Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [456,2,Mod(1,456)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(456, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("456.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 456 = 2^{3} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 456.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: | \(3.64117833217\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 456.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.56155 | −0.698348 | −0.349174 | − | 0.937058i | \(-0.613538\pi\) | ||||
−0.349174 | + | 0.937058i | \(0.613538\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.56155 | −0.590211 | −0.295106 | − | 0.955465i | \(-0.595355\pi\) | ||||
−0.295106 | + | 0.955465i | \(0.595355\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.56155 | 1.67687 | 0.838436 | − | 0.545001i | \(-0.183471\pi\) | ||||
0.838436 | + | 0.545001i | \(0.183471\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.12311 | 0.866194 | 0.433097 | − | 0.901347i | \(-0.357421\pi\) | ||||
0.433097 | + | 0.901347i | \(0.357421\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.56155 | −0.403191 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.68466 | 1.62127 | 0.810634 | − | 0.585553i | \(-0.199123\pi\) | ||||
0.810634 | + | 0.585553i | \(0.199123\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.56155 | −0.340759 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 9.12311 | 1.90230 | 0.951150 | − | 0.308731i | \(-0.0999042\pi\) | ||||
0.951150 | + | 0.308731i | \(0.0999042\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.56155 | −0.512311 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.24621 | −1.53128 | −0.765641 | − | 0.643268i | \(-0.777578\pi\) | ||||
−0.765641 | + | 0.643268i | \(0.777578\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.00000 | −0.359211 | −0.179605 | − | 0.983739i | \(-0.557482\pi\) | ||||
−0.179605 | + | 0.983739i | \(0.557482\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.56155 | 0.968142 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.43845 | 0.412173 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.00000 | −1.31519 | −0.657596 | − | 0.753371i | \(-0.728427\pi\) | ||||
−0.657596 | + | 0.753371i | \(0.728427\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.12311 | 0.500097 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.12311 | −0.800095 | −0.400047 | − | 0.916494i | \(-0.631006\pi\) | ||||
−0.400047 | + | 0.916494i | \(0.631006\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.56155 | −0.238135 | −0.119067 | − | 0.992886i | \(-0.537990\pi\) | ||||
−0.119067 | + | 0.992886i | \(0.537990\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.56155 | −0.232783 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.68466 | −0.975058 | −0.487529 | − | 0.873107i | \(-0.662102\pi\) | ||||
−0.487529 | + | 0.873107i | \(0.662102\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.56155 | −0.651650 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.68466 | 0.936039 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.24621 | 0.583262 | 0.291631 | − | 0.956531i | \(-0.405802\pi\) | ||||
0.291631 | + | 0.956531i | \(0.405802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.68466 | −1.17104 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.00000 | 0.132453 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.0000 | 1.56227 | 0.781133 | − | 0.624364i | \(-0.214642\pi\) | ||||
0.781133 | + | 0.624364i | \(0.214642\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.68466 | 0.855883 | 0.427941 | − | 0.903806i | \(-0.359239\pi\) | ||||
0.427941 | + | 0.903806i | \(0.359239\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.56155 | −0.196737 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.87689 | −0.604904 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.24621 | 0.763096 | 0.381548 | − | 0.924349i | \(-0.375391\pi\) | ||||
0.381548 | + | 0.924349i | \(0.375391\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 9.12311 | 1.09829 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −16.9309 | −1.98161 | −0.990804 | − | 0.135303i | \(-0.956799\pi\) | ||||
−0.990804 | + | 0.135303i | \(0.956799\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.56155 | −0.295783 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8.68466 | −0.989709 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.3693 | 1.27915 | 0.639574 | − | 0.768729i | \(-0.279111\pi\) | ||||
0.639574 | + | 0.768729i | \(0.279111\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.00000 | 0.439057 | 0.219529 | − | 0.975606i | \(-0.429548\pi\) | ||||
0.219529 | + | 0.975606i | \(0.429548\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.4384 | −1.13221 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.24621 | −0.884087 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.00000 | −0.635999 | −0.317999 | − | 0.948091i | \(-0.603011\pi\) | ||||
−0.317999 | + | 0.948091i | \(0.603011\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.87689 | −0.511237 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.00000 | −0.207390 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.56155 | −0.160212 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.24621 | 0.431137 | 0.215569 | − | 0.976489i | \(-0.430839\pi\) | ||||
0.215569 | + | 0.976489i | \(0.430839\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.56155 | 0.558957 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.12311 | 0.708776 | 0.354388 | − | 0.935099i | \(-0.384689\pi\) | ||||
0.354388 | + | 0.935099i | \(0.384689\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.00000 | −0.591198 | −0.295599 | − | 0.955312i | \(-0.595519\pi\) | ||||
−0.295599 | + | 0.955312i | \(0.595519\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.43845 | 0.237968 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.3693 | −1.29246 | −0.646230 | − | 0.763142i | \(-0.723655\pi\) | ||||
−0.646230 | + | 0.763142i | \(0.723655\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.24621 | −0.215148 | −0.107574 | − | 0.994197i | \(-0.534308\pi\) | ||||
−0.107574 | + | 0.994197i | \(0.534308\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.00000 | −0.759326 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.00000 | −0.188144 | −0.0940721 | − | 0.995565i | \(-0.529988\pi\) | ||||
