Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6016,2,Mod(1,6016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6016, 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("6016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6016 = 2^{7} \cdot 47 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6016.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: | \(48.0380018560\) |
Analytic rank: | \(0\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 4 x^{12} - 22 x^{11} + 96 x^{10} + 163 x^{9} - 840 x^{8} - 438 x^{7} + 3358 x^{6} + 5 x^{5} + \cdots - 832 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Root | \(-3.10994\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6016.1 |
$q$-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 | ||||||||
\(3\) | 3.10994 | 1.79553 | 0.897763 | − | 0.440478i | \(-0.145191\pi\) | ||||
0.897763 | + | 0.440478i | \(0.145191\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.407310 | 0.182155 | 0.0910773 | − | 0.995844i | \(-0.470969\pi\) | ||||
0.0910773 | + | 0.995844i | \(0.470969\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.05265 | 1.15379 | 0.576896 | − | 0.816817i | \(-0.304264\pi\) | ||||
0.576896 | + | 0.816817i | \(0.304264\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.67175 | 2.22392 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.16670 | 0.653286 | 0.326643 | − | 0.945148i | \(-0.394083\pi\) | ||||
0.326643 | + | 0.945148i | \(0.394083\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.550265 | 0.152616 | 0.0763080 | − | 0.997084i | \(-0.475687\pi\) | ||||
0.0763080 | + | 0.997084i | \(0.475687\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.26671 | 0.327063 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.34079 | −0.810261 | −0.405131 | − | 0.914259i | \(-0.632774\pi\) | ||||
−0.405131 | + | 0.914259i | \(0.632774\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.78215 | −1.55593 | −0.777966 | − | 0.628306i | \(-0.783748\pi\) | ||||
−0.777966 | + | 0.628306i | \(0.783748\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 9.49357 | 2.07167 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.22765 | 1.09004 | 0.545020 | − | 0.838423i | \(-0.316522\pi\) | ||||
0.545020 | + | 0.838423i | \(0.316522\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.83410 | −0.966820 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 11.4189 | 2.19758 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.25095 | −0.603685 | −0.301843 | − | 0.953358i | \(-0.597602\pi\) | ||||
−0.301843 | + | 0.953358i | \(0.597602\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.03298 | 1.44277 | 0.721383 | − | 0.692536i | \(-0.243507\pi\) | ||||
0.721383 | + | 0.692536i | \(0.243507\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.73833 | 1.17299 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.24337 | 0.210169 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.82204 | 1.61473 | 0.807366 | − | 0.590050i | \(-0.200892\pi\) | ||||
0.807366 | + | 0.590050i | \(0.200892\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.71129 | 0.274026 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.04458 | 1.25635 | 0.628176 | − | 0.778071i | \(-0.283802\pi\) | ||||
0.628176 | + | 0.778071i | \(0.283802\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.91084 | −0.596398 | −0.298199 | − | 0.954504i | \(-0.596386\pi\) | ||||
−0.298199 | + | 0.954504i | \(0.596386\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.71747 | 0.405097 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.00000 | −0.145865 | ||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.31866 | 0.331238 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −10.3897 | −1.45485 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.41908 | −0.881728 | −0.440864 | − | 0.897574i | \(-0.645328\pi\) | ||||
−0.440864 | + | 0.897574i | \(0.645328\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.882520 | 0.118999 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −21.0921 | −2.79372 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.73544 | −0.356124 | −0.178062 | − | 0.984019i | \(-0.556983\pi\) | ||||
−0.178062 | + | 0.984019i | \(0.556983\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.63323 | −0.593224 | −0.296612 | − | 0.954998i | \(-0.595857\pi\) | ||||
−0.296612 | + | 0.954998i | \(0.595857\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 20.3665 | 2.56594 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.224128 | 0.0277997 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.2924 | 1.37958 | 0.689791 | − | 0.724009i | \(-0.257703\pi\) | ||||
0.689791 | + | 0.724009i | \(0.257703\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 16.2577 | 1.95720 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.75360 | 0.682827 | 0.341414 | − | 0.939913i | \(-0.389094\pi\) | ||||
0.341414 | + | 0.939913i | \(0.389094\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.94230 | −0.812535 | −0.406267 | − | 0.913754i | \(-0.633170\pi\) | ||||
−0.406267 | + | 0.913754i | \(0.633170\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −15.0338 | −1.73595 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.61419 | 0.753757 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.0416 | 1.69231 | 0.846155 | − | 0.532937i | \(-0.178912\pi\) | ||||
0.846155 | + | 0.532937i | \(0.178912\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 15.4970 | 1.72189 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.73633 | 1.06870 | 0.534350 | − | 0.845263i | \(-0.320556\pi\) | ||||
0.534350 | + | 0.845263i | \(0.320556\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.36074 | −0.147593 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −10.1103 | −1.08393 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.09741 | 0.964324 | 0.482162 | − | 0.876082i | \(-0.339852\pi\) | ||||
0.482162 | + | 0.876082i | \(0.339852\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.67976 | 0.176087 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 24.9821 | 2.59052 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.76244 | −0.283420 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.1387 | −1.53710 | −0.768552 | − | 0.639787i | \(-0.779022\pi\) | ||||
−0.768552 | + | 0.639787i | \(0.779022\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 14.4557 | 1.45285 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.77611 | 0.375737 | 0.187869 | − | 0.982194i | \(-0.439842\pi\) | ||||
0.187869 | + | 0.982194i | \(0.439842\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.04840 | −0.398901 | −0.199451 | − | 0.979908i | \(-0.563916\pi\) | ||||
