Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3568,2,Mod(1,3568)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3568, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("3568.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3568 = 2^{4} \cdot 223 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3568.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: | \(28.4906234412\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 3x^{6} - 11x^{5} + 24x^{4} + 38x^{3} - 46x^{2} - 36x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 892) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.80512\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3568.1 |
$q$-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 | ||||||||
\(3\) | −2.80512 | −1.61954 | −0.809769 | − | 0.586749i | \(-0.800408\pi\) | ||||
−0.809769 | + | 0.586749i | \(0.800408\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.13650 | −1.84990 | −0.924950 | − | 0.380088i | \(-0.875894\pi\) | ||||
−0.924950 | + | 0.380088i | \(0.875894\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.96968 | 0.744467 | 0.372234 | − | 0.928139i | \(-0.378592\pi\) | ||||
0.372234 | + | 0.928139i | \(0.378592\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.86871 | 1.62290 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.47938 | 0.747562 | 0.373781 | − | 0.927517i | \(-0.378061\pi\) | ||||
0.373781 | + | 0.927517i | \(0.378061\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.26095 | −1.18177 | −0.590887 | − | 0.806754i | \(-0.701222\pi\) | ||||
−0.590887 | + | 0.806754i | \(0.701222\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 11.6034 | 2.99598 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.11132 | −0.754606 | −0.377303 | − | 0.926090i | \(-0.623149\pi\) | ||||
−0.377303 | + | 0.926090i | \(0.623149\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.960395 | 0.220330 | 0.110165 | − | 0.993913i | \(-0.464862\pi\) | ||||
0.110165 | + | 0.993913i | \(0.464862\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.52518 | −1.20569 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.32574 | 0.901979 | 0.450989 | − | 0.892529i | \(-0.351071\pi\) | ||||
0.450989 | + | 0.892529i | \(0.351071\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 12.1107 | 2.42213 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.24196 | −1.00882 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.724125 | −0.134467 | −0.0672334 | − | 0.997737i | \(-0.521417\pi\) | ||||
−0.0672334 | + | 0.997737i | \(0.521417\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.48409 | −1.70339 | −0.851697 | − | 0.524035i | \(-0.824426\pi\) | ||||
−0.851697 | + | 0.524035i | \(0.824426\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.95497 | −1.21071 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −8.14757 | −1.37719 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.3400 | −1.69989 | −0.849943 | − | 0.526874i | \(-0.823364\pi\) | ||||
−0.849943 | + | 0.526874i | \(0.823364\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 11.9525 | 1.91393 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.835446 | −0.130475 | −0.0652374 | − | 0.997870i | \(-0.520780\pi\) | ||||
−0.0652374 | + | 0.997870i | \(0.520780\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.60510 | −0.854770 | −0.427385 | − | 0.904070i | \(-0.640565\pi\) | ||||
−0.427385 | + | 0.904070i | \(0.640565\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −20.1394 | −3.00221 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.42708 | 0.791621 | 0.395811 | − | 0.918332i | \(-0.370464\pi\) | ||||
0.395811 | + | 0.918332i | \(0.370464\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.12038 | −0.445768 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.72764 | 1.22211 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.22884 | −0.718236 | −0.359118 | − | 0.933292i | \(-0.616922\pi\) | ||||
−0.359118 | + | 0.933292i | \(0.616922\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −10.2560 | −1.38292 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.69402 | −0.356832 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.73990 | −1.26803 | −0.634014 | − | 0.773322i | \(-0.718594\pi\) | ||||
−0.634014 | + | 0.773322i | \(0.718594\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.76465 | 0.353978 | 0.176989 | − | 0.984213i | \(-0.443364\pi\) | ||||
0.176989 | + | 0.984213i | \(0.443364\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 9.58978 | 1.20820 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 17.6254 | 2.18617 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.86871 | 0.716977 | 0.358488 | − | 0.933534i | \(-0.383292\pi\) | ||||
0.358488 | + | 0.933534i | \(0.383292\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −12.1342 | −1.46079 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.7387 | −1.51181 | −0.755903 | − | 0.654684i | \(-0.772802\pi\) | ||||
−0.755903 | + | 0.654684i | \(0.772802\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.83460 | 0.565847 | 0.282923 | − | 0.959143i | \(-0.408696\pi\) | ||||
0.282923 | + | 0.959143i | \(0.408696\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −33.9719 | −3.92274 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.88358 | 0.556536 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.83650 | −0.656657 | −0.328329 | − | 0.944564i | \(-0.606485\pi\) | ||||
−0.328329 | + | 0.944564i | \(0.606485\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.0982026 | 0.0109114 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.7751 | 1.51202 | 0.756009 | − | 0.654561i | \(-0.227147\pi\) | ||||
0.756009 | + | 0.654561i | \(0.227147\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.8700 | 1.39595 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.03126 | 0.217774 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.5514 | −1.54244 | −0.771222 | − | 0.636566i | \(-0.780354\pi\) | ||||
−0.771222 | + | 0.636566i | \(0.780354\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.39269 | −0.879793 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 26.6040 | 2.75871 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.97268 | −0.407588 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.44098 | −0.247843 | −0.123922 | − | 0.992292i | \(-0.539547\pi\) | ||||
−0.123922 | + | 0.992292i | \(0.539547\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 12.0714 | 1.21322 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.8875 | 1.58087 | 0.790435 | − | 0.612546i | \(-0.209855\pi\) | ||||