−0.0940721 | + | 0.995565i | \(0.529988\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −14.2462 | −1.32847 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.12311 | 0.288731 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −10.4384 | −0.956891 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 19.9309 | 1.81190 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.12311 | −0.461935 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.8078 | 1.05612 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.0000 | −1.59724 | −0.798621 | − | 0.601834i | \(-0.794437\pi\) | ||||
−0.798621 | + | 0.601834i | \(0.794437\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.56155 | −0.137487 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 20.6847 | 1.80723 | 0.903613 | − | 0.428349i | \(-0.140905\pi\) | ||||
0.903613 | + | 0.428349i | \(0.140905\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.56155 | −0.135404 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.56155 | −0.134397 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.8078 | −1.17968 | −0.589838 | − | 0.807521i | \(-0.700809\pi\) | ||||
−0.589838 | + | 0.807521i | \(0.700809\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.80776 | −0.662246 | −0.331123 | − | 0.943588i | \(-0.607427\pi\) | ||||
−0.331123 | + | 0.943588i | \(0.607427\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.68466 | −0.562950 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 17.3693 | 1.45250 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12.8769 | 1.06937 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.56155 | −0.376231 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.80776 | 0.311944 | 0.155972 | − | 0.987761i | \(-0.450149\pi\) | ||||
0.155972 | + | 0.987761i | \(0.450149\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.1231 | −1.39346 | −0.696729 | − | 0.717334i | \(-0.745362\pi\) | ||||
−0.696729 | + | 0.717334i | \(0.745362\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.68466 | 0.540423 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.12311 | 0.250854 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.2462 | −0.977354 | −0.488677 | − | 0.872465i | \(-0.662520\pi\) | ||||
−0.488677 | + | 0.872465i | \(0.662520\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.24621 | 0.336746 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −14.2462 | −1.12276 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.24621 | −0.175937 | −0.0879684 | − | 0.996123i | \(-0.528037\pi\) | ||||
−0.0879684 | + | 0.996123i | \(0.528037\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −8.68466 | −0.676100 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.87689 | −0.686915 | −0.343457 | − | 0.939168i | \(-0.611598\pi\) | ||||
−0.343457 | + | 0.939168i | \(0.611598\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.24621 | −0.249709 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.00000 | 0.0764719 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.24621 | −0.322833 | −0.161417 | − | 0.986886i | \(-0.551606\pi\) | ||||
−0.161417 | + | 0.986886i | \(0.551606\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.00000 | 0.302372 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 12.0000 | 0.901975 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −15.1231 | −1.13035 | −0.565177 | − | 0.824970i | \(-0.691192\pi\) | ||||
−0.565177 | + | 0.824970i | \(0.691192\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.1231 | 1.12409 | 0.562046 | − | 0.827106i | \(-0.310014\pi\) | ||||
0.562046 | + | 0.827106i | \(0.310014\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.68466 | 0.494144 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 12.4924 | 0.918461 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 37.1771 | 2.71866 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.56155 | −0.113586 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.31534 | −0.0951748 | −0.0475874 | − | 0.998867i | \(-0.515153\pi\) | ||||
−0.0475874 | + | 0.998867i | \(0.515153\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.8769 | 1.35879 | 0.679394 | − | 0.733773i | \(-0.262243\pi\) | ||||
0.679394 | + | 0.733773i | \(0.262243\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.87689 | −0.349242 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.36932 | −0.0975598 | −0.0487799 | − | 0.998810i | \(-0.515533\pi\) | ||||
−0.0487799 | + | 0.998810i | \(0.515533\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.93087 | 0.207764 | 0.103882 | − | 0.994590i | \(-0.466874\pi\) | ||||
0.103882 | + | 0.994590i | \(0.466874\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.24621 | 0.440574 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 12.8769 | 0.903781 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.00000 | 0.558744 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 9.12311 | 0.634100 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.56155 | 0.384701 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.75379 | 0.396107 | 0.198054 | − | 0.980191i | \(-0.436538\pi\) | ||||
0.198054 | + | 0.980191i | \(0.436538\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.43845 | 0.166301 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.12311 | 0.212010 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −16.9309 | −1.14408 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 20.8769 | 1.40433 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.3693 | −0.761346 | −0.380673 | − | 0.924710i | \(-0.624308\pi\) | ||||
−0.380673 | + | 0.924710i | \(0.624308\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.56155 | −0.170770 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.87689 | −0.589180 | −0.294590 | − | 0.955624i | \(-0.595183\pi\) | ||||
−0.294590 | + | 0.955624i | \(0.595183\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.56155 | 0.235354 | 0.117677 | − | 0.993052i | \(-0.462455\pi\) | ||||
0.117677 | + | 0.993052i | \(0.462455\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.68466 | −0.571409 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −14.6847 | −0.962024 | −0.481012 | − | 0.876714i | \(-0.659731\pi\) | ||||
−0.481012 | + | 0.876714i | \(0.659731\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.4384 | 0.680929 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 11.3693 | 0.738516 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.19224 | 0.400542 | 0.200271 | − | 0.979740i | \(-0.435818\pi\) | ||||
