Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1200,4,Mod(1,1200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1200, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("1200.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1200.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: | \(70.8022920069\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{109}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 27 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 600) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(5.72015\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1200.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 21.8806 | 1.18144 | 0.590721 | − | 0.806876i | \(-0.298843\pi\) | ||||
0.590721 | + | 0.806876i | \(0.298843\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −54.6418 | −1.49774 | −0.748870 | − | 0.662717i | \(-0.769403\pi\) | ||||
−0.748870 | + | 0.662717i | \(0.769403\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −82.7612 | −1.76568 | −0.882840 | − | 0.469674i | \(-0.844371\pi\) | ||||
−0.882840 | + | 0.469674i | \(0.844371\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 100.403 | 1.43243 | 0.716215 | − | 0.697879i | \(-0.245873\pi\) | ||||
0.716215 | + | 0.697879i | \(0.245873\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 84.1194 | 1.01570 | 0.507850 | − | 0.861445i | \(-0.330440\pi\) | ||||
0.507850 | + | 0.861445i | \(0.330440\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −65.6418 | −0.682106 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.880613 | −0.00798350 | −0.00399175 | − | 0.999992i | \(-0.501271\pi\) | ||||
−0.00399175 | + | 0.999992i | \(0.501271\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −99.1194 | −0.634690 | −0.317345 | − | 0.948310i | \(-0.602791\pi\) | ||||
−0.317345 | + | 0.948310i | \(0.602791\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 78.9255 | 0.457272 | 0.228636 | − | 0.973512i | \(-0.426573\pi\) | ||||
0.228636 | + | 0.973512i | \(0.426573\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 163.926 | 0.864720 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −390.806 | −1.73644 | −0.868218 | − | 0.496183i | \(-0.834735\pi\) | ||||
−0.868218 | + | 0.496183i | \(0.834735\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 248.284 | 1.01942 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 104.642 | 0.398593 | 0.199296 | − | 0.979939i | \(-0.436134\pi\) | ||||
0.199296 | + | 0.979939i | \(0.436134\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 241.403 | 0.856131 | 0.428065 | − | 0.903748i | \(-0.359195\pi\) | ||||
0.428065 | + | 0.903748i | \(0.359195\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 512.567 | 1.59076 | 0.795379 | − | 0.606112i | \(-0.207272\pi\) | ||||
0.795379 | + | 0.606112i | \(0.207272\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 135.761 | 0.395805 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −301.209 | −0.827014 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −284.642 | −0.737709 | −0.368854 | − | 0.929487i | \(-0.620250\pi\) | ||||
−0.368854 | + | 0.929487i | \(0.620250\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −252.358 | −0.586415 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 709.045 | 1.56457 | 0.782286 | − | 0.622919i | \(-0.214053\pi\) | ||||
0.782286 | + | 0.622919i | \(0.214053\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 470.522 | 0.987610 | 0.493805 | − | 0.869573i | \(-0.335606\pi\) | ||||
0.493805 | + | 0.869573i | \(0.335606\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 196.926 | 0.393814 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −667.583 | −1.21729 | −0.608643 | − | 0.793444i | \(-0.708286\pi\) | ||||
−0.608643 | + | 0.793444i | \(0.708286\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.64184 | 0.00460928 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 51.5378 | 0.0861466 | 0.0430733 | − | 0.999072i | \(-0.486285\pi\) | ||||
0.0430733 | + | 0.999072i | \(0.486285\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −371.284 | −0.595280 | −0.297640 | − | 0.954678i | \(-0.596200\pi\) | ||||
−0.297640 | + | 0.954678i | \(0.596200\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1195.60 | −1.76949 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 79.3428 | 0.112997 | 0.0564985 | − | 0.998403i | \(-0.482006\pi\) | ||||
0.0564985 | + | 0.998403i | \(0.482006\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −682.180 | −0.902156 | −0.451078 | − | 0.892485i | \(-0.648960\pi\) | ||||
−0.451078 | + | 0.892485i | \(0.648960\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 297.358 | 0.366438 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 628.478 | 0.748522 | 0.374261 | − | 0.927323i | \(-0.377896\pi\) | ||||
0.374261 | + | 0.927323i | \(0.377896\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1810.87 | −2.08605 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −236.777 | −0.264006 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1519.09 | −1.59011 | −0.795053 | − | 0.606541i | \(-0.792557\pi\) | ||||
−0.795053 | + | 0.606541i | \(0.792557\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −491.777 | −0.499246 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 977.777 | 0.963291 | 0.481646 | − | 0.876366i | \(-0.340039\pi\) | ||||
0.481646 | + | 0.876366i | \(0.340039\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 759.194 | 0.726268 | 0.363134 | − | 0.931737i | \(-0.381707\pi\) | ||||
0.363134 | + | 0.931737i | \(0.381707\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 945.448 | 0.854205 | 0.427102 | − | 0.904203i | \(-0.359534\pi\) | ||||
