Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [983,2,Mod(1,983)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(983, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("983.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 983 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 983.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: | \(7.84929451869\) |
Analytic rank: | \(1\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 983.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.912923 | 0.645534 | 0.322767 | − | 0.946478i | \(-0.395387\pi\) | ||||
0.322767 | + | 0.946478i | \(0.395387\pi\) | |||||||
\(3\) | −2.89686 | −1.67250 | −0.836252 | − | 0.548345i | \(-0.815258\pi\) | ||||
−0.836252 | + | 0.548345i | \(0.815258\pi\) | |||||||
\(4\) | −1.16657 | −0.583285 | ||||||||
\(5\) | −1.17872 | −0.527139 | −0.263570 | − | 0.964640i | \(-0.584900\pi\) | ||||
−0.263570 | + | 0.964640i | \(0.584900\pi\) | |||||||
\(6\) | −2.64461 | −1.07966 | ||||||||
\(7\) | 3.45815 | 1.30706 | 0.653529 | − | 0.756902i | \(-0.273288\pi\) | ||||
0.653529 | + | 0.756902i | \(0.273288\pi\) | |||||||
\(8\) | −2.89084 | −1.02207 | ||||||||
\(9\) | 5.39181 | 1.79727 | ||||||||
\(10\) | −1.07608 | −0.340286 | ||||||||
\(11\) | 1.56665 | 0.472364 | 0.236182 | − | 0.971709i | \(-0.424104\pi\) | ||||
0.236182 | + | 0.971709i | \(0.424104\pi\) | |||||||
\(12\) | 3.37940 | 0.975547 | ||||||||
\(13\) | 1.13134 | 0.313777 | 0.156889 | − | 0.987616i | \(-0.449854\pi\) | ||||
0.156889 | + | 0.987616i | \(0.449854\pi\) | |||||||
\(14\) | 3.15703 | 0.843751 | ||||||||
\(15\) | 3.41459 | 0.881642 | ||||||||
\(16\) | −0.305970 | −0.0764926 | ||||||||
\(17\) | −0.0116973 | −0.00283701 | −0.00141850 | − | 0.999999i | \(-0.500452\pi\) | ||||
−0.00141850 | + | 0.999999i | \(0.500452\pi\) | |||||||
\(18\) | 4.92231 | 1.16020 | ||||||||
\(19\) | 2.31580 | 0.531280 | 0.265640 | − | 0.964072i | \(-0.414417\pi\) | ||||
0.265640 | + | 0.964072i | \(0.414417\pi\) | |||||||
\(20\) | 1.37506 | 0.307473 | ||||||||
\(21\) | −10.0178 | −2.18606 | ||||||||
\(22\) | 1.43024 | 0.304927 | ||||||||
\(23\) | −7.71643 | −1.60899 | −0.804494 | − | 0.593961i | \(-0.797563\pi\) | ||||
−0.804494 | + | 0.593961i | \(0.797563\pi\) | |||||||
\(24\) | 8.37436 | 1.70941 | ||||||||
\(25\) | −3.61062 | −0.722124 | ||||||||
\(26\) | 1.03283 | 0.202554 | ||||||||
\(27\) | −6.92875 | −1.33344 | ||||||||
\(28\) | −4.03418 | −0.762388 | ||||||||
\(29\) | 2.15267 | 0.399742 | 0.199871 | − | 0.979822i | \(-0.435948\pi\) | ||||
0.199871 | + | 0.979822i | \(0.435948\pi\) | |||||||
\(30\) | 3.11726 | 0.569130 | ||||||||
\(31\) | −8.15054 | −1.46388 | −0.731941 | − | 0.681369i | \(-0.761385\pi\) | ||||
−0.731941 | + | 0.681369i | \(0.761385\pi\) | |||||||
\(32\) | 5.50235 | 0.972686 | ||||||||
\(33\) | −4.53838 | −0.790031 | ||||||||
\(34\) | −0.0106787 | −0.00183139 | ||||||||
\(35\) | −4.07619 | −0.689001 | ||||||||
\(36\) | −6.28993 | −1.04832 | ||||||||
\(37\) | −8.91976 | −1.46640 | −0.733200 | − | 0.680013i | \(-0.761974\pi\) | ||||
−0.733200 | + | 0.680013i | \(0.761974\pi\) | |||||||
\(38\) | 2.11414 | 0.342959 | ||||||||
\(39\) | −3.27734 | −0.524794 | ||||||||
\(40\) | 3.40748 | 0.538770 | ||||||||
\(41\) | −1.72063 | −0.268717 | −0.134358 | − | 0.990933i | \(-0.542897\pi\) | ||||
−0.134358 | + | 0.990933i | \(0.542897\pi\) | |||||||
\(42\) | −9.14547 | −1.41118 | ||||||||
\(43\) | −4.59687 | −0.701016 | −0.350508 | − | 0.936560i | \(-0.613991\pi\) | ||||
−0.350508 | + | 0.936560i | \(0.613991\pi\) | |||||||
\(44\) | −1.82761 | −0.275523 | ||||||||
\(45\) | −6.35543 | −0.947412 | ||||||||
\(46\) | −7.04451 | −1.03866 | ||||||||
\(47\) | 3.42907 | 0.500181 | 0.250090 | − | 0.968222i | \(-0.419540\pi\) | ||||
0.250090 | + | 0.968222i | \(0.419540\pi\) | |||||||
\(48\) | 0.886354 | 0.127934 | ||||||||
\(49\) | 4.95880 | 0.708400 | ||||||||
\(50\) | −3.29622 | −0.466156 | ||||||||
\(51\) | 0.0338854 | 0.00474491 | ||||||||
\(52\) | −1.31979 | −0.183022 | ||||||||
\(53\) | 2.09122 | 0.287251 | 0.143626 | − | 0.989632i | \(-0.454124\pi\) | ||||
0.143626 | + | 0.989632i | \(0.454124\pi\) | |||||||
\(54\) | −6.32542 | −0.860780 | ||||||||
\(55\) | −1.84665 | −0.249002 | ||||||||
\(56\) | −9.99695 | −1.33590 | ||||||||
\(57\) | −6.70854 | −0.888568 | ||||||||
\(58\) | 1.96523 | 0.258047 | ||||||||
\(59\) | 4.77995 | 0.622296 | 0.311148 | − | 0.950361i | \(-0.399287\pi\) | ||||
0.311148 | + | 0.950361i | \(0.399287\pi\) | |||||||
\(60\) | −3.98336 | −0.514249 | ||||||||
\(61\) | −5.07785 | −0.650152 | −0.325076 | − | 0.945688i | \(-0.605390\pi\) | ||||
−0.325076 | + | 0.945688i | \(0.605390\pi\) | |||||||
\(62\) | −7.44082 | −0.944985 | ||||||||
\(63\) | 18.6457 | 2.34914 | ||||||||
\(64\) | 5.63516 | 0.704395 | ||||||||
\(65\) | −1.33353 | −0.165404 | ||||||||
\(66\) | −4.14320 | −0.509992 | ||||||||
\(67\) | 3.58751 | 0.438284 | 0.219142 | − | 0.975693i | \(-0.429674\pi\) | ||||
0.219142 | + | 0.975693i | \(0.429674\pi\) | |||||||
\(68\) | 0.0136457 | 0.00165479 | ||||||||
\(69\) | 22.3534 | 2.69104 | ||||||||
\(70\) | −3.72125 | −0.444774 | ||||||||
\(71\) | 4.24949 | 0.504322 | 0.252161 | − | 0.967685i | \(-0.418859\pi\) | ||||
0.252161 | + | 0.967685i | \(0.418859\pi\) | |||||||
\(72\) | −15.5868 | −1.83693 | ||||||||
\(73\) | −14.4027 | −1.68571 | −0.842856 | − | 0.538139i | \(-0.819128\pi\) | ||||
−0.842856 | + | 0.538139i | \(0.819128\pi\) | |||||||
\(74\) | −8.14306 | −0.946611 | ||||||||
\(75\) | 10.4595 | 1.20776 | ||||||||
\(76\) | −2.70154 | −0.309888 | ||||||||
\(77\) | 5.41773 | 0.617407 | ||||||||
\(78\) | −2.99196 | −0.338772 | ||||||||
\(79\) | −11.5440 | −1.29880 | −0.649401 | − | 0.760446i | \(-0.724980\pi\) | ||||
−0.649401 | + | 0.760446i | \(0.724980\pi\) | |||||||
\(80\) | 0.360653 | 0.0403222 | ||||||||
\(81\) | 3.89620 | 0.432911 | ||||||||
\(82\) | −1.57080 | −0.173466 | ||||||||
\(83\) | 12.0979 | 1.32792 | 0.663961 | − | 0.747767i | \(-0.268874\pi\) | ||||
0.663961 | + | 0.747767i | \(0.268874\pi\) | |||||||
\(84\) | 11.6865 | 1.27510 | ||||||||
\(85\) | 0.0137878 | 0.00149550 | ||||||||
\(86\) | −4.19659 | −0.452530 | ||||||||
\(87\) | −6.23600 | −0.668570 | ||||||||
\(88\) | −4.52894 | −0.482787 | ||||||||
\(89\) | −3.42826 | −0.363394 | −0.181697 | − | 0.983355i | \(-0.558159\pi\) | ||||
−0.181697 | + | 0.983355i | \(0.558159\pi\) | |||||||
\(90\) | −5.80202 | −0.611587 | ||||||||
\(91\) | 3.91234 | 0.410125 | ||||||||
\(92\) | 9.00176 | 0.938499 | ||||||||
\(93\) | 23.6110 | 2.44835 | ||||||||
\(94\) | 3.13048 | 0.322884 | ||||||||
\(95\) | −2.72967 | −0.280058 | ||||||||
\(96\) | −15.9395 | −1.62682 | ||||||||
\(97\) | −14.6754 | −1.49006 | −0.745028 | − | 0.667033i | \(-0.767564\pi\) | ||||
−0.745028 | + | 0.667033i | \(0.767564\pi\) | |||||||
\(98\) | 4.52701 | 0.457297 | ||||||||
\(99\) | 8.44711 | 0.848966 | ||||||||
\(100\) | 4.21205 | 0.421205 | ||||||||
\(101\) | −4.63421 | −0.461121 | −0.230560 | − | 0.973058i | \(-0.574056\pi\) | ||||
−0.230560 | + | 0.973058i | \(0.574056\pi\) | |||||||
\(102\) | 0.0309348 | 0.00306300 | ||||||||
\(103\) | −11.7442 | −1.15719 | −0.578596 | − | 0.815614i | \(-0.696399\pi\) | ||||
−0.578596 | + | 0.815614i | \(0.696399\pi\) | |||||||
\(104\) | −3.27052 | −0.320701 | ||||||||
