Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6864,2,Mod(1,6864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6864, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 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("6864.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6864 = 2^{4} \cdot 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6864.a (trivial) |
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: | yes |
Analytic conductor: | \(54.8093159474\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.23252.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 6x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 3432) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(2.95372\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6864.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.77076 | 1.68634 | 0.843168 | − | 0.537651i | \(-0.180688\pi\) | ||||
0.843168 | + | 0.537651i | \(0.180688\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −5.23034 | −1.97688 | −0.988441 | − | 0.151609i | \(-0.951555\pi\) | ||||
−0.988441 | + | 0.151609i | \(0.951555\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.77076 | 0.973606 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.44787 | −0.593696 | −0.296848 | − | 0.954925i | \(-0.595935\pi\) | ||||
−0.296848 | + | 0.954925i | \(0.595935\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.23034 | −1.19992 | −0.599961 | − | 0.800029i | \(-0.704817\pi\) | ||||
−0.599961 | + | 0.800029i | \(0.704817\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.23034 | −1.14135 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.67711 | 0.558216 | 0.279108 | − | 0.960260i | \(-0.409961\pi\) | ||||
0.279108 | + | 0.960260i | \(0.409961\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.21863 | 1.84373 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.00110 | 1.67146 | 0.835731 | − | 0.549139i | \(-0.185044\pi\) | ||||
0.835731 | + | 0.549139i | \(0.185044\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.68991 | 1.56075 | 0.780377 | − | 0.625309i | \(-0.215027\pi\) | ||||
0.780377 | + | 0.625309i | \(0.215027\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −19.7223 | −3.33368 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.26167 | −0.536215 | −0.268108 | − | 0.963389i | \(-0.586398\pi\) | ||||
−0.268108 | + | 0.963389i | \(0.586398\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.58456 | 1.34068 | 0.670341 | − | 0.742053i | \(-0.266148\pi\) | ||||
0.670341 | + | 0.742053i | \(0.266148\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.447871 | 0.0682998 | 0.0341499 | − | 0.999417i | \(-0.489128\pi\) | ||||
0.0341499 | + | 0.999417i | \(0.489128\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.77076 | 0.562112 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.4490 | −1.67000 | −0.835002 | − | 0.550247i | \(-0.814533\pi\) | ||||
−0.835002 | + | 0.550247i | \(0.814533\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 20.3564 | 2.90806 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.44787 | −0.342771 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.435071 | 0.0597616 | 0.0298808 | − | 0.999553i | \(-0.490487\pi\) | ||||
0.0298808 | + | 0.999553i | \(0.490487\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.77076 | −0.508449 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.23034 | −0.692775 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.2500 | 1.33443 | 0.667216 | − | 0.744864i | \(-0.267486\pi\) | ||||
0.667216 | + | 0.744864i | \(0.267486\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.4490 | −1.72196 | −0.860982 | − | 0.508636i | \(-0.830150\pi\) | ||||
−0.860982 | + | 0.508636i | \(0.830150\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.23034 | −0.658960 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.77076 | −0.467705 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.33569 | 0.896197 | 0.448099 | − | 0.893984i | \(-0.352101\pi\) | ||||
0.448099 | + | 0.893984i | \(0.352101\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.67711 | 0.322286 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.2617 | 1.57387 | 0.786935 | − | 0.617035i | \(-0.211666\pi\) | ||||
0.786935 | + | 0.617035i | \(0.211666\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.95696 | 0.346086 | 0.173043 | − | 0.984914i | \(-0.444640\pi\) | ||||
0.173043 | + | 0.984914i | \(0.444640\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 9.21863 | 1.06448 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.23034 | 0.596052 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.7212 | 1.43125 | 0.715626 | − | 0.698484i | \(-0.246142\pi\) | ||||
0.715626 | + | 0.698484i | \(0.246142\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.18730 | 0.240087 | 0.120044 | − | 0.992769i | \(-0.461697\pi\) | ||||
0.120044 | + | 0.992769i | \(0.461697\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.23034 | −1.00117 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.00110 | 0.965019 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.67821 | −0.389889 | −0.194945 | − | 0.980814i | \(-0.562453\pi\) | ||||
−0.194945 | + | 0.980814i | \(0.562453\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.23034 | 0.548288 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.68991 | 0.901102 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −19.7223 | −2.02347 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.5298 | 1.06914 | 0.534570 | − | 0.845124i | \(-0.320473\pi\) | ||||
0.534570 | + | 0.845124i | \(0.320473\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.98939 | −0.197952 | −0.0989759 | − | 0.995090i | \(-0.531557\pi\) | ||||
−0.0989759 | + | 0.995090i | \(0.531557\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.75223 | 0.763850 | 0.381925 | − | 0.924193i | \(-0.375261\pi\) | ||||
0.381925 | + | 0.924193i | \(0.375261\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −19.7223 | −1.92470 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.27337 | −0.799817 | −0.399909 | − | 0.916555i | \(-0.630958\pi\) | ||||
−0.399909 | + | 0.916555i | \(0.630958\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.1495 | 1.35528 | 0.677638 | − | 0.735396i | \(-0.263004\pi\) | ||||
