Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1521,4,Mod(1,1521)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1521, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1521.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1521 = 3^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1521.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: | \(89.7419051187\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 52x^{6} + 805x^{4} - 4210x^{2} + 4992 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 117) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.28670\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1521.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.28670 | −0.454916 | −0.227458 | − | 0.973788i | \(-0.573041\pi\) | ||||
−0.227458 | + | 0.973788i | \(0.573041\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −6.34441 | −0.793052 | ||||||||
\(5\) | −12.4484 | −1.11342 | −0.556710 | − | 0.830707i | \(-0.687937\pi\) | ||||
−0.556710 | + | 0.830707i | \(0.687937\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −9.00273 | −0.486102 | −0.243051 | − | 0.970014i | \(-0.578148\pi\) | ||||
−0.243051 | + | 0.970014i | \(0.578148\pi\) | |||||||
\(8\) | 18.4569 | 0.815687 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 16.0173 | 0.506512 | ||||||||
\(11\) | 51.0774 | 1.40004 | 0.700019 | − | 0.714124i | \(-0.253175\pi\) | ||||
0.700019 | + | 0.714124i | \(0.253175\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 11.5838 | 0.221135 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 27.0069 | 0.421983 | ||||||||
\(17\) | 6.86199 | 0.0978987 | 0.0489493 | − | 0.998801i | \(-0.484413\pi\) | ||||
0.0489493 | + | 0.998801i | \(0.484413\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −83.1170 | −1.00360 | −0.501799 | − | 0.864984i | \(-0.667328\pi\) | ||||
−0.501799 | + | 0.864984i | \(0.667328\pi\) | |||||||
\(20\) | 78.9779 | 0.883000 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −65.7211 | −0.636900 | ||||||||
\(23\) | −187.579 | −1.70056 | −0.850279 | − | 0.526332i | \(-0.823567\pi\) | ||||
−0.850279 | + | 0.526332i | \(0.823567\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 29.9631 | 0.239705 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 57.1170 | 0.385504 | ||||||||
\(29\) | 223.614 | 1.43187 | 0.715933 | − | 0.698169i | \(-0.246002\pi\) | ||||
0.715933 | + | 0.698169i | \(0.246002\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 57.3882 | 0.332491 | 0.166246 | − | 0.986084i | \(-0.446836\pi\) | ||||
0.166246 | + | 0.986084i | \(0.446836\pi\) | |||||||
\(32\) | −182.405 | −1.00765 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −8.82930 | −0.0445357 | ||||||||
\(35\) | 112.070 | 0.541236 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −156.259 | −0.694291 | −0.347146 | − | 0.937811i | \(-0.612849\pi\) | ||||
−0.347146 | + | 0.937811i | \(0.612849\pi\) | |||||||
\(38\) | 106.946 | 0.456552 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −229.759 | −0.908203 | ||||||||
\(41\) | −222.281 | −0.846695 | −0.423348 | − | 0.905967i | \(-0.639145\pi\) | ||||
−0.423348 | + | 0.905967i | \(0.639145\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 347.974 | 1.23408 | 0.617041 | − | 0.786931i | \(-0.288331\pi\) | ||||
0.617041 | + | 0.786931i | \(0.288331\pi\) | |||||||
\(44\) | −324.056 | −1.11030 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 241.357 | 0.773611 | ||||||||
\(47\) | 45.0185 | 0.139715 | 0.0698577 | − | 0.997557i | \(-0.477745\pi\) | ||||
0.0698577 | + | 0.997557i | \(0.477745\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −261.951 | −0.763705 | ||||||||
\(50\) | −38.5534 | −0.109045 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −473.516 | −1.22722 | −0.613608 | − | 0.789611i | \(-0.710282\pi\) | ||||
−0.613608 | + | 0.789611i | \(0.710282\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −635.833 | −1.55883 | ||||||||
\(56\) | −166.163 | −0.396507 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −287.724 | −0.651379 | ||||||||
\(59\) | −615.494 | −1.35814 | −0.679072 | − | 0.734071i | \(-0.737618\pi\) | ||||
−0.679072 | + | 0.734071i | \(0.737618\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 195.325 | 0.409981 | 0.204990 | − | 0.978764i | \(-0.434284\pi\) | ||||
0.204990 | + | 0.978764i | \(0.434284\pi\) | |||||||
\(62\) | −73.8412 | −0.151255 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 18.6446 | 0.0364151 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −355.097 | −0.647492 | −0.323746 | − | 0.946144i | \(-0.604942\pi\) | ||||
−0.323746 | + | 0.946144i | \(0.604942\pi\) | |||||||
\(68\) | −43.5353 | −0.0776387 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −144.200 | −0.246217 | ||||||||
\(71\) | −763.420 | −1.27608 | −0.638038 | − | 0.770005i | \(-0.720254\pi\) | ||||
−0.638038 | + | 0.770005i | \(0.720254\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 331.595 | 0.531647 | 0.265824 | − | 0.964022i | \(-0.414356\pi\) | ||||
0.265824 | + | 0.964022i | \(0.414356\pi\) | |||||||
\(74\) | 201.057 | 0.315844 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 527.329 | 0.795905 | ||||||||
\(77\) | −459.836 | −0.680561 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −207.777 | −0.295908 | −0.147954 | − | 0.988994i | \(-0.547269\pi\) | ||||
−0.147954 | + | 0.988994i | \(0.547269\pi\) | |||||||
\(80\) | −336.193 | −0.469844 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 286.008 | 0.385175 | ||||||||
\(83\) | 251.185 | 0.332183 | 0.166091 | − | 0.986110i | \(-0.446885\pi\) | ||||
0.166091 | + | 0.986110i | \(0.446885\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −85.4209 | −0.109002 | ||||||||
\(86\) | −447.737 | −0.561403 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 942.731 | 1.14199 | ||||||||
\(89\) | −719.366 | −0.856771 | −0.428385 | − | 0.903596i | \(-0.640917\pi\) | ||||
−0.428385 | + | 0.903596i | \(0.640917\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1190.08 | 1.34863 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −57.9252 | −0.0635588 | ||||||||
\(95\) | 1034.68 | 1.11743 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1556.16 | −1.62891 | −0.814454 | − | 0.580228i | \(-0.802964\pi\) | ||||
−0.814454 | + | 0.580228i | \(0.802964\pi\) | |||||||
\(98\) | 337.051 | 0.347421 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −190.098 | −0.190098 | ||||||||
\(101\) | 783.385 | 0.771779 | 0.385890 | − | 0.922545i | \(-0.373895\pi\) | ||||
0.385890 | + | 0.922545i | \(0.373895\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1033.54 | 0.988720 | 0.494360 | − | 0.869257i | \(-0.335402\pi\) | ||||
