Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5520,2,Mod(1471,5520)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5520, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5520.1471");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5520 = 2^{4} \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5520.be (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: | \(44.0774219157\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1471.18 | ||
Character | \(\chi\) | \(=\) | 5520.1471 |
Dual form | 5520.2.be.c.1471.17 |
$q$-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 \(\left(\mathbb{Z}/5520\mathbb{Z}\right)^\times\).
\(n\) | \(1201\) | \(1381\) | \(1841\) | \(4417\) | \(4831\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.143131 | −0.0540986 | −0.0270493 | − | 0.999634i | \(-0.508611\pi\) | ||||
−0.0270493 | + | 0.999634i | \(0.508611\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.80659 | −1.44924 | −0.724621 | − | 0.689148i | \(-0.757985\pi\) | ||||
−0.724621 | + | 0.689148i | \(0.757985\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.78151 | 1.32615 | 0.663075 | − | 0.748553i | \(-0.269251\pi\) | ||||
0.663075 | + | 0.748553i | \(0.269251\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 4.86743i | − | 1.18053i | −0.807211 | − | 0.590263i | \(-0.799024\pi\) | ||
0.807211 | − | 0.590263i | \(-0.200976\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.379340 | −0.0870266 | −0.0435133 | − | 0.999053i | \(-0.513855\pi\) | ||||
−0.0435133 | + | 0.999053i | \(0.513855\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 0.143131i | − | 0.0312338i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.15365 | + | 4.65501i | −0.240552 | + | 0.970636i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.39933 | 1.55972 | 0.779858 | − | 0.625956i | \(-0.215291\pi\) | ||||
0.779858 | + | 0.625956i | \(0.215291\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 2.55983i | − | 0.459759i | −0.973219 | − | 0.229879i | \(-0.926167\pi\) | ||
0.973219 | − | 0.229879i | \(-0.0738332\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 4.80659i | − | 0.836720i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 0.143131i | − | 0.0241936i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.56282i | 0.914521i | 0.889333 | + | 0.457261i | \(0.151169\pi\) | ||||
−0.889333 | + | 0.457261i | \(0.848831\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.78151i | 0.765654i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.17202 | −0.807734 | −0.403867 | − | 0.914818i | \(-0.632334\pi\) | ||||
−0.403867 | + | 0.914818i | \(0.632334\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.03505 | −0.157843 | −0.0789215 | − | 0.996881i | \(-0.525148\pi\) | ||||
−0.0789215 | + | 0.996881i | \(0.525148\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 1.00000i | − | 0.149071i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.93486i | 1.30328i | 0.758527 | + | 0.651642i | \(0.225919\pi\) | ||||
−0.758527 | + | 0.651642i | \(0.774081\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.97951 | −0.997073 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.86743 | 0.681577 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13.3413i | 1.83256i | 0.400534 | + | 0.916282i | \(0.368825\pi\) | ||||
−0.400534 | + | 0.916282i | \(0.631175\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 4.80659i | − | 0.648121i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 0.379340i | − | 0.0502448i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.57340i | 0.855783i | 0.903830 | + | 0.427892i | \(0.140743\pi\) | ||||
−0.903830 | + | 0.427892i | \(0.859257\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 7.49837i | − | 0.960068i | −0.877250 | − | 0.480034i | \(-0.840624\pi\) | ||
0.877250 | − | 0.480034i | \(-0.159376\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.143131 | 0.0180329 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.78151i | 0.593073i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.96888 | −0.607046 | −0.303523 | − | 0.952824i | \(-0.598163\pi\) | ||||
−0.303523 | + | 0.952824i | \(0.598163\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.65501 | − | 1.15365i | −0.560397 | − | 0.138883i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 6.77385i | − | 0.803908i | −0.915660 | − | 0.401954i | \(-0.868331\pi\) | ||
0.915660 | − | 0.401954i | \(-0.131669\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.04529 | −0.941631 | −0.470815 | − | 0.882232i | \(-0.656040\pi\) | ||||
−0.470815 | + | 0.882232i | \(0.656040\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 1.00000i | − | 0.115470i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.687974 | 0.0784019 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.53132 | 0.172287 | 0.0861433 | − | 0.996283i | \(-0.472546\pi\) | ||||
0.0861433 | + | 0.996283i | \(0.472546\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −14.3973 | −1.58031 | −0.790157 | − | 0.612905i | \(-0.790001\pi\) | ||||
−0.790157 | + | 0.612905i | \(0.790001\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.86743 | 0.527947 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.39933i | 0.900503i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.6001i | 1.33561i | 0.744337 | + | 0.667804i | \(0.232766\pi\) | ||||
−0.744337 | + | 0.667804i | \(0.767234\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.684383 | −0.0717429 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.55983 | 0.265442 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 0.379340i | − | 0.0389195i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 5.67311i | − | 0.576017i | −0.957628 | − | 0.288009i | \(-0.907007\pi\) | ||
0.957628 | − | 0.288009i | \(-0.0929932\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.80659 | 0.483081 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −17.3244 | −1.72384 | −0.861921 | − | 0.507043i | \(-0.830739\pi\) | ||||
−0.861921 | + | 0.507043i | \(0.830739\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.2942 | −1.21138 | −0.605691 | − | 0.795700i | \(-0.707103\pi\) | ||||
−0.605691 | + | 0.795700i | \(0.707103\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.143131 | 0.0139682 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.02774 | −0.0993557 | −0.0496779 | − | 0.998765i | \(-0.515819\pi\) | ||||
−0.0496779 | + | 0.998765i | \(0.515819\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 16.9971i | − | 1.62802i | −0.580849 | − | 0.814011i | \(-0.697279\pi\) | ||
