Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6048,2,Mod(3025,6048)]
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([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6048.3025");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6048.c (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: | \(24\) |
Twist minimal: | no (minimal twist has level 1512) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3025.9 | ||
Character | \(\chi\) | \(=\) | 6048.3025 |
Dual form | 6048.2.c.g.3025.16 |
$q$-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 | ||||||||
\(5\) | − 1.53368i | − 0.685881i | −0.939357 | − | 0.342940i | \(-0.888577\pi\) | ||||
0.939357 | − | 0.342940i | \(-0.111423\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 2.28335i | − 0.688455i | −0.938886 | − | 0.344228i | \(-0.888141\pi\) | ||||
0.938886 | − | 0.344228i | \(-0.111859\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 7.10447i | − 1.97043i | −0.171333 | − | 0.985213i | \(-0.554807\pi\) | ||||
0.171333 | − | 0.985213i | \(-0.445193\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.81307 | 1.65241 | 0.826206 | − | 0.563368i | \(-0.190495\pi\) | ||||
0.826206 | + | 0.563368i | \(0.190495\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 1.60676i | − 0.368616i | −0.982869 | − | 0.184308i | \(-0.940996\pi\) | ||||
0.982869 | − | 0.184308i | \(-0.0590044\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.16757 | −0.243455 | −0.121727 | − | 0.992564i | \(-0.538843\pi\) | ||||
−0.121727 | + | 0.992564i | \(0.538843\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.64784 | 0.529568 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 4.07059i | − 0.755889i | −0.925828 | − | 0.377944i | \(-0.876631\pi\) | ||||
0.925828 | − | 0.377944i | \(-0.123369\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.90568 | 1.41990 | 0.709951 | − | 0.704251i | \(-0.248717\pi\) | ||||
0.709951 | + | 0.704251i | \(0.248717\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.53368i | 0.259238i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.04836i | 1.15874i | 0.815063 | + | 0.579372i | \(0.196702\pi\) | ||||
−0.815063 | + | 0.579372i | \(0.803298\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.1710 | 1.58844 | 0.794218 | − | 0.607633i | \(-0.207881\pi\) | ||||
0.794218 | + | 0.607633i | \(0.207881\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.344719i | 0.0525691i | 0.999655 | + | 0.0262846i | \(0.00836760\pi\) | ||||
−0.999655 | + | 0.0262846i | \(0.991632\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.10859 | −0.453434 | −0.226717 | − | 0.973961i | \(-0.572799\pi\) | ||||
−0.226717 | + | 0.973961i | \(0.572799\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.66835i | 0.778608i | 0.921109 | + | 0.389304i | \(0.127284\pi\) | ||||
−0.921109 | + | 0.389304i | \(0.872716\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.50191 | −0.472198 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 1.38165i | − 0.179875i | −0.995947 | − | 0.0899374i | \(-0.971333\pi\) | ||||
0.995947 | − | 0.0899374i | \(-0.0286667\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 5.50516i | − 0.704863i | −0.935838 | − | 0.352431i | \(-0.885355\pi\) | ||||
0.935838 | − | 0.352431i | \(-0.114645\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −10.8960 | −1.35148 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.35907i | 1.02122i | 0.859811 | + | 0.510612i | \(0.170581\pi\) | ||||
−0.859811 | + | 0.510612i | \(0.829419\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.2819 | −1.45759 | −0.728795 | − | 0.684732i | \(-0.759919\pi\) | ||||
−0.728795 | + | 0.684732i | \(0.759919\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.95132 | −0.696549 | −0.348275 | − | 0.937393i | \(-0.613232\pi\) | ||||
−0.348275 | + | 0.937393i | \(0.613232\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.28335i | 0.260212i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.0027 | 1.68794 | 0.843968 | − | 0.536393i | \(-0.180213\pi\) | ||||
0.843968 | + | 0.536393i | \(0.180213\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 14.7419i | − 1.61814i | −0.587715 | − | 0.809068i | \(-0.699973\pi\) | ||||
0.587715 | − | 0.809068i | \(-0.300027\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 10.4490i | − 1.13336i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.8923 | −1.26058 | −0.630290 | − | 0.776360i | \(-0.717064\pi\) | ||||
−0.630290 | + | 0.776360i | \(0.717064\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.10447i | 0.744751i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.46425 | −0.252827 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.60256 | −0.264250 | −0.132125 | − | 0.991233i | \(-0.542180\pi\) | ||||
−0.132125 | + | 0.991233i | \(0.542180\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 9.58182i | − 0.953427i | −0.879059 | − | 0.476713i | \(-0.841828\pi\) | ||||
0.879059 | − | 0.476713i | \(-0.158172\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.44175 | −0.930323 | −0.465162 | − | 0.885226i | \(-0.654004\pi\) | ||||
