Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3042,2,Mod(1,3042)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3042, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("3042.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3042 = 2 \cdot 3^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3042.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: | \(24.2904922949\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{14})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1014) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.80194\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3042.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 4.04892 | 1.81073 | 0.905365 | − | 0.424633i | \(-0.139597\pi\) | ||||
0.905365 | + | 0.424633i | \(0.139597\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.692021 | −0.261560 | −0.130780 | − | 0.991411i | \(-0.541748\pi\) | ||||
−0.130780 | + | 0.991411i | \(0.541748\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −4.04892 | −1.28038 | ||||||||
\(11\) | −4.85086 | −1.46259 | −0.731294 | − | 0.682062i | \(-0.761083\pi\) | ||||
−0.731294 | + | 0.682062i | \(0.761083\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0.692021 | 0.184951 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −7.38404 | −1.79089 | −0.895447 | − | 0.445169i | \(-0.853144\pi\) | ||||
−0.895447 | + | 0.445169i | \(0.853144\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.78017 | 0.408398 | 0.204199 | − | 0.978929i | \(-0.434541\pi\) | ||||
0.204199 | + | 0.978929i | \(0.434541\pi\) | |||||||
\(20\) | 4.04892 | 0.905365 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.85086 | 1.03421 | ||||||||
\(23\) | −5.10992 | −1.06549 | −0.532746 | − | 0.846275i | \(-0.678840\pi\) | ||||
−0.532746 | + | 0.846275i | \(0.678840\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 11.3937 | 2.27875 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.692021 | −0.130780 | ||||||||
\(29\) | 3.34481 | 0.621116 | 0.310558 | − | 0.950554i | \(-0.399484\pi\) | ||||
0.310558 | + | 0.950554i | \(0.399484\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.972853 | −0.174730 | −0.0873648 | − | 0.996176i | \(-0.527845\pi\) | ||||
−0.0873648 | + | 0.996176i | \(0.527845\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 7.38404 | 1.26635 | ||||||||
\(35\) | −2.80194 | −0.473614 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.28621 | −0.211451 | −0.105726 | − | 0.994395i | \(-0.533717\pi\) | ||||
−0.105726 | + | 0.994395i | \(0.533717\pi\) | |||||||
\(38\) | −1.78017 | −0.288781 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.04892 | −0.640190 | ||||||||
\(41\) | 1.50604 | 0.235204 | 0.117602 | − | 0.993061i | \(-0.462479\pi\) | ||||
0.117602 | + | 0.993061i | \(0.462479\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.31767 | −1.26843 | −0.634216 | − | 0.773156i | \(-0.718677\pi\) | ||||
−0.634216 | + | 0.773156i | \(0.718677\pi\) | |||||||
\(44\) | −4.85086 | −0.731294 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.10992 | 0.753416 | ||||||||
\(47\) | −7.20775 | −1.05136 | −0.525679 | − | 0.850683i | \(-0.676189\pi\) | ||||
−0.525679 | + | 0.850683i | \(0.676189\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.52111 | −0.931587 | ||||||||
\(50\) | −11.3937 | −1.61132 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −13.4765 | −1.85114 | −0.925570 | − | 0.378577i | \(-0.876414\pi\) | ||||
−0.925570 | + | 0.378577i | \(0.876414\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −19.6407 | −2.64835 | ||||||||
\(56\) | 0.692021 | 0.0924753 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.34481 | −0.439196 | ||||||||
\(59\) | 1.30798 | 0.170284 | 0.0851422 | − | 0.996369i | \(-0.472866\pi\) | ||||
0.0851422 | + | 0.996369i | \(0.472866\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.396125 | −0.0507185 | −0.0253593 | − | 0.999678i | \(-0.508073\pi\) | ||||
−0.0253593 | + | 0.999678i | \(0.508073\pi\) | |||||||
\(62\) | 0.972853 | 0.123552 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.05429 | −0.739650 | −0.369825 | − | 0.929101i | \(-0.620582\pi\) | ||||
−0.369825 | + | 0.929101i | \(0.620582\pi\) | |||||||
\(68\) | −7.38404 | −0.895447 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.80194 | 0.334896 | ||||||||
\(71\) | −1.32975 | −0.157812 | −0.0789061 | − | 0.996882i | \(-0.525143\pi\) | ||||
−0.0789061 | + | 0.996882i | \(0.525143\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.65279 | 0.895692 | 0.447846 | − | 0.894111i | \(-0.352191\pi\) | ||||
0.447846 | + | 0.894111i | \(0.352191\pi\) | |||||||
\(74\) | 1.28621 | 0.149519 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.78017 | 0.204199 | ||||||||
\(77\) | 3.35690 | 0.382554 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.33944 | −0.938260 | −0.469130 | − | 0.883129i | \(-0.655432\pi\) | ||||
−0.469130 | + | 0.883129i | \(0.655432\pi\) | |||||||
\(80\) | 4.04892 | 0.452683 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.50604 | −0.166314 | ||||||||
\(83\) | 15.3274 | 1.68240 | 0.841198 | − | 0.540727i | \(-0.181851\pi\) | ||||
0.841198 | + | 0.540727i | \(0.181851\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −29.8974 | −3.24283 | ||||||||
\(86\) | 8.31767 | 0.896917 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.85086 | 0.517103 | ||||||||
\(89\) | 3.10992 | 0.329650 | 0.164825 | − | 0.986323i | \(-0.447294\pi\) | ||||
0.164825 | + | 0.986323i | \(0.447294\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −5.10992 | −0.532746 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 7.20775 | 0.743423 | ||||||||
\(95\) | 7.20775 | 0.739500 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.54288 | 0.867398 | 0.433699 | − | 0.901058i | \(-0.357208\pi\) | ||||
0.433699 | + | 0.901058i | \(0.357208\pi\) | |||||||
\(98\) | 6.52111 | 0.658731 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 11.3937 | 1.13937 | ||||||||
\(101\) | 11.9976 | 1.19381 | 0.596903 | − | 0.802313i | \(-0.296398\pi\) | ||||
0.596903 | + | 0.802313i | \(0.296398\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.3230 | −1.21423 | −0.607113 | − | 0.794616i | \(-0.707672\pi\) | ||||
−0.607113 | + | 0.794616i | \(0.707672\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 13.4765 | 1.30895 | ||||||||
\(107\) | −5.89977 | −0.570353 | −0.285176 | − | 0.958475i | \(-0.592052\pi\) | ||||
−0.285176 | + | 0.958475i | \(0.592052\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.792249 | −0.0758837 | −0.0379418 | − | 0.999280i | \(-0.512080\pi\) | ||||
−0.0379418 | + | 0.999280i | \(0.512080\pi\) | |||||||
