Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4004,2,Mod(1,4004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4004, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4004 = 2^{2} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4004.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: | \(31.9721009693\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 3x^{8} - 19x^{7} + 51x^{6} + 116x^{5} - 247x^{4} - 249x^{3} + 288x^{2} + 189x - 14 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(1.32285\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4004.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.32285 | 0.763745 | 0.381873 | − | 0.924215i | \(-0.375279\pi\) | ||||
0.381873 | + | 0.924215i | \(0.375279\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.265081 | −0.118548 | −0.0592739 | − | 0.998242i | \(-0.518879\pi\) | ||||
−0.0592739 | + | 0.998242i | \(0.518879\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.25008 | −0.416693 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.350661 | −0.0905404 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.26714 | 1.52001 | 0.760003 | − | 0.649920i | \(-0.225198\pi\) | ||||
0.760003 | + | 0.649920i | \(0.225198\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.906059 | −0.207864 | −0.103932 | − | 0.994584i | \(-0.533142\pi\) | ||||
−0.103932 | + | 0.994584i | \(0.533142\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.32285 | 0.288669 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.91706 | 0.608249 | 0.304125 | − | 0.952632i | \(-0.401636\pi\) | ||||
0.304125 | + | 0.952632i | \(0.401636\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.92973 | −0.985946 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.62220 | −1.08199 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.05224 | 1.68096 | 0.840480 | − | 0.541843i | \(-0.182273\pi\) | ||||
0.840480 | + | 0.541843i | \(0.182273\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.90381 | −0.341935 | −0.170967 | − | 0.985277i | \(-0.554689\pi\) | ||||
−0.170967 | + | 0.985277i | \(0.554689\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.32285 | 0.230278 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.265081 | −0.0448069 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.42996 | −0.728280 | −0.364140 | − | 0.931344i | \(-0.618637\pi\) | ||||
−0.364140 | + | 0.931344i | \(0.618637\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.32285 | −0.211825 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.9830 | 1.71526 | 0.857632 | − | 0.514265i | \(-0.171935\pi\) | ||||
0.857632 | + | 0.514265i | \(0.171935\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.7925 | 1.79834 | 0.899169 | − | 0.437602i | \(-0.144172\pi\) | ||||
0.899169 | + | 0.437602i | \(0.144172\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.331373 | 0.0493981 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.57057 | −1.10428 | −0.552140 | − | 0.833751i | \(-0.686189\pi\) | ||||
−0.552140 | + | 0.833751i | \(0.686189\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.29046 | 1.16090 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.67340 | −1.05402 | −0.527011 | − | 0.849858i | \(-0.676687\pi\) | ||||
−0.527011 | + | 0.849858i | \(0.676687\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.265081 | −0.0357435 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.19858 | −0.158755 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.9826 | 1.42981 | 0.714904 | − | 0.699223i | \(-0.246471\pi\) | ||||
0.714904 | + | 0.699223i | \(0.246471\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.5005 | 1.34446 | 0.672228 | − | 0.740344i | \(-0.265338\pi\) | ||||
0.672228 | + | 0.740344i | \(0.265338\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.25008 | −0.157495 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.265081 | 0.0328793 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.49875 | −0.671780 | −0.335890 | − | 0.941901i | \(-0.609037\pi\) | ||||
−0.335890 | + | 0.941901i | \(0.609037\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.85882 | 0.464547 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.99897 | 0.830625 | 0.415313 | − | 0.909679i | \(-0.363672\pi\) | ||||
0.415313 | + | 0.909679i | \(0.363672\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.5064 | −1.69785 | −0.848924 | − | 0.528515i | \(-0.822749\pi\) | ||||
−0.848924 | + | 0.528515i | \(0.822749\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.52127 | −0.753012 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.79013 | 0.651440 | 0.325720 | − | 0.945466i | \(-0.394393\pi\) | ||||
0.325720 | + | 0.945466i | \(0.394393\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.68706 | −0.409673 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.5193 | −1.15464 | −0.577320 | − | 0.816518i | \(-0.695901\pi\) | ||||
−0.577320 | + | 0.816518i | \(0.695901\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.66130 | −0.180193 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 11.9747 | 1.28382 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 17.0323 | 1.80542 | 0.902709 | − | 0.430251i | \(-0.141575\pi\) | ||||
0.902709 | + | 0.430251i | \(0.141575\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | −0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.51845 | −0.261151 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.240179 | 0.0246419 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.68630 | 0.780426 | 0.390213 | − | 0.920725i | \(-0.372401\pi\) | ||||
0.390213 | + | 0.920725i | \(0.372401\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.25008 | −0.125638 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.82065 | −0.579177 | −0.289588 | − | 0.957151i | \(-0.593518\pi\) | ||||
−0.289588 | + | 0.957151i | \(0.593518\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.8559 | 1.75939 | 0.879695 | − | 0.475539i | \(-0.157747\pi\) | ||||
0.879695 | + | 0.475539i | \(0.157747\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.350661 | −0.0342210 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 18.5806 | 1.79625 | 0.898126 | − | 0.439739i | \(-0.144929\pi\) | ||||
0.898126 | + | 0.439739i | \(0.144929\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.75718 | −0.264090 | −0.132045 | − | 0.991244i | \(-0.542154\pi\) | ||||