0.790435 | + | 0.612546i | \(0.209855\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.15105 | −0.507548 | −0.253774 | − | 0.967263i | \(-0.581672\pi\) | ||||
−0.253774 | + | 0.967263i | \(0.581672\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 22.8549 | 2.23041 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.0952 | 1.45931 | 0.729656 | − | 0.683814i | \(-0.239680\pi\) | ||||
0.729656 | + | 0.683814i | \(0.239680\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.53963 | −0.530600 | −0.265300 | − | 0.964166i | \(-0.585471\pi\) | ||||
−0.265300 | + | 0.964166i | \(0.585471\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 29.0050 | 2.75303 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 20.0565 | 1.88676 | 0.943380 | − | 0.331714i | \(-0.107627\pi\) | ||||
0.943380 | + | 0.331714i | \(0.107627\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −17.8934 | −1.66857 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −20.7453 | −1.91791 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.12829 | −0.561780 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.85266 | −0.441151 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.34353 | 0.211309 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −29.4133 | −2.63081 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.14943 | 0.456938 | 0.228469 | − | 0.973551i | \(-0.426628\pi\) | ||||
0.228469 | + | 0.973551i | \(0.426628\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 15.7230 | 1.38433 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.72174 | 0.762022 | 0.381011 | − | 0.924570i | \(-0.375576\pi\) | ||||
0.381011 | + | 0.924570i | \(0.375576\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.89167 | 0.164028 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 21.6834 | 1.86621 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.70551 | −0.145711 | −0.0728557 | − | 0.997342i | \(-0.523211\pi\) | ||||
−0.0728557 | + | 0.997342i | \(0.523211\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −22.6104 | −1.91779 | −0.958895 | − | 0.283761i | \(-0.908418\pi\) | ||||
−0.958895 | + | 0.283761i | \(0.908418\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −15.2236 | −1.28206 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −10.5645 | −0.883450 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.99535 | 0.248750 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 8.75304 | 0.721939 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −11.4644 | −0.939198 | −0.469599 | − | 0.882880i | \(-0.655602\pi\) | ||||
−0.469599 | + | 0.882880i | \(0.655602\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.97196 | −0.241855 | −0.120927 | − | 0.992661i | \(-0.538587\pi\) | ||||
−0.120927 | + | 0.992661i | \(0.538587\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −15.1481 | −1.22465 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 39.2310 | 3.15111 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.47361 | 0.516651 | 0.258325 | − | 0.966058i | \(-0.416829\pi\) | ||||
0.258325 | + | 0.966058i | \(0.416829\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 14.6675 | 1.16321 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.52030 | 0.671494 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.3390 | 1.43642 | 0.718209 | − | 0.695828i | \(-0.244962\pi\) | ||||
0.718209 | + | 0.695828i | \(0.244962\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 28.7693 | 2.23969 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.8912 | 1.07493 | 0.537466 | − | 0.843285i | \(-0.319382\pi\) | ||||
0.537466 | + | 0.843285i | \(0.319382\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.15569 | 0.396592 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.67588 | 0.357574 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −24.9181 | −1.89449 | −0.947243 | − | 0.320516i | \(-0.896144\pi\) | ||||
−0.947243 | + | 0.320516i | \(0.896144\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 23.8541 | 1.80320 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 27.3216 | 2.05362 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.97596 | 0.222433 | 0.111217 | − | 0.993796i | \(-0.464525\pi\) | ||||
0.111217 | + | 0.993796i | \(0.464525\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.6526 | 1.53510 | 0.767549 | − | 0.640990i | \(-0.221476\pi\) | ||||
0.767549 | + | 0.640990i | \(0.221476\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.75519 | −0.573280 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 42.7715 | 3.14462 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.71416 | −0.564115 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −10.3250 | −0.751030 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.65220 | −0.191907 | −0.0959534 | − | 0.995386i | \(-0.530590\pi\) | ||||
−0.0959534 | + | 0.995386i | \(0.530590\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.64291 | 0.622130 | 0.311065 | − | 0.950389i | \(-0.399314\pi\) | ||||
0.311065 | + | 0.950389i | \(0.399314\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −49.4415 | −3.54058 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.712373 | 0.0507544 | 0.0253772 | − | 0.999678i | \(-0.491921\pi\) | ||||
0.0253772 | + | 0.999678i | \(0.491921\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.4503 | −0.740799 | −0.370399 | − | 0.928873i | \(-0.620779\pi\) | ||||
−0.370399 | + | 0.928873i | \(0.620779\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −16.4624 | −1.16117 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.42629 | −0.100106 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.45583 | 0.241365 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 21.0608 | 1.46382 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.38119 | 0.164710 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.9273 | 1.50954 | 0.754769 | − | 0.655991i | \(-0.227749\pi\) | ||||
0.754769 | + | 0.655991i | \(0.227749\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 35.7336 | 2.44843 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 23.1855 | 1.58124 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −18.6806 | −1.26812 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −13.5616 | −0.916410 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13.2572 | 0.891775 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.00000 | −0.0669650 | ||||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 58.9633 | 3.93089 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 25.3594 | 1.68316 | 0.841580 | − | 0.540132i | \(-0.181626\pi\) | ||||
