Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6048,2,Mod(5615,6048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6048.5615");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6048.j (of order \(2\), degree \(1\), not 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: | \(48.2935231425\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | no (minimal twist has level 1512) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 5615.21 | ||
Character | \(\chi\) | \(=\) | 6048.5615 |
Dual form | 6048.2.j.d.5615.22 |
$q$-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 \(\left(\mathbb{Z}/6048\mathbb{Z}\right)^\times\).
\(n\) | \(2593\) | \(3781\) | \(3809\) | \(4159\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.530075 | −0.237057 | −0.118528 | − | 0.992951i | \(-0.537818\pi\) | ||||
−0.118528 | + | 0.992951i | \(0.537818\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 1.00000i | − 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.905144i | 0.272911i | 0.990646 | + | 0.136456i | \(0.0435711\pi\) | ||||
−0.990646 | + | 0.136456i | \(0.956429\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.38398i | 1.21590i | 0.793976 | + | 0.607949i | \(0.208008\pi\) | ||||
−0.793976 | + | 0.607949i | \(0.791992\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.25430i | 0.304212i | 0.988364 | + | 0.152106i | \(0.0486055\pi\) | ||||
−0.988364 | + | 0.152106i | \(0.951395\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.00364927 | −0.000837200 0 | −0.000418600 | − | 1.00000i | \(-0.500133\pi\) | ||||
−0.000418600 | 1.00000i | \(0.500133\pi\) | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.778929 | −0.162418 | −0.0812090 | − | 0.996697i | \(-0.525878\pi\) | ||||
−0.0812090 | + | 0.996697i | \(0.525878\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.71902 | −0.943804 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.43228 | 1.00875 | 0.504375 | − | 0.863485i | \(-0.331723\pi\) | ||||
0.504375 | + | 0.863485i | \(0.331723\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 3.49953i | − 0.628533i | −0.949335 | − | 0.314267i | \(-0.898241\pi\) | ||||
0.949335 | − | 0.314267i | \(-0.101759\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.530075i | 0.0895990i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.34322i | 0.878421i | 0.898384 | + | 0.439210i | \(0.144742\pi\) | ||||
−0.898384 | + | 0.439210i | \(0.855258\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 1.74538i | − 0.272582i | −0.990669 | − | 0.136291i | \(-0.956482\pi\) | ||||
0.990669 | − | 0.136291i | \(-0.0435183\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.259493 | 0.0395723 | 0.0197862 | − | 0.999804i | \(-0.493701\pi\) | ||||
0.0197862 | + | 0.999804i | \(0.493701\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.75927 | 0.548346 | 0.274173 | − | 0.961680i | \(-0.411596\pi\) | ||||
0.274173 | + | 0.961680i | \(0.411596\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.08087 | 0.423190 | 0.211595 | − | 0.977357i | \(-0.432134\pi\) | ||||
0.211595 | + | 0.977357i | \(0.432134\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 0.479794i | − 0.0646955i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 5.73302i | − 0.746376i | −0.927756 | − | 0.373188i | \(-0.878265\pi\) | ||||
0.927756 | − | 0.373188i | \(-0.121735\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 0.555629i | − 0.0711410i | −0.999367 | − | 0.0355705i | \(-0.988675\pi\) | ||||
0.999367 | − | 0.0355705i | \(-0.0113248\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 2.32384i | − 0.288237i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.5465 | −1.41063 | −0.705313 | − | 0.708896i | \(-0.749194\pi\) | ||||
−0.705313 | + | 0.708896i | \(0.749194\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −16.0043 | −1.89936 | −0.949681 | − | 0.313218i | \(-0.898593\pi\) | ||||
−0.949681 | + | 0.313218i | \(0.898593\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −13.1552 | −1.53970 | −0.769851 | − | 0.638224i | \(-0.779669\pi\) | ||||
−0.769851 | + | 0.638224i | \(0.779669\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.905144 | 0.103151 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.96889i | 0.221517i | 0.993847 | + | 0.110759i | \(0.0353280\pi\) | ||||
−0.993847 | + | 0.110759i | \(0.964672\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.82561i | 0.639444i | 0.947511 | + | 0.319722i | \(0.103589\pi\) | ||||
−0.947511 | + | 0.319722i | \(0.896411\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 0.664872i | − 0.0721155i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.94491i | 0.206160i | 0.994673 | + | 0.103080i | \(0.0328697\pi\) | ||||
−0.994673 | + | 0.103080i | \(0.967130\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.38398 | 0.459566 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.00193439 | 0.000198464 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.8042 | −1.40161 | −0.700803 | − | 0.713355i | \(-0.747175\pi\) | ||||
−0.700803 | + | 0.713355i | \(0.747175\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.41639 | 0.538951 | 0.269475 | − | 0.963007i | \(-0.413150\pi\) | ||||
