Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1960,2,Mod(1569,1960)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1960, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1960.1569");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1960 = 2^{3} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1960.g (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(15.6506787962\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 25x^{10} + 230x^{8} + 950x^{6} + 1657x^{4} + 785x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | no (minimal twist has level 280) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1569.9 | ||
Root | \(2.03837i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1960.1569 |
Dual form | 1960.2.g.e.1569.4 |
$q$-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 \(\left(\mathbb{Z}/1960\mathbb{Z}\right)^\times\).
\(n\) | \(981\) | \(1081\) | \(1177\) | \(1471\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.03837i | 1.17685i | 0.808551 | + | 0.588426i | \(0.200252\pi\) | ||||
−0.808551 | + | 0.588426i | \(0.799748\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.240243 | + | 2.22312i | 0.107440 | + | 0.994212i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.15495 | −0.384982 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.04807 | 0.316006 | 0.158003 | − | 0.987439i | \(-0.449494\pi\) | ||||
0.158003 | + | 0.987439i | \(0.449494\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.15495i | − | 0.320324i | −0.987091 | − | 0.160162i | \(-0.948798\pi\) | ||
0.987091 | − | 0.160162i | \(-0.0512017\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.53155 | + | 0.489703i | −1.17004 | + | 0.126441i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.81986i | 1.65406i | 0.562158 | + | 0.827030i | \(0.309971\pi\) | ||||
−0.562158 | + | 0.827030i | \(0.690029\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.75120 | −1.09000 | −0.545000 | − | 0.838436i | \(-0.683470\pi\) | ||||
−0.545000 | + | 0.838436i | \(0.683470\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 3.19331i | − | 0.665852i | −0.942953 | − | 0.332926i | \(-0.891964\pi\) | ||
0.942953 | − | 0.332926i | \(-0.108036\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.88457 | + | 1.06818i | −0.976913 | + | 0.213636i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.76090i | 0.723786i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.14130 | −0.954716 | −0.477358 | − | 0.878709i | \(-0.658405\pi\) | ||||
−0.477358 | + | 0.878709i | \(0.658405\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.57372 | 1.00107 | 0.500534 | − | 0.865717i | \(-0.333137\pi\) | ||||
0.500534 | + | 0.865717i | \(0.333137\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.13636i | 0.371892i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.91769i | 0.808463i | 0.914657 | + | 0.404232i | \(0.132461\pi\) | ||||
−0.914657 | + | 0.404232i | \(0.867539\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.35420 | 0.376974 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.68948 | −1.51324 | −0.756621 | − | 0.653853i | \(-0.773151\pi\) | ||||
−0.756621 | + | 0.653853i | \(0.773151\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 7.44559i | − | 1.13544i | −0.823221 | − | 0.567721i | \(-0.807825\pi\) | ||
0.823221 | − | 0.567721i | \(-0.192175\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.277467 | − | 2.56759i | −0.0413624 | − | 0.382753i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.29130i | 1.35528i | 0.735396 | + | 0.677638i | \(0.236996\pi\) | ||||
−0.735396 | + | 0.677638i | \(0.763004\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −13.9014 | −1.94658 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.60119i | 0.769383i | 0.923045 | + | 0.384692i | \(0.125692\pi\) | ||||
−0.923045 | + | 0.384692i | \(0.874308\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.251792 | + | 2.33000i | 0.0339516 | + | 0.314177i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 9.68469i | − | 1.28277i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.8624 | 1.41416 | 0.707080 | − | 0.707134i | \(-0.250012\pi\) | ||||
0.707080 | + | 0.707134i | \(0.250012\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.33443 | 0.426930 | 0.213465 | − | 0.976951i | \(-0.431525\pi\) | ||||
0.213465 | + | 0.976951i | \(0.431525\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.56759 | − | 0.277467i | 0.318470 | − | 0.0344156i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.45101i | 0.665947i | 0.942936 | + | 0.332973i | \(0.108052\pi\) | ||||
−0.942936 | + | 0.332973i | \(0.891948\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.50915 | 0.783609 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.10916 | −0.487668 | −0.243834 | − | 0.969817i | \(-0.578405\pi\) | ||||
−0.243834 | + | 0.969817i | \(0.578405\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 6.46879i | − | 0.757114i | −0.925578 | − | 0.378557i | \(-0.876420\pi\) | ||
0.925578 | − | 0.378557i | \(-0.123580\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.17734 | − | 9.95655i | −0.251418 | − | 1.14968i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.612744 | −0.0689391 | −0.0344695 | − | 0.999406i | \(-0.510974\pi\) | ||||
−0.0344695 | + | 0.999406i | \(0.510974\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.1309 | −1.23677 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 0.275623i | − | 0.0302535i | −0.999886 | − | 0.0151268i | \(-0.995185\pi\) | ||
0.999886 | − | 0.0151268i | \(-0.00481518\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −15.1614 | + | 1.63842i | −1.64449 | + | 0.177712i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 10.4799i | − | 1.12356i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −17.2646 | −1.83005 | −0.915024 | − | 0.403399i | \(-0.867829\pi\) | ||||
−0.915024 | + | 0.403399i | \(0.867829\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 11.3613i | 1.17811i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.14144 | − | 10.5625i | −0.117109 | − | 1.08369i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 7.59854i | − | 0.771515i | −0.922600 | − | 0.385757i | \(-0.873940\pi\) | ||
0.922600 | − | 0.385757i | \(-0.126060\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.21047 | −0.121657 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.564671 | 0.0561869 | 0.0280934 | − | 0.999605i | \(-0.491056\pi\) | ||||
0.0280934 | + | 0.999605i | \(0.491056\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 15.5819i | − | 1.53533i | −0.640848 | − | 0.767667i | \(-0.721417\pi\) | ||