\(105\) | 11.8082 | 1.15236 | ||||||||
\(106\) | 1.90912 | 0.185431 | ||||||||
\(107\) | −13.9762 | −1.35113 | −0.675567 | − | 0.737298i | \(-0.736101\pi\) | ||||
−0.675567 | + | 0.737298i | \(0.736101\pi\) | |||||||
\(108\) | 8.08288 | 0.777775 | ||||||||
\(109\) | 4.31011 | 0.412834 | 0.206417 | − | 0.978464i | \(-0.433820\pi\) | ||||
0.206417 | + | 0.978464i | \(0.433820\pi\) | |||||||
\(110\) | −1.68585 | −0.160739 | ||||||||
\(111\) | 25.8393 | 2.45256 | ||||||||
\(112\) | −1.05809 | −0.0999803 | ||||||||
\(113\) | −2.59692 | −0.244298 | −0.122149 | − | 0.992512i | \(-0.538979\pi\) | ||||
−0.122149 | + | 0.992512i | \(0.538979\pi\) | |||||||
\(114\) | −6.12438 | −0.573601 | ||||||||
\(115\) | 9.09550 | 0.848160 | ||||||||
\(116\) | −2.51125 | −0.233163 | ||||||||
\(117\) | 6.09997 | 0.563943 | ||||||||
\(118\) | 4.36372 | 0.401713 | ||||||||
\(119\) | −0.0404510 | −0.00370813 | ||||||||
\(120\) | −9.87101 | −0.901096 | ||||||||
\(121\) | −8.54559 | −0.776872 | ||||||||
\(122\) | −4.63569 | −0.419695 | ||||||||
\(123\) | 4.98442 | 0.449430 | ||||||||
\(124\) | 9.50819 | 0.853861 | ||||||||
\(125\) | 10.1495 | 0.907799 | ||||||||
\(126\) | 17.0221 | 1.51645 | ||||||||
\(127\) | −3.05689 | −0.271255 | −0.135628 | − | 0.990760i | \(-0.543305\pi\) | ||||
−0.135628 | + | 0.990760i | \(0.543305\pi\) | |||||||
\(128\) | −5.86022 | −0.517975 | ||||||||
\(129\) | 13.3165 | 1.17245 | ||||||||
\(130\) | −1.21741 | −0.106774 | ||||||||
\(131\) | 9.78119 | 0.854587 | 0.427293 | − | 0.904113i | \(-0.359467\pi\) | ||||
0.427293 | + | 0.904113i | \(0.359467\pi\) | |||||||
\(132\) | 5.29434 | 0.460814 | ||||||||
\(133\) | 8.00837 | 0.694414 | ||||||||
\(134\) | 3.27512 | 0.282927 | ||||||||
\(135\) | 8.16705 | 0.702908 | ||||||||
\(136\) | 0.0338149 | 0.00289961 | ||||||||
\(137\) | −1.69275 | −0.144621 | −0.0723106 | − | 0.997382i | \(-0.523037\pi\) | ||||
−0.0723106 | + | 0.997382i | \(0.523037\pi\) | |||||||
\(138\) | 20.4070 | 1.73716 | ||||||||
\(139\) | 0.210599 | 0.0178628 | 0.00893141 | − | 0.999960i | \(-0.497157\pi\) | ||||
0.00893141 | + | 0.999960i | \(0.497157\pi\) | |||||||
\(140\) | 4.75516 | 0.401884 | ||||||||
\(141\) | −9.93354 | −0.836555 | ||||||||
\(142\) | 3.87946 | 0.325557 | ||||||||
\(143\) | 1.77242 | 0.148217 | ||||||||
\(144\) | −1.64974 | −0.137478 | ||||||||
\(145\) | −2.53740 | −0.210719 | ||||||||
\(146\) | −13.1486 | −1.08819 | ||||||||
\(147\) | −14.3650 | −1.18480 | ||||||||
\(148\) | 10.4055 | 0.855330 | ||||||||
\(149\) | −4.64956 | −0.380907 | −0.190454 | − | 0.981696i | \(-0.560996\pi\) | ||||
−0.190454 | + | 0.981696i | \(0.560996\pi\) | |||||||
\(150\) | 9.54870 | 0.779648 | ||||||||
\(151\) | 4.05735 | 0.330183 | 0.165091 | − | 0.986278i | \(-0.447208\pi\) | ||||
0.165091 | + | 0.986278i | \(0.447208\pi\) | |||||||
\(152\) | −6.69459 | −0.543003 | ||||||||
\(153\) | −0.0630695 | −0.00509887 | ||||||||
\(154\) | 4.94597 | 0.398558 | ||||||||
\(155\) | 9.60720 | 0.771669 | ||||||||
\(156\) | 3.82324 | 0.306105 | ||||||||
\(157\) | 13.5504 | 1.08144 | 0.540720 | − | 0.841203i | \(-0.318152\pi\) | ||||
0.540720 | + | 0.841203i | \(0.318152\pi\) | |||||||
\(158\) | −10.5388 | −0.838422 | ||||||||
\(159\) | −6.05798 | −0.480429 | ||||||||
\(160\) | −6.48572 | −0.512741 | ||||||||
\(161\) | −26.6846 | −2.10304 | ||||||||
\(162\) | 3.55693 | 0.279459 | ||||||||
\(163\) | −24.4802 | −1.91744 | −0.958719 | − | 0.284356i | \(-0.908220\pi\) | ||||
−0.958719 | + | 0.284356i | \(0.908220\pi\) | |||||||
\(164\) | 2.00723 | 0.156739 | ||||||||
\(165\) | 5.34948 | 0.416456 | ||||||||
\(166\) | 11.0445 | 0.857219 | ||||||||
\(167\) | 14.1666 | 1.09624 | 0.548122 | − | 0.836398i | \(-0.315343\pi\) | ||||
0.548122 | + | 0.836398i | \(0.315343\pi\) | |||||||
\(168\) | 28.9598 | 2.23430 | ||||||||
\(169\) | −11.7201 | −0.901544 | ||||||||
\(170\) | 0.0125872 | 0.000965395 0 | ||||||||
\(171\) | 12.4863 | 0.954854 | ||||||||
\(172\) | 5.36258 | 0.408893 | ||||||||
\(173\) | −11.4102 | −0.867502 | −0.433751 | − | 0.901033i | \(-0.642810\pi\) | ||||
−0.433751 | + | 0.901033i | \(0.642810\pi\) | |||||||
\(174\) | −5.69299 | −0.431585 | ||||||||
\(175\) | −12.4861 | −0.943858 | ||||||||
\(176\) | −0.479350 | −0.0361324 | ||||||||
\(177\) | −13.8468 | −1.04079 | ||||||||
\(178\) | −3.12974 | −0.234584 | ||||||||
\(179\) | 15.3156 | 1.14474 | 0.572370 | − | 0.819996i | \(-0.306024\pi\) | ||||
0.572370 | + | 0.819996i | \(0.306024\pi\) | |||||||
\(180\) | 7.41406 | 0.552611 | ||||||||
\(181\) | 15.1319 | 1.12475 | 0.562374 | − | 0.826883i | \(-0.309888\pi\) | ||||
0.562374 | + | 0.826883i | \(0.309888\pi\) | |||||||
\(182\) | 3.57167 | 0.264750 | ||||||||
\(183\) | 14.7098 | 1.08738 | ||||||||
\(184\) | 22.3069 | 1.64449 | ||||||||
\(185\) | 10.5139 | 0.772997 | ||||||||
\(186\) | 21.5550 | 1.58049 | ||||||||
\(187\) | −0.0183256 | −0.00134010 | ||||||||
\(188\) | −4.00025 | −0.291748 | ||||||||
\(189\) | −23.9607 | −1.74288 | ||||||||
\(190\) | −2.49198 | −0.180787 | ||||||||
\(191\) | −10.0153 | −0.724681 | −0.362341 | − | 0.932046i | \(-0.618022\pi\) | ||||
−0.362341 | + | 0.932046i | \(0.618022\pi\) | |||||||
\(192\) | −16.3243 | −1.17810 | ||||||||
\(193\) | 12.9628 | 0.933080 | 0.466540 | − | 0.884500i | \(-0.345500\pi\) | ||||
0.466540 | + | 0.884500i | \(0.345500\pi\) | |||||||
\(194\) | −13.3975 | −0.961883 | ||||||||
\(195\) | 3.86306 | 0.276639 | ||||||||
\(196\) | −5.78479 | −0.413200 | ||||||||
\(197\) | 8.22992 | 0.586358 | 0.293179 | − | 0.956058i | \(-0.405287\pi\) | ||||
0.293179 | + | 0.956058i | \(0.405287\pi\) | |||||||
\(198\) | 7.71156 | 0.548037 | ||||||||
\(199\) | −6.40798 | −0.454250 | −0.227125 | − | 0.973866i | \(-0.572933\pi\) | ||||
−0.227125 | + | 0.973866i | \(0.572933\pi\) | |||||||
\(200\) | 10.4377 | 0.738058 | ||||||||
\(201\) | −10.3925 | −0.733032 | ||||||||
\(202\) | −4.23068 | −0.297669 | ||||||||
\(203\) | 7.44427 | 0.522485 | ||||||||
\(204\) | −0.0395297 | −0.00276764 | ||||||||
\(205\) | 2.02813 | 0.141651 | ||||||||
\(206\) | −10.7216 | −0.747007 | ||||||||
\(207\) | −41.6055 | −2.89179 | ||||||||
\(208\) | −0.346157 | −0.0240016 | ||||||||
\(209\) | 3.62805 | 0.250958 | ||||||||
\(210\) | 10.7799 | 0.743886 | ||||||||
\(211\) | −0.523963 | −0.0360711 | −0.0180355 | − | 0.999837i | \(-0.505741\pi\) | ||||
−0.0180355 | + | 0.999837i | \(0.505741\pi\) | |||||||
\(212\) | −2.43956 | −0.167549 | ||||||||
\(213\) | −12.3102 | −0.843480 | ||||||||
\(214\) | −12.7592 | −0.872204 | ||||||||
\(215\) | 5.41842 | 0.369533 | ||||||||
\(216\) | 20.0299 | 1.36286 | ||||||||
\(217\) | −28.1858 | −1.91338 | ||||||||
\(218\) | 3.93480 | 0.266498 | ||||||||
\(219\) | 41.7227 | 2.81936 | ||||||||
\(220\) | 2.15424 | 0.145239 | ||||||||
\(221\) | −0.0132336 | −0.000890188 0 | ||||||||
\(222\) | 23.5893 | 1.58321 | ||||||||
\(223\) | 21.4972 | 1.43956 | 0.719780 | − | 0.694202i | \(-0.244243\pi\) | ||||
0.719780 | + | 0.694202i | \(0.244243\pi\) | |||||||
\(224\) | 19.0279 | 1.27136 | ||||||||
\(225\) | −19.4678 | −1.29785 | ||||||||
\(226\) | −2.37079 | −0.157703 | ||||||||
\(227\) | 2.98400 | 0.198055 | 0.0990275 | − | 0.995085i | \(-0.468427\pi\) | ||||
0.0990275 | + | 0.995085i | \(0.468427\pi\) | |||||||
\(228\) | 7.82599 | 0.518289 | ||||||||