0.269475 | + | 0.963007i | \(0.413150\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 2.14390i | − 0.211245i | −0.994406 | − | 0.105623i | \(-0.966316\pi\) | ||||
0.994406 | − | 0.105623i | \(-0.0336835\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.10325i | 0.880045i | 0.897987 | + | 0.440022i | \(0.145029\pi\) | ||||
−0.897987 | + | 0.440022i | \(0.854971\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.29567i | 0.124103i | 0.998073 | + | 0.0620515i | \(0.0197643\pi\) | ||||
−0.998073 | + | 0.0620515i | \(0.980236\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 14.0728i | − 1.32386i | −0.749567 | − | 0.661928i | \(-0.769738\pi\) | ||||
0.749567 | − | 0.661928i | \(-0.230262\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.412891 | 0.0385023 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.25430 | 0.114981 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.1807 | 0.925519 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.15181 | 0.460792 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 11.5015i | − 1.02060i | −0.859997 | − | 0.510298i | \(-0.829535\pi\) | ||||
0.859997 | − | 0.510298i | \(-0.170465\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.2828i | 0.898411i | 0.893429 | + | 0.449205i | \(0.148293\pi\) | ||||
−0.893429 | + | 0.449205i | \(0.851707\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.00364927i | 0 0.000316432i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 19.3027i | − 1.64914i | −0.565761 | − | 0.824570i | \(-0.691417\pi\) | ||||
0.565761 | − | 0.824570i | \(-0.308583\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.3098 | −1.29856 | −0.649280 | − | 0.760550i | \(-0.724930\pi\) | ||||
−0.649280 | + | 0.760550i | \(0.724930\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.96814 | −0.331832 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.87952 | −0.239131 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.53793 | 0.125992 | 0.0629962 | − | 0.998014i | \(-0.479934\pi\) | ||||
0.0629962 | + | 0.998014i | \(0.479934\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.1304i | 0.824398i | 0.911094 | + | 0.412199i | \(0.135239\pi\) | ||||
−0.911094 | + | 0.412199i | \(0.864761\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.85501i | 0.148998i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.61643i | 0.208814i | 0.994535 | + | 0.104407i | \(0.0332945\pi\) | ||||
−0.994535 | + | 0.104407i | \(0.966706\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.778929i | 0.0613882i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14.4604 | −1.13262 | −0.566312 | − | 0.824191i | \(-0.691630\pi\) | ||||
−0.566312 | + | 0.824191i | \(0.691630\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.65107 | −0.592058 | −0.296029 | − | 0.955179i | \(-0.595662\pi\) | ||||
−0.296029 | + | 0.955179i | \(0.595662\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.21931 | −0.478409 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.98644 | −0.759255 | −0.379628 | − | 0.925139i | \(-0.623948\pi\) | ||||
−0.379628 | + | 0.925139i | \(0.623948\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.71902i | 0.356724i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 16.1143i | 1.20444i | 0.798331 | + | 0.602219i | \(0.205717\pi\) | ||||
−0.798331 | + | 0.602219i | \(0.794283\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.4077i | 1.51689i | 0.651736 | + | 0.758446i | \(0.274041\pi\) | ||||
−0.651736 | + | 0.758446i | \(0.725959\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 2.83231i | − 0.208236i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.13532 | −0.0830228 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.05526 | 0.293428 | 0.146714 | − | 0.989179i | \(-0.453130\pi\) | ||||
0.146714 | + | 0.989179i | \(0.453130\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.82186 | −0.419066 | −0.209533 | − | 0.977802i | \(-0.567194\pi\) | ||||
−0.209533 | + | 0.977802i | \(0.567194\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.4557 | 1.10118 | 0.550588 | − | 0.834777i | \(-0.314404\pi\) | ||||
0.550588 | + | 0.834777i | \(0.314404\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.6803i | 0.969771i | 0.874578 | + | 0.484885i | \(0.161139\pi\) | ||||
−0.874578 | + | 0.484885i | \(0.838861\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 5.43228i | − 0.381271i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.925182i | 0.0646175i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 0.00330311i | 0 0.000228481i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.9961 | −0.757000 | −0.378500 | − | 0.925601i | \(-0.623560\pi\) | ||||
−0.378500 | + | 0.925601i | \(0.623560\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.137551 | −0.00938089 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.49953 | −0.237563 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.49882 | −0.369891 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.7956i | 1.25864i | 0.777144 | + | 0.629322i | \(0.216668\pi\) | ||||
−0.777144 | + | 0.629322i | \(0.783332\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 18.8278i | 1.24965i | 0.780767 | + | 0.624823i | \(0.214829\pi\) | ||||
