Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1900,2,Mod(1,1900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1900, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1900.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1900.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: | \(15.1715763840\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.257.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4x + 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.19869\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1900.1 |
$q$-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 | ||||||||
\(3\) | 1.19869 | 0.692065 | 0.346032 | − | 0.938223i | \(-0.387529\pi\) | ||||
0.346032 | + | 0.938223i | \(0.387529\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.19869 | 0.453063 | 0.226531 | − | 0.974004i | \(-0.427261\pi\) | ||||
0.226531 | + | 0.974004i | \(0.427261\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.56314 | −0.521046 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.86718 | −1.76902 | −0.884510 | − | 0.466521i | \(-0.845507\pi\) | ||||
−0.884510 | + | 0.466521i | \(0.845507\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.364448 | −0.101080 | −0.0505399 | − | 0.998722i | \(-0.516094\pi\) | ||||
−0.0505399 | + | 0.998722i | \(0.516094\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.19869 | 0.290725 | 0.145363 | − | 0.989378i | \(-0.453565\pi\) | ||||
0.145363 | + | 0.989378i | \(0.453565\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.43686 | 0.313549 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.23163 | −1.71641 | −0.858206 | − | 0.513305i | \(-0.828421\pi\) | ||||
−0.858206 | + | 0.513305i | \(0.828421\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.46980 | −1.05266 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.86718 | −1.46090 | −0.730449 | − | 0.682967i | \(-0.760689\pi\) | ||||
−0.730449 | + | 0.682967i | \(0.760689\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.30404 | 1.31184 | 0.655922 | − | 0.754829i | \(-0.272280\pi\) | ||||
0.655922 | + | 0.754829i | \(0.272280\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −7.03293 | −1.22428 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.13828 | 1.17353 | 0.586763 | − | 0.809759i | \(-0.300402\pi\) | ||||
0.586763 | + | 0.809759i | \(0.300402\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.436861 | −0.0699537 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.43686 | 0.380574 | 0.190287 | − | 0.981729i | \(-0.439058\pi\) | ||||
0.190287 | + | 0.981729i | \(0.439058\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.39738 | −1.12809 | −0.564045 | − | 0.825744i | \(-0.690756\pi\) | ||||
−0.564045 | + | 0.825744i | \(0.690756\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −13.7014 | −1.99856 | −0.999279 | − | 0.0379717i | \(-0.987910\pi\) | ||||
−0.999279 | + | 0.0379717i | \(0.987910\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.56314 | −0.794734 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.43686 | 0.201201 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.39738 | −1.01611 | −0.508054 | − | 0.861325i | \(-0.669635\pi\) | ||||
−0.508054 | + | 0.861325i | \(0.669635\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.19869 | −0.158771 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.8606 | 1.67431 | 0.837156 | − | 0.546964i | \(-0.184217\pi\) | ||||
0.837156 | + | 0.546964i | \(0.184217\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.30404 | −0.166965 | −0.0834825 | − | 0.996509i | \(-0.526604\pi\) | ||||
−0.0834825 | + | 0.996509i | \(0.526604\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.87372 | −0.236067 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.9330 | 1.45785 | 0.728927 | − | 0.684592i | \(-0.240019\pi\) | ||||
0.728927 | + | 0.684592i | \(0.240019\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −9.86718 | −1.18787 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.12628 | 0.252343 | 0.126171 | − | 0.992008i | \(-0.459731\pi\) | ||||
0.126171 | + | 0.992008i | \(0.459731\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.50273 | 0.292922 | 0.146461 | − | 0.989216i | \(-0.453212\pi\) | ||||
0.146461 | + | 0.989216i | \(0.453212\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.03293 | −0.801477 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.74090 | −0.870919 | −0.435460 | − | 0.900208i | \(-0.643414\pi\) | ||||
−0.435460 | + | 0.900208i | \(0.643414\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.86718 | −0.207464 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.02093 | −0.331590 | −0.165795 | − | 0.986160i | \(-0.553019\pi\) | ||||
−0.165795 | + | 0.986160i | \(0.553019\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −9.43032 | −1.01104 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.68942 | −0.603077 | −0.301539 | − | 0.953454i | \(-0.597500\pi\) | ||||
−0.301539 | + | 0.953454i | \(0.597500\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.436861 | −0.0457954 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.75529 | 0.907881 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.09334 | 0.111012 | 0.0555061 | − | 0.998458i | \(-0.482323\pi\) | ||||
0.0555061 | + | 0.998458i | \(0.482323\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 9.17122 | 0.921742 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.8672 | 1.08132 | 0.540662 | − | 0.841240i | \(-0.318174\pi\) | ||||
0.540662 | + | 0.841240i | \(0.318174\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.74090 | −0.959799 | −0.479900 | − | 0.877323i | \(-0.659327\pi\) | ||||