0.677638 | + | 0.735396i | \(0.263004\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.26167 | −0.309584 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.7106 | −1.38386 | −0.691930 | − | 0.721964i | \(-0.743239\pi\) | ||||
−0.691930 | + | 0.721964i | \(0.743239\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.0947 | 0.941340 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 12.8032 | 1.17367 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.58456 | 0.774044 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 15.9074 | 1.42281 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.2745 | −1.00045 | −0.500224 | − | 0.865896i | \(-0.666749\pi\) | ||||
−0.500224 | + | 0.865896i | \(0.666749\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.447871 | 0.0394329 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.16912 | 0.801110 | 0.400555 | − | 0.916273i | \(-0.368817\pi\) | ||||
0.400555 | + | 0.916273i | \(0.368817\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 27.3564 | 2.37210 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.77076 | 0.324535 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.94635 | −0.251724 | −0.125862 | − | 0.992048i | \(-0.540170\pi\) | ||||
−0.125862 | + | 0.992048i | \(0.540170\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.70954 | 0.823553 | 0.411776 | − | 0.911285i | \(-0.364909\pi\) | ||||
0.411776 | + | 0.911285i | \(0.364909\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −11.4490 | −0.964177 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.00000 | 0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 33.9410 | 2.81864 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 20.3564 | 1.67897 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.93878 | 0.814217 | 0.407108 | − | 0.913380i | \(-0.366537\pi\) | ||||
0.407108 | + | 0.913380i | \(0.366537\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 23.6910 | 1.92795 | 0.963973 | − | 0.265998i | \(-0.0857016\pi\) | ||||
0.963973 | + | 0.265998i | \(0.0857016\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.44787 | −0.197899 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 32.7676 | 2.63195 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.59626 | 0.287013 | 0.143507 | − | 0.989649i | \(-0.454162\pi\) | ||||
0.143507 | + | 0.989649i | \(0.454162\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.435071 | 0.0345034 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −14.0022 | −1.10353 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.40483 | 0.423339 | 0.211670 | − | 0.977341i | \(-0.432110\pi\) | ||||
0.211670 | + | 0.977341i | \(0.432110\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.77076 | −0.293553 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.62237 | −0.357690 | −0.178845 | − | 0.983877i | \(-0.557236\pi\) | ||||
−0.178845 | + | 0.983877i | \(0.557236\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.23034 | −0.399974 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −15.1585 | −1.15248 | −0.576240 | − | 0.817280i | \(-0.695481\pi\) | ||||
−0.576240 | + | 0.817280i | \(0.695481\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −48.2165 | −3.64483 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.2500 | 0.770435 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −22.0335 | −1.64686 | −0.823432 | − | 0.567416i | \(-0.807943\pi\) | ||||
−0.823432 | + | 0.567416i | \(0.807943\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.403737 | 0.0300095 | 0.0150048 | − | 0.999887i | \(-0.495224\pi\) | ||||
0.0150048 | + | 0.999887i | \(0.495224\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −13.4490 | −0.994176 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −12.2990 | −0.904239 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.44787 | 0.179006 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.23034 | −0.380451 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.60419 | −0.550220 | −0.275110 | − | 0.961413i | \(-0.588714\pi\) | ||||
−0.275110 | + | 0.961413i | \(0.588714\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.01963 | 0.217358 | 0.108679 | − | 0.994077i | \(-0.465338\pi\) | ||||
0.108679 | + | 0.994077i | \(0.465338\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.77076 | −0.270030 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 24.0634 | 1.71445 | 0.857224 | − | 0.514945i | \(-0.172187\pi\) | ||||
0.857224 | + | 0.514945i | \(0.172187\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.64578 | −0.187554 | −0.0937771 | − | 0.995593i | \(-0.529894\pi\) | ||||
−0.0937771 | + | 0.995593i | \(0.529894\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.33569 | 0.517420 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −47.0788 | −3.30428 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 32.3703 | 2.26084 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.67711 | 0.186072 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.23034 | 0.361790 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 25.8904 | 1.78237 | 0.891183 | − | 0.453644i | \(-0.149876\pi\) | ||||
0.891183 | + | 0.453644i | \(0.149876\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 13.2617 | 0.908675 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.68882 | 0.115176 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −45.4512 | −3.08543 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.95696 | 0.199813 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.44787 | 0.164662 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.6717 | 1.04946 | 0.524728 | − | 0.851270i | \(-0.324167\pi\) | ||||
0.524728 | + | 0.851270i | \(0.324167\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 9.21863 | 0.614575 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.2069 | −0.743830 | −0.371915 | − | 0.928267i | \(-0.621299\pi\) | ||||
−0.371915 | + | 0.928267i | \(0.621299\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.5788 | 1.09556 | 0.547780 | − | 0.836623i | \(-0.315473\pi\) | ||||
0.547780 | + | 0.836623i | \(0.315473\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.23034 | 0.344131 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.43836 | −0.356279 | −0.178139 | − | 0.984005i | \(-0.557008\pi\) | ||||
−0.178139 | + | 0.984005i | \(0.557008\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −43.1713 | −2.81619 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 12.7212 | 0.826334 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 23.7537 | 1.53650 | 0.768249 | − | 0.640151i | \(-0.221128\pi\) | ||||
