Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4017,2,Mod(1,4017)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4017, 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("4017.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4017 = 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4017.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0759064919\) |
Analytic rank: | \(0\) |
Dimension: | \(25\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 4017.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.39323 | 0.985161 | 0.492580 | − | 0.870267i | \(-0.336054\pi\) | ||||
0.492580 | + | 0.870267i | \(0.336054\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −0.0589163 | −0.0294581 | ||||||||
\(5\) | 0.623512 | 0.278843 | 0.139422 | − | 0.990233i | \(-0.455476\pi\) | ||||
0.139422 | + | 0.990233i | \(0.455476\pi\) | |||||||
\(6\) | −1.39323 | −0.568783 | ||||||||
\(7\) | −3.51013 | −1.32671 | −0.663353 | − | 0.748307i | \(-0.730867\pi\) | ||||
−0.663353 | + | 0.748307i | \(0.730867\pi\) | |||||||
\(8\) | −2.86854 | −1.01418 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.868695 | 0.274705 | ||||||||
\(11\) | −5.58599 | −1.68424 | −0.842120 | − | 0.539291i | \(-0.818692\pi\) | ||||
−0.842120 | + | 0.539291i | \(0.818692\pi\) | |||||||
\(12\) | 0.0589163 | 0.0170077 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | −4.89041 | −1.30702 | ||||||||
\(15\) | −0.623512 | −0.160990 | ||||||||
\(16\) | −3.87870 | −0.969674 | ||||||||
\(17\) | −2.32558 | −0.564036 | −0.282018 | − | 0.959409i | \(-0.591004\pi\) | ||||
−0.282018 | + | 0.959409i | \(0.591004\pi\) | |||||||
\(18\) | 1.39323 | 0.328387 | ||||||||
\(19\) | 1.21481 | 0.278695 | 0.139348 | − | 0.990244i | \(-0.455499\pi\) | ||||
0.139348 | + | 0.990244i | \(0.455499\pi\) | |||||||
\(20\) | −0.0367350 | −0.00821420 | ||||||||
\(21\) | 3.51013 | 0.765974 | ||||||||
\(22\) | −7.78256 | −1.65925 | ||||||||
\(23\) | 3.37640 | 0.704029 | 0.352014 | − | 0.935995i | \(-0.385497\pi\) | ||||
0.352014 | + | 0.935995i | \(0.385497\pi\) | |||||||
\(24\) | 2.86854 | 0.585538 | ||||||||
\(25\) | −4.61123 | −0.922246 | ||||||||
\(26\) | 1.39323 | 0.273234 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0.206804 | 0.0390823 | ||||||||
\(29\) | 0.198494 | 0.0368595 | 0.0184297 | − | 0.999830i | \(-0.494133\pi\) | ||||
0.0184297 | + | 0.999830i | \(0.494133\pi\) | |||||||
\(30\) | −0.868695 | −0.158601 | ||||||||
\(31\) | 7.68697 | 1.38062 | 0.690311 | − | 0.723513i | \(-0.257474\pi\) | ||||
0.690311 | + | 0.723513i | \(0.257474\pi\) | |||||||
\(32\) | 0.333171 | 0.0588969 | ||||||||
\(33\) | 5.58599 | 0.972396 | ||||||||
\(34\) | −3.24006 | −0.555666 | ||||||||
\(35\) | −2.18861 | −0.369943 | ||||||||
\(36\) | −0.0589163 | −0.00981938 | ||||||||
\(37\) | −6.15059 | −1.01115 | −0.505575 | − | 0.862782i | \(-0.668720\pi\) | ||||
−0.505575 | + | 0.862782i | \(0.668720\pi\) | |||||||
\(38\) | 1.69250 | 0.274560 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | −1.78857 | −0.282798 | ||||||||
\(41\) | −0.138445 | −0.0216215 | −0.0108108 | − | 0.999942i | \(-0.503441\pi\) | ||||
−0.0108108 | + | 0.999942i | \(0.503441\pi\) | |||||||
\(42\) | 4.89041 | 0.754607 | ||||||||
\(43\) | 2.99205 | 0.456284 | 0.228142 | − | 0.973628i | \(-0.426735\pi\) | ||||
0.228142 | + | 0.973628i | \(0.426735\pi\) | |||||||
\(44\) | 0.329106 | 0.0496145 | ||||||||
\(45\) | 0.623512 | 0.0929477 | ||||||||
\(46\) | 4.70410 | 0.693582 | ||||||||
\(47\) | 10.0482 | 1.46569 | 0.732843 | − | 0.680397i | \(-0.238193\pi\) | ||||
0.732843 | + | 0.680397i | \(0.238193\pi\) | |||||||
\(48\) | 3.87870 | 0.559842 | ||||||||
\(49\) | 5.32103 | 0.760148 | ||||||||
\(50\) | −6.42450 | −0.908561 | ||||||||
\(51\) | 2.32558 | 0.325646 | ||||||||
\(52\) | −0.0589163 | −0.00817021 | ||||||||
\(53\) | −4.89477 | −0.672348 | −0.336174 | − | 0.941800i | \(-0.609133\pi\) | ||||
−0.336174 | + | 0.941800i | \(0.609133\pi\) | |||||||
\(54\) | −1.39323 | −0.189594 | ||||||||
\(55\) | −3.48293 | −0.469639 | ||||||||
\(56\) | 10.0690 | 1.34552 | ||||||||
\(57\) | −1.21481 | −0.160905 | ||||||||
\(58\) | 0.276548 | 0.0363125 | ||||||||
\(59\) | −2.53206 | −0.329646 | −0.164823 | − | 0.986323i | \(-0.552705\pi\) | ||||
−0.164823 | + | 0.986323i | \(0.552705\pi\) | |||||||
\(60\) | 0.0367350 | 0.00474247 | ||||||||
\(61\) | −10.9607 | −1.40337 | −0.701685 | − | 0.712487i | \(-0.747569\pi\) | ||||
−0.701685 | + | 0.712487i | \(0.747569\pi\) | |||||||
\(62\) | 10.7097 | 1.36013 | ||||||||
\(63\) | −3.51013 | −0.442235 | ||||||||
\(64\) | 8.22158 | 1.02770 | ||||||||
\(65\) | 0.623512 | 0.0773372 | ||||||||
\(66\) | 7.78256 | 0.957967 | ||||||||
\(67\) | 11.8383 | 1.44628 | 0.723138 | − | 0.690704i | \(-0.242699\pi\) | ||||
0.723138 | + | 0.690704i | \(0.242699\pi\) | |||||||
\(68\) | 0.137014 | 0.0166154 | ||||||||
\(69\) | −3.37640 | −0.406471 | ||||||||
\(70\) | −3.04923 | −0.364453 | ||||||||
\(71\) | 12.6126 | 1.49683 | 0.748417 | − | 0.663228i | \(-0.230814\pi\) | ||||
0.748417 | + | 0.663228i | \(0.230814\pi\) | |||||||
\(72\) | −2.86854 | −0.338061 | ||||||||
\(73\) | 13.3432 | 1.56170 | 0.780850 | − | 0.624718i | \(-0.214786\pi\) | ||||
0.780850 | + | 0.624718i | \(0.214786\pi\) | |||||||
\(74\) | −8.56917 | −0.996146 | ||||||||
\(75\) | 4.61123 | 0.532459 | ||||||||
\(76\) | −0.0715718 | −0.00820985 | ||||||||
\(77\) | 19.6076 | 2.23449 | ||||||||
\(78\) | −1.39323 | −0.157752 | ||||||||
\(79\) | −1.41353 | −0.159034 | −0.0795172 | − | 0.996833i | \(-0.525338\pi\) | ||||
−0.0795172 | + | 0.996833i | \(0.525338\pi\) | |||||||
\(80\) | −2.41841 | −0.270387 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.192886 | −0.0213007 | ||||||||
\(83\) | −7.93349 | −0.870814 | −0.435407 | − | 0.900234i | \(-0.643396\pi\) | ||||
−0.435407 | + | 0.900234i | \(0.643396\pi\) | |||||||
\(84\) | −0.206804 | −0.0225642 | ||||||||
\(85\) | −1.45003 | −0.157278 | ||||||||
\(86\) | 4.16861 | 0.449513 | ||||||||
\(87\) | −0.198494 | −0.0212808 | ||||||||
\(88\) | 16.0236 | 1.70813 | ||||||||
\(89\) | 5.72890 | 0.607262 | 0.303631 | − | 0.952790i | \(-0.401801\pi\) | ||||
0.303631 | + | 0.952790i | \(0.401801\pi\) | |||||||
\(90\) | 0.868695 | 0.0915685 | ||||||||
\(91\) | −3.51013 | −0.367962 | ||||||||
\(92\) | −0.198925 | −0.0207394 | ||||||||
\(93\) | −7.68697 | −0.797102 | ||||||||
\(94\) | 13.9995 | 1.44394 | ||||||||
\(95\) | 0.757446 | 0.0777123 | ||||||||
\(96\) | −0.333171 | −0.0340041 | ||||||||
\(97\) | −6.43788 | −0.653667 | −0.326834 | − | 0.945082i | \(-0.605982\pi\) | ||||
−0.326834 | + | 0.945082i | \(0.605982\pi\) | |||||||
\(98\) | 7.41341 | 0.748868 | ||||||||
\(99\) | −5.58599 | −0.561413 | ||||||||
\(100\) | 0.271677 | 0.0271677 | ||||||||
\(101\) | 14.9176 | 1.48436 | 0.742178 | − | 0.670203i | \(-0.233793\pi\) | ||||
0.742178 | + | 0.670203i | \(0.233793\pi\) | |||||||
\(102\) | 3.24006 | 0.320814 | ||||||||
\(103\) | −1.00000 | −0.0985329 | ||||||||
\(104\) | −2.86854 | −0.281283 | ||||||||
\(105\) | 2.18861 | 0.213587 | ||||||||
\(106\) | −6.81952 | −0.662371 | ||||||||
\(107\) | 5.92763 | 0.573046 | 0.286523 | − | 0.958073i | \(-0.407501\pi\) | ||||
0.286523 | + | 0.958073i | \(0.407501\pi\) | |||||||
\(108\) | 0.0589163 | 0.00566922 | ||||||||
