297476 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.7217i | 0.703800i | 0.936038 | + | 0.351900i | \(0.114464\pi\) | ||||
−0.936038 | + | 0.351900i | \(0.885536\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.05402 | 0.181120 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 10.7408i | 0.478911i | 0.970907 | + | 0.239455i | \(0.0769689\pi\) | ||||
−0.970907 | + | 0.239455i | \(0.923031\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 20.9686 | − | 17.4767i | 0.933090 | − | 0.777703i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −28.2813 | −1.25602 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17.3015 | −0.766874 | −0.383437 | − | 0.923567i | \(-0.625260\pi\) | ||||
−0.383437 | + | 0.923567i | \(0.625260\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.84712 | 0.125949 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.92272 | 0.305646 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −16.1915 | − | 19.4266i | −0.713484 | − | 0.856040i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.2998 | −0.452985 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 24.8106i | − | 1.08906i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 28.2184i | 1.23627i | 0.786071 | + | 0.618136i | \(0.212112\pi\) | ||||
−0.786071 | + | 0.618136i | \(0.787888\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 22.2167i | 0.971467i | 0.874107 | + | 0.485734i | \(0.161448\pi\) | ||||
−0.874107 | + | 0.485734i | \(0.838552\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.96350 | + | 1.27548i | 0.303912 | + | 0.0556664i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 22.4788i | 0.979190i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.3930 | − | 8.44629i | 0.930130 | − | 0.367230i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 19.2406i | 0.834972i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 1.94142i | − | 0.0840922i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −22.2205 | − | 26.6602i | −0.960676 | − | 1.15262i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.35188i | 0.0583377i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 18.9050 | 0.814296 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 35.1024 | 1.50917 | 0.754585 | − | 0.656202i | \(-0.227838\pi\) | ||||
0.754585 | + | 0.656202i | \(0.227838\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.16243i | 0.0498847i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −19.5241 | − | 23.4251i | −0.836320 | − | 1.00342i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.1595 | 0.562659 | 0.281329 | − | 0.959611i | \(-0.409225\pi\) | ||||
0.281329 | + | 0.959611i | \(0.409225\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 17.0503i | 0.727691i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.46758 | −0.190325 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.03100i | 0.0863667i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 7.57251 | − | 6.31147i | 0.321435 | − | 0.267907i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −22.6673 | −0.960446 | −0.480223 | − | 0.877146i | \(-0.659444\pi\) | ||||
−0.480223 | + | 0.877146i | \(0.659444\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.33288 | −0.0563749 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 31.1762 | 1.31626 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 40.9106i | 1.72418i | 0.506759 | + | 0.862088i | \(0.330844\pi\) | ||||
−0.506759 | + | 0.862088i | \(0.669156\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12.8397 | − | 10.7015i | 0.540171 | − | 0.450216i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7.14870i | 0.300217i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 37.6655i | 1.57902i | 0.613737 | + | 0.789510i | \(0.289665\pi\) | ||||
−0.613737 | + | 0.789510i | \(0.710335\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.1278 | −0.842322 | −0.421161 | − | 0.906986i | \(-0.638377\pi\) | ||||
−0.421161 | + | 0.906986i | \(0.638377\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 28.7634 | 1.20161 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.164414 | − | 23.9786i | −0.00685655 | − | 0.999976i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.0377i | 0.750918i | 0.926839 | + | 0.375459i | \(0.122515\pi\) | ||||
−0.926839 | + | 0.375459i | \(0.877485\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 44.7982i | − | 1.86175i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.87914 | 0.243908 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.756763 | −0.0313419 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.07531 | − | 1.29016i | −0.0444586 | − | 0.0533416i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −32.6326 | −1.34689 | −0.673446 | − | 0.739236i | \(-0.735187\pi\) | ||||