−0.132045 | + | 0.991244i | \(0.542154\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.86015 | −0.556220 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.2154 | −0.960981 | −0.480490 | − | 0.877000i | \(-0.659541\pi\) | ||||
−0.480490 | + | 0.877000i | \(0.659541\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.773258 | −0.0721067 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.25008 | 0.115570 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.26714 | 0.574508 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 14.5289 | 1.31002 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.63218 | 0.235430 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.99069 | −0.442852 | −0.221426 | − | 0.975177i | \(-0.571071\pi\) | ||||
−0.221426 | + | 0.975177i | \(0.571071\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 15.5996 | 1.37347 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.0962 | 0.882107 | 0.441054 | − | 0.897481i | \(-0.354605\pi\) | ||||
0.441054 | + | 0.897481i | \(0.354605\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.906059 | −0.0785653 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.49034 | 0.128268 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.99537 | 0.597655 | 0.298827 | − | 0.954307i | \(-0.403405\pi\) | ||||
0.298827 | + | 0.954307i | \(0.403405\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.69846 | −0.822613 | −0.411306 | − | 0.911497i | \(-0.634927\pi\) | ||||
−0.411306 | + | 0.911497i | \(0.634927\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.0147 | −0.843389 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.00000 | −0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.39958 | −0.199274 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.32285 | 0.109106 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 20.9921 | 1.71974 | 0.859870 | − | 0.510513i | \(-0.170545\pi\) | ||||
0.859870 | + | 0.510513i | \(0.170545\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.8409 | 1.20773 | 0.603867 | − | 0.797085i | \(-0.293626\pi\) | ||||
0.603867 | + | 0.797085i | \(0.293626\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.83443 | −0.633376 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.504664 | 0.0405356 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.92728 | −0.712475 | −0.356237 | − | 0.934395i | \(-0.615941\pi\) | ||||
−0.356237 | + | 0.934395i | \(0.615941\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −10.1507 | −0.805004 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.91706 | 0.229897 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.66814 | 0.443963 | 0.221982 | − | 0.975051i | \(-0.428748\pi\) | ||||
0.221982 | + | 0.975051i | \(0.428748\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.350661 | −0.0272990 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.52644 | −0.272884 | −0.136442 | − | 0.990648i | \(-0.543567\pi\) | ||||
−0.136442 | + | 0.990648i | \(0.543567\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.13265 | 0.0866156 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −23.5914 | −1.79362 | −0.896812 | − | 0.442411i | \(-0.854123\pi\) | ||||
−0.896812 | + | 0.442411i | \(0.854123\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.92973 | −0.372653 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 14.5282 | 1.09201 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.88830 | −0.365369 | −0.182684 | − | 0.983172i | \(-0.558479\pi\) | ||||
−0.182684 | + | 0.983172i | \(0.558479\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.70984 | 0.498738 | 0.249369 | − | 0.968408i | \(-0.419777\pi\) | ||||
0.249369 | + | 0.968408i | \(0.419777\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 13.8906 | 1.02682 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.17430 | 0.0863361 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.26714 | 0.458299 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.62220 | −0.408955 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.75265 | −0.633319 | −0.316660 | − | 0.948539i | \(-0.602561\pi\) | ||||
−0.316660 | + | 0.948539i | \(0.602561\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.95829 | −0.716813 | −0.358407 | − | 0.933566i | \(-0.616680\pi\) | ||||
−0.358407 | + | 0.933566i | \(0.616680\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.350661 | 0.0251114 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.55983 | 0.538615 | 0.269308 | − | 0.963054i | \(-0.413205\pi\) | ||||
0.269308 | + | 0.963054i | \(0.413205\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.50958 | −0.177899 | −0.0889497 | − | 0.996036i | \(-0.528351\pi\) | ||||
−0.0889497 | + | 0.996036i | \(0.528351\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.27400 | −0.513068 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.05224 | 0.635343 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.91140 | −0.203341 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.64656 | −0.253453 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.906059 | −0.0626734 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.4873 | 1.47924 | 0.739622 | − | 0.673023i | \(-0.235004\pi\) | ||||
0.739622 | + | 0.673023i | \(0.235004\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.25856 | 0.634386 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.12597 | −0.213189 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.90381 | −0.129239 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −19.1898 | −1.29672 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.26714 | −0.421574 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.2219 | 1.08630 | 0.543150 | − | 0.839635i | \(-0.317231\pi\) | ||||
0.543150 | + | 0.839635i | \(0.317231\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.16256 | 0.410837 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −19.8036 | −1.31441 | −0.657207 | − | 0.753710i | \(-0.728262\pi\) | ||||
−0.657207 | + | 0.753710i | \(0.728262\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.1527 | 0.935240 | 0.467620 | − | 0.883930i | \(-0.345112\pi\) | ||||
0.467620 | + | 0.883930i | \(0.345112\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.32285 | 0.0870368 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.56928 | −0.626904 | −0.313452 | − | 0.949604i | \(-0.601486\pi\) | ||||