0.768249 | + | 0.640151i | \(0.221128\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.3330 | −1.24535 | −0.622674 | − | 0.782481i | \(-0.713954\pi\) | ||||
−0.622674 | + | 0.782481i | \(0.713954\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 76.7592 | 4.90396 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.23034 | 0.332798 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.18730 | 0.138614 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.6276 | −0.860166 | −0.430083 | − | 0.902789i | \(-0.641516\pi\) | ||||
−0.430083 | + | 0.902789i | \(0.641516\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.67711 | −0.168309 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −9.23034 | −0.578026 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.1064 | −0.692801 | −0.346401 | − | 0.938087i | \(-0.612596\pi\) | ||||
−0.346401 | + | 0.938087i | \(0.612596\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 17.0596 | 1.06003 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.00110 | 0.557154 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.647969 | 0.0399555 | 0.0199778 | − | 0.999800i | \(-0.493640\pi\) | ||||
0.0199778 | + | 0.999800i | \(0.493640\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.64055 | 0.100778 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.67821 | −0.225103 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.65101 | 0.588432 | 0.294216 | − | 0.955739i | \(-0.404941\pi\) | ||||
0.294216 | + | 0.955739i | \(0.404941\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −21.8783 | −1.32901 | −0.664506 | − | 0.747283i | \(-0.731358\pi\) | ||||
−0.664506 | + | 0.747283i | \(0.731358\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.23034 | 0.316554 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −9.21863 | −0.555904 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −29.3820 | −1.76539 | −0.882697 | − | 0.469942i | \(-0.844275\pi\) | ||||
−0.882697 | + | 0.469942i | \(0.844275\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.68991 | 0.520251 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.6336 | 1.11159 | 0.555793 | − | 0.831321i | \(-0.312415\pi\) | ||||
0.555793 | + | 0.831321i | \(0.312415\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.43617 | 0.323147 | 0.161573 | − | 0.986861i | \(-0.448343\pi\) | ||||
0.161573 | + | 0.986861i | \(0.448343\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −19.7223 | −1.16825 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −44.9001 | −2.65037 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.0079 | −0.647525 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.5298 | 0.617269 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 18.7719 | 1.09666 | 0.548332 | − | 0.836261i | \(-0.315263\pi\) | ||||
0.548332 | + | 0.836261i | \(0.315263\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 38.6502 | 2.25030 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.67711 | −0.154821 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.34252 | −0.135021 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.98939 | −0.114288 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −50.7128 | −2.90381 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.5611 | −0.716903 | −0.358451 | − | 0.933548i | \(-0.616695\pi\) | ||||
−0.358451 | + | 0.933548i | \(0.616695\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.75223 | 0.441009 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.65370 | −0.263887 | −0.131944 | − | 0.991257i | \(-0.542122\pi\) | ||||
−0.131944 | + | 0.991257i | \(0.542122\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −24.6815 | −1.39508 | −0.697540 | − | 0.716546i | \(-0.745722\pi\) | ||||
−0.697540 | + | 0.716546i | \(0.745722\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −19.7223 | −1.11123 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 19.9516 | 1.12059 | 0.560296 | − | 0.828292i | \(-0.310687\pi\) | ||||
0.560296 | + | 0.828292i | \(0.310687\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.00110 | −0.503965 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.27337 | −0.461775 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.8032 | 0.712389 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9.21863 | −0.511358 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 14.1495 | 0.782468 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 59.8819 | 3.30140 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.30058 | −0.346311 | −0.173155 | − | 0.984895i | \(-0.555396\pi\) | ||||
−0.173155 | + | 0.984895i | \(0.555396\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.26167 | −0.178738 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 27.6611 | 1.51129 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.75003 | −0.422171 | −0.211086 | − | 0.977468i | \(-0.567700\pi\) | ||||
−0.211086 | + | 0.977468i | \(0.567700\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −14.7106 | −0.798972 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.68991 | −0.470585 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −69.8585 | −3.77201 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 10.0947 | 0.543483 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 21.8084 | 1.17074 | 0.585369 | − | 0.810767i | \(-0.300950\pi\) | ||||
0.585369 | + | 0.810767i | \(0.300950\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.8798 | 1.27825 | 0.639127 | − | 0.769101i | \(-0.279296\pi\) | ||||
0.639127 | + | 0.769101i | \(0.279296\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 23.3123 | 1.24079 | 0.620394 | − | 0.784291i | \(-0.286973\pi\) | ||||
0.620394 | + | 0.784291i | \(0.286973\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 50.0066 | 2.65407 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 12.8032 | 0.677617 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7.62834 | −0.402608 | −0.201304 | − | 0.979529i | \(-0.564518\pi\) | ||||
−0.201304 | + | 0.979529i | \(0.564518\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.35642 | 0.439811 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.1500 | 0.583617 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.85648 | −0.357906 | −0.178953 | − | 0.983858i | \(-0.557271\pi\) | ||||