0.580849 | − | 0.814011i | \(-0.302721\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.56282 | −0.527999 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 0.637571i | − | 0.0599776i | −0.999550 | − | 0.0299888i | \(-0.990453\pi\) | ||
0.999550 | − | 0.0299888i | \(-0.00954716\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.65501 | − | 1.15365i | −0.434082 | − | 0.107578i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.78151 | −0.442050 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.696682i | 0.0638648i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 12.1033 | 1.10030 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 5.17202i | − | 0.466345i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.74112i | 0.331970i | 0.986128 | + | 0.165985i | \(0.0530804\pi\) | ||||
−0.986128 | + | 0.165985i | \(0.946920\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 1.03505i | − | 0.0911308i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 11.9550i | − | 1.04451i | −0.852790 | − | 0.522255i | \(-0.825091\pi\) | ||
0.852790 | − | 0.522255i | \(-0.174909\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.0542955 | 0.00470802 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 8.16863i | − | 0.697893i | −0.937143 | − | 0.348947i | \(-0.886539\pi\) | ||
0.937143 | − | 0.348947i | \(-0.113461\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 0.870322i | − | 0.0738198i | −0.999319 | − | 0.0369099i | \(-0.988249\pi\) | ||
0.999319 | − | 0.0369099i | \(-0.0117514\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.93486 | −0.752451 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −22.9827 | −1.92191 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.39933i | 0.697526i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 6.97951i | − | 0.575661i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11.4050i | 0.934337i | 0.884168 | + | 0.467168i | \(0.154726\pi\) | ||||
−0.884168 | + | 0.467168i | \(0.845274\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.66516i | 0.461024i | 0.973069 | + | 0.230512i | \(0.0740401\pi\) | ||||
−0.973069 | + | 0.230512i | \(0.925960\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.86743i | 0.393509i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.55983 | 0.205610 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 5.94964i | − | 0.474833i | −0.971408 | − | 0.237417i | \(-0.923699\pi\) | ||
0.971408 | − | 0.237417i | \(-0.0763006\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −13.3413 | −1.05803 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.165123 | − | 0.666278i | 0.0130135 | − | 0.0525100i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 12.0905i | − | 0.946997i | −0.880795 | − | 0.473499i | \(-0.842991\pi\) | ||
0.880795 | − | 0.473499i | \(-0.157009\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.80659 | 0.374193 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 14.1105i | 1.09191i | 0.837816 | + | 0.545953i | \(0.183832\pi\) | ||||
−0.837816 | + | 0.545953i | \(0.816168\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.86279 | 0.758676 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.379340 | 0.0290089 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.68070 | 0.279838 | 0.139919 | − | 0.990163i | \(-0.455316\pi\) | ||||
0.139919 | + | 0.990163i | \(0.455316\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.143131 | 0.0108197 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.57340 | −0.494087 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 9.27393i | − | 0.693166i | −0.938019 | − | 0.346583i | \(-0.887342\pi\) | ||
0.938019 | − | 0.346583i | \(-0.112658\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 5.10162i | − | 0.379200i | −0.981861 | − | 0.189600i | \(-0.939281\pi\) | ||
0.981861 | − | 0.189600i | \(-0.0607191\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.49837 | 0.554295 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.56282 | −0.408986 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 23.3958i | 1.71087i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.143131i | 0.0104113i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.1633 | −1.45897 | −0.729484 | − | 0.683997i | \(-0.760240\pi\) | ||||
−0.729484 | + | 0.683997i | \(0.760240\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.06748 | 0.0768392 | 0.0384196 | − | 0.999262i | \(-0.487768\pi\) | ||||
0.0384196 | + | 0.999262i | \(0.487768\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.78151 | −0.342411 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.31277 | 0.307272 | 0.153636 | − | 0.988128i | \(-0.450902\pi\) | ||||
0.153636 | + | 0.988128i | \(0.450902\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.35032 | −0.662827 | −0.331413 | − | 0.943486i | \(-0.607525\pi\) | ||||
−0.331413 | + | 0.943486i | \(0.607525\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 4.96888i | − | 0.350478i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.20221 | −0.0843784 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 5.17202i | − | 0.361230i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.15365 | − | 4.65501i | 0.0801840 | − | 0.323545i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.82333 | 0.126123 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.8715i | 1.36801i | 0.729478 | + | 0.684004i | \(0.239763\pi\) | ||||
−0.729478 | + | 0.684004i | \(0.760237\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.77385 | 0.464136 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 1.03505i | − | 0.0705896i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.366392i | 0.0248723i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 8.04529i | − | 0.543651i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 23.2737i | − | 1.56556i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 13.4715i | − | 0.902116i | −0.892495 | − | 0.451058i | \(-0.851047\pi\) | ||
0.892495 | − | 0.451058i | \(-0.148953\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.56731 | −0.236771 | −0.118385 | − | 0.992968i | \(-0.537772\pi\) | ||||
−0.118385 | + | 0.992968i | \(0.537772\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 9.73343i | − | 0.643203i | −0.946875 | − | 0.321602i | \(-0.895779\pi\) | ||
0.946875 | − | 0.321602i | \(-0.104221\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.687974i | 0.0452654i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 19.7008 | 1.29065 | 0.645323 | − | 0.763910i | \(-0.276723\pi\) | ||||
0.645323 | + | 0.763910i | \(0.276723\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.93486 | −0.582846 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.53132i | 0.0994697i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 9.71151i | − | 0.628185i | −0.949392 | − | 0.314093i | \(-0.898300\pi\) | ||
