Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2736,2,Mod(2015,2736)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2736, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("2736.2015");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2736.d (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: | \(21.8470699930\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2015.14 | ||
Character | \(\chi\) | \(=\) | 2736.2015 |
Dual form | 2736.2.d.b.2015.11 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).
\(n\) | \(1009\) | \(1217\) | \(1711\) | \(2053\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||||
\(5\) | 1.11119i | 0.496939i | 0.968640 | + | 0.248470i | \(0.0799276\pi\) | ||||
−0.968640 | + | 0.248470i | \(0.920072\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.19380i | 0.451213i | 0.974219 | + | 0.225606i | \(0.0724363\pi\) | ||||
−0.974219 | + | 0.225606i | \(0.927564\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.72045 | 1.12176 | 0.560879 | − | 0.827898i | \(-0.310463\pi\) | ||||
0.560879 | + | 0.827898i | \(0.310463\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.113448 | 0.0314648 | 0.0157324 | − | 0.999876i | \(-0.494992\pi\) | ||||
0.0157324 | + | 0.999876i | \(0.494992\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 2.89258i | − 0.701553i | −0.936459 | − | 0.350776i | \(-0.885918\pi\) | ||||
0.936459 | − | 0.350776i | \(-0.114082\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 1.00000i | − 0.229416i | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.35549 | 0.282639 | 0.141319 | − | 0.989964i | \(-0.454866\pi\) | ||||
0.141319 | + | 0.989964i | \(0.454866\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.76526 | 0.753051 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 0.860408i | − 0.159774i | −0.996804 | − | 0.0798869i | \(-0.974544\pi\) | ||||
0.996804 | − | 0.0798869i | \(-0.0254559\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 9.01283i | − 1.61875i | −0.587290 | − | 0.809376i | \(-0.699805\pi\) | ||||
0.587290 | − | 0.809376i | \(-0.300195\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.32654 | −0.224225 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.64396 | 0.927862 | 0.463931 | − | 0.885871i | \(-0.346439\pi\) | ||||
0.463931 | + | 0.885871i | \(0.346439\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.5323i | 1.64487i | 0.568859 | + | 0.822435i | \(0.307385\pi\) | ||||
−0.568859 | + | 0.822435i | \(0.692615\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 2.47195i | − 0.376969i | −0.982076 | − | 0.188484i | \(-0.939643\pi\) | ||||
0.982076 | − | 0.188484i | \(-0.0603575\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.05623 | −0.737527 | −0.368764 | − | 0.929523i | \(-0.620219\pi\) | ||||
−0.368764 | + | 0.929523i | \(0.620219\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.57485 | 0.796407 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.51146i | 1.30650i | 0.757143 | + | 0.653250i | \(0.226595\pi\) | ||||
−0.757143 | + | 0.653250i | \(0.773405\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.13413i | 0.557446i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.73964 | 1.13780 | 0.568902 | − | 0.822405i | \(-0.307368\pi\) | ||||
0.568902 | + | 0.822405i | \(0.307368\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.52172 | −1.09109 | −0.545547 | − | 0.838080i | \(-0.683678\pi\) | ||||
−0.545547 | + | 0.838080i | \(0.683678\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.126062i | 0.0156361i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 0.857080i | − 0.104709i | −0.998629 | − | 0.0523545i | \(-0.983327\pi\) | ||||
0.998629 | − | 0.0523545i | \(-0.0166726\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.91011 | −0.226689 | −0.113344 | − | 0.993556i | \(-0.536156\pi\) | ||||
−0.113344 | + | 0.993556i | \(0.536156\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.06213 | 0.358395 | 0.179198 | − | 0.983813i | \(-0.442650\pi\) | ||||
0.179198 | + | 0.983813i | \(0.442650\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.44146i | 0.506152i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 7.62732i | − 0.858141i | −0.903271 | − | 0.429071i | \(-0.858841\pi\) | ||||
0.903271 | − | 0.429071i | \(-0.141159\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.0020 | 1.09787 | 0.548933 | − | 0.835867i | \(-0.315034\pi\) | ||||
0.548933 | + | 0.835867i | \(0.315034\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.21420 | 0.348629 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.1659i | 1.39558i | 0.716300 | + | 0.697792i | \(0.245834\pi\) | ||||
−0.716300 | + | 0.697792i | \(0.754166\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.135434i | 0.0141973i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.11119 | 0.114006 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.6659 | 1.18450 | 0.592249 | − | 0.805755i | \(-0.298240\pi\) | ||||
0.592249 | + | 0.805755i | \(0.298240\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.64199i | 0.163384i | 0.996658 | + | 0.0816921i | \(0.0260324\pi\) | ||||