0.841580 | + | 0.540132i | \(0.181626\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.9096 | 1.05133 | 0.525667 | − | 0.850690i | \(-0.323816\pi\) | ||||
0.525667 | + | 0.850690i | \(0.323816\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −13.6990 | −0.901331 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.05957 | 0.331463 | 0.165732 | − | 0.986171i | \(-0.447001\pi\) | ||||
0.165732 | + | 0.986171i | \(0.447001\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −22.4491 | −1.46442 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 16.3721 | 1.06348 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.19119 | 0.271106 | 0.135553 | − | 0.990770i | \(-0.456719\pi\) | ||||
0.135553 | + | 0.990770i | \(0.456719\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.6165 | −1.26361 | −0.631805 | − | 0.775127i | \(-0.717686\pi\) | ||||
−0.631805 | + | 0.775127i | \(0.717686\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.4504 | 0.991144 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 12.9075 | 0.824627 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.09219 | −0.260380 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −38.6409 | −2.44877 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.8195 | −0.872282 | −0.436141 | − | 0.899878i | \(-0.643655\pi\) | ||||
−0.436141 | + | 0.899878i | \(0.643655\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.7252 | 0.674285 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −36.1019 | −2.26079 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.18776 | 0.198847 | 0.0994234 | − | 0.995045i | \(-0.468300\pi\) | ||||
0.0994234 | + | 0.995045i | \(0.468300\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −20.3665 | −1.26551 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.52556 | −0.218226 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 18.2099 | 1.12287 | 0.561435 | − | 0.827521i | \(-0.310250\pi\) | ||||
0.561435 | + | 0.827521i | \(0.310250\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 21.6291 | 1.32867 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 40.8184 | 2.49805 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.8522 | −0.661668 | −0.330834 | − | 0.943689i | \(-0.607330\pi\) | ||||
−0.330834 | + | 0.943689i | \(0.607330\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 31.9951 | 1.94356 | 0.971782 | − | 0.235881i | \(-0.0757975\pi\) | ||||
0.971782 | + | 0.235881i | \(0.0757975\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 23.5425 | 1.42486 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 30.0270 | 1.81070 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.64409 | 0.218952 | 0.109476 | − | 0.993989i | \(-0.465083\pi\) | ||||
0.109476 | + | 0.993989i | \(0.465083\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −46.1753 | −2.76444 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 23.1645 | 1.38188 | 0.690939 | − | 0.722913i | \(-0.257197\pi\) | ||||
0.690939 | + | 0.722913i | \(0.257197\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −22.8411 | −1.35776 | −0.678882 | − | 0.734248i | \(-0.737535\pi\) | ||||
−0.678882 | + | 0.734248i | \(0.737535\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 11.1438 | 0.660104 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.64556 | −0.0971342 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.31968 | −0.430569 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.84723 | 0.401392 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 19.1041 | 1.11608 | 0.558038 | − | 0.829816i | \(-0.311554\pi\) | ||||
0.558038 | + | 0.829816i | \(0.311554\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 40.2891 | 2.34572 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −12.9968 | −0.754152 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −18.4318 | −1.06594 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.0402 | −0.636348 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −44.5665 | −2.56028 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −11.4360 | −0.654823 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −19.0160 | −1.08530 | −0.542651 | − | 0.839958i | \(-0.682579\pi\) | ||||
−0.542651 | + | 0.839958i | \(0.682579\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.4493 | 0.821994 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.8722 | 0.843325 | 0.421662 | − | 0.906753i | \(-0.361447\pi\) | ||||
0.421662 | + | 0.906753i | \(0.361447\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.3817 | 1.32161 | 0.660807 | − | 0.750556i | \(-0.270214\pi\) | ||||
0.660807 | + | 0.750556i | \(0.270214\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −39.6682 | −2.23505 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 21.1390 | 1.18728 | 0.593641 | − | 0.804730i | \(-0.297690\pi\) | ||||
0.593641 | + | 0.804730i | \(0.297690\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.79538 | −0.100522 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −42.3440 | −2.36341 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.98810 | −0.166262 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −51.6029 | −2.86242 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 15.5393 | 0.859327 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10.6896 | 0.589336 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.9220 | 1.36984 | 0.684918 | − | 0.728620i | \(-0.259838\pi\) | ||||
0.684918 | + | 0.728620i | \(0.259838\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −50.3425 | −2.75875 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −24.2759 | −1.32634 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −16.3352 | −0.889833 | −0.444916 | − | 0.895572i | \(-0.646767\pi\) | ||||
−0.444916 | + | 0.895572i | \(0.646767\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −56.2610 | −3.05568 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −23.5147 | −1.27339 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.9339 | −1.07633 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 50.1933 | 2.70231 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.48755 | −0.509318 | −0.254659 | − | 0.967031i | \(-0.581963\pi\) | ||||
−0.254659 | + | 0.967031i | \(0.581963\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −29.7560 | −1.59280 | −0.796400 | − | 0.604770i | \(-0.793265\pi\) | ||||
−0.796400 | + | 0.604770i | \(0.793265\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 22.3357 | 1.19219 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.5570 | 0.774793 | 0.387396 | − | 0.921913i | \(-0.373375\pi\) | ||||