0.949392 | − | 0.314093i | \(-0.101700\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 11.3349i | − | 0.730144i | −0.930979 | − | 0.365072i | \(-0.881044\pi\) | ||
0.930979 | − | 0.365072i | \(-0.118956\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 6.97951i | − | 0.445905i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.81382 | −0.115410 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 14.3973i | − | 0.912394i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.4895 | −0.788329 | −0.394164 | − | 0.919040i | \(-0.628966\pi\) | ||||
−0.394164 | + | 0.919040i | \(0.628966\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.54511 | − | 22.3747i | 0.348618 | − | 1.40669i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.86743i | 0.304810i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.82467 | −0.300954 | −0.150477 | − | 0.988613i | \(-0.548081\pi\) | ||||
−0.150477 | + | 0.988613i | \(0.548081\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 0.796214i | − | 0.0494743i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.39933 | −0.519905 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.75865 | −0.416756 | −0.208378 | − | 0.978048i | \(-0.566818\pi\) | ||||
−0.208378 | + | 0.978048i | \(0.566818\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −13.3413 | −0.819547 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −12.6001 | −0.771114 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.49855 | 0.579137 | 0.289568 | − | 0.957157i | \(-0.406488\pi\) | ||||
0.289568 | + | 0.957157i | \(0.406488\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.6288i | 1.07087i | 0.844576 | + | 0.535435i | \(0.179852\pi\) | ||||
−0.844576 | + | 0.535435i | \(0.820148\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 0.684383i | − | 0.0414208i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.80659 | 0.289848 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.47253 | 0.509065 | 0.254533 | − | 0.967064i | \(-0.418078\pi\) | ||||
0.254533 | + | 0.967064i | \(0.418078\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.55983i | 0.153253i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.6546i | 0.635603i | 0.948157 | + | 0.317801i | \(0.102945\pi\) | ||||
−0.948157 | + | 0.317801i | \(0.897055\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.84325 | 0.585120 | 0.292560 | − | 0.956247i | \(-0.405493\pi\) | ||||
0.292560 | + | 0.956247i | \(0.405493\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.379340 | 0.0224702 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.740278 | 0.0436973 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.69189 | −0.393641 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.67311 | 0.332564 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 29.3775i | − | 1.71625i | −0.513439 | − | 0.858126i | \(-0.671629\pi\) | ||
0.513439 | − | 0.858126i | \(-0.328371\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.57340 | −0.382718 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.80659i | 0.278907i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.51617 | + | 22.2579i | −0.319008 | + | 1.28721i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.148148 | 0.00853909 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 17.3244i | − | 0.995260i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.49837 | 0.429355 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.6395i | 0.892591i | 0.894886 | + | 0.446296i | \(0.147257\pi\) | ||||
−0.894886 | + | 0.446296i | \(0.852743\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 12.2942i | − | 0.699391i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.7393i | 0.949201i | 0.880201 | + | 0.474600i | \(0.157407\pi\) | ||||
−0.880201 | + | 0.474600i | \(0.842593\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.0663i | 0.964646i | 0.875993 | + | 0.482323i | \(0.160207\pi\) | ||||
−0.875993 | + | 0.482323i | \(0.839793\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.143131i | 0.00806454i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −29.6407 | −1.66479 | −0.832394 | − | 0.554184i | \(-0.813030\pi\) | ||||
−0.832394 | + | 0.554184i | \(0.813030\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −40.3721 | −2.26041 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 1.02774i | − | 0.0573630i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.84641i | 0.102737i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.78151 | −0.265230 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 16.9971 | 0.939939 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 1.27886i | − | 0.0705058i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 4.03408i | − | 0.221733i | −0.993835 | − | 0.110866i | \(-0.964637\pi\) | ||
0.993835 | − | 0.110866i | \(-0.0353626\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 5.56282i | − | 0.304840i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 4.96888i | − | 0.271479i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.54962i | 0.0844132i | 0.999109 | + | 0.0422066i | \(0.0134388\pi\) | ||||
−0.999109 | + | 0.0422066i | \(0.986561\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.637571 | 0.0346281 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.3040i | 0.666302i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.00091 | 0.108039 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.15365 | − | 4.65501i | 0.0621103 | − | 0.250617i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 9.87984i | − | 0.530377i | −0.964197 | − | 0.265189i | \(-0.914566\pi\) | ||
0.964197 | − | 0.265189i | \(-0.0854343\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.41716 | 0.343503 | 0.171751 | − | 0.985140i | \(-0.445057\pi\) | ||||
0.171751 | + | 0.985140i | \(0.445057\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 4.78151i | − | 0.255218i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.23647 | −0.331934 | −0.165967 | − | 0.986131i | \(-0.553074\pi\) | ||||
−0.165967 | + | 0.986131i | \(0.553074\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.77385 | 0.359519 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.696682 | −0.0368723 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.19870 | −0.221599 | −0.110799 | − | 0.993843i | \(-0.535341\pi\) | ||||
−0.110799 | + | 0.993843i | \(0.535341\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.8561 | −0.992426 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 12.1033i | 0.635260i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 8.04529i | − | 0.421110i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.21796 | 0.272375 | 0.136188 | − | 0.990683i | \(-0.456515\pi\) | ||||