0.494360 | + | 0.869257i | \(0.335402\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 609.271 | 0.558279 | ||||||||
\(107\) | 241.358 | 0.218065 | 0.109033 | − | 0.994038i | \(-0.465225\pi\) | ||||
0.109033 | + | 0.994038i | \(0.465225\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1763.93 | 1.55003 | 0.775016 | − | 0.631941i | \(-0.217742\pi\) | ||||
0.775016 | + | 0.631941i | \(0.217742\pi\) | |||||||
\(110\) | 818.124 | 0.709137 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −243.136 | −0.205126 | ||||||||
\(113\) | −1867.83 | −1.55496 | −0.777482 | − | 0.628905i | \(-0.783503\pi\) | ||||
−0.777482 | + | 0.628905i | \(0.783503\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2335.06 | 1.89344 | ||||||||
\(116\) | −1418.70 | −1.13554 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 791.954 | 0.617841 | ||||||||
\(119\) | −61.7767 | −0.0475887 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1277.90 | 0.960108 | ||||||||
\(122\) | −251.324 | −0.186507 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −364.095 | −0.263683 | ||||||||
\(125\) | 1183.06 | 0.846528 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 238.885 | 0.166910 | 0.0834551 | − | 0.996512i | \(-0.473404\pi\) | ||||
0.0834551 | + | 0.996512i | \(0.473404\pi\) | |||||||
\(128\) | 1435.25 | 0.991088 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1158.72 | 0.772807 | 0.386403 | − | 0.922330i | \(-0.373717\pi\) | ||||
0.386403 | + | 0.922330i | \(0.373717\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 748.280 | 0.487851 | ||||||||
\(134\) | 456.902 | 0.294554 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 126.651 | 0.0798547 | ||||||||
\(137\) | 912.520 | 0.569064 | 0.284532 | − | 0.958666i | \(-0.408162\pi\) | ||||
0.284532 | + | 0.958666i | \(0.408162\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2315.04 | 1.41265 | 0.706326 | − | 0.707886i | \(-0.250351\pi\) | ||||
0.706326 | + | 0.707886i | \(0.250351\pi\) | |||||||
\(140\) | −711.017 | −0.429228 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 982.290 | 0.580507 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2783.64 | −1.59427 | ||||||||
\(146\) | −426.662 | −0.241855 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 991.370 | 0.550609 | ||||||||
\(149\) | 925.408 | 0.508808 | 0.254404 | − | 0.967098i | \(-0.418121\pi\) | ||||
0.254404 | + | 0.967098i | \(0.418121\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3523.78 | −1.89908 | −0.949541 | − | 0.313644i | \(-0.898450\pi\) | ||||
−0.949541 | + | 0.313644i | \(0.898450\pi\) | |||||||
\(152\) | −1534.08 | −0.818622 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 591.670 | 0.309598 | ||||||||
\(155\) | −714.392 | −0.370202 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1615.83 | 0.821384 | 0.410692 | − | 0.911774i | \(-0.365287\pi\) | ||||
0.410692 | + | 0.911774i | \(0.365287\pi\) | |||||||
\(158\) | 267.346 | 0.134613 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2270.65 | 1.12194 | ||||||||
\(161\) | 1688.72 | 0.826644 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1008.01 | 0.484375 | 0.242188 | − | 0.970229i | \(-0.422135\pi\) | ||||
0.242188 | + | 0.970229i | \(0.422135\pi\) | |||||||
\(164\) | 1410.24 | 0.671473 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −323.199 | −0.151115 | ||||||||
\(167\) | −2354.04 | −1.09078 | −0.545392 | − | 0.838181i | \(-0.683619\pi\) | ||||
−0.545392 | + | 0.838181i | \(0.683619\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 109.911 | 0.0495869 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2207.69 | −0.978691 | ||||||||
\(173\) | −3132.32 | −1.37657 | −0.688284 | − | 0.725442i | \(-0.741635\pi\) | ||||
−0.688284 | + | 0.725442i | \(0.741635\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −269.750 | −0.116521 | ||||||||
\(176\) | 1379.44 | 0.590792 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 925.605 | 0.389759 | ||||||||
\(179\) | 3180.82 | 1.32819 | 0.664093 | − | 0.747650i | \(-0.268818\pi\) | ||||
0.664093 | + | 0.747650i | \(0.268818\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4230.52 | 1.73731 | 0.868653 | − | 0.495421i | \(-0.164986\pi\) | ||||
0.868653 | + | 0.495421i | \(0.164986\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3462.12 | −1.38712 | ||||||||
\(185\) | 1945.17 | 0.773038 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 350.493 | 0.137062 | ||||||||
\(188\) | −285.616 | −0.110802 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1331.31 | −0.508335 | ||||||||
\(191\) | 3952.80 | 1.49746 | 0.748729 | − | 0.662876i | \(-0.230665\pi\) | ||||
0.748729 | + | 0.662876i | \(0.230665\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5042.45 | 1.88064 | 0.940319 | − | 0.340294i | \(-0.110527\pi\) | ||||
0.940319 | + | 0.340294i | \(0.110527\pi\) | |||||||
\(194\) | 2002.31 | 0.741016 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1661.92 | 0.605658 | ||||||||
\(197\) | −3572.12 | −1.29189 | −0.645947 | − | 0.763382i | \(-0.723537\pi\) | ||||
−0.645947 | + | 0.763382i | \(0.723537\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5006.84 | 1.78355 | 0.891773 | − | 0.452482i | \(-0.149461\pi\) | ||||
0.891773 | + | 0.452482i | \(0.149461\pi\) | |||||||
\(200\) | 553.026 | 0.195524 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1007.98 | −0.351095 | ||||||||
\(203\) | −2013.14 | −0.696033 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2767.05 | 0.942728 | ||||||||
\(206\) | −1329.86 | −0.449784 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4245.40 | −1.40508 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1759.23 | 0.573983 | 0.286992 | − | 0.957933i | \(-0.407345\pi\) | ||||
0.286992 | + | 0.957933i | \(0.407345\pi\) | |||||||
\(212\) | 3004.18 | 0.973245 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −310.555 | −0.0992014 | ||||||||
\(215\) | −4331.72 | −1.37405 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −516.651 | −0.161625 | ||||||||
\(218\) | −2269.64 | −0.705134 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4033.99 | 1.23623 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1712.52 | 0.514255 | 0.257127 | − | 0.966377i | \(-0.417224\pi\) | ||||
0.257127 | + | 0.966377i | \(0.417224\pi\) | |||||||
\(224\) | 1642.14 | 0.489822 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2403.33 | 0.707378 | ||||||||
\(227\) | −2576.65 | −0.753385 | −0.376693 | − | 0.926338i | \(-0.622939\pi\) | ||||
−0.376693 | + | 0.926338i | \(0.622939\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1963.10 | −0.566486 | −0.283243 | − | 0.959048i | \(-0.591410\pi\) | ||||