\(109\) | −11.2495 | −1.07751 | −0.538755 | − | 0.842462i | \(-0.681105\pi\) | ||||
−0.538755 | + | 0.842462i | \(0.681105\pi\) | |||||||
\(110\) | −4.85252 | −0.462670 | ||||||||
\(111\) | 6.15059 | 0.583788 | ||||||||
\(112\) | 13.6147 | 1.28647 | ||||||||
\(113\) | 8.05742 | 0.757978 | 0.378989 | − | 0.925401i | \(-0.376272\pi\) | ||||
0.378989 | + | 0.925401i | \(0.376272\pi\) | |||||||
\(114\) | −1.69250 | −0.158517 | ||||||||
\(115\) | 2.10523 | 0.196314 | ||||||||
\(116\) | −0.0116945 | −0.00108581 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | −3.52773 | −0.324754 | ||||||||
\(119\) | 8.16309 | 0.748309 | ||||||||
\(120\) | 1.78857 | 0.163273 | ||||||||
\(121\) | 20.2033 | 1.83666 | ||||||||
\(122\) | −15.2707 | −1.38254 | ||||||||
\(123\) | 0.138445 | 0.0124832 | ||||||||
\(124\) | −0.452888 | −0.0406705 | ||||||||
\(125\) | −5.99272 | −0.536005 | ||||||||
\(126\) | −4.89041 | −0.435673 | ||||||||
\(127\) | −9.49994 | −0.842984 | −0.421492 | − | 0.906832i | \(-0.638493\pi\) | ||||
−0.421492 | + | 0.906832i | \(0.638493\pi\) | |||||||
\(128\) | 10.7882 | 0.953550 | ||||||||
\(129\) | −2.99205 | −0.263435 | ||||||||
\(130\) | 0.868695 | 0.0761896 | ||||||||
\(131\) | 7.24489 | 0.632989 | 0.316495 | − | 0.948594i | \(-0.397494\pi\) | ||||
0.316495 | + | 0.948594i | \(0.397494\pi\) | |||||||
\(132\) | −0.329106 | −0.0286450 | ||||||||
\(133\) | −4.26413 | −0.369747 | ||||||||
\(134\) | 16.4934 | 1.42481 | ||||||||
\(135\) | −0.623512 | −0.0536634 | ||||||||
\(136\) | 6.67102 | 0.572035 | ||||||||
\(137\) | −14.1521 | −1.20910 | −0.604549 | − | 0.796568i | \(-0.706647\pi\) | ||||
−0.604549 | + | 0.796568i | \(0.706647\pi\) | |||||||
\(138\) | −4.70410 | −0.400440 | ||||||||
\(139\) | 6.78145 | 0.575195 | 0.287597 | − | 0.957751i | \(-0.407143\pi\) | ||||
0.287597 | + | 0.957751i | \(0.407143\pi\) | |||||||
\(140\) | 0.128945 | 0.0108978 | ||||||||
\(141\) | −10.0482 | −0.846215 | ||||||||
\(142\) | 17.5722 | 1.47462 | ||||||||
\(143\) | −5.58599 | −0.467124 | ||||||||
\(144\) | −3.87870 | −0.323225 | ||||||||
\(145\) | 0.123764 | 0.0102780 | ||||||||
\(146\) | 18.5901 | 1.53853 | ||||||||
\(147\) | −5.32103 | −0.438871 | ||||||||
\(148\) | 0.362370 | 0.0297866 | ||||||||
\(149\) | −10.6460 | −0.872153 | −0.436076 | − | 0.899910i | \(-0.643632\pi\) | ||||
−0.436076 | + | 0.899910i | \(0.643632\pi\) | |||||||
\(150\) | 6.42450 | 0.524558 | ||||||||
\(151\) | −10.0387 | −0.816935 | −0.408468 | − | 0.912773i | \(-0.633937\pi\) | ||||
−0.408468 | + | 0.912773i | \(0.633937\pi\) | |||||||
\(152\) | −3.48472 | −0.282648 | ||||||||
\(153\) | −2.32558 | −0.188012 | ||||||||
\(154\) | 27.3178 | 2.20133 | ||||||||
\(155\) | 4.79292 | 0.384977 | ||||||||
\(156\) | 0.0589163 | 0.00471708 | ||||||||
\(157\) | 15.6058 | 1.24548 | 0.622738 | − | 0.782430i | \(-0.286020\pi\) | ||||
0.622738 | + | 0.782430i | \(0.286020\pi\) | |||||||
\(158\) | −1.96937 | −0.156674 | ||||||||
\(159\) | 4.89477 | 0.388180 | ||||||||
\(160\) | 0.207736 | 0.0164230 | ||||||||
\(161\) | −11.8516 | −0.934039 | ||||||||
\(162\) | 1.39323 | 0.109462 | ||||||||
\(163\) | −18.7849 | −1.47135 | −0.735674 | − | 0.677336i | \(-0.763134\pi\) | ||||
−0.735674 | + | 0.677336i | \(0.763134\pi\) | |||||||
\(164\) | 0.00815668 | 0.000636930 0 | ||||||||
\(165\) | 3.48293 | 0.271146 | ||||||||
\(166\) | −11.0532 | −0.857892 | ||||||||
\(167\) | 17.1601 | 1.32789 | 0.663946 | − | 0.747780i | \(-0.268880\pi\) | ||||
0.663946 | + | 0.747780i | \(0.268880\pi\) | |||||||
\(168\) | −10.0690 | −0.776837 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −2.02022 | −0.154944 | ||||||||
\(171\) | 1.21481 | 0.0928985 | ||||||||
\(172\) | −0.176280 | −0.0134413 | ||||||||
\(173\) | −14.5383 | −1.10532 | −0.552662 | − | 0.833406i | \(-0.686388\pi\) | ||||
−0.552662 | + | 0.833406i | \(0.686388\pi\) | |||||||
\(174\) | −0.276548 | −0.0209650 | ||||||||
\(175\) | 16.1860 | 1.22355 | ||||||||
\(176\) | 21.6664 | 1.63316 | ||||||||
\(177\) | 2.53206 | 0.190321 | ||||||||
\(178\) | 7.98166 | 0.598251 | ||||||||
\(179\) | −9.18888 | −0.686809 | −0.343405 | − | 0.939188i | \(-0.611580\pi\) | ||||
−0.343405 | + | 0.939188i | \(0.611580\pi\) | |||||||
\(180\) | −0.0367350 | −0.00273807 | ||||||||
\(181\) | 2.04116 | 0.151718 | 0.0758590 | − | 0.997119i | \(-0.475830\pi\) | ||||
0.0758590 | + | 0.997119i | \(0.475830\pi\) | |||||||
\(182\) | −4.89041 | −0.362502 | ||||||||
\(183\) | 10.9607 | 0.810236 | ||||||||
\(184\) | −9.68535 | −0.714013 | ||||||||
\(185\) | −3.83497 | −0.281953 | ||||||||
\(186\) | −10.7097 | −0.785274 | ||||||||
\(187\) | 12.9907 | 0.949971 | ||||||||
\(188\) | −0.592005 | −0.0431764 | ||||||||
\(189\) | 3.51013 | 0.255325 | ||||||||
\(190\) | 1.05529 | 0.0765591 | ||||||||
\(191\) | 14.3314 | 1.03698 | 0.518490 | − | 0.855084i | \(-0.326494\pi\) | ||||
0.518490 | + | 0.855084i | \(0.326494\pi\) | |||||||
\(192\) | −8.22158 | −0.593341 | ||||||||
\(193\) | 9.12754 | 0.657014 | 0.328507 | − | 0.944501i | \(-0.393454\pi\) | ||||
0.328507 | + | 0.944501i | \(0.393454\pi\) | |||||||
\(194\) | −8.96943 | −0.643967 | ||||||||
\(195\) | −0.623512 | −0.0446506 | ||||||||
\(196\) | −0.313495 | −0.0223925 | ||||||||
\(197\) | −15.9455 | −1.13607 | −0.568034 | − | 0.823005i | \(-0.692296\pi\) | ||||
−0.568034 | + | 0.823005i | \(0.692296\pi\) | |||||||
\(198\) | −7.78256 | −0.553082 | ||||||||
\(199\) | 9.81013 | 0.695422 | 0.347711 | − | 0.937602i | \(-0.386959\pi\) | ||||
0.347711 | + | 0.937602i | \(0.386959\pi\) | |||||||
\(200\) | 13.2275 | 0.935326 | ||||||||
\(201\) | −11.8383 | −0.835007 | ||||||||
\(202\) | 20.7836 | 1.46233 | ||||||||
\(203\) | −0.696741 | −0.0489016 | ||||||||
\(204\) | −0.137014 | −0.00959293 | ||||||||
\(205\) | −0.0863224 | −0.00602902 | ||||||||
\(206\) | −1.39323 | −0.0970708 | ||||||||
\(207\) | 3.37640 | 0.234676 | ||||||||
\(208\) | −3.87870 | −0.268939 | ||||||||
\(209\) | −6.78589 | −0.469390 | ||||||||
\(210\) | 3.04923 | 0.210417 | ||||||||
\(211\) | −19.3221 | −1.33019 | −0.665095 | − | 0.746758i | \(-0.731609\pi\) | ||||
−0.665095 | + | 0.746758i | \(0.731609\pi\) | |||||||
\(212\) | 0.288381 | 0.0198061 | ||||||||
\(213\) | −12.6126 | −0.864198 | ||||||||
\(214\) | 8.25854 | 0.564542 | ||||||||
\(215\) | 1.86558 | 0.127232 | ||||||||
\(216\) | 2.86854 | 0.195179 | ||||||||
\(217\) | −26.9823 | −1.83168 | ||||||||
\(218\) | −15.6732 | −1.06152 | ||||||||
\(219\) | −13.3432 | −0.901648 | ||||||||
\(220\) | 0.205201 | 0.0138347 | ||||||||
\(221\) | −2.32558 | −0.156435 | ||||||||
\(222\) | 8.56917 | 0.575125 | ||||||||
\(223\) | 8.65778 | 0.579768 | 0.289884 | − | 0.957062i | \(-0.406383\pi\) | ||||
0.289884 | + | 0.957062i | \(0.406383\pi\) | |||||||
\(224\) | −1.16947 | −0.0781388 | ||||||||
\(225\) | −4.61123 | −0.307415 | ||||||||
\(226\) | 11.2258 | 0.746730 | ||||||||
\(227\) | 13.9306 | 0.924604 | 0.462302 | − | 0.886722i | \(-0.347024\pi\) | ||||
0.462302 | + | 0.886722i | \(0.347024\pi\) | |||||||
\(228\) | 0.0715718 | 0.00473996 | ||||||||
\(229\) | 26.1342 | 1.72700 | 0.863500 | − | 0.504350i | \(-0.168268\pi\) | ||||
0.863500 | + | 0.504350i | \(0.168268\pi\) | |||||||
\(230\) | 2.93306 | 0.193401 | ||||||||
\(231\) | −19.6076 | −1.29008 | ||||||||
