Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [567,4,Mod(1,567)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(567, 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("567.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 567 = 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 567.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: | \(33.4540829733\) |
Analytic rank: | \(1\) |
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: | \( x^{8} - 3x^{7} - 49x^{6} + 138x^{5} + 708x^{4} - 1941x^{3} - 2506x^{2} + 8592x - 4616 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2\cdot 3^{5} \) |
Twist minimal: | no (minimal twist has level 63) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-2.93948\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 567.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.93948 | 1.03926 | 0.519631 | − | 0.854391i | \(-0.326069\pi\) | ||||
0.519631 | + | 0.854391i | \(0.326069\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.640533 | 0.0800666 | ||||||||
\(5\) | 2.56885 | 0.229765 | 0.114883 | − | 0.993379i | \(-0.463351\pi\) | ||||
0.114883 | + | 0.993379i | \(0.463351\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −7.00000 | −0.377964 | ||||||||
\(8\) | −21.6330 | −0.956052 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 7.55109 | 0.238786 | ||||||||
\(11\) | 0.514272 | 0.0140963 | 0.00704814 | − | 0.999975i | \(-0.497756\pi\) | ||||
0.00704814 | + | 0.999975i | \(0.497756\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 65.4434 | 1.39621 | 0.698105 | − | 0.715996i | \(-0.254027\pi\) | ||||
0.698105 | + | 0.715996i | \(0.254027\pi\) | |||||||
\(14\) | −20.5763 | −0.392804 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −68.7140 | −1.07366 | ||||||||
\(17\) | 3.37738 | 0.0481843 | 0.0240922 | − | 0.999710i | \(-0.492330\pi\) | ||||
0.0240922 | + | 0.999710i | \(0.492330\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −123.871 | −1.49568 | −0.747838 | − | 0.663881i | \(-0.768908\pi\) | ||||
−0.747838 | + | 0.663881i | \(0.768908\pi\) | |||||||
\(20\) | 1.64544 | 0.0183965 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.51169 | 0.0146497 | ||||||||
\(23\) | 25.1184 | 0.227719 | 0.113860 | − | 0.993497i | \(-0.463679\pi\) | ||||
0.113860 | + | 0.993497i | \(0.463679\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −118.401 | −0.947208 | ||||||||
\(26\) | 192.369 | 1.45103 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −4.48373 | −0.0302623 | ||||||||
\(29\) | −237.463 | −1.52054 | −0.760272 | − | 0.649605i | \(-0.774934\pi\) | ||||
−0.760272 | + | 0.649605i | \(0.774934\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −89.9139 | −0.520936 | −0.260468 | − | 0.965482i | \(-0.583877\pi\) | ||||
−0.260468 | + | 0.965482i | \(0.583877\pi\) | |||||||
\(32\) | −28.9193 | −0.159758 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 9.92772 | 0.0500762 | ||||||||
\(35\) | −17.9820 | −0.0868431 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −67.4721 | −0.299793 | −0.149897 | − | 0.988702i | \(-0.547894\pi\) | ||||
−0.149897 | + | 0.988702i | \(0.547894\pi\) | |||||||
\(38\) | −364.115 | −1.55440 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −55.5720 | −0.219667 | ||||||||
\(41\) | −287.316 | −1.09442 | −0.547210 | − | 0.836995i | \(-0.684310\pi\) | ||||
−0.547210 | + | 0.836995i | \(0.684310\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −435.500 | −1.54449 | −0.772245 | − | 0.635325i | \(-0.780866\pi\) | ||||
−0.772245 | + | 0.635325i | \(0.780866\pi\) | |||||||
\(44\) | 0.329409 | 0.00112864 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 73.8349 | 0.236660 | ||||||||
\(47\) | −54.0547 | −0.167759 | −0.0838797 | − | 0.996476i | \(-0.526731\pi\) | ||||
−0.0838797 | + | 0.996476i | \(0.526731\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | −348.037 | −0.984398 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 41.9186 | 0.111790 | ||||||||
\(53\) | −272.147 | −0.705325 | −0.352662 | − | 0.935751i | \(-0.614724\pi\) | ||||
−0.352662 | + | 0.935751i | \(0.614724\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.32109 | 0.00323883 | ||||||||
\(56\) | 151.431 | 0.361354 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −698.017 | −1.58024 | ||||||||
\(59\) | 516.496 | 1.13970 | 0.569848 | − | 0.821750i | \(-0.307002\pi\) | ||||
0.569848 | + | 0.821750i | \(0.307002\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 251.711 | 0.528332 | 0.264166 | − | 0.964477i | \(-0.414903\pi\) | ||||
0.264166 | + | 0.964477i | \(0.414903\pi\) | |||||||
\(62\) | −264.300 | −0.541389 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 464.704 | 0.907625 | ||||||||
\(65\) | 168.114 | 0.320800 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 461.750 | 0.841967 | 0.420984 | − | 0.907068i | \(-0.361685\pi\) | ||||
0.420984 | + | 0.907068i | \(0.361685\pi\) | |||||||
\(68\) | 2.16332 | 0.00385796 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −52.8576 | −0.0902527 | ||||||||
\(71\) | −532.933 | −0.890809 | −0.445405 | − | 0.895329i | \(-0.646940\pi\) | ||||
−0.445405 | + | 0.895329i | \(0.646940\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −360.888 | −0.578613 | −0.289306 | − | 0.957237i | \(-0.593425\pi\) | ||||
−0.289306 | + | 0.957237i | \(0.593425\pi\) | |||||||
\(74\) | −198.333 | −0.311564 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −79.3432 | −0.119754 | ||||||||
\(77\) | −3.59991 | −0.00532789 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 762.674 | 1.08617 | 0.543086 | − | 0.839677i | \(-0.317256\pi\) | ||||
0.543086 | + | 0.839677i | \(0.317256\pi\) | |||||||
\(80\) | −176.516 | −0.246689 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −844.559 | −1.13739 | ||||||||
\(83\) | 944.843 | 1.24952 | 0.624759 | − | 0.780818i | \(-0.285197\pi\) | ||||
0.624759 | + | 0.780818i | \(0.285197\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.67598 | 0.0110711 | ||||||||
\(86\) | −1280.14 | −1.60513 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −11.1253 | −0.0134768 | ||||||||
\(89\) | −1494.37 | −1.77981 | −0.889906 | − | 0.456145i | \(-0.849230\pi\) | ||||
−0.889906 | + | 0.456145i | \(0.849230\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −458.104 | −0.527718 | ||||||||
\(92\) | 16.0891 | 0.0182327 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −158.893 | −0.174346 | ||||||||
\(95\) | −318.205 | −0.343654 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1345.58 | 1.40849 | 0.704243 | − | 0.709959i | \(-0.251287\pi\) | ||||
0.704243 | + | 0.709959i | \(0.251287\pi\) | |||||||
\(98\) | 144.034 | 0.148466 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −75.8398 | −0.0758398 | ||||||||
\(101\) | −1779.71 | −1.75334 | −0.876670 | − | 0.481092i | \(-0.840240\pi\) | ||||
