Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4012,2,Mod(1,4012)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4012, 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("4012.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4012 = 2^{2} \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4012.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: | \(32.0359812909\) |
Analytic rank: | \(1\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 5 x^{14} - 16 x^{13} + 123 x^{12} - 76 x^{11} - 630 x^{10} + 937 x^{9} + 1083 x^{8} - 2602 x^{7} + \cdots - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Root | \(3.62663\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4012.1 |
$q$-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 | ||||||||
\(3\) | 1.57548 | 0.909605 | 0.454802 | − | 0.890592i | \(-0.349710\pi\) | ||||
0.454802 | + | 0.890592i | \(0.349710\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.44709 | 1.54158 | 0.770792 | − | 0.637087i | \(-0.219861\pi\) | ||||
0.770792 | + | 0.637087i | \(0.219861\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.23195 | −1.59952 | −0.799762 | − | 0.600317i | \(-0.795041\pi\) | ||||
−0.799762 | + | 0.600317i | \(0.795041\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.517858 | −0.172619 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.87827 | −1.77237 | −0.886183 | − | 0.463336i | \(-0.846652\pi\) | ||||
−0.886183 | + | 0.463336i | \(0.846652\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.16420 | 1.43229 | 0.716146 | − | 0.697950i | \(-0.245904\pi\) | ||||
0.716146 | + | 0.697950i | \(0.245904\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.43082 | 1.40223 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.38694 | −1.23585 | −0.617925 | − | 0.786237i | \(-0.712026\pi\) | ||||
−0.617925 | + | 0.786237i | \(0.712026\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.66735 | −1.45494 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.25478 | −0.470155 | −0.235077 | − | 0.971977i | \(-0.575534\pi\) | ||||
−0.235077 | + | 0.971977i | \(0.575534\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.88240 | 1.37648 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.54232 | −1.06662 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.66616 | −1.79496 | −0.897481 | − | 0.441054i | \(-0.854605\pi\) | ||||
−0.897481 | + | 0.441054i | \(0.854605\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.16881 | 0.928346 | 0.464173 | − | 0.885745i | \(-0.346352\pi\) | ||||
0.464173 | + | 0.885745i | \(0.346352\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −9.26111 | −1.61215 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −14.5879 | −2.46580 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.63472 | −0.433146 | −0.216573 | − | 0.976266i | \(-0.569488\pi\) | ||||
−0.216573 | + | 0.976266i | \(0.569488\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 8.13611 | 1.30282 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.74011 | −0.740281 | −0.370141 | − | 0.928976i | \(-0.620691\pi\) | ||||
−0.370141 | + | 0.928976i | \(0.620691\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.3464 | 1.73031 | 0.865156 | − | 0.501503i | \(-0.167219\pi\) | ||||
0.865156 | + | 0.501503i | \(0.167219\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.78510 | −0.266107 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.12549 | −1.03936 | −0.519680 | − | 0.854361i | \(-0.673949\pi\) | ||||
−0.519680 | + | 0.854361i | \(0.673949\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 10.9094 | 1.55848 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.57548 | 0.220612 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.14259 | −0.706390 | −0.353195 | − | 0.935550i | \(-0.614905\pi\) | ||||
−0.353195 | + | 0.935550i | \(0.614905\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −20.2629 | −2.73225 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.48703 | −1.12413 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.00000 | −0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.57215 | 0.969514 | 0.484757 | − | 0.874649i | \(-0.338908\pi\) | ||||
0.484757 | + | 0.874649i | \(0.338908\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.19155 | 0.276109 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 17.8015 | 2.20800 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.377854 | 0.0461623 | 0.0230811 | − | 0.999734i | \(-0.492652\pi\) | ||||
0.0230811 | + | 0.999734i | \(0.492652\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.55237 | −0.427655 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.3156 | −1.34292 | −0.671460 | − | 0.741041i | \(-0.734333\pi\) | ||||
−0.671460 | + | 0.741041i | \(0.734333\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.63450 | 0.776509 | 0.388254 | − | 0.921552i | \(-0.373078\pi\) | ||||
0.388254 | + | 0.921552i | \(0.373078\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 10.8431 | 1.25205 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 24.8765 | 2.83494 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.7362 | −1.65795 | −0.828975 | − | 0.559285i | \(-0.811076\pi\) | ||||
−0.828975 | + | 0.559285i | \(0.811076\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.17825 | −0.797583 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.16094 | −1.00554 | −0.502772 | − | 0.864419i | \(-0.667686\pi\) | ||||
−0.502772 | + | 0.864419i | \(0.667686\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.44709 | 0.373889 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −15.2289 | −1.63271 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −16.1826 | −1.71536 | −0.857678 | − | 0.514187i | \(-0.828094\pi\) | ||||
−0.857678 | + | 0.514187i | \(0.828094\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −21.8546 | −2.29099 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.14336 | 0.844427 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −18.5693 | −1.90517 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.97258 | −0.606424 | −0.303212 | − | 0.952923i | \(-0.598059\pi\) | ||||
−0.303212 | + | 0.952923i | \(0.598059\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.04411 | 0.305945 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.85064 | 0.383153 | 0.191576 | − | 0.981478i | \(-0.438640\pi\) | ||||
0.191576 | + | 0.981478i | \(0.438640\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.0195 | 0.987249 | 0.493625 | − | 0.869675i | \(-0.335672\pi\) | ||||