\(232\) | −0.569389 | −0.0373822 | ||||||||
\(233\) | 23.5545 | 1.54311 | 0.771553 | − | 0.636165i | \(-0.219480\pi\) | ||||
0.771553 | + | 0.636165i | \(0.219480\pi\) | |||||||
\(234\) | 1.39323 | 0.0910782 | ||||||||
\(235\) | 6.26520 | 0.408697 | ||||||||
\(236\) | 0.149179 | 0.00971075 | ||||||||
\(237\) | 1.41353 | 0.0918185 | ||||||||
\(238\) | 11.3730 | 0.737205 | ||||||||
\(239\) | −8.80497 | −0.569546 | −0.284773 | − | 0.958595i | \(-0.591918\pi\) | ||||
−0.284773 | + | 0.958595i | \(0.591918\pi\) | |||||||
\(240\) | 2.41841 | 0.156108 | ||||||||
\(241\) | 14.9700 | 0.964303 | 0.482152 | − | 0.876088i | \(-0.339855\pi\) | ||||
0.482152 | + | 0.876088i | \(0.339855\pi\) | |||||||
\(242\) | 28.1478 | 1.80941 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0.645762 | 0.0413406 | ||||||||
\(245\) | 3.31773 | 0.211962 | ||||||||
\(246\) | 0.192886 | 0.0122980 | ||||||||
\(247\) | 1.21481 | 0.0772962 | ||||||||
\(248\) | −22.0504 | −1.40020 | ||||||||
\(249\) | 7.93349 | 0.502765 | ||||||||
\(250\) | −8.34923 | −0.528051 | ||||||||
\(251\) | −1.59917 | −0.100938 | −0.0504692 | − | 0.998726i | \(-0.516072\pi\) | ||||
−0.0504692 | + | 0.998726i | \(0.516072\pi\) | |||||||
\(252\) | 0.206804 | 0.0130274 | ||||||||
\(253\) | −18.8606 | −1.18575 | ||||||||
\(254\) | −13.2356 | −0.830475 | ||||||||
\(255\) | 1.45003 | 0.0908042 | ||||||||
\(256\) | −1.41275 | −0.0882969 | ||||||||
\(257\) | −13.0861 | −0.816290 | −0.408145 | − | 0.912917i | \(-0.633824\pi\) | ||||
−0.408145 | + | 0.912917i | \(0.633824\pi\) | |||||||
\(258\) | −4.16861 | −0.259526 | ||||||||
\(259\) | 21.5894 | 1.34150 | ||||||||
\(260\) | −0.0367350 | −0.00227821 | ||||||||
\(261\) | 0.198494 | 0.0122865 | ||||||||
\(262\) | 10.0938 | 0.623596 | ||||||||
\(263\) | −4.71375 | −0.290662 | −0.145331 | − | 0.989383i | \(-0.546425\pi\) | ||||
−0.145331 | + | 0.989383i | \(0.546425\pi\) | |||||||
\(264\) | −16.0236 | −0.986187 | ||||||||
\(265\) | −3.05195 | −0.187480 | ||||||||
\(266\) | −5.94090 | −0.364260 | ||||||||
\(267\) | −5.72890 | −0.350603 | ||||||||
\(268\) | −0.697467 | −0.0426046 | ||||||||
\(269\) | −0.151544 | −0.00923980 | −0.00461990 | − | 0.999989i | \(-0.501471\pi\) | ||||
−0.00461990 | + | 0.999989i | \(0.501471\pi\) | |||||||
\(270\) | −0.868695 | −0.0528671 | ||||||||
\(271\) | 9.25680 | 0.562310 | 0.281155 | − | 0.959662i | \(-0.409282\pi\) | ||||
0.281155 | + | 0.959662i | \(0.409282\pi\) | |||||||
\(272\) | 9.02022 | 0.546931 | ||||||||
\(273\) | 3.51013 | 0.212443 | ||||||||
\(274\) | −19.7171 | −1.19116 | ||||||||
\(275\) | 25.7583 | 1.55328 | ||||||||
\(276\) | 0.198925 | 0.0119739 | ||||||||
\(277\) | 24.5898 | 1.47746 | 0.738728 | − | 0.674004i | \(-0.235427\pi\) | ||||
0.738728 | + | 0.674004i | \(0.235427\pi\) | |||||||
\(278\) | 9.44810 | 0.566660 | ||||||||
\(279\) | 7.68697 | 0.460207 | ||||||||
\(280\) | 6.27812 | 0.375189 | ||||||||
\(281\) | −7.66509 | −0.457261 | −0.228630 | − | 0.973513i | \(-0.573425\pi\) | ||||
−0.228630 | + | 0.973513i | \(0.573425\pi\) | |||||||
\(282\) | −13.9995 | −0.833658 | ||||||||
\(283\) | 30.8950 | 1.83652 | 0.918260 | − | 0.395978i | \(-0.129595\pi\) | ||||
0.918260 | + | 0.395978i | \(0.129595\pi\) | |||||||
\(284\) | −0.743084 | −0.0440939 | ||||||||
\(285\) | −0.757446 | −0.0448672 | ||||||||
\(286\) | −7.78256 | −0.460192 | ||||||||
\(287\) | 0.485962 | 0.0286854 | ||||||||
\(288\) | 0.333171 | 0.0196323 | ||||||||
\(289\) | −11.5917 | −0.681864 | ||||||||
\(290\) | 0.172431 | 0.0101255 | ||||||||
\(291\) | 6.43788 | 0.377395 | ||||||||
\(292\) | −0.786130 | −0.0460048 | ||||||||
\(293\) | −8.39607 | −0.490504 | −0.245252 | − | 0.969459i | \(-0.578871\pi\) | ||||
−0.245252 | + | 0.969459i | \(0.578871\pi\) | |||||||
\(294\) | −7.41341 | −0.432359 | ||||||||
\(295\) | −1.57877 | −0.0919195 | ||||||||
\(296\) | 17.6432 | 1.02549 | ||||||||
\(297\) | 5.58599 | 0.324132 | ||||||||
\(298\) | −14.8323 | −0.859211 | ||||||||
\(299\) | 3.37640 | 0.195262 | ||||||||
\(300\) | −0.271677 | −0.0156853 | ||||||||
\(301\) | −10.5025 | −0.605354 | ||||||||
\(302\) | −13.9861 | −0.804812 | ||||||||
\(303\) | −14.9176 | −0.856994 | ||||||||
\(304\) | −4.71186 | −0.270244 | ||||||||
\(305\) | −6.83411 | −0.391320 | ||||||||
\(306\) | −3.24006 | −0.185222 | ||||||||
\(307\) | 16.9044 | 0.964787 | 0.482393 | − | 0.875955i | \(-0.339768\pi\) | ||||
0.482393 | + | 0.875955i | \(0.339768\pi\) | |||||||
\(308\) | −1.15520 | −0.0658239 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | 6.67763 | 0.379264 | ||||||||
\(311\) | 14.1865 | 0.804441 | 0.402221 | − | 0.915543i | \(-0.368238\pi\) | ||||
0.402221 | + | 0.915543i | \(0.368238\pi\) | |||||||
\(312\) | 2.86854 | 0.162399 | ||||||||
\(313\) | 20.0222 | 1.13172 | 0.565861 | − | 0.824501i | \(-0.308544\pi\) | ||||
0.565861 | + | 0.824501i | \(0.308544\pi\) | |||||||
\(314\) | 21.7424 | 1.22699 | ||||||||
\(315\) | −2.18861 | −0.123314 | ||||||||
\(316\) | 0.0832798 | 0.00468485 | ||||||||
\(317\) | −21.0736 | −1.18361 | −0.591807 | − | 0.806080i | \(-0.701585\pi\) | ||||
−0.591807 | + | 0.806080i | \(0.701585\pi\) | |||||||
\(318\) | 6.81952 | 0.382420 | ||||||||
\(319\) | −1.10879 | −0.0620802 | ||||||||
\(320\) | 5.12625 | 0.286566 | ||||||||
\(321\) | −5.92763 | −0.330848 | ||||||||
\(322\) | −16.5120 | −0.920179 | ||||||||
\(323\) | −2.82513 | −0.157194 | ||||||||
\(324\) | −0.0589163 | −0.00327313 | ||||||||
\(325\) | −4.61123 | −0.255785 | ||||||||
\(326\) | −26.1716 | −1.44951 | ||||||||
\(327\) | 11.2495 | 0.622101 | ||||||||
\(328\) | 0.397136 | 0.0219282 | ||||||||
\(329\) | −35.2707 | −1.94453 | ||||||||
\(330\) | 4.85252 | 0.267122 | ||||||||
\(331\) | −21.6470 | −1.18982 | −0.594912 | − | 0.803791i | \(-0.702813\pi\) | ||||
−0.594912 | + | 0.803791i | \(0.702813\pi\) | |||||||
\(332\) | 0.467412 | 0.0256525 | ||||||||
\(333\) | −6.15059 | −0.337050 | ||||||||
\(334\) | 23.9080 | 1.30819 | ||||||||
\(335\) | 7.38131 | 0.403284 | ||||||||
\(336\) | −13.6147 | −0.742745 | ||||||||
\(337\) | 7.03473 | 0.383206 | 0.191603 | − | 0.981473i | \(-0.438631\pi\) | ||||
0.191603 | + | 0.981473i | \(0.438631\pi\) | |||||||
\(338\) | 1.39323 | 0.0757816 | ||||||||
\(339\) | −8.05742 | −0.437619 | ||||||||
\(340\) | 0.0854302 | 0.00463310 | ||||||||
\(341\) | −42.9394 | −2.32530 | ||||||||
\(342\) | 1.69250 | 0.0915200 | ||||||||
\(343\) | 5.89340 | 0.318214 | ||||||||
\(344\) | −8.58282 | −0.462755 | ||||||||
\(345\) | −2.10523 | −0.113342 | ||||||||
\(346\) | −20.2551 | −1.08892 | ||||||||
\(347\) | −3.75732 | −0.201704 | −0.100852 | − | 0.994901i | \(-0.532157\pi\) | ||||
−0.100852 | + | 0.994901i | \(0.532157\pi\) | |||||||
\(348\) | 0.0116945 | 0.000626893 0 | ||||||||
\(349\) | −17.4340 | −0.933220 | −0.466610 | − | 0.884463i | \(-0.654525\pi\) | ||||
−0.466610 | + | 0.884463i | \(0.654525\pi\) | |||||||
\(350\) | 22.5508 | 1.20539 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | −1.86109 | −0.0991965 | ||||||||
\(353\) | 1.22134 | 0.0650054 | 0.0325027 | − | 0.999472i | \(-0.489652\pi\) | ||||
0.0325027 | + | 0.999472i | \(0.489652\pi\) | |||||||
\(354\) | 3.52773 | 0.187497 | ||||||||
\(355\) | 7.86408 | 0.417382 | ||||||||
\(356\) | −0.337525 | −0.0178888 | ||||||||
\(357\) | −8.16309 | −0.432037 | ||||||||