0.136188 | + | 0.990683i | \(0.456515\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.17202 | 0.269245 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 1.90955i | − | 0.0991391i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 24.8539i | 1.28689i | 0.765493 | + | 0.643444i | \(0.222495\pi\) | ||||
−0.765493 | + | 0.643444i | \(0.777505\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 40.1614 | 2.06842 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.2322 | 0.731058 | 0.365529 | − | 0.930800i | \(-0.380888\pi\) | ||||
0.365529 | + | 0.930800i | \(0.380888\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.74112 | −0.191663 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 23.6762 | 1.20980 | 0.604898 | − | 0.796303i | \(-0.293214\pi\) | ||||
0.604898 | + | 0.796303i | \(0.293214\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.687974i | 0.0350624i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.03505 | 0.0526144 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.73328i | 0.341391i | 0.985324 | + | 0.170695i | \(0.0546014\pi\) | ||||
−0.985324 | + | 0.170695i | \(0.945399\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 22.6579 | + | 5.61530i | 1.14586 | + | 0.283978i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 11.9550 | 0.603048 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.53132i | 0.0770489i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.27378 | 0.465438 | 0.232719 | − | 0.972544i | \(-0.425238\pi\) | ||||
0.232719 | + | 0.972544i | \(0.425238\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.0542955i | 0.00271817i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 38.6681i | 1.93099i | 0.260421 | + | 0.965495i | \(0.416139\pi\) | ||||
−0.260421 | + | 0.965495i | \(0.583861\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 12.2398i | − | 0.609709i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000i | 0.0496904i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 26.7382i | − | 1.32536i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −23.1274 | −1.14358 | −0.571789 | − | 0.820401i | \(-0.693750\pi\) | ||||
−0.571789 | + | 0.820401i | \(0.693750\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.16863 | 0.402929 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 0.940859i | − | 0.0462967i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 14.3973i | − | 0.706738i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.870322 | 0.0426199 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.95569 | −0.144395 | −0.0721974 | − | 0.997390i | \(-0.523001\pi\) | ||||
−0.0721974 | + | 0.997390i | \(0.523001\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 4.13502i | − | 0.201528i | −0.994910 | − | 0.100764i | \(-0.967871\pi\) | ||
0.994910 | − | 0.100764i | \(-0.0321288\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 8.93486i | − | 0.434428i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.86743i | 0.236105i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.07325i | 0.0519383i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 22.9827i | − | 1.10962i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.46802 | −0.407890 | −0.203945 | − | 0.978982i | \(-0.565376\pi\) | ||||
−0.203945 | + | 0.978982i | \(0.565376\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 17.3572i | − | 0.834132i | −0.908876 | − | 0.417066i | \(-0.863058\pi\) | ||
0.908876 | − | 0.417066i | \(-0.136942\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.39933 | −0.402717 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.437625 | − | 1.76583i | 0.0209344 | − | 0.0844712i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 24.8336i | 1.18524i | 0.805481 | + | 0.592622i | \(0.201907\pi\) | ||||
−0.805481 | + | 0.592622i | \(0.798093\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.97951 | 0.332358 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 26.8894i | − | 1.27756i | −0.769391 | − | 0.638778i | \(-0.779440\pi\) | ||
0.769391 | − | 0.638778i | \(-0.220560\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.6001 | −0.597302 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −11.4050 | −0.539440 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −33.4193 | −1.57716 | −0.788578 | − | 0.614935i | \(-0.789182\pi\) | ||||
−0.788578 | + | 0.614935i | \(0.789182\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 24.8598 | 1.17060 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.66516 | −0.266172 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 0.684383i | − | 0.0320844i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 7.03968i | − | 0.329302i | −0.986352 | − | 0.164651i | \(-0.947350\pi\) | ||
0.986352 | − | 0.164651i | \(-0.0526498\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.86743 | −0.227192 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −32.0115 | −1.49092 | −0.745462 | − | 0.666548i | \(-0.767771\pi\) | ||||
−0.745462 | + | 0.666548i | \(0.767771\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.1154i | 0.748945i | 0.927238 | + | 0.374472i | \(0.122176\pi\) | ||||
−0.927238 | + | 0.374472i | \(0.877824\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.55983i | 0.118709i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −40.8400 | −1.88985 | −0.944926 | − | 0.327285i | \(-0.893866\pi\) | ||||
−0.944926 | + | 0.327285i | \(0.893866\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.711203 | 0.0328403 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.94964 | 0.274145 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.97505 | 0.228753 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.379340 | 0.0174053 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 13.3413i | − | 0.610855i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12.5812 | −0.574848 | −0.287424 | − | 0.957803i | \(-0.592799\pi\) | ||||
−0.287424 | + | 0.957803i | \(0.592799\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 26.5986i | 1.21279i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.666278 | + | 0.165123i | 0.0303167 | + | 0.00751336i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.67311 | 0.257603 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 31.0193i | − | 1.40562i | −0.711378 | − | 0.702810i | \(-0.751928\pi\) | ||
0.711378 | − | 0.702810i | \(-0.248072\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 12.0905 | 0.546749 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 35.8601i | 1.61835i | 0.587571 | + | 0.809173i | \(0.300084\pi\) | ||||