−0.780767 | + | 0.624823i | \(0.785171\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.7721i | 1.04225i | 0.853480 | + | 0.521126i | \(0.174488\pi\) | ||||
−0.853480 | + | 0.521126i | \(0.825512\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.23089i | 0.277175i | 0.990350 | + | 0.138587i | \(0.0442562\pi\) | ||||
−0.990350 | + | 0.138587i | \(0.955744\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.99269 | −0.129989 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.80160 | −0.504644 | −0.252322 | − | 0.967643i | \(-0.581194\pi\) | ||||
−0.252322 | + | 0.967643i | \(0.581194\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20.2165 | −1.30226 | −0.651129 | − | 0.758967i | \(-0.725704\pi\) | ||||
−0.651129 | + | 0.758967i | \(0.725704\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.530075 | 0.0338653 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 0.0159983i | − 0.00101795i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 12.7749i | − 0.806345i | −0.915124 | − | 0.403172i | \(-0.867907\pi\) | ||||
0.915124 | − | 0.403172i | \(-0.132093\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 0.705043i | − 0.0443257i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 20.3263i | − 1.26792i | −0.773365 | − | 0.633961i | \(-0.781428\pi\) | ||||
0.773365 | − | 0.633961i | \(-0.218572\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.34322 | 0.332012 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.85204 | 0.299190 | 0.149595 | − | 0.988747i | \(-0.452203\pi\) | ||||
0.149595 | + | 0.988747i | \(0.452203\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.63309 | −0.100320 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 31.3976 | 1.91435 | 0.957174 | − | 0.289514i | \(-0.0934937\pi\) | ||||
0.957174 | + | 0.289514i | \(0.0934937\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.4088i | 1.48273i | 0.671103 | + | 0.741364i | \(0.265821\pi\) | ||||
−0.671103 | + | 0.741364i | \(0.734179\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 4.27139i | − 0.257575i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 12.8387i | − 0.771402i | −0.922624 | − | 0.385701i | \(-0.873960\pi\) | ||||
0.922624 | − | 0.385701i | \(-0.126040\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 27.8988i | 1.66431i | 0.554547 | + | 0.832153i | \(0.312892\pi\) | ||||
−0.554547 | + | 0.832153i | \(0.687108\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.65773 | −0.395761 | −0.197880 | − | 0.980226i | \(-0.563406\pi\) | ||||
−0.197880 | + | 0.980226i | \(0.563406\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.74538 | −0.103026 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.4267 | 0.907455 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −24.0566 | −1.40540 | −0.702699 | − | 0.711487i | \(-0.748022\pi\) | ||||
−0.702699 | + | 0.711487i | \(0.748022\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.03893i | 0.176933i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 3.41481i | − 0.197484i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 0.259493i | − 0.0149569i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.294525i | 0.0168645i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −23.6311 | −1.34870 | −0.674350 | − | 0.738411i | \(-0.735576\pi\) | ||||
−0.674350 | + | 0.738411i | \(0.735576\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −25.7037 | −1.45752 | −0.728761 | − | 0.684768i | \(-0.759904\pi\) | ||||
−0.728761 | + | 0.684768i | \(0.759904\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.99902 | −0.565178 | −0.282589 | − | 0.959241i | \(-0.591193\pi\) | ||||
−0.282589 | + | 0.959241i | \(0.591193\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −23.7177 | −1.33212 | −0.666059 | − | 0.745899i | \(-0.732020\pi\) | ||||
−0.666059 | + | 0.745899i | \(0.732020\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.91700i | 0.275299i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 0.00457727i | 0 0.000254686i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 20.6881i | − 1.14757i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 3.75927i | − 0.207255i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.8674 | −0.707254 | −0.353627 | − | 0.935386i | \(-0.615052\pi\) | ||||
−0.353627 | + | 0.935386i | \(0.615052\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.12050 | 0.334398 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.2878 | −0.560412 | −0.280206 | − | 0.959940i | \(-0.590403\pi\) | ||||
−0.280206 | + | 0.959940i | \(0.590403\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.16758 | 0.171534 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 2.21263i | − 0.118780i | −0.998235 | − | 0.0593901i | \(-0.981084\pi\) | ||||
0.998235 | − | 0.0593901i | \(-0.0189156\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 8.10593i | − 0.433900i | −0.976183 | − | 0.216950i | \(-0.930389\pi\) | ||||
0.976183 | − | 0.216950i | \(-0.0696109\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 16.8821i | 0.898546i | 0.893395 | + | 0.449273i | \(0.148317\pi\) | ||||