−0.465162 | + | 0.885226i | \(0.654004\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.04240i | 0.487467i | 0.969842 | + | 0.243733i | \(0.0783722\pi\) | ||||
−0.969842 | + | 0.243733i | \(0.921628\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.35923i | 0.225973i | 0.993597 | + | 0.112987i | \(0.0360417\pi\) | ||||
−0.993597 | + | 0.112987i | \(0.963958\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.0317 | −1.31999 | −0.659994 | − | 0.751271i | \(-0.729441\pi\) | ||||
−0.659994 | + | 0.751271i | \(0.729441\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.79067i | 0.166981i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.81307 | −0.624553 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.78632 | 0.526029 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 11.7293i | − 1.04910i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.0218 | 1.51044 | 0.755220 | − | 0.655472i | \(-0.227530\pi\) | ||||
0.755220 | + | 0.655472i | \(0.227530\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 17.8861i | − 1.56272i | −0.624082 | − | 0.781359i | \(-0.714527\pi\) | ||||
0.624082 | − | 0.781359i | \(-0.285473\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.60676i | 0.139324i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.18009 | 0.784308 | 0.392154 | − | 0.919900i | \(-0.371730\pi\) | ||||
0.392154 | + | 0.919900i | \(0.371730\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.0518i | 1.02222i | 0.859516 | + | 0.511108i | \(0.170765\pi\) | ||||
−0.859516 | + | 0.511108i | \(0.829235\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −16.2220 | −1.35655 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.24296 | −0.518449 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 7.71091i | − 0.631702i | −0.948809 | − | 0.315851i | \(-0.897710\pi\) | ||||
0.948809 | − | 0.315851i | \(-0.102290\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.91312 | −0.481203 | −0.240601 | − | 0.970624i | \(-0.577345\pi\) | ||||
−0.240601 | + | 0.970624i | \(0.577345\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 12.1247i | − 0.973883i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 0.906198i | − 0.0723225i | −0.999346 | − | 0.0361612i | \(-0.988487\pi\) | ||||
0.999346 | − | 0.0361612i | \(-0.0115130\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.16757 | 0.0920172 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 4.46083i | − 0.349400i | −0.984622 | − | 0.174700i | \(-0.944105\pi\) | ||||
0.984622 | − | 0.174700i | \(-0.0558955\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 22.6885 | 1.75569 | 0.877845 | − | 0.478944i | \(-0.158980\pi\) | ||||
0.877845 | + | 0.478944i | \(0.158980\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −37.4735 | −2.88258 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 24.2316i | 1.84229i | 0.389218 | + | 0.921145i | \(0.372745\pi\) | ||||
−0.389218 | + | 0.921145i | \(0.627255\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.64784 | −0.200158 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 8.82249i | − 0.659424i | −0.944082 | − | 0.329712i | \(-0.893048\pi\) | ||||
0.944082 | − | 0.329712i | \(-0.106952\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 4.29583i | − 0.319306i | −0.987173 | − | 0.159653i | \(-0.948962\pi\) | ||||
0.987173 | − | 0.159653i | \(-0.0510376\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.8099 | 0.794760 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 15.5566i | − 1.13761i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.224849 | 0.0162695 | 0.00813476 | − | 0.999967i | \(-0.497411\pi\) | ||||
0.00813476 | + | 0.999967i | \(0.497411\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.7447 | −0.845404 | −0.422702 | − | 0.906269i | \(-0.638918\pi\) | ||||
−0.422702 | + | 0.906269i | \(0.638918\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 14.7998i | − 1.05444i | −0.849729 | − | 0.527220i | \(-0.823234\pi\) | ||||
0.849729 | − | 0.527220i | \(-0.176766\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.6242 | 1.39112 | 0.695561 | − | 0.718467i | \(-0.255156\pi\) | ||||
0.695561 | + | 0.718467i | \(0.255156\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.07059i | 0.285699i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 15.5989i | − 1.08948i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.66879 | −0.253776 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.913482i | 0.0628867i | 0.999506 | + | 0.0314434i | \(0.0100104\pi\) | ||||
−0.999506 | + | 0.0314434i | \(0.989990\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.528687 | 0.0360561 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.90568 | −0.536673 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 48.4033i | − 3.25596i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.8646 | 0.794512 | 0.397256 | − | 0.917708i | \(-0.369963\pi\) | ||||
0.397256 | + | 0.917708i | \(0.369963\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 19.2403i | − 1.27702i | −0.769613 | − | 0.638510i | \(-0.779551\pi\) | ||||
0.769613 | − | 0.638510i | \(-0.220449\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 7.11176i | − 0.469958i | −0.972000 | − | 0.234979i | \(-0.924498\pi\) | ||||