−0.178953 | + | 0.983858i | \(0.557271\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.58456 | 0.446894 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.27557 | −0.118142 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.72663 | −0.503626 | −0.251813 | − | 0.967776i | \(-0.581027\pi\) | ||||
−0.251813 | + | 0.967776i | \(0.581027\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 15.9074 | 0.821457 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.00110 | −0.463580 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −31.7431 | −1.63053 | −0.815266 | − | 0.579087i | \(-0.803409\pi\) | ||||
−0.815266 | + | 0.579087i | \(0.803409\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11.2745 | −0.577609 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −23.1086 | −1.18080 | −0.590398 | − | 0.807112i | \(-0.701029\pi\) | ||||
−0.590398 | + | 0.807112i | \(0.701029\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 19.7223 | 1.00514 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.447871 | 0.0227666 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −16.1117 | −0.816895 | −0.408447 | − | 0.912782i | \(-0.633930\pi\) | ||||
−0.408447 | + | 0.912782i | \(0.633930\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.55322 | −0.331411 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.16912 | 0.462521 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 47.9688 | 2.41357 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.44678 | 0.373743 | 0.186871 | − | 0.982384i | \(-0.440165\pi\) | ||||
0.186871 | + | 0.982384i | \(0.440165\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 27.3564 | 1.36953 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.6483 | −0.781440 | −0.390720 | − | 0.920510i | \(-0.627774\pi\) | ||||
−0.390720 | + | 0.920510i | \(0.627774\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.68991 | −0.432875 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.77076 | 0.187371 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.26167 | 0.161675 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.4176 | −0.861247 | −0.430623 | − | 0.902532i | \(-0.641706\pi\) | ||||
−0.430623 | + | 0.902532i | \(0.641706\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.94635 | −0.145333 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −53.6108 | −2.63801 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.24777 | 0.404867 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.70954 | 0.475478 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.84404 | −0.0900871 | −0.0450435 | − | 0.998985i | \(-0.514343\pi\) | ||||
−0.0450435 | + | 0.998985i | \(0.514343\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.0438 | −0.733189 | −0.366595 | − | 0.930381i | \(-0.619476\pi\) | ||||
−0.366595 | + | 0.930381i | \(0.619476\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −11.4490 | −0.556668 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −22.5660 | −1.09461 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 70.3426 | 3.40412 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.00000 | 0.0482805 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.08608 | −0.293156 | −0.146578 | − | 0.989199i | \(-0.546826\pi\) | ||||
−0.146578 | + | 0.989199i | \(0.546826\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 33.6298 | 1.61614 | 0.808072 | − | 0.589083i | \(-0.200511\pi\) | ||||
0.808072 | + | 0.589083i | \(0.200511\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 33.9410 | 1.62735 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −14.0022 | −0.669816 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 33.3224 | 1.59039 | 0.795196 | − | 0.606353i | \(-0.207368\pi\) | ||||
0.795196 | + | 0.606353i | \(0.207368\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 20.3564 | 0.969353 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −41.2491 | −1.95980 | −0.979902 | − | 0.199477i | \(-0.936076\pi\) | ||||
−0.979902 | + | 0.199477i | \(0.936076\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −13.8696 | −0.657484 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 9.93878 | 0.470088 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −13.9581 | −0.658721 | −0.329361 | − | 0.944204i | \(-0.606833\pi\) | ||||
−0.329361 | + | 0.944204i | \(0.606833\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.58456 | −0.404231 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 23.6910 | 1.11310 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 19.7223 | 0.924598 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.87756 | −0.274941 | −0.137470 | − | 0.990506i | \(-0.543897\pi\) | ||||
−0.137470 | + | 0.990506i | \(0.543897\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.44787 | −0.114257 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16.9592 | 0.789867 | 0.394933 | − | 0.918710i | \(-0.370768\pi\) | ||||
0.394933 | + | 0.918710i | \(0.370768\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.34739 | −0.294988 | −0.147494 | − | 0.989063i | \(-0.547121\pi\) | ||||
−0.147494 | + | 0.989063i | \(0.547121\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 32.7676 | 1.51956 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.02830 | 0.417780 | 0.208890 | − | 0.977939i | \(-0.433015\pi\) | ||||
0.208890 | + | 0.977939i | \(0.433015\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −38.3681 | −1.77168 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.59626 | 0.165707 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.447871 | −0.0205932 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −48.2165 | −2.21233 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.435071 | 0.0199205 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 29.7144 | 1.35769 | 0.678843 | − | 0.734283i | \(-0.262482\pi\) | ||||
0.678843 | + | 0.734283i | \(0.262482\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.26167 | 0.148719 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −14.0022 | −0.637122 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 39.7054 | 1.80293 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 30.4101 | 1.37801 | 0.689006 | − | 0.724756i | \(-0.258047\pi\) | ||||
0.689006 | + | 0.724756i | \(0.258047\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.40483 | 0.244415 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −28.4074 | −1.28201 | −0.641004 | − | 0.767538i | \(-0.721482\pi\) | ||||