0.493625 | + | 0.869675i | \(0.335672\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −22.9829 | −2.24290 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 19.7726 | 1.91149 | 0.955746 | − | 0.294193i | \(-0.0950509\pi\) | ||||
0.955746 | + | 0.294193i | \(0.0950509\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.8591 | −1.13589 | −0.567947 | − | 0.823065i | \(-0.692262\pi\) | ||||
−0.567947 | + | 0.823065i | \(0.692262\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.15096 | −0.393992 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.49545 | 0.234752 | 0.117376 | − | 0.993088i | \(-0.462552\pi\) | ||||
0.117376 | + | 0.993088i | \(0.462552\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.77243 | −0.724783 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.67433 | −0.247241 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.23195 | −0.387942 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 23.5541 | 2.14128 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −7.46796 | −0.673363 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.48878 | 0.580374 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.48580 | −0.841729 | −0.420864 | − | 0.907124i | \(-0.638273\pi\) | ||||
−0.420864 | + | 0.907124i | \(0.638273\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 17.8761 | 1.57390 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −20.9381 | −1.82937 | −0.914685 | − | 0.404168i | \(-0.867561\pi\) | ||||
−0.914685 | + | 0.404168i | \(0.867561\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 22.7973 | 1.97677 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −19.1048 | −1.64428 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.1496 | −1.12344 | −0.561722 | − | 0.827326i | \(-0.689861\pi\) | ||||
−0.561722 | + | 0.827326i | \(0.689861\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.72218 | 0.654987 | 0.327493 | − | 0.944853i | \(-0.393796\pi\) | ||||
0.327493 | + | 0.944853i | \(0.393796\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −11.2261 | −0.945406 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −30.3566 | −2.53855 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −33.3201 | −2.76708 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 17.1875 | 1.41760 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.45799 | 0.529059 | 0.264530 | − | 0.964378i | \(-0.414783\pi\) | ||||
0.264530 | + | 0.964378i | \(0.414783\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.5912 | 1.10603 | 0.553017 | − | 0.833170i | \(-0.313476\pi\) | ||||
0.553017 | + | 0.833170i | \(0.313476\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.517858 | −0.0418664 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 17.8173 | 1.43112 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.29223 | 0.741601 | 0.370800 | − | 0.928713i | \(-0.379083\pi\) | ||||
0.370800 | + | 0.928713i | \(0.379083\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.10206 | −0.642535 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.54212 | 0.752024 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.40898 | −0.423664 | −0.211832 | − | 0.977306i | \(-0.567943\pi\) | ||||
−0.211832 | + | 0.977306i | \(0.567943\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −31.9238 | −2.48527 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −13.8062 | −1.06836 | −0.534178 | − | 0.845372i | \(-0.679379\pi\) | ||||
−0.534178 | + | 0.845372i | \(0.679379\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.6690 | 1.05146 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.78967 | 0.213332 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.5605 | 0.954957 | 0.477479 | − | 0.878643i | \(-0.341551\pi\) | ||||
0.477479 | + | 0.878643i | \(0.341551\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −29.1259 | −2.20171 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.57548 | −0.118420 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −16.0520 | −1.19979 | −0.599893 | − | 0.800080i | \(-0.704790\pi\) | ||||
−0.599893 | + | 0.800080i | \(0.704790\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.3408 | −1.14027 | −0.570134 | − | 0.821551i | \(-0.693109\pi\) | ||||
−0.570134 | + | 0.821551i | \(0.693109\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.9298 | 0.881875 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −9.08212 | −0.667730 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.87827 | −0.429862 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 23.4548 | 1.70609 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.2468 | 0.813793 | 0.406897 | − | 0.913474i | \(-0.366611\pi\) | ||||
0.406897 | + | 0.913474i | \(0.366611\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.17892 | 0.660713 | 0.330356 | − | 0.943856i | \(-0.392831\pi\) | ||||
0.330356 | + | 0.943856i | \(0.392831\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 28.0459 | 2.00841 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.13784 | 0.294809 | 0.147404 | − | 0.989076i | \(-0.452908\pi\) | ||||
0.147404 | + | 0.989076i | \(0.452908\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.59412 | −0.113004 | −0.0565019 | − | 0.998402i | \(-0.517995\pi\) | ||||
−0.0565019 | + | 0.998402i | \(0.517995\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.595303 | 0.0419894 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 40.9067 | 2.87109 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −16.3396 | −1.14121 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.16766 | 0.0811578 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 31.6659 | 2.19038 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.45799 | 0.582272 | 0.291136 | − | 0.956682i | \(-0.405967\pi\) | ||||
0.291136 | + | 0.956682i | \(0.405967\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −17.8276 | −1.22153 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 39.1121 | 2.66742 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −21.8741 | −1.48491 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 10.4525 | 0.706316 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.16420 | 0.347382 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 22.5298 | 1.50871 | 0.754354 | − | 0.656468i | \(-0.227950\pi\) | ||||
0.754354 | + | 0.656468i | \(0.227950\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.56410 | −0.237607 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.28963 | −0.0855956 | −0.0427978 | − | 0.999084i | \(-0.513627\pi\) | ||||