−0.876670 | + | 0.481092i | \(0.840240\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −37.3017 | −0.0356839 | −0.0178420 | − | 0.999841i | \(-0.505680\pi\) | ||||
−0.0178420 | + | 0.999841i | \(0.505680\pi\) | |||||||
\(104\) | −1415.74 | −1.33485 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −799.969 | −0.733018 | ||||||||
\(107\) | −389.494 | −0.351905 | −0.175953 | − | 0.984399i | \(-0.556301\pi\) | ||||
−0.175953 | + | 0.984399i | \(0.556301\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 115.830 | 0.101784 | 0.0508922 | − | 0.998704i | \(-0.483794\pi\) | ||||
0.0508922 | + | 0.998704i | \(0.483794\pi\) | |||||||
\(110\) | 3.88332 | 0.00336600 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 480.998 | 0.405804 | ||||||||
\(113\) | 1920.18 | 1.59854 | 0.799270 | − | 0.600971i | \(-0.205219\pi\) | ||||
0.799270 | + | 0.600971i | \(0.205219\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 64.5253 | 0.0523219 | ||||||||
\(116\) | −152.103 | −0.121745 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1518.23 | 1.18444 | ||||||||
\(119\) | −23.6416 | −0.0182120 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1330.74 | −0.999801 | ||||||||
\(122\) | 739.898 | 0.549076 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −57.5928 | −0.0417096 | ||||||||
\(125\) | −625.261 | −0.447401 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2674.36 | 1.86859 | 0.934295 | − | 0.356502i | \(-0.116031\pi\) | ||||
0.934295 | + | 0.356502i | \(0.116031\pi\) | |||||||
\(128\) | 1597.34 | 1.10302 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 494.169 | 0.333396 | ||||||||
\(131\) | −1237.50 | −0.825348 | −0.412674 | − | 0.910879i | \(-0.635405\pi\) | ||||
−0.412674 | + | 0.910879i | \(0.635405\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 867.094 | 0.565313 | ||||||||
\(134\) | 1357.31 | 0.875025 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −73.0627 | −0.0460668 | ||||||||
\(137\) | −2378.33 | −1.48317 | −0.741586 | − | 0.670858i | \(-0.765926\pi\) | ||||
−0.741586 | + | 0.670858i | \(0.765926\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1164.47 | 0.710569 | 0.355284 | − | 0.934758i | \(-0.384384\pi\) | ||||
0.355284 | + | 0.934758i | \(0.384384\pi\) | |||||||
\(140\) | −11.5180 | −0.00695323 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1566.54 | −0.925785 | ||||||||
\(143\) | 33.6557 | 0.0196814 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −610.007 | −0.349368 | ||||||||
\(146\) | −1060.82 | −0.601331 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −43.2181 | −0.0240034 | ||||||||
\(149\) | −1679.39 | −0.923362 | −0.461681 | − | 0.887046i | \(-0.652754\pi\) | ||||
−0.461681 | + | 0.887046i | \(0.652754\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 864.499 | 0.465907 | 0.232953 | − | 0.972488i | \(-0.425161\pi\) | ||||
0.232953 | + | 0.972488i | \(0.425161\pi\) | |||||||
\(152\) | 2679.69 | 1.42995 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −10.5819 | −0.00553708 | ||||||||
\(155\) | −230.976 | −0.119693 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1723.42 | 0.876074 | 0.438037 | − | 0.898957i | \(-0.355674\pi\) | ||||
0.438037 | + | 0.898957i | \(0.355674\pi\) | |||||||
\(158\) | 2241.86 | 1.12882 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −74.2895 | −0.0367069 | ||||||||
\(161\) | −175.828 | −0.0860697 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2035.48 | 0.978105 | 0.489052 | − | 0.872254i | \(-0.337343\pi\) | ||||
0.489052 | + | 0.872254i | \(0.337343\pi\) | |||||||
\(164\) | −184.035 | −0.0876266 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2777.35 | 1.29858 | ||||||||
\(167\) | −1610.71 | −0.746351 | −0.373175 | − | 0.927761i | \(-0.621731\pi\) | ||||
−0.373175 | + | 0.927761i | \(0.621731\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2085.83 | 0.949401 | ||||||||
\(170\) | 25.5029 | 0.0115058 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −278.952 | −0.123662 | ||||||||
\(173\) | −2011.71 | −0.884089 | −0.442045 | − | 0.896993i | \(-0.645747\pi\) | ||||
−0.442045 | + | 0.896993i | \(0.645747\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 828.807 | 0.358011 | ||||||||
\(176\) | −35.3377 | −0.0151345 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −4392.68 | −1.84969 | ||||||||
\(179\) | 1778.67 | 0.742704 | 0.371352 | − | 0.928492i | \(-0.378894\pi\) | ||||
0.371352 | + | 0.928492i | \(0.378894\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −608.294 | −0.249802 | −0.124901 | − | 0.992169i | \(-0.539861\pi\) | ||||
−0.124901 | + | 0.992169i | \(0.539861\pi\) | |||||||
\(182\) | −1346.59 | −0.548437 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −543.385 | −0.217711 | ||||||||
\(185\) | −173.326 | −0.0688820 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.73689 | 0.000679220 0 | ||||||||
\(188\) | −34.6239 | −0.0134319 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −935.357 | −0.357147 | ||||||||
\(191\) | 4394.84 | 1.66492 | 0.832459 | − | 0.554086i | \(-0.186932\pi\) | ||||
0.832459 | + | 0.554086i | \(0.186932\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1186.92 | 0.442675 | 0.221337 | − | 0.975197i | \(-0.428958\pi\) | ||||
0.221337 | + | 0.975197i | \(0.428958\pi\) | |||||||
\(194\) | 3955.31 | 1.46379 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 31.3861 | 0.0114381 | ||||||||
\(197\) | 816.364 | 0.295246 | 0.147623 | − | 0.989044i | \(-0.452838\pi\) | ||||
0.147623 | + | 0.989044i | \(0.452838\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5392.46 | −1.92091 | −0.960455 | − | 0.278434i | \(-0.910185\pi\) | ||||
−0.960455 | + | 0.278434i | \(0.910185\pi\) | |||||||
\(200\) | 2561.37 | 0.905580 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −5231.41 | −1.82218 | ||||||||
\(203\) | 1662.24 | 0.574711 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −738.073 | −0.251460 | ||||||||
\(206\) | −109.648 | −0.0370850 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4496.87 | −1.49905 | ||||||||
\(209\) | −63.7032 | −0.0210835 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2616.37 | 0.853643 | 0.426822 | − | 0.904336i | \(-0.359633\pi\) | ||||
0.426822 | + | 0.904336i | \(0.359633\pi\) | |||||||
\(212\) | −174.319 | −0.0564730 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1144.91 | −0.365722 | ||||||||
\(215\) | −1118.73 | −0.354870 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 629.397 | 0.196895 | ||||||||
\(218\) | 340.479 | 0.105781 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.846202 | 0.000259322 0 | ||||||||
\(221\) | 221.027 | 0.0672754 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −843.898 | −0.253415 | −0.126708 | − | 0.991940i | \(-0.540441\pi\) | ||||
−0.126708 | + | 0.991940i | \(0.540441\pi\) | |||||||
\(224\) | 202.435 | 0.0603829 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5644.32 | 1.66130 | ||||||||
\(227\) | 3349.28 | 0.979292 | 0.489646 | − | 0.871921i | \(-0.337126\pi\) | ||||