0.387396 | + | 0.921913i | \(0.373375\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 52.6937 | 2.79669 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 17.1906 | 0.909824 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.0934 | 1.27160 | 0.635801 | − | 0.771853i | \(-0.280670\pi\) | ||||
0.635801 | + | 0.771853i | \(0.280670\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.0776 | −0.951455 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 13.6123 | 0.714460 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −19.9983 | −1.04676 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.81012 | −0.0944873 | −0.0472437 | − | 0.998883i | \(-0.515044\pi\) | ||||
−0.0472437 | + | 0.998883i | \(0.515044\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.06755 | −0.211748 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.2991 | −0.534703 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.5131 | −0.958572 | −0.479286 | − | 0.877659i | \(-0.659104\pi\) | ||||
−0.479286 | + | 0.877659i | \(0.659104\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 82.5079 | 4.26069 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.08546 | 0.158909 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.9743 | −0.717813 | −0.358906 | − | 0.933374i | \(-0.616850\pi\) | ||||
−0.358906 | + | 0.933374i | \(0.616850\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −14.4448 | −0.740028 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.77104 | −0.345984 | −0.172992 | − | 0.984923i | \(-0.555343\pi\) | ||||
−0.172992 | + | 0.984923i | \(0.555343\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −20.2010 | −1.02954 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −27.2896 | −1.38721 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.0099 | 0.558224 | 0.279112 | − | 0.960259i | \(-0.409960\pi\) | ||||
0.279112 | + | 0.960259i | \(0.409960\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13.4588 | −0.680639 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −24.4656 | −1.23412 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 24.1427 | 1.21475 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.85407 | −0.394185 | −0.197092 | − | 0.980385i | \(-0.563150\pi\) | ||||
−0.197092 | + | 0.980385i | \(0.563150\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.30635 | −0.265650 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −37.4096 | −1.86814 | −0.934072 | − | 0.357084i | \(-0.883771\pi\) | ||||
−0.934072 | + | 0.357084i | \(0.883771\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 40.4113 | 2.01303 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.406215 | −0.0201850 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −25.6369 | −1.27077 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 33.5533 | 1.65910 | 0.829551 | − | 0.558430i | \(-0.188596\pi\) | ||||
0.829551 | + | 0.558430i | \(0.188596\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.78416 | 0.235985 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −19.1844 | −0.944005 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −56.9809 | −2.79708 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 63.4250 | 3.10593 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.23719 | −0.451266 | −0.225633 | − | 0.974212i | \(-0.572445\pi\) | ||||
−0.225633 | + | 0.974212i | \(0.572445\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.09928 | −0.248524 | −0.124262 | − | 0.992249i | \(-0.539656\pi\) | ||||
−0.124262 | + | 0.992249i | \(0.539656\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 26.4229 | 1.28472 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −37.6802 | −1.82776 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.44547 | 0.263525 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 29.6348 | 1.43078 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.25936 | −0.205166 | −0.102583 | − | 0.994724i | \(-0.532711\pi\) | ||||
−0.102583 | + | 0.994724i | \(0.532711\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −23.5901 | −1.13367 | −0.566834 | − | 0.823832i | \(-0.691832\pi\) | ||||
−0.566834 | + | 0.823832i | \(0.691832\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.40232 | −0.402860 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.15442 | 0.198733 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.56456 | −0.0746722 | −0.0373361 | − | 0.999303i | \(-0.511887\pi\) | ||||
−0.0373361 | + | 0.999303i | \(0.511887\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −15.1922 | −0.723439 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 22.8252 | 1.08446 | 0.542230 | − | 0.840230i | \(-0.317580\pi\) | ||||
0.542230 | + | 0.840230i | \(0.317580\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 60.1919 | 2.85337 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 32.1590 | 1.52107 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −16.2906 | −0.768801 | −0.384401 | − | 0.923166i | \(-0.625592\pi\) | ||||
−0.384401 | + | 0.923166i | \(0.625592\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.07139 | −0.0975381 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.33672 | 0.391693 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 34.7164 | 1.62753 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.71657 | −0.0802976 | −0.0401488 | − | 0.999194i | \(-0.512783\pi\) | ||||
−0.0401488 | + | 0.999194i | \(0.512783\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 16.3094 | 0.761258 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −35.0452 | −1.63222 | −0.816109 | − | 0.577898i | \(-0.803873\pi\) | ||||
−0.816109 | + | 0.577898i | \(0.803873\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.87067 | 0.458729 | 0.229364 | − | 0.973341i | \(-0.426335\pi\) | ||||
0.229364 | + | 0.973341i | \(0.426335\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −110.048 | −5.10334 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.86372 | 0.271341 | 0.135670 | − | 0.990754i | \(-0.456681\pi\) | ||||
0.135670 | + | 0.990754i | \(0.456681\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.5595 | 0.533766 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −18.1593 | −0.836735 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −13.8972 | −0.638994 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 11.6310 | 0.533668 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −25.4577 | −1.16563 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 25.2665 | 1.15446 | 0.577228 | − | 0.816583i | \(-0.304134\pi\) | ||||