0.972000 | − | 0.234979i | \(-0.0755022\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.5527 | −1.21542 | −0.607712 | − | 0.794157i | \(-0.707913\pi\) | ||||
−0.607712 | + | 0.794157i | \(0.707913\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.76757i | 0.311002i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.86610 | −0.250077 | −0.125039 | − | 0.992152i | \(-0.539905\pi\) | ||||
−0.125039 | + | 0.992152i | \(0.539905\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.5687 | −0.745205 | −0.372603 | − | 0.927991i | \(-0.621535\pi\) | ||||
−0.372603 | + | 0.927991i | \(0.621535\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 1.53368i | − 0.0979829i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.4152 | −0.726331 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.5653i | 0.856235i | 0.903723 | + | 0.428117i | \(0.140823\pi\) | ||||
−0.903723 | + | 0.428117i | \(0.859177\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.66596i | 0.167608i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.1567 | 0.695938 | 0.347969 | − | 0.937506i | \(-0.386871\pi\) | ||||
0.347969 | + | 0.937506i | \(0.386871\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 7.04836i | − 0.437964i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.9609 | 0.860864 | 0.430432 | − | 0.902623i | \(-0.358361\pi\) | ||||
0.430432 | + | 0.902623i | \(0.358361\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.69341 | 0.534032 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 16.1185i | − 0.982761i | −0.870945 | − | 0.491380i | \(-0.836493\pi\) | ||||
0.870945 | − | 0.491380i | \(-0.163507\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.91716 | −0.541679 | −0.270840 | − | 0.962624i | \(-0.587301\pi\) | ||||
−0.270840 | + | 0.962624i | \(0.587301\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 6.04594i | − 0.364584i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 26.8189i | 1.61139i | 0.592328 | + | 0.805697i | \(0.298209\pi\) | ||||
−0.592328 | + | 0.805697i | \(0.701791\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.0688 | −0.660306 | −0.330153 | − | 0.943927i | \(-0.607100\pi\) | ||||
−0.330153 | + | 0.943927i | \(0.607100\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.7405i | 1.29234i | 0.763194 | + | 0.646170i | \(0.223630\pi\) | ||||
−0.763194 | + | 0.646170i | \(0.776370\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.1710 | −0.600373 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 29.4179 | 1.73046 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 8.80042i | − 0.514126i | −0.966395 | − | 0.257063i | \(-0.917245\pi\) | ||||
0.966395 | − | 0.257063i | \(-0.0827548\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.11900 | −0.123373 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.29496i | 0.479710i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 0.344719i | − 0.0198693i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.44312 | −0.483452 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.11170i | 0.177594i | 0.996050 | + | 0.0887971i | \(0.0283023\pi\) | ||||
−0.996050 | + | 0.0887971i | \(0.971698\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.443815 | −0.0251664 | −0.0125832 | − | 0.999921i | \(-0.504005\pi\) | ||||
−0.0125832 | + | 0.999921i | \(0.504005\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.1601 | 1.08299 | 0.541497 | − | 0.840703i | \(-0.317858\pi\) | ||||
0.541497 | + | 0.840703i | \(0.317858\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 11.2142i | − 0.629854i | −0.949116 | − | 0.314927i | \(-0.898020\pi\) | ||||
0.949116 | − | 0.314927i | \(-0.101980\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.29456 | −0.520396 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 10.9470i | − 0.609105i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 18.8115i | − 1.04347i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.10859 | 0.171382 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.8007i | 0.978414i | 0.872168 | + | 0.489207i | \(0.162714\pi\) | ||||
−0.872168 | + | 0.489207i | \(0.837286\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.8201 | 0.700437 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.46393 | −0.188692 | −0.0943461 | − | 0.995539i | \(-0.530076\pi\) | ||||
−0.0943461 | + | 0.995539i | \(0.530076\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 18.0514i | − 0.977539i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 27.3962i | − 1.47070i | −0.677686 | − | 0.735352i | \(-0.737017\pi\) | ||||
0.677686 | − | 0.735352i | \(-0.262983\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.62149i | 0.0867961i | 0.999058 | + | 0.0433981i | \(0.0138184\pi\) | ||||
−0.999058 | + | 0.0433981i | \(0.986182\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −16.5882 | −0.882903 | −0.441452 | − | 0.897285i | \(-0.645536\pi\) | ||||
−0.441452 | + | 0.897285i | \(0.645536\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 18.8364i | 0.999732i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.84388 | 0.413984 | 0.206992 | − | 0.978343i | \(-0.433633\pi\) | ||||