0.489646 | + | 0.871921i | \(0.337126\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −690.623 | −0.199291 | −0.0996455 | − | 0.995023i | \(-0.531771\pi\) | ||||
−0.0996455 | + | 0.995023i | \(0.531771\pi\) | |||||||
\(230\) | 189.671 | 0.0543762 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5137.03 | 1.45372 | ||||||||
\(233\) | 4203.93 | 1.18201 | 0.591005 | − | 0.806668i | \(-0.298731\pi\) | ||||
0.591005 | + | 0.806668i | \(0.298731\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −138.859 | −0.0385453 | ||||||||
\(236\) | 330.833 | 0.0912516 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −69.4941 | −0.0189270 | ||||||||
\(239\) | −4307.31 | −1.16576 | −0.582881 | − | 0.812558i | \(-0.698074\pi\) | ||||
−0.582881 | + | 0.812558i | \(0.698074\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5338.50 | −1.42690 | −0.713450 | − | 0.700707i | \(-0.752868\pi\) | ||||
−0.713450 | + | 0.700707i | \(0.752868\pi\) | |||||||
\(242\) | −3911.67 | −1.03906 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 161.229 | 0.0423018 | ||||||||
\(245\) | 125.874 | 0.0328236 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8106.51 | −2.08828 | ||||||||
\(248\) | 1945.11 | 0.498042 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1837.94 | −0.464967 | ||||||||
\(251\) | −2972.68 | −0.747546 | −0.373773 | − | 0.927520i | \(-0.621936\pi\) | ||||
−0.373773 | + | 0.927520i | \(0.621936\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.9177 | 0.00320999 | ||||||||
\(254\) | 7861.22 | 1.94195 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 977.720 | 0.238701 | ||||||||
\(257\) | 5115.82 | 1.24170 | 0.620848 | − | 0.783931i | \(-0.286788\pi\) | ||||
0.620848 | + | 0.783931i | \(0.286788\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 472.305 | 0.113311 | ||||||||
\(260\) | 107.683 | 0.0256854 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3637.60 | −0.857753 | ||||||||
\(263\) | −7270.03 | −1.70452 | −0.852261 | − | 0.523116i | \(-0.824769\pi\) | ||||
−0.852261 | + | 0.523116i | \(0.824769\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −699.105 | −0.162059 | ||||||||
\(266\) | 2548.80 | 0.587508 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 295.766 | 0.0674135 | ||||||||
\(269\) | −793.367 | −0.179823 | −0.0899116 | − | 0.995950i | \(-0.528658\pi\) | ||||
−0.0899116 | + | 0.995950i | \(0.528658\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7063.92 | 1.58340 | 0.791702 | − | 0.610907i | \(-0.209195\pi\) | ||||
0.791702 | + | 0.610907i | \(0.209195\pi\) | |||||||
\(272\) | −232.073 | −0.0517334 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6991.05 | −1.54140 | ||||||||
\(275\) | −60.8904 | −0.0133521 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7158.56 | 1.55277 | 0.776383 | − | 0.630261i | \(-0.217052\pi\) | ||||
0.776383 | + | 0.630261i | \(0.217052\pi\) | |||||||
\(278\) | 3422.94 | 0.738468 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 389.004 | 0.0830265 | ||||||||
\(281\) | 7559.85 | 1.60492 | 0.802461 | − | 0.596705i | \(-0.203524\pi\) | ||||
0.802461 | + | 0.596705i | \(0.203524\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3796.47 | −0.797443 | −0.398722 | − | 0.917072i | \(-0.630546\pi\) | ||||
−0.398722 | + | 0.917072i | \(0.630546\pi\) | |||||||
\(284\) | −341.361 | −0.0713241 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 98.9303 | 0.0204541 | ||||||||
\(287\) | 2011.21 | 0.413652 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4901.59 | −0.997678 | ||||||||
\(290\) | −1793.10 | −0.363085 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −231.161 | −0.0463276 | ||||||||
\(293\) | −602.803 | −0.120192 | −0.0600958 | − | 0.998193i | \(-0.519141\pi\) | ||||
−0.0600958 | + | 0.998193i | \(0.519141\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1326.80 | 0.261862 | ||||||||
\(296\) | 1459.62 | 0.286618 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4936.53 | −0.959616 | ||||||||
\(299\) | 1643.83 | 0.317944 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3048.50 | 0.583763 | ||||||||
\(302\) | 2541.18 | 0.484200 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 8511.64 | 1.60584 | ||||||||
\(305\) | 646.608 | 0.121392 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9215.96 | 1.71330 | 0.856649 | − | 0.515900i | \(-0.172542\pi\) | ||||
0.856649 | + | 0.515900i | \(0.172542\pi\) | |||||||
\(308\) | −2.30586 | −0.000426586 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −678.948 | −0.124392 | ||||||||
\(311\) | −2193.57 | −0.399955 | −0.199977 | − | 0.979801i | \(-0.564087\pi\) | ||||
−0.199977 | + | 0.979801i | \(0.564087\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6208.20 | −1.12111 | −0.560556 | − | 0.828116i | \(-0.689413\pi\) | ||||
−0.560556 | + | 0.828116i | \(0.689413\pi\) | |||||||
\(314\) | 5065.95 | 0.910471 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 488.518 | 0.0869661 | ||||||||
\(317\) | −6756.19 | −1.19705 | −0.598526 | − | 0.801103i | \(-0.704247\pi\) | ||||
−0.598526 | + | 0.801103i | \(0.704247\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −122.121 | −0.0214340 | ||||||||
\(320\) | 1193.76 | 0.208541 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −516.844 | −0.0894490 | ||||||||
\(323\) | −418.357 | −0.0720682 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7748.56 | −1.32250 | ||||||||
\(326\) | 5983.25 | 1.01651 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6215.51 | 1.04632 | ||||||||
\(329\) | 378.383 | 0.0634071 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5692.19 | −0.945229 | −0.472615 | − | 0.881269i | \(-0.656690\pi\) | ||||
−0.472615 | + | 0.881269i | \(0.656690\pi\) | |||||||
\(332\) | 605.203 | 0.100045 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4734.65 | −0.775655 | ||||||||
\(335\) | 1186.17 | 0.193455 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9528.00 | 1.54013 | 0.770064 | − | 0.637967i | \(-0.220224\pi\) | ||||
0.770064 | + | 0.637967i | \(0.220224\pi\) | |||||||
\(338\) | 6131.27 | 0.986677 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 5.55725 | 0.000886424 0 | ||||||||
\(341\) | −46.2403 | −0.00734326 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | 9421.16 | 1.47661 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5913.38 | −0.918801 | ||||||||
\(347\) | −6723.08 | −1.04010 | −0.520049 | − | 0.854136i | \(-0.674086\pi\) | ||||
−0.520049 | + | 0.854136i | \(0.674086\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3224.96 | −0.494637 | −0.247319 | − | 0.968934i | \(-0.579549\pi\) | ||||
−0.247319 | + | 0.968934i | \(0.579549\pi\) | |||||||
\(350\) | 2436.26 | 0.372067 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −14.8724 | −0.00225199 | ||||||||
\(353\) | −7200.11 | −1.08562 | −0.542809 | − | 0.839856i | \(-0.682639\pi\) | ||||