0.577228 | + | 0.816583i | \(0.304134\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 44.0583 | 2.00888 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −23.9005 | −1.08751 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.0971 | 0.458486 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −19.4718 | −0.882352 | −0.441176 | − | 0.897421i | \(-0.645438\pi\) | ||||
−0.441176 | + | 0.897421i | \(0.645438\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −51.4430 | −2.32633 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.5127 | 0.654948 | 0.327474 | − | 0.944860i | \(-0.393803\pi\) | ||||
0.327474 | + | 0.944860i | \(0.393803\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.25299 | 0.101469 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −49.9334 | −2.24434 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −25.0911 | −1.12549 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −25.5687 | −1.14461 | −0.572305 | − | 0.820041i | \(-0.693951\pi\) | ||||
−0.572305 | + | 0.820041i | \(0.693951\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −38.9665 | −1.74089 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.01751 | −0.179132 | −0.0895659 | − | 0.995981i | \(-0.528548\pi\) | ||||
−0.0895659 | + | 0.995981i | \(0.528548\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −65.7189 | −2.92445 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −14.4623 | −0.642295 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 32.0977 | 1.42271 | 0.711354 | − | 0.702834i | \(-0.248082\pi\) | ||||
0.711354 | + | 0.702834i | \(0.248082\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.52259 | 0.421254 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.03435 | −0.222272 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 21.3074 | 0.938914 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.4558 | 0.591786 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 69.8982 | 3.06819 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 27.3141 | 1.19665 | 0.598327 | − | 0.801252i | \(-0.295832\pi\) | ||||
0.598327 | + | 0.801252i | \(0.295832\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18.5339 | −0.810433 | −0.405216 | − | 0.914221i | \(-0.632804\pi\) | ||||
−0.405216 | + | 0.914221i | \(0.632804\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −66.9136 | −2.92035 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 29.5081 | 1.28539 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.28799 | −0.186434 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −47.4208 | −2.05789 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.55980 | 0.154192 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −62.4415 | −2.69958 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8.34792 | −0.360239 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7.73662 | −0.333240 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.2563 | 0.440954 | 0.220477 | − | 0.975392i | \(-0.429239\pi\) | ||||
0.220477 | + | 0.975392i | \(0.429239\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −57.9332 | −2.48615 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 22.9147 | 0.981558 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.26173 | 0.396003 | 0.198001 | − | 0.980202i | \(-0.436555\pi\) | ||||
0.198001 | + | 0.980202i | \(0.436555\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 13.4603 | 0.574471 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.695446 | −0.0296270 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.4960 | −0.488860 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −119.979 | −5.09284 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −42.9335 | −1.81915 | −0.909576 | − | 0.415537i | \(-0.863594\pi\) | ||||
−0.909576 | + | 0.415537i | \(0.863594\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 23.8831 | 1.01015 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 21.6392 | 0.913606 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −14.8022 | −0.623840 | −0.311920 | − | 0.950108i | \(-0.600972\pi\) | ||||
−0.311920 | + | 0.950108i | \(0.600972\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −82.9639 | −3.49032 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.193427 | 0.00812318 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 46.2344 | 1.93825 | 0.969124 | − | 0.246574i | \(-0.0793048\pi\) | ||||
0.969124 | + | 0.246574i | \(0.0793048\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 33.4665 | 1.40053 | 0.700264 | − | 0.713884i | \(-0.253066\pi\) | ||||
0.700264 | + | 0.713884i | \(0.253066\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.43976 | 0.310800 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 52.3876 | 2.18471 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 31.6747 | 1.31864 | 0.659319 | − | 0.751864i | \(-0.270845\pi\) | ||||
0.659319 | + | 0.751864i | \(0.270845\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −24.2444 | −1.00756 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 27.1325 | 1.12565 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.9643 | −0.536926 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 85.8131 | 3.54794 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.40965 | −0.0581826 | −0.0290913 | − | 0.999577i | \(-0.509261\pi\) | ||||
−0.0290913 | + | 0.999577i | \(0.509261\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.10847 | −0.375308 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.99829 | −0.0821988 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 27.5495 | 1.13132 | 0.565661 | − | 0.824638i | \(-0.308621\pi\) | ||||
0.565661 | + | 0.824638i | \(0.308621\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 25.3497 | 1.03924 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 29.3142 | 1.19975 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 20.6171 | 0.842391 | 0.421196 | − | 0.906970i | \(-0.361611\pi\) | ||||
0.421196 | + | 0.906970i | \(0.361611\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −29.6549 | −1.20965 | −0.604825 | − | 0.796358i | \(-0.706757\pi\) | ||||
−0.604825 | + | 0.796358i | \(0.706757\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 28.5730 | 1.16358 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 20.0730 | 0.816085 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −42.3384 | −1.71846 | −0.859232 | − | 0.511586i | \(-0.829058\pi\) | ||||
−0.859232 | + | 0.511586i | \(0.829058\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.00092 | 0.162126 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −23.1245 | −0.935518 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.1001 | 0.569498 | 0.284749 | − | 0.958602i | \(-0.408090\pi\) | ||||