0.206992 | + | 0.978343i | \(0.433633\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.4183 | 0.864122 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.12740i | 0.477750i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.761448 | −0.0397472 | −0.0198736 | − | 0.999803i | \(-0.506326\pi\) | ||||
−0.0198736 | + | 0.999803i | \(0.506326\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 5.66835i | − 0.294286i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 13.3240i | − 0.689888i | −0.938623 | − | 0.344944i | \(-0.887898\pi\) | ||||
0.938623 | − | 0.344944i | \(-0.112102\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −28.9194 | −1.48942 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.6595i | 0.701640i | 0.936443 | + | 0.350820i | \(0.114097\pi\) | ||||
−0.936443 | + | 0.350820i | \(0.885903\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.70332 | −0.495816 | −0.247908 | − | 0.968784i | \(-0.579743\pi\) | ||||
−0.247908 | + | 0.968784i | \(0.579743\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.50191 | 0.178474 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 24.7223i | 1.25347i | 0.779233 | + | 0.626734i | \(0.215609\pi\) | ||||
−0.779233 | + | 0.626734i | \(0.784391\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.95472 | −0.402287 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 23.0093i | − 1.15772i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 29.1070i | 1.46084i | 0.682999 | + | 0.730420i | \(0.260675\pi\) | ||||
−0.682999 | + | 0.730420i | \(0.739325\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.7247 | −0.685380 | −0.342690 | − | 0.939449i | \(-0.611338\pi\) | ||||
−0.342690 | + | 0.939449i | \(0.611338\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 56.1657i | − 2.79781i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16.0939 | 0.797743 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.1707 | 0.898486 | 0.449243 | − | 0.893410i | \(-0.351694\pi\) | ||||
0.449243 | + | 0.893410i | \(0.351694\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.38165i | 0.0679863i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −22.6093 | −1.10985 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 32.9489i | 1.60966i | 0.593507 | + | 0.804829i | \(0.297743\pi\) | ||||
−0.593507 | + | 0.804829i | \(0.702257\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.5222i | 1.34135i | 0.741751 | + | 0.670675i | \(0.233996\pi\) | ||||
−0.741751 | + | 0.670675i | \(0.766004\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 18.0399 | 0.875064 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.50516i | 0.266413i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −40.3524 | −1.94371 | −0.971855 | − | 0.235582i | \(-0.924300\pi\) | ||||
−0.971855 | + | 0.235582i | \(0.924300\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −38.5928 | −1.85465 | −0.927327 | − | 0.374253i | \(-0.877899\pi\) | ||||
−0.927327 | + | 0.374253i | \(0.877899\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.87600i | 0.0897413i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.68908 | 0.0806152 | 0.0403076 | − | 0.999187i | \(-0.487166\pi\) | ||||
0.0403076 | + | 0.999187i | \(0.487166\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 18.3190i | 0.870361i | 0.900343 | + | 0.435180i | \(0.143315\pi\) | ||||
−0.900343 | + | 0.435180i | \(0.856685\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 18.2389i | 0.864607i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −34.2644 | −1.61704 | −0.808518 | − | 0.588471i | \(-0.799730\pi\) | ||||
−0.808518 | + | 0.588471i | \(0.799730\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 23.2238i | − 1.09357i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 10.8960 | 0.510810 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.08541 | 0.144330 | 0.0721648 | − | 0.997393i | \(-0.477009\pi\) | ||||
0.0721648 | + | 0.997393i | \(0.477009\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.62369i | 0.401645i | 0.979628 | + | 0.200823i | \(0.0643615\pi\) | ||||
−0.979628 | + | 0.200823i | \(0.935639\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.29178 | −0.152982 | −0.0764910 | − | 0.997070i | \(-0.524372\pi\) | ||||
−0.0764910 | + | 0.997070i | \(0.524372\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 31.3473i | 1.45058i | 0.688443 | + | 0.725290i | \(0.258294\pi\) | ||||
−0.688443 | + | 0.725290i | \(0.741706\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 8.35907i | − 0.385986i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.787113 | 0.0361915 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 4.25444i | − 0.195207i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −23.7139 | −1.08351 | −0.541757 | − | 0.840535i | \(-0.682241\pi\) | ||||
−0.541757 | + | 0.840535i | \(0.682241\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 50.0749 | 2.28322 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.99148i | 0.181244i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −35.7317 | −1.61916 | −0.809580 | − | 0.587010i | \(-0.800305\pi\) | ||||