−0.641004 | + | 0.767538i | \(0.721482\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −22.0335 | −0.992340 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.77076 | −0.169483 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −69.3630 | −3.11136 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −28.1846 | −1.26172 | −0.630858 | − | 0.775898i | \(-0.717297\pi\) | ||||
−0.630858 | + | 0.775898i | \(0.717297\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.62237 | −0.206512 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 34.6246 | 1.54383 | 0.771916 | − | 0.635724i | \(-0.219298\pi\) | ||||
0.771916 | + | 0.635724i | \(0.219298\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.50152 | −0.333813 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11.9984 | −0.531820 | −0.265910 | − | 0.963998i | \(-0.585672\pi\) | ||||
−0.265910 | + | 0.963998i | \(0.585672\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15.4659 | −0.684171 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.23034 | −0.230925 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 29.2318 | 1.28811 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.4490 | 0.503525 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −15.1585 | −0.665385 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.12986 | −0.399986 | −0.199993 | − | 0.979797i | \(-0.564092\pi\) | ||||
−0.199993 | + | 0.979797i | \(0.564092\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −24.9946 | −1.09294 | −0.546469 | − | 0.837479i | \(-0.684028\pi\) | ||||
−0.546469 | + | 0.837479i | \(0.684028\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −48.2165 | −2.10434 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −21.2718 | −0.926614 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.8331 | −0.688395 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.2500 | 0.444811 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.58456 | −0.371839 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −31.1969 | −1.34876 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −22.0335 | −0.950817 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −20.3564 | −0.876813 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.3278 | −0.615999 | −0.308000 | − | 0.951386i | \(-0.599660\pi\) | ||||
−0.308000 | + | 0.951386i | \(0.599660\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.403737 | 0.0173260 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 53.3543 | 2.28545 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.16279 | −0.0497174 | −0.0248587 | − | 0.999691i | \(-0.507914\pi\) | ||||
−0.0248587 | + | 0.999691i | \(0.507914\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −13.4490 | −0.573988 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −47.0788 | −2.00562 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −66.5364 | −2.82942 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −12.2990 | −0.522062 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.01440 | −0.0853529 | −0.0426764 | − | 0.999089i | \(-0.513588\pi\) | ||||
−0.0426764 | + | 0.999089i | \(0.513588\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.447871 | −0.0189429 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.44787 | 0.103349 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −12.6692 | −0.533943 | −0.266971 | − | 0.963704i | \(-0.586023\pi\) | ||||
−0.266971 | + | 0.963704i | \(0.586023\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −55.4703 | −2.33365 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5.23034 | −0.219653 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.52872 | −0.147932 | −0.0739658 | − | 0.997261i | \(-0.523566\pi\) | ||||
−0.0739658 | + | 0.997261i | \(0.523566\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.85953 | 0.370760 | 0.185380 | − | 0.982667i | \(-0.440648\pi\) | ||||
0.185380 | + | 0.982667i | \(0.440648\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.60419 | −0.317670 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 24.6793 | 1.02920 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −28.0436 | −1.16747 | −0.583736 | − | 0.811943i | \(-0.698410\pi\) | ||||
−0.583736 | + | 0.811943i | \(0.698410\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.01963 | 0.125492 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11.4403 | −0.474624 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.435071 | −0.0180188 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.77076 | −0.155902 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.48189 | −0.267536 | −0.133768 | − | 0.991013i | \(-0.542708\pi\) | ||||
−0.133768 | + | 0.991013i | \(0.542708\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −45.4512 | −1.87278 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 24.0634 | 0.989836 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11.4569 | 0.470478 | 0.235239 | − | 0.971938i | \(-0.424413\pi\) | ||||
0.235239 | + | 0.971938i | \(0.424413\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 48.2778 | 1.97920 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.64578 | −0.108284 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.35945 | −0.259840 | −0.129920 | − | 0.991524i | \(-0.541472\pi\) | ||||
−0.129920 | + | 0.991524i | \(0.541472\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 28.8511 | 1.17686 | 0.588431 | − | 0.808548i | \(-0.299746\pi\) | ||||
0.588431 | + | 0.808548i | \(0.299746\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.33569 | 0.298732 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.77076 | 0.153303 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20.3553 | 0.826197 | 0.413098 | − | 0.910686i | \(-0.364447\pi\) | ||||
0.413098 | + | 0.910686i | \(0.364447\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −47.0788 | −1.90773 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11.4490 | 0.463176 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.93659 | −0.320556 | −0.160278 | − | 0.987072i | \(-0.551239\pi\) | ||||
−0.160278 | + | 0.987072i | \(0.551239\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 32.3703 | 1.30530 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 32.2592 | 1.29871 | 0.649354 | − | 0.760486i | \(-0.275039\pi\) | ||||