0.640848 | − | 0.767667i | \(-0.278583\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 14.0241i | − | 1.35576i | −0.735172 | − | 0.677880i | \(-0.762899\pi\) | ||
0.735172 | − | 0.677880i | \(-0.237101\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.7978 | 1.51315 | 0.756577 | − | 0.653904i | \(-0.226870\pi\) | ||||
0.756577 | + | 0.653904i | \(0.226870\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.0241 | −0.951442 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 20.3625i | 1.91554i | 0.287536 | + | 0.957770i | \(0.407164\pi\) | ||||
−0.287536 | + | 0.957770i | \(0.592836\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.09913 | − | 0.767171i | 0.661998 | − | 0.0715390i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.33390i | 0.123319i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.90154 | −0.900140 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 19.7507i | − | 1.78086i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.54818 | − | 10.6024i | −0.317359 | − | 0.948306i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 0.358593i | − | 0.0318199i | −0.999873 | − | 0.0159100i | \(-0.994935\pi\) | ||
0.999873 | − | 0.0159100i | \(-0.00506451\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 15.1769 | 1.33625 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.5114 | 1.35524 | 0.677620 | − | 0.735412i | \(-0.263011\pi\) | ||||
0.677620 | + | 0.735412i | \(0.263011\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −8.36095 | + | 0.903529i | −0.719596 | + | 0.0777634i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 0.842399i | − | 0.0719710i | −0.999352 | − | 0.0359855i | \(-0.988543\pi\) | ||
0.999352 | − | 0.0359855i | \(-0.0114570\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.97876 | 0.252655 | 0.126327 | − | 0.991989i | \(-0.459681\pi\) | ||||
0.126327 | + | 0.991989i | \(0.459681\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −18.9391 | −1.59496 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 1.21047i | − | 0.101224i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.23516 | − | 11.4298i | −0.102575 | − | 0.949190i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.10290 | −0.0903533 | −0.0451767 | − | 0.998979i | \(-0.514385\pi\) | ||||
−0.0451767 | + | 0.998979i | \(0.514385\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.5525 | −1.02151 | −0.510753 | − | 0.859728i | \(-0.670633\pi\) | ||||
−0.510753 | + | 0.859728i | \(0.670633\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 7.87657i | − | 0.636783i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.33904 | + | 12.3911i | 0.107555 | + | 0.995274i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 21.0712i | 1.68166i | 0.541298 | + | 0.840831i | \(0.317933\pi\) | ||||
−0.541298 | + | 0.840831i | \(0.682067\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −11.4173 | −0.905451 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 21.8658i | − | 1.71266i | −0.516425 | − | 0.856332i | \(-0.672738\pi\) | ||
0.516425 | − | 0.856332i | \(-0.327262\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.74939 | + | 0.513245i | −0.369740 | + | 0.0399561i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.1680i | 0.786821i | 0.919363 | + | 0.393411i | \(0.128705\pi\) | ||||
−0.919363 | + | 0.393411i | \(0.871295\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.6661 | 0.897392 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.48737 | 0.419630 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.798446i | 0.0607048i | 0.999539 | + | 0.0303524i | \(0.00966295\pi\) | ||||
−0.999539 | + | 0.0303524i | \(0.990337\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 22.1415i | 1.66426i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.1755 | 0.910042 | 0.455021 | − | 0.890481i | \(-0.349632\pi\) | ||||
0.455021 | + | 0.890481i | \(0.349632\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.00613 | 0.297773 | 0.148887 | − | 0.988854i | \(-0.452431\pi\) | ||||
0.148887 | + | 0.988854i | \(0.452431\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.79680i | 0.502434i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −10.9326 | + | 1.18144i | −0.803784 | + | 0.0868612i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.14771i | 0.522693i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.6616 | 1.20559 | 0.602797 | − | 0.797895i | \(-0.294053\pi\) | ||||
0.602797 | + | 0.797895i | \(0.294053\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.42501i | 0.534464i | 0.963632 | + | 0.267232i | \(0.0861090\pi\) | ||||
−0.963632 | + | 0.267232i | \(0.913891\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.565581 | + | 5.23369i | 0.0405021 | + | 0.374792i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 1.88883i | − | 0.134574i | −0.997734 | − | 0.0672869i | \(-0.978566\pi\) | ||
0.997734 | − | 0.0672869i | \(-0.0214343\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.2373 | −1.22192 | −0.610960 | − | 0.791662i | \(-0.709216\pi\) | ||||
−0.610960 | + | 0.791662i | \(0.709216\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −11.1112 | −0.783721 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.32783 | − | 21.5409i | −0.162583 | − | 1.50448i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.68810i | 0.256341i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.97960 | −0.344446 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.25478 | −0.361754 | −0.180877 | − | 0.983506i | \(-0.557894\pi\) | ||||
−0.180877 | + | 0.983506i | \(0.557894\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 8.37598i | − | 0.573913i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 16.5525 | − | 1.78875i | 1.12887 | − | 0.121992i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 13.1858 | 0.891012 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.87657 | 0.529835 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.2760i | 0.889027i | 0.895772 | + | 0.444513i | \(0.146623\pi\) | ||||
−0.895772 | + | 0.444513i | \(0.853377\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.64141 | − | 1.23369i | 0.376094 | − | 0.0822459i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.8039i | 0.783455i | 0.920081 | + | 0.391727i | \(0.128122\pi\) | ||||
−0.920081 | + | 0.391727i | \(0.871878\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.4922 | 0.891592 | 0.445796 | − | 0.895135i | \(-0.352921\pi\) | ||||