−0.673446 | + | 0.739236i | \(0.735187\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 12.5057i | − | 0.515287i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 33.1517i | 1.36368i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 25.4394i | − | 1.04467i | −0.852740 | − | 0.522336i | \(-0.825061\pi\) | ||
0.852740 | − | 0.522336i | \(-0.174939\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.53576 | − | 5.44202i | −0.185948 | − | 0.223101i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 15.0202 | 0.614734 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.29234i | 0.379675i | 0.981816 | + | 0.189837i | \(0.0607961\pi\) | ||||
−0.981816 | + | 0.189837i | \(0.939204\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −28.2140 | −1.15087 | −0.575437 | − | 0.817846i | \(-0.695168\pi\) | ||||
−0.575437 | + | 0.817846i | \(0.695168\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 4.04356i | − | 0.164667i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.74585 | − | 3.95553i | 0.192946 | − | 0.160815i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.57912 | 0.185861 | 0.0929303 | − | 0.995673i | \(-0.470377\pi\) | ||||
0.0929303 | + | 0.995673i | \(0.470377\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 2.30619i | − | 0.0934516i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 1.45353i | − | 0.0588036i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −43.8068 | −1.76934 | −0.884671 | − | 0.466217i | \(-0.845617\pi\) | ||||
−0.884671 | + | 0.466217i | \(0.845617\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −18.1406 | + | 15.1196i | −0.731498 | + | 0.609682i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 39.1574 | 1.57642 | 0.788208 | − | 0.615409i | \(-0.211009\pi\) | ||||
0.788208 | + | 0.615409i | \(0.211009\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −41.9315 | −1.68537 | −0.842685 | − | 0.538407i | \(-0.819026\pi\) | ||||
−0.842685 | + | 0.538407i | \(0.819026\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 11.8910 | − | 2.26241i | 0.477170 | − | 0.0907872i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9.01749 | 0.361278 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.3770 | − | 8.86102i | −0.935078 | − | 0.354441i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −17.3443 | −0.692665 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9.86490 | −0.393339 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.85343 | 0.0737840 | 0.0368920 | − | 0.999319i | \(-0.488254\pi\) | ||||
0.0368920 | + | 0.999319i | \(0.488254\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.02799i | 0.239591i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.654237 | + | 0.545287i | −0.0259626 | + | 0.0216391i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.66792i | 0.105707i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 19.1381i | − | 0.757090i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 31.2121i | 1.23280i | 0.787432 | + | 0.616401i | \(0.211410\pi\) | ||||
−0.787432 | + | 0.616401i | \(0.788590\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 37.3161i | − | 1.47160i | −0.677198 | − | 0.735801i | \(-0.736806\pi\) | ||
0.677198 | − | 0.735801i | \(-0.263194\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 10.3804 | + | 12.4544i | 0.408727 | + | 0.490392i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 20.8936 | 0.821412 | 0.410706 | − | 0.911768i | \(-0.365282\pi\) | ||||
0.410706 | + | 0.911768i | \(0.365282\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 29.7773i | 1.16886i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.45550 | 0.253011 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 44.2036i | 1.72982i | 0.501927 | + | 0.864910i | \(0.332625\pi\) | ||||
−0.501927 | + | 0.864910i | \(0.667375\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 21.3313 | + | 25.5933i | 0.833482 | + | 1.00001i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.21626i | 0.320547i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 40.9875 | 1.59665 | 0.798323 | − | 0.602229i | \(-0.205721\pi\) | ||||
0.798323 | + | 0.602229i | \(0.205721\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.5000i | 0.875150i | 0.899182 | + | 0.437575i | \(0.144163\pi\) | ||||
−0.899182 | + | 0.437575i | \(0.855837\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.39965i | 0.170868i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.52339 | + | 3.02757i | 0.0978530 | + | 0.117404i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.67387 | + | 1.46004i | −0.297133 | + | 0.0565331i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −43.1925 | −1.66992 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 26.3875i | 1.01868i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.6567i | 0.680615i | 0.940314 | + | 0.340307i | \(0.110531\pi\) | ||||