0.649354 | + | 0.760486i | \(0.275039\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 46.3518 | 1.86304 | 0.931518 | − | 0.363696i | \(-0.118485\pi\) | ||||
0.931518 | + | 0.363696i | \(0.118485\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.67711 | 0.107429 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 19.2383 | 0.770765 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13.8900 | 0.555600 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.23034 | 0.208880 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.98415 | 0.318349 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −39.4582 | −1.57081 | −0.785404 | − | 0.618984i | \(-0.787545\pi\) | ||||
−0.785404 | + | 0.618984i | \(0.787545\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 25.8904 | 1.02905 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −42.5133 | −1.68709 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −20.3564 | −0.806551 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 13.2617 | 0.524624 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.956219 | −0.0377684 | −0.0188842 | − | 0.999822i | \(-0.506011\pi\) | ||||
−0.0188842 | + | 0.999822i | \(0.506011\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 25.0260 | 0.986927 | 0.493464 | − | 0.869766i | \(-0.335731\pi\) | ||||
0.493464 | + | 0.869766i | \(0.335731\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.68882 | 0.0664971 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.7704 | 0.502056 | 0.251028 | − | 0.967980i | \(-0.419231\pi\) | ||||
0.251028 | + | 0.967980i | \(0.419231\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.2500 | −0.402346 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −45.4512 | −1.78137 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 20.7084 | 0.810384 | 0.405192 | − | 0.914232i | \(-0.367205\pi\) | ||||
0.405192 | + | 0.914232i | \(0.367205\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 34.5745 | 1.35094 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.95696 | 0.115362 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.3659 | −0.481708 | −0.240854 | − | 0.970561i | \(-0.577428\pi\) | ||||
−0.240854 | + | 0.970561i | \(0.577428\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.60419 | 0.373560 | 0.186780 | − | 0.982402i | \(-0.440195\pi\) | ||||
0.186780 | + | 0.982402i | \(0.440195\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.44787 | 0.0950675 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 103.154 | 4.00016 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 24.0969 | 0.933037 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 15.6717 | 0.605904 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 13.4490 | 0.519192 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −40.8681 | −1.57535 | −0.787674 | − | 0.616093i | \(-0.788715\pi\) | ||||
−0.787674 | + | 0.616093i | \(0.788715\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 9.21863 | 0.354825 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15.0033 | 0.576623 | 0.288312 | − | 0.957537i | \(-0.406906\pi\) | ||||
0.288312 | + | 0.957537i | \(0.406906\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −55.0745 | −2.11356 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11.2069 | −0.429450 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 47.0532 | 1.80044 | 0.900219 | − | 0.435436i | \(-0.143406\pi\) | ||||
0.900219 | + | 0.435436i | \(0.143406\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11.1100 | −0.424491 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16.5788 | 0.632522 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.435071 | −0.0165749 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.6337 | 0.404526 | 0.202263 | − | 0.979331i | \(-0.435170\pi\) | ||||
0.202263 | + | 0.979331i | \(0.435170\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.23034 | 0.198684 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 36.6124 | 1.38879 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −21.0139 | −0.795958 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.43836 | −0.205698 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.112536 | 0.00425043 | 0.00212522 | − | 0.999998i | \(-0.499324\pi\) | ||||
0.00212522 | + | 0.999998i | \(0.499324\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17.0596 | 0.643416 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −43.1713 | −1.62593 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10.4052 | 0.391327 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.22460 | −0.271326 | −0.135663 | − | 0.990755i | \(-0.543316\pi\) | ||||
−0.135663 | + | 0.990755i | \(0.543316\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.7212 | 0.477084 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 23.2639 | 0.871238 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.77076 | 0.141018 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 23.7537 | 0.887097 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11.2681 | 0.420231 | 0.210115 | − | 0.977677i | \(-0.432616\pi\) | ||||
0.210115 | + | 0.977677i | \(0.432616\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −40.5467 | −1.51004 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −19.3330 | −0.719002 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 82.9778 | 3.08172 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.7470 | 0.398584 | 0.199292 | − | 0.979940i | \(-0.436136\pi\) | ||||
0.199292 | + | 0.979940i | \(0.436136\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.09633 | −0.0405493 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.4251 | 0.606673 | 0.303337 | − | 0.952883i | \(-0.401899\pi\) | ||||
0.303337 | + | 0.952883i | \(0.401899\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 76.7592 | 2.83130 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.33569 | −0.270214 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.80589 | −0.213573 | −0.106786 | − | 0.994282i | \(-0.534056\pi\) | ||||
−0.106786 | + | 0.994282i | \(0.534056\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.23034 | 0.192141 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.16693 | −0.262929 | −0.131464 | − | 0.991321i | \(-0.541968\pi\) | ||||