−0.0427978 | + | 0.999084i | \(0.513627\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.94642 | −0.194705 | −0.0973523 | − | 0.995250i | \(-0.531037\pi\) | ||||
−0.0973523 | + | 0.995250i | \(0.531037\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 39.1925 | 2.57868 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.1570 | 1.05848 | 0.529240 | − | 0.848472i | \(-0.322477\pi\) | ||||
0.529240 | + | 0.848472i | \(0.322477\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −24.5622 | −1.60226 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −23.2166 | −1.50808 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.6238 | 0.751880 | 0.375940 | − | 0.926644i | \(-0.377320\pi\) | ||||
0.375940 | + | 0.926644i | \(0.377320\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.5868 | −1.13287 | −0.566434 | − | 0.824107i | \(-0.691677\pi\) | ||||
−0.566434 | + | 0.824107i | \(0.691677\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.31776 | 0.341135 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 37.6055 | 2.40253 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −27.8193 | −1.77010 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −14.4329 | −0.914647 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 27.3663 | 1.72735 | 0.863673 | − | 0.504053i | \(-0.168158\pi\) | ||||
0.863673 | + | 0.504053i | \(0.168158\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 13.2542 | 0.833286 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.43082 | 0.340091 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 24.1406 | 1.50585 | 0.752926 | − | 0.658105i | \(-0.228642\pi\) | ||||
0.752926 | + | 0.658105i | \(0.228642\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.1500 | 0.692828 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.00570 | 0.309845 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.04841 | 0.249636 | 0.124818 | − | 0.992180i | \(-0.460165\pi\) | ||||
0.124818 | + | 0.992180i | \(0.460165\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −17.7270 | −1.08896 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −25.4954 | −1.56030 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −26.0957 | −1.59108 | −0.795542 | − | 0.605898i | \(-0.792814\pi\) | ||||
−0.795542 | + | 0.605898i | \(0.792814\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −30.0945 | −1.82811 | −0.914055 | − | 0.405591i | \(-0.867066\pi\) | ||||
−0.914055 | + | 0.405591i | \(0.867066\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −34.4316 | −2.08389 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −40.4566 | −2.43962 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.86888 | 0.592963 | 0.296482 | − | 0.955039i | \(-0.404187\pi\) | ||||
0.296482 | + | 0.955039i | \(0.404187\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.67671 | −0.160250 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 21.8448 | 1.30315 | 0.651576 | − | 0.758584i | \(-0.274108\pi\) | ||||
0.651576 | + | 0.758584i | \(0.274108\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.9114 | 0.767505 | 0.383752 | − | 0.923436i | \(-0.374632\pi\) | ||||
0.383752 | + | 0.923436i | \(0.374632\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −29.2555 | −1.73295 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 20.0599 | 1.18410 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.40969 | −0.551606 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.7543 | 0.686696 | 0.343348 | − | 0.939208i | \(-0.388439\pi\) | ||||
0.343348 | + | 0.939208i | \(0.388439\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.44709 | −0.200697 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 32.5793 | 1.89044 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −11.6442 | −0.673399 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −48.0174 | −2.76768 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.06661 | 0.348517 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 26.1018 | 1.49459 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.9299 | 1.30868 | 0.654340 | − | 0.756200i | \(-0.272947\pi\) | ||||
0.654340 | + | 0.756200i | \(0.272947\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 15.7855 | 0.898007 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.65598 | −0.434131 | −0.217065 | − | 0.976157i | \(-0.569648\pi\) | ||||
−0.217065 | + | 0.976157i | \(0.569648\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.83338 | 0.273199 | 0.136599 | − | 0.990626i | \(-0.456383\pi\) | ||||
0.136599 | + | 0.990626i | \(0.456383\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 7.55445 | 0.425645 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −25.0904 | −1.40922 | −0.704609 | − | 0.709596i | \(-0.748878\pi\) | ||||
−0.704609 | + | 0.709596i | \(0.748878\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 56.8203 | 3.18133 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 31.1514 | 1.73870 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.38694 | −0.299738 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 35.5421 | 1.97152 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −18.6838 | −1.03321 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 30.1547 | 1.66248 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.08862 | 0.0598361 | 0.0299180 | − | 0.999552i | \(-0.490475\pi\) | ||||
0.0299180 | + | 0.999552i | \(0.490475\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.36441 | 0.0747694 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.30250 | 0.0711630 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 25.4901 | 1.38854 | 0.694268 | − | 0.719717i | \(-0.255728\pi\) | ||||
0.694268 | + | 0.719717i | \(0.255728\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.93153 | 0.213531 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −30.3837 | −1.64537 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.5442 | −0.893303 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −12.2453 | −0.659266 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 19.9133 | 1.06900 | 0.534500 | − | 0.845168i | \(-0.320500\pi\) | ||||
0.534500 | + | 0.845168i | \(0.320500\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.96886 | −0.373035 | −0.186517 | − | 0.982452i | \(-0.559720\pi\) | ||||
−0.186517 | + | 0.982452i | \(0.559720\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −28.6217 | −1.52771 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −31.0887 | −1.65469 | −0.827343 | − | 0.561698i | \(-0.810148\pi\) | ||||