−0.940314 | + | 0.340307i | \(0.889469\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.27366 | − | 12.4131i | 0.0875133 | − | 0.477781i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −41.8438 | −1.60819 | −0.804093 | − | 0.594503i | \(-0.797349\pi\) | ||||
−0.804093 | + | 0.594503i | \(0.797349\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.66168i | 0.255652i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 39.8673i | − | 1.52772i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 35.4804 | 1.35762 | 0.678809 | − | 0.734315i | \(-0.262496\pi\) | ||||
0.678809 | + | 0.734315i | \(0.262496\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14.3930 | + | 11.9961i | −0.549928 | + | 0.458349i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 59.8721i | 2.28426i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 0.106796i | − | 0.00406861i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 42.0356i | 1.59911i | 0.600592 | + | 0.799556i | \(0.294932\pi\) | ||||
−0.600592 | + | 0.799556i | \(0.705068\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 3.42026i | − | 0.129925i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.83724 | − | 5.80373i | −0.183487 | − | 0.220148i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 23.6322 | 0.895132 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 9.38062i | − | 0.354808i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 41.2075i | 1.55639i | 0.628025 | + | 0.778193i | \(0.283864\pi\) | ||||
−0.628025 | + | 0.778193i | \(0.716136\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.48817 | 0.206990 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −13.5818 | + | 11.3200i | −0.511519 | + | 0.426336i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7.84476i | 0.295032i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 42.1883i | − | 1.58442i | −0.610251 | − | 0.792208i | \(-0.708931\pi\) | ||
0.610251 | − | 0.792208i | \(-0.291069\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.86107 | −0.219807 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.08696 | − | 21.4807i | −0.153058 | − | 0.804459i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.66418 | − | 1.99668i | −0.0622367 | − | 0.0746718i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 40.8152i | − | 1.52427i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 34.9606i | − | 1.30381i | −0.758301 | − | 0.651905i | \(-0.773970\pi\) | ||
0.758301 | − | 0.651905i | \(-0.226030\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.26789 | 0.270670 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 7.95069i | − | 0.295689i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.46731 | + | 8.01081i | −0.0544945 | + | 0.297514i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 25.1715i | − | 0.933560i | −0.884373 | − | 0.466780i | \(-0.845414\pi\) | ||
0.884373 | − | 0.466780i | \(-0.154586\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.94700 | −0.146185 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 16.2247i | − | 0.600091i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.42700 | −0.348194 | −0.174097 | − | 0.984728i | \(-0.555701\pi\) | ||||
−0.174097 | + | 0.984728i | \(0.555701\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 24.9289 | − | 20.7775i | 0.919517 | − | 0.766390i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 6.25792i | − | 0.230513i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 43.5175i | 1.60082i | 0.599455 | + | 0.800409i | \(0.295384\pi\) | ||||
−0.599455 | + | 0.800409i | \(0.704616\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 2.44767i | − | 0.0899174i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 35.2929i | − | 1.29477i | −0.762162 | − | 0.647386i | \(-0.775862\pi\) | ||
0.762162 | − | 0.647386i | \(-0.224138\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −25.3800 | − | 30.4510i | −0.929852 | − | 1.11564i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 16.9661i | 0.620757i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.97410 | 0.364446 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23.7239 | 0.865699 | 0.432849 | − | 0.901466i | \(-0.357508\pi\) | ||||
0.432849 | + | 0.901466i | \(0.357508\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8.41642 | −0.306712 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 24.2013 | + | 29.0368i | 0.880776 | + | 1.05676i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.88600 | −0.213930 | −0.106965 | − | 0.994263i | \(-0.534113\pi\) | ||||