−0.199451 | + | 0.979908i | \(0.563916\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.86682 | 0.377363 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −14.0615 | −1.35937 | −0.679687 | − | 0.733503i | \(-0.737884\pi\) | ||||
−0.679687 | + | 0.733503i | \(0.737884\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.62922 | 0.922312 | 0.461156 | − | 0.887319i | \(-0.347435\pi\) | ||||
0.461156 | + | 0.887319i | \(0.347435\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 30.5460 | 2.89930 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.99339 | −0.657883 | −0.328941 | − | 0.944350i | \(-0.606692\pi\) | ||||
−0.328941 | + | 0.944350i | \(0.606692\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.12927 | 0.198556 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.67123 | 0.339405 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −10.1983 | −0.934874 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.30539 | −0.573218 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 25.0182 | 2.25582 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.00553 | −0.358265 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.458497 | 0.0406851 | 0.0203425 | − | 0.999793i | \(-0.493524\pi\) | ||||
0.0203425 | + | 0.999793i | \(0.493524\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −12.1625 | −1.07085 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.47957 | 0.478752 | 0.239376 | − | 0.970927i | \(-0.423057\pi\) | ||||
0.239376 | + | 0.970927i | \(0.423057\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −20.7035 | −1.79522 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.65105 | 0.400298 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.6905 | 0.998790 | 0.499395 | − | 0.866374i | \(-0.333556\pi\) | ||||
0.499395 | + | 0.866374i | \(0.333556\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.69114 | 0.821992 | 0.410996 | − | 0.911637i | \(-0.365181\pi\) | ||||
0.410996 | + | 0.911637i | \(0.365181\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.10994 | −0.261905 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.19226 | 0.0997018 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.32414 | −0.109964 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.21091 | 0.594746 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.94488 | −0.814716 | −0.407358 | − | 0.913269i | \(-0.633550\pi\) | ||||
−0.407358 | + | 0.913269i | \(0.633550\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.83567 | −0.637657 | −0.318829 | − | 0.947812i | \(-0.603289\pi\) | ||||
−0.318829 | + | 0.947812i | \(0.603289\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −22.2889 | −1.80195 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.27191 | 0.262806 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.9714 | −1.43427 | −0.717135 | − | 0.696934i | \(-0.754547\pi\) | ||||
−0.717135 | + | 0.696934i | \(0.754547\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −19.9630 | −1.58317 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 15.9582 | 1.25768 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.23108 | 0.723034 | 0.361517 | − | 0.932366i | \(-0.382259\pi\) | ||||
0.361517 | + | 0.932366i | \(0.382259\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.74459 | 0.213666 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −16.7235 | −1.29411 | −0.647053 | − | 0.762445i | \(-0.723999\pi\) | ||||
−0.647053 | + | 0.762445i | \(0.723999\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.6972 | −0.976708 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −45.2488 | −3.46026 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.659422 | 0.0501349 | 0.0250675 | − | 0.999686i | \(-0.492020\pi\) | ||||
0.0250675 | + | 0.999686i | \(0.492020\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −14.7568 | −1.11551 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.50707 | −0.639430 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.422467 | −0.0315767 | −0.0157883 | − | 0.999875i | \(-0.505026\pi\) | ||||
−0.0157883 | + | 0.999875i | \(0.505026\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.4430 | 1.14787 | 0.573935 | − | 0.818901i | \(-0.305416\pi\) | ||||
0.573935 | + | 0.818901i | \(0.305416\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −14.4091 | −1.06515 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.00061 | 0.294131 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.23851 | −0.529332 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 34.8580 | 2.53555 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.20080 | −0.448674 | −0.224337 | − | 0.974512i | \(-0.572022\pi\) | ||||
−0.224337 | + | 0.974512i | \(0.572022\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.914661 | −0.0658387 | −0.0329194 | − | 0.999458i | \(-0.510480\pi\) | ||||
−0.0329194 | + | 0.999458i | \(0.510480\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.697026 | 0.0499151 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −27.3854 | −1.95113 | −0.975565 | − | 0.219712i | \(-0.929488\pi\) | ||||
−0.975565 | + | 0.219712i | \(0.929488\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.5462 | −1.17293 | −0.586464 | − | 0.809975i | \(-0.699481\pi\) | ||||
−0.586464 | + | 0.809975i | \(0.699481\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 35.1186 | 2.47707 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −9.92399 | −0.696528 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.27664 | 0.228850 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 34.8776 | 2.42416 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −14.6949 | −1.01647 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.9892 | −1.65149 | −0.825743 | − | 0.564046i | \(-0.809244\pi\) | ||||
−0.825743 | + | 0.564046i | \(0.809244\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 17.8934 | 1.22603 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.59292 | −0.108637 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 24.5219 | 1.66465 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −21.5902 | −1.45893 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.83832 | −0.123659 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.0889 | 1.01043 | 0.505215 | − | 0.862993i | \(-0.331413\pi\) | ||||
0.505215 | + | 0.862993i | \(0.331413\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −32.2519 | −2.15013 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −19.4047 | −1.28794 | −0.643968 | − | 0.765053i | \(-0.722713\pi\) | ||||