\(110\) | 19.6407 | 1.87267 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.692021 | −0.0653899 | ||||||||
\(113\) | −6.21983 | −0.585113 | −0.292556 | − | 0.956248i | \(-0.594506\pi\) | ||||
−0.292556 | + | 0.956248i | \(0.594506\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −20.6896 | −1.92932 | ||||||||
\(116\) | 3.34481 | 0.310558 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.30798 | −0.120409 | ||||||||
\(119\) | 5.10992 | 0.468425 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 12.5308 | 1.13916 | ||||||||
\(122\) | 0.396125 | 0.0358634 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.972853 | −0.0873648 | ||||||||
\(125\) | 25.8877 | 2.31547 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.00538 | −0.532891 | −0.266446 | − | 0.963850i | \(-0.585849\pi\) | ||||
−0.266446 | + | 0.963850i | \(0.585849\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.81700 | −0.770345 | −0.385173 | − | 0.922845i | \(-0.625858\pi\) | ||||
−0.385173 | + | 0.922845i | \(0.625858\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.23191 | −0.106821 | ||||||||
\(134\) | 6.05429 | 0.523011 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.38404 | 0.633176 | ||||||||
\(137\) | −15.7560 | −1.34613 | −0.673063 | − | 0.739585i | \(-0.735022\pi\) | ||||
−0.673063 | + | 0.739585i | \(0.735022\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.09783 | −0.517212 | −0.258606 | − | 0.965983i | \(-0.583263\pi\) | ||||
−0.258606 | + | 0.965983i | \(0.583263\pi\) | |||||||
\(140\) | −2.80194 | −0.236807 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.32975 | 0.111590 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 13.5429 | 1.12467 | ||||||||
\(146\) | −7.65279 | −0.633350 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.28621 | −0.105726 | ||||||||
\(149\) | −2.55257 | −0.209114 | −0.104557 | − | 0.994519i | \(-0.533343\pi\) | ||||
−0.104557 | + | 0.994519i | \(0.533343\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.7168 | 1.44177 | 0.720885 | − | 0.693054i | \(-0.243735\pi\) | ||||
0.720885 | + | 0.693054i | \(0.243735\pi\) | |||||||
\(152\) | −1.78017 | −0.144391 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.35690 | −0.270506 | ||||||||
\(155\) | −3.93900 | −0.316388 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.31767 | −0.504205 | −0.252102 | − | 0.967701i | \(-0.581122\pi\) | ||||
−0.252102 | + | 0.967701i | \(0.581122\pi\) | |||||||
\(158\) | 8.33944 | 0.663450 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −4.04892 | −0.320095 | ||||||||
\(161\) | 3.53617 | 0.278689 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.5918 | 1.14292 | 0.571459 | − | 0.820631i | \(-0.306378\pi\) | ||||
0.571459 | + | 0.820631i | \(0.306378\pi\) | |||||||
\(164\) | 1.50604 | 0.117602 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −15.3274 | −1.18963 | ||||||||
\(167\) | 19.5013 | 1.50905 | 0.754526 | − | 0.656270i | \(-0.227867\pi\) | ||||
0.754526 | + | 0.656270i | \(0.227867\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 29.8974 | 2.29302 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −8.31767 | −0.634216 | ||||||||
\(173\) | 9.29052 | 0.706345 | 0.353173 | − | 0.935558i | \(-0.385103\pi\) | ||||
0.353173 | + | 0.935558i | \(0.385103\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.88471 | −0.596028 | ||||||||
\(176\) | −4.85086 | −0.365647 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.10992 | −0.233098 | ||||||||
\(179\) | −22.7928 | −1.70362 | −0.851808 | − | 0.523853i | \(-0.824494\pi\) | ||||
−0.851808 | + | 0.523853i | \(0.824494\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.537500 | 0.0399520 | 0.0199760 | − | 0.999800i | \(-0.493641\pi\) | ||||
0.0199760 | + | 0.999800i | \(0.493641\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 5.10992 | 0.376708 | ||||||||
\(185\) | −5.20775 | −0.382881 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 35.8189 | 2.61934 | ||||||||
\(188\) | −7.20775 | −0.525679 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −7.20775 | −0.522905 | ||||||||
\(191\) | 9.79954 | 0.709070 | 0.354535 | − | 0.935043i | \(-0.384639\pi\) | ||||
0.354535 | + | 0.935043i | \(0.384639\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.1957 | −1.02183 | −0.510913 | − | 0.859632i | \(-0.670693\pi\) | ||||
−0.510913 | + | 0.859632i | \(0.670693\pi\) | |||||||
\(194\) | −8.54288 | −0.613343 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.52111 | −0.465793 | ||||||||
\(197\) | 3.00969 | 0.214431 | 0.107216 | − | 0.994236i | \(-0.465806\pi\) | ||||
0.107216 | + | 0.994236i | \(0.465806\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.8944 | 0.914059 | 0.457030 | − | 0.889451i | \(-0.348913\pi\) | ||||
0.457030 | + | 0.889451i | \(0.348913\pi\) | |||||||
\(200\) | −11.3937 | −0.805658 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −11.9976 | −0.844149 | ||||||||
\(203\) | −2.31468 | −0.162459 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.09783 | 0.425891 | ||||||||
\(206\) | 12.3230 | 0.858587 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.63533 | −0.597319 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.79954 | 0.536943 | 0.268471 | − | 0.963288i | \(-0.413482\pi\) | ||||
0.268471 | + | 0.963288i | \(0.413482\pi\) | |||||||
\(212\) | −13.4765 | −0.925570 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.89977 | 0.403300 | ||||||||
\(215\) | −33.6775 | −2.29679 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.673235 | 0.0457022 | ||||||||
\(218\) | 0.792249 | 0.0536579 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −19.6407 | −1.32418 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.1957 | −0.816682 | −0.408341 | − | 0.912829i | \(-0.633893\pi\) | ||||
−0.408341 | + | 0.912829i | \(0.633893\pi\) | |||||||
\(224\) | 0.692021 | 0.0462376 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.21983 | 0.413737 | ||||||||
\(227\) | −6.74333 | −0.447571 | −0.223785 | − | 0.974638i | \(-0.571841\pi\) | ||||
−0.223785 | + | 0.974638i | \(0.571841\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.8237 | −1.30999 | −0.654994 | − | 0.755634i | \(-0.727329\pi\) | ||||
−0.654994 | + | 0.755634i | \(0.727329\pi\) | |||||||
\(230\) | 20.6896 | 1.36423 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.34481 | −0.219598 | ||||||||
\(233\) | 30.0301 | 1.96734 | 0.983670 | − | 0.179983i | \(-0.0576044\pi\) | ||||
0.983670 | + | 0.179983i | \(0.0576044\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −29.1836 | −1.90373 | ||||||||
\(236\) | 1.30798 | 0.0851422 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −5.10992 | −0.331227 | ||||||||