−0.809580 | + | 0.587010i | \(0.800305\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 40.3543i | − 1.82116i | −0.413330 | − | 0.910581i | \(-0.635634\pi\) | ||||
0.413330 | − | 0.910581i | \(-0.364366\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 27.7332i | − 1.24904i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.2819 | 0.550917 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 41.0646i | − 1.83831i | −0.393902 | − | 0.919153i | \(-0.628875\pi\) | ||||
0.393902 | − | 0.919153i | \(-0.371125\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −13.5744 | −0.605252 | −0.302626 | − | 0.953109i | \(-0.597863\pi\) | ||||
−0.302626 | + | 0.953109i | \(0.597863\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −14.6954 | −0.653937 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13.3591i | 0.592132i | 0.955167 | + | 0.296066i | \(0.0956749\pi\) | ||||
−0.955167 | + | 0.296066i | \(0.904325\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.95132 | 0.263271 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 14.4806i | 0.638091i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.09799i | 0.312169i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −20.5338 | −0.899600 | −0.449800 | − | 0.893129i | \(-0.648505\pi\) | ||||
−0.449800 | + | 0.893129i | \(0.648505\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 4.37298i | − 0.191217i | −0.995419 | − | 0.0956086i | \(-0.969520\pi\) | ||||
0.995419 | − | 0.0956086i | \(-0.0304797\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 53.8619 | 2.34626 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.6368 | −0.940730 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 72.2593i | − 3.12990i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.73340 | 0.334344 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 2.28335i | − 0.0983507i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.8762i | 0.510598i | 0.966862 | + | 0.255299i | \(0.0821740\pi\) | ||||
−0.966862 | + | 0.255299i | \(0.917826\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.61829 | 0.154991 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.50044i | 0.235182i | 0.993062 | + | 0.117591i | \(0.0375171\pi\) | ||||
−0.993062 | + | 0.117591i | \(0.962483\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.54045 | −0.278633 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15.0027 | −0.637980 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.19596i | 0.347274i | 0.984810 | + | 0.173637i | \(0.0555519\pi\) | ||||
−0.984810 | + | 0.173637i | \(0.944448\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.44905 | 0.103584 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 0.145215i | − 0.00612008i | −0.999995 | − | 0.00306004i | \(-0.999026\pi\) | ||||
0.999995 | − | 0.00306004i | \(-0.000974043\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 21.5200i | 0.905354i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.09548 | 0.213613 | 0.106807 | − | 0.994280i | \(-0.465937\pi\) | ||||
0.106807 | + | 0.994280i | \(0.465937\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 25.3061i | − 1.05903i | −0.848301 | − | 0.529514i | \(-0.822374\pi\) | ||||
0.848301 | − | 0.529514i | \(-0.177626\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.09153 | −0.128926 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19.5004 | 0.811814 | 0.405907 | − | 0.913914i | \(-0.366956\pi\) | ||||
0.405907 | + | 0.913914i | \(0.366956\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14.7419i | 0.611598i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.9428 | 0.536037 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 36.0783i | − 1.48911i | −0.667561 | − | 0.744555i | \(-0.732662\pi\) | ||||
0.667561 | − | 0.744555i | \(-0.267338\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 12.7025i | − 0.523399i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16.7669 | 0.688535 | 0.344268 | − | 0.938872i | \(-0.388127\pi\) | ||||
0.344268 | + | 0.938872i | \(0.388127\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.4490i | 0.428369i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −31.1008 | −1.27074 | −0.635372 | − | 0.772206i | \(-0.719153\pi\) | ||||
−0.635372 | + | 0.772206i | \(0.719153\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.1858 | 0.701022 | 0.350511 | − | 0.936559i | \(-0.386008\pi\) | ||||
0.350511 | + | 0.936559i | \(0.386008\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 8.87434i | − 0.360793i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12.9692 | −0.526404 | −0.263202 | − | 0.964741i | \(-0.584779\pi\) | ||||
−0.263202 | + | 0.964741i | \(0.584779\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 22.0849i | 0.893459i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 26.5265i | − 1.07139i | −0.844410 | − | 0.535697i | \(-0.820049\pi\) | ||||
0.844410 | − | 0.535697i | \(-0.179951\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 37.3263 | 1.50270 | 0.751350 | − | 0.659904i | \(-0.229403\pi\) | ||||