\(229\) | −15.1667 | −1.00225 | −0.501123 | − | 0.865376i | \(-0.667080\pi\) | ||||
−0.501123 | + | 0.865376i | \(0.667080\pi\) | |||||||
\(230\) | 8.30350 | 0.547516 | ||||||||
\(231\) | −15.6944 | −1.03262 | ||||||||
\(232\) | −6.22303 | −0.408562 | ||||||||
\(233\) | −22.7236 | −1.48867 | −0.744335 | − | 0.667807i | \(-0.767233\pi\) | ||||
−0.744335 | + | 0.667807i | \(0.767233\pi\) | |||||||
\(234\) | 5.56881 | 0.364044 | ||||||||
\(235\) | −4.04191 | −0.263665 | ||||||||
\(236\) | −5.57615 | −0.362976 | ||||||||
\(237\) | 33.4414 | 2.17225 | ||||||||
\(238\) | −0.0369286 | −0.00239373 | ||||||||
\(239\) | 15.7446 | 1.01844 | 0.509218 | − | 0.860638i | \(-0.329935\pi\) | ||||
0.509218 | + | 0.860638i | \(0.329935\pi\) | |||||||
\(240\) | −1.04476 | −0.0674391 | ||||||||
\(241\) | 2.92341 | 0.188314 | 0.0941568 | − | 0.995557i | \(-0.469984\pi\) | ||||
0.0941568 | + | 0.995557i | \(0.469984\pi\) | |||||||
\(242\) | −7.80147 | −0.501498 | ||||||||
\(243\) | 9.49949 | 0.609393 | ||||||||
\(244\) | 5.92367 | 0.379224 | ||||||||
\(245\) | −5.84503 | −0.373426 | ||||||||
\(246\) | 4.55039 | 0.290122 | ||||||||
\(247\) | 2.61995 | 0.166704 | ||||||||
\(248\) | 23.5619 | 1.49618 | ||||||||
\(249\) | −35.0461 | −2.22095 | ||||||||
\(250\) | 9.26572 | 0.586015 | ||||||||
\(251\) | 5.41430 | 0.341747 | 0.170874 | − | 0.985293i | \(-0.445341\pi\) | ||||
0.170874 | + | 0.985293i | \(0.445341\pi\) | |||||||
\(252\) | −21.7515 | −1.37022 | ||||||||
\(253\) | −12.0890 | −0.760028 | ||||||||
\(254\) | −2.79071 | −0.175105 | ||||||||
\(255\) | −0.0399414 | −0.00250123 | ||||||||
\(256\) | −16.6203 | −1.03877 | ||||||||
\(257\) | −5.42898 | −0.338650 | −0.169325 | − | 0.985560i | \(-0.554159\pi\) | ||||
−0.169325 | + | 0.985560i | \(0.554159\pi\) | |||||||
\(258\) | 12.1569 | 0.756859 | ||||||||
\(259\) | −30.8459 | −1.91667 | ||||||||
\(260\) | 1.55566 | 0.0964779 | ||||||||
\(261\) | 11.6068 | 0.718444 | ||||||||
\(262\) | 8.92948 | 0.551665 | ||||||||
\(263\) | −8.27358 | −0.510171 | −0.255085 | − | 0.966919i | \(-0.582104\pi\) | ||||
−0.255085 | + | 0.966919i | \(0.582104\pi\) | |||||||
\(264\) | 13.1197 | 0.807463 | ||||||||
\(265\) | −2.46496 | −0.151421 | ||||||||
\(266\) | 7.31103 | 0.448268 | ||||||||
\(267\) | 9.93119 | 0.607779 | ||||||||
\(268\) | −4.18508 | −0.255645 | ||||||||
\(269\) | 3.94216 | 0.240358 | 0.120179 | − | 0.992752i | \(-0.461653\pi\) | ||||
0.120179 | + | 0.992752i | \(0.461653\pi\) | |||||||
\(270\) | 7.45589 | 0.453751 | ||||||||
\(271\) | 19.8719 | 1.20713 | 0.603567 | − | 0.797312i | \(-0.293746\pi\) | ||||
0.603567 | + | 0.797312i | \(0.293746\pi\) | |||||||
\(272\) | 0.00357902 | 0.000217010 0 | ||||||||
\(273\) | −11.3335 | −0.685936 | ||||||||
\(274\) | −1.54535 | −0.0933579 | ||||||||
\(275\) | −5.65660 | −0.341106 | ||||||||
\(276\) | −26.0769 | −1.56964 | ||||||||
\(277\) | −28.4935 | −1.71201 | −0.856004 | − | 0.516970i | \(-0.827060\pi\) | ||||
−0.856004 | + | 0.516970i | \(0.827060\pi\) | |||||||
\(278\) | 0.192261 | 0.0115311 | ||||||||
\(279\) | −43.9462 | −2.63099 | ||||||||
\(280\) | 11.7836 | 0.704204 | ||||||||
\(281\) | −31.0192 | −1.85045 | −0.925225 | − | 0.379419i | \(-0.876124\pi\) | ||||
−0.925225 | + | 0.379419i | \(0.876124\pi\) | |||||||
\(282\) | −9.06856 | −0.540025 | ||||||||
\(283\) | 31.5173 | 1.87351 | 0.936753 | − | 0.349991i | \(-0.113815\pi\) | ||||
0.936753 | + | 0.349991i | \(0.113815\pi\) | |||||||
\(284\) | −4.95733 | −0.294163 | ||||||||
\(285\) | 7.90748 | 0.468399 | ||||||||
\(286\) | 1.61808 | 0.0956792 | ||||||||
\(287\) | −5.95018 | −0.351228 | ||||||||
\(288\) | 29.6676 | 1.74818 | ||||||||
\(289\) | −16.9999 | −0.999992 | ||||||||
\(290\) | −2.31645 | −0.136027 | ||||||||
\(291\) | 42.5125 | 2.49213 | ||||||||
\(292\) | 16.8018 | 0.983252 | ||||||||
\(293\) | −10.8195 | −0.632079 | −0.316040 | − | 0.948746i | \(-0.602353\pi\) | ||||
−0.316040 | + | 0.948746i | \(0.602353\pi\) | |||||||
\(294\) | −13.1141 | −0.764831 | ||||||||
\(295\) | −5.63421 | −0.328037 | ||||||||
\(296\) | 25.7856 | 1.49876 | ||||||||
\(297\) | −10.8550 | −0.629869 | ||||||||
\(298\) | −4.24469 | −0.245889 | ||||||||
\(299\) | −8.72991 | −0.504863 | ||||||||
\(300\) | −12.2017 | −0.704467 | ||||||||
\(301\) | −15.8967 | −0.916269 | ||||||||
\(302\) | 3.70405 | 0.213144 | ||||||||
\(303\) | 13.4247 | 0.771227 | ||||||||
\(304\) | −0.708565 | −0.0406390 | ||||||||
\(305\) | 5.98536 | 0.342720 | ||||||||
\(306\) | −0.0575777 | −0.00329150 | ||||||||
\(307\) | −17.3475 | −0.990072 | −0.495036 | − | 0.868872i | \(-0.664845\pi\) | ||||
−0.495036 | + | 0.868872i | \(0.664845\pi\) | |||||||
\(308\) | −6.32016 | −0.360125 | ||||||||
\(309\) | 34.0214 | 1.93541 | ||||||||
\(310\) | 8.77064 | 0.498139 | ||||||||
\(311\) | −8.78677 | −0.498252 | −0.249126 | − | 0.968471i | \(-0.580143\pi\) | ||||
−0.249126 | + | 0.968471i | \(0.580143\pi\) | |||||||
\(312\) | 9.47424 | 0.536373 | ||||||||
\(313\) | 29.5409 | 1.66975 | 0.834876 | − | 0.550439i | \(-0.185539\pi\) | ||||
0.834876 | + | 0.550439i | \(0.185539\pi\) | |||||||
\(314\) | 12.3705 | 0.698106 | ||||||||
\(315\) | −21.9780 | −1.23832 | ||||||||
\(316\) | 13.4669 | 0.757573 | ||||||||
\(317\) | −18.5919 | −1.04422 | −0.522112 | − | 0.852877i | \(-0.674856\pi\) | ||||
−0.522112 | + | 0.852877i | \(0.674856\pi\) | |||||||
\(318\) | −5.53047 | −0.310133 | ||||||||
\(319\) | 3.37250 | 0.188824 | ||||||||
\(320\) | −6.64227 | −0.371314 | ||||||||
\(321\) | 40.4873 | 2.25978 | ||||||||
\(322\) | −24.3610 | −1.35758 | ||||||||
\(323\) | −0.0270885 | −0.00150724 | ||||||||
\(324\) | −4.54519 | −0.252511 | ||||||||
\(325\) | −4.08484 | −0.226586 | ||||||||
\(326\) | −22.3486 | −1.23777 | ||||||||
\(327\) | −12.4858 | −0.690466 | ||||||||
\(328\) | 4.97405 | 0.274646 | ||||||||
\(329\) | 11.8582 | 0.653765 | ||||||||
\(330\) | 4.88366 | 0.268837 | ||||||||
\(331\) | −3.35828 | −0.184588 | −0.0922938 | − | 0.995732i | \(-0.529420\pi\) | ||||
−0.0922938 | + | 0.995732i | \(0.529420\pi\) | |||||||
\(332\) | −14.1131 | −0.774557 | ||||||||
\(333\) | −48.0937 | −2.63552 | ||||||||
\(334\) | 12.9330 | 0.707663 | ||||||||
\(335\) | −4.22867 | −0.231037 | ||||||||
\(336\) | 3.06515 | 0.167217 | ||||||||
\(337\) | 17.2033 | 0.937125 | 0.468562 | − | 0.883430i | \(-0.344772\pi\) | ||||
0.468562 | + | 0.883430i | \(0.344772\pi\) | |||||||
\(338\) | −10.6995 | −0.581977 | ||||||||
\(339\) | 7.52293 | 0.408590 | ||||||||
\(340\) | −0.0160845 | −0.000872302 0 | ||||||||
\(341\) | −12.7691 | −0.691485 | ||||||||
\(342\) | 11.3991 | 0.616391 | ||||||||
\(343\) | −7.05877 | −0.381138 | ||||||||
\(344\) | 13.2888 | 0.716484 | ||||||||
\(345\) | −26.3484 | −1.41855 | ||||||||
\(346\) | −10.4166 | −0.560002 | ||||||||
\(347\) | −32.8198 | −1.76186 | −0.880929 | − | 0.473249i | \(-0.843081\pi\) | ||||
−0.880929 | + | 0.473249i | \(0.843081\pi\) | |||||||
\(348\) | 7.27474 | 0.389967 | ||||||||
\(349\) | −2.65295 | −0.142009 | −0.0710046 | − | 0.997476i | \(-0.522620\pi\) | ||||
−0.0710046 | + | 0.997476i | \(0.522620\pi\) | |||||||
\(350\) | −11.3988 | −0.609293 | ||||||||
\(351\) | −7.83877 | −0.418403 | ||||||||
\(352\) | 8.62027 | 0.459462 | ||||||||
\(353\) | −20.7549 | −1.10467 | −0.552335 | − | 0.833622i | \(-0.686263\pi\) | ||||