0.445796 | + | 0.895135i | \(0.352921\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 1.14060i | − | 0.0747230i | −0.999302 | − | 0.0373615i | \(-0.988105\pi\) | ||
0.999302 | − | 0.0373615i | \(-0.0118953\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −20.6557 | + | 2.23217i | −1.34743 | + | 0.145611i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 1.24900i | − | 0.0811311i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.94796 | −0.190688 | −0.0953438 | − | 0.995444i | \(-0.530395\pi\) | ||||
−0.0953438 | + | 0.995444i | \(0.530395\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.6131 | −0.683650 | −0.341825 | − | 0.939764i | \(-0.611045\pi\) | ||||
−0.341825 | + | 0.939764i | \(0.611045\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 11.4062i | − | 0.731711i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.48737i | 0.349153i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.561821 | 0.0356039 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.3119 | 0.777120 | 0.388560 | − | 0.921423i | \(-0.372973\pi\) | ||||
0.388560 | + | 0.921423i | \(0.372973\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 3.34683i | − | 0.210413i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.33971 | − | 30.9045i | −0.209141 | − | 1.93532i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 17.7484i | 1.10712i | 0.832811 | + | 0.553558i | \(0.186730\pi\) | ||||
−0.832811 | + | 0.553558i | \(0.813270\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.93792 | 0.367548 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.17570i | 0.257485i | 0.991678 | + | 0.128742i | \(0.0410940\pi\) | ||||
−0.991678 | + | 0.128742i | \(0.958906\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.4522 | + | 1.34565i | −0.764930 | + | 0.0826624i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 35.1917i | − | 2.15370i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 26.2681 | 1.60160 | 0.800798 | − | 0.598935i | \(-0.204409\pi\) | ||||
0.800798 | + | 0.598935i | \(0.204409\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −26.3074 | −1.59806 | −0.799031 | − | 0.601290i | \(-0.794654\pi\) | ||||
−0.799031 | + | 0.601290i | \(0.794654\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.11938 | + | 1.11953i | −0.308710 | + | 0.0675102i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.9321i | 1.25769i | 0.777530 | + | 0.628845i | \(0.216472\pi\) | ||||
−0.777530 | + | 0.628845i | \(0.783528\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.43734 | −0.385393 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.7097 | 0.937162 | 0.468581 | − | 0.883420i | \(-0.344765\pi\) | ||||
0.468581 | + | 0.883420i | \(0.344765\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.8087i | 0.642512i | 0.946992 | + | 0.321256i | \(0.104105\pi\) | ||||
−0.946992 | + | 0.321256i | \(0.895895\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 21.5303 | − | 2.32668i | 1.27534 | − | 0.137820i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −29.5105 | −1.73591 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 15.4886 | 0.907959 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.91887i | 0.579467i | 0.957107 | + | 0.289733i | \(0.0935667\pi\) | ||||
−0.957107 | + | 0.289733i | \(0.906433\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.60960 | + | 24.1484i | 0.151937 | + | 1.40597i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.94170i | 0.228721i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.68810 | −0.213288 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.15101i | 0.0661236i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.801074 | + | 7.41286i | 0.0458693 | + | 0.424459i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.64632i | 0.322252i | 0.986934 | + | 0.161126i | \(0.0515126\pi\) | ||||
−0.986934 | + | 0.161126i | \(0.948487\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 31.7617 | 1.80686 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.0190 | −0.681534 | −0.340767 | − | 0.940148i | \(-0.610687\pi\) | ||||
−0.340767 | + | 0.940148i | \(0.610687\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18.9785i | 1.07273i | 0.843987 | + | 0.536363i | \(0.180202\pi\) | ||||
−0.843987 | + | 0.536363i | \(0.819798\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.7418i | 0.715651i | 0.933788 | + | 0.357826i | \(0.116482\pi\) | ||||
−0.933788 | + | 0.357826i | \(0.883518\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.38846 | −0.301696 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 28.5863 | 1.59553 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 32.4025i | − | 1.80292i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.23369 | + | 5.64141i | 0.0684327 | + | 0.312929i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 32.2017i | 1.78076i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.8384 | 1.31027 | 0.655137 | − | 0.755510i | \(-0.272611\pi\) | ||||
0.655137 | + | 0.755510i | \(0.272611\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 5.67966i | − | 0.311244i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12.1183 | + | 1.30957i | −0.662092 | + | 0.0715492i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 23.7427i | − | 1.29335i | −0.762767 | − | 0.646673i | \(-0.776160\pi\) | ||
0.762767 | − | 0.646673i | \(-0.223840\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −41.5062 | −2.25431 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.84166 | 0.316344 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.56378 | + | 14.4707i | 0.0841909 | + | 0.779074i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 2.53548i | − | 0.136112i | −0.997682 | − | 0.0680558i | \(-0.978320\pi\) | ||
0.997682 | − | 0.0680558i | \(-0.0216796\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24.9321 | 1.33459 | 0.667293 | − | 0.744795i | \(-0.267453\pi\) | ||||
0.667293 | + | 0.744795i | \(0.267453\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.34363 | 0.231846 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.35067i | 0.125113i | 0.998041 | + | 0.0625567i | \(0.0199254\pi\) | ||||
−0.998041 | + | 0.0625567i | \(0.980075\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.987196 | − | 9.13517i | −0.0523949 | − | 0.484845i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 32.3016 | 1.70481 | 0.852407 | − | 0.522880i | \(-0.175142\pi\) | ||||