−0.893395 | + | 0.449273i | \(0.851683\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.48349 | 0.450257 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.06059 | 0.319866 | 0.159933 | − | 0.987128i | \(-0.448872\pi\) | ||||
0.159933 | + | 0.987128i | \(0.448872\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.0000 | −0.999999 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.97325 | 0.364997 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 4.36701i | − 0.227956i | −0.993483 | − | 0.113978i | \(-0.963641\pi\) | ||||
0.993483 | − | 0.113978i | \(-0.0363594\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 3.08087i | − 0.159951i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.3873i | 0.537835i | 0.963163 | + | 0.268918i | \(0.0866660\pi\) | ||||
−0.963163 | + | 0.268918i | \(0.913334\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 23.8150i | 1.22654i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −28.3525 | −1.45637 | −0.728186 | − | 0.685380i | \(-0.759636\pi\) | ||||
−0.728186 | + | 0.685380i | \(0.759636\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 26.3164 | 1.34470 | 0.672352 | − | 0.740232i | \(-0.265284\pi\) | ||||
0.672352 | + | 0.740232i | \(0.265284\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.479794 | −0.0244526 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −17.5966 | −0.892182 | −0.446091 | − | 0.894988i | \(-0.647184\pi\) | ||||
−0.446091 | + | 0.894988i | \(0.647184\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 0.977009i | − 0.0494095i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 1.04366i | − 0.0525121i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 5.06951i | − 0.254431i | −0.991875 | − | 0.127216i | \(-0.959396\pi\) | ||||
0.991875 | − | 0.127216i | \(-0.0406040\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 16.6708i | − 0.832498i | −0.909251 | − | 0.416249i | \(-0.863345\pi\) | ||||
0.909251 | − | 0.416249i | \(-0.136655\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 15.3419 | 0.764233 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.83639 | −0.239731 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.09197 | −0.251782 | −0.125891 | − | 0.992044i | \(-0.540179\pi\) | ||||
−0.125891 | + | 0.992044i | \(0.540179\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5.73302 | −0.282104 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 3.08801i | − 0.151584i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 37.4571i | − 1.82990i | −0.403570 | − | 0.914949i | \(-0.632231\pi\) | ||||
0.403570 | − | 0.914949i | \(-0.367769\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 35.9612i | − 1.75264i | −0.481728 | − | 0.876321i | \(-0.659991\pi\) | ||||
0.481728 | − | 0.876321i | \(-0.340009\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 5.91906i | − 0.287116i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.555629 | −0.0268888 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 20.6573 | 0.995025 | 0.497513 | − | 0.867457i | \(-0.334247\pi\) | ||||
0.497513 | + | 0.867457i | \(0.334247\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 23.8116 | 1.14431 | 0.572157 | − | 0.820144i | \(-0.306107\pi\) | ||||
0.572157 | + | 0.820144i | \(0.306107\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.00284252 | 0.000135976 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.5607i | 1.26767i | 0.773467 | + | 0.633836i | \(0.218521\pi\) | ||||
−0.773467 | + | 0.633836i | \(0.781479\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 0.346564i | − 0.0164658i | −0.999966 | − | 0.00823288i | \(-0.997379\pi\) | ||||
0.999966 | − | 0.00823288i | \(-0.00262064\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 1.03095i | − 0.0488716i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.4601i | 0.493641i | 0.969061 | + | 0.246821i | \(0.0793859\pi\) | ||||
−0.969061 | + | 0.246821i | \(0.920614\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.57982 | 0.0743908 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.32384 | −0.108943 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.0889 | −0.518717 | −0.259359 | − | 0.965781i | \(-0.583511\pi\) | ||||
−0.259359 | + | 0.965781i | \(0.583511\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 37.8447 | 1.76261 | 0.881303 | − | 0.472553i | \(-0.156667\pi\) | ||||
0.881303 | + | 0.472553i | \(0.156667\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 18.1959i | − 0.845634i | −0.906215 | − | 0.422817i | \(-0.861041\pi\) | ||||
0.906215 | − | 0.422817i | \(-0.138959\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.19184i | 0.286524i | 0.989685 | + | 0.143262i | \(0.0457592\pi\) | ||||
−0.989685 | + | 0.143262i | \(0.954241\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.5465i | 0.533167i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.234879i | 0.0107997i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.0172210 | 0.000790152 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.17517 | −0.190769 | −0.0953843 | − | 0.995441i | \(-0.530408\pi\) | ||||