−0.552335 | + | 0.833622i | \(0.686263\pi\) | |||||||
\(354\) | −12.6411 | −0.671867 | ||||||||
\(355\) | −5.00895 | −0.265848 | ||||||||
\(356\) | 3.99930 | 0.211963 | ||||||||
\(357\) | 0.117181 | 0.00620187 | ||||||||
\(358\) | 13.9819 | 0.738969 | ||||||||
\(359\) | 24.1576 | 1.27499 | 0.637495 | − | 0.770455i | \(-0.279971\pi\) | ||||
0.637495 | + | 0.770455i | \(0.279971\pi\) | |||||||
\(360\) | 18.3725 | 0.968316 | ||||||||
\(361\) | −13.6371 | −0.717742 | ||||||||
\(362\) | 13.8143 | 0.726064 | ||||||||
\(363\) | 24.7554 | 1.29932 | ||||||||
\(364\) | −4.56403 | −0.239220 | ||||||||
\(365\) | 16.9768 | 0.888605 | ||||||||
\(366\) | 13.4289 | 0.701942 | ||||||||
\(367\) | 29.2563 | 1.52716 | 0.763582 | − | 0.645711i | \(-0.223439\pi\) | ||||
0.763582 | + | 0.645711i | \(0.223439\pi\) | |||||||
\(368\) | 2.36100 | 0.123076 | ||||||||
\(369\) | −9.27729 | −0.482957 | ||||||||
\(370\) | 9.59838 | 0.498996 | ||||||||
\(371\) | 7.23176 | 0.375454 | ||||||||
\(372\) | −27.5439 | −1.42809 | ||||||||
\(373\) | 5.06956 | 0.262492 | 0.131246 | − | 0.991350i | \(-0.458102\pi\) | ||||
0.131246 | + | 0.991350i | \(0.458102\pi\) | |||||||
\(374\) | −0.0167299 | −0.000865081 0 | ||||||||
\(375\) | −29.4017 | −1.51830 | ||||||||
\(376\) | −9.91287 | −0.511217 | ||||||||
\(377\) | 2.43541 | 0.125430 | ||||||||
\(378\) | −21.8742 | −1.12509 | ||||||||
\(379\) | 7.03123 | 0.361170 | 0.180585 | − | 0.983559i | \(-0.442201\pi\) | ||||
0.180585 | + | 0.983559i | \(0.442201\pi\) | |||||||
\(380\) | 3.18436 | 0.163354 | ||||||||
\(381\) | 8.85539 | 0.453676 | ||||||||
\(382\) | −9.14320 | −0.467807 | ||||||||
\(383\) | 20.2528 | 1.03487 | 0.517436 | − | 0.855722i | \(-0.326887\pi\) | ||||
0.517436 | + | 0.855722i | \(0.326887\pi\) | |||||||
\(384\) | 16.9763 | 0.866316 | ||||||||
\(385\) | −6.38598 | −0.325459 | ||||||||
\(386\) | 11.8340 | 0.602335 | ||||||||
\(387\) | −24.7855 | −1.25992 | ||||||||
\(388\) | 17.1198 | 0.869129 | ||||||||
\(389\) | −19.6476 | −0.996174 | −0.498087 | − | 0.867127i | \(-0.665964\pi\) | ||||
−0.498087 | + | 0.867127i | \(0.665964\pi\) | |||||||
\(390\) | 3.52668 | 0.178580 | ||||||||
\(391\) | 0.0902613 | 0.00456471 | ||||||||
\(392\) | −14.3351 | −0.724031 | ||||||||
\(393\) | −28.3348 | −1.42930 | ||||||||
\(394\) | 7.51329 | 0.378514 | ||||||||
\(395\) | 13.6071 | 0.684650 | ||||||||
\(396\) | −9.85415 | −0.495190 | ||||||||
\(397\) | 2.23294 | 0.112068 | 0.0560341 | − | 0.998429i | \(-0.482154\pi\) | ||||
0.0560341 | + | 0.998429i | \(0.482154\pi\) | |||||||
\(398\) | −5.84999 | −0.293234 | ||||||||
\(399\) | −23.1991 | −1.16141 | ||||||||
\(400\) | 1.10474 | 0.0552372 | ||||||||
\(401\) | 25.4677 | 1.27180 | 0.635899 | − | 0.771772i | \(-0.280629\pi\) | ||||
0.635899 | + | 0.771772i | \(0.280629\pi\) | |||||||
\(402\) | −9.48758 | −0.473197 | ||||||||
\(403\) | −9.22104 | −0.459333 | ||||||||
\(404\) | 5.40613 | 0.268965 | ||||||||
\(405\) | −4.59253 | −0.228204 | ||||||||
\(406\) | 6.79605 | 0.337282 | ||||||||
\(407\) | −13.9742 | −0.692675 | ||||||||
\(408\) | −0.0979572 | −0.00484960 | ||||||||
\(409\) | 30.1656 | 1.49159 | 0.745796 | − | 0.666174i | \(-0.232069\pi\) | ||||
0.745796 | + | 0.666174i | \(0.232069\pi\) | |||||||
\(410\) | 1.85153 | 0.0914406 | ||||||||
\(411\) | 4.90366 | 0.241880 | ||||||||
\(412\) | 13.7005 | 0.674973 | ||||||||
\(413\) | 16.5298 | 0.813377 | ||||||||
\(414\) | −37.9827 | −1.86675 | ||||||||
\(415\) | −14.2601 | −0.700000 | ||||||||
\(416\) | 6.22502 | 0.305207 | ||||||||
\(417\) | −0.610078 | −0.0298756 | ||||||||
\(418\) | 3.31213 | 0.162002 | ||||||||
\(419\) | −28.7548 | −1.40476 | −0.702382 | − | 0.711801i | \(-0.747880\pi\) | ||||
−0.702382 | + | 0.711801i | \(0.747880\pi\) | |||||||
\(420\) | −13.7750 | −0.672154 | ||||||||
\(421\) | −13.4270 | −0.654393 | −0.327197 | − | 0.944956i | \(-0.606104\pi\) | ||||
−0.327197 | + | 0.944956i | \(0.606104\pi\) | |||||||
\(422\) | −0.478338 | −0.0232851 | ||||||||
\(423\) | 18.4889 | 0.898960 | ||||||||
\(424\) | −6.04538 | −0.293589 | ||||||||
\(425\) | 0.0422345 | 0.00204867 | ||||||||
\(426\) | −11.2383 | −0.544495 | ||||||||
\(427\) | −17.5600 | −0.849786 | ||||||||
\(428\) | 16.3043 | 0.788097 | ||||||||
\(429\) | −5.13445 | −0.247894 | ||||||||
\(430\) | 4.94660 | 0.238546 | ||||||||
\(431\) | 28.6125 | 1.37822 | 0.689108 | − | 0.724658i | \(-0.258002\pi\) | ||||
0.689108 | + | 0.724658i | \(0.258002\pi\) | |||||||
\(432\) | 2.11999 | 0.101998 | ||||||||
\(433\) | −14.8232 | −0.712355 | −0.356178 | − | 0.934418i | \(-0.615920\pi\) | ||||
−0.356178 | + | 0.934418i | \(0.615920\pi\) | |||||||
\(434\) | −25.7315 | −1.23515 | ||||||||
\(435\) | 7.35049 | 0.352429 | ||||||||
\(436\) | −5.02805 | −0.240800 | ||||||||
\(437\) | −17.8697 | −0.854822 | ||||||||
\(438\) | 38.0897 | 1.81999 | ||||||||
\(439\) | −1.35916 | −0.0648694 | −0.0324347 | − | 0.999474i | \(-0.510326\pi\) | ||||
−0.0324347 | + | 0.999474i | \(0.510326\pi\) | |||||||
\(440\) | 5.33835 | 0.254496 | ||||||||
\(441\) | 26.7369 | 1.27319 | ||||||||
\(442\) | −0.0120813 | −0.000574647 0 | ||||||||
\(443\) | 7.08781 | 0.336752 | 0.168376 | − | 0.985723i | \(-0.446148\pi\) | ||||
0.168376 | + | 0.985723i | \(0.446148\pi\) | |||||||
\(444\) | −30.1434 | −1.43054 | ||||||||
\(445\) | 4.04095 | 0.191559 | ||||||||
\(446\) | 19.6253 | 0.929286 | ||||||||
\(447\) | 13.4691 | 0.637069 | ||||||||
\(448\) | 19.4872 | 0.920685 | ||||||||
\(449\) | 24.2354 | 1.14374 | 0.571869 | − | 0.820345i | \(-0.306218\pi\) | ||||
0.571869 | + | 0.820345i | \(0.306218\pi\) | |||||||
\(450\) | −17.7726 | −0.837809 | ||||||||
\(451\) | −2.69563 | −0.126932 | ||||||||
\(452\) | 3.02950 | 0.142495 | ||||||||
\(453\) | −11.7536 | −0.552232 | ||||||||
\(454\) | 2.72416 | 0.127851 | ||||||||
\(455\) | −4.61155 | −0.216193 | ||||||||
\(456\) | 19.3933 | 0.908174 | ||||||||
\(457\) | −21.6697 | −1.01366 | −0.506832 | − | 0.862045i | \(-0.669184\pi\) | ||||
−0.506832 | + | 0.862045i | \(0.669184\pi\) | |||||||
\(458\) | −13.8461 | −0.646985 | ||||||||
\(459\) | 0.0810475 | 0.00378298 | ||||||||
\(460\) | −10.6105 | −0.494719 | ||||||||
\(461\) | 36.9294 | 1.71997 | 0.859986 | − | 0.510318i | \(-0.170472\pi\) | ||||
0.859986 | + | 0.510318i | \(0.170472\pi\) | |||||||
\(462\) | −14.3278 | −0.666589 | ||||||||
\(463\) | 23.4486 | 1.08975 | 0.544875 | − | 0.838517i | \(-0.316577\pi\) | ||||
0.544875 | + | 0.838517i | \(0.316577\pi\) | |||||||
\(464\) | −0.658655 | −0.0305773 | ||||||||
\(465\) | −27.8307 | −1.29062 | ||||||||
\(466\) | −20.7449 | −0.960987 | ||||||||
\(467\) | 3.89784 | 0.180371 | 0.0901853 | − | 0.995925i | \(-0.471254\pi\) | ||||
0.0901853 | + | 0.995925i | \(0.471254\pi\) | |||||||
\(468\) | −7.11605 | −0.328940 | ||||||||
\(469\) | 12.4061 | 0.572863 | ||||||||
\(470\) | −3.68995 | −0.170205 | ||||||||
\(471\) | −39.2536 | −1.80871 | ||||||||
\(472\) | −13.8180 | −0.636027 | ||||||||
\(473\) | −7.20171 | −0.331135 | ||||||||
\(474\) | 30.5294 | 1.40226 | ||||||||
\(475\) | −8.36146 | −0.383650 | ||||||||
\(476\) | 0.0471889 | 0.00216290 | ||||||||
\(477\) | 11.2755 | 0.516268 | ||||||||
\(478\) | 14.3736 | 0.657435 | ||||||||
\(479\) | −10.4410 | −0.477061 | −0.238531 | − | 0.971135i | \(-0.576666\pi\) | ||||