−0.827343 | + | 0.561698i | \(0.810148\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −39.0060 | −2.07022 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.66735 | −0.352874 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −19.2140 | −1.01408 | −0.507039 | − | 0.861923i | \(-0.669260\pi\) | ||||
−0.507039 | + | 0.861923i | \(0.669260\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.0192 | 0.527325 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 37.1090 | 1.94772 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 22.8697 | 1.19705 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.647712 | 0.0338103 | 0.0169051 | − | 0.999857i | \(-0.494619\pi\) | ||||
0.0169051 | + | 0.999857i | \(0.494619\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.45471 | 0.127787 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 21.7632 | 1.12989 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.8226 | 0.922820 | 0.461410 | − | 0.887187i | \(-0.347344\pi\) | ||||
0.461410 | + | 0.887187i | \(0.347344\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10.2229 | 0.527911 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −49.9180 | −2.57091 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −33.6058 | −1.72621 | −0.863106 | − | 0.505023i | \(-0.831484\pi\) | ||||
−0.863106 | + | 0.505023i | \(0.831484\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −14.9447 | −0.765640 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 13.6682 | 0.698414 | 0.349207 | − | 0.937046i | \(-0.386451\pi\) | ||||
0.349207 | + | 0.937046i | \(0.386451\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 85.7515 | 4.37030 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.87583 | −0.298685 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −15.2026 | −0.770801 | −0.385401 | − | 0.922749i | \(-0.625937\pi\) | ||||
−0.385401 | + | 0.922749i | \(0.625937\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.25478 | −0.114029 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −32.9876 | −1.66400 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −50.7969 | −2.55587 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −21.4298 | −1.07553 | −0.537766 | − | 0.843094i | \(-0.680732\pi\) | ||||
−0.537766 | + | 0.843094i | \(0.680732\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 35.9167 | 1.79808 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.27530 | 0.0636856 | 0.0318428 | − | 0.999493i | \(-0.489862\pi\) | ||||
0.0318428 | + | 0.999493i | \(0.489862\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 26.6928 | 1.32966 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −24.7440 | −1.22954 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 15.4876 | 0.767693 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.6163 | −0.871070 | −0.435535 | − | 0.900172i | \(-0.643441\pi\) | ||||
−0.435535 | + | 0.900172i | \(0.643441\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −20.7169 | −1.02189 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.23195 | 0.208240 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −31.5785 | −1.55013 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12.1662 | 0.595779 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −28.0308 | −1.36939 | −0.684696 | − | 0.728829i | \(-0.740065\pi\) | ||||
−0.684696 | + | 0.728829i | \(0.740065\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −22.2109 | −1.08249 | −0.541245 | − | 0.840865i | \(-0.682047\pi\) | ||||
−0.541245 | + | 0.840865i | \(0.682047\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.68999 | 0.179414 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.88240 | 0.333845 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −32.0449 | −1.55076 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −47.8262 | −2.30907 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.58659 | 0.461770 | 0.230885 | − | 0.972981i | \(-0.425838\pi\) | ||||
0.230885 | + | 0.972981i | \(0.425838\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.50507 | −0.120386 | −0.0601930 | − | 0.998187i | \(-0.519172\pi\) | ||||
−0.0601930 | + | 0.998187i | \(0.519172\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −52.4952 | −2.51695 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 12.1464 | 0.581041 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.7041 | −0.844969 | −0.422485 | − | 0.906370i | \(-0.638842\pi\) | ||||
−0.422485 | + | 0.906370i | \(0.638842\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.64950 | −0.269024 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.43854 | 0.0683471 | 0.0341736 | − | 0.999416i | \(-0.489120\pi\) | ||||
0.0341736 | + | 0.999416i | \(0.489120\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −55.7829 | −2.64436 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.1744 | 0.481235 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −25.4709 | −1.20205 | −0.601023 | − | 0.799232i | \(-0.705240\pi\) | ||||
−0.601023 | + | 0.799232i | \(0.705240\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 27.8637 | 1.31205 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 21.4127 | 1.00605 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −75.3348 | −3.53175 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.50285 | −0.397747 | −0.198873 | − | 0.980025i | \(-0.563728\pi\) | ||||
−0.198873 | + | 0.980025i | \(0.563728\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.54232 | −0.258693 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.12771 | 0.425120 | 0.212560 | − | 0.977148i | \(-0.431820\pi\) | ||||
0.212560 | + | 0.977148i | \(0.431820\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 25.8520 | 1.20144 | 0.600722 | − | 0.799458i | \(-0.294880\pi\) | ||||
0.600722 | + | 0.799458i | \(0.294880\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 28.0709 | 1.30176 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.20674 | −0.379763 | −0.189881 | − | 0.981807i | \(-0.560810\pi\) | ||||
−0.189881 | + | 0.981807i | \(0.560810\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.59906 | −0.0738377 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 14.6397 | 0.674564 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −66.6973 | −3.06675 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −37.0751 | −1.70112 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.66313 | 0.121937 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.47341 | 0.204396 | 0.102198 | − | 0.994764i | \(-0.467413\pi\) | ||||