−0.996658 | + | 0.0816921i | \(0.973968\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.09681i | 0.206605i | 0.994650 | + | 0.103302i | \(0.0329410\pi\) | ||||
−0.994650 | + | 0.103302i | \(0.967059\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.03841 | −0.197061 | −0.0985303 | − | 0.995134i | \(-0.531414\pi\) | ||||
−0.0985303 | + | 0.995134i | \(0.531414\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.32276 | −0.222480 | −0.111240 | − | 0.993794i | \(-0.535482\pi\) | ||||
−0.111240 | + | 0.993794i | \(0.535482\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.91983i | 0.556891i | 0.960452 | + | 0.278445i | \(0.0898191\pi\) | ||||
−0.960452 | + | 0.278445i | \(0.910181\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.50621i | 0.140454i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.45315 | 0.316550 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.84176 | 0.258342 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.73987i | 0.871160i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.4051i | 1.10078i | 0.834909 | + | 0.550388i | \(0.185520\pi\) | ||||
−0.834909 | + | 0.550388i | \(0.814480\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.9820 | 1.04687 | 0.523434 | − | 0.852066i | \(-0.324651\pi\) | ||||
0.523434 | + | 0.852066i | \(0.324651\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.19380 | 0.103515 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.69469i | 0.315658i | 0.987466 | + | 0.157829i | \(0.0504495\pi\) | ||||
−0.987466 | + | 0.157829i | \(0.949550\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 0.965743i | − 0.0819133i | −0.999161 | − | 0.0409566i | \(-0.986959\pi\) | ||||
0.999161 | − | 0.0409566i | \(-0.0130406\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.422078 | 0.0352960 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.956077 | 0.0793978 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 3.59705i | − 0.294682i | −0.989086 | − | 0.147341i | \(-0.952929\pi\) | ||||
0.989086 | − | 0.147341i | \(-0.0470715\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.17609i | 0.177088i | 0.996072 | + | 0.0885440i | \(0.0282214\pi\) | ||||
−0.996072 | + | 0.0885440i | \(0.971779\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.0150 | 0.804422 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 24.4292 | 1.94966 | 0.974832 | − | 0.222943i | \(-0.0715663\pi\) | ||||
0.974832 | + | 0.222943i | \(0.0715663\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.61818i | 0.127530i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 18.6476i | − 1.46059i | −0.683129 | − | 0.730297i | \(-0.739381\pi\) | ||||
0.683129 | − | 0.730297i | \(-0.260619\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.46847 | 0.732692 | 0.366346 | − | 0.930479i | \(-0.380609\pi\) | ||||
0.366346 | + | 0.930479i | \(0.380609\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9871 | −0.999010 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.52499i | 0.648143i | 0.946033 | + | 0.324071i | \(0.105052\pi\) | ||||
−0.946033 | + | 0.324071i | \(0.894948\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.49495i | 0.339786i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.16062 | −0.385723 | −0.192861 | − | 0.981226i | \(-0.561777\pi\) | ||||
−0.192861 | + | 0.981226i | \(0.561777\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.3864 | 1.29232 | 0.646160 | − | 0.763202i | \(-0.276374\pi\) | ||||
0.646160 | + | 0.763202i | \(0.276374\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.27151i | 0.461091i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 10.7617i | − 0.786973i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.768626 | 0.0556159 | 0.0278079 | − | 0.999613i | \(-0.491147\pi\) | ||||
0.0278079 | + | 0.999613i | \(0.491147\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.1274 | −0.872951 | −0.436475 | − | 0.899716i | \(-0.643773\pi\) | ||||
−0.436475 | + | 0.899716i | \(0.643773\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.95333i | 0.210416i | 0.994450 | + | 0.105208i | \(0.0335509\pi\) | ||||
−0.994450 | + | 0.105208i | \(0.966449\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 17.3465i | − 1.22966i | −0.788660 | − | 0.614829i | \(-0.789225\pi\) | ||||
0.788660 | − | 0.614829i | \(-0.210775\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.02715 | 0.0720920 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.7034 | −0.817400 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 3.72045i | − 0.257349i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 2.32941i | − 0.160363i | −0.996780 | − | 0.0801815i | \(-0.974450\pi\) | ||||
0.996780 | − | 0.0801815i | \(-0.0255500\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.74680 | 0.187331 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.7595 | 0.730402 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 0.328157i | − 0.0220742i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.1883i | 0.682257i | 0.940017 | + | 0.341129i | \(0.110809\pi\) | ||||
−0.940017 | + | 0.341129i | \(0.889191\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 14.2877 | 0.948305 | 0.474153 | − | 0.880443i | \(-0.342754\pi\) | ||||