−0.106965 | + | 0.994263i | \(0.534113\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −29.7920 | + | 5.66827i | −1.08138 | + | 0.205745i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.12950 | −0.330944 | −0.165472 | − | 0.986214i | \(-0.552915\pi\) | ||||
−0.165472 | + | 0.986214i | \(0.552915\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.76377 | 0.317270 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 15.7046 | − | 13.0894i | 0.567803 | − | 0.473247i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.20223 | −0.151734 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 5.71892i | − | 0.206230i | −0.994669 | − | 0.103115i | \(-0.967119\pi\) | ||
0.994669 | − | 0.103115i | \(-0.0328809\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.73992i | 0.0986758i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −8.00711 | −0.287996 | −0.143998 | − | 0.989578i | \(-0.545996\pi\) | ||||
−0.143998 | + | 0.989578i | \(0.545996\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −22.4239 | − | 4.10730i | −0.805490 | − | 0.147538i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.83303i | 0.101634i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −13.1473 | −0.471053 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 29.6185i | − | 1.05983i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.11101 | −0.146916 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −19.1556 | + | 15.9656i | −0.683692 | + | 0.569837i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.9386i | 0.389917i | 0.980811 | + | 0.194959i | \(0.0624573\pi\) | ||||
−0.980811 | + | 0.194959i | \(0.937543\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 22.1568i | 0.788801i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.80358i | 0.170796i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.72387 | −0.132238 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.997900 | + | 0.831720i | −0.0353919 | + | 0.0294981i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −23.0968 | −0.818132 | −0.409066 | − | 0.912505i | \(-0.634145\pi\) | ||||
−0.409066 | + | 0.912505i | \(0.634145\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 17.6933 | 0.625944 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 26.0228i | 0.919469i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 12.7157i | 0.448727i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.32382 | + | 4.37573i | 0.187640 | + | 0.154224i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.83598 | 0.170235 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 16.5248 | 0.580980 | 0.290490 | − | 0.956878i | \(-0.406182\pi\) | ||||
0.290490 | + | 0.956878i | \(0.406182\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 51.9334i | 1.82363i | 0.410604 | + | 0.911814i | \(0.365318\pi\) | ||||
−0.410604 | + | 0.911814i | \(0.634682\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 9.38593i | − | 0.329179i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.30509 | − | 3.58817i | 0.150801 | − | 0.125688i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.02631i | 0.315791i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.482674 | 0.0168660 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.2235 | 0.356802 | 0.178401 | − | 0.983958i | \(-0.442908\pi\) | ||||
0.178401 | + | 0.983958i | \(0.442908\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13.5688 | −0.472979 | −0.236490 | − | 0.971634i | \(-0.575997\pi\) | ||||
−0.236490 | + | 0.971634i | \(0.575997\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5.69648 | + | 31.1001i | −0.198326 | + | 1.08277i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 44.4177i | − | 1.54455i | −0.635286 | − | 0.772277i | \(-0.719118\pi\) | ||
0.635286 | − | 0.772277i | \(-0.280882\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23.7469 | −0.824765 | −0.412382 | − | 0.911011i | \(-0.635303\pi\) | ||||
−0.412382 | + | 0.911011i | \(0.635303\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 19.5563i | − | 0.678401i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −32.4755 | −1.12521 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.16051 | − | 2.63419i | 0.109374 | − | 0.0911599i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 11.5076i | − | 0.397759i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.77605 | 0.199412 | 0.0997058 | − | 0.995017i | \(-0.468210\pi\) | ||||