\(358\) | −12.8022 | −0.676618 | ||||||||
\(359\) | 6.72978 | 0.355184 | 0.177592 | − | 0.984104i | \(-0.443169\pi\) | ||||
0.177592 | + | 0.984104i | \(0.443169\pi\) | |||||||
\(360\) | −1.78857 | −0.0942659 | ||||||||
\(361\) | −17.5242 | −0.922329 | ||||||||
\(362\) | 2.84380 | 0.149467 | ||||||||
\(363\) | −20.2033 | −1.06040 | ||||||||
\(364\) | 0.206804 | 0.0108395 | ||||||||
\(365\) | 8.31963 | 0.435469 | ||||||||
\(366\) | 15.2707 | 0.798213 | ||||||||
\(367\) | 26.8652 | 1.40235 | 0.701177 | − | 0.712987i | \(-0.252658\pi\) | ||||
0.701177 | + | 0.712987i | \(0.252658\pi\) | |||||||
\(368\) | −13.0960 | −0.682679 | ||||||||
\(369\) | −0.138445 | −0.00720718 | ||||||||
\(370\) | −5.34299 | −0.277769 | ||||||||
\(371\) | 17.1813 | 0.892007 | ||||||||
\(372\) | 0.452888 | 0.0234811 | ||||||||
\(373\) | −32.8670 | −1.70179 | −0.850895 | − | 0.525335i | \(-0.823940\pi\) | ||||
−0.850895 | + | 0.525335i | \(0.823940\pi\) | |||||||
\(374\) | 18.0990 | 0.935875 | ||||||||
\(375\) | 5.99272 | 0.309463 | ||||||||
\(376\) | −28.8238 | −1.48647 | ||||||||
\(377\) | 0.198494 | 0.0102230 | ||||||||
\(378\) | 4.89041 | 0.251536 | ||||||||
\(379\) | 4.08694 | 0.209932 | 0.104966 | − | 0.994476i | \(-0.466527\pi\) | ||||
0.104966 | + | 0.994476i | \(0.466527\pi\) | |||||||
\(380\) | −0.0446259 | −0.00228926 | ||||||||
\(381\) | 9.49994 | 0.486697 | ||||||||
\(382\) | 19.9668 | 1.02159 | ||||||||
\(383\) | 15.9831 | 0.816699 | 0.408349 | − | 0.912826i | \(-0.366104\pi\) | ||||
0.408349 | + | 0.912826i | \(0.366104\pi\) | |||||||
\(384\) | −10.7882 | −0.550532 | ||||||||
\(385\) | 12.2256 | 0.623072 | ||||||||
\(386\) | 12.7167 | 0.647265 | ||||||||
\(387\) | 2.99205 | 0.152095 | ||||||||
\(388\) | 0.379296 | 0.0192558 | ||||||||
\(389\) | 16.2958 | 0.826232 | 0.413116 | − | 0.910678i | \(-0.364440\pi\) | ||||
0.413116 | + | 0.910678i | \(0.364440\pi\) | |||||||
\(390\) | −0.868695 | −0.0439881 | ||||||||
\(391\) | −7.85209 | −0.397098 | ||||||||
\(392\) | −15.2636 | −0.770928 | ||||||||
\(393\) | −7.24489 | −0.365456 | ||||||||
\(394\) | −22.2157 | −1.11921 | ||||||||
\(395\) | −0.881352 | −0.0443456 | ||||||||
\(396\) | 0.329106 | 0.0165382 | ||||||||
\(397\) | −2.71844 | −0.136434 | −0.0682172 | − | 0.997670i | \(-0.521731\pi\) | ||||
−0.0682172 | + | 0.997670i | \(0.521731\pi\) | |||||||
\(398\) | 13.6677 | 0.685102 | ||||||||
\(399\) | 4.26413 | 0.213473 | ||||||||
\(400\) | 17.8856 | 0.894279 | ||||||||
\(401\) | −12.3564 | −0.617049 | −0.308524 | − | 0.951216i | \(-0.599835\pi\) | ||||
−0.308524 | + | 0.951216i | \(0.599835\pi\) | |||||||
\(402\) | −16.4934 | −0.822617 | ||||||||
\(403\) | 7.68697 | 0.382915 | ||||||||
\(404\) | −0.878889 | −0.0437264 | ||||||||
\(405\) | 0.623512 | 0.0309826 | ||||||||
\(406\) | −0.970719 | −0.0481760 | ||||||||
\(407\) | 34.3571 | 1.70302 | ||||||||
\(408\) | −6.67102 | −0.330264 | ||||||||
\(409\) | −19.4791 | −0.963181 | −0.481591 | − | 0.876396i | \(-0.659941\pi\) | ||||
−0.481591 | + | 0.876396i | \(0.659941\pi\) | |||||||
\(410\) | −0.120267 | −0.00593955 | ||||||||
\(411\) | 14.1521 | 0.698073 | ||||||||
\(412\) | 0.0589163 | 0.00290260 | ||||||||
\(413\) | 8.88786 | 0.437343 | ||||||||
\(414\) | 4.70410 | 0.231194 | ||||||||
\(415\) | −4.94663 | −0.242821 | ||||||||
\(416\) | 0.333171 | 0.0163351 | ||||||||
\(417\) | −6.78145 | −0.332089 | ||||||||
\(418\) | −9.45429 | −0.462425 | ||||||||
\(419\) | 6.50214 | 0.317650 | 0.158825 | − | 0.987307i | \(-0.449229\pi\) | ||||
0.158825 | + | 0.987307i | \(0.449229\pi\) | |||||||
\(420\) | −0.128945 | −0.00629186 | ||||||||
\(421\) | −30.5827 | −1.49051 | −0.745255 | − | 0.666780i | \(-0.767672\pi\) | ||||
−0.745255 | + | 0.666780i | \(0.767672\pi\) | |||||||
\(422\) | −26.9201 | −1.31045 | ||||||||
\(423\) | 10.0482 | 0.488562 | ||||||||
\(424\) | 14.0408 | 0.681883 | ||||||||
\(425\) | 10.7238 | 0.520180 | ||||||||
\(426\) | −17.5722 | −0.851374 | ||||||||
\(427\) | 38.4734 | 1.86186 | ||||||||
\(428\) | −0.349234 | −0.0168809 | ||||||||
\(429\) | 5.58599 | 0.269694 | ||||||||
\(430\) | 2.59918 | 0.125344 | ||||||||
\(431\) | 32.7855 | 1.57922 | 0.789611 | − | 0.613607i | \(-0.210282\pi\) | ||||
0.789611 | + | 0.613607i | \(0.210282\pi\) | |||||||
\(432\) | 3.87870 | 0.186614 | ||||||||
\(433\) | −19.3376 | −0.929305 | −0.464653 | − | 0.885493i | \(-0.653821\pi\) | ||||
−0.464653 | + | 0.885493i | \(0.653821\pi\) | |||||||
\(434\) | −37.5925 | −1.80450 | ||||||||
\(435\) | −0.123764 | −0.00593401 | ||||||||
\(436\) | 0.662780 | 0.0317414 | ||||||||
\(437\) | 4.10167 | 0.196210 | ||||||||
\(438\) | −18.5901 | −0.888268 | ||||||||
\(439\) | −30.5692 | −1.45899 | −0.729493 | − | 0.683988i | \(-0.760244\pi\) | ||||
−0.729493 | + | 0.683988i | \(0.760244\pi\) | |||||||
\(440\) | 9.99093 | 0.476299 | ||||||||
\(441\) | 5.32103 | 0.253383 | ||||||||
\(442\) | −3.24006 | −0.154114 | ||||||||
\(443\) | −27.4515 | −1.30426 | −0.652130 | − | 0.758107i | \(-0.726124\pi\) | ||||
−0.652130 | + | 0.758107i | \(0.726124\pi\) | |||||||
\(444\) | −0.362370 | −0.0171973 | ||||||||
\(445\) | 3.57204 | 0.169331 | ||||||||
\(446\) | 12.0623 | 0.571164 | ||||||||
\(447\) | 10.6460 | 0.503538 | ||||||||
\(448\) | −28.8588 | −1.36345 | ||||||||
\(449\) | 34.0830 | 1.60847 | 0.804237 | − | 0.594308i | \(-0.202574\pi\) | ||||
0.804237 | + | 0.594308i | \(0.202574\pi\) | |||||||
\(450\) | −6.42450 | −0.302854 | ||||||||
\(451\) | 0.773355 | 0.0364158 | ||||||||
\(452\) | −0.474713 | −0.0223286 | ||||||||
\(453\) | 10.0387 | 0.471658 | ||||||||
\(454\) | 19.4085 | 0.910884 | ||||||||
\(455\) | −2.18861 | −0.102604 | ||||||||
\(456\) | 3.48472 | 0.163187 | ||||||||
\(457\) | −1.83623 | −0.0858953 | −0.0429476 | − | 0.999077i | \(-0.513675\pi\) | ||||
−0.0429476 | + | 0.999077i | \(0.513675\pi\) | |||||||
\(458\) | 36.4109 | 1.70137 | ||||||||
\(459\) | 2.32558 | 0.108549 | ||||||||
\(460\) | −0.124032 | −0.00578303 | ||||||||
\(461\) | 32.5255 | 1.51486 | 0.757432 | − | 0.652914i | \(-0.226454\pi\) | ||||
0.757432 | + | 0.652914i | \(0.226454\pi\) | |||||||
\(462\) | −27.3178 | −1.27094 | ||||||||
\(463\) | 4.40056 | 0.204511 | 0.102256 | − | 0.994758i | \(-0.467394\pi\) | ||||
0.102256 | + | 0.994758i | \(0.467394\pi\) | |||||||
\(464\) | −0.769899 | −0.0357417 | ||||||||
\(465\) | −4.79292 | −0.222266 | ||||||||
\(466\) | 32.8168 | 1.52021 | ||||||||
\(467\) | 22.8375 | 1.05679 | 0.528396 | − | 0.848998i | \(-0.322794\pi\) | ||||
0.528396 | + | 0.848998i | \(0.322794\pi\) | |||||||
\(468\) | −0.0589163 | −0.00272340 | ||||||||
\(469\) | −41.5539 | −1.91878 | ||||||||
\(470\) | 8.72885 | 0.402632 | ||||||||
\(471\) | −15.6058 | −0.719076 | ||||||||
\(472\) | 7.26331 | 0.334321 | ||||||||
\(473\) | −16.7136 | −0.768491 | ||||||||
\(474\) | 1.96937 | 0.0904560 | ||||||||
\(475\) | −5.60175 | −0.257026 | ||||||||
\(476\) | −0.480939 | −0.0220438 | ||||||||
\(477\) | −4.89477 | −0.224116 | ||||||||
\(478\) | −12.2673 | −0.561095 | ||||||||
\(479\) | −12.1490 | −0.555101 | −0.277551 | − | 0.960711i | \(-0.589523\pi\) | ||||
−0.277551 | + | 0.960711i | \(0.589523\pi\) | |||||||
\(480\) | −0.207736 | −0.00948182 | ||||||||
\(481\) | −6.15059 | −0.280443 | ||||||||
\(482\) | 20.8566 | 0.949994 | ||||||||
\(483\) | 11.8516 | 0.539268 | ||||||||