−0.587571 | + | 0.809173i | \(0.699916\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 40.8832i | − | 1.84129i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.80659i | 0.216040i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.969550i | 0.0434903i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 10.0149i | − | 0.448330i | −0.974551 | − | 0.224165i | \(-0.928035\pi\) | ||
0.974551 | − | 0.224165i | \(-0.0719654\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −14.1105 | −0.630413 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −38.5120 | −1.71716 | −0.858582 | − | 0.512676i | \(-0.828654\pi\) | ||||
−0.858582 | + | 0.512676i | \(0.828654\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 17.3244i | − | 0.770925i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.86279i | 0.438022i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 31.4747 | 1.39509 | 0.697546 | − | 0.716540i | \(-0.254275\pi\) | ||||
0.697546 | + | 0.716540i | \(0.254275\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.15153 | 0.0509409 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.379340i | 0.0167483i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 12.2942i | − | 0.541746i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 42.9462i | − | 1.88877i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.68070i | 0.161565i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.5620i | 0.944647i | 0.881425 | + | 0.472324i | \(0.156585\pi\) | ||||
−0.881425 | + | 0.472324i | \(0.843415\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 40.7270 | 1.78087 | 0.890434 | − | 0.455112i | \(-0.150401\pi\) | ||||
0.890434 | + | 0.455112i | \(0.150401\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.143131i | 0.00624677i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −12.4598 | −0.542757 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.3382 | − | 10.7405i | −0.884269 | − | 0.466977i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 6.57340i | − | 0.285261i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −24.7300 | −1.07118 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 1.02774i | − | 0.0444332i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.27393 | 0.400200 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 33.5477 | 1.44500 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −38.8931 | −1.67215 | −0.836073 | − | 0.548618i | \(-0.815154\pi\) | ||||
−0.836073 | + | 0.548618i | \(0.815154\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.10162 | 0.218931 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 16.9971 | 0.728074 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.658772i | 0.0281671i | 0.999901 | + | 0.0140835i | \(0.00448308\pi\) | ||||
−0.999901 | + | 0.0140835i | \(0.995517\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.49837i | 0.320023i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.18620 | −0.135737 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.219179 | −0.00932046 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − | 5.56282i | − | 0.236128i | ||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 4.89839i | − | 0.207551i | −0.994601 | − | 0.103776i | \(-0.966908\pi\) | ||
0.994601 | − | 0.103776i | \(-0.0330924\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.94908 | −0.209324 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −23.3958 | −0.987770 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8.22969 | −0.346840 | −0.173420 | − | 0.984848i | \(-0.555482\pi\) | ||||
−0.173420 | + | 0.984848i | \(0.555482\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.637571 | 0.0268228 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.143131 | −0.00601095 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.84217i | 0.202994i | 0.994836 | + | 0.101497i | \(0.0323632\pi\) | ||||
−0.994836 | + | 0.101497i | \(0.967637\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18.6944 | −0.782335 | −0.391167 | − | 0.920320i | \(-0.627929\pi\) | ||||
−0.391167 | + | 0.920320i | \(0.627929\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 20.1633i | − | 0.842336i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.15365 | − | 4.65501i | 0.0481104 | − | 0.194127i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 37.9160 | 1.57847 | 0.789233 | − | 0.614094i | \(-0.210479\pi\) | ||||
0.789233 | + | 0.614094i | \(0.210479\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.06748i | 0.0443631i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.06071 | 0.0854927 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 64.1260i | − | 2.65583i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 4.78151i | − | 0.197691i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.52386i | 0.186720i | 0.995632 | + | 0.0933599i | \(0.0297607\pi\) | ||||
−0.995632 | + | 0.0933599i | \(0.970239\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.971046i | 0.0400112i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.31277i | 0.177404i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 21.4620 | 0.881338 | 0.440669 | − | 0.897670i | \(-0.354741\pi\) | ||||
0.440669 | + | 0.897670i | \(0.354741\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.696682 | −0.0285612 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 9.35032i | − | 0.382683i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 43.6864i | 1.78498i | 0.451069 | + | 0.892489i | \(0.351043\pi\) | ||||
−0.451069 | + | 0.892489i | \(0.648957\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −43.6463 | −1.78037 | −0.890185 | − | 0.455599i | \(-0.849425\pi\) | ||||
−0.890185 | + | 0.455599i | \(0.849425\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.96888 | 0.202349 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 12.1033i | 0.492070i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 13.8775i | − | 0.563269i | −0.959522 | − | 0.281635i | \(-0.909123\pi\) | ||
0.959522 | − | 0.281635i | \(-0.0908766\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 1.20221i | − | 0.0487159i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 42.7221i | 1.72835i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 18.7574i | − | 0.757606i | −0.925477 | − | 0.378803i | \(-0.876336\pi\) | ||
0.925477 | − | 0.378803i | \(-0.123664\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.17202 | 0.208556 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 28.7105i | 1.15584i | 0.816092 | + | 0.577922i | \(0.196136\pi\) | ||||