−0.542809 | + | 0.839856i | \(0.682639\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1369.03 | −0.204677 | ||||||||
\(356\) | −957.195 | −0.142504 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5228.36 | 0.771864 | ||||||||
\(359\) | −3642.82 | −0.535545 | −0.267772 | − | 0.963482i | \(-0.586288\pi\) | ||||
−0.267772 | + | 0.963482i | \(0.586288\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8484.92 | 1.23705 | ||||||||
\(362\) | −1788.07 | −0.259610 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −293.431 | −0.0422526 | ||||||||
\(365\) | −927.068 | −0.132945 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2832.77 | −0.402914 | −0.201457 | − | 0.979497i | \(-0.564568\pi\) | ||||
−0.201457 | + | 0.979497i | \(0.564568\pi\) | |||||||
\(368\) | −1725.98 | −0.244492 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −509.488 | −0.0715865 | ||||||||
\(371\) | 1905.03 | 0.266588 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5166.34 | 0.717166 | 0.358583 | − | 0.933498i | \(-0.383260\pi\) | ||||
0.358583 | + | 0.933498i | \(0.383260\pi\) | |||||||
\(374\) | 5.10555 | 0.000705888 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1169.37 | 0.160387 | ||||||||
\(377\) | −15540.4 | −2.12300 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 56.3096 | 0.00763174 | 0.00381587 | − | 0.999993i | \(-0.498785\pi\) | ||||
0.00381587 | + | 0.999993i | \(0.498785\pi\) | |||||||
\(380\) | −203.821 | −0.0275152 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 12918.5 | 1.73029 | ||||||||
\(383\) | 5055.39 | 0.674461 | 0.337230 | − | 0.941422i | \(-0.390510\pi\) | ||||
0.337230 | + | 0.941422i | \(0.390510\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.24763 | −0.00122416 | ||||||||
\(386\) | 3488.92 | 0.460055 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 861.889 | 0.112773 | ||||||||
\(389\) | −2535.98 | −0.330539 | −0.165269 | − | 0.986248i | \(-0.552849\pi\) | ||||
−0.165269 | + | 0.986248i | \(0.552849\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 84.8341 | 0.0109725 | ||||||||
\(392\) | −1060.02 | −0.136579 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2399.68 | 0.306838 | ||||||||
\(395\) | 1959.20 | 0.249564 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3204.52 | 0.405114 | 0.202557 | − | 0.979270i | \(-0.435075\pi\) | ||||
0.202557 | + | 0.979270i | \(0.435075\pi\) | |||||||
\(398\) | −15851.0 | −1.99633 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 8135.80 | 1.01698 | ||||||||
\(401\) | −1551.92 | −0.193265 | −0.0966323 | − | 0.995320i | \(-0.530807\pi\) | ||||
−0.0966323 | + | 0.995320i | \(0.530807\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5884.27 | −0.727336 | ||||||||
\(404\) | −1139.96 | −0.140384 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4886.12 | 0.597276 | ||||||||
\(407\) | −34.6991 | −0.00422597 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 566.211 | 0.0684531 | 0.0342265 | − | 0.999414i | \(-0.489103\pi\) | ||||
0.0342265 | + | 0.999414i | \(0.489103\pi\) | |||||||
\(410\) | −2169.55 | −0.261333 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −23.8930 | −0.00285709 | ||||||||
\(413\) | −3615.47 | −0.430764 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2427.16 | 0.287096 | ||||||||
\(416\) | −1892.58 | −0.223056 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −187.254 | −0.0219113 | ||||||||
\(419\) | −10645.8 | −1.24125 | −0.620624 | − | 0.784108i | \(-0.713121\pi\) | ||||
−0.620624 | + | 0.784108i | \(0.713121\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9283.60 | −1.07471 | −0.537357 | − | 0.843355i | \(-0.680577\pi\) | ||||
−0.537357 | + | 0.843355i | \(0.680577\pi\) | |||||||
\(422\) | 7690.78 | 0.887159 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5887.35 | 0.674328 | ||||||||
\(425\) | −399.885 | −0.0456406 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1761.97 | −0.199691 | ||||||||
\(428\) | −249.484 | −0.0281759 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3288.50 | −0.368803 | ||||||||
\(431\) | 7494.55 | 0.837587 | 0.418793 | − | 0.908082i | \(-0.362453\pi\) | ||||
0.418793 | + | 0.908082i | \(0.362453\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1564.51 | −0.173639 | −0.0868195 | − | 0.996224i | \(-0.527670\pi\) | ||||
−0.0868195 | + | 0.996224i | \(0.527670\pi\) | |||||||
\(434\) | 1850.10 | 0.204626 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 74.1929 | 0.00814953 | ||||||||
\(437\) | −3111.42 | −0.340594 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11397.1 | 1.23907 | 0.619537 | − | 0.784967i | \(-0.287320\pi\) | ||||
0.619537 | + | 0.784967i | \(0.287320\pi\) | |||||||
\(440\) | −28.5791 | −0.00309649 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 649.704 | 0.0699169 | ||||||||
\(443\) | −4335.52 | −0.464982 | −0.232491 | − | 0.972599i | \(-0.574688\pi\) | ||||
−0.232491 | + | 0.972599i | \(0.574688\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3838.82 | −0.408939 | ||||||||
\(446\) | −2480.62 | −0.263365 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3252.93 | −0.343050 | ||||||||
\(449\) | 14016.9 | 1.47327 | 0.736634 | − | 0.676291i | \(-0.236414\pi\) | ||||
0.736634 | + | 0.676291i | \(0.236414\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −147.759 | −0.0154272 | ||||||||
\(452\) | 1229.94 | 0.127990 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 9845.13 | 1.01774 | ||||||||
\(455\) | −1176.80 | −0.121251 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2506.06 | 0.256518 | 0.128259 | − | 0.991741i | \(-0.459061\pi\) | ||||
0.128259 | + | 0.991741i | \(0.459061\pi\) | |||||||
\(458\) | −2030.07 | −0.207116 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 41.3306 | 0.00418924 | ||||||||
\(461\) | −13664.0 | −1.38047 | −0.690235 | − | 0.723585i | \(-0.742493\pi\) | ||||
−0.690235 | + | 0.723585i | \(0.742493\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1590.36 | 0.159634 | 0.0798168 | − | 0.996810i | \(-0.474566\pi\) | ||||
0.0798168 | + | 0.996810i | \(0.474566\pi\) | |||||||
\(464\) | 16317.0 | 1.63254 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 12357.4 | 1.22842 | ||||||||
\(467\) | 8980.42 | 0.889859 | 0.444930 | − | 0.895566i | \(-0.353229\pi\) | ||||
0.444930 | + | 0.895566i | \(0.353229\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3232.25 | −0.318234 | ||||||||
\(470\) | −408.172 | −0.0400587 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −11173.4 | −1.08961 | ||||||||
\(473\) | −223.966 | −0.0217716 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14666.4 | 1.41672 | ||||||||
\(476\) | −15.1432 | −0.00145817 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −12661.3 | −1.21153 | ||||||||
\(479\) | −4391.79 | −0.418927 | −0.209464 | − | 0.977816i | \(-0.567172\pi\) | ||||
−0.209464 | + | 0.977816i | \(0.567172\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4415.60 | −0.418574 | ||||||||