0.200271 | + | 0.979740i | \(0.435818\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.3693 | −0.732362 | −0.366181 | − | 0.930544i | \(-0.619335\pi\) | ||||
−0.366181 | + | 0.930544i | \(0.619335\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 7.12311 | 0.455079 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.12311 | 0.198718 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.00000 | 0.253490 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.80776 | −0.492822 | −0.246411 | − | 0.969165i | \(-0.579251\pi\) | ||||
−0.246411 | + | 0.969165i | \(0.579251\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 50.7386 | 3.18991 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −10.4384 | −0.653681 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.1231 | 0.818597 | 0.409298 | − | 0.912401i | \(-0.365773\pi\) | ||||
0.409298 | + | 0.912401i | \(0.365773\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12.4924 | 0.776241 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.24621 | −0.510428 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −14.6847 | −0.905495 | −0.452747 | − | 0.891639i | \(-0.649556\pi\) | ||||
−0.452747 | + | 0.891639i | \(0.649556\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.63068 | −0.407320 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.00000 | −0.367194 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.0000 | 0.609711 | 0.304855 | − | 0.952399i | \(-0.401392\pi\) | ||||
0.304855 | + | 0.952399i | \(0.401392\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.0000 | 1.21491 | 0.607457 | − | 0.794353i | \(-0.292190\pi\) | ||||
0.607457 | + | 0.794353i | \(0.292190\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.87689 | −0.295163 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −14.2462 | −0.859079 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.6847 | −1.12265 | −0.561326 | − | 0.827595i | \(-0.689709\pi\) | ||||
−0.561326 | + | 0.827595i | \(0.689709\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.00000 | −0.119737 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.2462 | −1.44641 | −0.723204 | − | 0.690635i | \(-0.757331\pi\) | ||||
−0.723204 | + | 0.690635i | \(0.757331\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 28.6847 | 1.70513 | 0.852563 | − | 0.522625i | \(-0.175047\pi\) | ||||
0.852563 | + | 0.522625i | \(0.175047\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.56155 | −0.0924984 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.00000 | 0.472225 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 27.6847 | 1.62851 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.24621 | 0.248917 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.12311 | −0.0656125 | −0.0328063 | − | 0.999462i | \(-0.510444\pi\) | ||||
−0.0328063 | + | 0.999462i | \(0.510444\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −18.7386 | −1.09101 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.56155 | 0.322714 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 28.4924 | 1.64776 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.43845 | 0.140550 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.12311 | 0.409212 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −10.4384 | −0.597704 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.49242 | −0.256396 | −0.128198 | − | 0.991749i | \(-0.540919\pi\) | ||||
−0.128198 | + | 0.991749i | \(0.540919\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.00000 | −0.341328 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −20.9309 | −1.18688 | −0.593440 | − | 0.804878i | \(-0.702231\pi\) | ||||
−0.593440 | + | 0.804878i | \(0.702231\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.0000 | −0.565233 | −0.282617 | − | 0.959233i | \(-0.591202\pi\) | ||||
−0.282617 | + | 0.959233i | \(0.591202\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.43845 | 0.137391 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −18.8769 | −1.06023 | −0.530116 | − | 0.847925i | \(-0.677852\pi\) | ||||
−0.530116 | + | 0.847925i | \(0.677852\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −45.8617 | −2.56776 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −13.3693 | −0.746203 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.68466 | 0.371944 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8.00000 | −0.443760 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.24621 | −0.124216 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10.4384 | 0.575490 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8.00000 | −0.438397 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −9.75379 | −0.532906 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.7386 | 1.12971 | 0.564853 | − | 0.825192i | \(-0.308933\pi\) | ||||
0.564853 | + | 0.825192i | \(0.308933\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.00000 | −0.108625 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.1231 | −0.602350 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.0540 | 0.974823 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −14.2462 | −0.766990 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 27.4233 | 1.47216 | 0.736080 | − | 0.676895i | \(-0.236675\pi\) | ||||
0.736080 | + | 0.676895i | \(0.236675\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.3153 | 0.926869 | 0.463434 | − | 0.886131i | \(-0.346617\pi\) | ||||
0.463434 | + | 0.886131i | \(0.346617\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.12311 | 0.166699 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −28.2462 | −1.50339 | −0.751697 | − | 0.659509i | \(-0.770764\pi\) | ||||
−0.751697 | + | 0.659509i | \(0.770764\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −10.4384 | −0.552461 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.438447 | 0.0231404 | 0.0115702 | − | 0.999933i | \(-0.496317\pi\) | ||||
0.0115702 | + | 0.999933i | \(0.496317\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 19.9309 | 1.04610 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 26.4384 | 1.38385 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.24621 | 0.117251 | 0.0586256 | − | 0.998280i | \(-0.481328\pi\) | ||||