−0.238531 | + | 0.971135i | \(0.576666\pi\) | |||||||
\(480\) | 18.7882 | 0.857562 | ||||||||
\(481\) | −10.0913 | −0.460123 | ||||||||
\(482\) | 2.66885 | 0.121563 | ||||||||
\(483\) | 77.3015 | 3.51734 | ||||||||
\(484\) | 9.96904 | 0.453138 | ||||||||
\(485\) | 17.2981 | 0.785467 | ||||||||
\(486\) | 8.67231 | 0.393384 | ||||||||
\(487\) | 11.8844 | 0.538532 | 0.269266 | − | 0.963066i | \(-0.413219\pi\) | ||||
0.269266 | + | 0.963066i | \(0.413219\pi\) | |||||||
\(488\) | 14.6792 | 0.664497 | ||||||||
\(489\) | 70.9158 | 3.20692 | ||||||||
\(490\) | −5.33607 | −0.241059 | ||||||||
\(491\) | 27.4571 | 1.23912 | 0.619562 | − | 0.784948i | \(-0.287310\pi\) | ||||
0.619562 | + | 0.784948i | \(0.287310\pi\) | |||||||
\(492\) | −5.81468 | −0.262146 | ||||||||
\(493\) | −0.0251804 | −0.00113407 | ||||||||
\(494\) | 2.39181 | 0.107613 | ||||||||
\(495\) | −9.95676 | −0.447523 | ||||||||
\(496\) | 2.49383 | 0.111976 | ||||||||
\(497\) | 14.6954 | 0.659178 | ||||||||
\(498\) | −31.9944 | −1.43370 | ||||||||
\(499\) | 36.5142 | 1.63460 | 0.817299 | − | 0.576214i | \(-0.195470\pi\) | ||||
0.817299 | + | 0.576214i | \(0.195470\pi\) | |||||||
\(500\) | −11.8401 | −0.529506 | ||||||||
\(501\) | −41.0387 | −1.83347 | ||||||||
\(502\) | 4.94284 | 0.220610 | ||||||||
\(503\) | −0.442602 | −0.0197347 | −0.00986733 | − | 0.999951i | \(-0.503141\pi\) | ||||
−0.00986733 | + | 0.999951i | \(0.503141\pi\) | |||||||
\(504\) | −53.9017 | −2.40097 | ||||||||
\(505\) | 5.46243 | 0.243075 | ||||||||
\(506\) | −11.0363 | −0.490624 | ||||||||
\(507\) | 33.9514 | 1.50784 | ||||||||
\(508\) | 3.56608 | 0.158219 | ||||||||
\(509\) | 31.8700 | 1.41261 | 0.706307 | − | 0.707906i | \(-0.250360\pi\) | ||||
0.706307 | + | 0.707906i | \(0.250360\pi\) | |||||||
\(510\) | −0.0364634 | −0.00161463 | ||||||||
\(511\) | −49.8068 | −2.20332 | ||||||||
\(512\) | −3.45258 | −0.152584 | ||||||||
\(513\) | −16.0456 | −0.708429 | ||||||||
\(514\) | −4.95624 | −0.218610 | ||||||||
\(515\) | 13.8431 | 0.610001 | ||||||||
\(516\) | −15.5346 | −0.683875 | ||||||||
\(517\) | 5.37216 | 0.236267 | ||||||||
\(518\) | −28.1599 | −1.23728 | ||||||||
\(519\) | 33.0538 | 1.45090 | ||||||||
\(520\) | 3.85502 | 0.169054 | ||||||||
\(521\) | 13.0585 | 0.572103 | 0.286051 | − | 0.958214i | \(-0.407657\pi\) | ||||
0.286051 | + | 0.958214i | \(0.407657\pi\) | |||||||
\(522\) | 10.5961 | 0.463780 | ||||||||
\(523\) | −2.04070 | −0.0892336 | −0.0446168 | − | 0.999004i | \(-0.514207\pi\) | ||||
−0.0446168 | + | 0.999004i | \(0.514207\pi\) | |||||||
\(524\) | −11.4105 | −0.498468 | ||||||||
\(525\) | 36.1704 | 1.57861 | ||||||||
\(526\) | −7.55314 | −0.329333 | ||||||||
\(527\) | 0.0953392 | 0.00415304 | ||||||||
\(528\) | 1.38861 | 0.0604315 | ||||||||
\(529\) | 36.5433 | 1.58884 | ||||||||
\(530\) | −2.25032 | −0.0977477 | ||||||||
\(531\) | 25.7726 | 1.11843 | ||||||||
\(532\) | −9.34233 | −0.405041 | ||||||||
\(533\) | −1.94661 | −0.0843172 | ||||||||
\(534\) | 9.06641 | 0.392342 | ||||||||
\(535\) | 16.4741 | 0.712236 | ||||||||
\(536\) | −10.3709 | −0.447955 | ||||||||
\(537\) | −44.3671 | −1.91458 | ||||||||
\(538\) | 3.59889 | 0.155159 | ||||||||
\(539\) | 7.76873 | 0.334623 | ||||||||
\(540\) | −9.52744 | −0.409996 | ||||||||
\(541\) | −32.4849 | −1.39663 | −0.698317 | − | 0.715788i | \(-0.746067\pi\) | ||||
−0.698317 | + | 0.715788i | \(0.746067\pi\) | |||||||
\(542\) | 18.1416 | 0.779247 | ||||||||
\(543\) | −43.8352 | −1.88115 | ||||||||
\(544\) | −0.0643625 | −0.00275952 | ||||||||
\(545\) | −5.08041 | −0.217621 | ||||||||
\(546\) | −10.3466 | −0.442795 | ||||||||
\(547\) | −5.77433 | −0.246892 | −0.123446 | − | 0.992351i | \(-0.539395\pi\) | ||||
−0.123446 | + | 0.992351i | \(0.539395\pi\) | |||||||
\(548\) | 1.97471 | 0.0843554 | ||||||||
\(549\) | −27.3788 | −1.16850 | ||||||||
\(550\) | −5.16404 | −0.220195 | ||||||||
\(551\) | 4.98515 | 0.212375 | ||||||||
\(552\) | −64.6201 | −2.75042 | ||||||||
\(553\) | −39.9209 | −1.69761 | ||||||||
\(554\) | −26.0124 | −1.10516 | ||||||||
\(555\) | −30.4573 | −1.29284 | ||||||||
\(556\) | −0.245679 | −0.0104191 | ||||||||
\(557\) | −22.4130 | −0.949670 | −0.474835 | − | 0.880075i | \(-0.657492\pi\) | ||||
−0.474835 | + | 0.880075i | \(0.657492\pi\) | |||||||
\(558\) | −40.1195 | −1.69839 | ||||||||
\(559\) | −5.20062 | −0.219963 | ||||||||
\(560\) | 1.24719 | 0.0527035 | ||||||||
\(561\) | 0.0530867 | 0.00224132 | ||||||||
\(562\) | −28.3181 | −1.19453 | ||||||||
\(563\) | −2.24085 | −0.0944407 | −0.0472203 | − | 0.998884i | \(-0.515036\pi\) | ||||
−0.0472203 | + | 0.998884i | \(0.515036\pi\) | |||||||
\(564\) | 11.5882 | 0.487950 | ||||||||
\(565\) | 3.06104 | 0.128779 | ||||||||
\(566\) | 28.7728 | 1.20941 | ||||||||
\(567\) | 13.4736 | 0.565840 | ||||||||
\(568\) | −12.2846 | −0.515450 | ||||||||
\(569\) | 3.11655 | 0.130653 | 0.0653264 | − | 0.997864i | \(-0.479191\pi\) | ||||
0.0653264 | + | 0.997864i | \(0.479191\pi\) | |||||||
\(570\) | 7.21893 | 0.302368 | ||||||||
\(571\) | 38.2090 | 1.59900 | 0.799499 | − | 0.600667i | \(-0.205098\pi\) | ||||
0.799499 | + | 0.600667i | \(0.205098\pi\) | |||||||
\(572\) | −2.06765 | −0.0864529 | ||||||||
\(573\) | 29.0129 | 1.21203 | ||||||||
\(574\) | −5.43206 | −0.226730 | ||||||||
\(575\) | 27.8611 | 1.16189 | ||||||||
\(576\) | 30.3837 | 1.26599 | ||||||||
\(577\) | −33.9440 | −1.41311 | −0.706554 | − | 0.707659i | \(-0.749751\pi\) | ||||
−0.706554 | + | 0.707659i | \(0.749751\pi\) | |||||||
\(578\) | −15.5196 | −0.645529 | ||||||||
\(579\) | −37.5513 | −1.56058 | ||||||||
\(580\) | 2.96005 | 0.122910 | ||||||||
\(581\) | 41.8365 | 1.73567 | ||||||||
\(582\) | 38.8107 | 1.60875 | ||||||||
\(583\) | 3.27622 | 0.135687 | ||||||||
\(584\) | 41.6359 | 1.72291 | ||||||||
\(585\) | −7.19015 | −0.297276 | ||||||||
\(586\) | −9.87733 | −0.408029 | ||||||||
\(587\) | 40.5865 | 1.67518 | 0.837592 | − | 0.546296i | \(-0.183962\pi\) | ||||
0.837592 | + | 0.546296i | \(0.183962\pi\) | |||||||
\(588\) | 16.7578 | 0.691078 | ||||||||
\(589\) | −18.8750 | −0.777731 | ||||||||
\(590\) | −5.14360 | −0.211759 | ||||||||
\(591\) | −23.8410 | −0.980686 | ||||||||
\(592\) | 2.72918 | 0.112169 | ||||||||
\(593\) | −25.5035 | −1.04730 | −0.523652 | − | 0.851932i | \(-0.675431\pi\) | ||||
−0.523652 | + | 0.851932i | \(0.675431\pi\) | |||||||
\(594\) | −9.90974 | −0.406602 | ||||||||
\(595\) | 0.0476803 | 0.00195470 | ||||||||
\(596\) | 5.42404 | 0.222178 | ||||||||
\(597\) | 18.5630 | 0.759734 | ||||||||
\(598\) | −7.96974 | −0.325907 | ||||||||
\(599\) | −13.4331 | −0.548861 | −0.274430 | − | 0.961607i | \(-0.588489\pi\) | ||||
−0.274430 | + | 0.961607i | \(0.588489\pi\) | |||||||
\(600\) | −30.2366 | −1.23441 | ||||||||
\(601\) | −6.16983 | −0.251673 | −0.125836 | − | 0.992051i | \(-0.540161\pi\) | ||||
−0.125836 | + | 0.992051i | \(0.540161\pi\) | |||||||
\(602\) | −14.5124 | −0.591483 | ||||||||
\(603\) | 19.3432 | 0.787715 | ||||||||
\(604\) | −4.73319 | −0.192591 | ||||||||
\(605\) | 10.0729 | 0.409520 | ||||||||
\(606\) | 12.2557 | 0.497853 | ||||||||
\(607\) | −1.75135 | −0.0710849 | −0.0355425 | − | 0.999368i | \(-0.511316\pi\) | ||||
−0.0355425 | + | 0.999368i | \(0.511316\pi\) | |||||||
\(608\) | 12.7423 | 0.516769 | ||||||||
\(609\) | −21.5650 | −0.873859 | ||||||||