0.102198 | + | 0.994764i | \(0.467413\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.6063 | −0.620392 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 15.0334 | 0.684045 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −20.5880 | −0.934852 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 30.9168 | 1.40097 | 0.700486 | − | 0.713666i | \(-0.252967\pi\) | ||||
0.700486 | + | 0.713666i | \(0.252967\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8.52175 | −0.385367 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.1068 | −0.862276 | −0.431138 | − | 0.902286i | \(-0.641888\pi\) | ||||
−0.431138 | + | 0.902286i | \(0.641888\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.66616 | −0.435342 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 10.4933 | 0.471639 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 47.8872 | 2.14803 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.128241 | −0.00574085 | −0.00287043 | − | 0.999996i | \(-0.500914\pi\) | ||||
−0.00287043 | + | 0.999996i | \(0.500914\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −21.7514 | −0.971782 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 32.5827 | 1.45279 | 0.726395 | − | 0.687277i | \(-0.241194\pi\) | ||||
0.726395 | + | 0.687277i | \(0.241194\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.2735 | 0.590662 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 21.5353 | 0.956415 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15.1279 | 0.670532 | 0.335266 | − | 0.942124i | \(-0.391174\pi\) | ||||
0.335266 | + | 0.942124i | \(0.391174\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −28.0768 | −1.24205 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 29.8562 | 1.31818 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 34.5380 | 1.52193 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 41.8856 | 1.84213 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 19.7888 | 0.868634 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 29.8544 | 1.30795 | 0.653973 | − | 0.756518i | \(-0.273101\pi\) | ||||
0.653973 | + | 0.756518i | \(0.273101\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19.7050 | 0.861638 | 0.430819 | − | 0.902438i | \(-0.358225\pi\) | ||||
0.430819 | + | 0.902438i | \(0.358225\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −45.8873 | −2.00269 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.16881 | 0.225157 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.9160 | −0.778954 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.517858 | 0.0224731 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −24.4789 | −1.06030 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 68.1579 | 2.94672 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −25.2897 | −1.09133 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −64.1282 | −2.76220 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −29.2189 | −1.25622 | −0.628110 | − | 0.778124i | \(-0.716171\pi\) | ||||
−0.628110 | + | 0.778124i | \(0.716171\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −24.1691 | −1.03719 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −40.8793 | −1.75108 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −33.0214 | −1.41189 | −0.705946 | − | 0.708265i | \(-0.749478\pi\) | ||||
−0.705946 | + | 0.708265i | \(0.749478\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.92130 | −0.167357 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 52.0711 | 2.21830 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 62.3627 | 2.65193 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −14.3087 | −0.607371 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 31.2342 | 1.32343 | 0.661717 | − | 0.749753i | \(-0.269828\pi\) | ||||
0.661717 | + | 0.749753i | \(0.269828\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 58.5952 | 2.47831 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.26111 | −0.391004 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.52616 | −0.232900 | −0.116450 | − | 0.993197i | \(-0.537151\pi\) | ||||
−0.116450 | + | 0.993197i | \(0.537151\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.60201 | 0.361889 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 30.3780 | 1.27575 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 28.1198 | 1.17884 | 0.589421 | − | 0.807826i | \(-0.299356\pi\) | ||||
0.589421 | + | 0.807826i | \(0.299356\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.4858 | −0.606212 | −0.303106 | − | 0.952957i | \(-0.598024\pi\) | ||||
−0.303106 | + | 0.952957i | \(0.598024\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 17.7192 | 0.740230 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −15.5183 | −0.647158 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.01021 | −0.375100 | −0.187550 | − | 0.982255i | \(-0.560055\pi\) | ||||
−0.187550 | + | 0.982255i | \(0.560055\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 14.4612 | 0.600987 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 38.7686 | 1.60839 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 30.2296 | 1.25198 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −9.21863 | −0.381143 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −35.2400 | −1.45451 | −0.727255 | − | 0.686368i | \(-0.759204\pi\) | ||||
−0.727255 | + | 0.686368i | \(0.759204\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −27.8441 | −1.14730 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.51909 | 0.268159 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −16.3059 | −0.669602 | −0.334801 | − | 0.942289i | \(-0.608669\pi\) | ||||
−0.334801 | + | 0.942289i | \(0.608669\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −14.5879 | −0.598045 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.51150 | −0.102789 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 29.5305 | 1.20658 | 0.603291 | − | 0.797521i | \(-0.293856\pi\) | ||||
0.603291 | + | 0.797521i | \(0.293856\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.2172 | −0.906256 | −0.453128 | − | 0.891445i | \(-0.649692\pi\) | ||||
−0.453128 | + | 0.891445i | \(0.649692\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.195675 | −0.00796850 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 81.1929 | 3.30096 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.94665 | 0.281956 | 0.140978 | − | 0.990013i | \(-0.454975\pi\) | ||||
0.140978 | + | 0.990013i | \(0.454975\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 64.4477 | 2.61155 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −36.7975 | −1.48867 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21.0517 | 0.850272 | 0.425136 | − | 0.905130i | \(-0.360226\pi\) | ||||