−0.313452 | + | 0.949604i | \(0.601486\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.00681 | 0.130910 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 7.65944 | 0.497534 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −22.2425 | −1.43875 | −0.719374 | − | 0.694623i | \(-0.755571\pi\) | ||||
−0.719374 | + | 0.694623i | \(0.755571\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.94928 | −0.640889 | −0.320445 | − | 0.947267i | \(-0.603832\pi\) | ||||
−0.320445 | + | 0.947267i | \(0.603832\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.9892 | 0.769107 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.265081 | −0.0169354 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.906059 | 0.0576511 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −13.9154 | −0.881850 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.4389 | −0.722017 | −0.361008 | − | 0.932563i | \(-0.617567\pi\) | ||||
−0.361008 | + | 0.932563i | \(0.617567\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.91706 | 0.183394 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.19765 | −0.137622 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 16.8781 | 1.05282 | 0.526412 | − | 0.850229i | \(-0.323537\pi\) | ||||
0.526412 | + | 0.850229i | \(0.323537\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.42996 | −0.275264 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −11.3160 | −0.700445 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −24.5628 | −1.51461 | −0.757305 | − | 0.653061i | \(-0.773484\pi\) | ||||
−0.757305 | + | 0.653061i | \(0.773484\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.03407 | 0.124952 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 22.5311 | 1.37888 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 26.0062 | 1.58562 | 0.792812 | − | 0.609466i | \(-0.208616\pi\) | ||||
0.792812 | + | 0.609466i | \(0.208616\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.47841 | −0.393536 | −0.196768 | − | 0.980450i | \(-0.563045\pi\) | ||||
−0.196768 | + | 0.980450i | \(0.563045\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.32285 | −0.0800622 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.92973 | −0.297274 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.37897 | 0.263107 | 0.131553 | − | 0.991309i | \(-0.458004\pi\) | ||||
0.131553 | + | 0.991309i | \(0.458004\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.37992 | 0.142482 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −21.2357 | −1.26681 | −0.633407 | − | 0.773819i | \(-0.718344\pi\) | ||||
−0.633407 | + | 0.773819i | \(0.718344\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.25664 | −0.253031 | −0.126515 | − | 0.991965i | \(-0.540379\pi\) | ||||
−0.126515 | + | 0.991965i | \(0.540379\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.317720 | 0.0188201 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.9830 | 0.648308 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 22.2771 | 1.31042 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.1678 | 0.596046 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −15.6572 | −0.914706 | −0.457353 | − | 0.889285i | \(-0.651202\pi\) | ||||
−0.457353 | + | 0.889285i | \(0.651202\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.91127 | −0.169501 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.62220 | −0.326233 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.91706 | −0.168698 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.7925 | 0.679708 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −7.69983 | −0.442343 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.78349 | −0.159382 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.9546 | 1.48131 | 0.740654 | − | 0.671886i | \(-0.234516\pi\) | ||||
0.740654 | + | 0.671886i | \(0.234516\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 23.6205 | 1.34373 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −19.7324 | −1.11892 | −0.559461 | − | 0.828857i | \(-0.688992\pi\) | ||||
−0.559461 | + | 0.828857i | \(0.688992\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.5661 | 0.597229 | 0.298614 | − | 0.954374i | \(-0.403476\pi\) | ||||
0.298614 | + | 0.954374i | \(0.403476\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.331373 | 0.0186707 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 24.9493 | 1.40129 | 0.700646 | − | 0.713509i | \(-0.252895\pi\) | ||||
0.700646 | + | 0.713509i | \(0.252895\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.05224 | 0.506828 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 24.5792 | 1.37188 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.67840 | −0.315955 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.92973 | 0.273452 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.64733 | −0.201698 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.57057 | −0.417379 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.6362 | −1.07931 | −0.539653 | − | 0.841888i | \(-0.681444\pi\) | ||||
−0.539653 | + | 0.841888i | \(0.681444\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.53780 | 0.303470 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.45762 | 0.0796381 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.6678 | 0.962425 | 0.481212 | − | 0.876604i | \(-0.340197\pi\) | ||||
0.481212 | + | 0.876604i | \(0.340197\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −13.5134 | −0.733945 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.90381 | −0.103097 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.02290 | −0.0550711 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.63288 | 0.409754 | 0.204877 | − | 0.978788i | \(-0.434321\pi\) | ||||
0.204877 | + | 0.978788i | \(0.434321\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −13.6761 | −0.732066 | −0.366033 | − | 0.930602i | \(-0.619284\pi\) | ||||
−0.366033 | + | 0.930602i | \(0.619284\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.62220 | 0.300091 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.1251 | 0.751805 | 0.375902 | − | 0.926659i | \(-0.377333\pi\) | ||||
0.375902 | + | 0.926659i | \(0.377333\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.85530 | −0.0984689 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 8.29046 | 0.438778 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −18.0695 | −0.953670 | −0.476835 | − | 0.878993i | \(-0.658216\pi\) | ||||