\(239\) | −22.0978 | −1.42939 | −0.714695 | − | 0.699436i | \(-0.753435\pi\) | ||||
−0.714695 | + | 0.699436i | \(0.753435\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.1274 | 0.652362 | 0.326181 | − | 0.945307i | \(-0.394238\pi\) | ||||
0.326181 | + | 0.945307i | \(0.394238\pi\) | |||||||
\(242\) | −12.5308 | −0.805510 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.396125 | −0.0253593 | ||||||||
\(245\) | −26.4034 | −1.68685 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0.972853 | 0.0617762 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −25.8877 | −1.63728 | ||||||||
\(251\) | −5.54719 | −0.350135 | −0.175068 | − | 0.984556i | \(-0.556014\pi\) | ||||
−0.175068 | + | 0.984556i | \(0.556014\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 24.7875 | 1.55837 | ||||||||
\(254\) | 6.00538 | 0.376811 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 13.7995 | 0.860792 | 0.430396 | − | 0.902640i | \(-0.358374\pi\) | ||||
0.430396 | + | 0.902640i | \(0.358374\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.890084 | 0.0553071 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 8.81700 | 0.544716 | ||||||||
\(263\) | 22.4698 | 1.38555 | 0.692773 | − | 0.721155i | \(-0.256389\pi\) | ||||
0.692773 | + | 0.721155i | \(0.256389\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −54.5652 | −3.35192 | ||||||||
\(266\) | 1.23191 | 0.0755335 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6.05429 | −0.369825 | ||||||||
\(269\) | 26.0140 | 1.58610 | 0.793051 | − | 0.609156i | \(-0.208491\pi\) | ||||
0.793051 | + | 0.609156i | \(0.208491\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.88471 | 0.175233 | 0.0876167 | − | 0.996154i | \(-0.472075\pi\) | ||||
0.0876167 | + | 0.996154i | \(0.472075\pi\) | |||||||
\(272\) | −7.38404 | −0.447723 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 15.7560 | 0.951855 | ||||||||
\(275\) | −55.2693 | −3.33287 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.46250 | −0.0878731 | −0.0439366 | − | 0.999034i | \(-0.513990\pi\) | ||||
−0.0439366 | + | 0.999034i | \(0.513990\pi\) | |||||||
\(278\) | 6.09783 | 0.365724 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.80194 | 0.167448 | ||||||||
\(281\) | −5.68233 | −0.338980 | −0.169490 | − | 0.985532i | \(-0.554212\pi\) | ||||
−0.169490 | + | 0.985532i | \(0.554212\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −25.2078 | −1.49845 | −0.749223 | − | 0.662318i | \(-0.769573\pi\) | ||||
−0.749223 | + | 0.662318i | \(0.769573\pi\) | |||||||
\(284\) | −1.32975 | −0.0789061 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.04221 | −0.0615199 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 37.5241 | 2.20730 | ||||||||
\(290\) | −13.5429 | −0.795265 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 7.65279 | 0.447846 | ||||||||
\(293\) | 7.14914 | 0.417658 | 0.208829 | − | 0.977952i | \(-0.433035\pi\) | ||||
0.208829 | + | 0.977952i | \(0.433035\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.29590 | 0.308339 | ||||||||
\(296\) | 1.28621 | 0.0747593 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.55257 | 0.147866 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.75600 | 0.331771 | ||||||||
\(302\) | −17.7168 | −1.01949 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.78017 | 0.102100 | ||||||||
\(305\) | −1.60388 | −0.0918376 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.9952 | −1.02704 | −0.513521 | − | 0.858077i | \(-0.671659\pi\) | ||||
−0.513521 | + | 0.858077i | \(0.671659\pi\) | |||||||
\(308\) | 3.35690 | 0.191277 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3.93900 | 0.223720 | ||||||||
\(311\) | −3.32975 | −0.188813 | −0.0944064 | − | 0.995534i | \(-0.530095\pi\) | ||||
−0.0944064 | + | 0.995534i | \(0.530095\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.8834 | −1.01083 | −0.505414 | − | 0.862877i | \(-0.668660\pi\) | ||||
−0.505414 | + | 0.862877i | \(0.668660\pi\) | |||||||
\(314\) | 6.31767 | 0.356527 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.33944 | −0.469130 | ||||||||
\(317\) | −4.39373 | −0.246777 | −0.123388 | − | 0.992358i | \(-0.539376\pi\) | ||||
−0.123388 | + | 0.992358i | \(0.539376\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −16.2252 | −0.908437 | ||||||||
\(320\) | 4.04892 | 0.226341 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3.53617 | −0.197063 | ||||||||
\(323\) | −13.1448 | −0.731398 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −14.5918 | −0.808165 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.50604 | −0.0831572 | ||||||||
\(329\) | 4.98792 | 0.274993 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −25.6775 | −1.41137 | −0.705683 | − | 0.708528i | \(-0.749360\pi\) | ||||
−0.705683 | + | 0.708528i | \(0.749360\pi\) | |||||||
\(332\) | 15.3274 | 0.841198 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −19.5013 | −1.06706 | ||||||||
\(335\) | −24.5133 | −1.33931 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −24.6504 | −1.34279 | −0.671396 | − | 0.741098i | \(-0.734305\pi\) | ||||
−0.671396 | + | 0.741098i | \(0.734305\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −29.8974 | −1.62141 | ||||||||
\(341\) | 4.71917 | 0.255557 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.35690 | 0.505225 | ||||||||
\(344\) | 8.31767 | 0.448459 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −9.29052 | −0.499461 | ||||||||
\(347\) | −14.2959 | −0.767444 | −0.383722 | − | 0.923449i | \(-0.625358\pi\) | ||||
−0.383722 | + | 0.923449i | \(0.625358\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.0616 | 0.592113 | 0.296057 | − | 0.955170i | \(-0.404328\pi\) | ||||
0.296057 | + | 0.955170i | \(0.404328\pi\) | |||||||
\(350\) | 7.88471 | 0.421455 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.85086 | 0.258551 | ||||||||
\(353\) | 10.5047 | 0.559109 | 0.279555 | − | 0.960130i | \(-0.409813\pi\) | ||||
0.279555 | + | 0.960130i | \(0.409813\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.38404 | −0.285755 | ||||||||
\(356\) | 3.10992 | 0.164825 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 22.7928 | 1.20464 | ||||||||
\(359\) | −5.10992 | −0.269691 | −0.134846 | − | 0.990867i | \(-0.543054\pi\) | ||||
−0.134846 | + | 0.990867i | \(0.543054\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.8310 | −0.833211 | ||||||||
\(362\) | −0.537500 | −0.0282504 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 30.9855 | 1.62186 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.44803 | −0.440983 | −0.220492 | − | 0.975389i | \(-0.570766\pi\) | ||||
−0.220492 | + | 0.975389i | \(0.570766\pi\) | |||||||