−0.0953843 | + | 0.995441i | \(0.530408\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −23.4246 | −1.06807 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.31727 | 0.332260 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 16.4966i | − 0.747534i | −0.927523 | − | 0.373767i | \(-0.878066\pi\) | ||||
0.927523 | − | 0.373767i | \(-0.121934\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 25.1039i | − 1.13292i | −0.824089 | − | 0.566461i | \(-0.808312\pi\) | ||||
0.824089 | − | 0.566461i | \(-0.191688\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.81370i | 0.306873i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 16.0043i | 0.717892i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −37.1869 | −1.66472 | −0.832358 | − | 0.554238i | \(-0.813010\pi\) | ||||
−0.832358 | + | 0.554238i | \(0.813010\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8.24722 | −0.367725 | −0.183863 | − | 0.982952i | \(-0.558860\pi\) | ||||
−0.183863 | + | 0.982952i | \(0.558860\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.87109 | −0.127762 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −29.7128 | −1.31700 | −0.658498 | − | 0.752582i | \(-0.728808\pi\) | ||||
−0.658498 | + | 0.752582i | \(0.728808\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13.1552i | 0.581953i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.13643i | 0.0500771i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.40268i | 0.149650i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.22757i | 0.404267i | 0.979358 | + | 0.202134i | \(0.0647875\pi\) | ||||
−0.979358 | + | 0.202134i | \(0.935212\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.55380 | −0.0679431 | −0.0339716 | − | 0.999423i | \(-0.510816\pi\) | ||||
−0.0339716 | + | 0.999423i | \(0.510816\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.38945 | 0.191207 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.3933 | −0.973620 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.65171 | 0.331433 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 4.82541i | − 0.208621i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 0.905144i | − 0.0389873i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.33522i | 0.315366i | 0.987490 | + | 0.157683i | \(0.0504024\pi\) | ||||
−0.987490 | + | 0.157683i | \(0.949598\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 0.686805i | − 0.0294195i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.4488 | −0.917086 | −0.458543 | − | 0.888672i | \(-0.651628\pi\) | ||||
−0.458543 | + | 0.888672i | \(0.651628\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.0198238 | −0.000844524 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.96889 | 0.0837256 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −29.9101 | −1.26733 | −0.633666 | − | 0.773607i | \(-0.718451\pi\) | ||||
−0.633666 | + | 0.773607i | \(0.718451\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.13761i | 0.0481159i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 42.7436i | − 1.80143i | −0.434414 | − | 0.900713i | \(-0.643044\pi\) | ||||
0.434414 | − | 0.900713i | \(-0.356956\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.45963i | 0.313829i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 20.9180i | 0.876927i | 0.898749 | + | 0.438464i | \(0.144477\pi\) | ||||
−0.898749 | + | 0.438464i | \(0.855523\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.23949 | 0.219266 | 0.109633 | − | 0.993972i | \(-0.465032\pi\) | ||||
0.109633 | + | 0.993972i | \(0.465032\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.67578 | 0.153291 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.71213 | −0.237799 | −0.118900 | − | 0.992906i | \(-0.537937\pi\) | ||||
−0.118900 | + | 0.992906i | \(0.537937\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.82561 | 0.241687 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.78863i | 0.115493i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 28.8731i | 1.19172i | 0.803088 | + | 0.595860i | \(0.203189\pi\) | ||||
−0.803088 | + | 0.595860i | \(0.796811\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.0127707i | 0 0.000526208i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 32.7752i | 1.34592i | 0.739680 | + | 0.672958i | \(0.234977\pi\) | ||||
−0.739680 | + | 0.672958i | \(0.765023\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.664872 | −0.0272571 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.9096 | 0.772625 | 0.386313 | − | 0.922368i | \(-0.373749\pi\) | ||||
0.386313 | + | 0.922368i | \(0.373749\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 36.4186 | 1.48555 | 0.742773 | − | 0.669543i | \(-0.233510\pi\) | ||||
0.742773 | + | 0.669543i | \(0.233510\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.39654 | −0.219401 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 8.21476i | − 0.333427i | −0.986005 | − | 0.166713i | \(-0.946685\pi\) | ||||
0.986005 | − | 0.166713i | \(-0.0533155\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 16.4806i | 0.666732i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 27.6348i | 1.11616i | 0.829787 | + | 0.558080i | \(0.188462\pi\) | ||||
−0.829787 | + | 0.558080i | \(0.811538\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 23.3314i | − 0.939287i | −0.882856 | − | 0.469643i | \(-0.844383\pi\) | ||||