−0.476835 | + | 0.878993i | \(0.658216\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.1791 | −0.956793 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.32285 | 0.0694314 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.84538 | 0.201276 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.7815 | 0.719389 | 0.359694 | − | 0.933070i | \(-0.382881\pi\) | ||||
0.359694 | + | 0.933070i | \(0.382881\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −13.7297 | −0.714739 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.67340 | −0.398383 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 31.1620 | 1.61350 | 0.806752 | − | 0.590890i | \(-0.201223\pi\) | ||||
0.806752 | + | 0.590890i | \(0.201223\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.48197 | 0.179808 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.05224 | −0.466214 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.7474 | −0.962990 | −0.481495 | − | 0.876449i | \(-0.659906\pi\) | ||||
−0.481495 | + | 0.876449i | \(0.659906\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.60191 | −0.338226 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −27.1478 | −1.38719 | −0.693593 | − | 0.720367i | \(-0.743973\pi\) | ||||
−0.693593 | + | 0.720367i | \(0.743973\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.265081 | −0.0135098 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −14.7416 | −0.749355 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −30.3823 | −1.54045 | −0.770223 | − | 0.637775i | \(-0.779855\pi\) | ||||
−0.770223 | + | 0.637775i | \(0.779855\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.2816 | 0.924542 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 13.3557 | 0.673705 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.53485 | −0.0772269 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −28.3928 | −1.42499 | −0.712497 | − | 0.701675i | \(-0.752436\pi\) | ||||
−0.712497 | + | 0.701675i | \(0.752436\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.19858 | −0.0600038 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.3809 | 0.518396 | 0.259198 | − | 0.965824i | \(-0.416542\pi\) | ||||
0.259198 | + | 0.965824i | \(0.416542\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.90381 | 0.0948356 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.977370 | 0.0485659 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.42996 | −0.219585 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.29337 | −0.360634 | −0.180317 | − | 0.983609i | \(-0.557712\pi\) | ||||
−0.180317 | + | 0.983609i | \(0.557712\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.25379 | 0.456456 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 10.9826 | 0.540416 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.78846 | 0.136880 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −12.8296 | −0.628266 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.70466 | 0.474104 | 0.237052 | − | 0.971497i | \(-0.423819\pi\) | ||||
0.237052 | + | 0.971497i | \(0.423819\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.4760 | 0.608042 | 0.304021 | − | 0.952665i | \(-0.401671\pi\) | ||||
0.304021 | + | 0.952665i | \(0.401671\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9.46382 | 0.460146 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −30.8953 | −1.49864 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.5005 | 0.508156 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.32285 | −0.0638676 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.80807 | −0.231597 | −0.115798 | − | 0.993273i | \(-0.536943\pi\) | ||||
−0.115798 | + | 0.993273i | \(0.536943\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.5011 | 0.889105 | 0.444552 | − | 0.895753i | \(-0.353363\pi\) | ||||
0.444552 | + | 0.895753i | \(0.353363\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.17427 | −0.152195 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.64303 | −0.126433 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.91267 | 0.329924 | 0.164962 | − | 0.986300i | \(-0.447250\pi\) | ||||
0.164962 | + | 0.986300i | \(0.447250\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.25008 | −0.0595276 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.8863 | −0.612247 | −0.306123 | − | 0.951992i | \(-0.599032\pi\) | ||||
−0.306123 | + | 0.951992i | \(0.599032\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.51494 | −0.214029 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 27.7693 | 1.31344 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.73958 | 0.129289 | 0.0646445 | − | 0.997908i | \(-0.479409\pi\) | ||||
0.0646445 | + | 0.997908i | \(0.479409\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.9830 | 0.517171 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 19.6322 | 0.922401 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.265081 | 0.0124272 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −25.7361 | −1.20388 | −0.601941 | − | 0.798540i | \(-0.705606\pi\) | ||||
−0.601941 | + | 0.798540i | \(0.705606\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −35.2351 | −1.64463 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.15202 | 0.0536551 | 0.0268275 | − | 0.999640i | \(-0.491460\pi\) | ||||
0.0268275 | + | 0.999640i | \(0.491460\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.60927 | 0.353633 | 0.176816 | − | 0.984244i | \(-0.443420\pi\) | ||||
0.176816 | + | 0.984244i | \(0.443420\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.667593 | 0.0309589 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −22.9299 | −1.06107 | −0.530536 | − | 0.847663i | \(-0.678009\pi\) | ||||
−0.530536 | + | 0.847663i | \(0.678009\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.49875 | −0.253909 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11.8094 | −0.544149 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11.7925 | 0.542219 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.46663 | 0.204943 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.59236 | 0.439204 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.7410 | 0.536461 | 0.268230 | − | 0.963355i | \(-0.413561\pi\) | ||||
0.268230 | + | 0.963355i | \(0.413561\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.42996 | 0.201989 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.85882 | 0.175582 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.03749 | −0.0925178 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.5378 | −0.522826 | −0.261413 | − | 0.965227i | \(-0.584188\pi\) | ||||