0.852407 | + | 0.522880i | \(0.175142\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.57387 | 0.188098 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 20.1830i | − | 1.05933i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.3809 | − | 1.55408i | 0.752732 | − | 0.0813442i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.55523i | 0.394380i | 0.980365 | + | 0.197190i | \(0.0631816\pi\) | ||||
−0.980365 | + | 0.197190i | \(0.936818\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 11.1908 | 0.582571 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 29.0647i | 1.50491i | 0.658641 | + | 0.752457i | \(0.271132\pi\) | ||||
−0.658641 | + | 0.752457i | \(0.728868\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 21.6116 | − | 7.23249i | 1.11602 | − | 0.373484i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.93792i | 0.305819i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.36318 | 0.480954 | 0.240477 | − | 0.970655i | \(-0.422696\pi\) | ||||
0.240477 | + | 0.970655i | \(0.422696\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.730944 | 0.0374474 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.93471i | 0.0988589i | 0.998778 | + | 0.0494295i | \(0.0157403\pi\) | ||||
−0.998778 | + | 0.0494295i | \(0.984260\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.59925i | 0.437124i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.757390 | −0.0384012 | −0.0192006 | − | 0.999816i | \(-0.506112\pi\) | ||||
−0.0192006 | + | 0.999816i | \(0.506112\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 21.7780 | 1.10136 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 31.6180i | 1.59492i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.147207 | − | 1.36221i | −0.00740680 | − | 0.0685400i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 33.4580i | 1.67921i | 0.543199 | + | 0.839604i | \(0.317213\pi\) | ||||
−0.543199 | + | 0.839604i | \(0.682787\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 30.5011 | 1.52315 | 0.761577 | − | 0.648074i | \(-0.224425\pi\) | ||||
0.761577 | + | 0.648074i | \(0.224425\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 6.43734i | − | 0.320667i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.67413 | − | 24.7455i | −0.132878 | − | 1.22961i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.15410i | 0.255479i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −18.6737 | −0.923353 | −0.461676 | − | 0.887048i | \(-0.652752\pi\) | ||||
−0.461676 | + | 0.887048i | \(0.652752\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.71712 | 0.0846992 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.612744 | − | 0.0662164i | 0.0300784 | − | 0.00325044i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.07180i | 0.297338i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −34.8449 | −1.70228 | −0.851142 | − | 0.524936i | \(-0.824089\pi\) | ||||
−0.851142 | + | 0.524936i | \(0.824089\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.53106 | 0.269567 | 0.134784 | − | 0.990875i | \(-0.456966\pi\) | ||||
0.134784 | + | 0.990875i | \(0.456966\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 10.7309i | − | 0.521757i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.28484 | − | 33.3121i | −0.353366 | − | 1.61587i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.46738 | 0.119126 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.5655 | 0.508922 | 0.254461 | − | 0.967083i | \(-0.418102\pi\) | ||||
0.254461 | + | 0.967083i | \(0.418102\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 14.3654i | − | 0.690358i | −0.938537 | − | 0.345179i | \(-0.887818\pi\) | ||
0.938537 | − | 0.345179i | \(-0.112182\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 23.2981 | − | 2.51771i | 1.11706 | − | 0.120715i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 15.1721i | 0.725778i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 31.6168 | 1.50899 | 0.754493 | − | 0.656308i | \(-0.227883\pi\) | ||||
0.754493 | + | 0.656308i | \(0.227883\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 11.9930i | − | 0.569804i | −0.958557 | − | 0.284902i | \(-0.908039\pi\) | ||
0.958557 | − | 0.284902i | \(-0.0919611\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.14771 | − | 38.3814i | −0.196620 | − | 1.81946i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 2.24812i | − | 0.106333i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.98107 | 0.235071 | 0.117536 | − | 0.993069i | \(-0.462501\pi\) | ||||
0.117536 | + | 0.993069i | \(0.462501\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.1553 | −0.478194 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 25.5866i | − | 1.20216i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 26.9785i | − | 1.26200i | −0.775783 | − | 0.631000i | \(-0.782645\pi\) | ||
0.775783 | − | 0.631000i | \(-0.217355\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −25.6488 | −1.19718 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −22.6886 | −1.05672 | −0.528358 | − | 0.849022i | \(-0.677192\pi\) | ||||
−0.528358 | + | 0.849022i | \(0.677192\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 27.0921i | 1.25908i | 0.776969 | + | 0.629539i | \(0.216756\pi\) | ||||
−0.776969 | + | 0.629539i | \(0.783244\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −25.2576 | + | 2.72947i | −1.17129 | + | 0.126576i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.55482i | 0.210772i | 0.994431 | + | 0.105386i | \(0.0336078\pi\) | ||||
−0.994431 | + | 0.105386i | \(0.966392\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −42.9508 | −1.97907 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 7.80352i | − | 0.358806i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 23.2075 | − | 5.07513i | 1.06483 | − | 0.232863i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 6.46907i | − | 0.296199i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.22937 | 0.376010 | 0.188005 | − | 0.982168i | \(-0.439798\pi\) | ||||
0.188005 | + | 0.982168i | \(0.439798\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.67966 | 0.258970 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 16.8925 | − | 1.82549i | 0.767049 | − | 0.0828914i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.0063i | 0.861259i | 0.902529 | + | 0.430629i | \(0.141708\pi\) | ||||
−0.902529 | + | 0.430629i | \(0.858292\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 44.5706 | 2.01555 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19.2359 | 0.868102 | 0.434051 | − | 0.900888i | \(-0.357084\pi\) | ||||
0.434051 | + | 0.900888i | \(0.357084\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 35.0630i | − | 1.57916i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.290806 | − | 2.69102i | −0.0130708 | − | 0.120952i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.2105 | −0.546618 | −0.273309 | − | 0.961926i | \(-0.588118\pi\) | ||||