0.427102 | + | 0.904203i | \(0.359534\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −688.314 | −0.604849 | −0.302425 | − | 0.953173i | \(-0.597796\pi\) | ||||
−0.302425 | + | 0.953173i | \(0.597796\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1172.42 | 1.00253 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 350.865 | 0.292094 | 0.146047 | − | 0.989278i | \(-0.453345\pi\) | ||||
0.146047 | + | 0.989278i | \(0.453345\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −744.851 | −0.588560 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2196.88 | 1.69233 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1654.73 | 1.24322 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −313.926 | −0.230128 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1588.21 | 1.10969 | 0.554846 | − | 0.831953i | \(-0.312777\pi\) | ||||
0.554846 | + | 0.831953i | \(0.312777\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −724.209 | −0.494287 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2156.02 | 1.43795 | 0.718977 | − | 0.695034i | \(-0.244611\pi\) | ||||
0.718977 | + | 0.695034i | \(0.244611\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1840.58 | 1.19999 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −316.716 | −0.197510 | −0.0987551 | − | 0.995112i | \(-0.531486\pi\) | ||||
−0.0987551 | + | 0.995112i | \(0.531486\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2624.87 | 1.60171 | 0.800857 | − | 0.598855i | \(-0.204377\pi\) | ||||
0.800857 | + | 0.598855i | \(0.204377\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1537.70 | −0.918425 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4522.23 | 2.64453 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −407.284 | −0.228518 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2782.87 | 1.53008 | 0.765038 | − | 0.643985i | \(-0.222720\pi\) | ||||
0.765038 | + | 0.643985i | \(0.222720\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1227.25 | −0.661407 | −0.330704 | − | 0.943735i | \(-0.607286\pi\) | ||||
−0.330704 | + | 0.943735i | \(0.607286\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 903.628 | 0.477477 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3187.33 | 1.62023 | 0.810117 | − | 0.586268i | \(-0.199404\pi\) | ||||
0.810117 | + | 0.586268i | \(0.199404\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 853.926 | 0.425916 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −19.2684 | −0.00943204 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2481.64 | 1.19250 | 0.596249 | − | 0.802800i | \(-0.296657\pi\) | ||||
0.596249 | + | 0.802800i | \(0.296657\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1904.55 | −0.882508 | −0.441254 | − | 0.897382i | \(-0.645466\pi\) | ||||
−0.441254 | + | 0.897382i | \(0.645466\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4652.42 | 2.11762 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 757.074 | 0.338567 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3788.88 | 1.66511 | 0.832553 | − | 0.553946i | \(-0.186879\pi\) | ||||
0.832553 | + | 0.553946i | \(0.186879\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2127.13 | −0.903306 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1390.63 | 0.580672 | 0.290336 | − | 0.956925i | \(-0.406233\pi\) | ||||
0.290336 | + | 0.956925i | \(0.406233\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2512.55 | 1.03180 | 0.515902 | − | 0.856647i | \(-0.327457\pi\) | ||||
0.515902 | + | 0.856647i | \(0.327457\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1411.57 | −0.570197 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5486.21 | −2.14541 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −590.777 | −0.227369 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2872.82 | −1.08833 | −0.544163 | − | 0.838980i | \(-0.683153\pi\) | ||||
−0.544163 | + | 0.838980i | \(0.683153\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4130.79 | −1.54063 | −0.770314 | − | 0.637665i | \(-0.779900\pi\) | ||||
−0.770314 | + | 0.637665i | \(0.779900\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2243.52 | −0.811393 | −0.405697 | − | 0.914008i | \(-0.632971\pi\) | ||||
−0.405697 | + | 0.914008i | \(0.632971\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1111.28 | −0.395864 | −0.197932 | − | 0.980216i | \(-0.563422\pi\) | ||||
−0.197932 | + | 0.980216i | \(0.563422\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2002.75 | 0.702801 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2168.79 | −0.749849 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7.92552 | −0.00266117 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4596.44 | −1.52125 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4546.63 | 1.48343 | 0.741713 | − | 0.670717i | \(-0.234014\pi\) | ||||
0.741713 | + | 0.670717i | \(0.234014\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −154.613 | −0.0497368 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1726.94 | 0.540241 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1113.85 | 0.343685 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8309.48 | −2.52921 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3012.93 | 0.904755 | 0.452378 | − | 0.891826i | \(-0.350576\pi\) | ||||
0.452378 | + | 0.891826i | \(0.350576\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1515.27 | 0.443049 | 0.221524 | − | 0.975155i | \(-0.428897\pi\) | ||||
0.221524 | + | 0.975155i | \(0.428897\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2539.98 | 0.732956 | 0.366478 | − | 0.930427i | \(-0.380564\pi\) | ||||