−0.261413 | + | 0.965227i | \(0.584188\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.49807 | 0.339075 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 25.5592 | 1.15347 | 0.576735 | − | 0.816931i | \(-0.304327\pi\) | ||||
0.576735 | + | 0.816931i | \(0.304327\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 56.7317 | 2.55507 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.331373 | 0.0148941 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.99897 | 0.313947 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.8716 | −0.486678 | −0.243339 | − | 0.969941i | \(-0.578243\pi\) | ||||
−0.243339 | + | 0.969941i | \(0.578243\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.66494 | −0.208414 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −39.0853 | −1.74273 | −0.871363 | − | 0.490639i | \(-0.836763\pi\) | ||||
−0.871363 | + | 0.490639i | \(0.836763\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.54295 | 0.0686602 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.32285 | 0.0587496 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −26.8541 | −1.19029 | −0.595144 | − | 0.803619i | \(-0.702905\pi\) | ||||
−0.595144 | + | 0.803619i | \(0.702905\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.5064 | −0.641726 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.09404 | 0.224907 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.73325 | −0.208572 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.57057 | −0.332953 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −31.2078 | −1.36987 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.50250 | −0.372501 | −0.186251 | − | 0.982502i | \(-0.559634\pi\) | ||||
−0.186251 | + | 0.982502i | \(0.559634\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 36.3165 | 1.58801 | 0.794005 | − | 0.607911i | \(-0.207992\pi\) | ||||
0.794005 | + | 0.607911i | \(0.207992\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.52127 | −0.284612 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −11.9315 | −0.519742 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.4908 | −0.630033 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −13.7291 | −0.595791 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10.9830 | −0.475728 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.92536 | −0.212942 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.46647 | −0.279049 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.05641 | 0.174398 | 0.0871992 | − | 0.996191i | \(-0.472208\pi\) | ||||
0.0871992 | + | 0.996191i | \(0.472208\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.87608 | 0.380909 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.730877 | 0.0313073 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.9673 | −0.682712 | −0.341356 | − | 0.939934i | \(-0.610886\pi\) | ||||
−0.341356 | + | 0.939934i | \(0.610886\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −13.1265 | −0.560226 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.20187 | −0.349411 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.79013 | 0.246221 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.55341 | 0.0659388 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9.45131 | −0.400465 | −0.200232 | − | 0.979748i | \(-0.564170\pi\) | ||||
−0.200232 | + | 0.979748i | \(0.564170\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11.7925 | −0.498769 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.29046 | 0.350024 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 22.6366 | 0.954019 | 0.477010 | − | 0.878898i | \(-0.341721\pi\) | ||||
0.477010 | + | 0.878898i | \(0.341721\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.70790 | 0.113922 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.68706 | −0.154842 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12.0891 | 0.506803 | 0.253401 | − | 0.967361i | \(-0.418451\pi\) | ||||
0.253401 | + | 0.967361i | \(0.418451\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −23.8055 | −0.996231 | −0.498115 | − | 0.867111i | \(-0.665974\pi\) | ||||
−0.498115 | + | 0.867111i | \(0.665974\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −11.5784 | −0.483695 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −14.3803 | −0.599701 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 32.5932 | 1.35687 | 0.678436 | − | 0.734660i | \(-0.262658\pi\) | ||||
0.678436 | + | 0.734660i | \(0.262658\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −13.1733 | −0.547463 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.5193 | −0.436413 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.67340 | −0.317800 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.331373 | −0.0137006 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.932270 | 0.0384789 | 0.0192394 | − | 0.999815i | \(-0.493876\pi\) | ||||
0.0192394 | + | 0.999815i | \(0.493876\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.72496 | 0.0710759 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 10.0005 | 0.411365 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 27.2128 | 1.11750 | 0.558748 | − | 0.829338i | \(-0.311282\pi\) | ||||
0.558748 | + | 0.829338i | \(0.311282\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.66130 | −0.0681067 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3.31979 | −0.135870 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −20.7953 | −0.849674 | −0.424837 | − | 0.905270i | \(-0.639669\pi\) | ||||
−0.424837 | + | 0.905270i | \(0.639669\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 35.5409 | 1.44974 | 0.724871 | − | 0.688884i | \(-0.241899\pi\) | ||||
0.724871 | + | 0.688884i | \(0.241899\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.87388 | 0.279926 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.265081 | −0.0107771 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −26.6990 | −1.08368 | −0.541839 | − | 0.840482i | \(-0.682272\pi\) | ||||
−0.541839 | + | 0.840482i | \(0.682272\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 11.9747 | 0.485240 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.57057 | 0.306272 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −36.0041 | −1.45419 | −0.727095 | − | 0.686537i | \(-0.759130\pi\) | ||||
−0.727095 | + | 0.686537i | \(0.759130\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.85133 | −0.155301 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17.5314 | −0.705790 | −0.352895 | − | 0.935663i | \(-0.614803\pi\) | ||||