\(368\) | −5.10992 | −0.266373 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 5.20775 | 0.270738 | ||||||||
\(371\) | 9.32603 | 0.484183 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.69096 | 0.398223 | 0.199111 | − | 0.979977i | \(-0.436194\pi\) | ||||
0.199111 | + | 0.979977i | \(0.436194\pi\) | |||||||
\(374\) | −35.8189 | −1.85215 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.20775 | 0.371711 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.4034 | −0.585754 | −0.292877 | − | 0.956150i | \(-0.594613\pi\) | ||||
−0.292877 | + | 0.956150i | \(0.594613\pi\) | |||||||
\(380\) | 7.20775 | 0.369750 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −9.79954 | −0.501388 | ||||||||
\(383\) | −20.6703 | −1.05620 | −0.528100 | − | 0.849182i | \(-0.677095\pi\) | ||||
−0.528100 | + | 0.849182i | \(0.677095\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13.5918 | 0.692702 | ||||||||
\(386\) | 14.1957 | 0.722541 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 8.54288 | 0.433699 | ||||||||
\(389\) | −17.4776 | −0.886148 | −0.443074 | − | 0.896485i | \(-0.646112\pi\) | ||||
−0.443074 | + | 0.896485i | \(0.646112\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 37.7318 | 1.90818 | ||||||||
\(392\) | 6.52111 | 0.329366 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.00969 | −0.151626 | ||||||||
\(395\) | −33.7657 | −1.69894 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −19.3599 | −0.971645 | −0.485822 | − | 0.874058i | \(-0.661480\pi\) | ||||
−0.485822 | + | 0.874058i | \(0.661480\pi\) | |||||||
\(398\) | −12.8944 | −0.646338 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 11.3937 | 0.569687 | ||||||||
\(401\) | 14.4832 | 0.723257 | 0.361628 | − | 0.932322i | \(-0.382221\pi\) | ||||
0.361628 | + | 0.932322i | \(0.382221\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 11.9976 | 0.596903 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.31468 | 0.114876 | ||||||||
\(407\) | 6.23921 | 0.309266 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −18.8984 | −0.934468 | −0.467234 | − | 0.884134i | \(-0.654749\pi\) | ||||
−0.467234 | + | 0.884134i | \(0.654749\pi\) | |||||||
\(410\) | −6.09783 | −0.301151 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −12.3230 | −0.607113 | ||||||||
\(413\) | −0.905149 | −0.0445395 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 62.0592 | 3.04637 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 8.63533 | 0.422368 | ||||||||
\(419\) | 21.7603 | 1.06306 | 0.531531 | − | 0.847039i | \(-0.321617\pi\) | ||||
0.531531 | + | 0.847039i | \(0.321617\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.5918 | 1.00358 | 0.501791 | − | 0.864989i | \(-0.332675\pi\) | ||||
0.501791 | + | 0.864989i | \(0.332675\pi\) | |||||||
\(422\) | −7.79954 | −0.379676 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 13.4765 | 0.654477 | ||||||||
\(425\) | −84.1318 | −4.08099 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.274127 | 0.0132659 | ||||||||
\(428\) | −5.89977 | −0.285176 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 33.6775 | 1.62408 | ||||||||
\(431\) | −34.5133 | −1.66245 | −0.831224 | − | 0.555937i | \(-0.812360\pi\) | ||||
−0.831224 | + | 0.555937i | \(0.812360\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.12631 | −0.102184 | −0.0510920 | − | 0.998694i | \(-0.516270\pi\) | ||||
−0.0510920 | + | 0.998694i | \(0.516270\pi\) | |||||||
\(434\) | −0.673235 | −0.0323163 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.792249 | −0.0379418 | ||||||||
\(437\) | −9.09651 | −0.435145 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.8321 | 1.04199 | 0.520994 | − | 0.853560i | \(-0.325561\pi\) | ||||
0.520994 | + | 0.853560i | \(0.325561\pi\) | |||||||
\(440\) | 19.6407 | 0.936334 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.54048 | 0.358259 | 0.179130 | − | 0.983825i | \(-0.442672\pi\) | ||||
0.179130 | + | 0.983825i | \(0.442672\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.5918 | 0.596908 | ||||||||
\(446\) | 12.1957 | 0.577482 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.692021 | −0.0326949 | ||||||||
\(449\) | −19.7560 | −0.932343 | −0.466172 | − | 0.884694i | \(-0.654367\pi\) | ||||
−0.466172 | + | 0.884694i | \(0.654367\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.30559 | −0.344007 | ||||||||
\(452\) | −6.21983 | −0.292556 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 6.74333 | 0.316480 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 23.8582 | 1.11604 | 0.558019 | − | 0.829828i | \(-0.311562\pi\) | ||||
0.558019 | + | 0.829828i | \(0.311562\pi\) | |||||||
\(458\) | 19.8237 | 0.926301 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −20.6896 | −0.964659 | ||||||||
\(461\) | 17.5773 | 0.818657 | 0.409329 | − | 0.912387i | \(-0.365763\pi\) | ||||
0.409329 | + | 0.912387i | \(0.365763\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23.8431 | 1.10808 | 0.554041 | − | 0.832489i | \(-0.313085\pi\) | ||||
0.554041 | + | 0.832489i | \(0.313085\pi\) | |||||||
\(464\) | 3.34481 | 0.155279 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −30.0301 | −1.39112 | ||||||||
\(467\) | −8.61058 | −0.398450 | −0.199225 | − | 0.979954i | \(-0.563842\pi\) | ||||
−0.199225 | + | 0.979954i | \(0.563842\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.18970 | 0.193462 | ||||||||
\(470\) | 29.1836 | 1.34614 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.30798 | −0.0602046 | ||||||||
\(473\) | 40.3478 | 1.85519 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 20.2828 | 0.930636 | ||||||||
\(476\) | 5.10992 | 0.234213 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 22.0978 | 1.01073 | ||||||||
\(479\) | −6.58104 | −0.300695 | −0.150348 | − | 0.988633i | \(-0.548039\pi\) | ||||
−0.150348 | + | 0.988633i | \(0.548039\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −10.1274 | −0.461289 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 12.5308 | 0.569582 | ||||||||
\(485\) | 34.5894 | 1.57062 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −23.2760 | −1.05474 | −0.527369 | − | 0.849636i | \(-0.676822\pi\) | ||||
−0.527369 | + | 0.849636i | \(0.676822\pi\) | |||||||
\(488\) | 0.396125 | 0.0179317 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 26.4034 | 1.19278 | ||||||||
\(491\) | 15.5405 | 0.701332 | 0.350666 | − | 0.936501i | \(-0.385955\pi\) | ||||
0.350666 | + | 0.936501i | \(0.385955\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −24.6983 | −1.11235 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.972853 | −0.0436824 | ||||||||
\(497\) | 0.920215 | 0.0412773 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.53617 | 0.426898 | 0.213449 | − | 0.976954i | \(-0.431530\pi\) | ||||