−0.273309 | + | 0.961926i | \(0.588118\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −20.7261 | −0.925972 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.17917i | 0.0971646i | 0.998819 | + | 0.0485823i | \(0.0154703\pi\) | ||||
−0.998819 | + | 0.0485823i | \(0.984530\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.135658 | + | 1.25533i | 0.00603671 | + | 0.0558616i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 23.7798i | 1.05610i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.4401 | 0.551398 | 0.275699 | − | 0.961244i | \(-0.411091\pi\) | ||||
0.275699 | + | 0.961244i | \(0.411091\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 17.8688i | − | 0.788926i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 34.6406 | − | 3.74345i | 1.52645 | − | 0.164956i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.73797i | 0.428275i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.62753 | −0.0714405 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.8545 | −0.826030 | −0.413015 | − | 0.910724i | \(-0.635524\pi\) | ||||
−0.413015 | + | 0.910724i | \(0.635524\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 19.0063i | − | 0.831088i | −0.909573 | − | 0.415544i | \(-0.863591\pi\) | ||
0.909573 | − | 0.415544i | \(-0.136409\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 38.0120i | 1.65583i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12.8027 | 0.556641 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −12.5454 | −0.544426 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11.1908i | 0.484728i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 31.1773 | − | 3.36919i | 1.34791 | − | 0.145663i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 24.8182i | 1.07099i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 24.3621 | 1.04741 | 0.523703 | − | 0.851901i | \(-0.324550\pi\) | ||||
0.523703 | + | 0.851901i | \(0.324550\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.16596i | 0.350435i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.79531 | + | 35.1205i | 0.162573 | + | 1.50440i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.44667i | 0.147369i | 0.997282 | + | 0.0736845i | \(0.0234758\pi\) | ||||
−0.997282 | + | 0.0736845i | \(0.976524\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.85109 | −0.164360 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 24.4273 | 1.04064 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.40821 | − | 22.2847i | −0.102223 | − | 0.945935i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 38.5215i | 1.63221i | 0.577905 | + | 0.816104i | \(0.303870\pi\) | ||||
−0.577905 | + | 0.816104i | \(0.696130\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.59925 | −0.363709 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −14.5697 | −0.615132 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.7673i | 0.453788i | 0.973919 | + | 0.226894i | \(0.0728571\pi\) | ||||
−0.973919 | + | 0.226894i | \(0.927143\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −45.2683 | + | 4.89194i | −1.90445 | + | 0.205805i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 23.3706 | 0.979747 | 0.489873 | − | 0.871794i | \(-0.337043\pi\) | ||||
0.489873 | + | 0.871794i | \(0.337043\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.5645 | −0.483960 | −0.241980 | − | 0.970281i | \(-0.577797\pi\) | ||||
−0.241980 | + | 0.970281i | \(0.577797\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 33.9625i | 1.41881i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.41103 | + | 15.5980i | 0.142250 | + | 0.650480i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 2.16239i | − | 0.0900213i | −0.998987 | − | 0.0450107i | \(-0.985668\pi\) | ||
0.998987 | − | 0.0450107i | \(-0.0143322\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −15.1349 | −0.628985 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.87046i | 0.243130i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.96542 | + | 0.320460i | −0.122605 | + | 0.0132494i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.65367i | 0.0682544i | 0.999417 | + | 0.0341272i | \(0.0108651\pi\) | ||||
−0.999417 | + | 0.0341272i | \(0.989135\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −26.4818 | −1.09116 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.85014 | 0.158374 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 25.5873i | − | 1.05074i | −0.850873 | − | 0.525372i | \(-0.823926\pi\) | ||
0.850873 | − | 0.525372i | \(-0.176074\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 35.1360i | − | 1.43802i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −11.7773 | −0.481209 | −0.240604 | − | 0.970623i | \(-0.577346\pi\) | ||||
−0.240604 | + | 0.970623i | \(0.577346\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18.5454 | −0.756484 | −0.378242 | − | 0.925707i | \(-0.623471\pi\) | ||||
−0.378242 | + | 0.925707i | \(0.623471\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 6.29562i | − | 0.256377i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.37877 | − | 22.0124i | −0.0967109 | − | 0.894930i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 7.14662i | − | 0.290072i | −0.989426 | − | 0.145036i | \(-0.953670\pi\) | ||
0.989426 | − | 0.145036i | \(-0.0463298\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.7309 | 0.434128 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 20.5746i | − | 0.831002i | −0.909593 | − | 0.415501i | \(-0.863606\pi\) | ||
0.909593 | − | 0.415501i | \(-0.136394\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 43.9083 | − | 4.74497i | 1.77055 | − | 0.191336i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 44.4857i | − | 1.79093i | −0.445134 | − | 0.895464i | \(-0.646844\pi\) | ||
0.445134 | − | 0.895464i | \(-0.353156\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −28.8136 | −1.15812 | −0.579058 | − | 0.815286i | \(-0.696580\pi\) | ||||
−0.579058 | + | 0.815286i | \(0.696580\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 12.0097 | 0.481934 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22.7180 | − | 10.4352i | 0.908719 | − | 0.417407i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 10.1503i | − | 0.405362i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −33.5380 | −1.33725 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 48.6854 | 1.93813 | 0.969067 | − | 0.246796i | \(-0.0793777\pi\) | ||||