0.0586256 | + | 0.998280i | \(0.481328\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.12311 | −0.266698 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.63068 | −0.344248 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −36.4924 | −1.88951 | −0.944753 | − | 0.327783i | \(-0.893698\pi\) | ||||
−0.944753 | + | 0.327783i | \(0.893698\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 11.8078 | 0.609750 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −25.7538 | −1.32639 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.8769 | −1.07237 | −0.536187 | − | 0.844099i | \(-0.680136\pi\) | ||||
−0.536187 | + | 0.844099i | \(0.680136\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −18.0000 | −0.922168 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.8769 | 0.657979 | 0.328989 | − | 0.944334i | \(-0.393292\pi\) | ||||
0.328989 | + | 0.944334i | \(0.393292\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13.5616 | 0.691161 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.56155 | −0.0793782 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 18.9309 | 0.959833 | 0.479917 | − | 0.877314i | \(-0.340667\pi\) | ||||
0.479917 | + | 0.877314i | \(0.340667\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 60.9848 | 3.08414 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 20.6847 | 1.04340 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −17.7538 | −0.893290 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.6847 | −1.13851 | −0.569255 | − | 0.822161i | \(-0.692768\pi\) | ||||
−0.569255 | + | 0.822161i | \(0.692768\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.56155 | −0.0781754 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.630683 | −0.0314948 | −0.0157474 | − | 0.999876i | \(-0.505013\pi\) | ||||
−0.0157474 | + | 0.999876i | \(0.505013\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.24621 | −0.311146 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.56155 | −0.0775942 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −44.4924 | −2.20541 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.246211 | −0.0121744 | −0.00608718 | − | 0.999981i | \(-0.501938\pi\) | ||||
−0.00608718 | + | 0.999981i | \(0.501938\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −13.8078 | −0.681087 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −18.7386 | −0.922068 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.24621 | −0.306614 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.80776 | −0.382348 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −26.7386 | −1.30627 | −0.653134 | − | 0.757242i | \(-0.726546\pi\) | ||||
−0.653134 | + | 0.757242i | \(0.726546\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.87689 | 0.237685 | 0.118843 | − | 0.992913i | \(-0.462082\pi\) | ||||
0.118843 | + | 0.992913i | \(0.462082\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.68466 | −0.325019 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −17.1231 | −0.830593 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.4384 | −0.505152 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 17.3693 | 0.838599 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.6155 | −0.559500 | −0.279750 | − | 0.960073i | \(-0.590252\pi\) | ||||
−0.279750 | + | 0.960073i | \(0.590252\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.24621 | −0.396288 | −0.198144 | − | 0.980173i | \(-0.563491\pi\) | ||||
−0.198144 | + | 0.980173i | \(0.563491\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 12.8769 | 0.617400 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9.12311 | 0.436417 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 28.2462 | 1.34812 | 0.674059 | − | 0.738677i | \(-0.264549\pi\) | ||||
0.674059 | + | 0.738677i | \(0.264549\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.56155 | −0.217217 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.1922 | 0.579271 | 0.289635 | − | 0.957137i | \(-0.406466\pi\) | ||||
0.289635 | + | 0.957137i | \(0.406466\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.36932 | 0.444148 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.80776 | 0.180101 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 35.3693 | 1.66918 | 0.834591 | − | 0.550871i | \(-0.185704\pi\) | ||||
0.834591 | + | 0.550871i | \(0.185704\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −28.4924 | −1.34166 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −17.1231 | −0.804514 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7.61553 | 0.357021 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −40.0540 | −1.87365 | −0.936823 | − | 0.349804i | \(-0.886248\pi\) | ||||
−0.936823 | + | 0.349804i | \(0.886248\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.68466 | 0.312013 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 32.3002 | 1.50437 | 0.752185 | − | 0.658952i | \(-0.229000\pi\) | ||||
0.752185 | + | 0.658952i | \(0.229000\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 31.8078 | 1.47823 | 0.739116 | − | 0.673578i | \(-0.235243\pi\) | ||||
0.739116 | + | 0.673578i | \(0.235243\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.12311 | 0.144831 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10.9309 | 0.505820 | 0.252910 | − | 0.967490i | \(-0.418612\pi\) | ||||
0.252910 | + | 0.967490i | \(0.418612\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.75379 | −0.450388 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −12.2462 | −0.564276 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.68466 | −0.399321 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.56155 | −0.117532 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.24621 | 0.194421 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 15.3693 | 0.702242 | 0.351121 | − | 0.936330i | \(-0.385801\pi\) | ||||
0.351121 | + | 0.936330i | \(0.385801\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −24.9848 | −1.13921 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −14.2462 | −0.648225 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.63068 | −0.301084 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −33.1231 | −1.50095 | −0.750476 | − | 0.660898i | \(-0.770176\pi\) | ||||
−0.750476 | + | 0.660898i | \(0.770176\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.24621 | −0.101577 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.7386 | −0.665145 | −0.332573 | − | 0.943078i | \(-0.607917\pi\) | ||||