0.0997058 | + | 0.995017i | \(0.468210\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.3470 | −0.908516 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 18.9021i | − | 0.651024i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −22.0481 | + | 18.3764i | −0.758476 | + | 0.632167i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.77552i | 0.0610075i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 7.49548i | − | 0.257244i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.42691 | − | 1.79358i | 0.323150 | − | 0.0614831i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 29.8835i | 1.02319i | 0.859227 | + | 0.511595i | \(0.170945\pi\) | ||||
−0.859227 | + | 0.511595i | \(0.829055\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.73701 | + | 7.28204i | −0.298799 | + | 0.249040i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 43.5873i | − | 1.48891i | −0.667670 | − | 0.744457i | \(-0.732708\pi\) | ||
0.667670 | − | 0.744457i | \(-0.267292\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 1.90651i | − | 0.0650492i | −0.999471 | − | 0.0325246i | \(-0.989645\pi\) | ||
0.999471 | − | 0.0325246i | \(-0.0103547\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 6.78674i | − | 0.231292i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −28.0711 | −0.955551 | −0.477775 | − | 0.878482i | \(-0.658557\pi\) | ||||
−0.477775 | + | 0.878482i | \(0.658557\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −16.1212 | − | 19.3423i | −0.548138 | − | 0.657658i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16.0994 | −0.546765 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.07074 | −0.307704 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.883132 | 0.0299238 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −19.2243 | −0.650646 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.25751 | − | 3.53033i | 0.211542 | − | 0.119347i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 47.8183i | 1.61471i | 0.590066 | + | 0.807355i | \(0.299102\pi\) | ||||
−0.590066 | + | 0.807355i | \(0.700898\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 63.6875 | 2.14813 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 13.1731i | − | 0.443813i | −0.975068 | − | 0.221906i | \(-0.928772\pi\) | ||
0.975068 | − | 0.221906i | \(-0.0712279\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.6396 | 0.896494 | 0.448247 | − | 0.893910i | \(-0.352049\pi\) | ||||
0.448247 | + | 0.893910i | \(0.352049\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 32.7267 | + | 39.2656i | 1.10010 | + | 1.31990i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 15.8626 | 0.532615 | 0.266307 | − | 0.963888i | \(-0.414196\pi\) | ||||
0.266307 | + | 0.963888i | \(0.414196\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 0.244763i | − | 0.00820908i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −31.9272 | −1.06960 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9.84336 | −0.329395 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.878411 | + | 1.05392i | 0.0293621 | + | 0.0352287i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.799919 | − | 4.20431i | −0.0267085 | − | 0.140378i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 7.42641i | 0.247684i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.29999 | 0.0433089 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.65944 | −0.155056 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.755316 | + | 0.906230i | 0.0251076 | + | 0.0301241i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 33.0630i | − | 1.09784i | −0.835875 | − | 0.548920i | \(-0.815039\pi\) | ||
0.835875 | − | 0.548920i | \(-0.184961\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −22.6385 | −0.750871 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 56.1545 | 1.86048 | 0.930240 | − | 0.366951i | \(-0.119598\pi\) | ||||
0.930240 | + | 0.366951i | \(0.119598\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 26.2571i | 0.868984i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 29.0012 | + | 34.7957i | 0.958750 | + | 1.15031i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.57496 | −0.316193 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 34.7455 | 1.14615 | 0.573074 | − | 0.819503i | \(-0.305751\pi\) | ||||
0.573074 | + | 0.819503i | \(0.305751\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.06929 | −0.265892 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.17984 | 0.137581 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.80250 | − | 9.84082i | 0.0592660 | − | 0.323564i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 20.9737i | 0.688868i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.36655 | 0.176071 | 0.0880354 | − | 0.996117i | \(-0.471941\pi\) | ||||