0.882856 | − | 0.469643i | \(-0.155617\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.9819 | 0.923719 | 0.461859 | − | 0.886953i | \(-0.347182\pi\) | ||||
0.461859 | + | 0.886953i | \(0.347182\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.94491 | 0.0779211 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 20.8643 | 0.834570 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.70199 | −0.267226 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 44.4382i | − 1.76906i | −0.466486 | − | 0.884528i | \(-0.654480\pi\) | ||||
0.466486 | − | 0.884528i | \(-0.345520\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.09668i | 0.241939i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 4.38398i | − 0.173700i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 37.6567i | − 1.48735i | −0.668541 | − | 0.743675i | \(-0.733081\pi\) | ||||
0.668541 | − | 0.743675i | \(-0.266919\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.1342 | 0.872886 | 0.436443 | − | 0.899732i | \(-0.356238\pi\) | ||||
0.436443 | + | 0.899732i | \(0.356238\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 20.8560 | 0.819936 | 0.409968 | − | 0.912100i | \(-0.365540\pi\) | ||||
0.409968 | + | 0.912100i | \(0.365540\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.18921 | 0.203694 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −12.5052 | −0.489366 | −0.244683 | − | 0.969603i | \(-0.578684\pi\) | ||||
−0.244683 | + | 0.969603i | \(0.578684\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 5.45065i | − 0.212974i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 27.7704i | − 1.08178i | −0.841092 | − | 0.540891i | \(-0.818087\pi\) | ||||
0.841092 | − | 0.540891i | \(-0.181913\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 17.8134i | − 0.692862i | −0.938075 | − | 0.346431i | \(-0.887393\pi\) | ||||
0.938075 | − | 0.346431i | \(-0.112607\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 0.00193439i | 0 7.50123e-5i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.23136 | −0.163839 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.502924 | 0.0194152 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.2911 | −0.627975 | −0.313987 | − | 0.949427i | \(-0.601665\pi\) | ||||
−0.313987 | + | 0.949427i | \(0.601665\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.61803 | −0.177485 | −0.0887426 | − | 0.996055i | \(-0.528285\pi\) | ||||
−0.0887426 | + | 0.996055i | \(0.528285\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.8042i | 0.529757i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 30.9791i | 1.18538i | 0.805429 | + | 0.592692i | \(0.201935\pi\) | ||||
−0.805429 | + | 0.592692i | \(0.798065\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.2319i | 0.390940i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 13.5065i | 0.514556i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29.0382 | 1.10467 | 0.552333 | − | 0.833624i | \(-0.313738\pi\) | ||||
0.552333 | + | 0.833624i | \(0.313738\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.11534 | 0.307832 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.18923 | 0.0829228 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −27.6010 | −1.04248 | −0.521238 | − | 0.853411i | \(-0.674530\pi\) | ||||
−0.521238 | + | 0.853411i | \(0.674530\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 0.0194989i | 0 0.000735413i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 5.41639i | − 0.203704i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 37.8212i | 1.42040i | 0.703998 | + | 0.710202i | \(0.251396\pi\) | ||||
−0.703998 | + | 0.710202i | \(0.748604\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.72588i | 0.102085i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.10341 | 0.0786631 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 41.2974 | 1.54013 | 0.770067 | − | 0.637963i | \(-0.220223\pi\) | ||||
0.770067 | + | 0.637963i | \(0.220223\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.14390 | −0.0798432 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −25.6350 | −0.952061 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.9168i | 0.441971i | 0.975277 | + | 0.220985i | \(0.0709273\pi\) | ||||
−0.975277 | + | 0.220985i | \(0.929073\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.325482i | 0.0120384i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 47.2142i | 1.74390i | 0.489597 | + | 0.871949i | \(0.337144\pi\) | ||||
−0.489597 | + | 0.871949i | \(0.662856\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 10.4512i | − 0.384976i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13.4529 | 0.494874 | 0.247437 | − | 0.968904i | \(-0.420412\pi\) | ||||
0.247437 | + | 0.968904i | \(0.420412\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10.7698 | −0.395106 | −0.197553 | − | 0.980292i | \(-0.563299\pi\) | ||||
−0.197553 | + | 0.980292i | \(0.563299\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.815220 | −0.0298673 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.10325 | 0.332626 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.1004i | 0.514530i | 0.966341 | + | 0.257265i | \(0.0828213\pi\) | ||||