0.474153 | + | 0.880443i | \(0.342754\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.84008 | 0.319842 | 0.159921 | − | 0.987130i | \(-0.448876\pi\) | ||||
0.159921 | + | 0.987130i | \(0.448876\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 14.5288i | − 0.951813i | −0.879496 | − | 0.475907i | \(-0.842120\pi\) | ||||
0.879496 | − | 0.475907i | \(-0.157880\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 5.61843i | − 0.366506i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −29.9420 | −1.93679 | −0.968395 | − | 0.249422i | \(-0.919759\pi\) | ||||
−0.968395 | + | 0.249422i | \(0.919759\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.0657 | −0.648390 | −0.324195 | − | 0.945990i | \(-0.605093\pi\) | ||||
−0.324195 | + | 0.945990i | \(0.605093\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.19472i | 0.395766i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 0.113448i | − 0.00721853i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.6664 | 1.05197 | 0.525986 | − | 0.850493i | \(-0.323696\pi\) | ||||
0.525986 | + | 0.850493i | \(0.323696\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.04303 | 0.317053 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 21.7438i | 1.35634i | 0.734906 | + | 0.678169i | \(0.237226\pi\) | ||||
−0.734906 | + | 0.678169i | \(0.762774\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.73774i | 0.418663i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −30.8883 | −1.90466 | −0.952328 | − | 0.305075i | \(-0.901319\pi\) | ||||
−0.952328 | + | 0.305075i | \(0.901319\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.5690 | −0.649251 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 4.71830i | − 0.287680i | −0.989601 | − | 0.143840i | \(-0.954055\pi\) | ||||
0.989601 | − | 0.143840i | \(-0.0459450\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 4.77033i | − 0.289777i | −0.989448 | − | 0.144888i | \(-0.953718\pi\) | ||||
0.989448 | − | 0.144888i | \(-0.0462823\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 14.0085 | 0.844742 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.73084 | −0.344333 | −0.172166 | − | 0.985068i | \(-0.555077\pi\) | ||||
−0.172166 | + | 0.985068i | \(0.555077\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.7428i | 0.760171i | 0.924951 | + | 0.380085i | \(0.124105\pi\) | ||||
−0.924951 | + | 0.380085i | \(0.875895\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 24.1940i | − 1.43818i | −0.694914 | − | 0.719092i | \(-0.744558\pi\) | ||||
0.694914 | − | 0.719092i | \(-0.255442\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.5734 | −0.742186 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.63300 | 0.507824 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 8.35727i | − 0.488237i | −0.969745 | − | 0.244118i | \(-0.921501\pi\) | ||||
0.969745 | − | 0.244118i | \(-0.0784986\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.71140i | 0.565420i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.153778 | 0.00889319 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.95100 | 0.170093 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 9.46925i | − 0.542208i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.0461i | 0.744578i | 0.928117 | + | 0.372289i | \(0.121427\pi\) | ||||
−0.928117 | + | 0.372289i | \(0.878573\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.71584 | 0.210706 | 0.105353 | − | 0.994435i | \(-0.466403\pi\) | ||||
0.105353 | + | 0.994435i | \(0.466403\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.32643 | 0.414114 | 0.207057 | − | 0.978329i | \(-0.433611\pi\) | ||||
0.207057 | + | 0.978329i | \(0.433611\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 4.42123i | − 0.248321i | −0.992262 | − | 0.124161i | \(-0.960376\pi\) | ||||
0.992262 | − | 0.124161i | \(-0.0396238\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 3.20111i | − 0.179228i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.89258 | −0.160947 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.427161 | 0.0236946 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 6.03611i | − 0.332782i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 1.97474i | − 0.108541i | −0.998526 | − | 0.0542707i | \(-0.982717\pi\) | ||||
0.998526 | − | 0.0542707i | \(-0.0172834\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.952379 | 0.0520340 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 24.4795 | 1.33348 | 0.666741 | − | 0.745290i | \(-0.267689\pi\) | ||||
0.666741 | + | 0.745290i | \(0.267689\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 33.5318i | − 1.81585i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.0118i | 0.810562i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 18.8988 | 1.01454 | 0.507271 | − | 0.861787i | \(-0.330654\pi\) | ||||
0.507271 | + | 0.861787i | \(0.330654\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.1508 | −0.543361 | −0.271680 | − | 0.962388i | \(-0.587579\pi\) | ||||