0.213449 | + | 0.976954i | \(0.431530\pi\) | |||||||
\(500\) | 25.8877 | 1.15773 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5.54719 | 0.247583 | ||||||||
\(503\) | 13.8345 | 0.616848 | 0.308424 | − | 0.951249i | \(-0.400198\pi\) | ||||
0.308424 | + | 0.951249i | \(0.400198\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 48.5773 | 2.16166 | ||||||||
\(506\) | −24.7875 | −1.10194 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −6.00538 | −0.266446 | ||||||||
\(509\) | 40.9638 | 1.81569 | 0.907843 | − | 0.419310i | \(-0.137728\pi\) | ||||
0.907843 | + | 0.419310i | \(0.137728\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.29590 | −0.234277 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −13.7995 | −0.608672 | ||||||||
\(515\) | −49.8950 | −2.19864 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 34.9638 | 1.53770 | ||||||||
\(518\) | −0.890084 | −0.0391080 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −36.3672 | −1.59327 | −0.796637 | − | 0.604457i | \(-0.793390\pi\) | ||||
−0.796637 | + | 0.604457i | \(0.793390\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.03013 | −0.263679 | −0.131840 | − | 0.991271i | \(-0.542088\pi\) | ||||
−0.131840 | + | 0.991271i | \(0.542088\pi\) | |||||||
\(524\) | −8.81700 | −0.385173 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −22.4698 | −0.979730 | ||||||||
\(527\) | 7.18359 | 0.312922 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.11124 | 0.135271 | ||||||||
\(530\) | 54.5652 | 2.37016 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.23191 | −0.0534103 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −23.8877 | −1.03275 | ||||||||
\(536\) | 6.05429 | 0.261506 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −26.0140 | −1.12154 | ||||||||
\(539\) | 31.6329 | 1.36253 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.92154 | −0.340574 | −0.170287 | − | 0.985395i | \(-0.554469\pi\) | ||||
−0.170287 | + | 0.985395i | \(0.554469\pi\) | |||||||
\(542\) | −2.88471 | −0.123909 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 7.38404 | 0.316588 | ||||||||
\(545\) | −3.20775 | −0.137405 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.4155 | 0.787390 | 0.393695 | − | 0.919241i | \(-0.371197\pi\) | ||||
0.393695 | + | 0.919241i | \(0.371197\pi\) | |||||||
\(548\) | −15.7560 | −0.673063 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 55.2693 | 2.35669 | ||||||||
\(551\) | 5.95433 | 0.253663 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.77107 | 0.245411 | ||||||||
\(554\) | 1.46250 | 0.0621357 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.09783 | −0.258606 | ||||||||
\(557\) | 23.9758 | 1.01589 | 0.507944 | − | 0.861390i | \(-0.330406\pi\) | ||||
0.507944 | + | 0.861390i | \(0.330406\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −2.80194 | −0.118403 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 5.68233 | 0.239695 | ||||||||
\(563\) | 2.29291 | 0.0966348 | 0.0483174 | − | 0.998832i | \(-0.484614\pi\) | ||||
0.0483174 | + | 0.998832i | \(0.484614\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −25.1836 | −1.05948 | ||||||||
\(566\) | 25.2078 | 1.05956 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.32975 | 0.0557950 | ||||||||
\(569\) | 44.3430 | 1.85896 | 0.929478 | − | 0.368878i | \(-0.120258\pi\) | ||||
0.929478 | + | 0.368878i | \(0.120258\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.2707 | −0.639058 | −0.319529 | − | 0.947577i | \(-0.603525\pi\) | ||||
−0.319529 | + | 0.947577i | \(0.603525\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.04221 | 0.0435011 | ||||||||
\(575\) | −58.2210 | −2.42798 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.77048 | 0.365120 | 0.182560 | − | 0.983195i | \(-0.441562\pi\) | ||||
0.182560 | + | 0.983195i | \(0.441562\pi\) | |||||||
\(578\) | −37.5241 | −1.56080 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 13.5429 | 0.562337 | ||||||||
\(581\) | −10.6069 | −0.440047 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 65.3726 | 2.70745 | ||||||||
\(584\) | −7.65279 | −0.316675 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.14914 | −0.295328 | ||||||||
\(587\) | 38.1430 | 1.57433 | 0.787166 | − | 0.616742i | \(-0.211548\pi\) | ||||
0.787166 | + | 0.616742i | \(0.211548\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.73184 | −0.0713593 | ||||||||
\(590\) | −5.29590 | −0.218029 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.28621 | −0.0528628 | ||||||||
\(593\) | 37.9517 | 1.55849 | 0.779244 | − | 0.626720i | \(-0.215603\pi\) | ||||
0.779244 | + | 0.626720i | \(0.215603\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 20.6896 | 0.848192 | ||||||||
\(596\) | −2.55257 | −0.104557 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.57971 | 0.146263 | 0.0731315 | − | 0.997322i | \(-0.476701\pi\) | ||||
0.0731315 | + | 0.997322i | \(0.476701\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.71678 | −0.233192 | −0.116596 | − | 0.993179i | \(-0.537198\pi\) | ||||
−0.116596 | + | 0.993179i | \(0.537198\pi\) | |||||||
\(602\) | −5.75600 | −0.234597 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 17.7168 | 0.720885 | ||||||||
\(605\) | 50.7362 | 2.06272 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22.4286 | 0.910351 | 0.455175 | − | 0.890402i | \(-0.349577\pi\) | ||||
0.455175 | + | 0.890402i | \(0.349577\pi\) | |||||||
\(608\) | −1.78017 | −0.0721953 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.60388 | 0.0649390 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −39.9603 | −1.61398 | −0.806991 | − | 0.590564i | \(-0.798905\pi\) | ||||
−0.806991 | + | 0.590564i | \(0.798905\pi\) | |||||||
\(614\) | 17.9952 | 0.726228 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.35690 | −0.135253 | ||||||||
\(617\) | −31.4470 | −1.26601 | −0.633003 | − | 0.774149i | \(-0.718178\pi\) | ||||
−0.633003 | + | 0.774149i | \(0.718178\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −29.3685 | −1.18042 | −0.590210 | − | 0.807250i | \(-0.700955\pi\) | ||||
−0.590210 | + | 0.807250i | \(0.700955\pi\) | |||||||
\(620\) | −3.93900 | −0.158194 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3.32975 | 0.133511 | ||||||||
\(623\) | −2.15213 | −0.0862232 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 47.8485 | 1.91394 | ||||||||
\(626\) | 17.8834 | 0.714764 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −6.31767 | −0.252102 | ||||||||
\(629\) | 9.49742 | 0.378687 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.6799 | 0.863065 | 0.431532 | − | 0.902097i | \(-0.357973\pi\) | ||||