−0.966341 | + | 0.257265i | \(0.917179\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 5.36986i | − 0.195429i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 13.8374i | − 0.502929i | −0.967866 | − | 0.251465i | \(-0.919088\pi\) | ||||
0.967866 | − | 0.251465i | \(-0.0809122\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 33.1367i | − 1.20121i | −0.799548 | − | 0.600603i | \(-0.794927\pi\) | ||||
0.799548 | − | 0.600603i | \(-0.205073\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.29567 | 0.0469066 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 25.1335 | 0.907517 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30.1190 | 1.08612 | 0.543060 | − | 0.839694i | \(-0.317266\pi\) | ||||
0.543060 | + | 0.839694i | \(0.317266\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −16.0579 | −0.577561 | −0.288780 | − | 0.957395i | \(-0.593250\pi\) | ||||
−0.288780 | + | 0.957395i | \(0.593250\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 16.5143i | 0.593212i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.00636936i | 0 0.000228206i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 14.4862i | − 0.518357i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 1.38691i | − 0.0495008i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11.2848 | −0.402258 | −0.201129 | − | 0.979565i | \(-0.564461\pi\) | ||||
−0.201129 | + | 0.979565i | \(0.564461\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14.0728 | −0.500371 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.43587 | 0.0865002 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 39.3545 | 1.39401 | 0.697004 | − | 0.717068i | \(-0.254516\pi\) | ||||
0.697004 | + | 0.717068i | \(0.254516\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.71524i | 0.166813i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 11.9074i | − 0.420202i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 0.412891i | − 0.0145525i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 0.183323i | − 0.00644529i | −0.999995 | − | 0.00322265i | \(-0.998974\pi\) | ||||
0.999995 | − | 0.00322265i | \(-0.00102580\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 46.7136 | 1.64033 | 0.820167 | − | 0.572124i | \(-0.193880\pi\) | ||||
0.820167 | + | 0.572124i | \(0.193880\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.66508 | 0.268496 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.000946960 0 | −3.31299e−5 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19.7408 | 0.688959 | 0.344480 | − | 0.938794i | \(-0.388055\pi\) | ||||
0.344480 | + | 0.938794i | \(0.388055\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 11.6881i | − 0.407421i | −0.979031 | − | 0.203711i | \(-0.934700\pi\) | ||||
0.979031 | − | 0.203711i | \(-0.0653002\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 30.8036i | 1.07115i | 0.844489 | + | 0.535573i | \(0.179904\pi\) | ||||
−0.844489 | + | 0.535573i | \(0.820096\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 33.2395i | − 1.15446i | −0.816583 | − | 0.577228i | \(-0.804134\pi\) | ||||
0.816583 | − | 0.577228i | \(-0.195866\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 1.25430i | − 0.0434588i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.05564 | 0.140351 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −42.9568 | −1.48303 | −0.741517 | − | 0.670934i | \(-0.765893\pi\) | ||||
−0.741517 | + | 0.670934i | \(0.765893\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.509663 | 0.0175746 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.29670 | 0.113410 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 10.1807i | − 0.349813i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 4.16199i | − 0.142671i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 31.5917i | 1.08168i | 0.841126 | + | 0.540840i | \(0.181893\pi\) | ||||
−0.841126 | + | 0.540840i | \(0.818107\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 37.4806i | 1.28031i | 0.768245 | + | 0.640156i | \(0.221130\pi\) | ||||
−0.768245 | + | 0.640156i | \(0.778870\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 41.4525 | 1.41434 | 0.707171 | − | 0.707042i | \(-0.249971\pi\) | ||||
0.707171 | + | 0.707042i | \(0.249971\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 43.8203 | 1.49166 | 0.745830 | − | 0.666136i | \(-0.232053\pi\) | ||||
0.745830 | + | 0.666136i | \(0.232053\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.29356 | 0.179987 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.78213 | −0.0604545 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 50.6195i | − 1.71518i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 5.15181i | − 0.174163i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 33.3035i | 1.12458i | 0.826940 | + | 0.562289i | \(0.190079\pi\) | ||||
−0.826940 | + | 0.562289i | \(0.809921\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 35.6627i | 1.20151i | 0.799434 | + | 0.600754i | \(0.205133\pi\) | ||||
−0.799434 | + | 0.600754i | \(0.794867\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.32201 | −0.280058 | −0.140029 | − | 0.990147i | \(-0.544720\pi\) | ||||