−0.271680 | + | 0.962388i | \(0.587579\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 20.6591i | − 1.09957i | −0.835306 | − | 0.549785i | \(-0.814709\pi\) | ||||
0.835306 | − | 0.549785i | \(-0.185291\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 2.12250i | − 0.112650i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.15543 | 0.0609810 | 0.0304905 | − | 0.999535i | \(-0.490293\pi\) | ||||
0.0304905 | + | 0.999535i | \(0.490293\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.40261i | 0.178101i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 25.9993i | 1.35715i | 0.734530 | + | 0.678576i | \(0.237403\pi\) | ||||
−0.734530 | + | 0.678576i | \(0.762597\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.3547 | −0.589509 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.6006 | 0.963102 | 0.481551 | − | 0.876418i | \(-0.340074\pi\) | ||||
0.481551 | + | 0.876418i | \(0.340074\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 0.0976116i | − 0.00502726i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 6.01294i | − 0.308864i | −0.988003 | − | 0.154432i | \(-0.950645\pi\) | ||||
0.988003 | − | 0.154432i | \(-0.0493547\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.6395 | −0.543653 | −0.271827 | − | 0.962346i | \(-0.587628\pi\) | ||||
−0.271827 | + | 0.962346i | \(0.587628\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.93531 | −0.251527 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.2848i | 0.774971i | 0.921876 | + | 0.387485i | \(0.126656\pi\) | ||||
−0.921876 | + | 0.387485i | \(0.873344\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 3.92085i | − 0.198286i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.47541 | 0.426444 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.7056 | −0.587487 | −0.293743 | − | 0.955884i | \(-0.594901\pi\) | ||||
−0.293743 | + | 0.955884i | \(0.594901\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 3.79270i | − 0.189399i | −0.995506 | − | 0.0946993i | \(-0.969811\pi\) | ||||
0.995506 | − | 0.0946993i | \(-0.0301890\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 1.02249i | − 0.0509338i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 20.9981 | 1.04084 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.556303 | 0.0275074 | 0.0137537 | − | 0.999905i | \(-0.495622\pi\) | ||||
0.0137537 | + | 0.999905i | \(0.495622\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 10.4334i | 0.513392i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.1142i | 0.545572i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −26.4184 | −1.29063 | −0.645313 | − | 0.763918i | \(-0.723273\pi\) | ||||
−0.645313 | + | 0.763918i | \(0.723273\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −24.0288 | −1.17109 | −0.585546 | − | 0.810639i | \(-0.699120\pi\) | ||||
−0.585546 | + | 0.810639i | \(0.699120\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 10.8913i | − 0.528305i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 10.1732i | − 0.492316i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −30.3393 | −1.46139 | −0.730697 | − | 0.682702i | \(-0.760805\pi\) | ||||
−0.730697 | + | 0.682702i | \(0.760805\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15.1246 | −0.726843 | −0.363421 | − | 0.931625i | \(-0.618391\pi\) | ||||
−0.363421 | + | 0.931625i | \(0.618391\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 1.35549i | − 0.0648418i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 28.6582i | 1.36778i | 0.729585 | + | 0.683890i | \(0.239713\pi\) | ||||
−0.729585 | + | 0.683890i | \(0.760287\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −36.9951 | −1.75769 | −0.878845 | − | 0.477108i | \(-0.841685\pi\) | ||||
−0.878845 | + | 0.477108i | \(0.841685\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.6298 | −0.693521 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 17.4824i | − 0.825044i | −0.910948 | − | 0.412522i | \(-0.864648\pi\) | ||||
0.910948 | − | 0.412522i | \(-0.135352\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 39.1849i | 1.84515i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.150493 | −0.00705522 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −33.2001 | −1.55303 | −0.776517 | − | 0.630096i | \(-0.783015\pi\) | ||||
−0.776517 | + | 0.630096i | \(0.783015\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 13.2270i | − 0.616043i | −0.951379 | − | 0.308022i | \(-0.900333\pi\) | ||||
0.951379 | − | 0.308022i | \(-0.0996669\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.7916i | 0.919794i | 0.887972 | + | 0.459897i | \(0.152114\pi\) | ||||
−0.887972 | + | 0.459897i | \(0.847886\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.7076 | 0.588038 | 0.294019 | − | 0.955800i | \(-0.405007\pi\) | ||||
0.294019 | + | 0.955800i | \(0.405007\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.02318 | 0.0472460 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 9.19677i | − 0.422868i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 3.76526i | − 0.172762i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.28722 | −0.287271 | −0.143635 | − | 0.989631i | \(-0.545879\pi\) | ||||