−0.131464 | + | 0.991321i | \(0.541968\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 37.4768 | 1.37304 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.18730 | 0.0800290 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 43.2725 | 1.58114 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.17131 | −0.115723 | −0.0578614 | − | 0.998325i | \(-0.518428\pi\) | ||||
−0.0578614 | + | 0.998325i | \(0.518428\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −13.6276 | −0.496617 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 89.3331 | 3.25116 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.11960 | 0.222421 | 0.111210 | − | 0.993797i | \(-0.464527\pi\) | ||||
0.111210 | + | 0.993797i | \(0.464527\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.67711 | −0.0971730 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28.6728 | 1.03939 | 0.519695 | − | 0.854352i | \(-0.326046\pi\) | ||||
0.519695 | + | 0.854352i | \(0.326046\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −74.0066 | −2.67922 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −9.23034 | −0.333724 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −10.2500 | −0.370105 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 38.3660 | 1.38351 | 0.691757 | − | 0.722130i | \(-0.256837\pi\) | ||||
0.691757 | + | 0.722130i | \(0.256837\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.1064 | −0.399989 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 29.9794 | 1.07828 | 0.539142 | − | 0.842215i | \(-0.318749\pi\) | ||||
0.539142 | + | 0.842215i | \(0.318749\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 80.1091 | 2.87760 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 17.0596 | 0.612011 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −44.9001 | −1.60871 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.2617 | −0.474540 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.00110 | 0.321673 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 13.5606 | 0.484000 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 46.1049 | 1.64346 | 0.821730 | − | 0.569876i | \(-0.193009\pi\) | ||||
0.821730 | + | 0.569876i | \(0.193009\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.647969 | 0.0230683 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 76.9416 | 2.73573 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 13.4490 | 0.477587 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.64055 | 0.0581842 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 35.7288 | 1.26558 | 0.632790 | − | 0.774324i | \(-0.281910\pi\) | ||||
0.632790 | + | 0.774324i | \(0.281910\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 28.0256 | 0.991474 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.67821 | −0.129963 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.95696 | −0.104349 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −52.7989 | −1.86092 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9.65101 | 0.339732 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −14.9690 | −0.526283 | −0.263141 | − | 0.964757i | \(-0.584759\pi\) | ||||
−0.263141 | + | 0.964757i | \(0.584759\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −28.4358 | −0.998516 | −0.499258 | − | 0.866453i | \(-0.666394\pi\) | ||||
−0.499258 | + | 0.866453i | \(0.666394\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −21.8783 | −0.767306 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 20.3803 | 0.713892 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.34252 | −0.0819543 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.23034 | 0.182763 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −50.0156 | −1.74556 | −0.872778 | − | 0.488117i | \(-0.837684\pi\) | ||||
−0.872778 | + | 0.488117i | \(0.837684\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.8489 | 0.726748 | 0.363374 | − | 0.931643i | \(-0.381625\pi\) | ||||
0.363374 | + | 0.931643i | \(0.381625\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −9.21863 | −0.320952 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.18656 | 0.145581 | 0.0727904 | − | 0.997347i | \(-0.476810\pi\) | ||||
0.0727904 | + | 0.997347i | \(0.476810\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.61933 | −0.264630 | −0.132315 | − | 0.991208i | \(-0.542241\pi\) | ||||
−0.132315 | + | 0.991208i | \(0.542241\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −29.3820 | −1.01925 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −49.8299 | −1.72650 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −17.4298 | −0.603185 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.68991 | 0.300367 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 23.3776 | 0.807085 | 0.403543 | − | 0.914961i | \(-0.367779\pi\) | ||||
0.403543 | + | 0.914961i | \(0.367779\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 52.0197 | 1.79378 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 18.6336 | 0.641774 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.77076 | 0.129718 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.23034 | −0.179716 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.43617 | 0.186569 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.73185 | −0.299324 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12.0393 | 0.412216 | 0.206108 | − | 0.978529i | \(-0.433920\pi\) | ||||
0.206108 | + | 0.978529i | \(0.433920\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −19.7223 | −0.674490 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −24.2307 | −0.827705 | −0.413852 | − | 0.910344i | \(-0.635817\pi\) | ||||
−0.413852 | + | 0.910344i | \(0.635817\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 40.7150 | 1.38918 | 0.694589 | − | 0.719406i | \(-0.255586\pi\) | ||||
0.694589 | + | 0.719406i | \(0.255586\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −44.9001 | −1.53019 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −41.2106 | −1.40282 | −0.701412 | − | 0.712756i | \(-0.747447\pi\) | ||||
−0.701412 | + | 0.712756i | \(0.747447\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −57.1591 | −1.94347 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −11.0079 | −0.373849 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12.7212 | −0.431539 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.33569 | −0.248560 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 10.5298 | 0.356380 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −83.2013 | −2.81272 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.39885 | −0.0472358 | −0.0236179 | − | 0.999721i | \(-0.507519\pi\) | ||||