0.366478 | + | 0.930427i | \(0.380564\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3586.79 | 1.02162 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4772.91 | 1.34199 | 0.670996 | − | 0.741461i | \(-0.265867\pi\) | ||||
0.670996 | + | 0.741461i | \(0.265867\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −238.029 | −0.0652389 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −244.344 | −0.0661309 | −0.0330655 | − | 0.999453i | \(-0.510527\pi\) | ||||
−0.0330655 | + | 0.999453i | \(0.510527\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5573.18 | 1.48963 | 0.744813 | − | 0.667273i | \(-0.232538\pi\) | ||||
0.744813 | + | 0.667273i | \(0.232538\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6961.82 | −1.79340 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2046.54 | 0.520860 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5786.78 | 1.45521 | 0.727606 | − | 0.685995i | \(-0.240633\pi\) | ||||
0.727606 | + | 0.685995i | \(0.240633\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 48.1183 | 0.0119572 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7780.75 | 1.88852 | 0.944260 | − | 0.329200i | \(-0.106779\pi\) | ||||
0.944260 | + | 0.329200i | \(0.106779\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8551.08 | −2.05150 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −892.074 | −0.211563 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5122.61 | −1.20104 | −0.600521 | − | 0.799609i | \(-0.705040\pi\) | ||||
−0.600521 | + | 0.799609i | \(0.705040\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1885.43 | −0.432160 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7125.12 | 1.61497 | 0.807484 | − | 0.589890i | \(-0.200829\pi\) | ||||
0.807484 | + | 0.589890i | \(0.200829\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1761.58 | −0.394865 | −0.197433 | − | 0.980316i | \(-0.563260\pi\) | ||||
−0.197433 | + | 0.980316i | \(0.563260\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5432.60 | 1.20438 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5810.41 | −1.26034 | −0.630169 | − | 0.776458i | \(-0.717014\pi\) | ||||
−0.630169 | + | 0.776458i | \(0.717014\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 710.330 | 0.152424 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4126.19 | −0.875972 | −0.437986 | − | 0.898982i | \(-0.644308\pi\) | ||||
−0.437986 | + | 0.898982i | \(0.644308\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 718.330 | 0.150884 | 0.0754422 | − | 0.997150i | \(-0.475963\pi\) | ||||
0.0754422 | + | 0.997150i | \(0.475963\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2289.63 | 0.470914 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5167.78 | 1.05186 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4557.27 | 0.918048 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3756.21 | 0.748942 | 0.374471 | − | 0.927239i | \(-0.377824\pi\) | ||||
0.374471 | + | 0.927239i | \(0.377824\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1475.33 | 0.288240 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 72.8806 | 0.0140963 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5282.05 | 1.01147 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2933.33 | −0.556156 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7599.52 | −1.41279 | −0.706397 | − | 0.707816i | \(-0.749681\pi\) | ||||
−0.706397 | + | 0.707816i | \(0.749681\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2277.58 | −0.419311 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2850.03 | −0.519648 | −0.259824 | − | 0.965656i | \(-0.583664\pi\) | ||||
−0.259824 | + | 0.965656i | \(0.583664\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −799.684 | −0.144411 | −0.0722057 | − | 0.997390i | \(-0.523004\pi\) | ||||
−0.0722057 | + | 0.997390i | \(0.523004\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1003.79 | 0.177850 | 0.0889250 | − | 0.996038i | \(-0.471657\pi\) | ||||
0.0889250 | + | 0.996038i | \(0.471657\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5416.07 | 0.950600 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2836.34 | −0.493175 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8445.84 | 1.45492 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2064.94 | 0.349210 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 11215.3 | 1.87939 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8367.68 | −1.38951 | −0.694757 | − | 0.719245i | \(-0.744488\pi\) | ||||
−0.694757 | + | 0.719245i | \(0.744488\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3517.26 | −0.578812 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5034.79 | 0.813835 | 0.406918 | − | 0.913465i | \(-0.366604\pi\) | ||||
0.406918 | + | 0.913465i | \(0.366604\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1052.60 | −0.168641 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4312.64 | −0.684875 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4534.51 | −0.713821 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2105.53 | −0.325737 | −0.162868 | − | 0.986648i | \(-0.552075\pi\) | ||||
−0.162868 | + | 0.986648i | \(0.552075\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8813.47 | −1.35179 | −0.675894 | − | 0.736999i | \(-0.736242\pi\) | ||||
−0.675894 | + | 0.736999i | \(0.736242\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2234.55 | 0.339805 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9348.98 | −1.40962 | −0.704810 | − | 0.709396i | \(-0.748968\pi\) | ||||
−0.704810 | + | 0.709396i | \(0.748968\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6590.64 | −0.977069 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9233.33 | 1.35743 | 0.678714 | − | 0.734403i | \(-0.262538\pi\) | ||||