−0.643968 | + | 0.765053i | \(0.722713\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.07540 | 0.335392 | 0.167696 | − | 0.985839i | \(-0.446367\pi\) | ||||
0.167696 | + | 0.985839i | \(0.446367\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 20.5697 | 1.35339 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 28.1567 | 1.84461 | 0.922304 | − | 0.386465i | \(-0.126304\pi\) | ||||
0.922304 | + | 0.386465i | \(0.126304\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.407310 | −0.0265700 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 46.7785 | 3.03859 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.86942 | 0.509030 | 0.254515 | − | 0.967069i | \(-0.418084\pi\) | ||||
0.254515 | + | 0.967069i | \(0.418084\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.8599 | 1.02162 | 0.510812 | − | 0.859693i | \(-0.329345\pi\) | ||||
0.510812 | + | 0.859693i | \(0.329345\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.9380 | 0.894122 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.944415 | 0.0603365 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.73198 | −0.237460 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 30.2794 | 1.91888 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −26.3744 | −1.66474 | −0.832369 | − | 0.554222i | \(-0.813016\pi\) | ||||
−0.832369 | + | 0.554222i | \(0.813016\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.3268 | 0.712108 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.23182 | −0.265007 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −21.0078 | −1.31043 | −0.655217 | − | 0.755441i | \(-0.727423\pi\) | ||||
−0.655217 | + | 0.755441i | \(0.727423\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 29.9832 | 1.86307 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −21.6895 | −1.34255 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.00628 | 0.247038 | 0.123519 | − | 0.992342i | \(-0.460582\pi\) | ||||
0.123519 | + | 0.992342i | \(0.460582\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.61455 | −0.160611 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 28.2924 | 1.73147 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.17613 | −0.437536 | −0.218768 | − | 0.975777i | \(-0.570204\pi\) | ||||
−0.218768 | + | 0.975777i | \(0.570204\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −18.5170 | −1.12483 | −0.562414 | − | 0.826856i | \(-0.690127\pi\) | ||||
−0.562414 | + | 0.826856i | \(0.690127\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.22397 | 0.316169 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −10.4741 | −0.631610 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.5411 | 0.633354 | 0.316677 | − | 0.948533i | \(-0.397433\pi\) | ||||
0.316677 | + | 0.948533i | \(0.397433\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 53.5940 | 3.20859 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.60641 | 0.453760 | 0.226880 | − | 0.973923i | \(-0.427147\pi\) | ||||
0.226880 | + | 0.973923i | \(0.427147\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.8983 | −0.766724 | −0.383362 | − | 0.923598i | \(-0.625234\pi\) | ||||
−0.383362 | + | 0.923598i | \(0.625234\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8.59102 | −0.508888 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 24.5573 | 1.44957 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.83910 | −0.343476 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −47.0806 | −2.75991 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.98565 | −0.116003 | −0.0580015 | − | 0.998316i | \(-0.518473\pi\) | ||||
−0.0580015 | + | 0.998316i | \(0.518473\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.11417 | −0.0648696 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 24.7415 | 1.43564 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.87659 | 0.166357 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.9384 | −0.688119 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 11.7435 | 0.674646 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.88716 | −0.108058 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.55506 | 0.431190 | 0.215595 | − | 0.976483i | \(-0.430831\pi\) | ||||
0.215595 | + | 0.976483i | \(0.430831\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.5903 | −0.716238 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 21.5882 | 1.22415 | 0.612077 | − | 0.790799i | \(-0.290334\pi\) | ||||
0.612077 | + | 0.790799i | \(0.290334\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.6067 | −0.825622 | −0.412811 | − | 0.910817i | \(-0.635453\pi\) | ||||
−0.412811 | + | 0.910817i | \(0.635453\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 8.29548 | 0.467397 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.34814 | 0.468878 | 0.234439 | − | 0.972131i | \(-0.424675\pi\) | ||||
0.234439 | + | 0.972131i | \(0.424675\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.04384 | −0.394379 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −43.7304 | −2.44079 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 22.6578 | 1.26071 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.66003 | −0.147552 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 29.9463 | 1.65604 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.05265 | −0.168298 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −31.8095 | −1.74841 | −0.874205 | − | 0.485558i | \(-0.838617\pi\) | ||||
−0.874205 | + | 0.485558i | \(0.838617\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 65.5302 | 3.59103 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.59949 | 0.251297 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.01424 | −0.327616 | −0.163808 | − | 0.986492i | \(-0.552378\pi\) | ||||
−0.163808 | + | 0.986492i | \(0.552378\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −21.7490 | −1.18125 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 17.4051 | 0.942539 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.2905 | −0.771613 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6.62192 | 0.356512 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.8677 | −0.690775 | −0.345387 | − | 0.938460i | \(-0.612253\pi\) | ||||
−0.345387 | + | 0.938460i | \(0.612253\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.9705 | −0.587237 | −0.293619 | − | 0.955923i | \(-0.594860\pi\) | ||||
−0.293619 | + | 0.955923i | \(0.594860\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.28344 | 0.335385 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 24.9810 | 1.32961 | 0.664803 | − | 0.747019i | \(-0.268516\pi\) | ||||