−0.352895 | + | 0.935663i | \(0.614803\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19.7846 | −0.795211 | −0.397606 | − | 0.917556i | \(-0.630159\pi\) | ||||
−0.397606 | + | 0.917556i | \(0.630159\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −16.4003 | −0.658121 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 17.0323 | 0.682384 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.9509 | 0.958037 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.19858 | −0.0478665 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −27.7632 | −1.10699 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28.2437 | 1.12437 | 0.562183 | − | 0.827013i | \(-0.309962\pi\) | ||||
0.562183 | + | 0.827013i | \(0.309962\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 28.4243 | 1.12976 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.32294 | 0.0524992 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.74928 | −0.346116 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 31.9757 | 1.26296 | 0.631482 | − | 0.775391i | \(-0.282447\pi\) | ||||
0.631482 | + | 0.775391i | \(0.282447\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22.5812 | −0.890514 | −0.445257 | − | 0.895403i | \(-0.646888\pi\) | ||||
−0.445257 | + | 0.895403i | \(0.646888\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.13517 | −0.162822 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.39460 | −0.133456 | −0.0667278 | − | 0.997771i | \(-0.521256\pi\) | ||||
−0.0667278 | + | 0.997771i | \(0.521256\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.9826 | 0.431103 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.51845 | −0.0987057 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.23714 | 0.283211 | 0.141606 | − | 0.989923i | \(-0.454774\pi\) | ||||
0.141606 | + | 0.989923i | \(0.454774\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.67631 | −0.104572 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 18.1342 | 0.707482 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21.5392 | 0.839047 | 0.419524 | − | 0.907744i | \(-0.362197\pi\) | ||||
0.419524 | + | 0.907744i | \(0.362197\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −37.8960 | −1.47398 | −0.736991 | − | 0.675903i | \(-0.763754\pi\) | ||||
−0.736991 | + | 0.675903i | \(0.763754\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −8.29046 | −0.321975 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.240179 | 0.00931375 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 26.4060 | 1.02244 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 21.4591 | 0.829657 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.5005 | 0.405369 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.3029 | −0.628430 | −0.314215 | − | 0.949352i | \(-0.601741\pi\) | ||||
−0.314215 | + | 0.949352i | \(0.601741\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 27.7159 | 1.06679 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 24.1809 | 0.929346 | 0.464673 | − | 0.885482i | \(-0.346172\pi\) | ||||
0.464673 | + | 0.885482i | \(0.346172\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.68630 | 0.294973 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −26.1972 | −1.00388 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −25.9657 | −0.993548 | −0.496774 | − | 0.867880i | \(-0.665482\pi\) | ||||
−0.496774 | + | 0.867880i | \(0.665482\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.85434 | −0.0708507 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 18.7219 | 0.714285 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.67340 | 0.292333 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15.5423 | −0.591256 | −0.295628 | − | 0.955303i | \(-0.595529\pi\) | ||||
−0.295628 | + | 0.955303i | \(0.595529\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.25008 | −0.0474866 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.57088 | 0.0975190 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 68.8323 | 2.60721 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −12.6587 | −0.478795 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 47.6404 | 1.79935 | 0.899677 | − | 0.436556i | \(-0.143802\pi\) | ||||
0.899677 | + | 0.436556i | \(0.143802\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.01380 | 0.151383 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.65471 | 0.0999820 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.82065 | −0.218908 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.13047 | 0.0800114 | 0.0400057 | − | 0.999199i | \(-0.487262\pi\) | ||||
0.0400057 | + | 0.999199i | \(0.487262\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.23812 | −0.271451 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.55353 | −0.207981 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.265081 | 0.00991347 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −29.4234 | −1.09884 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 38.8042 | 1.44715 | 0.723576 | − | 0.690245i | \(-0.242497\pi\) | ||||
0.723576 | + | 0.690245i | \(0.242497\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 17.8559 | 0.664987 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −13.1614 | −0.489476 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −44.6251 | −1.65734 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −39.4060 | −1.46149 | −0.730744 | − | 0.682652i | \(-0.760827\pi\) | ||||
−0.730744 | + | 0.682652i | \(0.760827\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.9210 | 0.997075 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 73.9052 | 2.73348 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11.5509 | −0.426641 | −0.213320 | − | 0.976982i | \(-0.568428\pi\) | ||||
−0.213320 | + | 0.976982i | \(0.568428\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.350661 | −0.0129343 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.49875 | −0.202549 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −35.9578 | −1.32273 | −0.661365 | − | 0.750064i | \(-0.730023\pi\) | ||||
−0.661365 | + | 0.750064i | \(0.730023\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.19858 | 0.0440308 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −27.7002 | −1.01622 | −0.508111 | − | 0.861292i | \(-0.669656\pi\) | ||||