−0.283243 | + | 0.959048i | \(0.591410\pi\) | |||||||
\(230\) | −3004.51 | −0.861354 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4127.23 | 1.16796 | ||||||||
\(233\) | 1078.11 | 0.303131 | 0.151565 | − | 0.988447i | \(-0.451569\pi\) | ||||
0.151565 | + | 0.988447i | \(0.451569\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −560.409 | −0.155562 | ||||||||
\(236\) | 3904.95 | 1.07708 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 79.4878 | 0.0216489 | ||||||||
\(239\) | −3998.43 | −1.08216 | −0.541081 | − | 0.840970i | \(-0.681985\pi\) | ||||
−0.541081 | + | 0.840970i | \(0.681985\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3574.72 | −0.955470 | −0.477735 | − | 0.878504i | \(-0.658542\pi\) | ||||
−0.477735 | + | 0.878504i | \(0.658542\pi\) | |||||||
\(242\) | −1644.27 | −0.436768 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1239.22 | −0.325136 | ||||||||
\(245\) | 3260.87 | 0.850325 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 1059.21 | 0.271209 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1522.24 | −0.385099 | ||||||||
\(251\) | −2150.69 | −0.540839 | −0.270419 | − | 0.962743i | \(-0.587162\pi\) | ||||
−0.270419 | + | 0.962743i | \(0.587162\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9581.03 | −2.38085 | ||||||||
\(254\) | −307.372 | −0.0759301 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1995.89 | −0.487277 | ||||||||
\(257\) | −4274.80 | −1.03757 | −0.518784 | − | 0.854906i | \(-0.673615\pi\) | ||||
−0.518784 | + | 0.854906i | \(0.673615\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1406.75 | 0.337496 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1490.92 | −0.351562 | ||||||||
\(263\) | −8371.65 | −1.96281 | −0.981403 | − | 0.191960i | \(-0.938516\pi\) | ||||
−0.981403 | + | 0.191960i | \(0.938516\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5894.52 | 1.36641 | ||||||||
\(266\) | −962.810 | −0.221931 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2252.88 | 0.513495 | ||||||||
\(269\) | 5079.64 | 1.15134 | 0.575672 | − | 0.817681i | \(-0.304741\pi\) | ||||
0.575672 | + | 0.817681i | \(0.304741\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4931.93 | 1.10551 | 0.552756 | − | 0.833343i | \(-0.313576\pi\) | ||||
0.552756 | + | 0.833343i | \(0.313576\pi\) | |||||||
\(272\) | 185.321 | 0.0413115 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1174.14 | −0.258876 | ||||||||
\(275\) | 1530.44 | 0.335596 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5172.52 | 1.12197 | 0.560987 | − | 0.827825i | \(-0.310422\pi\) | ||||
0.560987 | + | 0.827825i | \(0.310422\pi\) | |||||||
\(278\) | −2978.75 | −0.642638 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2068.46 | 0.441479 | ||||||||
\(281\) | 217.515 | 0.0461773 | 0.0230887 | − | 0.999733i | \(-0.492650\pi\) | ||||
0.0230887 | + | 0.999733i | \(0.492650\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4922.98 | 1.03407 | 0.517033 | − | 0.855966i | \(-0.327036\pi\) | ||||
0.517033 | + | 0.855966i | \(0.327036\pi\) | |||||||
\(284\) | 4843.45 | 1.01199 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2001.14 | 0.411580 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4865.91 | −0.990416 | ||||||||
\(290\) | 3581.70 | 0.725258 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2103.78 | −0.421624 | ||||||||
\(293\) | 2642.25 | 0.526832 | 0.263416 | − | 0.964682i | \(-0.415151\pi\) | ||||
0.263416 | + | 0.964682i | \(0.415151\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7661.93 | 1.51219 | ||||||||
\(296\) | −2884.05 | −0.566325 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1190.72 | −0.231465 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3132.72 | −0.599889 | ||||||||
\(302\) | 4534.04 | 0.863922 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2244.73 | −0.423501 | ||||||||
\(305\) | −2431.49 | −0.456481 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3386.22 | −0.629517 | −0.314759 | − | 0.949172i | \(-0.601924\pi\) | ||||
−0.314759 | + | 0.949172i | \(0.601924\pi\) | |||||||
\(308\) | 2917.39 | 0.539720 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 919.206 | 0.168411 | ||||||||
\(311\) | 3.29813 | 0.000601349 0 | 0.000300675 | − | 1.00000i | \(-0.499904\pi\) | ||||
0.000300675 | 1.00000i | \(0.499904\pi\) | ||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2882.62 | 0.520560 | 0.260280 | − | 0.965533i | \(-0.416185\pi\) | ||||
0.260280 | + | 0.965533i | \(0.416185\pi\) | |||||||
\(314\) | −2079.08 | −0.373660 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1318.22 | 0.234671 | ||||||||
\(317\) | 1442.70 | 0.255616 | 0.127808 | − | 0.991799i | \(-0.459206\pi\) | ||||
0.127808 | + | 0.991799i | \(0.459206\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11421.6 | 2.00467 | ||||||||
\(320\) | −232.095 | −0.0405454 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2172.87 | −0.376054 | ||||||||
\(323\) | −570.349 | −0.0982509 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1297.00 | −0.220350 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4102.62 | −0.690639 | ||||||||
\(329\) | −405.290 | −0.0679159 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3824.98 | −0.635166 | −0.317583 | − | 0.948230i | \(-0.602871\pi\) | ||||
−0.317583 | + | 0.948230i | \(0.602871\pi\) | |||||||
\(332\) | −1593.62 | −0.263438 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3028.93 | 0.496215 | ||||||||
\(335\) | 4420.39 | 0.720931 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2290.22 | 0.370197 | 0.185098 | − | 0.982720i | \(-0.440740\pi\) | ||||
0.185098 | + | 0.982720i | \(0.440740\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 541.946 | 0.0864445 | ||||||||
\(341\) | 2931.24 | 0.465500 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5446.21 | 0.857340 | ||||||||
\(344\) | 6422.52 | 1.00663 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4030.35 | 0.626222 | ||||||||
\(347\) | 334.993 | 0.0518252 | 0.0259126 | − | 0.999664i | \(-0.491751\pi\) | ||||
0.0259126 | + | 0.999664i | \(0.491751\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8975.27 | −1.37661 | −0.688303 | − | 0.725424i | \(-0.741644\pi\) | ||||
−0.688303 | + | 0.725424i | \(0.741644\pi\) | |||||||
\(350\) | 347.086 | 0.0530072 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −9316.77 | −1.41075 | ||||||||
\(353\) | 9925.87 | 1.49660 | 0.748302 | − | 0.663359i | \(-0.230870\pi\) | ||||
0.748302 | + | 0.663359i | \(0.230870\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9503.38 | 1.42081 | ||||||||