−0.143635 | + | 0.989631i | \(0.545879\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.640297 | 0.0291950 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12.9631i | 0.588623i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 18.6477i | − 0.845008i | −0.906361 | − | 0.422504i | \(-0.861151\pi\) | ||||
0.906361 | − | 0.422504i | \(-0.138849\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.8097 | 0.713480 | 0.356740 | − | 0.934204i | \(-0.383888\pi\) | ||||
0.356740 | + | 0.934204i | \(0.383888\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.48880 | −0.112090 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 2.28029i | − 0.102285i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 13.1361i | − 0.588052i | −0.955797 | − | 0.294026i | \(-0.905005\pi\) | ||||
0.955797 | − | 0.294026i | \(-0.0949952\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.07107 | 0.136932 | 0.0684661 | − | 0.997653i | \(-0.478189\pi\) | ||||
0.0684661 | + | 0.997653i | \(0.478189\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.82456 | −0.0811920 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 21.1047i | − 0.935449i | −0.883874 | − | 0.467725i | \(-0.845074\pi\) | ||||
0.883874 | − | 0.467725i | \(-0.154926\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.65556i | 0.161713i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.32995 | −0.102670 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −18.8115 | −0.827327 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 19.1133i | − 0.837367i | −0.908132 | − | 0.418684i | \(-0.862492\pi\) | ||||
0.908132 | − | 0.418684i | \(-0.137508\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 29.0588i | − 1.27065i | −0.772244 | − | 0.635326i | \(-0.780866\pi\) | ||||
0.772244 | − | 0.635326i | \(-0.219134\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −26.0703 | −1.13564 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.1627 | −0.920115 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.19487i | 0.0517556i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 2.26506i | − 0.0979272i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 20.7410 | 0.893376 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.90913 | −0.254053 | −0.127027 | − | 0.991899i | \(-0.540543\pi\) | ||||
−0.127027 | + | 0.991899i | \(0.540543\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 2.58103i | − 0.110559i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 13.7241i | − 0.586802i | −0.955990 | − | 0.293401i | \(-0.905213\pi\) | ||||
0.955990 | − | 0.293401i | \(-0.0947870\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.860408 | −0.0366546 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.10548 | 0.387204 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.35820i | 0.311777i | 0.987775 | + | 0.155889i | \(0.0498241\pi\) | ||||
−0.987775 | + | 0.155889i | \(0.950176\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 0.280438i | − 0.0118613i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.41425 | 0.396763 | 0.198382 | − | 0.980125i | \(-0.436431\pi\) | ||||
0.198382 | + | 0.980125i | \(0.436431\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.57805 | −0.276741 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 14.6116i | − 0.612551i | −0.951943 | − | 0.306276i | \(-0.900917\pi\) | ||||
0.951943 | − | 0.306276i | \(-0.0990829\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 39.1353i | − 1.63776i | −0.573963 | − | 0.818881i | \(-0.694595\pi\) | ||||
0.573963 | − | 0.818881i | \(-0.305405\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.10376 | 0.212842 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.36547 | −0.0568451 | −0.0284226 | − | 0.999596i | \(-0.509048\pi\) | ||||
−0.0284226 | + | 0.999596i | \(0.509048\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11.9404i | 0.495371i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 35.3869i | 1.46558i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22.0683 | 0.910855 | 0.455427 | − | 0.890273i | \(-0.349486\pi\) | ||||
0.455427 | + | 0.890273i | \(0.349486\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.01283 | −0.371367 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 12.0401i | − 0.494429i | −0.968961 | − | 0.247215i | \(-0.920485\pi\) | ||||
0.968961 | − | 0.247215i | \(-0.0795153\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.83710i | 0.157306i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −40.0405 | −1.63601 | −0.818006 | − | 0.575210i | \(-0.804920\pi\) | ||||
−0.818006 | + | 0.575210i | \(0.804920\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −32.8278 | −1.33907 | −0.669537 | − | 0.742778i | \(-0.733508\pi\) | ||||
−0.669537 | + | 0.742778i | \(0.733508\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.15774i | 0.128380i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.55151i | 0.184740i | 0.995725 | + | 0.0923700i | \(0.0294443\pi\) | ||||
−0.995725 | + | 0.0923700i | \(0.970556\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.573620 | −0.0232062 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −42.4038 | −1.71267 | −0.856336 | − | 0.516419i | \(-0.827265\pi\) | ||||