0.664803 | + | 0.747019i | \(0.268516\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.34350 | 0.124380 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −31.7160 | −1.67859 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −23.2115 | −1.22506 | −0.612528 | − | 0.790449i | \(-0.709847\pi\) | ||||
−0.612528 | + | 0.790449i | \(0.709847\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 26.9976 | 1.42092 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −19.6094 | −1.02923 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.82767 | −0.148007 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.5333 | 0.967430 | 0.483715 | − | 0.875226i | \(-0.339287\pi\) | ||||
0.483715 | + | 0.875226i | \(0.339287\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 53.6714 | 2.79402 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −19.5952 | −1.01733 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −32.7310 | −1.69475 | −0.847373 | − | 0.530998i | \(-0.821817\pi\) | ||||
−0.847373 | + | 0.530998i | \(0.821817\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −12.4570 | −0.643275 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.78888 | −0.0921320 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.8297 | −0.967215 | −0.483608 | − | 0.875285i | \(-0.660674\pi\) | ||||
−0.483608 | + | 0.875285i | \(0.660674\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.42590 | 0.0730511 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 37.4769 | 1.91498 | 0.957489 | − | 0.288470i | \(-0.0931466\pi\) | ||||
0.957489 | + | 0.288470i | \(0.0931466\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.69402 | 0.137300 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −26.0922 | −1.32634 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.88039 | 0.500956 | 0.250478 | − | 0.968122i | \(-0.419412\pi\) | ||||
0.250478 | + | 0.968122i | \(0.419412\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −17.4645 | −0.883217 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 17.0411 | 0.859612 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.12659 | 0.308262 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.26429 | −0.414773 | −0.207387 | − | 0.978259i | \(-0.566496\pi\) | ||||
−0.207387 | + | 0.978259i | \(0.566496\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −64.3868 | −3.22337 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 28.0473 | 1.40061 | 0.700307 | − | 0.713841i | \(-0.253046\pi\) | ||||
0.700307 | + | 0.713841i | \(0.253046\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.42026 | 0.220189 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 6.31208 | 0.313650 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 21.2814 | 1.05488 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.98600 | 0.295989 | 0.147994 | − | 0.988988i | \(-0.452718\pi\) | ||||
0.147994 | + | 0.988988i | \(0.452718\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 36.3569 | 1.79335 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.35034 | −0.410893 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.96570 | 0.194669 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 30.1389 | 1.47591 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.61266 | 0.176490 | 0.0882449 | − | 0.996099i | \(-0.471874\pi\) | ||||
0.0882449 | + | 0.996099i | \(0.471874\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 37.4594 | 1.82566 | 0.912829 | − | 0.408341i | \(-0.133893\pi\) | ||||
0.912829 | + | 0.408341i | \(0.133893\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.67175 | −0.324392 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 16.1497 | 0.783377 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −14.1436 | −0.684458 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.70786 | 0.179017 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.49150 | −0.312685 | −0.156342 | − | 0.987703i | \(-0.549970\pi\) | ||||
−0.156342 | + | 0.987703i | \(0.549970\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.1159 | 0.678369 | 0.339184 | − | 0.940720i | \(-0.389849\pi\) | ||||
0.339184 | + | 0.940720i | \(0.389849\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.11801 | −0.197443 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −35.4547 | −1.69603 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 23.0935 | 1.10219 | 0.551097 | − | 0.834441i | \(-0.314209\pi\) | ||||
0.551097 | + | 0.834441i | \(0.314209\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 15.4695 | 0.736645 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.41824 | −0.209917 | −0.104958 | − | 0.994477i | \(-0.533471\pi\) | ||||
−0.104958 | + | 0.994477i | \(0.533471\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.70547 | 0.175656 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −30.9280 | −1.46284 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 34.6386 | 1.63470 | 0.817348 | − | 0.576144i | \(-0.195443\pi\) | ||||
0.817348 | + | 0.576144i | \(0.195443\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 17.4302 | 0.820758 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −24.3685 | −1.14493 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.684185 | 0.0320751 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.1776 | 1.03742 | 0.518712 | − | 0.854949i | \(-0.326412\pi\) | ||||
0.518712 | + | 0.854949i | \(0.326412\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −38.1483 | −1.78061 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 22.1451 | 1.03140 | 0.515699 | − | 0.856770i | \(-0.327532\pi\) | ||||
0.515699 | + | 0.856770i | \(0.327532\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −33.6623 | −1.56442 | −0.782210 | − | 0.623015i | \(-0.785908\pi\) | ||||
−0.782210 | + | 0.623015i | \(0.785908\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 10.1755 | 0.471876 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −27.6298 | −1.27855 | −0.639276 | − | 0.768977i | \(-0.720766\pi\) | ||||
−0.639276 | + | 0.768977i | \(0.720766\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 34.4716 | 1.59175 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −55.8899 | −2.57527 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.47364 | −0.389618 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 32.7856 | 1.50431 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −42.8265 | −1.96089 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 19.8209 | 0.905640 | 0.452820 | − | 0.891602i | \(-0.350418\pi\) | ||||