−0.479900 | + | 0.877323i | \(0.659327\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.3634 | 1.58191 | 0.790953 | − | 0.611877i | \(-0.209585\pi\) | ||||
0.790953 | + | 0.611877i | \(0.209585\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.29749 | 0.890538 | 0.445269 | − | 0.895397i | \(-0.353108\pi\) | ||||
0.445269 | + | 0.895397i | \(0.353108\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.55660 | 0.812156 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.96707 | −0.279118 | −0.139559 | − | 0.990214i | \(-0.544568\pi\) | ||||
−0.139559 | + | 0.990214i | \(0.544568\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.569683 | 0.0526672 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.43686 | 0.131717 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 23.4238 | 2.12943 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.92104 | 0.263382 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.3579 | −1.00785 | −0.503926 | − | 0.863747i | \(-0.668111\pi\) | ||||
−0.503926 | + | 0.863747i | \(0.668111\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.86718 | −0.780711 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.56314 | −0.136572 | −0.0682861 | − | 0.997666i | \(-0.521753\pi\) | ||||
−0.0682861 | + | 0.997666i | \(0.521753\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.19869 | −0.103940 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −15.8397 | −1.35328 | −0.676639 | − | 0.736315i | \(-0.736564\pi\) | ||||
−0.676639 | + | 0.736315i | \(0.736564\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −19.8606 | −1.68456 | −0.842278 | − | 0.539043i | \(-0.818786\pi\) | ||||
−0.842278 | + | 0.539043i | \(0.818786\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −16.4238 | −1.38313 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.13828 | 0.178812 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.66849 | −0.550007 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.68942 | 0.220326 | 0.110163 | − | 0.993914i | \(-0.464863\pi\) | ||||
0.110163 | + | 0.993914i | \(0.464863\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.1647 | 1.39684 | 0.698421 | − | 0.715688i | \(-0.253887\pi\) | ||||
0.698421 | + | 0.715688i | \(0.253887\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.87372 | −0.151481 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.3634 | −1.30594 | −0.652969 | − | 0.757384i | \(-0.726477\pi\) | ||||
−0.652969 | + | 0.757384i | \(0.726477\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.86718 | −0.703213 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.86718 | −0.777643 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.28549 | −0.648970 | −0.324485 | − | 0.945891i | \(-0.605191\pi\) | ||||
−0.324485 | + | 0.945891i | \(0.605191\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.49727 | −0.580156 | −0.290078 | − | 0.957003i | \(-0.593681\pi\) | ||||
−0.290078 | + | 0.957003i | \(0.593681\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.8672 | −0.989783 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.56314 | 0.119536 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −14.7464 | −1.12114 | −0.560572 | − | 0.828105i | \(-0.689419\pi\) | ||||
−0.560572 | + | 0.828105i | \(0.689419\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 15.4159 | 1.15873 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.2526 | 0.990543 | 0.495271 | − | 0.868738i | \(-0.335069\pi\) | ||||
0.495271 | + | 0.868738i | \(0.335069\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.7344 | 1.24385 | 0.621927 | − | 0.783075i | \(-0.286350\pi\) | ||||
0.621927 | + | 0.783075i | \(0.286350\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.56314 | −0.115551 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.03293 | −0.514299 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −6.55660 | −0.476922 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.13282 | −0.299041 | −0.149520 | − | 0.988759i | \(-0.547773\pi\) | ||||
−0.149520 | + | 0.988759i | \(0.547773\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.08680 | 0.510119 | 0.255060 | − | 0.966925i | \(-0.417905\pi\) | ||||
0.255060 | + | 0.966925i | \(0.417905\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 20.4753 | 1.45880 | 0.729401 | − | 0.684087i | \(-0.239799\pi\) | ||||
0.729401 | + | 0.684087i | \(0.239799\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.74090 | 0.619626 | 0.309813 | − | 0.950798i | \(-0.399734\pi\) | ||||
0.309813 | + | 0.950798i | \(0.399734\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 14.3040 | 1.00893 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −9.43032 | −0.661878 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 12.8672 | 0.894331 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.86718 | 0.405841 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.7344 | −1.28973 | −0.644863 | − | 0.764298i | \(-0.723086\pi\) | ||||
−0.644863 | + | 0.764298i | \(0.723086\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.54875 | 0.174638 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.75529 | 0.594348 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.00000 | 0.202721 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.436861 | −0.0293864 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.27110 | 0.286014 | 0.143007 | − | 0.989722i | \(-0.454323\pi\) | ||||
0.143007 | + | 0.989722i | \(0.454323\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −21.5631 | −1.43120 | −0.715598 | − | 0.698512i | \(-0.753846\pi\) | ||||
−0.715598 | + | 0.698512i | \(0.753846\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 27.4172 | 1.81178 | 0.905891 | − | 0.423511i | \(-0.139203\pi\) | ||||