−0.816092 | + | 0.577922i | \(0.803864\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.458137 | −0.0184141 | −0.00920703 | − | 0.999958i | \(-0.502931\pi\) | ||||
−0.00920703 | + | 0.999958i | \(0.502931\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.65501 | + | 1.15365i | 0.186799 | + | 0.0462943i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 1.80347i | − | 0.0722545i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.82333i | 0.0728169i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 27.0766 | 1.07962 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −37.7755 | −1.50382 | −0.751910 | − | 0.659265i | \(-0.770867\pi\) | ||||
−0.751910 | + | 0.659265i | \(0.770867\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −19.8715 | −0.789820 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.74112 | −0.148462 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −33.3726 | −1.32227 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.77385i | 0.267969i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 29.5885i | 1.16868i | 0.811510 | + | 0.584338i | \(0.198646\pi\) | ||||
−0.811510 | + | 0.584338i | \(0.801354\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −47.0949 | −1.85724 | −0.928620 | − | 0.371032i | \(-0.879004\pi\) | ||||
−0.928620 | + | 0.371032i | \(0.879004\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.03505 | 0.0407549 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 26.6440i | 1.04748i | 0.851877 | + | 0.523741i | \(0.175464\pi\) | ||||
−0.851877 | + | 0.523741i | \(0.824536\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 31.5956i | − | 1.24024i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.366392 | −0.0143600 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 32.1606 | 1.25854 | 0.629272 | − | 0.777185i | \(-0.283353\pi\) | ||||
0.629272 | + | 0.777185i | \(0.283353\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11.9550 | 0.467119 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.04529 | 0.313877 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.56508 | 0.0609670 | 0.0304835 | − | 0.999535i | \(-0.490295\pi\) | ||||
0.0304835 | + | 0.999535i | \(0.490295\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 11.9297i | − | 0.464010i | −0.972715 | − | 0.232005i | \(-0.925471\pi\) | ||
0.972715 | − | 0.232005i | \(-0.0745285\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 23.2737 | 0.903874 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.0542955i | 0.00210549i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.68987 | + | 39.0989i | −0.375193 | + | 1.51392i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 13.4715 | 0.520837 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 36.0416i | 1.39137i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 27.9834 | 1.07868 | 0.539340 | − | 0.842088i | \(-0.318674\pi\) | ||||
0.539340 | + | 0.842088i | \(0.318674\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000i | 0.0384900i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 49.5307i | 1.90362i | 0.306691 | + | 0.951809i | \(0.400778\pi\) | ||||
−0.306691 | + | 0.951809i | \(0.599222\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.812001i | 0.0311617i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 3.56731i | − | 0.136700i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 18.2648i | − | 0.698884i | −0.936958 | − | 0.349442i | \(-0.886371\pi\) | ||
0.936958 | − | 0.349442i | \(-0.113629\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.16863 | 0.312107 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9.73343 | 0.371354 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 63.7913i | 2.43026i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24.6191i | 0.936554i | 0.883582 | + | 0.468277i | \(0.155125\pi\) | ||||
−0.883582 | + | 0.468277i | \(0.844875\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.687974 | −0.0261340 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.870322 | 0.0330132 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 25.1745i | 0.953550i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 19.7008i | 0.745154i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 35.5895i | − | 1.34420i | −0.740461 | − | 0.672099i | \(-0.765393\pi\) | ||
0.740461 | − | 0.672099i | \(-0.234607\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 2.11020i | − | 0.0795877i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 8.93486i | − | 0.336506i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.47966 | 0.0932574 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 8.00880i | − | 0.300777i | −0.988627 | − | 0.150388i | \(-0.951948\pi\) | ||
0.988627 | − | 0.150388i | \(-0.0480524\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.53132 | −0.0574289 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 11.9160 | + | 2.95314i | 0.446258 | + | 0.110596i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 22.9827i | − | 0.859506i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 9.71151 | 0.362683 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 40.1847i | − | 1.49864i | −0.662210 | − | 0.749318i | \(-0.730381\pi\) | ||
0.662210 | − | 0.749318i | \(-0.269619\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.75968 | 0.0655340 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 11.3349 | 0.421549 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8.39933 | −0.311943 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 46.1258 | 1.71071 | 0.855355 | − | 0.518042i | \(-0.173339\pi\) | ||||
0.855355 | + | 0.518042i | \(0.173339\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.03802i | 0.186338i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.4344i | 0.422340i | 0.977449 | + | 0.211170i | \(0.0677274\pi\) | ||||
−0.977449 | + | 0.211170i | \(0.932273\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6.97951 | 0.257443 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 23.8834 | 0.879756 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10.7005i | 0.393625i | 0.980441 | + | 0.196813i | \(0.0630591\pi\) | ||||
−0.980441 | + | 0.196813i | \(0.936941\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 1.81382i | − | 0.0666322i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −44.7313 | −1.64103 | −0.820515 | − | 0.571624i | \(-0.806313\pi\) | ||||
−0.820515 | + | 0.571624i | \(0.806313\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11.4050 | −0.417848 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 14.3973 | 0.526771 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.147102 | 0.00537500 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.5462 | 0.567289 | 0.283644 | − | 0.958930i | \(-0.408456\pi\) | ||||