−0.332573 | + | 0.943078i | \(0.607917\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −55.1231 | −2.48262 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8.68466 | −0.390346 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.17708 | −0.410823 | −0.205411 | − | 0.978676i | \(-0.565853\pi\) | ||||
−0.205411 | + | 0.978676i | \(0.565853\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.87689 | −0.396590 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 25.6155 | 1.14214 | 0.571070 | − | 0.820901i | \(-0.306528\pi\) | ||||
0.571070 | + | 0.820901i | \(0.306528\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.1231 | −0.494972 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.24621 | −0.144169 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 26.0000 | 1.15243 | 0.576215 | − | 0.817298i | \(-0.304529\pi\) | ||||
0.576215 | + | 0.817298i | \(0.304529\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 26.4384 | 1.16957 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.00000 | 0.0441511 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9.36932 | 0.412861 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −37.1771 | −1.63505 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.24621 | −0.186388 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.61553 | 0.421264 | 0.210632 | − | 0.977565i | \(-0.432448\pi\) | ||||
0.210632 | + | 0.977565i | \(0.432448\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.3693 | 0.759507 | 0.379754 | − | 0.925088i | \(-0.376009\pi\) | ||||
0.379754 | + | 0.925088i | \(0.376009\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.00000 | 0.174574 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −13.3693 | −0.582377 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 60.2311 | 2.61874 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.0000 | 0.520756 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −16.0000 | −0.693037 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 20.8769 | 0.902587 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −15.1231 | −0.652610 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −25.3693 | −1.09273 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.8078 | −0.765616 | −0.382808 | − | 0.923828i | \(-0.625043\pi\) | ||||
−0.382808 | + | 0.923828i | \(0.625043\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 15.1231 | 0.648995 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.50758 | 0.150248 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.384472 | −0.0164388 | −0.00821942 | − | 0.999966i | \(-0.502616\pi\) | ||||
−0.00821942 | + | 0.999966i | \(0.502616\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.68466 | 0.285294 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.24621 | −0.351300 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −17.7538 | −0.754968 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 12.4924 | 0.530274 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 45.5616 | 1.93050 | 0.965252 | − | 0.261319i | \(-0.0841575\pi\) | ||||
0.965252 | + | 0.261319i | \(0.0841575\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.87689 | −0.206271 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 37.1771 | 1.56962 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.00000 | 0.168580 | 0.0842900 | − | 0.996441i | \(-0.473138\pi\) | ||||
0.0842900 | + | 0.996441i | \(0.473138\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.12311 | 0.131390 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.56155 | −0.0655791 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −18.4924 | −0.775243 | −0.387621 | − | 0.921819i | \(-0.626703\pi\) | ||||
−0.387621 | + | 0.921819i | \(0.626703\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.73863 | 0.282003 | 0.141002 | − | 0.990009i | \(-0.454968\pi\) | ||||
0.141002 | + | 0.990009i | \(0.454968\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.31534 | −0.0549492 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −23.3693 | −0.974568 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.5616 | −0.481314 | −0.240657 | − | 0.970610i | \(-0.577363\pi\) | ||||
−0.240657 | + | 0.970610i | \(0.577363\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 18.8769 | 0.784497 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.24621 | −0.259137 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 23.6155 | 0.978055 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.87689 | −0.201635 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −18.0540 | −0.745167 | −0.372584 | − | 0.927999i | \(-0.621528\pi\) | ||||
−0.372584 | + | 0.927999i | \(0.621528\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.00000 | −0.0824086 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.36932 | −0.0563262 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 38.4924 | 1.58069 | 0.790347 | − | 0.612659i | \(-0.209900\pi\) | ||||
0.790347 | + | 0.612659i | \(0.209900\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 16.3002 | 0.668242 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.93087 | 0.119953 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.5076 | 0.633622 | 0.316811 | − | 0.948489i | \(-0.397388\pi\) | ||||
0.316811 | + | 0.948489i | \(0.397388\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 39.8617 | 1.62599 | 0.812997 | − | 0.582268i | \(-0.197834\pi\) | ||||
0.812997 | + | 0.582268i | \(0.197834\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.24621 | 0.254365 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −31.1231 | −1.26533 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22.9848 | −0.932926 | −0.466463 | − | 0.884541i | \(-0.654472\pi\) | ||||
−0.466463 | + | 0.884541i | \(0.654472\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 12.8769 | 0.521798 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −20.8769 | −0.844589 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 38.7926 | 1.56682 | 0.783409 | − | 0.621506i | \(-0.213479\pi\) | ||||
0.783409 | + | 0.621506i | \(0.213479\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8.00000 | 0.322591 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14.3002 | −0.575704 | −0.287852 | − | 0.957675i | \(-0.592941\pi\) | ||||
−0.287852 | + | 0.957675i | \(0.592941\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.00000 | −0.160774 | −0.0803868 | − | 0.996764i | \(-0.525616\pi\) | ||||