\(482\) | −15692.4 | −1.48292 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −852.380 | −0.0800507 | ||||||||
\(485\) | 3456.60 | 0.323621 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9440.93 | 0.878458 | 0.439229 | − | 0.898375i | \(-0.355252\pi\) | ||||
0.439229 | + | 0.898375i | \(0.355252\pi\) | |||||||
\(488\) | −5445.26 | −0.505113 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 370.003 | 0.0341123 | ||||||||
\(491\) | 7309.23 | 0.671814 | 0.335907 | − | 0.941895i | \(-0.390957\pi\) | ||||
0.335907 | + | 0.941895i | \(0.390957\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −802.001 | −0.0732664 | ||||||||
\(494\) | −23828.9 | −2.17027 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6178.34 | 0.559306 | ||||||||
\(497\) | 3730.53 | 0.336694 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8594.72 | −0.771047 | −0.385524 | − | 0.922698i | \(-0.625979\pi\) | ||||
−0.385524 | + | 0.922698i | \(0.625979\pi\) | |||||||
\(500\) | −400.501 | −0.0358219 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −8738.14 | −0.776897 | ||||||||
\(503\) | −13124.1 | −1.16337 | −0.581684 | − | 0.813415i | \(-0.697606\pi\) | ||||
−0.581684 | + | 0.813415i | \(0.697606\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4571.80 | −0.402856 | ||||||||
\(506\) | 37.9712 | 0.00333602 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1713.01 | 0.149612 | ||||||||
\(509\) | −21261.2 | −1.85145 | −0.925725 | − | 0.378198i | \(-0.876544\pi\) | ||||
−0.925725 | + | 0.378198i | \(0.876544\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2526.21 | 0.218695 | ||||||||
\(512\) | −9904.75 | −0.854946 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 15037.8 | 1.29045 | ||||||||
\(515\) | −95.8226 | −0.00819893 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −27.7989 | −0.00236478 | ||||||||
\(518\) | 1388.33 | 0.117760 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3636.82 | −0.306702 | ||||||||
\(521\) | −18918.3 | −1.59084 | −0.795419 | − | 0.606059i | \(-0.792749\pi\) | ||||
−0.795419 | + | 0.606059i | \(0.792749\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3728.42 | −0.311725 | −0.155863 | − | 0.987779i | \(-0.549816\pi\) | ||||
−0.155863 | + | 0.987779i | \(0.549816\pi\) | |||||||
\(524\) | −792.658 | −0.0660829 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −21370.1 | −1.77145 | ||||||||
\(527\) | −303.673 | −0.0251010 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11536.1 | −0.948144 | ||||||||
\(530\) | −2055.00 | −0.168422 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 555.402 | 0.0452627 | ||||||||
\(533\) | −18802.9 | −1.52804 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1000.55 | −0.0808555 | ||||||||
\(536\) | −9989.04 | −0.804965 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −2332.09 | −0.186884 | ||||||||
\(539\) | 25.1994 | 0.00201375 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20984.0 | −1.66761 | −0.833803 | − | 0.552062i | \(-0.813841\pi\) | ||||
−0.833803 | + | 0.552062i | \(0.813841\pi\) | |||||||
\(542\) | 20764.2 | 1.64557 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −97.6714 | −0.00769784 | ||||||||
\(545\) | 297.550 | 0.0233865 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2840.49 | −0.222030 | −0.111015 | − | 0.993819i | \(-0.535410\pi\) | ||||
−0.111015 | + | 0.993819i | \(0.535410\pi\) | |||||||
\(548\) | −1523.40 | −0.118753 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −178.986 | −0.0138763 | ||||||||
\(551\) | 29414.7 | 2.27424 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5338.72 | −0.410534 | ||||||||
\(554\) | 21042.4 | 1.61373 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 745.882 | 0.0568929 | ||||||||
\(557\) | −5824.36 | −0.443063 | −0.221532 | − | 0.975153i | \(-0.571106\pi\) | ||||
−0.221532 | + | 0.975153i | \(0.571106\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −28500.6 | −2.15643 | ||||||||
\(560\) | 1235.61 | 0.0932396 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 22222.0 | 1.66793 | ||||||||
\(563\) | −7380.87 | −0.552516 | −0.276258 | − | 0.961083i | \(-0.589094\pi\) | ||||
−0.276258 | + | 0.961083i | \(0.589094\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4932.65 | 0.367289 | ||||||||
\(566\) | −11159.6 | −0.828753 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 11528.9 | 0.851660 | ||||||||
\(569\) | 12051.2 | 0.887892 | 0.443946 | − | 0.896053i | \(-0.353578\pi\) | ||||
0.443946 | + | 0.896053i | \(0.353578\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18270.9 | −1.33908 | −0.669538 | − | 0.742778i | \(-0.733508\pi\) | ||||
−0.669538 | + | 0.742778i | \(0.733508\pi\) | |||||||
\(572\) | 21.5576 | 0.00157582 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 5911.92 | 0.429893 | ||||||||
\(575\) | −2974.04 | −0.215697 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10165.1 | 0.733413 | 0.366707 | − | 0.930337i | \(-0.380485\pi\) | ||||
0.366707 | + | 0.930337i | \(0.380485\pi\) | |||||||
\(578\) | −14408.1 | −1.03685 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −390.730 | −0.0279727 | ||||||||
\(581\) | −6613.90 | −0.472273 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −139.958 | −0.00994245 | ||||||||
\(584\) | 7807.08 | 0.553184 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1771.93 | −0.124911 | ||||||||
\(587\) | 4635.34 | 0.325930 | 0.162965 | − | 0.986632i | \(-0.447894\pi\) | ||||
0.162965 | + | 0.986632i | \(0.447894\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11137.7 | 0.779152 | ||||||||
\(590\) | 3900.11 | 0.272144 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4636.28 | 0.321875 | ||||||||
\(593\) | −16282.3 | −1.12755 | −0.563773 | − | 0.825930i | \(-0.690651\pi\) | ||||
−0.563773 | + | 0.825930i | \(0.690651\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −60.7319 | −0.00418448 | ||||||||
\(596\) | −1075.70 | −0.0739305 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4832.00 | 0.330427 | ||||||||
\(599\) | −9759.63 | −0.665722 | −0.332861 | − | 0.942976i | \(-0.608014\pi\) | ||||
−0.332861 | + | 0.942976i | \(0.608014\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11844.3 | 0.803894 | 0.401947 | − | 0.915663i | \(-0.368334\pi\) | ||||
0.401947 | + | 0.915663i | \(0.368334\pi\) | |||||||
\(602\) | 8960.99 | 0.606683 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 553.740 | 0.0373036 | ||||||||
\(605\) | −3418.46 | −0.229719 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22206.1 | −1.48488 | −0.742438 | − | 0.669915i | \(-0.766331\pi\) | ||||
−0.742438 | + | 0.669915i | \(0.766331\pi\) | |||||||
\(608\) | 3582.25 | 0.238947 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1900.69 | 0.126158 | ||||||||
\(611\) | −3537.52 | −0.234227 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19461.8 | −1.28231 | −0.641154 | − | 0.767412i | \(-0.721544\pi\) | ||||