0.431532 | + | 0.902097i | \(0.357973\pi\) | |||||||
\(632\) | 8.33944 | 0.331725 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 4.39373 | 0.174497 | ||||||||
\(635\) | −24.3153 | −0.964922 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 16.2252 | 0.642362 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −4.04892 | −0.160048 | ||||||||
\(641\) | −14.0108 | −0.553391 | −0.276696 | − | 0.960958i | \(-0.589239\pi\) | ||||
−0.276696 | + | 0.960958i | \(0.589239\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 30.7875 | 1.21414 | 0.607070 | − | 0.794649i | \(-0.292345\pi\) | ||||
0.607070 | + | 0.794649i | \(0.292345\pi\) | |||||||
\(644\) | 3.53617 | 0.139345 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 13.1448 | 0.517177 | ||||||||
\(647\) | 16.6025 | 0.652713 | 0.326357 | − | 0.945247i | \(-0.394179\pi\) | ||||
0.326357 | + | 0.945247i | \(0.394179\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.34481 | −0.249056 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 14.5918 | 0.571459 | ||||||||
\(653\) | −28.5459 | −1.11709 | −0.558543 | − | 0.829476i | \(-0.688639\pi\) | ||||
−0.558543 | + | 0.829476i | \(0.688639\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −35.6993 | −1.39489 | ||||||||
\(656\) | 1.50604 | 0.0588010 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −4.98792 | −0.194449 | ||||||||
\(659\) | −27.7187 | −1.07977 | −0.539884 | − | 0.841740i | \(-0.681532\pi\) | ||||
−0.539884 | + | 0.841740i | \(0.681532\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.8009 | 0.420105 | 0.210053 | − | 0.977690i | \(-0.432636\pi\) | ||||
0.210053 | + | 0.977690i | \(0.432636\pi\) | |||||||
\(662\) | 25.6775 | 0.997986 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −15.3274 | −0.594817 | ||||||||
\(665\) | −4.98792 | −0.193423 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −17.0917 | −0.661794 | ||||||||
\(668\) | 19.5013 | 0.754526 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 24.5133 | 0.947033 | ||||||||
\(671\) | 1.92154 | 0.0741803 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.3260 | 0.629322 | 0.314661 | − | 0.949204i | \(-0.398109\pi\) | ||||
0.314661 | + | 0.949204i | \(0.398109\pi\) | |||||||
\(674\) | 24.6504 | 0.949498 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −41.4252 | −1.59210 | −0.796050 | − | 0.605231i | \(-0.793081\pi\) | ||||
−0.796050 | + | 0.605231i | \(0.793081\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.91185 | −0.226876 | ||||||||
\(680\) | 29.8974 | 1.14651 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −4.71917 | −0.180706 | ||||||||
\(683\) | −31.2325 | −1.19508 | −0.597539 | − | 0.801840i | \(-0.703855\pi\) | ||||
−0.597539 | + | 0.801840i | \(0.703855\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −63.7948 | −2.43747 | ||||||||
\(686\) | −9.35690 | −0.357248 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −8.31767 | −0.317108 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24.9638 | 0.949666 | 0.474833 | − | 0.880076i | \(-0.342508\pi\) | ||||
0.474833 | + | 0.880076i | \(0.342508\pi\) | |||||||
\(692\) | 9.29052 | 0.353173 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 14.2959 | 0.542665 | ||||||||
\(695\) | −24.6896 | −0.936531 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −11.1207 | −0.421225 | ||||||||
\(698\) | −11.0616 | −0.418687 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −7.88471 | −0.298014 | ||||||||
\(701\) | −8.17151 | −0.308634 | −0.154317 | − | 0.988021i | \(-0.549318\pi\) | ||||
−0.154317 | + | 0.988021i | \(0.549318\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.28967 | −0.0863564 | ||||||||
\(704\) | −4.85086 | −0.182823 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −10.5047 | −0.395350 | ||||||||
\(707\) | −8.30260 | −0.312251 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −36.7982 | −1.38199 | −0.690993 | − | 0.722861i | \(-0.742826\pi\) | ||||
−0.690993 | + | 0.722861i | \(0.742826\pi\) | |||||||
\(710\) | 5.38404 | 0.202060 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.10992 | −0.116549 | ||||||||
\(713\) | 4.97120 | 0.186173 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −22.7928 | −0.851808 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 5.10992 | 0.190700 | ||||||||
\(719\) | −35.2223 | −1.31357 | −0.656786 | − | 0.754077i | \(-0.728084\pi\) | ||||
−0.656786 | + | 0.754077i | \(0.728084\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.52781 | 0.317592 | ||||||||
\(722\) | 15.8310 | 0.589169 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0.537500 | 0.0199760 | ||||||||
\(725\) | 38.1099 | 1.41537 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 40.6872 | 1.50901 | 0.754503 | − | 0.656297i | \(-0.227878\pi\) | ||||
0.754503 | + | 0.656297i | \(0.227878\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −30.9855 | −1.14683 | ||||||||
\(731\) | 61.4180 | 2.27163 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 27.1400 | 1.00244 | 0.501220 | − | 0.865320i | \(-0.332885\pi\) | ||||
0.501220 | + | 0.865320i | \(0.332885\pi\) | |||||||
\(734\) | 8.44803 | 0.311822 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.10992 | 0.188354 | ||||||||
\(737\) | 29.3685 | 1.08180 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.72587 | 0.137058 | 0.0685292 | − | 0.997649i | \(-0.478169\pi\) | ||||
0.0685292 | + | 0.997649i | \(0.478169\pi\) | |||||||
\(740\) | −5.20775 | −0.191441 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −9.32603 | −0.342369 | ||||||||
\(743\) | −21.8586 | −0.801915 | −0.400958 | − | 0.916097i | \(-0.631323\pi\) | ||||
−0.400958 | + | 0.916097i | \(0.631323\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.3351 | −0.378650 | ||||||||
\(746\) | −7.69096 | −0.281586 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 35.8189 | 1.30967 | ||||||||
\(749\) | 4.08277 | 0.149181 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 53.3642 | 1.94729 | 0.973644 | − | 0.228075i | \(-0.0732432\pi\) | ||||
0.973644 | + | 0.228075i | \(0.0732432\pi\) | |||||||
\(752\) | −7.20775 | −0.262840 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 71.7338 | 2.61066 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.63533 | −0.168474 | −0.0842370 | − | 0.996446i | \(-0.526845\pi\) | ||||
−0.0842370 | + | 0.996446i | \(0.526845\pi\) | |||||||
\(758\) | 11.4034 | 0.414191 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −7.20775 | −0.261453 | ||||||||
\(761\) | −11.5603 | −0.419062 | −0.209531 | − | 0.977802i | \(-0.567194\pi\) | ||||
−0.209531 | + | 0.977802i | \(0.567194\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.548253 | 0.0198481 | ||||||||