0.452820 | + | 0.891602i | \(0.350418\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.40472 | 0.246434 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 49.6290 | 2.25820 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.16615 | −0.279990 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.49345 | −0.203618 | −0.101809 | − | 0.994804i | \(-0.532463\pi\) | ||||
−0.101809 | + | 0.994804i | \(0.532463\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 28.7081 | 1.29823 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.6023 | −0.478475 | −0.239238 | − | 0.970961i | \(-0.576897\pi\) | ||||
−0.239238 | + | 0.970961i | \(0.576897\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.8607 | 0.489143 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.88795 | 0.264644 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 17.5637 | 0.787841 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19.4794 | 0.872016 | 0.436008 | − | 0.899943i | \(-0.356392\pi\) | ||||
0.436008 | + | 0.899943i | \(0.356392\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −52.0092 | −2.32360 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7.10841 | −0.316948 | −0.158474 | − | 0.987363i | \(-0.550657\pi\) | ||||
−0.158474 | + | 0.987363i | \(0.550657\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.53805 | 0.0684422 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −39.4876 | −1.75371 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.46106 | 0.197733 | 0.0988666 | − | 0.995101i | \(-0.468478\pi\) | ||||
0.0988666 | + | 0.995101i | \(0.468478\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −21.1924 | −0.937497 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −77.4449 | −3.41928 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.64896 | −0.0726617 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.16670 | −0.0952915 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.05077 | 0.0900186 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −29.6999 | −1.30118 | −0.650589 | − | 0.759430i | \(-0.725478\pi\) | ||||
−0.650589 | + | 0.759430i | \(0.725478\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −39.9686 | −1.74771 | −0.873853 | − | 0.486191i | \(-0.838386\pi\) | ||||
−0.873853 | + | 0.486191i | \(0.838386\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −45.8928 | −2.00293 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −26.8365 | −1.16902 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.32829 | 0.188186 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −18.2502 | −0.791990 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.42665 | 0.191739 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.72738 | −0.247616 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.31385 | −0.0566968 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.02386 | 0.216393 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.3928 | −0.575801 | −0.287901 | − | 0.957660i | \(-0.592957\pi\) | ||||
−0.287901 | + | 0.957660i | \(0.592957\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 48.0269 | 2.06103 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.92208 | 0.168003 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.7590 | −1.22965 | −0.614824 | − | 0.788665i | \(-0.710773\pi\) | ||||
−0.614824 | + | 0.788665i | \(0.710773\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −30.9117 | −1.31928 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 22.0484 | 0.939294 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 45.9167 | 1.95258 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 12.4417 | 0.528120 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 19.6279 | 0.831659 | 0.415830 | − | 0.909442i | \(-0.363491\pi\) | ||||
0.415830 | + | 0.909442i | \(0.363491\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.15200 | −0.0910198 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −22.5114 | −0.950430 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 29.6491 | 1.24956 | 0.624780 | − | 0.780801i | \(-0.285188\pi\) | ||||
0.624780 | + | 0.780801i | \(0.285188\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.84848 | −0.119836 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 47.3069 | 1.98670 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 44.2613 | 1.85553 | 0.927765 | − | 0.373164i | \(-0.121727\pi\) | ||||
0.927765 | + | 0.373164i | \(0.121727\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −28.6496 | −1.19895 | −0.599475 | − | 0.800393i | \(-0.704624\pi\) | ||||
−0.599475 | + | 0.800393i | \(0.704624\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −19.2841 | −0.805607 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −25.2710 | −1.05387 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.20852 | 0.216833 | 0.108417 | − | 0.994106i | \(-0.465422\pi\) | ||||
0.108417 | + | 0.994106i | \(0.465422\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.84454 | −0.118215 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 29.7216 | 1.23306 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13.9082 | −0.576020 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.49533 | 0.0618242 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.64376 | −0.274217 | −0.137109 | − | 0.990556i | \(-0.543781\pi\) | ||||
−0.137109 | + | 0.990556i | \(0.543781\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −54.4809 | −2.24485 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −85.1671 | −3.50331 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −0.225118 | −0.00924447 | −0.00462223 | − | 0.999989i | \(-0.501471\pi\) | ||||
−0.00462223 | + | 0.999989i | \(0.501471\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.15386 | −0.170291 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −51.4577 | −2.10603 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −17.4269 | −0.712045 | −0.356023 | − | 0.934477i | \(-0.615867\pi\) | ||||
−0.356023 | + | 0.934477i | \(0.615867\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −34.2190 | −1.39582 | −0.697910 | − | 0.716185i | \(-0.745887\pi\) | ||||
−0.697910 | + | 0.716185i | \(0.745887\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 75.3398 | 3.06807 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.56825 | −0.104414 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −29.8314 | −1.21082 | −0.605410 | − | 0.795914i | \(-0.706991\pi\) | ||||
−0.605410 | + | 0.795914i | \(0.706991\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −30.8631 | −1.25063 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.550265 | −0.0222613 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −39.6737 | −1.60241 | −0.801203 | − | 0.598393i | \(-0.795806\pi\) | ||||