0.969067 | + | 0.246796i | \(0.0793777\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 10.7112i | − | 0.425731i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.797196 | − | 0.0861493i | 0.0316358 | − | 0.00341873i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.74585 | 0.187743 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 36.2497 | 1.43178 | 0.715888 | − | 0.698216i | \(-0.246022\pi\) | ||||
0.715888 | + | 0.698216i | \(0.246022\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 17.4717i | − | 0.689015i | −0.938784 | − | 0.344507i | \(-0.888046\pi\) | ||
0.938784 | − | 0.344507i | \(-0.111954\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.64613 | + | 33.7400i | 0.143566 | + | 1.32851i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 6.67004i | − | 0.262226i | −0.991367 | − | 0.131113i | \(-0.958145\pi\) | ||
0.991367 | − | 0.131113i | \(-0.0418551\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.3845 | 0.446883 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 16.0250i | − | 0.627107i | −0.949570 | − | 0.313554i | \(-0.898480\pi\) | ||
0.949570 | − | 0.313554i | \(-0.101520\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.72651 | + | 34.4839i | 0.145607 | + | 1.34740i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.47109i | 0.291475i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.3934 | −0.482780 | −0.241390 | − | 0.970428i | \(-0.577603\pi\) | ||||
−0.241390 | + | 0.970428i | \(0.577603\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.3132 | −0.478928 | −0.239464 | − | 0.970905i | \(-0.576972\pi\) | ||||
−0.239464 | + | 0.970905i | \(0.576972\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 16.0553i | 0.623538i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16.4178i | 0.635699i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −27.0614 | −1.04625 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.49473 | 0.134913 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.3139i | 0.397572i | 0.980043 | + | 0.198786i | \(0.0636998\pi\) | ||||
−0.980043 | + | 0.198786i | \(0.936300\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.01732 | − | 18.3704i | −0.154627 | − | 0.707076i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 30.3992i | − | 1.16834i | −0.811633 | − | 0.584168i | \(-0.801421\pi\) | ||
0.811633 | − | 0.584168i | \(-0.198579\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −24.0608 | −0.922010 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25.7960i | 0.987057i | 0.869730 | + | 0.493529i | \(0.164293\pi\) | ||||
−0.869730 | + | 0.493529i | \(0.835707\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.87276 | − | 0.202380i | 0.0715544 | − | 0.00773255i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 27.5021i | 1.04927i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.46907 | 0.246452 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.6453 | 0.595176 | 0.297588 | − | 0.954694i | \(-0.403818\pi\) | ||||
0.297588 | + | 0.954694i | \(0.403818\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.715625 | + | 6.62215i | 0.0271452 | + | 0.251192i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 66.0809i | − | 2.50299i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.32496 | 0.0879379 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.3083 | 1.14473 | 0.572365 | − | 0.819999i | \(-0.306026\pi\) | ||||
0.572365 | + | 0.819999i | \(0.306026\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 23.3649i | − | 0.881224i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.54998 | − | 42.1040i | −0.171362 | − | 1.58573i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −40.7086 | −1.52885 | −0.764423 | − | 0.644715i | \(-0.776976\pi\) | ||||
−0.764423 | + | 0.644715i | \(0.776976\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.707686 | 0.0265403 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 17.7986i | − | 0.666564i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.69102 | − | 0.290806i | 0.100638 | − | 0.0108755i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 6.00902i | − | 0.224411i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11.2692 | 0.420269 | 0.210134 | − | 0.977673i | \(-0.432610\pi\) | ||||
0.210134 | + | 0.977673i | \(0.432610\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 21.6334i | − | 0.804555i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 25.1130 | − | 5.49183i | 0.932675 | − | 0.203962i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25.5742i | 0.948495i | 0.880392 | + | 0.474248i | \(0.157280\pi\) | ||||
−0.880392 | + | 0.474248i | \(0.842720\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −10.1427 | −0.375655 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 50.7779 | 1.87809 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 7.86641i | − | 0.290552i | −0.989391 | − | 0.145276i | \(-0.953593\pi\) | ||
0.989391 | − | 0.145276i | \(-0.0464071\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.71306i | 0.210443i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14.0515 | −0.516892 | −0.258446 | − | 0.966026i | \(-0.583210\pi\) | ||||
−0.258446 | + | 0.966026i | \(0.583210\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −11.1853 | −0.410902 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11.3464i | 0.416258i | 0.978101 | + | 0.208129i | \(0.0667374\pi\) | ||||
−0.978101 | + | 0.208129i | \(0.933263\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.264964 | − | 2.45189i | −0.00970754 | − | 0.0898303i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.318329i | 0.0116471i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −48.1936 | −1.75861 | −0.879306 | − | 0.476258i | \(-0.841993\pi\) | ||||
−0.879306 | + | 0.476258i | \(0.841993\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 25.0962i | 0.914556i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.01564 | − | 27.9057i | −0.109750 | − | 1.01559i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20.3236i | 0.738676i | 0.929295 | + | 0.369338i | \(0.120415\pi\) | ||||
−0.929295 | + | 0.369338i | \(0.879585\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.82206 | 0.247625 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.92883 | −0.251170 | −0.125585 | − | 0.992083i | \(-0.540081\pi\) | ||||
−0.125585 | + | 0.992083i | \(0.540081\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 17.5106 | − | 1.89229i | 0.633097 | − | 0.0684158i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 12.5454i | − | 0.452989i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −32.5653 | −1.17434 | −0.587168 | − | 0.809465i | \(-0.699757\pi\) | ||||