\(484\) | −1.19030 | −0.0541046 | ||||||||
\(485\) | −4.01409 | −0.182271 | ||||||||
\(486\) | −1.39323 | −0.0631981 | ||||||||
\(487\) | −28.5484 | −1.29365 | −0.646826 | − | 0.762638i | \(-0.723904\pi\) | ||||
−0.646826 | + | 0.762638i | \(0.723904\pi\) | |||||||
\(488\) | 31.4411 | 1.42327 | ||||||||
\(489\) | 18.7849 | 0.849483 | ||||||||
\(490\) | 4.62235 | 0.208817 | ||||||||
\(491\) | 7.58496 | 0.342304 | 0.171152 | − | 0.985245i | \(-0.445251\pi\) | ||||
0.171152 | + | 0.985245i | \(0.445251\pi\) | |||||||
\(492\) | −0.00815668 | −0.000367732 0 | ||||||||
\(493\) | −0.461614 | −0.0207901 | ||||||||
\(494\) | 1.69250 | 0.0761492 | ||||||||
\(495\) | −3.48293 | −0.156546 | ||||||||
\(496\) | −29.8154 | −1.33875 | ||||||||
\(497\) | −44.2717 | −1.98586 | ||||||||
\(498\) | 11.0532 | 0.495304 | ||||||||
\(499\) | 21.0538 | 0.942499 | 0.471250 | − | 0.882000i | \(-0.343803\pi\) | ||||
0.471250 | + | 0.882000i | \(0.343803\pi\) | |||||||
\(500\) | 0.353069 | 0.0157897 | ||||||||
\(501\) | −17.1601 | −0.766659 | ||||||||
\(502\) | −2.22800 | −0.0994406 | ||||||||
\(503\) | −11.6612 | −0.519946 | −0.259973 | − | 0.965616i | \(-0.583714\pi\) | ||||
−0.259973 | + | 0.965616i | \(0.583714\pi\) | |||||||
\(504\) | 10.0690 | 0.448507 | ||||||||
\(505\) | 9.30131 | 0.413903 | ||||||||
\(506\) | −26.2771 | −1.16816 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 0.559701 | 0.0248327 | ||||||||
\(509\) | 34.5093 | 1.52960 | 0.764798 | − | 0.644270i | \(-0.222839\pi\) | ||||
0.764798 | + | 0.644270i | \(0.222839\pi\) | |||||||
\(510\) | 2.02022 | 0.0894568 | ||||||||
\(511\) | −46.8363 | −2.07192 | ||||||||
\(512\) | −23.5447 | −1.04054 | ||||||||
\(513\) | −1.21481 | −0.0536350 | ||||||||
\(514\) | −18.2319 | −0.804177 | ||||||||
\(515\) | −0.623512 | −0.0274752 | ||||||||
\(516\) | 0.176280 | 0.00776032 | ||||||||
\(517\) | −56.1294 | −2.46857 | ||||||||
\(518\) | 30.0789 | 1.32159 | ||||||||
\(519\) | 14.5383 | 0.638159 | ||||||||
\(520\) | −1.78857 | −0.0784340 | ||||||||
\(521\) | 24.2192 | 1.06106 | 0.530531 | − | 0.847665i | \(-0.321992\pi\) | ||||
0.530531 | + | 0.847665i | \(0.321992\pi\) | |||||||
\(522\) | 0.276548 | 0.0121042 | ||||||||
\(523\) | −37.5545 | −1.64214 | −0.821071 | − | 0.570826i | \(-0.806623\pi\) | ||||
−0.821071 | + | 0.570826i | \(0.806623\pi\) | |||||||
\(524\) | −0.426842 | −0.0186467 | ||||||||
\(525\) | −16.1860 | −0.706417 | ||||||||
\(526\) | −6.56733 | −0.286349 | ||||||||
\(527\) | −17.8767 | −0.778720 | ||||||||
\(528\) | −21.6664 | −0.942907 | ||||||||
\(529\) | −11.5999 | −0.504343 | ||||||||
\(530\) | −4.25206 | −0.184698 | ||||||||
\(531\) | −2.53206 | −0.109882 | ||||||||
\(532\) | 0.251226 | 0.0108920 | ||||||||
\(533\) | −0.138445 | −0.00599673 | ||||||||
\(534\) | −7.98166 | −0.345400 | ||||||||
\(535\) | 3.69595 | 0.159790 | ||||||||
\(536\) | −33.9586 | −1.46679 | ||||||||
\(537\) | 9.18888 | 0.396529 | ||||||||
\(538\) | −0.211135 | −0.00910269 | ||||||||
\(539\) | −29.7232 | −1.28027 | ||||||||
\(540\) | 0.0367350 | 0.00158082 | ||||||||
\(541\) | 7.66595 | 0.329585 | 0.164792 | − | 0.986328i | \(-0.447305\pi\) | ||||
0.164792 | + | 0.986328i | \(0.447305\pi\) | |||||||
\(542\) | 12.8968 | 0.553966 | ||||||||
\(543\) | −2.04116 | −0.0875944 | ||||||||
\(544\) | −0.774816 | −0.0332200 | ||||||||
\(545\) | −7.01422 | −0.300456 | ||||||||
\(546\) | 4.89041 | 0.209290 | ||||||||
\(547\) | 30.3058 | 1.29578 | 0.647892 | − | 0.761732i | \(-0.275651\pi\) | ||||
0.647892 | + | 0.761732i | \(0.275651\pi\) | |||||||
\(548\) | 0.833791 | 0.0356178 | ||||||||
\(549\) | −10.9607 | −0.467790 | ||||||||
\(550\) | 35.8872 | 1.53023 | ||||||||
\(551\) | 0.241132 | 0.0102726 | ||||||||
\(552\) | 9.68535 | 0.412236 | ||||||||
\(553\) | 4.96167 | 0.210992 | ||||||||
\(554\) | 34.2592 | 1.45553 | ||||||||
\(555\) | 3.83497 | 0.162785 | ||||||||
\(556\) | −0.399538 | −0.0169442 | ||||||||
\(557\) | −21.0984 | −0.893969 | −0.446985 | − | 0.894542i | \(-0.647502\pi\) | ||||
−0.446985 | + | 0.894542i | \(0.647502\pi\) | |||||||
\(558\) | 10.7097 | 0.453378 | ||||||||
\(559\) | 2.99205 | 0.126550 | ||||||||
\(560\) | 8.48896 | 0.358724 | ||||||||
\(561\) | −12.9907 | −0.548466 | ||||||||
\(562\) | −10.6792 | −0.450476 | ||||||||
\(563\) | −1.49987 | −0.0632119 | −0.0316060 | − | 0.999500i | \(-0.510062\pi\) | ||||
−0.0316060 | + | 0.999500i | \(0.510062\pi\) | |||||||
\(564\) | 0.592005 | 0.0249279 | ||||||||
\(565\) | 5.02390 | 0.211357 | ||||||||
\(566\) | 43.0438 | 1.80927 | ||||||||
\(567\) | −3.51013 | −0.147412 | ||||||||
\(568\) | −36.1796 | −1.51806 | ||||||||
\(569\) | 1.58922 | 0.0666238 | 0.0333119 | − | 0.999445i | \(-0.489395\pi\) | ||||
0.0333119 | + | 0.999445i | \(0.489395\pi\) | |||||||
\(570\) | −1.05529 | −0.0442014 | ||||||||
\(571\) | 19.7581 | 0.826851 | 0.413426 | − | 0.910538i | \(-0.364332\pi\) | ||||
0.413426 | + | 0.910538i | \(0.364332\pi\) | |||||||
\(572\) | 0.329106 | 0.0137606 | ||||||||
\(573\) | −14.3314 | −0.598701 | ||||||||
\(574\) | 0.677055 | 0.0282597 | ||||||||
\(575\) | −15.5694 | −0.649288 | ||||||||
\(576\) | 8.22158 | 0.342566 | ||||||||
\(577\) | 27.2376 | 1.13391 | 0.566957 | − | 0.823747i | \(-0.308120\pi\) | ||||
0.566957 | + | 0.823747i | \(0.308120\pi\) | |||||||
\(578\) | −16.1499 | −0.671745 | ||||||||
\(579\) | −9.12754 | −0.379327 | ||||||||
\(580\) | −0.00729169 | −0.000302771 0 | ||||||||
\(581\) | 27.8476 | 1.15531 | ||||||||
\(582\) | 8.96943 | 0.371795 | ||||||||
\(583\) | 27.3421 | 1.13239 | ||||||||
\(584\) | −38.2754 | −1.58385 | ||||||||
\(585\) | 0.623512 | 0.0257791 | ||||||||
\(586\) | −11.6976 | −0.483225 | ||||||||
\(587\) | 21.6708 | 0.894448 | 0.447224 | − | 0.894422i | \(-0.352413\pi\) | ||||
0.447224 | + | 0.894422i | \(0.352413\pi\) | |||||||
\(588\) | 0.313495 | 0.0129283 | ||||||||
\(589\) | 9.33818 | 0.384773 | ||||||||
\(590\) | −2.19959 | −0.0905555 | ||||||||
\(591\) | 15.9455 | 0.655909 | ||||||||
\(592\) | 23.8563 | 0.980487 | ||||||||
\(593\) | 1.93250 | 0.0793584 | 0.0396792 | − | 0.999212i | \(-0.487366\pi\) | ||||
0.0396792 | + | 0.999212i | \(0.487366\pi\) | |||||||
\(594\) | 7.78256 | 0.319322 | ||||||||
\(595\) | 5.08979 | 0.208661 | ||||||||
\(596\) | 0.627221 | 0.0256920 | ||||||||
\(597\) | −9.81013 | −0.401502 | ||||||||
\(598\) | 4.70410 | 0.192365 | ||||||||
\(599\) | 27.8408 | 1.13754 | 0.568771 | − | 0.822496i | \(-0.307419\pi\) | ||||
0.568771 | + | 0.822496i | \(0.307419\pi\) | |||||||
\(600\) | −13.2275 | −0.540011 | ||||||||
\(601\) | −31.1724 | −1.27155 | −0.635774 | − | 0.771875i | \(-0.719319\pi\) | ||||
−0.635774 | + | 0.771875i | \(0.719319\pi\) | |||||||
\(602\) | −14.6324 | −0.596371 | ||||||||
\(603\) | 11.8383 | 0.482092 | ||||||||
\(604\) | 0.591441 | 0.0240654 | ||||||||
\(605\) | 12.5970 | 0.512141 | ||||||||
\(606\) | −20.7836 | −0.844277 | ||||||||
\(607\) | −40.6348 | −1.64932 | −0.824659 | − | 0.565631i | \(-0.808633\pi\) | ||||
−0.824659 | + | 0.565631i | \(0.808633\pi\) | |||||||
\(608\) | 0.404738 | 0.0164143 | ||||||||
\(609\) | 0.696741 | 0.0282334 | ||||||||
\(610\) | −9.52147 | −0.385513 | ||||||||
\(611\) | 10.0482 | 0.406508 | ||||||||
\(612\) | 0.137014 | 0.00553848 | ||||||||
\(613\) | 20.6548 | 0.834241 | 0.417120 | − | 0.908851i | \(-0.363039\pi\) | ||||