\(356\) | 4563.95 | 0.679463 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4092.74 | −0.604213 | ||||||||
\(359\) | −215.661 | −0.0317052 | −0.0158526 | − | 0.999874i | \(-0.505046\pi\) | ||||
−0.0158526 | + | 0.999874i | \(0.505046\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 49.4437 | 0.00720858 | ||||||||
\(362\) | −5443.40 | −0.790328 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4127.83 | −0.591947 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2861.52 | −0.407003 | −0.203502 | − | 0.979075i | \(-0.565232\pi\) | ||||
−0.203502 | + | 0.979075i | \(0.565232\pi\) | |||||||
\(368\) | −5065.91 | −0.717606 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2502.85 | −0.351667 | ||||||||
\(371\) | 4262.94 | 0.596551 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −17.0145 | −0.00236186 | −0.00118093 | − | 0.999999i | \(-0.500376\pi\) | ||||
−0.00118093 | + | 0.999999i | \(0.500376\pi\) | |||||||
\(374\) | −450.978 | −0.0623516 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 830.902 | 0.113964 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1901.97 | −0.257777 | −0.128888 | − | 0.991659i | \(-0.541141\pi\) | ||||
−0.128888 | + | 0.991659i | \(0.541141\pi\) | |||||||
\(380\) | −6564.41 | −0.886177 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −5086.05 | −0.681217 | ||||||||
\(383\) | 7729.78 | 1.03126 | 0.515631 | − | 0.856811i | \(-0.327558\pi\) | ||||
0.515631 | + | 0.856811i | \(0.327558\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5724.23 | 0.757751 | ||||||||
\(386\) | −6488.09 | −0.855532 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 9872.92 | 1.29181 | ||||||||
\(389\) | 14445.5 | 1.88282 | 0.941408 | − | 0.337271i | \(-0.109504\pi\) | ||||
0.941408 | + | 0.337271i | \(0.109504\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1287.16 | −0.166482 | ||||||||
\(392\) | −4834.80 | −0.622945 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4596.23 | 0.587703 | ||||||||
\(395\) | 2586.50 | 0.329470 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1033.07 | 0.130600 | 0.0653000 | − | 0.997866i | \(-0.479200\pi\) | ||||
0.0653000 | + | 0.997866i | \(0.479200\pi\) | |||||||
\(398\) | −6442.29 | −0.811364 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 809.210 | 0.101151 | ||||||||
\(401\) | 4611.73 | 0.574311 | 0.287155 | − | 0.957884i | \(-0.407290\pi\) | ||||
0.287155 | + | 0.957884i | \(0.407290\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −4970.12 | −0.612061 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2590.30 | 0.316636 | ||||||||
\(407\) | −7981.29 | −0.972034 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2668.56 | 0.322621 | 0.161311 | − | 0.986904i | \(-0.448428\pi\) | ||||
0.161311 | + | 0.986904i | \(0.448428\pi\) | |||||||
\(410\) | −3560.35 | −0.428862 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −6557.23 | −0.784106 | ||||||||
\(413\) | 5541.13 | 0.660197 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3126.86 | −0.369859 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 5462.55 | 0.639191 | ||||||||
\(419\) | −6189.83 | −0.721701 | −0.360851 | − | 0.932624i | \(-0.617514\pi\) | ||||
−0.360851 | + | 0.932624i | \(0.617514\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8991.13 | 1.04086 | 0.520429 | − | 0.853905i | \(-0.325772\pi\) | ||||
0.520429 | + | 0.853905i | \(0.325772\pi\) | |||||||
\(422\) | −2263.60 | −0.261114 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −8739.63 | −1.00102 | ||||||||
\(425\) | 205.606 | 0.0234668 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1758.46 | −0.199292 | ||||||||
\(428\) | −1531.28 | −0.172937 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5573.61 | 0.625078 | ||||||||
\(431\) | −2069.01 | −0.231232 | −0.115616 | − | 0.993294i | \(-0.536884\pi\) | ||||
−0.115616 | + | 0.993294i | \(0.536884\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14934.7 | −1.65754 | −0.828769 | − | 0.559592i | \(-0.810958\pi\) | ||||
−0.828769 | + | 0.559592i | \(0.810958\pi\) | |||||||
\(434\) | 664.772 | 0.0735256 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −11191.1 | −1.22926 | ||||||||
\(437\) | 15591.0 | 1.70668 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6000.24 | −0.652336 | −0.326168 | − | 0.945312i | \(-0.605758\pi\) | ||||
−0.326168 | + | 0.945312i | \(0.605758\pi\) | |||||||
\(440\) | −11735.5 | −1.27152 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5392.60 | 0.578352 | 0.289176 | − | 0.957276i | \(-0.406619\pi\) | ||||
0.289176 | + | 0.957276i | \(0.406619\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8954.96 | 0.953946 | ||||||||
\(446\) | −2203.49 | −0.233943 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −167.852 | −0.0177015 | ||||||||
\(449\) | 6046.60 | 0.635538 | 0.317769 | − | 0.948168i | \(-0.397066\pi\) | ||||
0.317769 | + | 0.948168i | \(0.397066\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11353.6 | −1.18541 | ||||||||
\(452\) | 11850.3 | 1.23317 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3315.37 | 0.342727 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1014.57 | 0.103851 | 0.0519253 | − | 0.998651i | \(-0.483464\pi\) | ||||
0.0519253 | + | 0.998651i | \(0.483464\pi\) | |||||||
\(458\) | 2525.91 | 0.257704 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −14814.6 | −1.50159 | ||||||||
\(461\) | 15978.9 | 1.61434 | 0.807171 | − | 0.590318i | \(-0.200997\pi\) | ||||
0.807171 | + | 0.590318i | \(0.200997\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −128.805 | −0.0129289 | −0.00646445 | − | 0.999979i | \(-0.502058\pi\) | ||||
−0.00646445 | + | 0.999979i | \(0.502058\pi\) | |||||||
\(464\) | 6039.12 | 0.604223 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1387.20 | −0.137899 | ||||||||
\(467\) | −18832.4 | −1.86608 | −0.933039 | − | 0.359776i | \(-0.882853\pi\) | ||||
−0.933039 | + | 0.359776i | \(0.882853\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3196.84 | 0.314747 | ||||||||
\(470\) | 721.076 | 0.0707676 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −11360.1 | −1.10782 | ||||||||
\(473\) | 17773.6 | 1.72776 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2490.44 | −0.240567 | ||||||||
\(476\) | 391.937 | 0.0377403 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 5144.76 | 0.492293 | ||||||||
\(479\) | 9231.59 | 0.880589 | 0.440294 | − | 0.897853i | \(-0.354874\pi\) | ||||
0.440294 | + | 0.897853i | \(0.354874\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 4599.58 | 0.434658 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8107.55 | −0.761415 | ||||||||