0.283644 | + | 0.958930i | \(0.408456\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 12.4895i | − | 0.455142i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.66516 | −0.206176 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 15.3689i | − | 0.558594i | −0.960205 | − | 0.279297i | \(-0.909899\pi\) | ||
0.960205 | − | 0.279297i | \(-0.0901014\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 22.3747 | + | 5.54511i | 0.812151 | + | 0.201275i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −26.4309 | −0.958121 | −0.479060 | − | 0.877782i | \(-0.659023\pi\) | ||||
−0.479060 | + | 0.877782i | \(0.659023\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.43281i | 0.0880737i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.86743 | −0.175982 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 31.4307i | 1.13490i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 51.7442i | 1.86594i | 0.359948 | + | 0.932972i | \(0.382794\pi\) | ||||
−0.359948 | + | 0.932972i | \(0.617206\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 4.82467i | − | 0.173756i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 11.3165i | 0.407026i | 0.979072 | + | 0.203513i | \(0.0652360\pi\) | ||||
−0.979072 | + | 0.203513i | \(0.934764\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.55983i | 0.0919517i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.796214 | 0.0285640 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.96195 | 0.0702943 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 32.5591i | 1.16506i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 8.39933i | − | 0.300168i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.94964 | 0.212352 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.8240 | 0.742296 | 0.371148 | − | 0.928574i | \(-0.378964\pi\) | ||||
0.371148 | + | 0.928574i | \(0.378964\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 6.75865i | − | 0.240614i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.0912564i | 0.00324470i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 35.8535i | − | 1.27319i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 13.3413i | − | 0.473166i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 34.5644i | 1.22433i | 0.790729 | + | 0.612166i | \(0.209702\pi\) | ||||
−0.790729 | + | 0.612166i | \(0.790298\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 43.4898 | 1.53856 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 12.6001i | − | 0.445203i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 38.6704 | 1.36465 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.666278 | + | 0.165123i | 0.0234832 | + | 0.00581983i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9.49855i | 0.334365i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −14.4517 | −0.508095 | −0.254047 | − | 0.967192i | \(-0.581762\pi\) | ||||
−0.254047 | + | 0.967192i | \(0.581762\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 24.2239i | − | 0.850616i | −0.905049 | − | 0.425308i | \(-0.860166\pi\) | ||
0.905049 | − | 0.425308i | \(-0.139834\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −17.6288 | −0.618268 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12.0905 | 0.423510 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.392635 | 0.0137365 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.684383 | 0.0239143 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19.2778 | 0.672799 | 0.336400 | − | 0.941719i | \(-0.390791\pi\) | ||||
0.336400 | + | 0.941719i | \(0.390791\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 32.9410i | 1.14825i | 0.818767 | + | 0.574126i | \(0.194658\pi\) | ||||
−0.818767 | + | 0.574126i | \(0.805342\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.80659i | 0.167344i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 26.6343 | 0.926164 | 0.463082 | − | 0.886316i | \(-0.346744\pi\) | ||||
0.463082 | + | 0.886316i | \(0.346744\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.05373 | −0.175523 | −0.0877616 | − | 0.996142i | \(-0.527971\pi\) | ||||
−0.0877616 | + | 0.996142i | \(0.527971\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.47253i | 0.293909i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 33.9723i | 1.17707i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.1105 | −0.488316 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.55983 | −0.0884806 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 11.1301 | 0.384254 | 0.192127 | − | 0.981370i | \(-0.438461\pi\) | ||||
0.192127 | + | 0.981370i | \(0.438461\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 41.5487 | 1.43272 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −10.6546 | −0.366965 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.86279i | 0.339290i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.73237 | −0.0595248 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9.84325i | 0.337819i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −25.8950 | − | 6.41753i | −0.887668 | − | 0.219990i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 17.8102 | 0.609809 | 0.304904 | − | 0.952383i | \(-0.401375\pi\) | ||||
0.304904 | + | 0.952383i | \(0.401375\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.379340i | 0.0129732i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −42.1930 | −1.44129 | −0.720643 | − | 0.693307i | \(-0.756153\pi\) | ||||
−0.720643 | + | 0.693307i | \(0.756153\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 48.2853i | − | 1.64747i | −0.566972 | − | 0.823737i | \(-0.691885\pi\) | ||
0.566972 | − | 0.823737i | \(-0.308115\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.740278i | 0.0252286i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 56.5320i | − | 1.92437i | −0.272392 | − | 0.962186i | \(-0.587815\pi\) | ||
0.272392 | − | 0.962186i | \(-0.412185\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.68070i | 0.125148i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 6.69189i | − | 0.227269i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.36041 | −0.249685 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −23.7587 | −0.805034 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.67311i | 0.192006i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.143131i | 0.00483872i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 29.6117 | 0.999915 | 0.499958 | − | 0.866050i | \(-0.333349\pi\) | ||||
0.499958 | + | 0.866050i | \(0.333349\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 29.3775 | 0.990879 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 10.6754i | − | 0.359662i | −0.983698 | − | 0.179831i | \(-0.942445\pi\) | ||