0.417120 | + | 0.908851i | \(0.363039\pi\) | |||||||
\(614\) | 23.5517 | 0.950470 | ||||||||
\(615\) | 0.0863224 | 0.00348085 | ||||||||
\(616\) | −56.2451 | −2.26618 | ||||||||
\(617\) | 35.6280 | 1.43433 | 0.717164 | − | 0.696905i | \(-0.245440\pi\) | ||||
0.717164 | + | 0.696905i | \(0.245440\pi\) | |||||||
\(618\) | 1.39323 | 0.0560438 | ||||||||
\(619\) | −14.6429 | −0.588547 | −0.294274 | − | 0.955721i | \(-0.595078\pi\) | ||||
−0.294274 | + | 0.955721i | \(0.595078\pi\) | |||||||
\(620\) | −0.282381 | −0.0113407 | ||||||||
\(621\) | −3.37640 | −0.135490 | ||||||||
\(622\) | 19.7650 | 0.792504 | ||||||||
\(623\) | −20.1092 | −0.805658 | ||||||||
\(624\) | 3.87870 | 0.155272 | ||||||||
\(625\) | 19.3196 | 0.772785 | ||||||||
\(626\) | 27.8955 | 1.11493 | ||||||||
\(627\) | 6.78589 | 0.271002 | ||||||||
\(628\) | −0.919434 | −0.0366894 | ||||||||
\(629\) | 14.3037 | 0.570325 | ||||||||
\(630\) | −3.04923 | −0.121484 | ||||||||
\(631\) | −7.38635 | −0.294046 | −0.147023 | − | 0.989133i | \(-0.546969\pi\) | ||||
−0.147023 | + | 0.989133i | \(0.546969\pi\) | |||||||
\(632\) | 4.05476 | 0.161290 | ||||||||
\(633\) | 19.3221 | 0.767986 | ||||||||
\(634\) | −29.3604 | −1.16605 | ||||||||
\(635\) | −5.92333 | −0.235060 | ||||||||
\(636\) | −0.288381 | −0.0114351 | ||||||||
\(637\) | 5.32103 | 0.210827 | ||||||||
\(638\) | −1.54479 | −0.0611589 | ||||||||
\(639\) | 12.6126 | 0.498945 | ||||||||
\(640\) | 6.72657 | 0.265891 | ||||||||
\(641\) | −11.1588 | −0.440746 | −0.220373 | − | 0.975416i | \(-0.570728\pi\) | ||||
−0.220373 | + | 0.975416i | \(0.570728\pi\) | |||||||
\(642\) | −8.25854 | −0.325939 | ||||||||
\(643\) | 34.2972 | 1.35255 | 0.676275 | − | 0.736650i | \(-0.263593\pi\) | ||||
0.676275 | + | 0.736650i | \(0.263593\pi\) | |||||||
\(644\) | 0.698253 | 0.0275150 | ||||||||
\(645\) | −1.86558 | −0.0734572 | ||||||||
\(646\) | −3.93604 | −0.154862 | ||||||||
\(647\) | −12.3868 | −0.486976 | −0.243488 | − | 0.969904i | \(-0.578292\pi\) | ||||
−0.243488 | + | 0.969904i | \(0.578292\pi\) | |||||||
\(648\) | −2.86854 | −0.112687 | ||||||||
\(649\) | 14.1441 | 0.555203 | ||||||||
\(650\) | −6.42450 | −0.251990 | ||||||||
\(651\) | 26.9823 | 1.05752 | ||||||||
\(652\) | 1.10674 | 0.0433431 | ||||||||
\(653\) | 15.8968 | 0.622088 | 0.311044 | − | 0.950396i | \(-0.399321\pi\) | ||||
0.311044 | + | 0.950396i | \(0.399321\pi\) | |||||||
\(654\) | 15.6732 | 0.612869 | ||||||||
\(655\) | 4.51728 | 0.176505 | ||||||||
\(656\) | 0.536988 | 0.0209658 | ||||||||
\(657\) | 13.3432 | 0.520567 | ||||||||
\(658\) | −49.1401 | −1.91568 | ||||||||
\(659\) | 0.893369 | 0.0348007 | 0.0174003 | − | 0.999849i | \(-0.494461\pi\) | ||||
0.0174003 | + | 0.999849i | \(0.494461\pi\) | |||||||
\(660\) | −0.205201 | −0.00798745 | ||||||||
\(661\) | −2.77680 | −0.108005 | −0.0540025 | − | 0.998541i | \(-0.517198\pi\) | ||||
−0.0540025 | + | 0.998541i | \(0.517198\pi\) | |||||||
\(662\) | −30.1591 | −1.17217 | ||||||||
\(663\) | 2.32558 | 0.0903180 | ||||||||
\(664\) | 22.7575 | 0.883164 | ||||||||
\(665\) | −2.65874 | −0.103101 | ||||||||
\(666\) | −8.56917 | −0.332049 | ||||||||
\(667\) | 0.670197 | 0.0259501 | ||||||||
\(668\) | −1.01101 | −0.0391172 | ||||||||
\(669\) | −8.65778 | −0.334729 | ||||||||
\(670\) | 10.2838 | 0.397300 | ||||||||
\(671\) | 61.2262 | 2.36361 | ||||||||
\(672\) | 1.16947 | 0.0451135 | ||||||||
\(673\) | 23.6763 | 0.912653 | 0.456326 | − | 0.889812i | \(-0.349165\pi\) | ||||
0.456326 | + | 0.889812i | \(0.349165\pi\) | |||||||
\(674\) | 9.80098 | 0.377520 | ||||||||
\(675\) | 4.61123 | 0.177486 | ||||||||
\(676\) | −0.0589163 | −0.00226601 | ||||||||
\(677\) | 8.05264 | 0.309488 | 0.154744 | − | 0.987955i | \(-0.450545\pi\) | ||||
0.154744 | + | 0.987955i | \(0.450545\pi\) | |||||||
\(678\) | −11.2258 | −0.431125 | ||||||||
\(679\) | 22.5978 | 0.867224 | ||||||||
\(680\) | 4.15946 | 0.159508 | ||||||||
\(681\) | −13.9306 | −0.533821 | ||||||||
\(682\) | −59.8243 | −2.29079 | ||||||||
\(683\) | 22.0387 | 0.843287 | 0.421643 | − | 0.906762i | \(-0.361453\pi\) | ||||
0.421643 | + | 0.906762i | \(0.361453\pi\) | |||||||
\(684\) | −0.0715718 | −0.00273662 | ||||||||
\(685\) | −8.82403 | −0.337149 | ||||||||
\(686\) | 8.21084 | 0.313491 | ||||||||
\(687\) | −26.1342 | −0.997083 | ||||||||
\(688\) | −11.6053 | −0.442446 | ||||||||
\(689\) | −4.89477 | −0.186476 | ||||||||
\(690\) | −2.93306 | −0.111660 | ||||||||
\(691\) | 0.281085 | 0.0106930 | 0.00534649 | − | 0.999986i | \(-0.498298\pi\) | ||||
0.00534649 | + | 0.999986i | \(0.498298\pi\) | |||||||
\(692\) | 0.856540 | 0.0325608 | ||||||||
\(693\) | 19.6076 | 0.744830 | ||||||||
\(694\) | −5.23481 | −0.198711 | ||||||||
\(695\) | 4.22832 | 0.160389 | ||||||||
\(696\) | 0.569389 | 0.0215826 | ||||||||
\(697\) | 0.321966 | 0.0121953 | ||||||||
\(698\) | −24.2895 | −0.919372 | ||||||||
\(699\) | −23.5545 | −0.890913 | ||||||||
\(700\) | −0.953621 | −0.0360435 | ||||||||
\(701\) | −12.7370 | −0.481069 | −0.240534 | − | 0.970641i | \(-0.577323\pi\) | ||||
−0.240534 | + | 0.970641i | \(0.577323\pi\) | |||||||
\(702\) | −1.39323 | −0.0525840 | ||||||||
\(703\) | −7.47177 | −0.281803 | ||||||||
\(704\) | −45.9256 | −1.73089 | ||||||||
\(705\) | −6.26520 | −0.235961 | ||||||||
\(706\) | 1.70161 | 0.0640408 | ||||||||
\(707\) | −52.3628 | −1.96930 | ||||||||
\(708\) | −0.149179 | −0.00560650 | ||||||||
\(709\) | −46.4397 | −1.74408 | −0.872039 | − | 0.489436i | \(-0.837203\pi\) | ||||
−0.872039 | + | 0.489436i | \(0.837203\pi\) | |||||||
\(710\) | 10.9565 | 0.411188 | ||||||||
\(711\) | −1.41353 | −0.0530115 | ||||||||
\(712\) | −16.4336 | −0.615874 | ||||||||
\(713\) | 25.9543 | 0.971997 | ||||||||
\(714\) | −11.3730 | −0.425626 | ||||||||
\(715\) | −3.48293 | −0.130254 | ||||||||
\(716\) | 0.541374 | 0.0202321 | ||||||||
\(717\) | 8.80497 | 0.328828 | ||||||||
\(718\) | 9.37612 | 0.349914 | ||||||||
\(719\) | −0.212425 | −0.00792212 | −0.00396106 | − | 0.999992i | \(-0.501261\pi\) | ||||
−0.00396106 | + | 0.999992i | \(0.501261\pi\) | |||||||
\(720\) | −2.41841 | −0.0901290 | ||||||||
\(721\) | 3.51013 | 0.130724 | ||||||||
\(722\) | −24.4153 | −0.908642 | ||||||||
\(723\) | −14.9700 | −0.556741 | ||||||||
\(724\) | −0.120257 | −0.00446933 | ||||||||
\(725\) | −0.915303 | −0.0339935 | ||||||||
\(726\) | −28.1478 | −1.04466 | ||||||||
\(727\) | −47.5945 | −1.76518 | −0.882591 | − | 0.470142i | \(-0.844203\pi\) | ||||
−0.882591 | + | 0.470142i | \(0.844203\pi\) | |||||||
\(728\) | 10.0690 | 0.373180 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 11.5911 | 0.429007 | ||||||||
\(731\) | −6.95825 | −0.257360 | ||||||||
\(732\) | −0.645762 | −0.0238680 | ||||||||
\(733\) | −15.5758 | −0.575306 | −0.287653 | − | 0.957735i | \(-0.592875\pi\) | ||||
−0.287653 | + | 0.957735i | \(0.592875\pi\) | |||||||
\(734\) | 37.4294 | 1.38154 | ||||||||
\(735\) | −3.31773 | −0.122376 | ||||||||
\(736\) | 1.12492 | 0.0414651 | ||||||||
\(737\) | −66.1285 | −2.43587 | ||||||||
\(738\) | −0.192886 | −0.00710023 | ||||||||
\(739\) | 26.3314 | 0.968616 | 0.484308 | − | 0.874897i | \(-0.339071\pi\) | ||||
0.484308 | + | 0.874897i | \(0.339071\pi\) | |||||||
\(740\) | 0.225942 | 0.00830579 | ||||||||