0.425136 | + | 0.905130i | \(0.360226\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −25.7427 | −1.03805 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.1645 | −0.529981 | −0.264991 | − | 0.964251i | \(-0.585369\pi\) | ||||
−0.264991 | + | 0.964251i | \(0.585369\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17.1341 | 0.688676 | 0.344338 | − | 0.938846i | \(-0.388103\pi\) | ||||
0.344338 | + | 0.938846i | \(0.388103\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 12.4967 | 0.501477 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 68.4840 | 2.74376 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.0446 | −0.481784 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 49.8891 | 1.99238 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.63472 | −0.105053 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.01244 | 0.199542 | 0.0997710 | − | 0.995010i | \(-0.468189\pi\) | ||||
0.0997710 | + | 0.995010i | \(0.468189\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 13.3254 | 0.529637 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −32.6984 | −1.29759 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 56.3382 | 2.23220 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.85990 | 0.231814 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.4038 | −0.489920 | −0.244960 | − | 0.969533i | \(-0.578775\pi\) | ||||
−0.244960 | + | 0.969533i | \(0.578775\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 48.7051 | 1.92074 | 0.960370 | − | 0.278727i | \(-0.0899126\pi\) | ||||
0.960370 | + | 0.278727i | \(0.0899126\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 61.6203 | 2.42630 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −21.7790 | −0.856219 | −0.428110 | − | 0.903727i | \(-0.640820\pi\) | ||||
−0.428110 | + | 0.903727i | \(0.640820\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.87827 | 0.230742 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −34.4623 | −1.35068 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −21.4710 | −0.840224 | −0.420112 | − | 0.907472i | \(-0.638009\pi\) | ||||
−0.420112 | + | 0.907472i | \(0.638009\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −72.1754 | −2.82013 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.43573 | −0.134040 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −35.8336 | −1.39588 | −0.697939 | − | 0.716158i | \(-0.745899\pi\) | ||||
−0.697939 | + | 0.716158i | \(0.745899\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.8612 | 0.539139 | 0.269570 | − | 0.962981i | \(-0.413119\pi\) | ||||
0.269570 | + | 0.962981i | \(0.413119\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8.13611 | 0.315980 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 78.5841 | 3.04736 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 21.7951 | 0.843910 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 35.4953 | 1.37233 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −44.5111 | −1.71833 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.7367 | −0.568059 | −0.284030 | − | 0.958816i | \(-0.591671\pi\) | ||||
−0.284030 | + | 0.958816i | \(0.591671\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −38.1444 | −1.46818 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −36.3703 | −1.39782 | −0.698911 | − | 0.715208i | \(-0.746332\pi\) | ||||
−0.698911 | + | 0.715208i | \(0.746332\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 25.2756 | 0.969990 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.03179 | −0.0778582 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 32.3920 | 1.23945 | 0.619723 | − | 0.784821i | \(-0.287245\pi\) | ||||
0.619723 | + | 0.784821i | \(0.287245\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −45.3277 | −1.73188 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.64202 | −0.177104 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −26.5574 | −1.01176 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.70724 | −0.217114 | −0.108557 | − | 0.994090i | \(-0.534623\pi\) | ||||
−0.108557 | + | 0.994090i | \(0.534623\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −12.8825 | −0.489366 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 26.6190 | 1.00972 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.74011 | −0.179545 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 25.4550 | 0.962798 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.78793 | 0.0675292 | 0.0337646 | − | 0.999430i | \(-0.489250\pi\) | ||||
0.0337646 | + | 0.999430i | \(0.489250\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14.1931 | 0.535303 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −38.6973 | −1.45742 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −16.2957 | −0.612862 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 40.4253 | 1.51820 | 0.759102 | − | 0.650971i | \(-0.225638\pi\) | ||||
0.759102 | + | 0.650971i | \(0.225638\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.63126 | 0.286194 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −11.6545 | −0.436466 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −104.642 | −3.91338 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 18.3131 | 0.683913 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 37.7534 | 1.40796 | 0.703982 | − | 0.710218i | \(-0.251404\pi\) | ||||
0.703982 | + | 0.710218i | \(0.251404\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −42.4019 | −1.57913 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −27.7077 | −1.03046 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −66.5264 | −2.47073 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14.6561 | −0.543566 | −0.271783 | − | 0.962359i | \(-0.587613\pi\) | ||||
−0.271783 | + | 0.962359i | \(0.587613\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.9128 | 1.10788 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 11.3464 | 0.419662 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −34.8082 | −1.28567 | −0.642835 | − | 0.766005i | \(-0.722242\pi\) | ||||
−0.642835 | + | 0.766005i | \(0.722242\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 59.2468 | 2.18535 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.22113 | −0.0818164 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14.3544 | −0.528035 | −0.264017 | − | 0.964518i | \(-0.585048\pi\) | ||||