\(764\) | 9.79954 | 0.354535 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 20.6703 | 0.746847 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14.7439 | 0.531679 | 0.265840 | − | 0.964017i | \(-0.414351\pi\) | ||||
0.265840 | + | 0.964017i | \(0.414351\pi\) | |||||||
\(770\) | −13.5918 | −0.489814 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −14.1957 | −0.510913 | ||||||||
\(773\) | 6.42268 | 0.231008 | 0.115504 | − | 0.993307i | \(-0.463152\pi\) | ||||
0.115504 | + | 0.993307i | \(0.463152\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −11.0844 | −0.398164 | ||||||||
\(776\) | −8.54288 | −0.306671 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 17.4776 | 0.626601 | ||||||||
\(779\) | 2.68100 | 0.0960570 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.45042 | 0.230814 | ||||||||
\(782\) | −37.7318 | −1.34929 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.52111 | −0.232897 | ||||||||
\(785\) | −25.5797 | −0.912979 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 43.4336 | 1.54824 | 0.774119 | − | 0.633040i | \(-0.218193\pi\) | ||||
0.774119 | + | 0.633040i | \(0.218193\pi\) | |||||||
\(788\) | 3.00969 | 0.107216 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 33.7657 | 1.20133 | ||||||||
\(791\) | 4.30426 | 0.153042 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 19.3599 | 0.687056 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 12.8944 | 0.457030 | ||||||||
\(797\) | −21.0164 | −0.744439 | −0.372219 | − | 0.928145i | \(-0.621403\pi\) | ||||
−0.372219 | + | 0.928145i | \(0.621403\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 53.2223 | 1.88287 | ||||||||
\(800\) | −11.3937 | −0.402829 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −14.4832 | −0.511420 | ||||||||
\(803\) | −37.1226 | −1.31003 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 14.3177 | 0.504631 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −11.9976 | −0.422074 | ||||||||
\(809\) | 8.32245 | 0.292602 | 0.146301 | − | 0.989240i | \(-0.453263\pi\) | ||||
0.146301 | + | 0.989240i | \(0.453263\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14.4638 | 0.507894 | 0.253947 | − | 0.967218i | \(-0.418271\pi\) | ||||
0.253947 | + | 0.967218i | \(0.418271\pi\) | |||||||
\(812\) | −2.31468 | −0.0812295 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −6.23921 | −0.218684 | ||||||||
\(815\) | 59.0810 | 2.06952 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −14.8068 | −0.518026 | ||||||||
\(818\) | 18.8984 | 0.660769 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.09783 | 0.212946 | ||||||||
\(821\) | −38.4161 | −1.34073 | −0.670365 | − | 0.742031i | \(-0.733863\pi\) | ||||
−0.670365 | + | 0.742031i | \(0.733863\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −40.9748 | −1.42829 | −0.714145 | − | 0.699997i | \(-0.753184\pi\) | ||||
−0.714145 | + | 0.699997i | \(0.753184\pi\) | |||||||
\(824\) | 12.3230 | 0.429294 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.905149 | 0.0314942 | ||||||||
\(827\) | 3.51035 | 0.122067 | 0.0610335 | − | 0.998136i | \(-0.480560\pi\) | ||||
0.0610335 | + | 0.998136i | \(0.480560\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13.2185 | −0.459098 | −0.229549 | − | 0.973297i | \(-0.573725\pi\) | ||||
−0.229549 | + | 0.973297i | \(0.573725\pi\) | |||||||
\(830\) | −62.0592 | −2.15411 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 48.1521 | 1.66837 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 78.9590 | 2.73249 | ||||||||
\(836\) | −8.63533 | −0.298659 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −21.7603 | −0.751698 | ||||||||
\(839\) | 55.8491 | 1.92812 | 0.964062 | − | 0.265678i | \(-0.0855959\pi\) | ||||
0.964062 | + | 0.265678i | \(0.0855959\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.8122 | −0.614214 | ||||||||
\(842\) | −20.5918 | −0.709640 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 7.79954 | 0.268471 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.67158 | −0.297959 | ||||||||
\(848\) | −13.4765 | −0.462785 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 84.1318 | 2.88570 | ||||||||
\(851\) | 6.57242 | 0.225300 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21.8103 | −0.746770 | −0.373385 | − | 0.927676i | \(-0.621803\pi\) | ||||
−0.373385 | + | 0.927676i | \(0.621803\pi\) | |||||||
\(854\) | −0.274127 | −0.00938042 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.89977 | 0.201650 | ||||||||
\(857\) | −28.8961 | −0.987070 | −0.493535 | − | 0.869726i | \(-0.664296\pi\) | ||||
−0.493535 | + | 0.869726i | \(0.664296\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17.2755 | −0.589431 | −0.294715 | − | 0.955585i | \(-0.595225\pi\) | ||||
−0.294715 | + | 0.955585i | \(0.595225\pi\) | |||||||
\(860\) | −33.6775 | −1.14839 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 34.5133 | 1.17553 | ||||||||
\(863\) | 44.7741 | 1.52413 | 0.762063 | − | 0.647503i | \(-0.224187\pi\) | ||||
0.762063 | + | 0.647503i | \(0.224187\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 37.6165 | 1.27900 | ||||||||
\(866\) | 2.12631 | 0.0722549 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.673235 | 0.0228511 | ||||||||
\(869\) | 40.4534 | 1.37229 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0.792249 | 0.0268289 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 9.09651 | 0.307694 | ||||||||
\(875\) | −17.9148 | −0.605632 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −40.2741 | −1.35996 | −0.679980 | − | 0.733230i | \(-0.738012\pi\) | ||||
−0.679980 | + | 0.733230i | \(0.738012\pi\) | |||||||
\(878\) | −21.8321 | −0.736797 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −19.6407 | −0.662088 | ||||||||
\(881\) | −9.40821 | −0.316971 | −0.158485 | − | 0.987361i | \(-0.550661\pi\) | ||||
−0.158485 | + | 0.987361i | \(0.550661\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −51.2271 | −1.72393 | −0.861965 | − | 0.506968i | \(-0.830766\pi\) | ||||
−0.861965 | + | 0.506968i | \(0.830766\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −7.54048 | −0.253328 | ||||||||
\(887\) | 39.9215 | 1.34043 | 0.670217 | − | 0.742165i | \(-0.266201\pi\) | ||||
0.670217 | + | 0.742165i | \(0.266201\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.15585 | 0.139383 | ||||||||
\(890\) | −12.5918 | −0.422078 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −12.1957 | −0.408341 | ||||||||
\(893\) | −12.8310 | −0.429373 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −92.2863 | −3.08479 | ||||||||
\(896\) | 0.692021 | 0.0231188 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 19.7560 | 0.659266 | ||||||||