−0.801203 | + | 0.598393i | \(0.795806\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 10.1902 | 0.410907 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −25.4005 | −1.02259 | −0.511294 | − | 0.859406i | \(-0.670834\pi\) | ||||
−0.511294 | + | 0.859406i | \(0.670834\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.43419 | −0.298805 | −0.149403 | − | 0.988776i | \(-0.547735\pi\) | ||||
−0.149403 | + | 0.988776i | \(0.547735\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 59.6942 | 2.39544 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 27.7712 | 1.11263 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22.5390 | 0.901560 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −45.7004 | −1.82510 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −32.8134 | −1.30836 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.0345 | 1.27527 | 0.637636 | − | 0.770338i | \(-0.279912\pi\) | ||||
0.637636 | + | 0.770338i | \(0.279912\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −74.6051 | −2.96529 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.186751 | 0.00741097 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.27588 | 0.0505521 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 38.3866 | 1.51855 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17.2147 | 0.679938 | 0.339969 | − | 0.940437i | \(-0.389583\pi\) | ||||
0.339969 | + | 0.940437i | \(0.389583\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.1099 | 0.556439 | 0.278219 | − | 0.960518i | \(-0.410256\pi\) | ||||
0.278219 | + | 0.960518i | \(0.410256\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.95391 | −0.195060 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16.4499 | 0.646714 | 0.323357 | − | 0.946277i | \(-0.395189\pi\) | ||||
0.323357 | + | 0.946277i | \(0.395189\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.92689 | −0.232651 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 76.2616 | 2.98893 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 27.6510 | 1.08207 | 0.541035 | − | 0.841000i | \(-0.318033\pi\) | ||||
0.541035 | + | 0.841000i | \(0.318033\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.23188 | 0.0872068 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −46.3173 | −1.80701 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.95658 | −0.309945 | −0.154972 | − | 0.987919i | \(-0.549529\pi\) | ||||
−0.154972 | + | 0.987919i | \(0.549529\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 45.3923 | 1.76555 | 0.882777 | − | 0.469792i | \(-0.155671\pi\) | ||||
0.882777 | + | 0.469792i | \(0.155671\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.71707 | −0.222033 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.43275 | −0.327008 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −16.9948 | −0.658041 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 46.9258 | 1.81426 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10.0388 | −0.387545 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.24632 | −0.317872 | −0.158936 | − | 0.987289i | \(-0.550806\pi\) | ||||
−0.158936 | + | 0.987289i | \(0.550806\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −55.2003 | −2.12466 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.09676 | −0.349617 | −0.174808 | − | 0.984602i | \(-0.555931\pi\) | ||||
−0.174808 | + | 0.984602i | \(0.555931\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −46.2132 | −1.77350 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −60.3475 | −2.31252 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 26.9031 | 1.02942 | 0.514710 | − | 0.857364i | \(-0.327900\pi\) | ||||
0.514710 | + | 0.857364i | \(0.327900\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.76167 | 0.181934 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 15.7842 | 0.602205 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.53219 | −0.134566 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.1874 | 0.501673 | 0.250836 | − | 0.968029i | \(-0.419294\pi\) | ||||
0.250836 | + | 0.968029i | \(0.419294\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 44.1282 | 1.67629 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.94730 | 0.149730 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −26.8753 | −1.01797 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 87.5658 | 3.31204 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.53505 | 0.246825 | 0.123413 | − | 0.992355i | \(-0.460616\pi\) | ||||
0.123413 | + | 0.992355i | \(0.460616\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −66.6145 | −2.51241 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.26671 | −0.0477071 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11.5271 | 0.433523 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −43.6864 | −1.64068 | −0.820339 | − | 0.571877i | \(-0.806215\pi\) | ||||
−0.820339 | + | 0.571877i | \(0.806215\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 100.354 | 3.76356 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 41.9936 | 1.57267 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.485620 | 0.0181611 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 24.4734 | 0.913977 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.47228 | 0.204082 | 0.102041 | − | 0.994780i | \(-0.467463\pi\) | ||||
0.102041 | + | 0.994780i | \(0.467463\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.3584 | −0.460249 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 49.3233 | 1.83435 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 15.7154 | 0.583655 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.64274 | 0.172190 | 0.0860948 | − | 0.996287i | \(-0.472561\pi\) | ||||
0.0860948 | + | 0.996287i | \(0.472561\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.14464 | −0.116468 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 13.0653 | 0.483238 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.4222 | 0.532696 | 0.266348 | − | 0.963877i | \(-0.414183\pi\) | ||||
0.266348 | + | 0.963877i | \(0.414183\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.93708 | 0.108336 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 24.4672 | 0.901261 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −36.1648 | −1.33034 | −0.665172 | − | 0.746690i | \(-0.731642\pi\) | ||||
−0.665172 | + | 0.746690i | \(0.731642\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −11.6062 | −0.426366 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −45.9267 | −1.68489 | −0.842444 | − | 0.538784i | \(-0.818884\pi\) | ||||