−0.856336 | + | 0.516419i | \(0.827265\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 16.9498i | − 0.682373i | −0.939996 | − | 0.341187i | \(-0.889171\pi\) | ||||
0.939996 | − | 0.341187i | \(-0.110829\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.7120i | 0.912872i | 0.889756 | + | 0.456436i | \(0.150874\pi\) | ||||
−0.889756 | + | 0.456436i | \(0.849126\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −15.7174 | −0.629705 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.00344 | 0.320138 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 16.3256i | − 0.650944i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 0.732322i | − 0.0291533i | −0.999894 | − | 0.0145766i | \(-0.995360\pi\) | ||||
0.999894 | − | 0.0145766i | \(-0.00464005\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −13.7844 | −0.547019 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.632456 | 0.0250588 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 7.90566i | − 0.312255i | −0.987737 | − | 0.156127i | \(-0.950099\pi\) | ||||
0.987737 | − | 0.156127i | \(-0.0499010\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 36.9435i | 1.45691i | 0.685095 | + | 0.728454i | \(0.259761\pi\) | ||||
−0.685095 | + | 0.728454i | \(0.740239\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.47909 | −0.136777 | −0.0683886 | − | 0.997659i | \(-0.521786\pi\) | ||||
−0.0683886 | + | 0.997659i | \(0.521786\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 32.5154 | 1.27634 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 37.0587i | − 1.45022i | −0.688634 | − | 0.725109i | \(-0.741790\pi\) | ||||
0.688634 | − | 0.725109i | \(-0.258210\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13.3142i | 0.520230i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −38.8706 | −1.51418 | −0.757091 | − | 0.653309i | \(-0.773380\pi\) | ||||
−0.757091 | + | 0.653309i | \(0.773380\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.6229 | 0.685450 | 0.342725 | − | 0.939436i | \(-0.388650\pi\) | ||||
0.342725 | + | 0.939436i | \(0.388650\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.32654i | 0.0514408i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 1.16627i | − 0.0451583i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −31.7047 | −1.22394 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20.3151 | −0.783090 | −0.391545 | − | 0.920159i | \(-0.628059\pi\) | ||||
−0.391545 | + | 0.920159i | \(0.628059\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 11.8396i | − 0.455032i | −0.973774 | − | 0.227516i | \(-0.926940\pi\) | ||||
0.973774 | − | 0.227516i | \(-0.0730604\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.9268i | 0.534460i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 50.6817 | 1.93928 | 0.969640 | − | 0.244535i | \(-0.0786355\pi\) | ||||
0.969640 | + | 0.244535i | \(0.0786355\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.10550 | −0.156863 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.07906i | 0.0411088i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 32.6962i | − 1.24382i | −0.783088 | − | 0.621910i | \(-0.786357\pi\) | ||||
0.783088 | − | 0.621910i | \(-0.213643\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.07312 | 0.0407059 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 30.4655 | 1.15396 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 50.1158i | − 1.89285i | −0.322924 | − | 0.946425i | \(-0.604666\pi\) | ||||
0.322924 | − | 0.946425i | \(-0.395334\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 5.64396i | − 0.212866i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.96020 | −0.0737210 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12.4838 | −0.468840 | −0.234420 | − | 0.972135i | \(-0.575319\pi\) | ||||
−0.234420 | + | 0.972135i | \(0.575319\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 12.2168i | − 0.457522i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.469009i | 0.0175399i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −20.4623 | −0.763116 | −0.381558 | − | 0.924345i | \(-0.624612\pi\) | ||||
−0.381558 | + | 0.924345i | \(0.624612\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.50317 | −0.0932228 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 3.23966i | − 0.120318i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20.7963i | 0.771292i | 0.922647 | + | 0.385646i | \(0.126021\pi\) | ||||
−0.922647 | + | 0.385646i | \(0.873979\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.15030 | −0.264463 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.3029 | 0.491352 | 0.245676 | − | 0.969352i | \(-0.420990\pi\) | ||||
0.245676 | + | 0.969352i | \(0.420990\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 3.18873i | − 0.117458i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 6.39272i | − 0.235160i | −0.993063 | − | 0.117580i | \(-0.962486\pi\) | ||||
0.993063 | − | 0.117580i | \(-0.0375136\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 34.2605 | 1.25689 | 0.628447 | − | 0.777852i | \(-0.283691\pi\) | ||||