−0.0803868 | + | 0.996764i | \(0.525616\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 9.12311 | 0.366098 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9.36932 | 0.375374 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.63068 | −0.225227 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.56155 | 0.222107 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −53.4773 | −2.13228 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.9309 | 0.912864 | 0.456432 | − | 0.889758i | \(-0.349127\pi\) | ||||
0.456432 | + | 0.889758i | \(0.349127\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.75379 | 0.228693 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 28.1080 | 1.11543 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −14.2462 | −0.564455 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −40.7386 | −1.60908 | −0.804540 | − | 0.593899i | \(-0.797588\pi\) | ||||
−0.804540 | + | 0.593899i | \(0.797588\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.94602 | 0.392233 | 0.196116 | − | 0.980581i | \(-0.437167\pi\) | ||||
0.196116 | + | 0.980581i | \(0.437167\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.43845 | 0.0960138 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −21.8078 | −0.857352 | −0.428676 | − | 0.903458i | \(-0.641020\pi\) | ||||
−0.428676 | + | 0.903458i | \(0.641020\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 66.7386 | 2.61972 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.12311 | 0.122404 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 40.3002 | 1.57707 | 0.788534 | − | 0.614991i | \(-0.210840\pi\) | ||||
0.788534 | + | 0.614991i | \(0.210840\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −32.3002 | −1.26207 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −16.9309 | −0.660536 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21.3693 | 0.832430 | 0.416215 | − | 0.909266i | \(-0.363356\pi\) | ||||
0.416215 | + | 0.909266i | \(0.363356\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −42.7386 | −1.66234 | −0.831170 | − | 0.556018i | \(-0.812328\pi\) | ||||
−0.831170 | + | 0.556018i | \(0.812328\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 20.8769 | 0.810791 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.43845 | 0.0945589 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −75.2311 | −2.91296 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −11.3693 | −0.439563 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 37.1771 | 1.43521 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −31.8617 | −1.22818 | −0.614090 | − | 0.789236i | \(-0.710477\pi\) | ||||
−0.614090 | + | 0.789236i | \(0.710477\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.56155 | −0.0985942 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 38.0000 | 1.46046 | 0.730229 | − | 0.683202i | \(-0.239413\pi\) | ||||
0.730229 | + | 0.683202i | \(0.239413\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.63068 | −0.254462 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.87689 | −0.340163 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.86174 | −0.377349 | −0.188674 | − | 0.982040i | \(-0.560419\pi\) | ||||
−0.188674 | + | 0.982040i | \(0.560419\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 21.5616 | 0.823825 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.56155 | 0.135882 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 13.2614 | 0.505218 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21.0691 | 0.801507 | 0.400754 | − | 0.916186i | \(-0.368748\pi\) | ||||
0.400754 | + | 0.916186i | \(0.368748\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −8.68466 | −0.329903 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 12.1922 | 0.462478 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −34.2462 | −1.29717 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −14.6847 | −0.555425 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23.1231 | 0.873348 | 0.436674 | − | 0.899620i | \(-0.356156\pi\) | ||||
0.436674 | + | 0.899620i | \(0.356156\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.00000 | −0.301726 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 10.4384 | 0.393135 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −11.1231 | −0.418327 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.50758 | 0.357065 | 0.178532 | − | 0.983934i | \(-0.442865\pi\) | ||||
0.178532 | + | 0.983934i | \(0.442865\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11.3693 | 0.426383 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −18.2462 | −0.683326 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −27.1231 | −1.01435 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.19224 | 0.231253 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 37.4233 | 1.39565 | 0.697827 | − | 0.716267i | \(-0.254151\pi\) | ||||
0.697827 | + | 0.716267i | \(0.254151\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.36932 | 0.348932 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −11.3693 | −0.422829 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 21.1231 | 0.784492 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13.5616 | 0.502970 | 0.251485 | − | 0.967861i | \(-0.419081\pi\) | ||||
0.251485 | + | 0.967861i | \(0.419081\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10.4384 | −0.386080 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18.4924 | −0.683033 | −0.341517 | − | 0.939876i | \(-0.610941\pi\) | ||||
−0.341517 | + | 0.939876i | \(0.610941\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 7.12311 | 0.262740 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 34.7386 | 1.27961 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.1771 | 0.926154 | 0.463077 | − | 0.886318i | \(-0.346745\pi\) | ||||
0.463077 | + | 0.886318i | \(0.346745\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.12311 | 0.114730 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 40.4924 | 1.48552 | 0.742761 | − | 0.669556i | \(-0.233516\pi\) | ||||
0.742761 | + | 0.669556i | \(0.233516\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.94602 | −0.217845 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.00000 | 0.146352 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 20.8769 | 0.762825 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 33.6155 | 1.22665 | 0.613324 | − | 0.789831i | \(-0.289832\pi\) | ||||