0.905891 | + | 0.423511i | \(0.139203\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.43032 | −0.554674 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.86718 | 0.515396 | 0.257698 | − | 0.966226i | \(-0.417036\pi\) | ||||
0.257698 | + | 0.966226i | \(0.417036\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −9.27895 | −0.602732 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.30404 | 0.601828 | 0.300914 | − | 0.953651i | \(-0.402708\pi\) | ||||
0.300914 | + | 0.953651i | \(0.402708\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.9056 | −1.41106 | −0.705531 | − | 0.708679i | \(-0.749291\pi\) | ||||
−0.705531 | + | 0.708679i | \(0.749291\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.1712 | 0.909084 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.364448 | 0.0231893 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.62116 | −0.229482 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.43032 | −0.468997 | −0.234499 | − | 0.972116i | \(-0.575345\pi\) | ||||
−0.234499 | + | 0.972116i | \(0.575345\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 48.2964 | 3.03637 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.05387 | 0.315251 | 0.157626 | − | 0.987499i | \(-0.449616\pi\) | ||||
0.157626 | + | 0.987499i | \(0.449616\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.55660 | 0.531681 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 12.2975 | 0.761196 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −17.7673 | −1.09558 | −0.547789 | − | 0.836617i | \(-0.684530\pi\) | ||||
−0.547789 | + | 0.836617i | \(0.684530\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.81986 | −0.417368 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.17776 | 0.559578 | 0.279789 | − | 0.960062i | \(-0.409736\pi\) | ||||
0.279789 | + | 0.960062i | \(0.409736\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.7278 | −1.25912 | −0.629562 | − | 0.776950i | \(-0.716766\pi\) | ||||
−0.629562 | + | 0.776950i | \(0.716766\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.523661 | −0.0316934 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.5895 | 1.47744 | 0.738721 | − | 0.674012i | \(-0.235430\pi\) | ||||
0.738721 | + | 0.674012i | \(0.235430\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −11.4172 | −0.683532 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.73436 | 0.222773 | 0.111386 | − | 0.993777i | \(-0.464471\pi\) | ||||
0.111386 | + | 0.993777i | \(0.464471\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.0318 | −0.774663 | −0.387332 | − | 0.921941i | \(-0.626603\pi\) | ||||
−0.387332 | + | 0.921941i | \(0.626603\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.92104 | 0.172424 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.5631 | −0.915479 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.31058 | 0.0768277 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 19.9001 | 1.16258 | 0.581288 | − | 0.813698i | \(-0.302549\pi\) | ||||
0.581288 | + | 0.813698i | \(0.302549\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 32.0923 | 1.86218 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.00000 | 0.173494 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.86718 | −0.511096 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 13.0264 | 0.748347 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.02093 | 0.457779 | 0.228889 | − | 0.973452i | \(-0.426491\pi\) | ||||
0.228889 | + | 0.973452i | \(0.426491\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.6763 | −0.664243 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.1778 | −0.917357 | −0.458678 | − | 0.888602i | \(-0.651677\pi\) | ||||
−0.458678 | + | 0.888602i | \(0.651677\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.13828 | −0.403480 | −0.201740 | − | 0.979439i | \(-0.564660\pi\) | ||||
−0.201740 | + | 0.979439i | \(0.564660\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.96052 | 0.222445 | 0.111223 | − | 0.993796i | \(-0.464523\pi\) | ||||
0.111223 | + | 0.993796i | \(0.464523\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 46.1581 | 2.58436 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 19.6146 | 1.09478 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.19869 | −0.0666970 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 11.1448 | 0.616310 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −16.4238 | −0.905472 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.94852 | −0.326960 | −0.163480 | − | 0.986547i | \(-0.552272\pi\) | ||||
−0.163480 | + | 0.986547i | \(0.552272\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −11.1581 | −0.611462 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.90666 | 0.485176 | 0.242588 | − | 0.970129i | \(-0.422004\pi\) | ||||
0.242588 | + | 0.970129i | \(0.422004\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.55660 | −0.193168 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −42.8541 | −2.32068 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.0593 | −0.813127 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −18.5961 | −0.998290 | −0.499145 | − | 0.866519i | \(-0.666352\pi\) | ||||
−0.499145 | + | 0.866519i | \(0.666352\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.3040 | −0.765678 | −0.382839 | − | 0.923815i | \(-0.625054\pi\) | ||||
−0.382839 | + | 0.923815i | \(0.625054\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.99346 | 0.106403 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.7673 | −0.679534 | −0.339767 | − | 0.940510i | \(-0.610348\pi\) | ||||