−0.842444 | + | 0.538784i | \(0.818884\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.05065 | −0.148404 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 64.9583 | 2.37670 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −42.9247 | −1.56844 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 30.5643 | 1.11531 | 0.557653 | − | 0.830074i | \(-0.311702\pi\) | ||||
0.557653 | + | 0.830074i | \(0.311702\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −82.0229 | −2.98908 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.19154 | −0.116152 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.46143 | −0.0531164 | −0.0265582 | − | 0.999647i | \(-0.508455\pi\) | ||||
−0.0265582 | + | 0.999647i | \(0.508455\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 35.2256 | 1.27861 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −26.1612 | −0.948343 | −0.474171 | − | 0.880433i | \(-0.657252\pi\) | ||||
−0.474171 | + | 0.880433i | \(0.657252\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 29.3946 | 1.06416 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −9.07851 | −0.328234 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.50522 | −0.0543502 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −34.7026 | −1.25141 | −0.625704 | − | 0.780061i | \(-0.715188\pi\) | ||||
−0.625704 | + | 0.780061i | \(0.715188\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −65.3332 | −2.35292 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 35.1723 | 1.26506 | 0.632530 | − | 0.774536i | \(-0.282017\pi\) | ||||
0.632530 | + | 0.774536i | \(0.282017\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −38.8322 | −1.39489 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 93.2462 | 3.34519 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −54.5596 | −1.95480 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.4664 | 0.446081 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −37.1223 | −1.32664 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.31991 | −0.261259 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.57031 | −0.0559756 | −0.0279878 | − | 0.999608i | \(-0.508910\pi\) | ||||
−0.0279878 | + | 0.999608i | \(0.508910\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 12.4593 | 0.443563 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −21.3484 | −0.759060 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.54950 | −0.0905354 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8.13111 | −0.288381 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −11.3579 | −0.402318 | −0.201159 | − | 0.979559i | \(-0.564471\pi\) | ||||
−0.201159 | + | 0.979559i | \(0.564471\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.34079 | 0.118189 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 60.6957 | 2.14458 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −15.0419 | −0.530818 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.49992 | 0.229092 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −22.3174 | −0.785608 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 35.4551 | 1.24653 | 0.623267 | − | 0.782009i | \(-0.285805\pi\) | ||||
0.623267 | + | 0.782009i | \(0.285805\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.60023 | 0.0561917 | 0.0280959 | − | 0.999605i | \(-0.491056\pi\) | ||||
0.0280959 | + | 0.999605i | \(0.491056\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −57.5868 | −2.01966 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.75991 | 0.131704 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 26.5239 | 0.927954 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 11.2070 | 0.391603 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.29436 | −0.324375 | −0.162188 | − | 0.986760i | \(-0.551855\pi\) | ||||
−0.162188 | + | 0.986760i | \(0.551855\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.5978 | 0.613421 | 0.306711 | − | 0.951803i | \(-0.400772\pi\) | ||||
0.306711 | + | 0.951803i | \(0.400772\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −32.5737 | −1.13407 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 49.0737 | 1.70646 | 0.853230 | − | 0.521535i | \(-0.174641\pi\) | ||||
0.853230 | + | 0.521535i | \(0.174641\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.75210 | −0.269241 | −0.134621 | − | 0.990897i | \(-0.542982\pi\) | ||||
−0.134621 | + | 0.990897i | \(0.542982\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 32.7823 | 1.13720 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7.74618 | −0.268389 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.81166 | −0.235727 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 91.7281 | 3.17059 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −39.9387 | −1.37884 | −0.689419 | − | 0.724363i | \(-0.742134\pi\) | ||||
−0.689419 | + | 0.724363i | \(0.742134\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.4314 | −0.635564 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 23.6555 | 0.814739 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.17170 | −0.177912 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −19.2481 | −0.661374 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −40.1130 | −1.37667 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 51.3461 | 1.76012 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12.4661 | −0.426832 | −0.213416 | − | 0.976961i | \(-0.568459\pi\) | ||||
−0.213416 | + | 0.976961i | \(0.568459\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −18.4303 | −0.630303 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 15.2044 | 0.519373 | 0.259686 | − | 0.965693i | \(-0.416381\pi\) | ||||
0.259686 | + | 0.965693i | \(0.416381\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −41.5280 | −1.41692 | −0.708459 | − | 0.705752i | \(-0.750609\pi\) | ||||
−0.708459 | + | 0.705752i | \(0.750609\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 76.3718 | 2.60274 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −8.60696 | −0.292984 | −0.146492 | − | 0.989212i | \(-0.546798\pi\) | ||||
−0.146492 | + | 0.989212i | \(0.546798\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.268589 | 0.00913231 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −18.1593 | −0.616721 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 32.5907 | 1.10556 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.21378 | 0.210546 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −101.002 | −3.41839 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −12.2275 | −0.413364 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.78883 | 0.0604044 | 0.0302022 | − | 0.999544i | \(-0.490385\pi\) | ||||