−0.587168 | + | 0.809465i | \(0.699757\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −36.1778 | −1.30291 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 31.4728i | 1.13200i | 0.824407 | + | 0.565998i | \(0.191509\pi\) | ||||
−0.824407 | + | 0.565998i | \(0.808491\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −27.2252 | + | 5.95373i | −0.977957 | + | 0.213864i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 46.0366 | 1.64943 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.30670 | −0.154106 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 19.3359i | − | 0.691010i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −46.8438 | + | 5.06220i | −1.67193 | + | 0.180678i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 45.9267i | 1.63711i | 0.574428 | + | 0.818555i | \(0.305224\pi\) | ||||
−0.574428 | + | 0.818555i | \(0.694776\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −8.51162 | −0.303022 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 3.85109i | − | 0.136756i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.74292 | − | 25.3821i | −0.0972815 | − | 0.900209i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 13.5988i | − | 0.481696i | −0.970563 | − | 0.240848i | \(-0.922575\pi\) | ||
0.970563 | − | 0.240848i | \(-0.0774255\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −63.3654 | −2.24171 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 19.9397 | 0.704535 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 6.77976i | − | 0.239253i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 53.5441i | 1.88484i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −17.0751 | −0.600329 | −0.300165 | − | 0.953887i | \(-0.597042\pi\) | ||||
−0.300165 | + | 0.953887i | \(0.597042\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 35.7020 | 1.25367 | 0.626833 | − | 0.779153i | \(-0.284351\pi\) | ||||
0.626833 | + | 0.779153i | \(0.284351\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 53.6242i | − | 1.88068i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 48.6105 | − | 5.25311i | 1.70275 | − | 0.184008i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 35.3755i | 1.23763i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16.4670 | −0.574701 | −0.287351 | − | 0.957825i | \(-0.592774\pi\) | ||||
−0.287351 | + | 0.957825i | \(0.592774\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 29.0400i | − | 1.01227i | −0.862454 | − | 0.506135i | \(-0.831074\pi\) | ||
0.862454 | − | 0.506135i | \(-0.168926\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.28201 | − | 10.4352i | −0.0794495 | − | 0.363307i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 47.8903i | − | 1.66531i | −0.553794 | − | 0.832654i | \(-0.686821\pi\) | ||
0.553794 | − | 0.832654i | \(-0.313179\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 24.1186 | 0.837672 | 0.418836 | − | 0.908062i | \(-0.362438\pi\) | ||||
0.418836 | + | 0.908062i | \(0.362438\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −42.6674 | −1.48012 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −22.6047 | + | 2.44278i | −0.782267 | + | 0.0845359i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 20.9622i | 0.724559i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 25.1230 | 0.867343 | 0.433672 | − | 0.901071i | \(-0.357218\pi\) | ||||
0.433672 | + | 0.901071i | \(0.357218\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.56701 | −0.0885175 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 32.0222i | 1.10290i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.80270 | + | 25.9352i | 0.0964157 | + | 0.892198i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −22.0321 | −0.756141 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 15.7037 | 0.538317 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.78647i | 0.0954069i | 0.998862 | + | 0.0477035i | \(0.0151902\pi\) | ||||
−0.998862 | + | 0.0477035i | \(0.984810\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.31830 | + | 12.1991i | 0.0450850 | + | 0.417201i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 33.7254i | − | 1.15204i | −0.817436 | − | 0.576019i | \(-0.804605\pi\) | ||
0.817436 | − | 0.576019i | \(-0.195395\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19.1171 | 0.652266 | 0.326133 | − | 0.945324i | \(-0.394254\pi\) | ||||
0.326133 | + | 0.945324i | \(0.394254\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 33.0437i | 1.12482i | 0.826859 | + | 0.562410i | \(0.190126\pi\) | ||||
−0.826859 | + | 0.562410i | \(0.809874\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.77505 | + | 0.191821i | −0.0603534 | + | 0.00652211i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 60.1533i | − | 2.04291i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.642200 | −0.0217852 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.29562 | 0.213319 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8.77590i | 0.297019i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 0.185101i | − | 0.00625043i | −0.999995 | − | 0.00312521i | \(-0.999005\pi\) | ||
0.999995 | − | 0.00312521i | \(-0.000994788\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −20.2183 | −0.681947 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −43.7063 | −1.47250 | −0.736252 | − | 0.676708i | \(-0.763406\pi\) | ||||
−0.736252 | + | 0.676708i | \(0.763406\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.70129i | 0.158211i | 0.996866 | + | 0.0791055i | \(0.0252064\pi\) | ||||
−0.996866 | + | 0.0791055i | \(0.974794\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −49.2233 | + | 5.31934i | −1.65462 | + | 0.178807i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 28.9752i | 0.972893i | 0.873710 | + | 0.486447i | \(0.161707\pi\) | ||||
−0.873710 | + | 0.486447i | \(0.838293\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −11.6660 | −0.390827 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 44.1448i | − | 1.47725i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.92508 | + | 27.0677i | 0.0977748 | + | 0.904774i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 7.51771i | − | 0.251009i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −28.6562 | −0.955736 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −38.1994 | −1.27261 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.962443 | + | 8.90612i | 0.0319927 | + | 0.296049i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 35.9661i | 1.19423i | 0.802154 | + | 0.597117i | \(0.203687\pi\) | ||||