−0.339767 | + | 0.940510i | \(0.610348\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.72235 | 0.0911566 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.69596 | 0.142287 | 0.0711437 | − | 0.997466i | \(-0.477335\pi\) | ||||
0.0711437 | + | 0.997466i | \(0.477335\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 28.0779 | 1.47371 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.43140 | 0.179118 | 0.0895589 | − | 0.995982i | \(-0.471454\pi\) | ||||
0.0895589 | + | 0.995982i | \(0.471454\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.80915 | −0.198297 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.86718 | −0.460361 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15.5697 | 0.806168 | 0.403084 | − | 0.915163i | \(-0.367938\pi\) | ||||
0.403084 | + | 0.915163i | \(0.367938\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.86718 | 0.147667 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.164672 | −0.00845864 | −0.00422932 | − | 0.999991i | \(-0.501346\pi\) | ||||
−0.00422932 | + | 0.999991i | \(0.501346\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −13.6146 | −0.697498 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 22.3514 | 1.14210 | 0.571051 | − | 0.820915i | \(-0.306536\pi\) | ||||
0.571051 | + | 0.820915i | \(0.306536\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 11.5631 | 0.587787 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9.34243 | −0.473680 | −0.236840 | − | 0.971549i | \(-0.576112\pi\) | ||||
−0.236840 | + | 0.971549i | \(0.576112\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.86718 | −0.499005 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.87372 | −0.0945167 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.83533 | 0.242678 | 0.121339 | − | 0.992611i | \(-0.461281\pi\) | ||||
0.121339 | + | 0.992611i | \(0.461281\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.43686 | −0.0719330 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 37.4622 | 1.87077 | 0.935386 | − | 0.353629i | \(-0.115053\pi\) | ||||
0.935386 | + | 0.353629i | \(0.115053\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.66194 | −0.132601 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −41.8816 | −2.07599 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.42377 | 0.465976 | 0.232988 | − | 0.972480i | \(-0.425150\pi\) | ||||
0.232988 | + | 0.972480i | \(0.425150\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −18.9869 | −0.936555 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 15.4159 | 0.758568 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −23.8068 | −1.16582 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 27.4303 | 1.34006 | 0.670029 | − | 0.742335i | \(-0.266282\pi\) | ||||
0.670029 | + | 0.742335i | \(0.266282\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.4303 | 0.898239 | 0.449119 | − | 0.893472i | \(-0.351738\pi\) | ||||
0.449119 | + | 0.893472i | \(0.351738\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 21.4172 | 1.04134 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.56314 | −0.0756456 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.56314 | 0.123750 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.5117 | −0.747170 | −0.373585 | − | 0.927596i | \(-0.621872\pi\) | ||||
−0.373585 | + | 0.927596i | \(0.621872\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −31.8870 | −1.53239 | −0.766196 | − | 0.642607i | \(-0.777853\pi\) | ||||
−0.766196 | + | 0.642607i | \(0.777853\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.23163 | 0.393772 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.7278 | 0.702920 | 0.351460 | − | 0.936203i | \(-0.385685\pi\) | ||||
0.351460 | + | 0.936203i | \(0.385685\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.69596 | 0.414093 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.46087 | −0.306965 | −0.153483 | − | 0.988151i | \(-0.549049\pi\) | ||||
−0.153483 | + | 0.988151i | \(0.549049\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.22378 | 0.152480 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 21.2910 | 1.00478 | 0.502391 | − | 0.864641i | \(-0.332454\pi\) | ||||
0.502391 | + | 0.864641i | \(0.332454\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −14.2975 | −0.673243 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 20.5751 | 0.966705 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.6465 | 0.919023 | 0.459512 | − | 0.888172i | \(-0.348024\pi\) | ||||
0.459512 | + | 0.888172i | \(0.348024\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.55660 | −0.306036 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.16467 | 0.0542442 | 0.0271221 | − | 0.999632i | \(-0.491366\pi\) | ||||
0.0271221 | + | 0.999632i | \(0.491366\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.15375 | 0.239515 | 0.119758 | − | 0.992803i | \(-0.461788\pi\) | ||||
0.119758 | + | 0.992803i | \(0.461788\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.17122 | 0.193021 | 0.0965104 | − | 0.995332i | \(-0.469232\pi\) | ||||
0.0965104 | + | 0.995332i | \(0.469232\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14.3040 | 0.660499 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −19.6146 | −0.903794 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 43.4018 | 1.99561 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11.5631 | 0.529440 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.35552 | −0.107626 | −0.0538132 | − | 0.998551i | \(-0.517138\pi\) | ||||
−0.0538132 | + | 0.998551i | \(0.517138\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.60153 | −0.118620 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −11.8277 | −0.538179 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −19.9056 | −0.902008 | −0.451004 | − | 0.892522i | \(-0.648934\pi\) | ||||