0.751350 | + | 0.659904i | \(0.229403\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.8774i | 0.437200i | 0.975815 | + | 0.218600i | \(0.0701489\pi\) | ||||
−0.975815 | + | 0.218600i | \(0.929851\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 11.8923 | 0.476454 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.74975 | −0.189990 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 48.0210i | 1.91472i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.2943 | 0.967140 | 0.483570 | − | 0.875306i | \(-0.339340\pi\) | ||||
0.483570 | + | 0.875306i | \(0.339340\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 26.1059i | − 1.03598i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 7.10447i | − 0.281489i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.5765 | 0.654731 | 0.327365 | − | 0.944898i | \(-0.393839\pi\) | ||||
0.327365 | + | 0.944898i | \(0.393839\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.15319i | 0.282094i | 0.990003 | + | 0.141047i | \(0.0450469\pi\) | ||||
−0.990003 | + | 0.141047i | \(0.954953\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7.94968 | −0.312534 | −0.156267 | − | 0.987715i | \(-0.549946\pi\) | ||||
−0.156267 | + | 0.987715i | \(0.549946\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.15478 | −0.123836 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 7.45217i | − 0.291626i | −0.989312 | − | 0.145813i | \(-0.953420\pi\) | ||||
0.989312 | − | 0.145813i | \(-0.0465798\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −27.4315 | −1.07184 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 26.2741i | − 1.02349i | −0.859136 | − | 0.511747i | \(-0.828999\pi\) | ||||
0.859136 | − | 0.511747i | \(-0.171001\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.98821i | 0.155123i | 0.996988 | + | 0.0775617i | \(0.0247135\pi\) | ||||
−0.996988 | + | 0.0775617i | \(0.975287\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.46425 | 0.0955594 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.75268i | 0.184025i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12.5702 | −0.485267 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30.5709 | 1.17842 | 0.589211 | − | 0.807979i | \(-0.299439\pi\) | ||||
0.589211 | + | 0.807979i | \(0.299439\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 21.9032i | − 0.841808i | −0.907105 | − | 0.420904i | \(-0.861713\pi\) | ||||
0.907105 | − | 0.420904i | \(-0.138287\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.60256 | 0.0998770 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 13.0423i | 0.499051i | 0.968368 | + | 0.249525i | \(0.0802746\pi\) | ||||
−0.968368 | + | 0.249525i | \(0.919725\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 14.0793i | − 0.537942i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 40.2707 | 1.53419 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.25399i | 0.123788i | 0.998083 | + | 0.0618938i | \(0.0197140\pi\) | ||||
−0.998083 | + | 0.0618938i | \(0.980286\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 18.4835 | 0.701118 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 69.2954 | 2.62475 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 2.70404i | − 0.102130i | −0.998695 | − | 0.0510650i | \(-0.983738\pi\) | ||||
0.998695 | − | 0.0510650i | \(-0.0162616\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.3250 | 0.427132 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.58182i | 0.360361i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 49.0447i | 1.84191i | 0.389668 | + | 0.920955i | \(0.372590\pi\) | ||||
−0.389668 | + | 0.920955i | \(0.627410\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.23042 | −0.345682 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 24.8793i | 0.930431i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −21.3291 | −0.795442 | −0.397721 | − | 0.917506i | \(-0.630199\pi\) | ||||
−0.397721 | + | 0.917506i | \(0.630199\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.44175 | 0.351629 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 10.7783i | − 0.400294i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23.5713 | 0.874210 | 0.437105 | − | 0.899411i | \(-0.356004\pi\) | ||||
0.437105 | + | 0.899411i | \(0.356004\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.34859i | 0.0868658i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.28803i | 0.0845105i | 0.999107 | + | 0.0422552i | \(0.0134543\pi\) | ||||
−0.999107 | + | 0.0422552i | \(0.986546\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 19.0867 | 0.703067 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 33.6953i | − 1.23950i | −0.784798 | − | 0.619751i | \(-0.787234\pi\) | ||||
0.784798 | − | 0.619751i | \(-0.212766\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 35.7898 | 1.31300 | 0.656501 | − | 0.754326i | \(-0.272036\pi\) | ||||
0.656501 | + | 0.754326i | \(0.272036\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11.8260 | −0.433272 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 5.04240i | − 0.184245i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.35858 | −0.268518 | −0.134259 | − | 0.990946i | \(-0.542865\pi\) | ||||