\(741\) | −1.21481 | −0.0446270 | ||||||||
\(742\) | 23.9374 | 0.878771 | ||||||||
\(743\) | 39.0347 | 1.43205 | 0.716023 | − | 0.698077i | \(-0.245961\pi\) | ||||
0.716023 | + | 0.698077i | \(0.245961\pi\) | |||||||
\(744\) | 22.0504 | 0.808406 | ||||||||
\(745\) | −6.63790 | −0.243194 | ||||||||
\(746\) | −45.7913 | −1.67654 | ||||||||
\(747\) | −7.93349 | −0.290271 | ||||||||
\(748\) | −0.765361 | −0.0279844 | ||||||||
\(749\) | −20.8068 | −0.760263 | ||||||||
\(750\) | 8.34923 | 0.304871 | ||||||||
\(751\) | 8.77940 | 0.320365 | 0.160182 | − | 0.987087i | \(-0.448792\pi\) | ||||
0.160182 | + | 0.987087i | \(0.448792\pi\) | |||||||
\(752\) | −38.9741 | −1.42124 | ||||||||
\(753\) | 1.59917 | 0.0582768 | ||||||||
\(754\) | 0.276548 | 0.0100713 | ||||||||
\(755\) | −6.25923 | −0.227797 | ||||||||
\(756\) | −0.206804 | −0.00752138 | ||||||||
\(757\) | −0.806275 | −0.0293046 | −0.0146523 | − | 0.999893i | \(-0.504664\pi\) | ||||
−0.0146523 | + | 0.999893i | \(0.504664\pi\) | |||||||
\(758\) | 5.69404 | 0.206817 | ||||||||
\(759\) | 18.8606 | 0.684595 | ||||||||
\(760\) | −2.17276 | −0.0788144 | ||||||||
\(761\) | −33.1652 | −1.20224 | −0.601119 | − | 0.799160i | \(-0.705278\pi\) | ||||
−0.601119 | + | 0.799160i | \(0.705278\pi\) | |||||||
\(762\) | 13.2356 | 0.479475 | ||||||||
\(763\) | 39.4874 | 1.42954 | ||||||||
\(764\) | −0.844350 | −0.0305475 | ||||||||
\(765\) | −1.45003 | −0.0524258 | ||||||||
\(766\) | 22.2681 | 0.804580 | ||||||||
\(767\) | −2.53206 | −0.0914273 | ||||||||
\(768\) | 1.41275 | 0.0509783 | ||||||||
\(769\) | −8.04302 | −0.290039 | −0.145019 | − | 0.989429i | \(-0.546324\pi\) | ||||
−0.145019 | + | 0.989429i | \(0.546324\pi\) | |||||||
\(770\) | 17.0330 | 0.613826 | ||||||||
\(771\) | 13.0861 | 0.471285 | ||||||||
\(772\) | −0.537760 | −0.0193544 | ||||||||
\(773\) | 6.13164 | 0.220540 | 0.110270 | − | 0.993902i | \(-0.464828\pi\) | ||||
0.110270 | + | 0.993902i | \(0.464828\pi\) | |||||||
\(774\) | 4.16861 | 0.149838 | ||||||||
\(775\) | −35.4464 | −1.27327 | ||||||||
\(776\) | 18.4673 | 0.662937 | ||||||||
\(777\) | −21.5894 | −0.774515 | ||||||||
\(778\) | 22.7038 | 0.813971 | ||||||||
\(779\) | −0.168184 | −0.00602582 | ||||||||
\(780\) | 0.0367350 | 0.00131532 | ||||||||
\(781\) | −70.4536 | −2.52103 | ||||||||
\(782\) | −10.9398 | −0.391205 | ||||||||
\(783\) | −0.198494 | −0.00709361 | ||||||||
\(784\) | −20.6387 | −0.737095 | ||||||||
\(785\) | 9.73039 | 0.347293 | ||||||||
\(786\) | −10.0938 | −0.360033 | ||||||||
\(787\) | −1.36104 | −0.0485160 | −0.0242580 | − | 0.999706i | \(-0.507722\pi\) | ||||
−0.0242580 | + | 0.999706i | \(0.507722\pi\) | |||||||
\(788\) | 0.939447 | 0.0334664 | ||||||||
\(789\) | 4.71375 | 0.167814 | ||||||||
\(790\) | −1.22792 | −0.0436876 | ||||||||
\(791\) | −28.2826 | −1.00561 | ||||||||
\(792\) | 16.0236 | 0.569375 | ||||||||
\(793\) | −10.9607 | −0.389225 | ||||||||
\(794\) | −3.78740 | −0.134410 | ||||||||
\(795\) | 3.05195 | 0.108241 | ||||||||
\(796\) | −0.577976 | −0.0204858 | ||||||||
\(797\) | −33.5832 | −1.18958 | −0.594788 | − | 0.803882i | \(-0.702764\pi\) | ||||
−0.594788 | + | 0.803882i | \(0.702764\pi\) | |||||||
\(798\) | 5.94090 | 0.210306 | ||||||||
\(799\) | −23.3680 | −0.826700 | ||||||||
\(800\) | −1.53633 | −0.0543175 | ||||||||
\(801\) | 5.72890 | 0.202421 | ||||||||
\(802\) | −17.2153 | −0.607892 | ||||||||
\(803\) | −74.5348 | −2.63028 | ||||||||
\(804\) | 0.697467 | 0.0245978 | ||||||||
\(805\) | −7.38964 | −0.260450 | ||||||||
\(806\) | 10.7097 | 0.377233 | ||||||||
\(807\) | 0.151544 | 0.00533460 | ||||||||
\(808\) | −42.7917 | −1.50541 | ||||||||
\(809\) | 51.2511 | 1.80189 | 0.900947 | − | 0.433929i | \(-0.142873\pi\) | ||||
0.900947 | + | 0.433929i | \(0.142873\pi\) | |||||||
\(810\) | 0.868695 | 0.0305228 | ||||||||
\(811\) | −30.0690 | −1.05587 | −0.527933 | − | 0.849286i | \(-0.677033\pi\) | ||||
−0.527933 | + | 0.849286i | \(0.677033\pi\) | |||||||
\(812\) | 0.0410494 | 0.00144055 | ||||||||
\(813\) | −9.25680 | −0.324650 | ||||||||
\(814\) | 47.8673 | 1.67775 | ||||||||
\(815\) | −11.7126 | −0.410275 | ||||||||
\(816\) | −9.02022 | −0.315771 | ||||||||
\(817\) | 3.63476 | 0.127164 | ||||||||
\(818\) | −27.1389 | −0.948888 | ||||||||
\(819\) | −3.51013 | −0.122654 | ||||||||
\(820\) | 0.00508579 | 0.000177604 0 | ||||||||
\(821\) | 33.5984 | 1.17259 | 0.586296 | − | 0.810097i | \(-0.300586\pi\) | ||||
0.586296 | + | 0.810097i | \(0.300586\pi\) | |||||||
\(822\) | 19.7171 | 0.687714 | ||||||||
\(823\) | 4.22395 | 0.147238 | 0.0736189 | − | 0.997286i | \(-0.476545\pi\) | ||||
0.0736189 | + | 0.997286i | \(0.476545\pi\) | |||||||
\(824\) | 2.86854 | 0.0999303 | ||||||||
\(825\) | −25.7583 | −0.896789 | ||||||||
\(826\) | 12.3828 | 0.430853 | ||||||||
\(827\) | 8.27238 | 0.287659 | 0.143829 | − | 0.989603i | \(-0.454058\pi\) | ||||
0.143829 | + | 0.989603i | \(0.454058\pi\) | |||||||
\(828\) | −0.198925 | −0.00691312 | ||||||||
\(829\) | −29.0396 | −1.00859 | −0.504294 | − | 0.863532i | \(-0.668247\pi\) | ||||
−0.504294 | + | 0.863532i | \(0.668247\pi\) | |||||||
\(830\) | −6.89178 | −0.239217 | ||||||||
\(831\) | −24.5898 | −0.853010 | ||||||||
\(832\) | 8.22158 | 0.285032 | ||||||||
\(833\) | −12.3745 | −0.428750 | ||||||||
\(834\) | −9.44810 | −0.327161 | ||||||||
\(835\) | 10.6996 | 0.370274 | ||||||||
\(836\) | 0.399799 | 0.0138273 | ||||||||
\(837\) | −7.68697 | −0.265701 | ||||||||
\(838\) | 9.05896 | 0.312937 | ||||||||
\(839\) | −31.5299 | −1.08853 | −0.544267 | − | 0.838912i | \(-0.683192\pi\) | ||||
−0.544267 | + | 0.838912i | \(0.683192\pi\) | |||||||
\(840\) | −6.27812 | −0.216616 | ||||||||
\(841\) | −28.9606 | −0.998641 | ||||||||
\(842\) | −42.6087 | −1.46839 | ||||||||
\(843\) | 7.66509 | 0.264000 | ||||||||
\(844\) | 1.13839 | 0.0391849 | ||||||||
\(845\) | 0.623512 | 0.0214495 | ||||||||
\(846\) | 13.9995 | 0.481312 | ||||||||
\(847\) | −70.9162 | −2.43671 | ||||||||
\(848\) | 18.9853 | 0.651958 | ||||||||
\(849\) | −30.8950 | −1.06032 | ||||||||
\(850\) | 14.9407 | 0.512461 | ||||||||
\(851\) | −20.7669 | −0.711879 | ||||||||
\(852\) | 0.743084 | 0.0254576 | ||||||||
\(853\) | 16.2194 | 0.555342 | 0.277671 | − | 0.960676i | \(-0.410438\pi\) | ||||
0.277671 | + | 0.960676i | \(0.410438\pi\) | |||||||
\(854\) | 53.6022 | 1.83423 | ||||||||
\(855\) | 0.757446 | 0.0259041 | ||||||||
\(856\) | −17.0036 | −0.581173 | ||||||||
\(857\) | −6.11563 | −0.208906 | −0.104453 | − | 0.994530i | \(-0.533309\pi\) | ||||
−0.104453 | + | 0.994530i | \(0.533309\pi\) | |||||||
\(858\) | 7.78256 | 0.265692 | ||||||||
\(859\) | 49.2920 | 1.68182 | 0.840911 | − | 0.541173i | \(-0.182020\pi\) | ||||
0.840911 | + | 0.541173i | \(0.182020\pi\) | |||||||
\(860\) | −0.109913 | −0.00374800 | ||||||||
\(861\) | −0.485962 | −0.0165615 | ||||||||
\(862\) | 45.6777 | 1.55579 | ||||||||
\(863\) | 30.1735 | 1.02712 | 0.513558 | − | 0.858055i | \(-0.328327\pi\) | ||||
0.513558 | + | 0.858055i | \(0.328327\pi\) | |||||||
\(864\) | −0.333171 | −0.0113347 | ||||||||
\(865\) | −9.06479 | −0.308212 | ||||||||
\(866\) | −26.9417 | −0.915515 | ||||||||
\(867\) | 11.5917 | 0.393674 | ||||||||
\(868\) | 1.58970 | 0.0539578 | ||||||||
\(869\) | 7.89596 | 0.267852 | ||||||||
\(870\) | −0.172431 | −0.00584595 | ||||||||