−0.451004 | + | 0.892522i | \(0.648934\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9.93175 | −0.449129 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.90557 | 0.356773 | 0.178387 | − | 0.983960i | \(-0.442912\pi\) | ||||
0.178387 | + | 0.983960i | \(0.442912\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.43032 | −0.424720 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.54875 | 0.114327 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −35.7147 | −1.59881 | −0.799405 | − | 0.600792i | \(-0.794852\pi\) | ||||
−0.799405 | + | 0.600792i | \(0.794852\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.98691 | −0.401506 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 30.7991 | 1.37327 | 0.686633 | − | 0.727004i | \(-0.259088\pi\) | ||||
0.686633 | + | 0.727004i | \(0.259088\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −15.4238 | −0.684994 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17.5631 | 0.778472 | 0.389236 | − | 0.921138i | \(-0.372739\pi\) | ||||
0.389236 | + | 0.921138i | \(0.372739\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.00000 | 0.132712 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.46980 | 0.241497 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 80.3887 | 3.53549 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −17.6763 | −0.775905 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −24.6081 | −1.07810 | −0.539050 | − | 0.842274i | \(-0.681217\pi\) | ||||
−0.539050 | + | 0.842274i | \(0.681217\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 43.7147 | 1.91151 | 0.955756 | − | 0.294162i | \(-0.0950404\pi\) | ||||
0.955756 | + | 0.294162i | \(0.0950404\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.75529 | 0.381386 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 44.7597 | 1.94607 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −20.1030 | −0.872394 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.888109 | −0.0384683 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 15.8857 | 0.685520 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 32.6399 | 1.40590 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.38538 | −0.360516 | −0.180258 | − | 0.983619i | \(-0.557693\pi\) | ||||
−0.180258 | + | 0.983619i | \(0.557693\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 20.0593 | 0.860828 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −26.3040 | −1.12468 | −0.562340 | − | 0.826906i | \(-0.690099\pi\) | ||||
−0.562340 | + | 0.826906i | \(0.690099\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.03839 | 0.0869965 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.86718 | 0.335153 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.27895 | −0.394581 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.66740 | −0.113021 | −0.0565107 | − | 0.998402i | \(-0.517998\pi\) | ||||
−0.0565107 | + | 0.998402i | \(0.517998\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.69596 | 0.114027 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.43032 | −0.355928 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −37.7751 | −1.59203 | −0.796016 | − | 0.605276i | \(-0.793063\pi\) | ||||
−0.796016 | + | 0.605276i | \(0.793063\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.23817 | −0.0939943 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 38.8606 | 1.62912 | 0.814561 | − | 0.580078i | \(-0.196978\pi\) | ||||
0.814561 | + | 0.580078i | \(0.196978\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.17122 | 0.174560 | 0.0872800 | − | 0.996184i | \(-0.472183\pi\) | ||||
0.0872800 | + | 0.996184i | \(0.472183\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.95398 | −0.206955 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −39.3413 | −1.63780 | −0.818901 | − | 0.573935i | \(-0.805416\pi\) | ||||
−0.818901 | + | 0.573935i | \(0.805416\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.49489 | 0.353035 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.62116 | −0.150231 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 43.4018 | 1.79752 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 17.8672 | 0.737457 | 0.368729 | − | 0.929537i | \(-0.379793\pi\) | ||||
0.368729 | + | 0.929537i | \(0.379793\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.30404 | −0.300958 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 24.5435 | 1.00959 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13.0803 | 0.537142 | 0.268571 | − | 0.963260i | \(-0.413449\pi\) | ||||
0.268571 | + | 0.963260i | \(0.413449\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 10.4776 | 0.428821 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10.7278 | 0.438326 | 0.219163 | − | 0.975688i | \(-0.429667\pi\) | ||||
0.219163 | + | 0.975688i | \(0.429667\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 39.8026 | 1.62358 | 0.811791 | − | 0.583948i | \(-0.198493\pi\) | ||||
0.811791 | + | 0.583948i | \(0.198493\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −18.6530 | −0.759609 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −43.0318 | −1.74661 | −0.873304 | − | 0.487175i | \(-0.838027\pi\) | ||||
−0.873304 | + | 0.487175i | \(0.838027\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −11.3040 | −0.458063 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.99346 | 0.202014 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.4722 | 0.624915 | 0.312458 | − | 0.949932i | \(-0.398848\pi\) | ||||
0.312458 | + | 0.949932i | \(0.398848\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −35.5237 | −1.43013 | −0.715064 | − | 0.699059i | \(-0.753603\pi\) | ||||