\(610\) | 5.46417 | 0.221238 | ||||||||
\(611\) | 3.87944 | 0.156945 | ||||||||
\(612\) | 0.0735751 | 0.00297410 | ||||||||
\(613\) | −9.24279 | −0.373313 | −0.186656 | − | 0.982425i | \(-0.559765\pi\) | ||||
−0.186656 | + | 0.982425i | \(0.559765\pi\) | |||||||
\(614\) | −15.8369 | −0.639126 | ||||||||
\(615\) | −5.87523 | −0.236912 | ||||||||
\(616\) | −15.6618 | −0.631030 | ||||||||
\(617\) | 35.7600 | 1.43964 | 0.719822 | − | 0.694159i | \(-0.244223\pi\) | ||||
0.719822 | + | 0.694159i | \(0.244223\pi\) | |||||||
\(618\) | 31.0589 | 1.24937 | ||||||||
\(619\) | −24.1365 | −0.970128 | −0.485064 | − | 0.874479i | \(-0.661204\pi\) | ||||
−0.485064 | + | 0.874479i | \(0.661204\pi\) | |||||||
\(620\) | −11.2075 | −0.450103 | ||||||||
\(621\) | 53.4652 | 2.14549 | ||||||||
\(622\) | −8.02164 | −0.321639 | ||||||||
\(623\) | −11.8554 | −0.474978 | ||||||||
\(624\) | 1.00277 | 0.0401428 | ||||||||
\(625\) | 6.08970 | 0.243588 | ||||||||
\(626\) | 26.9686 | 1.07788 | ||||||||
\(627\) | −10.5100 | −0.419728 | ||||||||
\(628\) | −15.8075 | −0.630788 | ||||||||
\(629\) | 0.104337 | 0.00416019 | ||||||||
\(630\) | −20.0643 | −0.799379 | ||||||||
\(631\) | −19.4991 | −0.776247 | −0.388123 | − | 0.921607i | \(-0.626877\pi\) | ||||
−0.388123 | + | 0.921607i | \(0.626877\pi\) | |||||||
\(632\) | 33.3718 | 1.32746 | ||||||||
\(633\) | 1.51785 | 0.0603290 | ||||||||
\(634\) | −16.9730 | −0.674082 | ||||||||
\(635\) | 3.60322 | 0.142989 | ||||||||
\(636\) | 7.06706 | 0.280227 | ||||||||
\(637\) | 5.61009 | 0.222280 | ||||||||
\(638\) | 3.07883 | 0.121892 | ||||||||
\(639\) | 22.9124 | 0.906402 | ||||||||
\(640\) | 6.90755 | 0.273045 | ||||||||
\(641\) | −29.3032 | −1.15741 | −0.578703 | − | 0.815538i | \(-0.696441\pi\) | ||||
−0.578703 | + | 0.815538i | \(0.696441\pi\) | |||||||
\(642\) | 36.9618 | 1.45876 | ||||||||
\(643\) | −33.5527 | −1.32319 | −0.661594 | − | 0.749862i | \(-0.730120\pi\) | ||||
−0.661594 | + | 0.749862i | \(0.730120\pi\) | |||||||
\(644\) | 31.1295 | 1.22667 | ||||||||
\(645\) | −15.6964 | −0.618046 | ||||||||
\(646\) | −0.0247297 | −0.000972978 0 | ||||||||
\(647\) | −7.93160 | −0.311824 | −0.155912 | − | 0.987771i | \(-0.549832\pi\) | ||||
−0.155912 | + | 0.987771i | \(0.549832\pi\) | |||||||
\(648\) | −11.2633 | −0.442463 | ||||||||
\(649\) | 7.48852 | 0.293950 | ||||||||
\(650\) | −3.72915 | −0.146269 | ||||||||
\(651\) | 81.6504 | 3.20013 | ||||||||
\(652\) | 28.5579 | 1.11841 | ||||||||
\(653\) | 2.14051 | 0.0837645 | 0.0418822 | − | 0.999123i | \(-0.486665\pi\) | ||||
0.0418822 | + | 0.999123i | \(0.486665\pi\) | |||||||
\(654\) | −11.3986 | −0.445720 | ||||||||
\(655\) | −11.5293 | −0.450486 | ||||||||
\(656\) | 0.526461 | 0.0205548 | ||||||||
\(657\) | −77.6568 | −3.02968 | ||||||||
\(658\) | 10.8257 | 0.422028 | ||||||||
\(659\) | 48.2328 | 1.87888 | 0.939442 | − | 0.342708i | \(-0.111344\pi\) | ||||
0.939442 | + | 0.342708i | \(0.111344\pi\) | |||||||
\(660\) | −6.24054 | −0.242913 | ||||||||
\(661\) | 30.0091 | 1.16722 | 0.583609 | − | 0.812035i | \(-0.301640\pi\) | ||||
0.583609 | + | 0.812035i | \(0.301640\pi\) | |||||||
\(662\) | −3.06585 | −0.119158 | ||||||||
\(663\) | 0.0383359 | 0.00148884 | ||||||||
\(664\) | −34.9732 | −1.35722 | ||||||||
\(665\) | −9.43961 | −0.366053 | ||||||||
\(666\) | −43.9058 | −1.70132 | ||||||||
\(667\) | −16.6110 | −0.643179 | ||||||||
\(668\) | −16.5263 | −0.639423 | ||||||||
\(669\) | −62.2745 | −2.40767 | ||||||||
\(670\) | −3.86045 | −0.149142 | ||||||||
\(671\) | −7.95523 | −0.307108 | ||||||||
\(672\) | −55.1213 | −2.12635 | ||||||||
\(673\) | −28.5885 | −1.10201 | −0.551003 | − | 0.834503i | \(-0.685755\pi\) | ||||
−0.551003 | + | 0.834503i | \(0.685755\pi\) | |||||||
\(674\) | 15.7053 | 0.604946 | ||||||||
\(675\) | 25.0171 | 0.962908 | ||||||||
\(676\) | 13.6723 | 0.525857 | ||||||||
\(677\) | 6.82078 | 0.262144 | 0.131072 | − | 0.991373i | \(-0.458158\pi\) | ||||
0.131072 | + | 0.991373i | \(0.458158\pi\) | |||||||
\(678\) | 6.86786 | 0.263759 | ||||||||
\(679\) | −50.7496 | −1.94759 | ||||||||
\(680\) | −0.0398583 | −0.00152850 | ||||||||
\(681\) | −8.64423 | −0.331248 | ||||||||
\(682\) | −11.6572 | −0.446377 | ||||||||
\(683\) | −10.8759 | −0.416157 | −0.208078 | − | 0.978112i | \(-0.566721\pi\) | ||||
−0.208078 | + | 0.978112i | \(0.566721\pi\) | |||||||
\(684\) | −14.5662 | −0.556952 | ||||||||
\(685\) | 1.99527 | 0.0762355 | ||||||||
\(686\) | −6.44411 | −0.246037 | ||||||||
\(687\) | 43.9360 | 1.67626 | ||||||||
\(688\) | 1.40651 | 0.0536226 | ||||||||
\(689\) | 2.36588 | 0.0901329 | ||||||||
\(690\) | −24.0541 | −0.915724 | ||||||||
\(691\) | 1.74582 | 0.0664141 | 0.0332070 | − | 0.999448i | \(-0.489428\pi\) | ||||
0.0332070 | + | 0.999448i | \(0.489428\pi\) | |||||||
\(692\) | 13.3108 | 0.506001 | ||||||||
\(693\) | 29.2114 | 1.10965 | ||||||||
\(694\) | −29.9619 | −1.13734 | ||||||||
\(695\) | −0.248238 | −0.00941619 | ||||||||
\(696\) | 18.0273 | 0.683322 | ||||||||
\(697\) | 0.0201267 | 0.000762351 0 | ||||||||
\(698\) | −2.42194 | −0.0916718 | ||||||||
\(699\) | 65.8270 | 2.48981 | ||||||||
\(700\) | 14.5659 | 0.550539 | ||||||||
\(701\) | −14.3245 | −0.541029 | −0.270514 | − | 0.962716i | \(-0.587194\pi\) | ||||
−0.270514 | + | 0.962716i | \(0.587194\pi\) | |||||||
\(702\) | −7.15620 | −0.270093 | ||||||||
\(703\) | −20.6563 | −0.779069 | ||||||||
\(704\) | 8.82835 | 0.332731 | ||||||||
\(705\) | 11.7088 | 0.440981 | ||||||||
\(706\) | −18.9476 | −0.713103 | ||||||||
\(707\) | −16.0258 | −0.602712 | ||||||||
\(708\) | 16.1533 | 0.607079 | ||||||||
\(709\) | 21.3801 | 0.802945 | 0.401472 | − | 0.915871i | \(-0.368499\pi\) | ||||
0.401472 | + | 0.915871i | \(0.368499\pi\) | |||||||
\(710\) | −4.57279 | −0.171614 | ||||||||
\(711\) | −62.2431 | −2.33430 | ||||||||
\(712\) | 9.91053 | 0.371413 | ||||||||
\(713\) | 62.8931 | 2.35537 | ||||||||
\(714\) | 0.106977 | 0.00400352 | ||||||||
\(715\) | −2.08918 | −0.0781310 | ||||||||
\(716\) | −17.8667 | −0.667710 | ||||||||
\(717\) | −45.6100 | −1.70334 | ||||||||
\(718\) | 22.0540 | 0.823050 | ||||||||
\(719\) | −41.8105 | −1.55927 | −0.779634 | − | 0.626235i | \(-0.784595\pi\) | ||||
−0.779634 | + | 0.626235i | \(0.784595\pi\) | |||||||
\(720\) | 1.94457 | 0.0724700 | ||||||||
\(721\) | −40.6133 | −1.51252 | ||||||||
\(722\) | −12.4496 | −0.463327 | ||||||||
\(723\) | −8.46873 | −0.314955 | ||||||||
\(724\) | −17.6525 | −0.656050 | ||||||||
\(725\) | −7.77249 | −0.288663 | ||||||||
\(726\) | 22.5998 | 0.838757 | ||||||||
\(727\) | −26.7352 | −0.991554 | −0.495777 | − | 0.868450i | \(-0.665117\pi\) | ||||
−0.495777 | + | 0.868450i | \(0.665117\pi\) | |||||||
\(728\) | −11.3099 | −0.419174 | ||||||||
\(729\) | −39.2073 | −1.45212 | ||||||||
\(730\) | 15.4985 | 0.573625 | ||||||||
\(731\) | 0.0537709 | 0.00198879 | ||||||||
\(732\) | −17.1601 | −0.634254 | ||||||||
\(733\) | 13.5766 | 0.501462 | 0.250731 | − | 0.968057i | \(-0.419329\pi\) | ||||
0.250731 | + | 0.968057i | \(0.419329\pi\) | |||||||
\(734\) | 26.7087 | 0.985837 | ||||||||
\(735\) | 16.9323 | 0.624556 | ||||||||
\(736\) | −42.4585 | −1.56504 | ||||||||
\(737\) | 5.62039 | 0.207030 | ||||||||
\(738\) | −8.46946 | −0.311765 | ||||||||
\(739\) | −32.9194 | −1.21096 | −0.605481 | − | 0.795860i | \(-0.707019\pi\) | ||||