\(871\) | 11.8383 | 0.401125 | ||||||||
\(872\) | 32.2697 | 1.09279 | ||||||||
\(873\) | −6.43788 | −0.217889 | ||||||||
\(874\) | 5.71457 | 0.193298 | ||||||||
\(875\) | 21.0352 | 0.711121 | ||||||||
\(876\) | 0.786130 | 0.0265609 | ||||||||
\(877\) | −40.3418 | −1.36225 | −0.681124 | − | 0.732168i | \(-0.738508\pi\) | ||||
−0.681124 | + | 0.732168i | \(0.738508\pi\) | |||||||
\(878\) | −42.5898 | −1.43734 | ||||||||
\(879\) | 8.39607 | 0.283192 | ||||||||
\(880\) | 13.5092 | 0.455396 | ||||||||
\(881\) | −23.7382 | −0.799760 | −0.399880 | − | 0.916568i | \(-0.630948\pi\) | ||||
−0.399880 | + | 0.916568i | \(0.630948\pi\) | |||||||
\(882\) | 7.41341 | 0.249623 | ||||||||
\(883\) | 47.4707 | 1.59752 | 0.798758 | − | 0.601652i | \(-0.205491\pi\) | ||||
0.798758 | + | 0.601652i | \(0.205491\pi\) | |||||||
\(884\) | 0.137014 | 0.00460829 | ||||||||
\(885\) | 1.57877 | 0.0530697 | ||||||||
\(886\) | −38.2462 | −1.28491 | ||||||||
\(887\) | −42.1842 | −1.41641 | −0.708203 | − | 0.706009i | \(-0.750494\pi\) | ||||
−0.708203 | + | 0.706009i | \(0.750494\pi\) | |||||||
\(888\) | −17.6432 | −0.592067 | ||||||||
\(889\) | 33.3461 | 1.11839 | ||||||||
\(890\) | 4.97666 | 0.166818 | ||||||||
\(891\) | −5.58599 | −0.187138 | ||||||||
\(892\) | −0.510084 | −0.0170789 | ||||||||
\(893\) | 12.2067 | 0.408480 | ||||||||
\(894\) | 14.8323 | 0.496066 | ||||||||
\(895\) | −5.72938 | −0.191512 | ||||||||
\(896\) | −37.8680 | −1.26508 | ||||||||
\(897\) | −3.37640 | −0.112735 | ||||||||
\(898\) | 47.4853 | 1.58461 | ||||||||
\(899\) | 1.52582 | 0.0508889 | ||||||||
\(900\) | 0.271677 | 0.00905588 | ||||||||
\(901\) | 11.3832 | 0.379228 | ||||||||
\(902\) | 1.07746 | 0.0358755 | ||||||||
\(903\) | 10.5025 | 0.349501 | ||||||||
\(904\) | −23.1130 | −0.768728 | ||||||||
\(905\) | 1.27269 | 0.0423055 | ||||||||
\(906\) | 13.9861 | 0.464659 | ||||||||
\(907\) | −9.59254 | −0.318515 | −0.159258 | − | 0.987237i | \(-0.550910\pi\) | ||||
−0.159258 | + | 0.987237i | \(0.550910\pi\) | |||||||
\(908\) | −0.820737 | −0.0272371 | ||||||||
\(909\) | 14.9176 | 0.494785 | ||||||||
\(910\) | −3.04923 | −0.101081 | ||||||||
\(911\) | −22.1358 | −0.733390 | −0.366695 | − | 0.930341i | \(-0.619511\pi\) | ||||
−0.366695 | + | 0.930341i | \(0.619511\pi\) | |||||||
\(912\) | 4.71186 | 0.156025 | ||||||||
\(913\) | 44.3164 | 1.46666 | ||||||||
\(914\) | −2.55829 | −0.0846207 | ||||||||
\(915\) | 6.83411 | 0.225929 | ||||||||
\(916\) | −1.53973 | −0.0508742 | ||||||||
\(917\) | −25.4305 | −0.839790 | ||||||||
\(918\) | 3.24006 | 0.106938 | ||||||||
\(919\) | −22.2798 | −0.734942 | −0.367471 | − | 0.930035i | \(-0.619776\pi\) | ||||
−0.367471 | + | 0.930035i | \(0.619776\pi\) | |||||||
\(920\) | −6.03893 | −0.199098 | ||||||||
\(921\) | −16.9044 | −0.557020 | ||||||||
\(922\) | 45.3154 | 1.49238 | ||||||||
\(923\) | 12.6126 | 0.415147 | ||||||||
\(924\) | 1.15520 | 0.0380034 | ||||||||
\(925\) | 28.3618 | 0.932530 | ||||||||
\(926\) | 6.13098 | 0.201477 | ||||||||
\(927\) | −1.00000 | −0.0328443 | ||||||||
\(928\) | 0.0661326 | 0.00217091 | ||||||||
\(929\) | 44.2081 | 1.45042 | 0.725211 | − | 0.688527i | \(-0.241742\pi\) | ||||
0.725211 | + | 0.688527i | \(0.241742\pi\) | |||||||
\(930\) | −6.67763 | −0.218968 | ||||||||
\(931\) | 6.46402 | 0.211850 | ||||||||
\(932\) | −1.38774 | −0.0454570 | ||||||||
\(933\) | −14.1865 | −0.464444 | ||||||||
\(934\) | 31.8178 | 1.04111 | ||||||||
\(935\) | 8.09984 | 0.264893 | ||||||||
\(936\) | −2.86854 | −0.0937611 | ||||||||
\(937\) | −35.1138 | −1.14712 | −0.573558 | − | 0.819165i | \(-0.694437\pi\) | ||||
−0.573558 | + | 0.819165i | \(0.694437\pi\) | |||||||
\(938\) | −57.8941 | −1.89031 | ||||||||
\(939\) | −20.0222 | −0.653400 | ||||||||
\(940\) | −0.369122 | −0.0120394 | ||||||||
\(941\) | 8.68663 | 0.283176 | 0.141588 | − | 0.989926i | \(-0.454779\pi\) | ||||
0.141588 | + | 0.989926i | \(0.454779\pi\) | |||||||
\(942\) | −21.7424 | −0.708406 | ||||||||
\(943\) | −0.467448 | −0.0152222 | ||||||||
\(944\) | 9.82108 | 0.319649 | ||||||||
\(945\) | 2.18861 | 0.0711955 | ||||||||
\(946\) | −23.2858 | −0.757087 | ||||||||
\(947\) | −33.2171 | −1.07941 | −0.539705 | − | 0.841854i | \(-0.681464\pi\) | ||||
−0.539705 | + | 0.841854i | \(0.681464\pi\) | |||||||
\(948\) | −0.0832798 | −0.00270480 | ||||||||
\(949\) | 13.3432 | 0.433138 | ||||||||
\(950\) | −7.80451 | −0.253212 | ||||||||
\(951\) | 21.0736 | 0.683360 | ||||||||
\(952\) | −23.4161 | −0.758922 | ||||||||
\(953\) | 26.7923 | 0.867889 | 0.433944 | − | 0.900940i | \(-0.357121\pi\) | ||||
0.433944 | + | 0.900940i | \(0.357121\pi\) | |||||||
\(954\) | −6.81952 | −0.220790 | ||||||||
\(955\) | 8.93578 | 0.289155 | ||||||||
\(956\) | 0.518756 | 0.0167778 | ||||||||
\(957\) | 1.10879 | 0.0358420 | ||||||||
\(958\) | −16.9263 | −0.546864 | ||||||||
\(959\) | 49.6759 | 1.60412 | ||||||||
\(960\) | −5.12625 | −0.165449 | ||||||||
\(961\) | 28.0896 | 0.906115 | ||||||||
\(962\) | −8.56917 | −0.276281 | ||||||||
\(963\) | 5.92763 | 0.191015 | ||||||||
\(964\) | −0.881977 | −0.0284066 | ||||||||
\(965\) | 5.69113 | 0.183204 | ||||||||
\(966\) | 16.5120 | 0.531265 | ||||||||
\(967\) | 29.5840 | 0.951358 | 0.475679 | − | 0.879619i | \(-0.342202\pi\) | ||||
0.475679 | + | 0.879619i | \(0.342202\pi\) | |||||||
\(968\) | −57.9539 | −1.86271 | ||||||||
\(969\) | 2.82513 | 0.0907561 | ||||||||
\(970\) | −5.59255 | −0.179566 | ||||||||
\(971\) | −6.03890 | −0.193798 | −0.0968988 | − | 0.995294i | \(-0.530892\pi\) | ||||
−0.0968988 | + | 0.995294i | \(0.530892\pi\) | |||||||
\(972\) | 0.0589163 | 0.00188974 | ||||||||
\(973\) | −23.8038 | −0.763114 | ||||||||
\(974\) | −39.7744 | −1.27446 | ||||||||
\(975\) | 4.61123 | 0.147678 | ||||||||
\(976\) | 42.5131 | 1.36081 | ||||||||
\(977\) | 31.6161 | 1.01149 | 0.505744 | − | 0.862684i | \(-0.331218\pi\) | ||||
0.505744 | + | 0.862684i | \(0.331218\pi\) | |||||||
\(978\) | 26.1716 | 0.836877 | ||||||||
\(979\) | −32.0016 | −1.02277 | ||||||||
\(980\) | −0.195468 | −0.00624400 | ||||||||
\(981\) | −11.2495 | −0.359170 | ||||||||
\(982\) | 10.5676 | 0.337225 | ||||||||
\(983\) | 58.8338 | 1.87651 | 0.938254 | − | 0.345948i | \(-0.112443\pi\) | ||||
0.938254 | + | 0.345948i | \(0.112443\pi\) | |||||||
\(984\) | −0.397136 | −0.0126602 | ||||||||
\(985\) | −9.94219 | −0.316785 | ||||||||
\(986\) | −0.643134 | −0.0204815 | ||||||||
\(987\) | 35.2707 | 1.12268 | ||||||||
\(988\) | −0.0715718 | −0.00227700 | ||||||||
\(989\) | 10.1024 | 0.321237 | ||||||||
\(990\) | −4.85252 | −0.154223 | ||||||||
\(991\) | 6.31025 | 0.200452 | 0.100226 | − | 0.994965i | \(-0.468043\pi\) | ||||
0.100226 | + | 0.994965i | \(0.468043\pi\) | |||||||
\(992\) | 2.56108 | 0.0813143 | ||||||||
\(993\) | 21.6470 | 0.686945 | ||||||||
\(994\) | −61.6806 | −1.95639 | ||||||||
\(995\) | 6.11674 | 0.193914 | ||||||||
\(996\) | −0.467412 | −0.0148105 | ||||||||
\(997\) | −8.71738 | −0.276082 | −0.138041 | − | 0.990426i | \(-0.544081\pi\) | ||||
−0.138041 | + | 0.990426i | \(0.544081\pi\) | |||||||
\(998\) | 29.3328 | 0.928514 | ||||||||
\(999\) | 6.15059 | 0.194596 |
(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 | 4017.2.a.j.1.17 | ✓ | 25 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4017.2.a.j.1.17 | ✓ | 25 | 1.1 | even | 1 | trivial |