\(899\) | −3.25401 | −0.108527 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 99.5111 | 3.31519 | ||||||||
\(902\) | 7.30559 | 0.243249 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 6.21983 | 0.206869 | ||||||||
\(905\) | 2.17629 | 0.0723424 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −34.8310 | −1.15654 | −0.578272 | − | 0.815844i | \(-0.696273\pi\) | ||||
−0.578272 | + | 0.815844i | \(0.696273\pi\) | |||||||
\(908\) | −6.74333 | −0.223785 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −13.2125 | −0.437751 | −0.218875 | − | 0.975753i | \(-0.570239\pi\) | ||||
−0.218875 | + | 0.975753i | \(0.570239\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −74.3508 | −2.46065 | ||||||||
\(914\) | −23.8582 | −0.789157 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −19.8237 | −0.654994 | ||||||||
\(917\) | 6.10156 | 0.201491 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 21.0175 | 0.693302 | 0.346651 | − | 0.937994i | \(-0.387319\pi\) | ||||
0.346651 | + | 0.937994i | \(0.387319\pi\) | |||||||
\(920\) | 20.6896 | 0.682117 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −17.5773 | −0.578878 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −14.6547 | −0.481844 | ||||||||
\(926\) | −23.8431 | −0.783532 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.34481 | −0.109799 | ||||||||
\(929\) | 26.9965 | 0.885728 | 0.442864 | − | 0.896589i | \(-0.353962\pi\) | ||||
0.442864 | + | 0.896589i | \(0.353962\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −11.6087 | −0.380459 | ||||||||
\(932\) | 30.0301 | 0.983670 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 8.61058 | 0.281747 | ||||||||
\(935\) | 145.028 | 4.74292 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23.1745 | 0.757078 | 0.378539 | − | 0.925585i | \(-0.376427\pi\) | ||||
0.378539 | + | 0.925585i | \(0.376427\pi\) | |||||||
\(938\) | −4.18970 | −0.136799 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −29.1836 | −0.951864 | ||||||||
\(941\) | −7.54048 | −0.245813 | −0.122906 | − | 0.992418i | \(-0.539221\pi\) | ||||
−0.122906 | + | 0.992418i | \(0.539221\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.69574 | −0.250608 | ||||||||
\(944\) | 1.30798 | 0.0425711 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −40.3478 | −1.31182 | ||||||||
\(947\) | −20.6601 | −0.671363 | −0.335681 | − | 0.941976i | \(-0.608967\pi\) | ||||
−0.335681 | + | 0.941976i | \(0.608967\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −20.2828 | −0.658059 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −5.10992 | −0.165613 | ||||||||
\(953\) | 30.2935 | 0.981303 | 0.490651 | − | 0.871356i | \(-0.336759\pi\) | ||||
0.490651 | + | 0.871356i | \(0.336759\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 39.6775 | 1.28394 | ||||||||
\(956\) | −22.0978 | −0.714695 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 6.58104 | 0.212624 | ||||||||
\(959\) | 10.9035 | 0.352092 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.0536 | −0.969470 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 10.1274 | 0.326181 | ||||||||
\(965\) | −57.4771 | −1.85025 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −20.7289 | −0.666595 | −0.333298 | − | 0.942822i | \(-0.608161\pi\) | ||||
−0.333298 | + | 0.942822i | \(0.608161\pi\) | |||||||
\(968\) | −12.5308 | −0.402755 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −34.5894 | −1.11060 | ||||||||
\(971\) | 39.1094 | 1.25508 | 0.627541 | − | 0.778584i | \(-0.284062\pi\) | ||||
0.627541 | + | 0.778584i | \(0.284062\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.21983 | 0.135282 | ||||||||
\(974\) | 23.2760 | 0.745813 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.396125 | −0.0126796 | ||||||||
\(977\) | −7.27545 | −0.232762 | −0.116381 | − | 0.993205i | \(-0.537129\pi\) | ||||
−0.116381 | + | 0.993205i | \(0.537129\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −15.0858 | −0.482143 | ||||||||
\(980\) | −26.4034 | −0.843426 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −15.5405 | −0.495917 | ||||||||
\(983\) | −53.4857 | −1.70593 | −0.852965 | − | 0.521969i | \(-0.825198\pi\) | ||||
−0.852965 | + | 0.521969i | \(0.825198\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.1860 | 0.388278 | ||||||||
\(986\) | 24.6983 | 0.786553 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 42.5026 | 1.35150 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.0575 | 0.510085 | 0.255042 | − | 0.966930i | \(-0.417911\pi\) | ||||
0.255042 | + | 0.966930i | \(0.417911\pi\) | |||||||
\(992\) | 0.972853 | 0.0308881 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −0.920215 | −0.0291874 | ||||||||
\(995\) | 52.2083 | 1.65512 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22.4263 | 0.710247 | 0.355123 | − | 0.934819i | \(-0.384439\pi\) | ||||
0.355123 | + | 0.934819i | \(0.384439\pi\) | |||||||
\(998\) | −9.53617 | −0.301862 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3042.2.a.bd.1.3 | 3 | ||
3.2 | odd | 2 | 1014.2.a.o.1.1 | yes | 3 | ||
12.11 | even | 2 | 8112.2.a.bz.1.1 | 3 | |||
13.5 | odd | 4 | 3042.2.b.r.1351.4 | 6 | |||
13.8 | odd | 4 | 3042.2.b.r.1351.3 | 6 | |||
13.12 | even | 2 | 3042.2.a.be.1.1 | 3 | |||
39.2 | even | 12 | 1014.2.i.g.823.6 | 12 | |||
39.5 | even | 4 | 1014.2.b.g.337.3 | 6 | |||
39.8 | even | 4 | 1014.2.b.g.337.4 | 6 | |||
39.11 | even | 12 | 1014.2.i.g.823.1 | 12 | |||
39.17 | odd | 6 | 1014.2.e.m.991.3 | 6 | |||
39.20 | even | 12 | 1014.2.i.g.361.4 | 12 | |||
39.23 | odd | 6 | 1014.2.e.m.529.3 | 6 | |||
39.29 | odd | 6 | 1014.2.e.k.529.1 | 6 | |||
39.32 | even | 12 | 1014.2.i.g.361.3 | 12 | |||
39.35 | odd | 6 | 1014.2.e.k.991.1 | 6 | |||
39.38 | odd | 2 | 1014.2.a.m.1.3 | ✓ | 3 | ||
156.155 | even | 2 | 8112.2.a.ce.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1014.2.a.m.1.3 | ✓ | 3 | 39.38 | odd | 2 | ||
1014.2.a.o.1.1 | yes | 3 | 3.2 | odd | 2 | ||
1014.2.b.g.337.3 | 6 | 39.5 | even | 4 | |||
1014.2.b.g.337.4 | 6 | 39.8 | even | 4 | |||
1014.2.e.k.529.1 | 6 | 39.29 | odd | 6 | |||
1014.2.e.k.991.1 | 6 | 39.35 | odd | 6 | |||
1014.2.e.m.529.3 | 6 | 39.23 | odd | 6 | |||
1014.2.e.m.991.3 | 6 | 39.17 | odd | 6 | |||
1014.2.i.g.361.3 | 12 | 39.32 | even | 12 | |||
1014.2.i.g.361.4 | 12 | 39.20 | even | 12 | |||
1014.2.i.g.823.1 | 12 | 39.11 | even | 12 | |||
1014.2.i.g.823.6 | 12 | 39.2 | even | 12 | |||
3042.2.a.bd.1.3 | 3 | 1.1 | even | 1 | trivial | ||
3042.2.a.be.1.1 | 3 | 13.12 | even | 2 | |||
3042.2.b.r.1351.3 | 6 | 13.8 | odd | 4 | |||
3042.2.b.r.1351.4 | 6 | 13.5 | odd | 4 | |||
8112.2.a.bz.1.1 | 3 | 12.11 | even | 2 | |||
8112.2.a.ce.1.3 | 3 | 156.155 | even | 2 |