−0.140029 | + | 0.990147i | \(0.544720\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −43.3551 | −1.45572 | −0.727861 | − | 0.685725i | \(-0.759485\pi\) | ||||
−0.727861 | + | 0.685725i | \(0.759485\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −11.5015 | −0.385749 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.0137186 | −0.000459075 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 8.54178i | − 0.285520i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 19.0104i | − 0.634032i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.86433i | 0.128739i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 10.8176i | − 0.359590i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.89354 | 0.262101 | 0.131050 | − | 0.991376i | \(-0.458165\pi\) | ||||
0.131050 | + | 0.991376i | \(0.458165\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 47.9212 | 1.58770 | 0.793850 | − | 0.608113i | \(-0.208073\pi\) | ||||
0.793850 | + | 0.608113i | \(0.208073\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.27302 | −0.174511 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10.2828 | 0.339567 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 22.2192i | 0.732943i | 0.930429 | + | 0.366471i | \(0.119434\pi\) | ||||
−0.930429 | + | 0.366471i | \(0.880566\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 70.1627i | − 2.30943i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 25.2148i | − 0.829057i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 34.2658i | 1.12422i | 0.827061 | + | 0.562112i | \(0.190011\pi\) | ||||
−0.827061 | + | 0.562112i | \(0.809989\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.00364927 | 0.000119600 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.601805 | 0.0196811 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.43172 | 0.177447 | 0.0887233 | − | 0.996056i | \(-0.471721\pi\) | ||||
0.0887233 | + | 0.996056i | \(0.471721\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −18.1273 | −0.590932 | −0.295466 | − | 0.955353i | \(-0.595475\pi\) | ||||
−0.295466 | + | 0.955353i | \(0.595475\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.35953i | 0.0442723i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 11.9799i | − 0.389295i | −0.980873 | − | 0.194647i | \(-0.937644\pi\) | ||||
0.980873 | − | 0.194647i | \(-0.0623562\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 57.6723i | − 1.87212i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 22.7578i | 0.737197i | 0.929589 | + | 0.368599i | \(0.120162\pi\) | ||||
−0.929589 | + | 0.368599i | \(0.879838\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.14959 | −0.0695592 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −19.3027 | −0.623316 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18.7533 | 0.604946 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.08602 | 0.0993425 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 41.9989i | − 1.35060i | −0.737545 | − | 0.675298i | \(-0.764015\pi\) | ||||
0.737545 | − | 0.675298i | \(-0.235985\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 36.5508i | 1.17297i | 0.809959 | + | 0.586486i | \(0.199489\pi\) | ||||
−0.809959 | + | 0.586486i | \(0.800511\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 15.3098i | 0.490809i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 30.6094i | − 0.979281i | −0.871925 | − | 0.489640i | \(-0.837128\pi\) | ||||
0.871925 | − | 0.489640i | \(-0.162872\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.76042 | −0.0562633 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −36.1930 | −1.15438 | −0.577189 | − | 0.816610i | \(-0.695850\pi\) | ||||
−0.577189 | + | 0.816610i | \(0.695850\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.19270 | −0.261041 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.202127 | −0.00642726 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 52.1154i | − 1.65550i | −0.561097 | − | 0.827750i | \(-0.689621\pi\) | ||||
0.561097 | − | 0.827750i | \(-0.310379\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 7.25159i | − 0.229891i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 20.2906i | − 0.642609i | −0.946976 | − | 0.321305i | \(-0.895879\pi\) | ||||
0.946976 | − | 0.321305i | \(-0.104121\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 6048.2.j.d.5615.21 | 48 | ||
3.2 | odd | 2 | inner | 6048.2.j.d.5615.28 | 48 | ||
4.3 | odd | 2 | 1512.2.j.d.323.44 | yes | 48 | ||
8.3 | odd | 2 | inner | 6048.2.j.d.5615.27 | 48 | ||
8.5 | even | 2 | 1512.2.j.d.323.6 | yes | 48 | ||
12.11 | even | 2 | 1512.2.j.d.323.5 | ✓ | 48 | ||
24.5 | odd | 2 | 1512.2.j.d.323.43 | yes | 48 | ||
24.11 | even | 2 | inner | 6048.2.j.d.5615.22 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.j.d.323.5 | ✓ | 48 | 12.11 | even | 2 | ||
1512.2.j.d.323.6 | yes | 48 | 8.5 | even | 2 | ||
1512.2.j.d.323.43 | yes | 48 | 24.5 | odd | 2 | ||
1512.2.j.d.323.44 | yes | 48 | 4.3 | odd | 2 | ||
6048.2.j.d.5615.21 | 48 | 1.1 | even | 1 | trivial | ||
6048.2.j.d.5615.22 | 48 | 24.11 | even | 2 | inner | ||
6048.2.j.d.5615.27 | 48 | 8.3 | odd | 2 | inner | ||
6048.2.j.d.5615.28 | 48 | 3.2 | odd | 2 | inner |