−0.802154 | + | 0.597117i | \(0.796313\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.652164 | −0.0216309 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 29.1414 | 0.965499 | 0.482749 | − | 0.875759i | \(-0.339638\pi\) | ||||
0.482749 | + | 0.875759i | \(0.339638\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 0.288873i | − | 0.00956030i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −15.1101 | + | 1.63288i | −0.499526 | + | 0.0539814i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −27.6014 | −0.910485 | −0.455243 | − | 0.890367i | \(-0.650447\pi\) | ||||
−0.455243 | + | 0.890367i | \(0.650447\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11.5093 | −0.379244 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.74585i | 0.156212i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.25298 | − | 24.0208i | −0.172717 | − | 0.789799i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 17.9963i | 0.591076i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 41.4287 | 1.35923 | 0.679616 | − | 0.733568i | \(-0.262147\pi\) | ||||
0.679616 | + | 0.733568i | \(0.262147\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 24.4991i | − | 0.802065i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −15.8903 | + | 1.71719i | −0.519667 | + | 0.0561580i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17.6450i | 0.576438i | 0.957564 | + | 0.288219i | \(0.0930632\pi\) | ||||
−0.957564 | + | 0.288219i | \(0.906937\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −38.6851 | −1.26244 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24.1005 | −0.785653 | −0.392827 | − | 0.919613i | \(-0.628503\pi\) | ||||
−0.392827 | + | 0.919613i | \(0.628503\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 30.9415i | 1.00760i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 9.64168i | − | 0.313312i | −0.987653 | − | 0.156656i | \(-0.949929\pi\) | ||
0.987653 | − | 0.156656i | \(-0.0500715\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.47109 | −0.242522 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −25.9725 | −0.842216 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12.3033i | 0.398544i | 0.979944 | + | 0.199272i | \(0.0638577\pi\) | ||||
−0.979944 | + | 0.199272i | \(0.936142\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.00284 | + | 37.0409i | 0.129529 | + | 1.19861i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 10.9837i | − | 0.355052i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.0662997 | 0.00213870 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 16.1971i | 0.521943i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −16.5067 | + | 1.78380i | −0.531370 | + | 0.0574227i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 15.7098i | − | 0.505193i | −0.967572 | − | 0.252597i | \(-0.918715\pi\) | ||
0.967572 | − | 0.252597i | \(-0.0812846\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 66.0482 | 2.12178 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.71582 | 0.151338 | 0.0756689 | − | 0.997133i | \(-0.475891\pi\) | ||||
0.0756689 | + | 0.997133i | \(0.475891\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −11.4993 | + | 2.51471i | −0.368271 | + | 0.0805352i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 29.0115i | 0.928159i | 0.885794 | + | 0.464079i | \(0.153615\pi\) | ||||
−0.885794 | + | 0.464079i | \(0.846385\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −18.0946 | −0.578306 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −18.2456 | −0.582537 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 29.6408i | − | 0.945394i | −0.881225 | − | 0.472697i | \(-0.843280\pi\) | ||
0.881225 | − | 0.472697i | \(-0.156720\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.19911 | − | 0.453779i | 0.133795 | − | 0.0144586i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −23.7761 | −0.756036 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 39.0278 | 1.23976 | 0.619879 | − | 0.784697i | \(-0.287182\pi\) | ||||
0.619879 | + | 0.784697i | \(0.287182\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 48.5913i | 1.54200i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.14114 | − | 38.3207i | −0.131283 | − | 1.21485i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 12.3710i | − | 0.391792i | −0.980625 | − | 0.195896i | \(-0.937238\pi\) | ||
0.980625 | − | 0.195896i | \(-0.0627615\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −18.4949 | −0.585154 |
(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 | 1960.2.g.e.1569.9 | 12 | ||
5.2 | odd | 4 | 9800.2.a.cw.1.5 | 6 | |||
5.3 | odd | 4 | 9800.2.a.cy.1.2 | 6 | |||
5.4 | even | 2 | inner | 1960.2.g.e.1569.4 | 12 | ||
7.3 | odd | 6 | 280.2.bg.a.9.4 | ✓ | 24 | ||
7.5 | odd | 6 | 280.2.bg.a.249.9 | yes | 24 | ||
7.6 | odd | 2 | 1960.2.g.f.1569.4 | 12 | |||
28.3 | even | 6 | 560.2.bw.f.289.9 | 24 | |||
28.19 | even | 6 | 560.2.bw.f.529.4 | 24 | |||
35.3 | even | 12 | 1400.2.q.o.401.2 | 12 | |||
35.12 | even | 12 | 1400.2.q.n.1201.5 | 12 | |||
35.13 | even | 4 | 9800.2.a.cv.1.5 | 6 | |||
35.17 | even | 12 | 1400.2.q.n.401.5 | 12 | |||
35.19 | odd | 6 | 280.2.bg.a.249.4 | yes | 24 | ||
35.24 | odd | 6 | 280.2.bg.a.9.9 | yes | 24 | ||
35.27 | even | 4 | 9800.2.a.cx.1.2 | 6 | |||
35.33 | even | 12 | 1400.2.q.o.1201.2 | 12 | |||
35.34 | odd | 2 | 1960.2.g.f.1569.9 | 12 | |||
140.19 | even | 6 | 560.2.bw.f.529.9 | 24 | |||
140.59 | even | 6 | 560.2.bw.f.289.4 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.bg.a.9.4 | ✓ | 24 | 7.3 | odd | 6 | ||
280.2.bg.a.9.9 | yes | 24 | 35.24 | odd | 6 | ||
280.2.bg.a.249.4 | yes | 24 | 35.19 | odd | 6 | ||
280.2.bg.a.249.9 | yes | 24 | 7.5 | odd | 6 | ||
560.2.bw.f.289.4 | 24 | 140.59 | even | 6 | |||
560.2.bw.f.289.9 | 24 | 28.3 | even | 6 | |||
560.2.bw.f.529.4 | 24 | 28.19 | even | 6 | |||
560.2.bw.f.529.9 | 24 | 140.19 | even | 6 | |||
1400.2.q.n.401.5 | 12 | 35.17 | even | 12 | |||
1400.2.q.n.1201.5 | 12 | 35.12 | even | 12 | |||
1400.2.q.o.401.2 | 12 | 35.3 | even | 12 | |||
1400.2.q.o.1201.2 | 12 | 35.33 | even | 12 | |||
1960.2.g.e.1569.4 | 12 | 5.4 | even | 2 | inner | ||
1960.2.g.e.1569.9 | 12 | 1.1 | even | 1 | trivial | ||
1960.2.g.f.1569.4 | 12 | 7.6 | odd | 2 | |||
1960.2.g.f.1569.9 | 12 | 35.34 | odd | 2 | |||
9800.2.a.cv.1.5 | 6 | 35.13 | even | 4 | |||
9800.2.a.cw.1.5 | 6 | 5.2 | odd | 4 | |||
9800.2.a.cx.1.2 | 6 | 35.27 | even | 4 | |||
9800.2.a.cy.1.2 | 6 | 5.3 | odd | 4 |