0.284749 | + | 0.958602i | \(0.408090\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −9.69402 | −0.390901 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.9805 | 0.683611 | 0.341806 | − | 0.939771i | \(-0.388962\pi\) | ||||
0.341806 | + | 0.939771i | \(0.388962\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.5659 | 0.907000 | 0.453500 | − | 0.891256i | \(-0.350175\pi\) | ||||
0.453500 | + | 0.891256i | \(0.350175\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −22.6753 | −0.909930 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −28.6615 | −1.14830 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 61.1149 | 2.44460 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.67952 | −0.266754 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 32.1711 | 1.28275 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 35.0492 | 1.39529 | 0.697644 | − | 0.716444i | \(-0.254232\pi\) | ||||
0.697644 | + | 0.716444i | \(0.254232\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −61.5087 | −2.44475 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −21.3006 | −0.845289 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13.2958 | 0.526798 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −62.0210 | −2.45351 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17.7215 | 0.699955 | 0.349978 | − | 0.936758i | \(-0.386189\pi\) | ||||
0.349978 | + | 0.936758i | \(0.386189\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.78855 | 0.346587 | 0.173293 | − | 0.984870i | \(-0.444559\pi\) | ||||
0.173293 | + | 0.984870i | \(0.444559\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −65.0382 | −2.56088 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 23.6010 | 0.927849 | 0.463925 | − | 0.885875i | \(-0.346441\pi\) | ||||
0.463925 | + | 0.885875i | \(0.346441\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −24.1490 | −0.947930 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 52.4013 | 2.05377 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 25.3303 | 0.991251 | 0.495625 | − | 0.868536i | \(-0.334939\pi\) | ||||
0.495625 | + | 0.868536i | \(0.334939\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −36.0775 | −1.40967 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 23.5382 | 0.918314 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.0085 | 0.389876 | 0.194938 | − | 0.980816i | \(-0.437550\pi\) | ||||
0.194938 | + | 0.980816i | \(0.437550\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 28.2211 | 1.09768 | 0.548838 | − | 0.835929i | \(-0.315071\pi\) | ||||
0.548838 | + | 0.835929i | \(0.315071\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −37.1880 | −1.44426 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.82488 | −0.303436 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.13238 | −0.121286 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.80512 | 0.108452 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.85464 | 0.264620 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −31.6135 | −1.21861 | −0.609306 | − | 0.792935i | \(-0.708552\pi\) | ||||
−0.609306 | + | 0.792935i | \(0.708552\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −63.4836 | −2.44349 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −10.6518 | −0.409381 | −0.204690 | − | 0.978827i | \(-0.565619\pi\) | ||||
−0.204690 | + | 0.978827i | \(0.565619\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.80793 | −0.184511 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −71.1361 | −2.72594 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 43.3219 | 1.65766 | 0.828832 | − | 0.559497i | \(-0.189006\pi\) | ||||
0.828832 | + | 0.559497i | \(0.189006\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.05485 | 0.269552 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −44.6283 | −1.70268 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 22.2798 | 0.848794 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.3875 | 0.547326 | 0.273663 | − | 0.961826i | \(-0.411765\pi\) | ||||
0.273663 | + | 0.961826i | \(0.411765\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 23.7767 | 0.903204 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 93.5281 | 3.54772 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.59934 | 0.0984571 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −14.1927 | −0.536818 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.54714 | 0.322821 | 0.161411 | − | 0.986887i | \(-0.448396\pi\) | ||||
0.161411 | + | 0.986887i | \(0.448396\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.93049 | −0.374536 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 62.9726 | 2.37168 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 31.2933 | 1.17691 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.965486 | −0.0362596 | −0.0181298 | − | 0.999836i | \(-0.505771\pi\) | ||||
−0.0181298 | + | 0.999836i | \(0.505771\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −28.4162 | −1.06569 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −41.0257 | −1.53642 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 43.7002 | 1.63430 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −11.7568 | −0.439066 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11.0744 | 0.413004 | 0.206502 | − | 0.978446i | \(-0.433792\pi\) | ||||
0.206502 | + | 0.978446i | \(0.433792\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.1459 | −0.377853 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 55.0267 | 2.04647 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8.76964 | −0.325696 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23.7985 | 0.882638 | 0.441319 | − | 0.897350i | \(-0.354511\pi\) | ||||
0.441319 | + | 0.897350i | \(0.354511\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −43.6349 | −1.61611 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 17.4393 | 0.645015 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.56039 | 0.0576342 | 0.0288171 | − | 0.999585i | \(-0.490826\pi\) | ||||
0.0288171 | + | 0.999585i | \(0.490826\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −36.2070 | −1.33552 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 14.5508 | 0.535985 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 38.6650 | 1.42231 | 0.711157 | − | 0.703033i | \(-0.248172\pi\) | ||||
0.711157 | + | 0.703033i | \(0.248172\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 11.4791 | 0.421695 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −34.6028 | −1.26945 | −0.634726 | − | 0.772737i | \(-0.718887\pi\) | ||||