−0.605481 | + | 0.795860i | \(0.707019\pi\) | |||||||
\(740\) | −12.2652 | −0.450878 | ||||||||
\(741\) | −7.58964 | −0.278812 | ||||||||
\(742\) | 6.60204 | 0.242368 | ||||||||
\(743\) | −29.9445 | −1.09856 | −0.549278 | − | 0.835640i | \(-0.685097\pi\) | ||||
−0.549278 | + | 0.835640i | \(0.685097\pi\) | |||||||
\(744\) | −68.2556 | −2.50237 | ||||||||
\(745\) | 5.48053 | 0.200791 | ||||||||
\(746\) | 4.62812 | 0.169447 | ||||||||
\(747\) | 65.2298 | 2.38663 | ||||||||
\(748\) | 0.0213781 | 0.000781661 0 | ||||||||
\(749\) | −48.3319 | −1.76601 | ||||||||
\(750\) | −26.8415 | −0.980113 | ||||||||
\(751\) | −7.68814 | −0.280544 | −0.140272 | − | 0.990113i | \(-0.544798\pi\) | ||||
−0.140272 | + | 0.990113i | \(0.544798\pi\) | |||||||
\(752\) | −1.04919 | −0.0382601 | ||||||||
\(753\) | −15.6845 | −0.571574 | ||||||||
\(754\) | 2.22334 | 0.0809692 | ||||||||
\(755\) | −4.78248 | −0.174052 | ||||||||
\(756\) | 27.9518 | 1.01660 | ||||||||
\(757\) | −19.4003 | −0.705116 | −0.352558 | − | 0.935790i | \(-0.614688\pi\) | ||||
−0.352558 | + | 0.935790i | \(0.614688\pi\) | |||||||
\(758\) | 6.41897 | 0.233148 | ||||||||
\(759\) | 35.0201 | 1.27115 | ||||||||
\(760\) | 7.89104 | 0.286238 | ||||||||
\(761\) | 38.8358 | 1.40780 | 0.703899 | − | 0.710300i | \(-0.251441\pi\) | ||||
0.703899 | + | 0.710300i | \(0.251441\pi\) | |||||||
\(762\) | 8.08430 | 0.292863 | ||||||||
\(763\) | 14.9050 | 0.539598 | ||||||||
\(764\) | 11.6836 | 0.422696 | ||||||||
\(765\) | 0.0743413 | 0.00268781 | ||||||||
\(766\) | 18.4893 | 0.668046 | ||||||||
\(767\) | 5.40774 | 0.195262 | ||||||||
\(768\) | 48.1466 | 1.73734 | ||||||||
\(769\) | −4.94505 | −0.178323 | −0.0891616 | − | 0.996017i | \(-0.528419\pi\) | ||||
−0.0891616 | + | 0.996017i | \(0.528419\pi\) | |||||||
\(770\) | −5.82991 | −0.210095 | ||||||||
\(771\) | 15.7270 | 0.566394 | ||||||||
\(772\) | −15.1220 | −0.544252 | ||||||||
\(773\) | −13.1002 | −0.471183 | −0.235592 | − | 0.971852i | \(-0.575703\pi\) | ||||
−0.235592 | + | 0.971852i | \(0.575703\pi\) | |||||||
\(774\) | −22.6272 | −0.813319 | ||||||||
\(775\) | 29.4285 | 1.05710 | ||||||||
\(776\) | 42.4241 | 1.52294 | ||||||||
\(777\) | 89.3563 | 3.20564 | ||||||||
\(778\) | −17.9368 | −0.643064 | ||||||||
\(779\) | −3.98462 | −0.142764 | ||||||||
\(780\) | −4.50653 | −0.161360 | ||||||||
\(781\) | 6.65748 | 0.238223 | ||||||||
\(782\) | 0.0824016 | 0.00294668 | ||||||||
\(783\) | −14.9153 | −0.533031 | ||||||||
\(784\) | −1.51725 | −0.0541874 | ||||||||
\(785\) | −15.9721 | −0.570069 | ||||||||
\(786\) | −25.8675 | −0.922662 | ||||||||
\(787\) | −28.6833 | −1.02245 | −0.511224 | − | 0.859447i | \(-0.670808\pi\) | ||||
−0.511224 | + | 0.859447i | \(0.670808\pi\) | |||||||
\(788\) | −9.60079 | −0.342014 | ||||||||
\(789\) | 23.9674 | 0.853263 | ||||||||
\(790\) | 12.4223 | 0.441965 | ||||||||
\(791\) | −8.98055 | −0.319312 | ||||||||
\(792\) | −24.4192 | −0.867699 | ||||||||
\(793\) | −5.74477 | −0.204003 | ||||||||
\(794\) | 2.03851 | 0.0723439 | ||||||||
\(795\) | 7.14065 | 0.253253 | ||||||||
\(796\) | 7.47536 | 0.264957 | ||||||||
\(797\) | −14.3201 | −0.507242 | −0.253621 | − | 0.967304i | \(-0.581622\pi\) | ||||
−0.253621 | + | 0.967304i | \(0.581622\pi\) | |||||||
\(798\) | −21.1790 | −0.749730 | ||||||||
\(799\) | −0.0401108 | −0.00141902 | ||||||||
\(800\) | −19.8669 | −0.702401 | ||||||||
\(801\) | −18.4845 | −0.653118 | ||||||||
\(802\) | 23.2501 | 0.820989 | ||||||||
\(803\) | −22.5641 | −0.796270 | ||||||||
\(804\) | 12.1236 | 0.427567 | ||||||||
\(805\) | 31.4536 | 1.10859 | ||||||||
\(806\) | −8.41810 | −0.296515 | ||||||||
\(807\) | −11.4199 | −0.402000 | ||||||||
\(808\) | 13.3967 | 0.471296 | ||||||||
\(809\) | 14.6335 | 0.514486 | 0.257243 | − | 0.966347i | \(-0.417186\pi\) | ||||
0.257243 | + | 0.966347i | \(0.417186\pi\) | |||||||
\(810\) | −4.19262 | −0.147314 | ||||||||
\(811\) | −5.35024 | −0.187872 | −0.0939362 | − | 0.995578i | \(-0.529945\pi\) | ||||
−0.0939362 | + | 0.995578i | \(0.529945\pi\) | |||||||
\(812\) | −8.68427 | −0.304758 | ||||||||
\(813\) | −57.5663 | −2.01894 | ||||||||
\(814\) | −12.7574 | −0.447145 | ||||||||
\(815\) | 28.8553 | 1.01076 | ||||||||
\(816\) | −0.0103679 | −0.000362950 0 | ||||||||
\(817\) | −10.6454 | −0.372436 | ||||||||
\(818\) | 27.5389 | 0.962874 | ||||||||
\(819\) | 21.0946 | 0.737106 | ||||||||
\(820\) | −2.36596 | −0.0826230 | ||||||||
\(821\) | −7.30505 | −0.254948 | −0.127474 | − | 0.991842i | \(-0.540687\pi\) | ||||
−0.127474 | + | 0.991842i | \(0.540687\pi\) | |||||||
\(822\) | 4.47666 | 0.156142 | ||||||||
\(823\) | −19.2893 | −0.672383 | −0.336192 | − | 0.941794i | \(-0.609139\pi\) | ||||
−0.336192 | + | 0.941794i | \(0.609139\pi\) | |||||||
\(824\) | 33.9506 | 1.18273 | ||||||||
\(825\) | 16.3864 | 0.570501 | ||||||||
\(826\) | 15.0904 | 0.525063 | ||||||||
\(827\) | 7.82472 | 0.272092 | 0.136046 | − | 0.990703i | \(-0.456561\pi\) | ||||
0.136046 | + | 0.990703i | \(0.456561\pi\) | |||||||
\(828\) | 48.5358 | 1.68674 | ||||||||
\(829\) | 26.6166 | 0.924432 | 0.462216 | − | 0.886767i | \(-0.347054\pi\) | ||||
0.462216 | + | 0.886767i | \(0.347054\pi\) | |||||||
\(830\) | −13.0184 | −0.451874 | ||||||||
\(831\) | 82.5417 | 2.86334 | ||||||||
\(832\) | 6.37528 | 0.221023 | ||||||||
\(833\) | −0.0580045 | −0.00200974 | ||||||||
\(834\) | −0.556954 | −0.0192857 | ||||||||
\(835\) | −16.6984 | −0.577873 | ||||||||
\(836\) | −4.23238 | −0.146380 | ||||||||
\(837\) | 56.4731 | 1.95200 | ||||||||
\(838\) | −26.2509 | −0.906823 | ||||||||
\(839\) | 48.8846 | 1.68768 | 0.843842 | − | 0.536591i | \(-0.180288\pi\) | ||||
0.843842 | + | 0.536591i | \(0.180288\pi\) | |||||||
\(840\) | −34.1354 | −1.17778 | ||||||||
\(841\) | −24.3660 | −0.840207 | ||||||||
\(842\) | −12.2579 | −0.422433 | ||||||||
\(843\) | 89.8583 | 3.09489 | ||||||||
\(844\) | 0.611240 | 0.0210397 | ||||||||
\(845\) | 13.8147 | 0.475239 | ||||||||
\(846\) | 16.8789 | 0.580310 | ||||||||
\(847\) | −29.5519 | −1.01542 | ||||||||
\(848\) | −0.639852 | −0.0219726 | ||||||||
\(849\) | −91.3011 | −3.13345 | ||||||||
\(850\) | 0.0385568 | 0.00132249 | ||||||||
\(851\) | 68.8287 | 2.35942 | ||||||||
\(852\) | 14.3607 | 0.491990 | ||||||||
\(853\) | 10.6286 | 0.363915 | 0.181957 | − | 0.983306i | \(-0.441757\pi\) | ||||
0.181957 | + | 0.983306i | \(0.441757\pi\) | |||||||
\(854\) | −16.0309 | −0.548566 | ||||||||
\(855\) | −14.7179 | −0.503341 | ||||||||
\(856\) | 40.4030 | 1.38095 | ||||||||
\(857\) | −8.99177 | −0.307153 | −0.153577 | − | 0.988137i | \(-0.549079\pi\) | ||||
−0.153577 | + | 0.988137i | \(0.549079\pi\) | |||||||
\(858\) | −4.68736 | −0.160024 | ||||||||
\(859\) | 23.6253 | 0.806086 | 0.403043 | − | 0.915181i | \(-0.367953\pi\) | ||||
0.403043 | + | 0.915181i | \(0.367953\pi\) | |||||||
\(860\) | −6.32097 | −0.215543 | ||||||||
\(861\) | 17.2369 | 0.587431 | ||||||||
\(862\) | 26.1210 | 0.889686 | ||||||||
\(863\) | 34.7106 | 1.18156 | 0.590781 | − | 0.806832i | \(-0.298820\pi\) | ||||
0.590781 | + | 0.806832i | \(0.298820\pi\) | |||||||
\(864\) | −38.1244 | −1.29702 | ||||||||
\(865\) | 13.4494 | 0.457294 | ||||||||
\(866\) | −13.5324 | −0.459850 | ||||||||
\(867\) | 49.2463 | 1.67249 | ||||||||
\(868\) | 32.8807 | 1.11605 | ||||||||
\(869\) | −18.0855 | −0.613508 | ||||||||