−0.715064 | + | 0.699059i | \(0.753603\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15.0449 | −0.604707 | −0.302354 | − | 0.953196i | \(-0.597772\pi\) | ||||
−0.302354 | + | 0.953196i | \(0.597772\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 45.0253 | 1.80680 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.81986 | −0.273232 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.03293 | 0.280868 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.55660 | 0.341174 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 35.6399 | 1.41880 | 0.709402 | − | 0.704805i | \(-0.248965\pi\) | ||||
0.709402 | + | 0.704805i | \(0.248965\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −22.4567 | −0.892574 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.02748 | 0.0803315 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.32367 | −0.131482 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.98691 | 0.275966 | 0.137983 | − | 0.990435i | \(-0.455938\pi\) | ||||
0.137983 | + | 0.990435i | \(0.455938\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.74744 | −0.147785 | −0.0738924 | − | 0.997266i | \(-0.523542\pi\) | ||||
−0.0738924 | + | 0.997266i | \(0.523542\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −34.1658 | −1.34319 | −0.671597 | − | 0.740916i | \(-0.734391\pi\) | ||||
−0.671597 | + | 0.740916i | \(0.734391\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −75.4556 | −2.96189 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10.4949 | 0.411327 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 13.5446 | 0.530041 | 0.265020 | − | 0.964243i | \(-0.414621\pi\) | ||||
0.265020 | + | 0.964243i | \(0.414621\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.91211 | −0.152626 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22.6334 | −0.881671 | −0.440836 | − | 0.897588i | \(-0.645318\pi\) | ||||
−0.440836 | + | 0.897588i | \(0.645318\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.96161 | −0.154089 | −0.0770443 | − | 0.997028i | \(-0.524548\pi\) | ||||
−0.0770443 | + | 0.997028i | \(0.524548\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.523661 | −0.0203373 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 64.7597 | 2.50750 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.11973 | 0.197940 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.65102 | 0.295365 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28.9605 | −1.11635 | −0.558173 | − | 0.829725i | \(-0.688497\pi\) | ||||
−0.558173 | + | 0.829725i | \(0.688497\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −24.7518 | −0.951290 | −0.475645 | − | 0.879637i | \(-0.657785\pi\) | ||||
−0.475645 | + | 0.879637i | \(0.657785\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.31058 | 0.0502955 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −25.8475 | −0.990480 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −40.0593 | −1.53283 | −0.766414 | − | 0.642347i | \(-0.777961\pi\) | ||||
−0.766414 | + | 0.642347i | \(0.777961\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 32.8648 | 1.25387 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.69596 | 0.102708 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 35.2162 | 1.33969 | 0.669843 | − | 0.742503i | \(-0.266361\pi\) | ||||
0.669843 | + | 0.742503i | \(0.266361\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 10.9935 | 0.417607 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.92104 | 0.110642 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9.43032 | 0.356687 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −38.1283 | −1.44008 | −0.720042 | − | 0.693930i | \(-0.755878\pi\) | ||||
−0.720042 | + | 0.693930i | \(0.755878\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.13828 | −0.269225 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 13.0264 | 0.489908 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.08789 | −0.228635 | −0.114318 | − | 0.993444i | \(-0.536468\pi\) | ||||
−0.114318 | + | 0.993444i | \(0.536468\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.1001 | 0.453789 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −60.1241 | −2.25167 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 11.1527 | 0.416504 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −12.1647 | −0.453666 | −0.226833 | − | 0.973934i | \(-0.572837\pi\) | ||||
−0.226833 | + | 0.973934i | \(0.572837\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.6763 | −0.434849 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −26.2580 | −0.976546 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25.6859 | 0.952639 | 0.476320 | − | 0.879272i | \(-0.341971\pi\) | ||||
0.476320 | + | 0.879272i | \(0.341971\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 22.5884 | 0.836609 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.86718 | −0.327964 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 43.4502 | 1.60487 | 0.802434 | − | 0.596741i | \(-0.203538\pi\) | ||||
0.802434 | + | 0.596741i | \(0.203538\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −70.0133 | −2.57897 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −43.4172 | −1.59713 | −0.798564 | − | 0.601910i | \(-0.794407\pi\) | ||||
−0.798564 | + | 0.601910i | \(0.794407\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.436861 | 0.0160485 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −26.6709 | −0.978459 | −0.489230 | − | 0.872155i | \(-0.662722\pi\) | ||||