\(485\) | 19371.7 | 1.81366 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7233.01 | 0.673016 | 0.336508 | − | 0.941681i | \(-0.390754\pi\) | ||||
0.336508 | + | 0.941681i | \(0.390754\pi\) | |||||||
\(488\) | 3605.10 | 0.334416 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −4195.75 | −0.386826 | ||||||||
\(491\) | 655.131 | 0.0602152 | 0.0301076 | − | 0.999547i | \(-0.490415\pi\) | ||||
0.0301076 | + | 0.999547i | \(0.490415\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1534.44 | 0.140178 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1549.88 | 0.140305 | ||||||||
\(497\) | 6872.87 | 0.620302 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4560.07 | −0.409092 | −0.204546 | − | 0.978857i | \(-0.565572\pi\) | ||||
−0.204546 | + | 0.978857i | \(0.565572\pi\) | |||||||
\(500\) | −7505.82 | −0.671341 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2767.29 | 0.246036 | ||||||||
\(503\) | −9068.67 | −0.803881 | −0.401941 | − | 0.915666i | \(-0.631664\pi\) | ||||
−0.401941 | + | 0.915666i | \(0.631664\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9751.90 | −0.859315 | ||||||||
\(506\) | 12327.9 | 1.08308 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1515.58 | −0.132368 | ||||||||
\(509\) | 15880.9 | 1.38292 | 0.691461 | − | 0.722413i | \(-0.256967\pi\) | ||||
0.691461 | + | 0.722413i | \(0.256967\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2985.26 | −0.258435 | ||||||||
\(512\) | −8913.89 | −0.769418 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5500.37 | 0.472006 | ||||||||
\(515\) | −12866.0 | −1.10086 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2299.43 | 0.195607 | ||||||||
\(518\) | −1810.07 | −0.153532 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10998.0 | 0.924821 | 0.462410 | − | 0.886666i | \(-0.346985\pi\) | ||||
0.462410 | + | 0.886666i | \(0.346985\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18631.8 | 1.55776 | 0.778882 | − | 0.627171i | \(-0.215787\pi\) | ||||
0.778882 | + | 0.627171i | \(0.215787\pi\) | |||||||
\(524\) | −7351.39 | −0.612875 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10771.8 | 0.892911 | ||||||||
\(527\) | 393.797 | 0.0325504 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 23018.7 | 1.89190 | ||||||||
\(530\) | −7584.46 | −0.621600 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4747.40 | −0.386891 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3004.53 | −0.242798 | ||||||||
\(536\) | −6553.99 | −0.528151 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −6535.96 | −0.523764 | ||||||||
\(539\) | −13379.8 | −1.06922 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14270.1 | −1.13405 | −0.567023 | − | 0.823702i | \(-0.691905\pi\) | ||||
−0.567023 | + | 0.823702i | \(0.691905\pi\) | |||||||
\(542\) | −6345.90 | −0.502915 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1251.66 | −0.0986480 | ||||||||
\(545\) | −21958.1 | −1.72584 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14379.7 | 1.12400 | 0.562002 | − | 0.827136i | \(-0.310031\pi\) | ||||
0.562002 | + | 0.827136i | \(0.310031\pi\) | |||||||
\(548\) | −5789.40 | −0.451298 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1969.21 | −0.152668 | ||||||||
\(551\) | −18586.2 | −1.43702 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1870.56 | 0.143842 | ||||||||
\(554\) | −6655.46 | −0.510404 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −14687.5 | −1.12031 | ||||||||
\(557\) | 9035.10 | 0.687306 | 0.343653 | − | 0.939097i | \(-0.388336\pi\) | ||||
0.343653 | + | 0.939097i | \(0.388336\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 3026.65 | 0.228392 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −279.875 | −0.0210068 | ||||||||
\(563\) | 7293.47 | 0.545973 | 0.272987 | − | 0.962018i | \(-0.411988\pi\) | ||||
0.272987 | + | 0.962018i | \(0.411988\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 23251.6 | 1.73133 | ||||||||
\(566\) | −6334.37 | −0.470413 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −14090.4 | −1.04088 | ||||||||
\(569\) | −26415.8 | −1.94623 | −0.973117 | − | 0.230310i | \(-0.926026\pi\) | ||||
−0.973117 | + | 0.230310i | \(0.926026\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −23940.9 | −1.75463 | −0.877317 | − | 0.479912i | \(-0.840669\pi\) | ||||
−0.877317 | + | 0.479912i | \(0.840669\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2574.86 | −0.187234 | ||||||||
\(575\) | −5620.43 | −0.407632 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10182.8 | 0.734691 | 0.367346 | − | 0.930085i | \(-0.380267\pi\) | ||||
0.367346 | + | 0.930085i | \(0.380267\pi\) | |||||||
\(578\) | 6260.95 | 0.450556 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 17660.6 | 1.26434 | ||||||||
\(581\) | −2261.35 | −0.161475 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −24186.0 | −1.71815 | ||||||||
\(584\) | 6120.22 | 0.433658 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3399.77 | −0.239664 | ||||||||
\(587\) | −19107.5 | −1.34353 | −0.671763 | − | 0.740766i | \(-0.734463\pi\) | ||||
−0.671763 | + | 0.740766i | \(0.734463\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4769.94 | −0.333687 | ||||||||
\(590\) | −9858.58 | −0.687917 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4220.06 | −0.292979 | ||||||||
\(593\) | 13597.5 | 0.941621 | 0.470810 | − | 0.882234i | \(-0.343962\pi\) | ||||
0.470810 | + | 0.882234i | \(0.343962\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 769.022 | 0.0529863 | ||||||||
\(596\) | −5871.17 | −0.403511 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4150.37 | −0.283104 | −0.141552 | − | 0.989931i | \(-0.545209\pi\) | ||||
−0.141552 | + | 0.989931i | \(0.545209\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19177.5 | 1.30161 | 0.650803 | − | 0.759247i | \(-0.274433\pi\) | ||||
0.650803 | + | 0.759247i | \(0.274433\pi\) | |||||||
\(602\) | 4030.85 | 0.272899 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 22356.3 | 1.50607 | ||||||||
\(605\) | −15907.9 | −1.06900 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7994.36 | 0.534565 | 0.267282 | − | 0.963618i | \(-0.413874\pi\) | ||||
0.267282 | + | 0.963618i | \(0.413874\pi\) | |||||||
\(608\) | 15161.0 | 1.01128 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3128.59 | 0.207660 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15613.4 | 1.02874 | 0.514371 | − | 0.857568i | \(-0.328026\pi\) | ||||
0.514371 | + | 0.857568i | \(0.328026\pi\) | |||||||
\(614\) | 4357.04 | 0.286377 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −8487.15 | −0.555125 | ||||||||
\(617\) | −21636.2 | −1.41174 | −0.705868 | − | 0.708343i | \(-0.749443\pi\) | ||||