−0.641154 | + | 0.767412i | \(0.721544\pi\) | |||||||
\(614\) | 27090.1 | 1.78057 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 77.8768 | 0.00509374 | ||||||||
\(617\) | 15820.2 | 1.03225 | 0.516124 | − | 0.856514i | \(-0.327375\pi\) | ||||
0.516124 | + | 0.856514i | \(0.327375\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15398.0 | −0.999838 | −0.499919 | − | 0.866072i | \(-0.666637\pi\) | ||||
−0.499919 | + | 0.866072i | \(0.666637\pi\) | |||||||
\(620\) | −147.948 | −0.00958341 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −6447.95 | −0.415658 | ||||||||
\(623\) | 10460.6 | 0.672705 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13193.9 | 0.844411 | ||||||||
\(626\) | −18248.9 | −1.16513 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1103.91 | 0.0701443 | ||||||||
\(629\) | −227.879 | −0.0144453 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15072.8 | 0.950930 | 0.475465 | − | 0.879735i | \(-0.342280\pi\) | ||||
0.475465 | + | 0.879735i | \(0.342280\pi\) | |||||||
\(632\) | −16498.9 | −1.03844 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −19859.7 | −1.24405 | ||||||||
\(635\) | 6870.03 | 0.429337 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3206.73 | 0.199459 | ||||||||
\(638\) | −358.971 | −0.0222755 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 4103.34 | 0.253435 | ||||||||
\(641\) | −20448.2 | −1.25999 | −0.629996 | − | 0.776598i | \(-0.716944\pi\) | ||||
−0.629996 | + | 0.776598i | \(0.716944\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8343.12 | 0.511696 | 0.255848 | − | 0.966717i | \(-0.417645\pi\) | ||||
0.255848 | + | 0.966717i | \(0.417645\pi\) | |||||||
\(644\) | −112.624 | −0.00689131 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1229.75 | −0.0748978 | ||||||||
\(647\) | 2134.15 | 0.129679 | 0.0648394 | − | 0.997896i | \(-0.479347\pi\) | ||||
0.0648394 | + | 0.997896i | \(0.479347\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 265.620 | 0.0160655 | ||||||||
\(650\) | −22776.7 | −1.37443 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1303.79 | 0.0783136 | ||||||||
\(653\) | 25095.3 | 1.50391 | 0.751956 | − | 0.659213i | \(-0.229110\pi\) | ||||
0.751956 | + | 0.659213i | \(0.229110\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3178.95 | −0.189636 | ||||||||
\(656\) | 19742.6 | 1.17503 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1112.25 | 0.0658966 | ||||||||
\(659\) | −21027.4 | −1.24296 | −0.621481 | − | 0.783429i | \(-0.713469\pi\) | ||||
−0.621481 | + | 0.783429i | \(0.713469\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2656.34 | −0.156308 | −0.0781541 | − | 0.996941i | \(-0.524903\pi\) | ||||
−0.0781541 | + | 0.996941i | \(0.524903\pi\) | |||||||
\(662\) | −16732.1 | −0.982341 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −20439.8 | −1.19460 | ||||||||
\(665\) | 2227.44 | 0.129889 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5964.68 | −0.346257 | ||||||||
\(668\) | −1031.71 | −0.0597578 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 3486.72 | 0.201050 | ||||||||
\(671\) | 129.448 | 0.00744751 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15791.3 | −0.904471 | −0.452235 | − | 0.891899i | \(-0.649373\pi\) | ||||
−0.452235 | + | 0.891899i | \(0.649373\pi\) | |||||||
\(674\) | 28007.3 | 1.60060 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1336.05 | 0.0760154 | ||||||||
\(677\) | −4012.08 | −0.227765 | −0.113882 | − | 0.993494i | \(-0.536329\pi\) | ||||
−0.113882 | + | 0.993494i | \(0.536329\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9419.07 | −0.532357 | ||||||||
\(680\) | −187.687 | −0.0105845 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −135.922 | −0.00763157 | ||||||||
\(683\) | 7438.45 | 0.416727 | 0.208363 | − | 0.978051i | \(-0.433186\pi\) | ||||
0.208363 | + | 0.978051i | \(0.433186\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6109.58 | −0.340781 | ||||||||
\(686\) | −1008.24 | −0.0561149 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 29924.9 | 1.65825 | ||||||||
\(689\) | −17810.2 | −0.984781 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16071.1 | 0.884764 | 0.442382 | − | 0.896827i | \(-0.354133\pi\) | ||||
0.442382 | + | 0.896827i | \(0.354133\pi\) | |||||||
\(692\) | −1288.57 | −0.0707860 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −19762.4 | −1.08093 | ||||||||
\(695\) | 2991.35 | 0.163264 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −970.374 | −0.0527339 | ||||||||
\(698\) | −9479.71 | −0.514058 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 530.878 | 0.0286647 | ||||||||
\(701\) | 27269.4 | 1.46926 | 0.734630 | − | 0.678467i | \(-0.237356\pi\) | ||||
0.734630 | + | 0.678467i | \(0.237356\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8357.81 | 0.448394 | ||||||||
\(704\) | 238.985 | 0.0127941 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −21164.6 | −1.12824 | ||||||||
\(707\) | 12457.9 | 0.662700 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12825.7 | 0.679377 | 0.339689 | − | 0.940538i | \(-0.389678\pi\) | ||||
0.339689 | + | 0.940538i | \(0.389678\pi\) | |||||||
\(710\) | −4024.22 | −0.212713 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 32327.8 | 1.70159 | ||||||||
\(713\) | −2258.49 | −0.118627 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 86.4566 | 0.00452209 | ||||||||
\(716\) | 1139.30 | 0.0594658 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −10708.0 | −0.556572 | ||||||||
\(719\) | 9140.58 | 0.474111 | 0.237056 | − | 0.971496i | \(-0.423818\pi\) | ||||
0.237056 | + | 0.971496i | \(0.423818\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 261.112 | 0.0134873 | ||||||||
\(722\) | 24941.2 | 1.28562 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −389.632 | −0.0200008 | ||||||||
\(725\) | 28115.8 | 1.44027 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11651.7 | −0.594412 | −0.297206 | − | 0.954813i | \(-0.596055\pi\) | ||||
−0.297206 | + | 0.954813i | \(0.596055\pi\) | |||||||
\(728\) | 9910.15 | 0.504526 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2725.10 | −0.138165 | ||||||||
\(731\) | −1470.85 | −0.0744203 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18831.0 | 0.948894 | 0.474447 | − | 0.880284i | \(-0.342648\pi\) | ||||
0.474447 | + | 0.880284i | \(0.342648\pi\) | |||||||
\(734\) | −8326.86 | −0.418733 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −726.406 | −0.0363800 | ||||||||
\(737\) | 237.466 | 0.0118686 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7467.51 | 0.371714 | 0.185857 | − | 0.982577i | \(-0.440494\pi\) | ||||
0.185857 | + | 0.982577i | \(0.440494\pi\) | |||||||
\(740\) | −111.021 | −0.00551515 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5599.79 | 0.277055 | ||||||||
\(743\) | 12467.1 | 0.615576 | 0.307788 | − | 0.951455i | \(-0.400411\pi\) | ||||