0.613324 | + | 0.789831i | \(0.289832\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7.80776 | −0.284531 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 26.7386 | 0.973119 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −32.0540 | −1.16502 | −0.582511 | − | 0.812823i | \(-0.697930\pi\) | ||||
−0.582511 | + | 0.812823i | \(0.697930\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 50.7386 | 1.84170 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 47.6695 | 1.72802 | 0.864009 | − | 0.503476i | \(-0.167946\pi\) | ||||
0.864009 | + | 0.503476i | \(0.167946\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.50758 | 0.126983 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −10.4384 | −0.377403 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 37.4773 | 1.35323 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −34.3002 | −1.23690 | −0.618448 | − | 0.785826i | \(-0.712238\pi\) | ||||
−0.618448 | + | 0.785826i | \(0.712238\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 13.1231 | 0.472617 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 17.6155 | 0.633587 | 0.316793 | − | 0.948495i | \(-0.397394\pi\) | ||||
0.316793 | + | 0.948495i | \(0.397394\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.12311 | 0.184027 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 12.4924 | 0.448163 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.12311 | −0.183554 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8.24621 | −0.294696 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 19.1231 | 0.682533 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.2462 | 0.365238 | 0.182619 | − | 0.983184i | \(-0.441543\pi\) | ||||
0.182619 | + | 0.983184i | \(0.441543\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −14.6847 | −0.522788 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.12311 | 0.111045 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 20.8769 | 0.741360 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −6.63068 | −0.235166 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 41.6155 | 1.47410 | 0.737049 | − | 0.675840i | \(-0.236219\pi\) | ||||
0.737049 | + | 0.675840i | \(0.236219\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −44.6847 | −1.58083 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.00000 | −0.212000 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −94.1619 | −3.32290 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 22.2462 | 0.784076 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10.0000 | 0.352017 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7.94602 | −0.279367 | −0.139684 | − | 0.990196i | \(-0.544609\pi\) | ||||
−0.139684 | + | 0.990196i | \(0.544609\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −35.1231 | −1.23334 | −0.616670 | − | 0.787222i | \(-0.711519\pi\) | ||||
−0.616670 | + | 0.787222i | \(0.711519\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 20.0000 | 0.701431 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.50758 | 0.122865 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.56155 | −0.0546318 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.87689 | −0.170412 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.94602 | −0.0679167 | −0.0339584 | − | 0.999423i | \(-0.510811\pi\) | ||||
−0.0339584 | + | 0.999423i | \(0.510811\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −40.3002 | −1.40478 | −0.702388 | − | 0.711794i | \(-0.747883\pi\) | ||||
−0.702388 | + | 0.711794i | \(0.747883\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −14.2462 | −0.495989 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14.7386 | −0.512513 | −0.256256 | − | 0.966609i | \(-0.582489\pi\) | ||||
−0.256256 | + | 0.966609i | \(0.582489\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.00000 | 0.138926 | 0.0694629 | − | 0.997585i | \(-0.477871\pi\) | ||||
0.0694629 | + | 0.997585i | \(0.477871\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −18.6847 | −0.648164 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −30.4924 | −1.05650 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 13.8617 | 0.479705 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.00000 | −0.0691301 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −49.8617 | −1.72142 | −0.860709 | − | 0.509097i | \(-0.829979\pi\) | ||||
−0.860709 | + | 0.509097i | \(0.829979\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 39.0000 | 1.34483 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −24.2462 | −0.835084 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.06913 | 0.174383 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −31.1231 | −1.06940 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 28.6847 | 0.984455 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −72.9848 | −2.50189 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.26137 | −0.248624 | −0.124312 | − | 0.992243i | \(-0.539672\pi\) | ||||
−0.124312 | + | 0.992243i | \(0.539672\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.56155 | −0.0534040 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 15.8617 | 0.541827 | 0.270913 | − | 0.962604i | \(-0.412674\pi\) | ||||
0.270913 | + | 0.962604i | \(0.412674\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −28.3002 | −0.965590 | −0.482795 | − | 0.875733i | \(-0.660378\pi\) | ||||
−0.482795 | + | 0.875733i | \(0.660378\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.00000 | 0.272639 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −12.0000 | −0.408485 | −0.204242 | − | 0.978920i | \(-0.565473\pi\) | ||||
−0.204242 | + | 0.978920i | \(0.565473\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.63068 | 0.225450 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 27.6847 | 0.940220 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 63.2311 | 2.14497 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 19.5076 | 0.660989 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.24621 | 0.143712 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −18.4384 | −0.623333 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −22.6307 | −0.764184 | −0.382092 | − | 0.924124i | \(-0.624796\pi\) | ||||
−0.382092 | + | 0.924124i | \(0.624796\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.12311 | −0.0378814 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −30.3002 | −1.02084 | −0.510420 | − | 0.859925i | \(-0.670510\pi\) | ||||