−0.134259 | + | 0.990946i | \(0.542865\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9.06881i | 0.330048i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 23.2086i | − 0.843530i | −0.906705 | − | 0.421765i | \(-0.861411\pi\) | ||||
0.906705 | − | 0.421765i | \(-0.138589\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22.1491 | 0.802902 | 0.401451 | − | 0.915880i | \(-0.368506\pi\) | ||||
0.401451 | + | 0.915880i | \(0.368506\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 2.35923i | − 0.0854099i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.81586 | −0.354430 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −27.4818 | −0.991020 | −0.495510 | − | 0.868602i | \(-0.665019\pi\) | ||||
−0.495510 | + | 0.868602i | \(0.665019\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 39.9693i | 1.43760i | 0.695219 | + | 0.718798i | \(0.255308\pi\) | ||||
−0.695219 | + | 0.718798i | \(0.744692\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 20.9330 | 0.751935 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 16.3423i | − 0.585523i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 28.0438i | 1.00348i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.38981 | −0.0496046 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 34.5651i | − 1.23211i | −0.787702 | − | 0.616057i | \(-0.788729\pi\) | ||||
0.787702 | − | 0.616057i | \(-0.211271\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 14.0317 | 0.498908 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −39.1112 | −1.38888 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 16.9968i | 0.602059i | 0.953615 | + | 0.301029i | \(0.0973302\pi\) | ||||
−0.953615 | + | 0.301029i | \(0.902670\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −21.1790 | −0.749260 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 13.5889i | 0.479543i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 1.79067i | − 0.0631128i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.33018 | −0.0819249 | −0.0409624 | − | 0.999161i | \(-0.513042\pi\) | ||||
−0.0409624 | + | 0.999161i | \(0.513042\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.79524i | 0.308843i | 0.988005 | + | 0.154421i | \(0.0493513\pi\) | ||||
−0.988005 | + | 0.154421i | \(0.950649\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.84147 | −0.239646 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.553880 | 0.0193778 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 14.1689i | 0.494497i | 0.968952 | + | 0.247249i | \(0.0795265\pi\) | ||||
−0.968952 | + | 0.247249i | \(0.920474\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.53482 | −0.192932 | −0.0964659 | − | 0.995336i | \(-0.530754\pi\) | ||||
−0.0964659 | + | 0.995336i | \(0.530754\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 7.32030i | − 0.254552i | −0.991867 | − | 0.127276i | \(-0.959377\pi\) | ||||
0.991867 | − | 0.127276i | \(-0.0406234\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 32.7046i | 1.13588i | 0.823071 | + | 0.567939i | \(0.192259\pi\) | ||||
−0.823071 | + | 0.567939i | \(0.807741\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.81307 | 0.236059 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 34.7968i | − 1.20419i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −19.2836 | −0.665744 | −0.332872 | − | 0.942972i | \(-0.608018\pi\) | ||||
−0.332872 | + | 0.942972i | \(0.608018\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.4303 | 0.428632 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 57.4723i | 1.97711i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.78632 | −0.198820 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 8.22944i | − 0.282102i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 24.5003i | 0.838874i | 0.907784 | + | 0.419437i | \(0.137772\pi\) | ||||
−0.907784 | + | 0.419437i | \(0.862228\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −24.0113 | −0.820211 | −0.410105 | − | 0.912038i | \(-0.634508\pi\) | ||||
−0.410105 | + | 0.912038i | \(0.634508\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.15328i | 0.0734689i | 0.999325 | + | 0.0367344i | \(0.0116956\pi\) | ||||
−0.999325 | + | 0.0367344i | \(0.988304\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.94727 | 0.236488 | 0.118244 | − | 0.992985i | \(-0.462274\pi\) | ||||
0.118244 | + | 0.992985i | \(0.462274\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 37.1633 | 1.26359 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 34.2564i | − 1.16207i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 59.3868 | 2.01225 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 11.7293i | 0.396523i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 24.2307i | − 0.818211i | −0.912487 | − | 0.409106i | \(-0.865841\pi\) | ||||
0.912487 | − | 0.409106i | \(-0.134159\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −42.4462 | −1.43005 | −0.715024 | − | 0.699100i | \(-0.753584\pi\) | ||||
−0.715024 | + | 0.699100i | \(0.753584\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 0.397509i | − 0.0133773i | −0.999978 | − | 0.00668863i | \(-0.997871\pi\) | ||||