−0.264017 | + | 0.964518i | \(0.585048\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −43.8288 | −1.61009 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23.1839 | 0.850536 | 0.425268 | − | 0.905068i | \(-0.360180\pi\) | ||||
0.425268 | + | 0.905068i | \(0.360180\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 22.2612 | 0.815589 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.74407 | 0.173576 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −83.6767 | −3.05748 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −36.8698 | −1.34540 | −0.672699 | − | 0.739916i | \(-0.734865\pi\) | ||||
−0.672699 | + | 0.739916i | \(0.734865\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 43.1151 | 1.57120 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 46.8500 | 1.70504 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.86701 | 0.213240 | 0.106620 | − | 0.994300i | \(-0.465997\pi\) | ||||
0.106620 | + | 0.994300i | \(0.465997\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 20.8818 | 0.757961 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14.5000 | 0.525626 | 0.262813 | − | 0.964847i | \(-0.415350\pi\) | ||||
0.262813 | + | 0.964847i | \(0.415350\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 50.1870 | 1.81689 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.78510 | −0.0645405 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.16420 | −0.186469 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −19.1731 | −0.691399 | −0.345699 | − | 0.938345i | \(-0.612358\pi\) | ||||
−0.345699 | + | 0.938345i | \(0.612358\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 38.0331 | 1.36973 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 23.9339 | 0.860844 | 0.430422 | − | 0.902628i | \(-0.358365\pi\) | ||||
0.430422 | + | 0.902628i | \(0.358365\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 35.5738 | 1.27785 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 17.5666 | 0.630199 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 25.5347 | 0.914876 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 66.5164 | 2.38015 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 53.5730 | 1.91454 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 32.0311 | 1.14324 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 37.4553 | 1.33514 | 0.667569 | − | 0.744548i | \(-0.267335\pi\) | ||||
0.667569 | + | 0.744548i | \(0.267335\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.37820 | 0.227070 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.5606 | −0.375491 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 39.1041 | 1.38863 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −27.9285 | −0.990522 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −15.1630 | −0.537103 | −0.268551 | − | 0.963265i | \(-0.586545\pi\) | ||||
−0.268551 | + | 0.963265i | \(0.586545\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.12549 | −0.252082 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.38031 | 0.296104 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −38.9994 | −1.37626 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 32.8925 | 1.15931 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −41.1133 | −1.44726 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −37.6661 | −1.32427 | −0.662135 | − | 0.749384i | \(-0.730350\pi\) | ||||
−0.662135 | + | 0.749384i | \(0.730350\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 34.4522 | 1.20978 | 0.604890 | − | 0.796309i | \(-0.293217\pi\) | ||||
0.604890 | + | 0.796309i | \(0.293217\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −47.4133 | −1.66286 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −18.6452 | −0.653113 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −61.1225 | −2.13841 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 11.3176 | 0.395469 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.44994 | 0.225105 | 0.112552 | − | 0.993646i | \(-0.464097\pi\) | ||||
0.112552 | + | 0.993646i | \(0.464097\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −33.8079 | −1.17847 | −0.589235 | − | 0.807962i | \(-0.700571\pi\) | ||||
−0.589235 | + | 0.807962i | \(0.700571\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −63.7386 | −2.21909 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.64538 | −0.0919890 | −0.0459945 | − | 0.998942i | \(-0.514646\pi\) | ||||
−0.0459945 | + | 0.998942i | \(0.514646\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.83827 | −0.341697 | −0.170849 | − | 0.985297i | \(-0.554651\pi\) | ||||
−0.170849 | + | 0.985297i | \(0.554651\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 15.5482 | 0.539362 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10.9094 | 0.377987 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −47.5912 | −1.64696 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −28.6472 | −0.990192 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −16.6616 | −0.575221 | −0.287610 | − | 0.957747i | \(-0.592861\pi\) | ||||
−0.287610 | + | 0.957747i | \(0.592861\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 64.4347 | 2.22189 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 34.4161 | 1.18535 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 47.1182 | 1.62092 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −99.6795 | −3.42503 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 20.3417 | 0.698126 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.94073 | 0.203646 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.33938 | −0.217056 | −0.108528 | − | 0.994093i | \(-0.534614\pi\) | ||||
−0.108528 | + | 0.994093i | \(0.534614\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9.61624 | 0.328868 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −27.7025 | −0.946298 | −0.473149 | − | 0.880982i | \(-0.656883\pi\) | ||||
−0.473149 | + | 0.880982i | \(0.656883\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −26.8824 | −0.917217 | −0.458608 | − | 0.888638i | \(-0.651652\pi\) | ||||
−0.458608 | + | 0.888638i | \(0.651652\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 31.6040 | 1.07706 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 19.9192 | 0.678058 | 0.339029 | − | 0.940776i | \(-0.389902\pi\) | ||||
0.339029 | + | 0.940776i | \(0.389902\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 43.2971 | 1.47215 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.57548 | 0.0535062 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 86.6233 | 2.93849 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.95132 | 0.0661179 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.09295 | 0.104680 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −27.4602 | −0.928323 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −27.6210 | −0.932696 | −0.466348 | − | 0.884601i | \(-0.654430\pi\) | ||||