0.0302022 | + | 0.999544i | \(0.490385\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.17526 | −0.208286 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5.30452 | −0.178714 | −0.0893570 | − | 0.996000i | \(-0.528481\pi\) | ||||
−0.0893570 | + | 0.996000i | \(0.528481\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.44640 | 0.149633 | 0.0748167 | − | 0.997197i | \(-0.476163\pi\) | ||||
0.0748167 | + | 0.997197i | \(0.476163\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.46501 | −0.116475 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −32.9646 | −1.10684 | −0.553421 | − | 0.832902i | \(-0.686678\pi\) | ||||
−0.553421 | + | 0.832902i | \(0.686678\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.39963 | 0.0469421 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 33.5774 | 1.12489 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.78215 | 0.226956 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.172075 | −0.00575183 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.94603 | 0.298699 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −26.1148 | −0.870977 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 21.4448 | 0.714430 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −37.1278 | −1.23554 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.29009 | 0.209090 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 39.7603 | 1.32022 | 0.660110 | − | 0.751169i | \(-0.270510\pi\) | ||||
0.660110 | + | 0.751169i | \(0.270510\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 25.1933 | 0.835608 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23.2653 | 0.770813 | 0.385407 | − | 0.922747i | \(-0.374061\pi\) | ||||
0.385407 | + | 0.922747i | \(0.374061\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 21.0957 | 0.698167 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5.86896 | −0.194022 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 16.7272 | 0.552380 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11.7907 | 0.388939 | 0.194469 | − | 0.980909i | \(-0.437702\pi\) | ||||
0.194469 | + | 0.980909i | \(0.437702\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 23.4958 | 0.774213 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.16600 | 0.104210 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −47.4807 | −1.56116 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −27.0099 | −0.887123 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 20.8905 | 0.685397 | 0.342698 | − | 0.939446i | \(-0.388659\pi\) | ||||
0.342698 | + | 0.939446i | \(0.388659\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15.7255 | −0.515383 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 67.1380 | 2.19800 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.94832 | −0.0964203 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32.9342 | 1.07591 | 0.537957 | − | 0.842972i | \(-0.319196\pi\) | ||||
0.537957 | + | 0.842972i | \(0.319196\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −45.4262 | −1.48243 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −45.1275 | −1.47111 | −0.735556 | − | 0.677463i | \(-0.763079\pi\) | ||||
−0.735556 | + | 0.677463i | \(0.763079\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 42.0542 | 1.36947 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 14.1980 | 0.461861 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 30.4571 | 0.989721 | 0.494861 | − | 0.868972i | \(-0.335219\pi\) | ||||
0.494861 | + | 0.868972i | \(0.335219\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.82010 | −0.124006 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 25.9622 | 0.841883 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 8.75634 | 0.283646 | 0.141823 | − | 0.989892i | \(-0.454704\pi\) | ||||
0.141823 | + | 0.989892i | \(0.454704\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.52565 | −0.0817281 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −21.9059 | −0.708118 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 35.6871 | 1.15240 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 33.5288 | 1.08157 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −93.8146 | −3.02313 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.372550 | −0.0119928 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 47.9641 | 1.54242 | 0.771210 | − | 0.636581i | \(-0.219652\pi\) | ||||
0.771210 | + | 0.636581i | \(0.219652\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 70.4644 | 2.26364 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 56.6897 | 1.81926 | 0.909629 | − | 0.415422i | \(-0.136366\pi\) | ||||
0.909629 | + | 0.415422i | \(0.136366\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 29.5836 | 0.948408 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −8.27255 | −0.264934 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −9.49520 | −0.303778 | −0.151889 | − | 0.988398i | \(-0.548536\pi\) | ||||
−0.151889 | + | 0.988398i | \(0.548536\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 19.7114 | 0.629979 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 64.2437 | 2.05114 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.08823 | −0.0666042 | −0.0333021 | − | 0.999445i | \(-0.510602\pi\) | ||||
−0.0333021 | + | 0.999445i | \(0.510602\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.1543 | −0.355407 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −9.49357 | −0.302184 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −20.4445 | −0.650097 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.54116 | 0.0489567 | 0.0244784 | − | 0.999700i | \(-0.492208\pi\) | ||||
0.0244784 | + | 0.999700i | \(0.492208\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −98.9258 | −3.13932 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.73943 | −0.213654 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −37.2343 | −1.17922 | −0.589611 | − | 0.807687i | \(-0.700719\pi\) | ||||
−0.589611 | + | 0.807687i | \(0.700719\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 112.157 | 3.54850 |
(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 | 6016.2.a.n.1.13 | yes | 13 | |
4.3 | odd | 2 | 6016.2.a.p.1.1 | yes | 13 | ||
8.3 | odd | 2 | 6016.2.a.m.1.13 | ✓ | 13 | ||
8.5 | even | 2 | 6016.2.a.o.1.1 | yes | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6016.2.a.m.1.13 | ✓ | 13 | 8.3 | odd | 2 | ||
6016.2.a.n.1.13 | yes | 13 | 1.1 | even | 1 | trivial | |
6016.2.a.o.1.1 | yes | 13 | 8.5 | even | 2 | ||
6016.2.a.p.1.1 | yes | 13 | 4.3 | odd | 2 |