0.628447 | + | 0.777852i | \(0.283691\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.99701 | 0.146439 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 2.43345i | − 0.0889163i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 45.5988i | 1.66392i | 0.554833 | + | 0.831962i | \(0.312782\pi\) | ||||
−0.554833 | + | 0.831962i | \(0.687218\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.41805 | −0.0880020 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.1493 | 0.914066 | 0.457033 | − | 0.889450i | \(-0.348912\pi\) | ||||
0.457033 | + | 0.889450i | \(0.348912\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.3805i | 0.448793i | 0.974498 | + | 0.224396i | \(0.0720411\pi\) | ||||
−0.974498 | + | 0.224396i | \(0.927959\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 2.77291i | − 0.100386i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.991496 | 0.0358008 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −37.9127 | −1.36717 | −0.683584 | − | 0.729872i | \(-0.739580\pi\) | ||||
−0.683584 | + | 0.729872i | \(0.739580\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 41.1007i | 1.47829i | 0.673546 | + | 0.739145i | \(0.264770\pi\) | ||||
−0.673546 | + | 0.739145i | \(0.735230\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 33.9356i | − 1.21900i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 10.5323 | 0.377359 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.10648 | −0.254290 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 27.1455i | 0.968864i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.408338i | 0.0145557i | 0.999974 | + | 0.00727783i | \(0.00231663\pi\) | ||||
−0.999974 | + | 0.00727783i | \(0.997683\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.06707 | −0.251276 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.966773 | −0.0343311 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 14.1914i | − 0.502686i | −0.967898 | − | 0.251343i | \(-0.919128\pi\) | ||||
0.967898 | − | 0.251343i | \(-0.0808723\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 14.6255i | 0.517414i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 11.3925 | 0.402033 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.79810 | −0.0633748 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 15.2844i | 0.537370i | 0.963228 | + | 0.268685i | \(0.0865890\pi\) | ||||
−0.963228 | + | 0.268685i | \(0.913411\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.35096i | 0.0474386i | 0.999719 | + | 0.0237193i | \(0.00755080\pi\) | ||||
−0.999719 | + | 0.0237193i | \(0.992449\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 20.7211 | 0.725827 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.47195 | −0.0864825 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 45.3093i | − 1.58131i | −0.612264 | − | 0.790653i | \(-0.709741\pi\) | ||||
0.612264 | − | 0.790653i | \(-0.290259\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.98709i | 0.104123i | 0.998644 | + | 0.0520617i | \(0.0165793\pi\) | ||||
−0.998644 | + | 0.0520617i | \(0.983421\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −20.0319 | −0.696579 | −0.348289 | − | 0.937387i | \(-0.613237\pi\) | ||||
−0.348289 | + | 0.937387i | \(0.613237\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17.6585 | −0.613304 | −0.306652 | − | 0.951822i | \(-0.599209\pi\) | ||||
−0.306652 | + | 0.951822i | \(0.599209\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 16.1257i | − 0.558722i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.5213i | 0.364103i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.22764 | 0.318574 | 0.159287 | − | 0.987232i | \(-0.449081\pi\) | ||||
0.159287 | + | 0.987232i | \(0.449081\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.2597 | 0.974472 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 14.4312i | − 0.496447i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.39249i | 0.116567i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.65033 | 0.262250 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −34.7289 | −1.18909 | −0.594547 | − | 0.804061i | \(-0.702669\pi\) | ||||
−0.594547 | + | 0.804061i | \(0.702669\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 28.3620i | 0.968828i | 0.874839 | + | 0.484414i | \(0.160967\pi\) | ||||
−0.874839 | + | 0.484414i | \(0.839033\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 13.7817i | − 0.470226i | −0.971968 | − | 0.235113i | \(-0.924454\pi\) | ||||
0.971968 | − | 0.235113i | \(-0.0755460\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −36.1403 | −1.23023 | −0.615114 | − | 0.788438i | \(-0.710890\pi\) | ||||
−0.615114 | + | 0.788438i | \(0.710890\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.47288 | −0.322088 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 28.3771i | − 0.962627i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 0.0972341i | − 0.00329465i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −11.6274 | −0.393079 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 34.2580 | 1.15681 | 0.578405 | − | 0.815750i | \(-0.303675\pi\) | ||||