−0.466348 | + | 0.884601i | \(0.654430\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 18.5187 | 0.624622 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.7158 | 0.462098 | 0.231049 | − | 0.972942i | \(-0.425784\pi\) | ||||
0.231049 | + | 0.972942i | \(0.425784\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.39120 | −0.114123 | −0.0570614 | − | 0.998371i | \(-0.518173\pi\) | ||||
−0.0570614 | + | 0.998371i | \(0.518173\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5.43082 | −0.182555 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.86338 | 0.0625661 | 0.0312831 | − | 0.999511i | \(-0.490041\pi\) | ||||
0.0312831 | + | 0.999511i | \(0.490041\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 40.1434 | 1.34637 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 42.1957 | 1.41361 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 38.3846 | 1.28449 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −55.3328 | −1.84957 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −18.3452 | −0.612527 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −49.9626 | −1.66634 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.14259 | −0.171325 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −75.6505 | −2.51749 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −52.8809 | −1.75782 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.11163 | 0.302547 | 0.151273 | − | 0.988492i | \(-0.451663\pi\) | ||||
0.151273 | + | 0.988492i | \(0.451663\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.99408 | −0.0661396 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18.8415 | −0.624246 | −0.312123 | − | 0.950042i | \(-0.601040\pi\) | ||||
−0.312123 | + | 0.950042i | \(0.601040\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 53.8505 | 1.78219 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 41.1230 | 1.35948 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 88.6089 | 2.92612 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.190478 | 0.00628328 | 0.00314164 | − | 0.999995i | \(-0.499000\pi\) | ||||
0.00314164 | + | 0.999995i | \(0.499000\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 36.1257 | 1.19038 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −58.4363 | −1.92345 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −18.1332 | −0.596216 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.18867 | −0.170418 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −17.8425 | −0.585392 | −0.292696 | − | 0.956206i | \(-0.594552\pi\) | ||||
−0.292696 | + | 0.956206i | \(0.594552\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −58.7681 | −1.92605 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −12.0619 | −0.394887 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −20.2629 | −0.662668 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.06183 | 0.0346886 | 0.0173443 | − | 0.999850i | \(-0.494479\pi\) | ||||
0.0173443 | + | 0.999850i | \(0.494479\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.61490 | 0.248503 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 57.3762 | 1.87041 | 0.935206 | − | 0.354105i | \(-0.115215\pi\) | ||||
0.935206 | + | 0.354105i | \(0.115215\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.6879 | 0.348047 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 80.8507 | 2.63007 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −51.0069 | −1.65750 | −0.828750 | − | 0.559619i | \(-0.810947\pi\) | ||||
−0.828750 | + | 0.559619i | \(0.810947\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 34.2619 | 1.11219 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −39.5295 | −1.28183 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −14.7579 | −0.478054 | −0.239027 | − | 0.971013i | \(-0.576828\pi\) | ||||
−0.239027 | + | 0.971013i | \(0.576828\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 38.7688 | 1.25453 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 89.5194 | 2.89375 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 55.6482 | 1.79698 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.28341 | −0.138175 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −10.2394 | −0.329961 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 31.6405 | 1.01854 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24.5207 | −0.788532 | −0.394266 | − | 0.918996i | \(-0.629001\pi\) | ||||
−0.394266 | + | 0.918996i | \(0.629001\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.48703 | −0.272643 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −48.3283 | −1.55093 | −0.775465 | − | 0.631391i | \(-0.782484\pi\) | ||||
−0.775465 | + | 0.631391i | \(0.782484\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −32.6798 | −1.04767 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 55.9959 | 1.79330 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 8.08764 | 0.258746 | 0.129373 | − | 0.991596i | \(-0.458703\pi\) | ||||
0.129373 | + | 0.991596i | \(0.458703\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 95.1259 | 3.04024 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.14132 | 0.196077 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −6.52400 | −0.208083 | −0.104042 | − | 0.994573i | \(-0.533178\pi\) | ||||
−0.104042 | + | 0.994573i | \(0.533178\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14.2635 | 0.454472 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 47.5082 | 1.51220 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −25.5837 | −0.813515 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −50.2997 | −1.59782 | −0.798911 | − | 0.601449i | \(-0.794590\pi\) | ||||
−0.798911 | + | 0.601449i | \(0.794590\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.71510 | 0.0544272 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.49505 | −0.174205 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28.8940 | 0.915082 | 0.457541 | − | 0.889189i | \(-0.348730\pi\) | ||||
0.457541 | + | 0.889189i | \(0.348730\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 14.6025 | 0.462002 |
(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 | 4012.2.a.h.1.11 | ✓ | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4012.2.a.h.1.11 | ✓ | 15 | 1.1 | even | 1 | trivial |