−0.705868 | + | 0.708343i | \(0.749443\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10394.0 | 0.674911 | 0.337456 | − | 0.941341i | \(-0.390434\pi\) | ||||
0.337456 | + | 0.941341i | \(0.390434\pi\) | |||||||
\(620\) | 4532.40 | 0.293590 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −4.24369 | −0.000273563 0 | ||||||||
\(623\) | 6476.25 | 0.416478 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −18472.6 | −1.18225 | ||||||||
\(626\) | −3709.06 | −0.236811 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −10251.5 | −0.651400 | ||||||||
\(629\) | −1072.25 | −0.0679702 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4644.14 | 0.292996 | 0.146498 | − | 0.989211i | \(-0.453200\pi\) | ||||
0.146498 | + | 0.989211i | \(0.453200\pi\) | |||||||
\(632\) | −3834.92 | −0.241369 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1856.32 | −0.116284 | ||||||||
\(635\) | −2973.74 | −0.185841 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −14696.2 | −0.911955 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −17866.6 | −1.10350 | ||||||||
\(641\) | −153.922 | −0.00948451 | −0.00474225 | − | 0.999989i | \(-0.501510\pi\) | ||||
−0.00474225 | + | 0.999989i | \(0.501510\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8438.05 | −0.517518 | −0.258759 | − | 0.965942i | \(-0.583314\pi\) | ||||
−0.258759 | + | 0.965942i | \(0.583314\pi\) | |||||||
\(644\) | −10713.9 | −0.655572 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 733.865 | 0.0446959 | ||||||||
\(647\) | −665.236 | −0.0404221 | −0.0202111 | − | 0.999796i | \(-0.506434\pi\) | ||||
−0.0202111 | + | 0.999796i | \(0.506434\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −31437.9 | −1.90145 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6395.21 | −0.384134 | ||||||||
\(653\) | 22414.7 | 1.34327 | 0.671636 | − | 0.740882i | \(-0.265592\pi\) | ||||
0.671636 | + | 0.740882i | \(0.265592\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14424.2 | −0.860458 | ||||||||
\(656\) | −6003.12 | −0.357291 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 521.485 | 0.0308960 | ||||||||
\(659\) | 25585.6 | 1.51240 | 0.756202 | − | 0.654338i | \(-0.227053\pi\) | ||||
0.756202 | + | 0.654338i | \(0.227053\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13317.5 | −0.783647 | −0.391824 | − | 0.920040i | \(-0.628156\pi\) | ||||
−0.391824 | + | 0.920040i | \(0.628156\pi\) | |||||||
\(662\) | 4921.59 | 0.288947 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4636.10 | 0.270957 | ||||||||
\(665\) | −9314.91 | −0.543183 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −41945.2 | −2.43497 | ||||||||
\(668\) | 14935.0 | 0.865048 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −5687.70 | −0.327963 | ||||||||
\(671\) | 9976.71 | 0.573989 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9778.28 | 0.560067 | 0.280034 | − | 0.959990i | \(-0.409654\pi\) | ||||
0.280034 | + | 0.959990i | \(0.409654\pi\) | |||||||
\(674\) | −2946.82 | −0.168408 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −12392.8 | −0.703537 | −0.351769 | − | 0.936087i | \(-0.614420\pi\) | ||||
−0.351769 | + | 0.936087i | \(0.614420\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14009.7 | 0.791815 | ||||||||
\(680\) | −1576.61 | −0.0889119 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3771.62 | −0.211763 | ||||||||
\(683\) | 18941.7 | 1.06118 | 0.530588 | − | 0.847630i | \(-0.321971\pi\) | ||||
0.530588 | + | 0.847630i | \(0.321971\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11359.4 | −0.633608 | ||||||||
\(686\) | −7007.62 | −0.390018 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 9397.69 | 0.520761 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 32377.6 | 1.78249 | 0.891247 | − | 0.453519i | \(-0.149832\pi\) | ||||
0.891247 | + | 0.453519i | \(0.149832\pi\) | |||||||
\(692\) | 19872.8 | 1.09169 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −431.034 | −0.0235761 | ||||||||
\(695\) | −28818.5 | −1.57288 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1525.29 | −0.0828903 | ||||||||
\(698\) | 11548.4 | 0.626240 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1711.40 | 0.0924071 | ||||||||
\(701\) | −6072.34 | −0.327174 | −0.163587 | − | 0.986529i | \(-0.552306\pi\) | ||||
−0.163587 | + | 0.986529i | \(0.552306\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12987.8 | 0.696789 | ||||||||
\(704\) | 952.316 | 0.0509826 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −12771.6 | −0.680829 | ||||||||
\(707\) | −7052.61 | −0.375163 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3398.52 | −0.180020 | −0.0900100 | − | 0.995941i | \(-0.528690\pi\) | ||||
−0.0900100 | + | 0.995941i | \(0.528690\pi\) | |||||||
\(710\) | −12228.0 | −0.646348 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −13277.3 | −0.698857 | ||||||||
\(713\) | −10764.8 | −0.565421 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −20180.4 | −1.05332 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 277.491 | 0.0144232 | ||||||||
\(719\) | −28833.6 | −1.49556 | −0.747782 | − | 0.663944i | \(-0.768881\pi\) | ||||
−0.747782 | + | 0.663944i | \(0.768881\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9304.72 | −0.480619 | ||||||||
\(722\) | −63.6190 | −0.00327930 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −26840.2 | −1.37777 | ||||||||
\(725\) | 6700.17 | 0.343225 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12894.7 | −0.657822 | −0.328911 | − | 0.944361i | \(-0.606682\pi\) | ||||
−0.328911 | + | 0.944361i | \(0.606682\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 5311.27 | 0.269286 | ||||||||
\(731\) | 2387.79 | 0.120815 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −23754.7 | −1.19700 | −0.598499 | − | 0.801124i | \(-0.704236\pi\) | ||||
−0.598499 | + | 0.801124i | \(0.704236\pi\) | |||||||
\(734\) | 3681.91 | 0.185152 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 34215.2 | 1.71357 | ||||||||
\(737\) | −18137.4 | −0.906514 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −26047.2 | −1.29656 | −0.648282 | − | 0.761400i | \(-0.724512\pi\) | ||||
−0.648282 | + | 0.761400i | \(0.724512\pi\) | |||||||
\(740\) | −12341.0 | −0.613059 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5485.10 | −0.271381 | ||||||||
\(743\) | −15919.3 | −0.786033 | −0.393016 | − | 0.919531i | \(-0.628568\pi\) | ||||
−0.393016 | + | 0.919531i | \(0.628568\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11519.9 | −0.566517 | ||||||||
\(746\) | 21.8924 | 0.00107445 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2223.67 | −0.108697 | ||||||||