−0.634726 | + | 0.772737i | \(0.718887\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 47.4224 | 1.73742 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 67.0671 | 2.45386 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 29.7327 | 1.08641 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.4696 | 0.892908 | 0.446454 | − | 0.894807i | \(-0.352687\pi\) | ||||
0.446454 | + | 0.894807i | \(0.352687\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 38.7655 | 1.41269 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.2935 | 0.447408 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 39.9968 | 1.45371 | 0.726854 | − | 0.686793i | \(-0.240982\pi\) | ||||
0.726854 | + | 0.686793i | \(0.240982\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −30.0854 | −1.09203 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 30.1342 | 1.09236 | 0.546182 | − | 0.837667i | \(-0.316081\pi\) | ||||
0.546182 | + | 0.837667i | \(0.316081\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.9113 | −0.395015 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 62.6603 | 2.26549 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 41.5012 | 1.49852 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.23445 | −0.116637 | −0.0583186 | − | 0.998298i | \(-0.518574\pi\) | ||||
−0.0583186 | + | 0.998298i | \(0.518574\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.94205 | −0.322040 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.10656 | 0.0398002 | 0.0199001 | − | 0.999802i | \(-0.493665\pi\) | ||||
0.0199001 | + | 0.999802i | \(0.493665\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −114.859 | −4.12585 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 57.1304 | 2.04954 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.802358 | −0.0287475 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −31.5841 | −1.13017 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.79583 | 0.135652 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −26.7781 | −0.955752 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 53.1254 | 1.89372 | 0.946858 | − | 0.321650i | \(-0.104238\pi\) | ||||
0.946858 | + | 0.321650i | \(0.104238\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −51.0809 | −1.81853 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 39.5049 | 1.40463 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11.7800 | −0.418322 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −60.6723 | −2.15182 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −21.5294 | −0.762611 | −0.381306 | − | 0.924449i | \(-0.624525\pi\) | ||||
−0.381306 | + | 0.924449i | \(0.624525\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −16.8854 | −0.597362 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −70.8465 | −2.50324 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 11.9868 | 0.423006 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −35.2443 | −1.24220 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 30.4416 | 1.07160 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −42.7019 | −1.50132 | −0.750660 | − | 0.660688i | \(-0.770264\pi\) | ||||
−0.750660 | + | 0.660688i | \(0.770264\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.75273 | −0.237121 | −0.118560 | − | 0.992947i | \(-0.537828\pi\) | ||||
−0.118560 | + | 0.992947i | \(0.537828\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −89.7502 | −3.14768 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −75.8592 | −2.65723 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.38311 | −0.188331 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −40.8616 | −1.42782 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21.0124 | 0.733337 | 0.366668 | − | 0.930352i | \(-0.380498\pi\) | ||||
0.366668 | + | 0.930352i | \(0.380498\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −37.9581 | −1.32314 | −0.661569 | − | 0.749884i | \(-0.730109\pi\) | ||||
−0.661569 | + | 0.749884i | \(0.730109\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −84.2294 | −2.93249 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 31.0210 | 1.07871 | 0.539353 | − | 0.842080i | \(-0.318669\pi\) | ||||
0.539353 | + | 0.842080i | \(0.318669\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.3531 | −0.741622 | −0.370811 | − | 0.928708i | \(-0.620920\pi\) | ||||
−0.370811 | + | 0.928708i | \(0.620920\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −10.2221 | −0.354601 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 9.70850 | 0.336380 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −57.4609 | −1.98852 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 49.7152 | 1.71841 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −41.4426 | −1.43076 | −0.715379 | − | 0.698737i | \(-0.753746\pi\) | ||||
−0.715379 | + | 0.698737i | \(0.753746\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.4756 | −0.981919 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −64.9793 | −2.23801 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −21.3265 | −0.733655 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.55816 | −0.328422 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 64.0721 | 2.19895 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −44.7282 | −1.53326 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −38.8606 | −1.33056 | −0.665281 | − | 0.746593i | \(-0.731688\pi\) | ||||
−0.665281 | + | 0.746593i | \(0.731688\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −19.3418 | −0.661476 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9.11511 | −0.311366 | −0.155683 | − | 0.987807i | \(-0.549758\pi\) | ||||
−0.155683 | + | 0.987807i | \(0.549758\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.71506 | −0.0585171 | −0.0292585 | − | 0.999572i | \(-0.509315\pi\) | ||||
−0.0292585 | + | 0.999572i | \(0.509315\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.61599 | 0.157313 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −10.5773 | −0.360054 | −0.180027 | − | 0.983662i | \(-0.557618\pi\) | ||||
−0.180027 | + | 0.983662i | \(0.557618\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 103.074 | 3.50461 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 20.5326 | 0.697324 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −14.4709 | −0.490892 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −25.0063 | −0.847305 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −11.8844 | −0.402226 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −57.9347 | −1.95855 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 54.3570 | 1.83551 | 0.917753 | − | 0.397151i | \(-0.130001\pi\) | ||||