\(870\) | 6.71044 | 0.227505 | ||||||||
\(871\) | 4.05869 | 0.137524 | ||||||||
\(872\) | −12.4598 | −0.421943 | ||||||||
\(873\) | −79.1268 | −2.67804 | ||||||||
\(874\) | −16.3136 | −0.551817 | ||||||||
\(875\) | 35.0985 | 1.18655 | ||||||||
\(876\) | −48.6725 | −1.64449 | ||||||||
\(877\) | 34.6146 | 1.16885 | 0.584426 | − | 0.811447i | \(-0.301320\pi\) | ||||
0.584426 | + | 0.811447i | \(0.301320\pi\) | |||||||
\(878\) | −1.24081 | −0.0418754 | ||||||||
\(879\) | 31.3425 | 1.05716 | ||||||||
\(880\) | 0.565019 | 0.0190468 | ||||||||
\(881\) | 6.82337 | 0.229885 | 0.114943 | − | 0.993372i | \(-0.463332\pi\) | ||||
0.114943 | + | 0.993372i | \(0.463332\pi\) | |||||||
\(882\) | 24.4088 | 0.821886 | ||||||||
\(883\) | 38.3041 | 1.28904 | 0.644519 | − | 0.764589i | \(-0.277058\pi\) | ||||
0.644519 | + | 0.764589i | \(0.277058\pi\) | |||||||
\(884\) | 0.0154379 | 0.000519234 0 | ||||||||
\(885\) | 16.3215 | 0.548643 | ||||||||
\(886\) | 6.47063 | 0.217385 | ||||||||
\(887\) | −31.7409 | −1.06575 | −0.532877 | − | 0.846193i | \(-0.678889\pi\) | ||||
−0.532877 | + | 0.846193i | \(0.678889\pi\) | |||||||
\(888\) | −74.6973 | −2.50668 | ||||||||
\(889\) | −10.5712 | −0.354546 | ||||||||
\(890\) | 3.68908 | 0.123658 | ||||||||
\(891\) | 6.10400 | 0.204492 | ||||||||
\(892\) | −25.0780 | −0.839675 | ||||||||
\(893\) | 7.94102 | 0.265736 | ||||||||
\(894\) | 12.2963 | 0.411250 | ||||||||
\(895\) | −18.0528 | −0.603437 | ||||||||
\(896\) | −20.2655 | −0.677024 | ||||||||
\(897\) | 25.2893 | 0.844386 | ||||||||
\(898\) | 22.1251 | 0.738323 | ||||||||
\(899\) | −17.5455 | −0.585174 | ||||||||
\(900\) | 22.7106 | 0.757019 | ||||||||
\(901\) | −0.0244616 | −0.000814934 0 | ||||||||
\(902\) | −2.46090 | −0.0819390 | ||||||||
\(903\) | 46.0505 | 1.53246 | ||||||||
\(904\) | 7.50728 | 0.249689 | ||||||||
\(905\) | −17.8363 | −0.592899 | ||||||||
\(906\) | −10.7301 | −0.356485 | ||||||||
\(907\) | 28.6943 | 0.952778 | 0.476389 | − | 0.879235i | \(-0.341945\pi\) | ||||
0.476389 | + | 0.879235i | \(0.341945\pi\) | |||||||
\(908\) | −3.48105 | −0.115523 | ||||||||
\(909\) | −24.9868 | −0.828759 | ||||||||
\(910\) | −4.20999 | −0.139560 | ||||||||
\(911\) | −16.6615 | −0.552019 | −0.276010 | − | 0.961155i | \(-0.589012\pi\) | ||||
−0.276010 | + | 0.961155i | \(0.589012\pi\) | |||||||
\(912\) | 2.05262 | 0.0679689 | ||||||||
\(913\) | 18.9533 | 0.627263 | ||||||||
\(914\) | −19.7828 | −0.654355 | ||||||||
\(915\) | −17.3388 | −0.573201 | ||||||||
\(916\) | 17.6931 | 0.584596 | ||||||||
\(917\) | 33.8248 | 1.11699 | ||||||||
\(918\) | 0.0739902 | 0.00244204 | ||||||||
\(919\) | 51.3529 | 1.69398 | 0.846989 | − | 0.531611i | \(-0.178413\pi\) | ||||
0.846989 | + | 0.531611i | \(0.178413\pi\) | |||||||
\(920\) | −26.2936 | −0.866875 | ||||||||
\(921\) | 50.2532 | 1.65590 | ||||||||
\(922\) | 33.7137 | 1.11030 | ||||||||
\(923\) | 4.80762 | 0.158245 | ||||||||
\(924\) | 18.3086 | 0.602310 | ||||||||
\(925\) | 32.2059 | 1.05892 | ||||||||
\(926\) | 21.4068 | 0.703471 | ||||||||
\(927\) | −63.3226 | −2.07979 | ||||||||
\(928\) | 11.8448 | 0.388823 | ||||||||
\(929\) | −25.9849 | −0.852536 | −0.426268 | − | 0.904597i | \(-0.640172\pi\) | ||||
−0.426268 | + | 0.904597i | \(0.640172\pi\) | |||||||
\(930\) | −25.4073 | −0.833139 | ||||||||
\(931\) | 11.4836 | 0.376359 | ||||||||
\(932\) | 26.5086 | 0.868319 | ||||||||
\(933\) | 25.4541 | 0.833328 | ||||||||
\(934\) | 3.55843 | 0.116435 | ||||||||
\(935\) | 0.0216007 | 0.000706419 0 | ||||||||
\(936\) | −17.6340 | −0.576386 | ||||||||
\(937\) | 33.1421 | 1.08271 | 0.541353 | − | 0.840795i | \(-0.317912\pi\) | ||||
0.541353 | + | 0.840795i | \(0.317912\pi\) | |||||||
\(938\) | 11.3259 | 0.369802 | ||||||||
\(939\) | −85.5760 | −2.79267 | ||||||||
\(940\) | 4.71517 | 0.153792 | ||||||||
\(941\) | 59.0258 | 1.92419 | 0.962093 | − | 0.272722i | \(-0.0879239\pi\) | ||||
0.962093 | + | 0.272722i | \(0.0879239\pi\) | |||||||
\(942\) | −35.8356 | −1.16759 | ||||||||
\(943\) | 13.2771 | 0.432362 | ||||||||
\(944\) | −1.46252 | −0.0476010 | ||||||||
\(945\) | 28.2429 | 0.918741 | ||||||||
\(946\) | −6.57461 | −0.213759 | ||||||||
\(947\) | −56.3189 | −1.83012 | −0.915059 | − | 0.403321i | \(-0.867856\pi\) | ||||
−0.915059 | + | 0.403321i | \(0.867856\pi\) | |||||||
\(948\) | −39.0118 | −1.26704 | ||||||||
\(949\) | −16.2944 | −0.528938 | ||||||||
\(950\) | −7.63337 | −0.247659 | ||||||||
\(951\) | 53.8581 | 1.74647 | ||||||||
\(952\) | 0.116937 | 0.00378995 | ||||||||
\(953\) | −36.9075 | −1.19555 | −0.597775 | − | 0.801664i | \(-0.703948\pi\) | ||||
−0.597775 | + | 0.801664i | \(0.703948\pi\) | |||||||
\(954\) | 10.2936 | 0.333269 | ||||||||
\(955\) | 11.8052 | 0.382008 | ||||||||
\(956\) | −18.3672 | −0.594039 | ||||||||
\(957\) | −9.76966 | −0.315808 | ||||||||
\(958\) | −9.53183 | −0.307959 | ||||||||
\(959\) | −5.85378 | −0.189028 | ||||||||
\(960\) | 19.2417 | 0.621025 | ||||||||
\(961\) | 35.4314 | 1.14295 | ||||||||
\(962\) | −9.21257 | −0.297025 | ||||||||
\(963\) | −75.3573 | −2.42835 | ||||||||
\(964\) | −3.41037 | −0.109841 | ||||||||
\(965\) | −15.2794 | −0.491863 | ||||||||
\(966\) | 70.5704 | 2.27057 | ||||||||
\(967\) | 51.5376 | 1.65734 | 0.828669 | − | 0.559739i | \(-0.189098\pi\) | ||||
0.828669 | + | 0.559739i | \(0.189098\pi\) | |||||||
\(968\) | 24.7039 | 0.794014 | ||||||||
\(969\) | 0.0784717 | 0.00252087 | ||||||||
\(970\) | 15.7919 | 0.507046 | ||||||||
\(971\) | 7.44496 | 0.238920 | 0.119460 | − | 0.992839i | \(-0.461884\pi\) | ||||
0.119460 | + | 0.992839i | \(0.461884\pi\) | |||||||
\(972\) | −11.0818 | −0.355450 | ||||||||
\(973\) | 0.728284 | 0.0233477 | ||||||||
\(974\) | 10.8495 | 0.347641 | ||||||||
\(975\) | 11.8332 | 0.378966 | ||||||||
\(976\) | 1.55367 | 0.0497318 | ||||||||
\(977\) | 54.1913 | 1.73373 | 0.866866 | − | 0.498541i | \(-0.166131\pi\) | ||||
0.866866 | + | 0.498541i | \(0.166131\pi\) | |||||||
\(978\) | 64.7407 | 2.07018 | ||||||||
\(979\) | −5.37089 | −0.171654 | ||||||||
\(980\) | 6.81865 | 0.217814 | ||||||||
\(981\) | 23.2393 | 0.741974 | ||||||||
\(982\) | 25.0663 | 0.799897 | ||||||||
\(983\) | −1.00000 | −0.0318950 | ||||||||
\(984\) | −14.4091 | −0.459347 | ||||||||
\(985\) | −9.70077 | −0.309092 | ||||||||
\(986\) | −0.0229878 | −0.000732081 0 | ||||||||
\(987\) | −34.3517 | −1.09343 | ||||||||
\(988\) | −3.05636 | −0.0972357 | ||||||||
\(989\) | 35.4714 | 1.12793 | ||||||||
\(990\) | −9.08976 | −0.288892 | ||||||||
\(991\) | −8.62792 | −0.274075 | −0.137037 | − | 0.990566i | \(-0.543758\pi\) | ||||
−0.137037 | + | 0.990566i | \(0.543758\pi\) | |||||||
\(992\) | −44.8471 | −1.42390 | ||||||||
\(993\) | 9.72846 | 0.308723 | ||||||||
\(994\) | 13.4157 | 0.425522 | ||||||||
\(995\) | 7.55321 | 0.239453 | ||||||||
\(996\) | 40.8837 | 1.29545 | ||||||||
\(997\) | −48.3754 | −1.53206 | −0.766032 | − | 0.642802i | \(-0.777772\pi\) | ||||
−0.766032 | + | 0.642802i | \(0.777772\pi\) | |||||||
\(998\) | 33.3346 | 1.05519 | ||||||||
\(999\) | 61.8028 | 1.95535 |
(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 | 983.2.a.a.1.20 | ✓ | 28 | |
3.2 | odd | 2 | 8847.2.a.b.1.9 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
983.2.a.a.1.20 | ✓ | 28 | 1.1 | even | 1 | trivial | |
8847.2.a.b.1.9 | 28 | 3.2 | odd | 2 |