0.307788 | + | 0.951455i | \(0.400411\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4314.10 | −0.212156 | ||||||||
\(746\) | 15186.3 | 0.745324 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.11254 | 5.43828e−5 0 | ||||||||
\(749\) | 2726.46 | 0.133008 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2456.69 | −0.119368 | −0.0596842 | − | 0.998217i | \(-0.519009\pi\) | ||||
−0.0596842 | + | 0.998217i | \(0.519009\pi\) | |||||||
\(752\) | 3714.32 | 0.180116 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −45680.6 | −2.20635 | ||||||||
\(755\) | 2220.77 | 0.107049 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7246.72 | −0.347935 | −0.173967 | − | 0.984751i | \(-0.555659\pi\) | ||||
−0.173967 | + | 0.984751i | \(0.555659\pi\) | |||||||
\(758\) | 165.521 | 0.00793138 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6883.73 | 0.328552 | ||||||||
\(761\) | 12683.0 | 0.604149 | 0.302075 | − | 0.953284i | \(-0.402321\pi\) | ||||
0.302075 | + | 0.953284i | \(0.402321\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −810.809 | −0.0384709 | ||||||||
\(764\) | 2815.04 | 0.133304 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 14860.2 | 0.700942 | ||||||||
\(767\) | 33801.2 | 1.59125 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14297.4 | −0.670454 | −0.335227 | − | 0.942137i | \(-0.608813\pi\) | ||||
−0.335227 | + | 0.942137i | \(0.608813\pi\) | |||||||
\(770\) | −27.1832 | −0.00127223 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 760.260 | 0.0354435 | ||||||||
\(773\) | −6703.00 | −0.311889 | −0.155944 | − | 0.987766i | \(-0.549842\pi\) | ||||
−0.155944 | + | 0.987766i | \(0.549842\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10645.9 | 0.493435 | ||||||||
\(776\) | −29109.0 | −1.34659 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −7454.47 | −0.343516 | ||||||||
\(779\) | 35590.0 | 1.63690 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −274.073 | −0.0125571 | ||||||||
\(782\) | 249.368 | 0.0114033 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3366.99 | −0.153379 | ||||||||
\(785\) | 4427.20 | 0.201291 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 34935.0 | 1.58233 | 0.791167 | − | 0.611600i | \(-0.209474\pi\) | ||||
0.791167 | + | 0.611600i | \(0.209474\pi\) | |||||||
\(788\) | 522.908 | 0.0236394 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 5759.02 | 0.259363 | ||||||||
\(791\) | −13441.2 | −0.604192 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16472.8 | 0.737662 | ||||||||
\(794\) | 9419.62 | 0.421020 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3454.05 | −0.153801 | ||||||||
\(797\) | −2614.16 | −0.116184 | −0.0580918 | − | 0.998311i | \(-0.518502\pi\) | ||||
−0.0580918 | + | 0.998311i | \(0.518502\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −182.563 | −0.00808338 | ||||||||
\(800\) | 3424.08 | 0.151324 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −4561.83 | −0.200853 | ||||||||
\(803\) | −185.595 | −0.00815628 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −451.677 | −0.0197758 | ||||||||
\(806\) | −17296.7 | −0.755893 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 38500.4 | 1.67628 | ||||||||
\(809\) | −14079.7 | −0.611885 | −0.305942 | − | 0.952050i | \(-0.598971\pi\) | ||||
−0.305942 | + | 0.952050i | \(0.598971\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 360.517 | 0.0156097 | 0.00780485 | − | 0.999970i | \(-0.497516\pi\) | ||||
0.00780485 | + | 0.999970i | \(0.497516\pi\) | |||||||
\(812\) | 1064.72 | 0.0460152 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −101.997 | −0.00439189 | ||||||||
\(815\) | 5228.85 | 0.224734 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 53945.6 | 2.31006 | ||||||||
\(818\) | 1664.36 | 0.0711407 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −472.760 | −0.0201335 | ||||||||
\(821\) | 20005.9 | 0.850439 | 0.425220 | − | 0.905090i | \(-0.360197\pi\) | ||||
0.425220 | + | 0.905090i | \(0.360197\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11187.2 | 0.473828 | 0.236914 | − | 0.971531i | \(-0.423864\pi\) | ||||
0.236914 | + | 0.971531i | \(0.423864\pi\) | |||||||
\(824\) | 806.948 | 0.0341157 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −10627.6 | −0.447677 | ||||||||
\(827\) | 10206.8 | 0.429172 | 0.214586 | − | 0.976705i | \(-0.431160\pi\) | ||||
0.214586 | + | 0.976705i | \(0.431160\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12084.0 | 0.506267 | 0.253134 | − | 0.967431i | \(-0.418539\pi\) | ||||
0.253134 | + | 0.967431i | \(0.418539\pi\) | |||||||
\(830\) | 7134.59 | 0.298368 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 30411.8 | 1.26724 | ||||||||
\(833\) | 165.491 | 0.00688348 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4137.68 | −0.171485 | ||||||||
\(836\) | −40.8040 | −0.00168808 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −31293.2 | −1.28998 | ||||||||
\(839\) | 5470.25 | 0.225094 | 0.112547 | − | 0.993646i | \(-0.464099\pi\) | ||||
0.112547 | + | 0.993646i | \(0.464099\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 31999.6 | 1.31205 | ||||||||
\(842\) | −27288.9 | −1.11691 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1675.87 | 0.0683483 | ||||||||
\(845\) | 5358.20 | 0.218139 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9315.15 | 0.377889 | ||||||||
\(848\) | 18700.3 | 0.757276 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1175.45 | −0.0474326 | ||||||||
\(851\) | −1694.79 | −0.0682686 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2405.08 | −0.0965398 | −0.0482699 | − | 0.998834i | \(-0.515371\pi\) | ||||
−0.0482699 | + | 0.998834i | \(0.515371\pi\) | |||||||
\(854\) | −5179.29 | −0.207531 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8425.93 | 0.336440 | ||||||||
\(857\) | 66.0880 | 0.00263422 | 0.00131711 | − | 0.999999i | \(-0.499581\pi\) | ||||
0.00131711 | + | 0.999999i | \(0.499581\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 30565.7 | 1.21407 | 0.607037 | − | 0.794673i | \(-0.292358\pi\) | ||||
0.607037 | + | 0.794673i | \(0.292358\pi\) | |||||||
\(860\) | −716.587 | −0.0284133 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 22030.1 | 0.870473 | ||||||||
\(863\) | 3384.92 | 0.133516 | 0.0667579 | − | 0.997769i | \(-0.478734\pi\) | ||||
0.0667579 | + | 0.997769i | \(0.478734\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5167.78 | −0.203133 | ||||||||
\(866\) | −4598.85 | −0.180456 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 403.150 | 0.0157647 | ||||||||
\(869\) | 392.222 | 0.0153110 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 30218.5 | 1.17556 | ||||||||
\(872\) | −2505.75 | −0.0973111 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −9145.97 | −0.353967 | ||||||||
\(875\) | 4376.83 | 0.169102 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −21340.0 | −0.821664 | −0.410832 | − | 0.911711i | \(-0.634762\pi\) | ||||