−0.489230 | + | 0.872155i | \(0.662722\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.72214 | 0.172774 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 19.6146 | 0.716703 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.52674 | −0.0557114 | −0.0278557 | − | 0.999612i | \(-0.508868\pi\) | ||||
−0.0278557 | + | 0.999612i | \(0.508868\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8.90666 | −0.324577 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.38191 | 0.340991 | 0.170496 | − | 0.985358i | \(-0.445463\pi\) | ||||
0.170496 | + | 0.985358i | \(0.445463\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 57.8925 | 2.10136 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.70251 | −0.242966 | −0.121483 | − | 0.992594i | \(-0.538765\pi\) | ||||
−0.121483 | + | 0.992594i | \(0.538765\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11.1448 | 0.403470 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.68703 | −0.169239 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −36.0637 | −1.30049 | −0.650245 | − | 0.759724i | \(-0.725334\pi\) | ||||
−0.650245 | + | 0.759724i | \(0.725334\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.05802 | 0.218174 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 11.6763 | 0.419968 | 0.209984 | − | 0.977705i | \(-0.432659\pi\) | ||||
0.209984 | + | 0.977705i | \(0.432659\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 10.2567 | 0.367958 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.43686 | −0.0873096 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.4753 | −0.446400 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 43.0318 | 1.53783 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −43.1880 | −1.53949 | −0.769743 | − | 0.638354i | \(-0.779616\pi\) | ||||
−0.769743 | + | 0.638354i | \(0.779616\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −21.2975 | −0.758211 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.55660 | −0.126458 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.475254 | 0.0168768 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −29.1658 | −1.03310 | −0.516552 | − | 0.856256i | \(-0.672785\pi\) | ||||
−0.516552 | + | 0.856256i | \(0.672785\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −16.4238 | −0.581031 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.89335 | 0.314231 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −14.6840 | −0.518186 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 11.0013 | 0.387264 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.43032 | 0.0854454 | 0.0427227 | − | 0.999087i | \(-0.486397\pi\) | ||||
0.0427227 | + | 0.999087i | \(0.486397\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −42.2779 | −1.48458 | −0.742288 | − | 0.670081i | \(-0.766259\pi\) | ||||
−0.742288 | + | 0.670081i | \(0.766259\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −24.8462 | −0.871396 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.39738 | 0.258802 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.682874 | 0.0238616 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 52.5136 | 1.83274 | 0.916369 | − | 0.400334i | \(-0.131106\pi\) | ||||
0.916369 | + | 0.400334i | \(0.131106\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 36.3150 | 1.26586 | 0.632930 | − | 0.774209i | \(-0.281852\pi\) | ||||
0.632930 | + | 0.774209i | \(0.281852\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −46.3150 | −1.61053 | −0.805264 | − | 0.592916i | \(-0.797977\pi\) | ||||
−0.805264 | + | 0.592916i | \(0.797977\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.0899 | 0.697750 | 0.348875 | − | 0.937169i | \(-0.386564\pi\) | ||||
0.348875 | + | 0.937169i | \(0.386564\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 29.4753 | 1.02249 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.66849 | −0.231049 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −39.9516 | −1.38093 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −10.5930 | −0.365711 | −0.182855 | − | 0.983140i | \(-0.558534\pi\) | ||||
−0.182855 | + | 0.983140i | \(0.558534\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 32.8925 | 1.13422 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.47634 | 0.154173 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 28.0779 | 0.964767 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −15.6212 | −0.536117 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −58.7597 | −2.01426 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −40.0648 | −1.37179 | −0.685896 | − | 0.727700i | \(-0.740590\pi\) | ||||
−0.685896 | + | 0.727700i | \(0.740590\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 38.3019 | 1.30837 | 0.654183 | − | 0.756336i | \(-0.273012\pi\) | ||||
0.654183 | + | 0.756336i | \(0.273012\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −39.9056 | −1.36156 | −0.680780 | − | 0.732488i | \(-0.738359\pi\) | ||||
−0.680780 | + | 0.732488i | \(0.738359\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.50143 | 0.119328 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −23.3315 | −0.794214 | −0.397107 | − | 0.917772i | \(-0.629986\pi\) | ||||
−0.397107 | + | 0.917772i | \(0.629986\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −18.6554 | −0.633571 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 45.4172 | 1.54067 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.34898 | −0.147359 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.70905 | −0.0578426 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.4105 | 0.351537 | 0.175768 | − | 0.984432i | \(-0.443759\pi\) | ||||
0.175768 | + | 0.984432i | \(0.443759\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 23.8541 | 0.804578 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −23.7662 | −0.800704 | −0.400352 | − | 0.916361i | \(-0.631112\pi\) | ||||