0.578405 | + | 0.815750i | \(0.303675\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 21.4623i | 0.723085i | 0.932356 | + | 0.361542i | \(0.117750\pi\) | ||||
−0.932356 | + | 0.361542i | \(0.882250\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 5.60029i | − 0.188465i | −0.995550 | − | 0.0942323i | \(-0.969960\pi\) | ||||
0.995550 | − | 0.0942323i | \(-0.0300396\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −38.9684 | −1.30843 | −0.654216 | − | 0.756308i | \(-0.727001\pi\) | ||||
−0.654216 | + | 0.756308i | \(0.727001\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −14.8092 | −0.496685 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.05623i | 0.169200i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 5.73443i | − 0.191681i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.75471 | −0.258634 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 27.5126 | 0.916578 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 19.3196i | 0.642205i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 23.8500i | 0.791927i | 0.918266 | + | 0.395964i | \(0.129589\pi\) | ||||
−0.918266 | + | 0.395964i | \(0.870411\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.5268 | 0.415032 | 0.207516 | − | 0.978232i | \(-0.433462\pi\) | ||||
0.207516 | + | 0.978232i | \(0.433462\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 37.2121 | 1.23154 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 14.3040i | 0.472360i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 22.4838i | − 0.741671i | −0.928699 | − | 0.370836i | \(-0.879071\pi\) | ||||
0.928699 | − | 0.370836i | \(-0.120929\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.216699 | −0.00713272 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 21.2510 | 0.698727 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 34.9715i | − 1.14738i | −0.819073 | − | 0.573689i | \(-0.805512\pi\) | ||||
0.819073 | − | 0.573689i | \(-0.194488\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 5.57485i | − 0.182708i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 11.9583 | 0.391078 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19.0472 | 0.622245 | 0.311122 | − | 0.950370i | \(-0.399295\pi\) | ||||
0.311122 | + | 0.950370i | \(0.399295\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 21.1518i | 0.689527i | 0.938690 | + | 0.344764i | \(0.112041\pi\) | ||||
−0.938690 | + | 0.344764i | \(0.887959\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 14.2764i | 0.464904i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −20.6426 | −0.670793 | −0.335396 | − | 0.942077i | \(-0.608870\pi\) | ||||
−0.335396 | + | 0.942077i | \(0.608870\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.347393 | 0.0112768 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 48.3617i | − 1.56659i | −0.621650 | − | 0.783295i | \(-0.713537\pi\) | ||||
0.621650 | − | 0.783295i | \(-0.286463\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.854090i | 0.0276377i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.41071 | −0.142429 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −50.2312 | −1.62036 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 13.4759i | − 0.433804i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 62.1680i | − 1.99919i | −0.0285042 | − | 0.999594i | \(-0.509074\pi\) | ||||
0.0285042 | − | 0.999594i | \(-0.490926\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −39.5108 | −1.26796 | −0.633981 | − | 0.773348i | \(-0.718580\pi\) | ||||
−0.633981 | + | 0.773348i | \(0.718580\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.15290 | 0.0369603 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 36.3792i | 1.16387i | 0.813234 | + | 0.581937i | \(0.197705\pi\) | ||||
−0.813234 | + | 0.581937i | \(0.802295\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 48.9832i | 1.56551i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −51.8584 | −1.65403 | −0.827013 | − | 0.562182i | \(-0.809962\pi\) | ||||
−0.827013 | + | 0.562182i | \(0.809962\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.28171 | −0.104564 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 3.35070i | − 0.106546i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 51.5075i | − 1.63619i | −0.575083 | − | 0.818095i | \(-0.695030\pi\) | ||||
0.575083 | − | 0.818095i | \(-0.304970\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 19.2752 | 0.611066 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −19.9320 | −0.631252 | −0.315626 | − | 0.948884i | \(-0.602214\pi\) | ||||
−0.315626 | + | 0.948884i | \(0.602214\pi\) | |||||||
\(998\) | 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 | 2736.2.d.b.2015.14 | yes | 24 | |
3.2 | odd | 2 | inner | 2736.2.d.b.2015.12 | yes | 24 | |
4.3 | odd | 2 | inner | 2736.2.d.b.2015.13 | yes | 24 | |
12.11 | even | 2 | inner | 2736.2.d.b.2015.11 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2736.2.d.b.2015.11 | ✓ | 24 | 12.11 | even | 2 | inner | |
2736.2.d.b.2015.12 | yes | 24 | 3.2 | odd | 2 | inner | |
2736.2.d.b.2015.13 | yes | 24 | 4.3 | odd | 2 | inner | |
2736.2.d.b.2015.14 | yes | 24 | 1.1 | even | 1 | trivial |