\(749\) | −2172.88 | −0.106002 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2237.59 | 0.108723 | 0.0543613 | − | 0.998521i | \(-0.482688\pi\) | ||||
0.0543613 | + | 0.998521i | \(0.482688\pi\) | |||||||
\(752\) | 1215.81 | 0.0589575 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 43865.5 | 2.11448 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3263.91 | 0.156709 | 0.0783545 | − | 0.996926i | \(-0.475033\pi\) | ||||
0.0783545 | + | 0.996926i | \(0.475033\pi\) | |||||||
\(758\) | 2447.25 | 0.117267 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 19096.9 | 0.911471 | ||||||||
\(761\) | 1904.91 | 0.0907398 | 0.0453699 | − | 0.998970i | \(-0.485553\pi\) | ||||
0.0453699 | + | 0.998970i | \(0.485553\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15880.2 | −0.753474 | ||||||||
\(764\) | −25078.2 | −1.18756 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −9945.88 | −0.469137 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3429.87 | 0.160838 | 0.0804190 | − | 0.996761i | \(-0.474374\pi\) | ||||
0.0804190 | + | 0.996761i | \(0.474374\pi\) | |||||||
\(770\) | −7365.35 | −0.344713 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −31991.4 | −1.49144 | ||||||||
\(773\) | 28243.5 | 1.31416 | 0.657082 | − | 0.753819i | \(-0.271790\pi\) | ||||
0.657082 | + | 0.753819i | \(0.271790\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1719.53 | 0.0796997 | ||||||||
\(776\) | −28721.9 | −1.32868 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −18587.0 | −0.856522 | ||||||||
\(779\) | 18475.4 | 0.849741 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −38993.5 | −1.78655 | ||||||||
\(782\) | 1656.19 | 0.0757355 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −7074.48 | −0.322270 | ||||||||
\(785\) | −20114.5 | −0.914545 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6626.72 | 0.300149 | 0.150074 | − | 0.988675i | \(-0.452049\pi\) | ||||
0.150074 | + | 0.988675i | \(0.452049\pi\) | |||||||
\(788\) | 22663.0 | 1.02454 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −3328.03 | −0.149881 | ||||||||
\(791\) | 16815.6 | 0.755871 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −1329.25 | −0.0594120 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −31765.5 | −1.41444 | ||||||||
\(797\) | 20750.8 | 0.922249 | 0.461125 | − | 0.887335i | \(-0.347446\pi\) | ||||
0.461125 | + | 0.887335i | \(0.347446\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 308.917 | 0.0136780 | ||||||||
\(800\) | −5465.41 | −0.241539 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −5933.89 | −0.261263 | ||||||||
\(803\) | 16937.0 | 0.744327 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −21021.9 | −0.920403 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 14458.9 | 0.629531 | ||||||||
\(809\) | −10005.3 | −0.434818 | −0.217409 | − | 0.976081i | \(-0.569761\pi\) | ||||
−0.217409 | + | 0.976081i | \(0.569761\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32773.5 | 1.41903 | 0.709515 | − | 0.704690i | \(-0.248914\pi\) | ||||
0.709515 | + | 0.704690i | \(0.248914\pi\) | |||||||
\(812\) | 12772.2 | 0.551990 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 10269.5 | 0.442194 | ||||||||
\(815\) | −12548.1 | −0.539313 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −28922.6 | −1.23852 | ||||||||
\(818\) | −3433.63 | −0.146765 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −17555.3 | −0.747632 | ||||||||
\(821\) | 3031.74 | 0.128878 | 0.0644388 | − | 0.997922i | \(-0.479474\pi\) | ||||
0.0644388 | + | 0.997922i | \(0.479474\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 31057.0 | 1.31541 | 0.657704 | − | 0.753277i | \(-0.271528\pi\) | ||||
0.657704 | + | 0.753277i | \(0.271528\pi\) | |||||||
\(824\) | 19076.0 | 0.806486 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7129.75 | −0.300334 | ||||||||
\(827\) | 8770.13 | 0.368764 | 0.184382 | − | 0.982855i | \(-0.440972\pi\) | ||||
0.184382 | + | 0.982855i | \(0.440972\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −38698.9 | −1.62131 | −0.810656 | − | 0.585523i | \(-0.800889\pi\) | ||||
−0.810656 | + | 0.585523i | \(0.800889\pi\) | |||||||
\(830\) | 4023.32 | 0.168255 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1797.50 | −0.0747657 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 29304.0 | 1.21450 | ||||||||
\(836\) | 26934.6 | 1.11430 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 7964.43 | 0.328313 | ||||||||
\(839\) | 22543.7 | 0.927647 | 0.463824 | − | 0.885928i | \(-0.346477\pi\) | ||||
0.463824 | + | 0.885928i | \(0.346477\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25614.3 | 1.05024 | ||||||||
\(842\) | −11568.9 | −0.473502 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −11161.3 | −0.455198 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −11504.6 | −0.466710 | ||||||||
\(848\) | −12788.2 | −0.517863 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −264.553 | −0.0106754 | ||||||||
\(851\) | 29310.8 | 1.18068 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7751.80 | −0.311156 | −0.155578 | − | 0.987824i | \(-0.549724\pi\) | ||||
−0.155578 | + | 0.987824i | \(0.549724\pi\) | |||||||
\(854\) | 2262.60 | 0.0906613 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4454.73 | 0.177873 | ||||||||
\(857\) | −30235.6 | −1.20517 | −0.602583 | − | 0.798056i | \(-0.705862\pi\) | ||||
−0.602583 | + | 0.798056i | \(0.705862\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3568.09 | 0.141725 | 0.0708624 | − | 0.997486i | \(-0.477425\pi\) | ||||
0.0708624 | + | 0.997486i | \(0.477425\pi\) | |||||||
\(860\) | 27482.2 | 1.08969 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2662.19 | 0.105191 | ||||||||
\(863\) | 406.509 | 0.0160345 | 0.00801723 | − | 0.999968i | \(-0.497448\pi\) | ||||
0.00801723 | + | 0.999968i | \(0.497448\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 38992.5 | 1.53270 | ||||||||
\(866\) | 19216.4 | 0.754040 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3277.85 | 0.128177 | ||||||||
\(869\) | −10612.7 | −0.414283 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 32556.6 | 1.26434 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −20060.8 | −0.776394 | ||||||||
\(875\) | −10650.8 | −0.411499 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18961.9 | 0.730102 | 0.365051 | − | 0.930988i | \(-0.381052\pi\) | ||||
0.365051 | + | 0.930988i | \(0.381052\pi\) | |||||||
\(878\) | 7720.48 | 0.296758 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −17171.9 | −0.657800 | ||||||||
\(881\) | 31028.9 | 1.18660 | 0.593298 | − | 0.804983i | \(-0.297826\pi\) | ||||