−0.400352 | + | 0.916361i | \(0.631112\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −28.3908 | −0.955428 | −0.477714 | − | 0.878515i | \(-0.658534\pi\) | ||||
−0.477714 | + | 0.878515i | \(0.658534\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −32.5644 | −1.09341 | −0.546703 | − | 0.837326i | \(-0.684117\pi\) | ||||
−0.546703 | + | 0.837326i | \(0.684117\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −13.6146 | −0.456620 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 10.9551 | 0.367008 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 13.7014 | 0.458501 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.59607 | 0.120069 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −57.4622 | −1.91647 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.86718 | −0.295409 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −10.6290 | −0.353711 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 57.2109 | 1.89966 | 0.949829 | − | 0.312771i | \(-0.101257\pi\) | ||||
0.949829 | + | 0.312771i | \(0.101257\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −16.9869 | −0.563420 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −42.0617 | −1.39357 | −0.696783 | − | 0.717282i | \(-0.745386\pi\) | ||||
−0.696783 | + | 0.717282i | \(0.745386\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17.7243 | 0.586590 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.87372 | −0.0618757 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.68287 | 0.187461 | 0.0937304 | − | 0.995598i | \(-0.470121\pi\) | ||||
0.0937304 | + | 0.995598i | \(0.470121\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.61462 | 0.316813 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.774918 | −0.0255067 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 15.2264 | 0.500100 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −30.9289 | −1.01474 | −0.507372 | − | 0.861727i | \(-0.669383\pi\) | ||||
−0.507372 | + | 0.861727i | \(0.669383\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.56314 | 0.182325 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −19.3921 | −0.634870 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 44.5357 | 1.45492 | 0.727458 | − | 0.686152i | \(-0.240701\pi\) | ||||
0.727458 | + | 0.686152i | \(0.240701\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −8.55660 | −0.279234 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.08134 | −0.0678498 | −0.0339249 | − | 0.999424i | \(-0.510801\pi\) | ||||
−0.0339249 | + | 0.999424i | \(0.510801\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −20.0593 | −0.653221 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −52.7189 | −1.71313 | −0.856567 | − | 0.516036i | \(-0.827407\pi\) | ||||
−0.856567 | + | 0.516036i | \(0.827407\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.912115 | −0.0296085 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.74744 | 0.153946 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.22071 | −0.104329 | −0.0521645 | − | 0.998639i | \(-0.516612\pi\) | ||||
−0.0521645 | + | 0.998639i | \(0.516612\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 55.3293 | 1.78854 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −18.9869 | −0.613119 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 22.3490 | 0.720935 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −25.5782 | −0.824247 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.65956 | −0.0855256 | −0.0427628 | − | 0.999085i | \(-0.513616\pi\) | ||||
−0.0427628 | + | 0.999085i | \(0.513616\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.43686 | −0.0461586 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 35.1263 | 1.12726 | 0.563628 | − | 0.826029i | \(-0.309405\pi\) | ||||
0.563628 | + | 0.826029i | \(0.309405\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −23.8068 | −0.763210 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −18.1668 | −0.581209 | −0.290604 | − | 0.956843i | \(-0.593856\pi\) | ||||
−0.290604 | + | 0.956843i | \(0.593856\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 33.3808 | 1.06686 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14.5333 | −0.464012 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −48.4556 | −1.54549 | −0.772747 | − | 0.634714i | \(-0.781118\pi\) | ||||
−0.772747 | + | 0.634714i | \(0.781118\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −19.6870 | −0.626645 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 60.8925 | 1.93627 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.8157 | 0.947127 | 0.473563 | − | 0.880760i | \(-0.342967\pi\) | ||||
0.473563 | + | 0.880760i | \(0.342967\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −7.13044 | −0.226278 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −29.6894 | −0.940273 | −0.470137 | − | 0.882594i | \(-0.655795\pi\) | ||||
−0.470137 | + | 0.882594i | \(0.655795\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −39.0449 | −1.23533 |
(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 | 1900.2.a.f.1.3 | ✓ | 3 | |
4.3 | odd | 2 | 7600.2.a.by.1.1 | 3 | |||
5.2 | odd | 4 | 1900.2.c.g.1749.2 | 6 | |||
5.3 | odd | 4 | 1900.2.c.g.1749.5 | 6 | |||
5.4 | even | 2 | 1900.2.a.h.1.1 | yes | 3 | ||
20.19 | odd | 2 | 7600.2.a.bj.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1900.2.a.f.1.3 | ✓ | 3 | 1.1 | even | 1 | trivial | |
1900.2.a.h.1.1 | yes | 3 | 5.4 | even | 2 | ||
1900.2.c.g.1749.2 | 6 | 5.2 | odd | 4 | |||
1900.2.c.g.1749.5 | 6 | 5.3 | odd | 4 | |||
7600.2.a.bj.1.3 | 3 | 20.19 | odd | 2 | |||
7600.2.a.by.1.1 | 3 | 4.3 | odd | 2 |