−0.508111 | + | 0.861292i | \(0.669656\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.56461 | −0.203872 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 13.1499 | 0.481131 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 18.5806 | 0.678919 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −31.4638 | −1.14813 | −0.574066 | − | 0.818809i | \(-0.694635\pi\) | ||||
−0.574066 | + | 0.818809i | \(0.694635\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −15.1319 | −0.551437 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.93404 | −0.143174 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.6973 | −0.497837 | −0.248919 | − | 0.968524i | \(-0.580075\pi\) | ||||
−0.248919 | + | 0.968524i | \(0.580075\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.85882 | 0.140066 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.3047 | 0.772296 | 0.386148 | − | 0.922437i | \(-0.373805\pi\) | ||||
0.386148 | + | 0.922437i | \(0.373805\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.75718 | −0.0998167 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.07676 | 0.0750854 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −10.9826 | −0.396557 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.9356 | −0.538590 | −0.269295 | − | 0.963058i | \(-0.586791\pi\) | ||||
−0.269295 | + | 0.963058i | \(0.586791\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 22.3271 | 0.804090 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −16.6355 | −0.598337 | −0.299168 | − | 0.954200i | \(-0.596709\pi\) | ||||
−0.299168 | + | 0.954200i | \(0.596709\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.38528 | 0.337129 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.86015 | −0.210232 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.95128 | −0.356542 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.99897 | 0.250443 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −50.8935 | −1.81879 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.36645 | 0.0844624 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.08534 | 0.252565 | 0.126283 | − | 0.991994i | \(-0.459695\pi\) | ||||
0.126283 | + | 0.991994i | \(0.459695\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −32.4928 | −1.15678 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.2154 | −0.363217 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.5005 | −0.372885 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.69076 | 0.0954315 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −34.8957 | −1.23607 | −0.618035 | − | 0.786151i | \(-0.712071\pi\) | ||||
−0.618035 | + | 0.786151i | \(0.712071\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −47.4458 | −1.67851 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −21.2917 | −0.752306 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −14.5064 | −0.511920 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.773258 | −0.0272538 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 34.4021 | 1.21101 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.58554 | 0.266693 | 0.133347 | − | 0.991069i | \(-0.457428\pi\) | ||||
0.133347 | + | 0.991069i | \(0.457428\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −26.4792 | −0.929809 | −0.464904 | − | 0.885361i | \(-0.653911\pi\) | ||||
−0.464904 | + | 0.885361i | \(0.653911\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.56994 | −0.300561 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.50252 | −0.0526309 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.6847 | −0.373810 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.25008 | 0.0436813 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −43.6089 | −1.52196 | −0.760981 | − | 0.648775i | \(-0.775282\pi\) | ||||
−0.760981 | + | 0.648775i | \(0.775282\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −31.0230 | −1.08139 | −0.540697 | − | 0.841217i | \(-0.681840\pi\) | ||||
−0.540697 | + | 0.841217i | \(0.681840\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6.52127 | −0.227042 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36.6638 | 1.27493 | 0.637463 | − | 0.770481i | \(-0.279984\pi\) | ||||
0.637463 | + | 0.770481i | \(0.279984\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.77612 | −0.131150 | −0.0655750 | − | 0.997848i | \(-0.520888\pi\) | ||||
−0.0655750 | + | 0.997848i | \(0.520888\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.79270 | 0.200946 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.26714 | 0.217144 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.934793 | 0.0323499 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 10.7036 | 0.369971 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −7.89129 | −0.272437 | −0.136219 | − | 0.990679i | \(-0.543495\pi\) | ||||
−0.136219 | + | 0.990679i | \(0.543495\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 52.9431 | 1.82563 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −28.0915 | −0.967523 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.265081 | −0.00911907 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.00000 | 0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5.63087 | −0.193251 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −12.9225 | −0.442976 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.998656 | 0.0341933 | 0.0170967 | − | 0.999854i | \(-0.494558\pi\) | ||||
0.0170967 | + | 0.999854i | \(0.494558\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.300243 | −0.0102681 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12.4632 | 0.425735 | 0.212868 | − | 0.977081i | \(-0.431720\pi\) | ||||
0.212868 | + | 0.977081i | \(0.431720\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.6856 | 0.705782 | 0.352891 | − | 0.935664i | \(-0.385199\pi\) | ||||
0.352891 | + | 0.935664i | \(0.385199\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 14.5289 | 0.495142 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7.26678 | 0.247364 | 0.123682 | − | 0.992322i | \(-0.460530\pi\) | ||||
0.123682 | + | 0.992322i | \(0.460530\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.25365 | 0.212630 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 29.4691 | 1.00082 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.79013 | 0.196417 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.49875 | 0.186318 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −9.60849 | −0.325198 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.63218 | 0.0889841 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13.7870 | 0.465555 | 0.232777 | − | 0.972530i | \(-0.425219\pi\) | ||||