0.593298 | + | 0.804983i | \(0.297826\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33896.2 | 1.29184 | 0.645922 | − | 0.763404i | \(-0.276473\pi\) | ||||
0.645922 | + | 0.763404i | \(0.276473\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6938.64 | −0.263102 | ||||||||
\(887\) | 1773.35 | 0.0671288 | 0.0335644 | − | 0.999437i | \(-0.489314\pi\) | ||||
0.0335644 | + | 0.999437i | \(0.489314\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2150.62 | −0.0811354 | ||||||||
\(890\) | −11522.3 | −0.433965 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −10864.9 | −0.407831 | ||||||||
\(893\) | −3741.81 | −0.140218 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −39596.1 | −1.47883 | ||||||||
\(896\) | −12921.2 | −0.481770 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −7780.14 | −0.289116 | ||||||||
\(899\) | 12832.8 | 0.476083 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3249.26 | −0.120143 | ||||||||
\(902\) | 14608.6 | 0.539260 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −34474.4 | −1.26836 | ||||||||
\(905\) | −52663.3 | −1.93435 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14401.6 | 0.527231 | 0.263615 | − | 0.964628i | \(-0.415085\pi\) | ||||
0.263615 | + | 0.964628i | \(0.415085\pi\) | |||||||
\(908\) | 16347.3 | 0.597473 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19324.5 | 0.702799 | 0.351400 | − | 0.936226i | \(-0.385706\pi\) | ||||
0.351400 | + | 0.936226i | \(0.385706\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12829.9 | 0.465069 | ||||||||
\(914\) | −1305.45 | −0.0472433 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 12454.7 | 0.449253 | ||||||||
\(917\) | −10431.6 | −0.375663 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18649.1 | 0.669399 | 0.334700 | − | 0.942325i | \(-0.391365\pi\) | ||||
0.334700 | + | 0.942325i | \(0.391365\pi\) | |||||||
\(920\) | 43097.9 | 1.54445 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −20560.0 | −0.734390 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4681.99 | −0.166425 | ||||||||
\(926\) | 165.733 | 0.00588156 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −40788.3 | −1.44283 | ||||||||
\(929\) | −27326.4 | −0.965070 | −0.482535 | − | 0.875877i | \(-0.660284\pi\) | ||||
−0.482535 | + | 0.875877i | \(0.660284\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 21772.6 | 0.766453 | ||||||||
\(932\) | −6839.98 | −0.240398 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 24231.5 | 0.848908 | ||||||||
\(935\) | −4363.08 | −0.152608 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28699.1 | 1.00060 | 0.500298 | − | 0.865853i | \(-0.333224\pi\) | ||||
0.500298 | + | 0.865853i | \(0.333224\pi\) | |||||||
\(938\) | −4113.36 | −0.143183 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 3555.47 | 0.123369 | ||||||||
\(941\) | 55401.1 | 1.91926 | 0.959630 | − | 0.281264i | \(-0.0907538\pi\) | ||||
0.959630 | + | 0.281264i | \(0.0907538\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 41695.2 | 1.43985 | ||||||||
\(944\) | −16622.6 | −0.573113 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −22869.2 | −0.785986 | ||||||||
\(947\) | −33258.4 | −1.14124 | −0.570619 | − | 0.821215i | \(-0.693297\pi\) | ||||
−0.570619 | + | 0.821215i | \(0.693297\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 3204.44 | 0.109438 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1140.21 | −0.0388175 | ||||||||
\(953\) | −4411.89 | −0.149963 | −0.0749817 | − | 0.997185i | \(-0.523890\pi\) | ||||
−0.0749817 | + | 0.997185i | \(0.523890\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −49206.1 | −1.66730 | ||||||||
\(956\) | 25367.7 | 0.858211 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −11878.3 | −0.400594 | ||||||||
\(959\) | −8215.17 | −0.276623 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26497.6 | −0.889450 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 22679.5 | 0.757737 | ||||||||
\(965\) | −62770.5 | −2.09394 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 26014.3 | 0.865114 | 0.432557 | − | 0.901607i | \(-0.357611\pi\) | ||||
0.432557 | + | 0.901607i | \(0.357611\pi\) | |||||||
\(968\) | 23586.1 | 0.783148 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −24925.5 | −0.825063 | ||||||||
\(971\) | 36204.9 | 1.19657 | 0.598286 | − | 0.801283i | \(-0.295849\pi\) | ||||
0.598286 | + | 0.801283i | \(0.295849\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −20841.6 | −0.686693 | ||||||||
\(974\) | −9306.69 | −0.306166 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5275.12 | 0.173005 | ||||||||
\(977\) | 13916.4 | 0.455706 | 0.227853 | − | 0.973696i | \(-0.426830\pi\) | ||||
0.227853 | + | 0.973696i | \(0.426830\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −36743.3 | −1.19951 | ||||||||
\(980\) | −20688.3 | −0.674351 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −842.954 | −0.0273928 | ||||||||
\(983\) | 13585.3 | 0.440796 | 0.220398 | − | 0.975410i | \(-0.429264\pi\) | ||||
0.220398 | + | 0.975410i | \(0.429264\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 44467.2 | 1.43842 | ||||||||
\(986\) | −1974.36 | −0.0637691 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −65272.4 | −2.09863 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1024.49 | −0.0328396 | −0.0164198 | − | 0.999865i | \(-0.505227\pi\) | ||||
−0.0164198 | + | 0.999865i | \(0.505227\pi\) | |||||||
\(992\) | −10467.9 | −0.335036 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −8843.29 | −0.282185 | ||||||||
\(995\) | −62327.3 | −1.98584 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18514.9 | 0.588136 | 0.294068 | − | 0.955784i | \(-0.404991\pi\) | ||||
0.294068 | + | 0.955784i | \(0.404991\pi\) | |||||||
\(998\) | 5867.43 | 0.186102 | ||||||||
\(999\) | 0 | 0 |
(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 | 1521.4.a.bc.1.4 | 8 | ||
3.2 | odd | 2 | inner | 1521.4.a.bc.1.5 | 8 | ||
13.3 | even | 3 | 117.4.g.f.100.5 | yes | 16 | ||
13.9 | even | 3 | 117.4.g.f.55.5 | yes | 16 | ||
13.12 | even | 2 | 1521.4.a.bd.1.5 | 8 | |||
39.29 | odd | 6 | 117.4.g.f.100.4 | yes | 16 | ||
39.35 | odd | 6 | 117.4.g.f.55.4 | ✓ | 16 | ||
39.38 | odd | 2 | 1521.4.a.bd.1.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
117.4.g.f.55.4 | ✓ | 16 | 39.35 | odd | 6 | ||
117.4.g.f.55.5 | yes | 16 | 13.9 | even | 3 | ||
117.4.g.f.100.4 | yes | 16 | 39.29 | odd | 6 | ||
117.4.g.f.100.5 | yes | 16 | 13.3 | even | 3 | ||
1521.4.a.bc.1.4 | 8 | 1.1 | even | 1 | trivial | ||
1521.4.a.bc.1.5 | 8 | 3.2 | odd | 2 | inner | ||
1521.4.a.bd.1.4 | 8 | 39.38 | odd | 2 | |||
1521.4.a.bd.1.5 | 8 | 13.12 | even | 2 |