−0.0236179 | + | 0.999721i | \(0.507519\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 18.7719 | 0.633159 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −32.6660 | −1.10055 | −0.550273 | − | 0.834985i | \(-0.685476\pi\) | ||||
−0.550273 | + | 0.834985i | \(0.685476\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −20.4841 | −0.689344 | −0.344672 | − | 0.938723i | \(-0.612010\pi\) | ||||
−0.344672 | + | 0.938723i | \(0.612010\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 38.6502 | 1.29921 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 19.4021 | 0.651460 | 0.325730 | − | 0.945463i | \(-0.394390\pi\) | ||||
0.325730 | + | 0.945463i | \(0.394390\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 58.9693 | 1.97777 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 59.8819 | 2.00387 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −83.0831 | −2.77716 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.67711 | −0.0893861 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 78.2187 | 2.60874 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.06500 | −0.0354802 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.34252 | −0.0779541 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.52239 | 0.0506061 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19.3520 | −0.642574 | −0.321287 | − | 0.946982i | \(-0.604115\pi\) | ||||
−0.321287 | + | 0.946982i | \(0.604115\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.98939 | −0.0659840 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19.8873 | 0.658896 | 0.329448 | − | 0.944174i | \(-0.393137\pi\) | ||||
0.329448 | + | 0.944174i | \(0.393137\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.18730 | −0.0723890 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −50.7128 | −1.67651 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −47.9576 | −1.58370 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 39.3001 | 1.29639 | 0.648195 | − | 0.761474i | \(-0.275524\pi\) | ||||
0.648195 | + | 0.761474i | \(0.275524\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12.5611 | −0.413904 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −13.2617 | −0.436513 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −30.0681 | −0.988634 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7.75223 | 0.254617 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 19.0973 | 0.626562 | 0.313281 | − | 0.949661i | \(-0.398572\pi\) | ||||
0.313281 | + | 0.949661i | \(0.398572\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −106.471 | −3.48944 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4.65370 | −0.152355 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 9.23034 | 0.301864 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 27.3243 | 0.892647 | 0.446324 | − | 0.894872i | \(-0.352733\pi\) | ||||
0.446324 | + | 0.894872i | \(0.352733\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −24.6815 | −0.805450 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −34.1283 | −1.11255 | −0.556275 | − | 0.830998i | \(-0.687770\pi\) | ||||
−0.556275 | + | 0.830998i | \(0.687770\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 22.9818 | 0.748391 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −19.7223 | −0.641568 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.04806 | 0.0340575 | 0.0170287 | − | 0.999855i | \(-0.494579\pi\) | ||||
0.0170287 | + | 0.999855i | \(0.494579\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.95696 | −0.0959870 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 19.9516 | 0.646974 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 40.0085 | 1.29600 | 0.648002 | − | 0.761639i | \(-0.275605\pi\) | ||||
0.648002 | + | 0.761639i | \(0.275605\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −28.6736 | −0.927855 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −9.00110 | −0.290964 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 15.4104 | 0.497628 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 44.5146 | 1.43595 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8.27337 | −0.266606 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 11.3863 | 0.366538 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.38127 | 0.0444188 | 0.0222094 | − | 0.999753i | \(-0.492930\pi\) | ||||
0.0222094 | + | 0.999753i | \(0.492930\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 12.8032 | 0.411298 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −24.8432 | −0.797256 | −0.398628 | − | 0.917113i | \(-0.630514\pi\) | ||||
−0.398628 | + | 0.917113i | \(0.630514\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −50.7842 | −1.62807 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −9.21863 | −0.295232 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 26.2613 | 0.840174 | 0.420087 | − | 0.907484i | \(-0.362000\pi\) | ||||
0.420087 | + | 0.907484i | \(0.362000\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.67821 | 0.117556 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.1495 | 0.451758 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −33.7159 | −1.07537 | −0.537685 | − | 0.843146i | \(-0.680701\pi\) | ||||
−0.537685 | + | 0.843146i | \(0.680701\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 90.7373 | 2.89113 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 59.8819 | 1.90606 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.19900 | 0.0381260 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.37982 | −0.0438316 | −0.0219158 | − | 0.999760i | \(-0.506977\pi\) | ||||
−0.0219158 | + | 0.999760i | \(0.506977\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6.30058 | −0.199943 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.97659 | −0.316279 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −29.7137 | −0.941042 | −0.470521 | − | 0.882389i | \(-0.655934\pi\) | ||||
−0.470521 | + | 0.882389i | \(0.655934\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.26167 | −0.103195 |
(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 | 6864.2.a.cc.1.4 | 4 | ||
4.3 | odd | 2 | 3432.2.a.t.1.4 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3432.2.a.t.1.4 | ✓ | 4 | 4.3 | odd | 2 | ||
6864.2.a.cc.1.4 | 4 | 1.1 | even | 1 | trivial |