−0.410832 | + | 0.911711i | \(0.634762\pi\) | |||||||
\(878\) | 33501.5 | 1.28772 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −90.7774 | −0.00347739 | ||||||||
\(881\) | −24424.6 | −0.934037 | −0.467019 | − | 0.884247i | \(-0.654672\pi\) | ||||
−0.467019 | + | 0.884247i | \(0.654672\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −39237.6 | −1.49541 | −0.747707 | − | 0.664029i | \(-0.768845\pi\) | ||||
−0.747707 | + | 0.664029i | \(0.768845\pi\) | |||||||
\(884\) | 141.575 | 0.00538652 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −12744.2 | −0.483238 | ||||||||
\(887\) | 16580.6 | 0.627647 | 0.313823 | − | 0.949481i | \(-0.398390\pi\) | ||||
0.313823 | + | 0.949481i | \(0.398390\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18720.5 | −0.706260 | ||||||||
\(890\) | −11284.1 | −0.424995 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −540.545 | −0.0202901 | ||||||||
\(893\) | 6695.79 | 0.250914 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4569.14 | 0.170647 | ||||||||
\(896\) | −11181.4 | −0.416902 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 41202.3 | 1.53111 | ||||||||
\(899\) | 21351.2 | 0.792106 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −919.142 | −0.0339856 | ||||||||
\(902\) | −434.334 | −0.0160330 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −41539.2 | −1.52829 | ||||||||
\(905\) | −1562.62 | −0.0573958 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −31392.2 | −1.14924 | −0.574619 | − | 0.818421i | \(-0.694850\pi\) | ||||
−0.574619 | + | 0.818421i | \(0.694850\pi\) | |||||||
\(908\) | 2145.32 | 0.0784087 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −3459.18 | −0.126012 | ||||||||
\(911\) | 51535.7 | 1.87426 | 0.937131 | − | 0.348977i | \(-0.113471\pi\) | ||||
0.937131 | + | 0.348977i | \(0.113471\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 485.907 | 0.0176135 | ||||||||
\(914\) | 7366.52 | 0.266589 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −442.367 | −0.0159566 | ||||||||
\(917\) | 8662.48 | 0.311952 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 27365.1 | 0.982253 | 0.491127 | − | 0.871088i | \(-0.336585\pi\) | ||||
0.491127 | + | 0.871088i | \(0.336585\pi\) | |||||||
\(920\) | −1395.88 | −0.0500225 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −40165.1 | −1.43467 | ||||||||
\(923\) | −34876.9 | −1.24376 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7988.77 | 0.283967 | ||||||||
\(926\) | 4674.83 | 0.165901 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 6867.26 | 0.242919 | ||||||||
\(929\) | −33324.4 | −1.17690 | −0.588450 | − | 0.808534i | \(-0.700261\pi\) | ||||
−0.588450 | + | 0.808534i | \(0.700261\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6069.66 | −0.213668 | ||||||||
\(932\) | 2692.76 | 0.0946396 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 26397.8 | 0.924797 | ||||||||
\(935\) | 4.46182 | 0.000156061 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 49600.6 | 1.72933 | 0.864664 | − | 0.502351i | \(-0.167531\pi\) | ||||
0.864664 | + | 0.502351i | \(0.167531\pi\) | |||||||
\(938\) | −9501.14 | −0.330728 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −88.9436 | −0.00308619 | ||||||||
\(941\) | 12149.0 | 0.420878 | 0.210439 | − | 0.977607i | \(-0.432511\pi\) | ||||
0.210439 | + | 0.977607i | \(0.432511\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7216.91 | −0.249220 | ||||||||
\(944\) | −35490.5 | −1.22364 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −658.342 | −0.0226264 | ||||||||
\(947\) | 3637.85 | 0.124830 | 0.0624151 | − | 0.998050i | \(-0.480120\pi\) | ||||
0.0624151 | + | 0.998050i | \(0.480120\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −23617.7 | −0.807865 | ||||||||
\(950\) | 43111.6 | 1.47234 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 511.439 | 0.0174116 | ||||||||
\(953\) | 26019.5 | 0.884421 | 0.442210 | − | 0.896911i | \(-0.354194\pi\) | ||||
0.442210 | + | 0.896911i | \(0.354194\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 11289.7 | 0.382540 | ||||||||
\(956\) | −2758.98 | −0.0933386 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −12909.6 | −0.435375 | ||||||||
\(959\) | 16648.3 | 0.560586 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21706.5 | −0.728626 | ||||||||
\(962\) | −12979.6 | −0.435009 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −3419.48 | −0.114247 | ||||||||
\(965\) | 3049.02 | 0.101711 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21914.7 | −0.728779 | −0.364390 | − | 0.931247i | \(-0.618722\pi\) | ||||
−0.364390 | + | 0.931247i | \(0.618722\pi\) | |||||||
\(968\) | 28787.8 | 0.955862 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 10160.6 | 0.336327 | ||||||||
\(971\) | 11091.9 | 0.366587 | 0.183293 | − | 0.983058i | \(-0.441324\pi\) | ||||
0.183293 | + | 0.983058i | \(0.441324\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8151.29 | −0.268570 | ||||||||
\(974\) | 27751.4 | 0.912949 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −17296.0 | −0.567247 | ||||||||
\(977\) | −56320.9 | −1.84428 | −0.922142 | − | 0.386853i | \(-0.873562\pi\) | ||||
−0.922142 | + | 0.386853i | \(0.873562\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −768.515 | −0.0250887 | ||||||||
\(980\) | 80.6263 | 0.00262807 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 21485.3 | 0.698192 | ||||||||
\(983\) | 141.191 | 0.00458117 | 0.00229059 | − | 0.999997i | \(-0.499271\pi\) | ||||
0.00229059 | + | 0.999997i | \(0.499271\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2097.12 | 0.0678373 | ||||||||
\(986\) | −2357.47 | −0.0761430 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5192.49 | −0.167201 | ||||||||
\(989\) | −10939.0 | −0.351710 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −43398.1 | −1.39111 | −0.695553 | − | 0.718475i | \(-0.744840\pi\) | ||||
−0.695553 | + | 0.718475i | \(0.744840\pi\) | |||||||
\(992\) | 2600.25 | 0.0832238 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 10965.8 | 0.349914 | ||||||||
\(995\) | −13852.4 | −0.441358 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 39006.1 | 1.23905 | 0.619527 | − | 0.784976i | \(-0.287325\pi\) | ||||
0.619527 | + | 0.784976i | \(0.287325\pi\) | |||||||
\(998\) | −25264.0 | −0.801320 | ||||||||
\(999\) | 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 | 567.4.a.g.1.6 | 8 | ||
3.2 | odd | 2 | 567.4.a.i.1.3 | 8 | |||
9.2 | odd | 6 | 63.4.f.b.22.6 | ✓ | 16 | ||
9.4 | even | 3 | 189.4.f.b.127.3 | 16 | |||
9.5 | odd | 6 | 63.4.f.b.43.6 | yes | 16 | ||
9.7 | even | 3 | 189.4.f.b.64.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.4.f.b.22.6 | ✓ | 16 | 9.2 | odd | 6 | ||
63.4.f.b.43.6 | yes | 16 | 9.5 | odd | 6 | ||
189.4.f.b.64.3 | 16 | 9.7 | even | 3 | |||
189.4.f.b.127.3 | 16 | 9.4 | even | 3 | |||
567.4.a.g.1.6 | 8 | 1.1 | even | 1 | trivial | ||
567.4.a.i.1.3 | 8 | 3.2 | odd | 2 |