−0.510420 | + | 0.859925i | \(0.670510\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35.3153 | −1.18846 | −0.594228 | − | 0.804297i | \(-0.702542\pi\) | ||||
−0.594228 | + | 0.804297i | \(0.702542\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −18.7386 | −0.629892 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 51.2311 | 1.72017 | 0.860085 | − | 0.510150i | \(-0.170410\pi\) | ||||
0.860085 | + | 0.510150i | \(0.170410\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 28.1080 | 0.942710 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.56155 | 0.186319 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.68466 | −0.223694 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 23.6155 | 0.789380 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 28.4924 | 0.951334 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 16.4924 | 0.550053 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 28.3845 | 0.945624 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.43845 | 0.0811464 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −23.6155 | −0.785007 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −43.1231 | −1.43188 | −0.715940 | − | 0.698162i | \(-0.754001\pi\) | ||||
−0.715940 | + | 0.698162i | \(0.754001\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.12311 | 0.236259 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.12311 | −0.235999 | −0.118000 | − | 0.993014i | \(-0.537648\pi\) | ||||
−0.118000 | + | 0.993014i | \(0.537648\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 22.2462 | 0.736242 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −10.4384 | −0.345084 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −32.3002 | −1.06665 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11.5076 | 0.379600 | 0.189800 | − | 0.981823i | \(-0.439216\pi\) | ||||
0.189800 | + | 0.981823i | \(0.439216\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.49242 | −0.148030 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 20.4924 | 0.673787 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −6.00000 | −0.197066 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 14.0000 | 0.459325 | 0.229663 | − | 0.973270i | \(-0.426238\pi\) | ||||
0.229663 | + | 0.973270i | \(0.426238\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.56155 | −0.149499 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −20.9309 | −0.685246 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −58.0540 | −1.89857 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12.4384 | −0.406346 | −0.203173 | − | 0.979143i | \(-0.565125\pi\) | ||||
−0.203173 | + | 0.979143i | \(0.565125\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −10.0000 | −0.326338 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −30.0000 | −0.977972 | −0.488986 | − | 0.872292i | \(-0.662633\pi\) | ||||
−0.488986 | + | 0.872292i | \(0.662633\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −46.7386 | −1.52202 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.43845 | 0.0793227 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.00000 | 0.129983 | 0.0649913 | − | 0.997886i | \(-0.479298\pi\) | ||||
0.0649913 | + | 0.997886i | \(0.479298\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −52.8769 | −1.71646 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −18.8769 | −0.612125 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 29.6155 | 0.959341 | 0.479671 | − | 0.877449i | \(-0.340756\pi\) | ||||
0.479671 | + | 0.877449i | \(0.340756\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.05398 | 0.0664651 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −45.8617 | −1.48250 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 21.5616 | 0.696259 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −13.3693 | −0.430820 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −29.4773 | −0.948907 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 22.7386 | 0.731225 | 0.365613 | − | 0.930767i | \(-0.380860\pi\) | ||||
0.365613 | + | 0.930767i | \(0.380860\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.68466 | 0.214742 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 20.0000 | 0.641831 | 0.320915 | − | 0.947108i | \(-0.396010\pi\) | ||||
0.320915 | + | 0.947108i | \(0.396010\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.1922 | 0.390865 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −8.00000 | −0.256205 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −58.9848 | −1.88709 | −0.943546 | − | 0.331241i | \(-0.892533\pi\) | ||||
−0.943546 | + | 0.331241i | \(0.892533\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −33.3693 | −1.06649 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.24621 | −0.0717160 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −18.7386 | −0.597670 | −0.298835 | − | 0.954305i | \(-0.596598\pi\) | ||||
−0.298835 | + | 0.954305i | \(0.596598\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.13826 | 0.0681306 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 10.4384 | 0.332259 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −14.2462 | −0.453003 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 35.8617 | 1.13919 | 0.569593 | − | 0.821927i | \(-0.307101\pi\) | ||||
0.569593 | + | 0.821927i | \(0.307101\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.57671 | −0.145091 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 30.7926 | 0.975212 | 0.487606 | − | 0.873064i | \(-0.337870\pi\) | ||||
0.487606 | + | 0.873064i | \(0.337870\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.00000 | −0.253109 |
(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 | 456.2.a.f.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 1368.2.a.k.1.2 | 2 | |||
4.3 | odd | 2 | 912.2.a.m.1.1 | 2 | |||
8.3 | odd | 2 | 3648.2.a.br.1.2 | 2 | |||
8.5 | even | 2 | 3648.2.a.bl.1.2 | 2 | |||
12.11 | even | 2 | 2736.2.a.z.1.2 | 2 | |||
19.18 | odd | 2 | 8664.2.a.r.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
456.2.a.f.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
912.2.a.m.1.1 | 2 | 4.3 | odd | 2 | |||
1368.2.a.k.1.2 | 2 | 3.2 | odd | 2 | |||
2736.2.a.z.1.2 | 2 | 12.11 | even | 2 | |||
3648.2.a.bl.1.2 | 2 | 8.5 | even | 2 | |||
3648.2.a.br.1.2 | 2 | 8.3 | odd | 2 | |||
8664.2.a.r.1.1 | 2 | 19.18 | odd | 2 |