0.917753 | + | 0.397151i | \(0.130001\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −53.5894 | −1.80753 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 17.5910 | 0.592655 | 0.296328 | − | 0.955086i | \(-0.404238\pi\) | ||||
0.296328 | + | 0.955086i | \(0.404238\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.5786 | −0.557914 | −0.278957 | − | 0.960304i | \(-0.589989\pi\) | ||||
−0.278957 | + | 0.960304i | \(0.589989\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −113.016 | −3.79899 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −22.0105 | −0.739040 | −0.369520 | − | 0.929223i | \(-0.620478\pi\) | ||||
−0.369520 | + | 0.929223i | \(0.620478\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.1427 | 0.340175 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.243482 | 0.00815695 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.21214 | 0.174418 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12.3101 | −0.411480 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 51.7033 | 1.72632 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.86767 | 0.229050 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.2686 | 0.541986 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 30.9692 | 1.03059 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −85.4297 | −2.83978 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.98058 | 0.298195 | 0.149098 | − | 0.988822i | \(-0.452363\pi\) | ||||
0.149098 | + | 0.988822i | \(0.452363\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 77.3518 | 2.56560 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −56.4895 | −1.87158 | −0.935791 | − | 0.352556i | \(-0.885313\pi\) | ||||
−0.935791 | + | 0.352556i | \(0.885313\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 34.1538 | 1.13033 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 32.0794 | 1.06051 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 17.1790 | 0.567301 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26.5270 | 0.875046 | 0.437523 | − | 0.899207i | \(-0.355856\pi\) | ||||
0.437523 | + | 0.899207i | \(0.355856\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 53.3423 | 1.75769 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 54.2790 | 1.78661 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −125.224 | −4.11735 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −25.0790 | −0.823702 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 12.9236 | 0.424011 | 0.212006 | − | 0.977268i | \(-0.432000\pi\) | ||||
0.212006 | + | 0.977268i | \(0.432000\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.99679 | −0.0982160 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −41.7183 | −1.36580 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 31.9097 | 1.04356 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15.2432 | −0.497974 | −0.248987 | − | 0.968507i | \(-0.580098\pi\) | ||||
−0.248987 | + | 0.968507i | \(0.580098\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −65.5886 | −2.14040 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −52.9385 | −1.72575 | −0.862873 | − | 0.505421i | \(-0.831337\pi\) | ||||
−0.862873 | + | 0.505421i | \(0.831337\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.61392 | −0.117686 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 42.7092 | 1.38933 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 30.5444 | 0.992560 | 0.496280 | − | 0.868162i | \(-0.334699\pi\) | ||||
0.496280 | + | 0.868162i | \(0.334699\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −20.6000 | −0.668703 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −59.2974 | −1.92285 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21.3202 | 0.690631 | 0.345315 | − | 0.938487i | \(-0.387772\pi\) | ||||
0.345315 | + | 0.938487i | \(0.387772\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10.9709 | 0.355009 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.03627 | 0.162800 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.35930 | −0.108477 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 58.9481 | 1.90155 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 73.4943 | 2.36832 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −35.7514 | −1.15088 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −20.5426 | −0.660607 | −0.330303 | − | 0.943875i | \(-0.607151\pi\) | ||||
−0.330303 | + | 0.943875i | \(0.607151\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.38198 | 0.269268 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 16.4845 | 0.529013 | 0.264507 | − | 0.964384i | \(-0.414791\pi\) | ||||
0.264507 | + | 0.964384i | \(0.414791\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −44.5352 | −1.42773 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 144.753 | 4.63579 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −6.79369 | −0.217350 | −0.108675 | − | 0.994077i | \(-0.534661\pi\) | ||||
−0.108675 | + | 0.994077i | \(0.534661\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −36.0785 | −1.15307 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −26.9708 | −0.861113 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −25.7642 | −0.821752 | −0.410876 | − | 0.911691i | \(-0.634777\pi\) | ||||
−0.410876 | + | 0.911691i | \(0.634777\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.94673 | −0.0938907 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −29.9856 | −0.954452 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −24.2462 | −0.770984 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18.9580 | −0.602220 | −0.301110 | − | 0.953589i | \(-0.597357\pi\) | ||||
−0.301110 | + | 0.953589i | \(0.597357\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −69.9092 | −2.21850 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 43.2275 | 1.37040 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.7748 | 0.372912 | 0.186456 | − | 0.982463i | \(-0.440300\pi\) | ||||
0.186456 | + | 0.982463i | \(0.440300\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 54.2019 | 1.71487 |
(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 | 3568.2.a.m.1.1 | 7 | ||
4.3 | odd | 2 | 892.2.a.d.1.7 | ✓ | 7 | ||
12.11 | even | 2 | 8028.2.a.j.1.7 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
892.2.a.d.1.7 | ✓ | 7 | 4.3 | odd | 2 | ||
3568.2.a.m.1.1 | 7 | 1.1 | even | 1 | trivial | ||
8028.2.a.j.1.7 | 7 | 12.11 | even | 2 |