0.983698 | − | 0.179831i | \(-0.0575551\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 13.9342i | − | 0.468922i | −0.972126 | − | 0.234461i | \(-0.924667\pi\) | ||
0.972126 | − | 0.234461i | \(-0.0753325\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 6.57340i | − | 0.220962i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 47.6768i | 1.60083i | 0.599446 | + | 0.800415i | \(0.295387\pi\) | ||||
−0.599446 | + | 0.800415i | \(0.704613\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 0.535471i | − | 0.0179591i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.80659 | −0.161027 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 3.38935i | − | 0.113420i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.27393 | 0.309993 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −22.2579 | − | 5.51617i | −0.743171 | − | 0.184180i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 21.5008i | − | 0.717093i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 64.9377 | 2.16339 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.148148i | 0.00493004i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.10162 | 0.169583 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12.0207 | −0.399141 | −0.199571 | − | 0.979883i | \(-0.563955\pi\) | ||||
−0.199571 | + | 0.979883i | \(0.563955\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 17.3244 | 0.574614 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.73661 | −0.322588 | −0.161294 | − | 0.986906i | \(-0.551567\pi\) | ||||
−0.161294 | + | 0.986906i | \(0.551567\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 69.2021 | 2.29026 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 7.49837i | 0.247888i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.71113i | 0.0565065i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 38.9231 | 1.28396 | 0.641978 | − | 0.766723i | \(-0.278114\pi\) | ||||
0.641978 | + | 0.766723i | \(0.278114\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −15.6395 | −0.515338 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 32.3892i | − | 1.06610i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 5.56282i | − | 0.182904i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 12.2942 | 0.403794 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 43.8793 | 1.43963 | 0.719817 | − | 0.694164i | \(-0.244226\pi\) | ||||
0.719817 | + | 0.694164i | \(0.244226\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.64761 | 0.0867719 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −16.7393 | −0.548021 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −23.3958 | −0.765123 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 39.3915i | 1.28686i | 0.765504 | + | 0.643432i | \(0.222490\pi\) | ||||
−0.765504 | + | 0.643432i | \(0.777510\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −17.0663 | −0.556939 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 45.6529i | 1.48824i | 0.668045 | + | 0.744120i | \(0.267131\pi\) | ||||
−0.668045 | + | 0.744120i | \(0.732869\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.96669 | − | 24.0758i | 0.194302 | − | 0.784016i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.143131 | −0.00465606 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 0.780609i | − | 0.0253664i | −0.999920 | − | 0.0126832i | \(-0.995963\pi\) | ||
0.999920 | − | 0.0126832i | \(-0.00403729\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −38.4686 | −1.24874 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 29.6407i | − | 0.961166i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 0.373697i | − | 0.0121052i | −0.999982 | − | 0.00605261i | \(-0.998073\pi\) | ||
0.999982 | − | 0.00605261i | \(-0.00192662\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 20.1633i | − | 0.652471i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 40.3721i | − | 1.30505i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.16919i | 0.0377550i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 24.4473 | 0.788622 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.02774 | 0.0331186 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.06748i | 0.0343635i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 11.2527i | − | 0.361862i | −0.983496 | − | 0.180931i | \(-0.942089\pi\) | ||
0.983496 | − | 0.180931i | \(-0.0579110\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.84641 | −0.0593153 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 61.0936 | 1.96059 | 0.980294 | − | 0.197544i | \(-0.0632966\pi\) | ||||
0.980294 | + | 0.197544i | \(0.0632966\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.124570i | 0.00399354i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 4.78151i | − | 0.153131i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 10.4612i | − | 0.334685i | −0.985899 | − | 0.167342i | \(-0.946481\pi\) | ||
0.985899 | − | 0.167342i | \(-0.0535185\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 60.5636i | − | 1.93562i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16.9971i | 0.542674i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −57.0974 | −1.82112 | −0.910562 | − | 0.413373i | \(-0.864351\pi\) | ||||
−0.910562 | + | 0.413373i | \(0.864351\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.31277i | 0.137416i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.27886 | 0.0407065 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.19408 | − | 4.81815i | 0.0379695 | − | 0.153208i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.99297i | 0.285671i | 0.989746 | + | 0.142836i | \(0.0456220\pi\) | ||||
−0.989746 | + | 0.142836i | \(0.954378\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.03408 | 0.128018 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 9.35032i | − | 0.296425i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −39.7082 | −1.25757 | −0.628786 | − | 0.777578i | \(-0.716448\pi\) | ||||
−0.628786 | + | 0.777578i | \(0.716448\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.56282 | 0.176000 |
(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 | 5520.2.be.c.1471.18 | yes | 32 | |
4.3 | odd | 2 | 5520.2.be.d.1471.17 | yes | 32 | ||
23.22 | odd | 2 | 5520.2.be.d.1471.18 | yes | 32 | ||
92.91 | even | 2 | inner | 5520.2.be.c.1471.17 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5520.2.be.c.1471.17 | ✓ | 32 | 92.91 | even | 2 | inner | |
5520.2.be.c.1471.18 | yes | 32 | 1.1 | even | 1 | trivial | |
5520.2.be.d.1471.17 | yes | 32 | 4.3 | odd | 2 | ||
5520.2.be.d.1471.18 | yes | 32 | 23.22 | odd | 2 |