0.232777 | + | 0.972530i | \(0.425219\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −20.7121 | −0.698602 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 23.8073 | 0.802090 | 0.401045 | − | 0.916058i | \(-0.368647\pi\) | ||||
0.401045 | + | 0.916058i | \(0.368647\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −17.5886 | −0.591904 | −0.295952 | − | 0.955203i | \(-0.595637\pi\) | ||||
−0.295952 | + | 0.955203i | \(0.595637\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.85116 | −0.129455 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −31.6100 | −1.06136 | −0.530681 | − | 0.847572i | \(-0.678064\pi\) | ||||
−0.530681 | + | 0.847572i | \(0.678064\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.99069 | −0.167382 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.68706 | −0.123521 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.85938 | 0.229540 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.29580 | 0.0433137 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.85882 | −0.128842 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −17.2338 | −0.574778 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −48.0903 | −1.60212 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 15.5996 | 0.519123 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.77865 | −0.0591244 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −27.9021 | −0.926475 | −0.463238 | − | 0.886234i | \(-0.653312\pi\) | ||||
−0.463238 | + | 0.886234i | \(0.653312\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.27628 | 0.241339 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −39.3855 | −1.30490 | −0.652451 | − | 0.757831i | \(-0.726259\pi\) | ||||
−0.652451 | + | 0.757831i | \(0.726259\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.5193 | −0.348137 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.68213 | −0.121728 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10.0962 | 0.333405 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.67607 | −0.187236 | −0.0936182 | − | 0.995608i | \(-0.529843\pi\) | ||||
−0.0936182 | + | 0.995608i | \(0.529843\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 34.3339 | 1.13134 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6.99897 | −0.230374 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 21.8385 | 0.718045 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −22.3212 | −0.733126 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 27.0701 | 0.888142 | 0.444071 | − | 0.895992i | \(-0.353534\pi\) | ||||
0.444071 | + | 0.895992i | \(0.353534\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.906059 | −0.0296949 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −26.1029 | −0.854571 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.66130 | −0.0543304 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 35.0768 | 1.14591 | 0.572954 | − | 0.819588i | \(-0.305797\pi\) | ||||
0.572954 | + | 0.819588i | \(0.305797\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 13.9773 | 0.456131 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −16.8702 | −0.549954 | −0.274977 | − | 0.961451i | \(-0.588670\pi\) | ||||
−0.274977 | + | 0.961451i | \(0.588670\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 32.0382 | 1.04331 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.49034 | 0.0484807 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −19.6718 | −0.639247 | −0.319623 | − | 0.947545i | \(-0.603556\pi\) | ||||
−0.319623 | + | 0.947545i | \(0.603556\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14.5064 | 0.470898 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 33.0040 | 1.07023 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −50.7375 | −1.64355 | −0.821775 | − | 0.569813i | \(-0.807016\pi\) | ||||
−0.821775 | + | 0.569813i | \(0.807016\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.32016 | 0.0750787 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 11.9747 | 0.387088 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.99537 | 0.225892 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.3755 | −0.883081 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −23.2272 | −0.748486 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.63975 | 0.0849767 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −35.5690 | −1.14382 | −0.571911 | − | 0.820316i | \(-0.693798\pi\) | ||||
−0.571911 | + | 0.820316i | \(0.693798\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7.51164 | −0.241309 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 37.3057 | 1.19720 | 0.598598 | − | 0.801050i | \(-0.295725\pi\) | ||||
0.598598 | + | 0.801050i | \(0.295725\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.69846 | −0.310918 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 6.52127 | 0.208848 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −57.4095 | −1.83669 | −0.918346 | − | 0.395778i | \(-0.870475\pi\) | ||||
−0.918346 | + | 0.395778i | \(0.870475\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17.0323 | 0.544354 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.44670 | 0.110045 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.91259 | −0.124792 | −0.0623961 | − | 0.998051i | \(-0.519874\pi\) | ||||
−0.0623961 | + | 0.998051i | \(0.519874\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.00397 | −0.0638517 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −10.0147 | −0.318771 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 34.3994 | 1.09384 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 39.0959 | 1.24192 | 0.620960 | − | 0.783842i | \(-0.286743\pi\) | ||||
0.620960 | + | 0.783842i | \(0.286743\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −25.9757 | −0.824314 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.665243 | 0.0210896 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 46.0451 | 1.45826 | 0.729132 | − | 0.684373i | \(-0.239924\pi\) | ||||
0.729132 | + | 0.684373i | \(0.239924\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 24.9061 | 0.787994 |
(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 | 4004.2.a.h.1.6 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4004.2.a.h.1.6 | ✓ | 9 | 1.1 | even | 1 | trivial |