0.0880354 | + | 0.996117i | \(0.471941\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18.0672 | 0.592128 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 18.6554i | − | 0.610749i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 24.3049 | − | 20.2574i | 0.794855 | − | 0.662488i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −38.4772 | −1.25700 | −0.628498 | − | 0.777811i | \(-0.716330\pi\) | ||||
−0.628498 | + | 0.777811i | \(0.716330\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −40.9135 | −1.33516 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 46.7397i | 1.52367i | 0.647770 | + | 0.761836i | \(0.275702\pi\) | ||||
−0.647770 | + | 0.761836i | \(0.724298\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −22.5829 | + | 4.29667i | −0.735401 | + | 0.139919i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.32199 | + | 2.78594i | 0.0755345 | + | 0.0906265i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −50.6457 | −1.64576 | −0.822881 | − | 0.568213i | \(-0.807635\pi\) | ||||
−0.822881 | + | 0.568213i | \(0.807635\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.79447 | −0.0582508 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.48336i | 0.0481012i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −47.8691 | −1.55063 | −0.775316 | − | 0.631574i | \(-0.782409\pi\) | ||||
−0.775316 | + | 0.631574i | \(0.782409\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 22.4239 | − | 18.6896i | 0.725620 | − | 0.604783i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 10.2998 | 0.332946 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 5.38470i | − | 0.173881i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.2120 | 0.329419 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 28.7834i | 0.927532i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −29.1086 | − | 34.9246i | −0.937039 | − | 1.12426i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20.7095 | 0.665973 | 0.332987 | − | 0.942932i | \(-0.391944\pi\) | ||||
0.332987 | + | 0.942932i | \(0.391944\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 29.7946 | 0.957139 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 47.4132 | 1.52156 | 0.760780 | − | 0.649009i | \(-0.224816\pi\) | ||||
0.760780 | + | 0.649009i | \(0.224816\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.17129 | 0.0696083 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.38891 | − | 0.803900i | −0.140558 | − | 0.0257454i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −45.9036 | −1.46859 | −0.734293 | − | 0.678833i | \(-0.762486\pi\) | ||||
−0.734293 | + | 0.678833i | \(0.762486\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 40.2735i | 1.28715i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 25.2906i | 0.807466i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 25.1206i | 0.801222i | 0.916248 | + | 0.400611i | \(0.131202\pi\) | ||||
−0.916248 | + | 0.400611i | \(0.868798\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 21.5410 | + | 25.8450i | 0.686354 | + | 0.823490i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 5.08120i | − | 0.161736i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.94988 | + | 15.5043i | 0.0938006 | + | 0.493008i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.60466i | 0.0509737i | 0.999675 | + | 0.0254868i | \(0.00811359\pi\) | ||||
−0.999675 | + | 0.0254868i | \(0.991886\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 25.0786i | 0.795844i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11.7097 | − | 9.75968i | 0.371222 | − | 0.309403i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 23.0326i | − | 0.729450i | −0.931115 | − | 0.364725i | \(-0.881163\pi\) | ||
0.931115 | − | 0.364725i | \(-0.118837\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.05014 | 0.159779 |
(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 | 1840.2.m.g.1839.10 | yes | 40 | |
4.3 | odd | 2 | inner | 1840.2.m.g.1839.31 | yes | 40 | |
5.4 | even | 2 | inner | 1840.2.m.g.1839.29 | yes | 40 | |
20.19 | odd | 2 | inner | 1840.2.m.g.1839.12 | yes | 40 | |
23.22 | odd | 2 | inner | 1840.2.m.g.1839.9 | ✓ | 40 | |
92.91 | even | 2 | inner | 1840.2.m.g.1839.32 | yes | 40 | |
115.114 | odd | 2 | inner | 1840.2.m.g.1839.30 | yes | 40 | |
460.459 | even | 2 | inner | 1840.2.m.g.1839.11 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1840.2.m.g.1839.9 | ✓ | 40 | 23.22 | odd | 2 | inner | |
1840.2.m.g.1839.10 | yes | 40 | 1.1 | even | 1 | trivial | |
1840.2.m.g.1839.11 | yes | 40 | 460.459 | even | 2 | inner | |
1840.2.m.g.1839.12 | yes | 40 | 20.19 | odd | 2 | inner | |
1840.2.m.g.1839.29 | yes | 40 | 5.4 | even | 2 | inner | |
1840.2.m.g.1839.30 | yes | 40 | 115.114 | odd | 2 | inner | |
1840.2.m.g.1839.31 | yes | 40 | 4.3 | odd | 2 | inner | |
1840.2.m.g.1839.32 | yes | 40 | 92.91 | even | 2 | inner |