0.999978 | − | 0.00668863i | \(-0.00212907\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 36.3698 | 1.22118 | 0.610590 | − | 0.791947i | \(-0.290932\pi\) | ||||
0.610590 | + | 0.791947i | \(0.290932\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −17.0218 | −0.570892 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.99476i | 0.167143i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −13.5308 | −0.452286 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 32.1807i | − 1.07329i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 38.6189i | 1.28658i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6.58840 | −0.219006 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 52.1212i | 1.73066i | 0.501205 | + | 0.865329i | \(0.332890\pi\) | ||||
−0.501205 | + | 0.865329i | \(0.667110\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25.8160 | −0.855322 | −0.427661 | − | 0.903939i | \(-0.640662\pi\) | ||||
−0.427661 | + | 0.903939i | \(0.640662\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −33.6609 | −1.11401 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 17.8861i | 0.590652i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.71609 | 0.155569 | 0.0777847 | − | 0.996970i | \(-0.475215\pi\) | ||||
0.0777847 | + | 0.996970i | \(0.475215\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 87.2562i | 2.87207i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 18.6629i | 0.613634i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 48.4774 | 1.59049 | 0.795246 | − | 0.606287i | \(-0.207342\pi\) | ||||
0.795246 | + | 0.606287i | \(0.207342\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 1.60676i | − 0.0526594i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −23.8588 | −0.780266 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11.5193 | 0.376319 | 0.188159 | − | 0.982138i | \(-0.439748\pi\) | ||||
0.188159 | + | 0.982138i | \(0.439748\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 32.3390i | − 1.05422i | −0.849796 | − | 0.527111i | \(-0.823275\pi\) | ||||
0.849796 | − | 0.527111i | \(-0.176725\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11.8753 | −0.386712 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 37.4382i | 1.21658i | 0.793715 | + | 0.608289i | \(0.208144\pi\) | ||||
−0.793715 | + | 0.608289i | \(0.791856\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 42.2810i | 1.37250i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −18.4974 | −0.599190 | −0.299595 | − | 0.954066i | \(-0.596852\pi\) | ||||
−0.299595 | + | 0.954066i | \(0.596852\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 0.344846i | − 0.0111590i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9.18009 | −0.296441 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 31.4998 | 1.01612 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 18.0126i | 0.579846i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −44.4221 | −1.42852 | −0.714259 | − | 0.699882i | \(-0.753236\pi\) | ||||
−0.714259 | + | 0.699882i | \(0.753236\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 37.5434i | 1.20482i | 0.798185 | + | 0.602412i | \(0.205794\pi\) | ||||
−0.798185 | + | 0.602412i | \(0.794206\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 12.0518i | − 0.386361i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −6.89949 | −0.220734 | −0.110367 | − | 0.993891i | \(-0.535203\pi\) | ||||
−0.110367 | + | 0.993891i | \(0.535203\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 27.1542i | 0.867853i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −28.9252 | −0.922571 | −0.461285 | − | 0.887252i | \(-0.652612\pi\) | ||||
−0.461285 | + | 0.887252i | \(0.652612\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −22.6980 | −0.723220 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 0.402483i | − 0.0127982i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −37.7278 | −1.19846 | −0.599232 | − | 0.800575i | \(-0.704527\pi\) | ||||
−0.599232 | + | 0.800575i | \(0.704527\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 30.0971i | − 0.954144i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 53.0914i | − 1.68142i | −0.541484 | − | 0.840711i | \(-0.682137\pi\) | ||||
0.541484 | − | 0.840711i | \(-0.317863\pi\) | |||||||
\(998\) | 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.c.g.3025.9 | 24 | ||
3.2 | odd | 2 | inner | 6048.2.c.g.3025.15 | 24 | ||
4.3 | odd | 2 | 1512.2.c.f.757.22 | yes | 24 | ||
8.3 | odd | 2 | 1512.2.c.f.757.21 | yes | 24 | ||
8.5 | even | 2 | inner | 6048.2.c.g.3025.16 | 24 | ||
12.11 | even | 2 | 1512.2.c.f.757.3 | ✓ | 24 | ||
24.5 | odd | 2 | inner | 6048.2.c.g.3025.10 | 24 | ||
24.11 | even | 2 | 1512.2.c.f.757.4 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.c.f.757.3 | ✓ | 24 | 12.11 | even | 2 | ||
1512.2.c.f.757.4 | yes | 24 | 24.11 | even | 2 | ||
1512.2.c.f.757.21 | yes | 24 | 8.3 | odd | 2 | ||
1512.2.c.f.757.22 | yes | 24 | 4.3 | odd | 2 | ||
6048.2.c.g.3025.9 | 24 | 1.1 | even | 1 | trivial | ||
6048.2.c.g.3025.10 | 24 | 24.5 | odd | 2 | inner | ||
6048.2.c.g.3025.15 | 24 | 3.2 | odd | 2 | inner | ||
6048.2.c.g.3025.16 | 24 | 8.5 | even | 2 | inner |