0.678714 | + | 0.734403i | \(0.262538\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 217.071 | 0.0316477 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4964.19 | −0.717775 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6996.60 | −0.995148 | −0.497574 | − | 0.867421i | \(-0.665776\pi\) | ||||
−0.497574 | + | 0.867421i | \(0.665776\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 941.777 | 0.132864 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6228.14 | −0.871560 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2945.48 | −0.408877 | −0.204438 | − | 0.978879i | \(-0.565537\pi\) | ||||
−0.204438 | + | 0.978879i | \(0.565537\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8203.24 | 1.12066 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8499.83 | −1.15200 | −0.575998 | − | 0.817451i | \(-0.695387\pi\) | ||||
−0.575998 | + | 0.817451i | \(0.695387\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4764.63 | −0.640681 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6426.01 | −0.857320 | −0.428660 | − | 0.903466i | \(-0.641014\pi\) | ||||
−0.428660 | + | 0.903466i | \(0.641014\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2172.63 | 0.285377 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −675.805 | −0.0880840 | −0.0440420 | − | 0.999030i | \(-0.514024\pi\) | ||||
−0.0440420 | + | 0.999030i | \(0.514024\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −88.4162 | −0.0114358 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6468.05 | −0.830203 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9331.43 | 1.17967 | 0.589837 | − | 0.807522i | \(-0.299192\pi\) | ||||
0.589837 | + | 0.807522i | \(0.299192\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5521.75 | −0.692815 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −427.213 | −0.0532021 | −0.0266010 | − | 0.999646i | \(-0.508468\pi\) | ||||
−0.0266010 | + | 0.999646i | \(0.508468\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6531.97 | −0.807396 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 21354.4 | 2.60073 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1243.18 | 0.150297 | 0.0751484 | − | 0.997172i | \(-0.476057\pi\) | ||||
0.0751484 | + | 0.997172i | \(0.476057\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 950.149 | 0.114033 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 15514.3 | 1.84845 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7874.60 | −0.924750 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3802.17 | 0.443313 | 0.221656 | − | 0.975125i | \(-0.428854\pi\) | ||||
0.221656 | + | 0.975125i | \(0.428854\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12785.6 | −1.48012 | −0.740059 | − | 0.672542i | \(-0.765203\pi\) | ||||
−0.740059 | + | 0.672542i | \(0.765203\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4613.11 | 0.530253 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10295.3 | 1.16680 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −13566.7 | −1.52682 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9588.11 | 1.07156 | 0.535781 | − | 0.844357i | \(-0.320017\pi\) | ||||
0.535781 | + | 0.844357i | \(0.320017\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8493.83 | −0.942697 | −0.471348 | − | 0.881947i | \(-0.656233\pi\) | ||||
−0.471348 | + | 0.881947i | \(0.656233\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −74.0766 | −0.00810885 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5167.40 | −0.561792 | −0.280896 | − | 0.959738i | \(-0.590632\pi\) | ||||
−0.280896 | + | 0.959738i | \(0.590632\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1221.85 | 0.131935 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8192.86 | 0.878679 | 0.439339 | − | 0.898321i | \(-0.355213\pi\) | ||||
0.439339 | + | 0.898321i | \(0.355213\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8348.60 | −0.883390 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18252.3 | −1.91844 | −0.959218 | − | 0.282666i | \(-0.908781\pi\) | ||||
−0.959218 | + | 0.282666i | \(0.908781\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5717.82 | −0.596988 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3681.76 | 0.381864 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 330.123 | 0.0337910 | 0.0168955 | − | 0.999857i | \(-0.494622\pi\) | ||||
0.0168955 | + | 0.999857i | \(0.494622\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2710.88 | −0.275671 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4773.18 | −0.482232 | −0.241116 | − | 0.970496i | \(-0.577513\pi\) | ||||
−0.241116 | + | 0.970496i | \(0.577513\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7860.46 | 0.788999 | 0.394499 | − | 0.918896i | \(-0.370918\pi\) | ||||
0.394499 | + | 0.918896i | \(0.370918\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10520.8 | 1.04250 | 0.521249 | − | 0.853404i | \(-0.325466\pi\) | ||||
0.521249 | + | 0.853404i | \(0.325466\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14607.1 | −1.43815 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9561.99 | −0.935442 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −13190.7 | −1.28226 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2561.78 | −0.245903 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3013.64 | 0.287467 | 0.143734 | − | 0.989616i | \(-0.454089\pi\) | ||||
0.143734 | + | 0.989616i | \(0.454089\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 32343.6 | 3.06599 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 57.8051 | 0.00544559 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7048.81 | 0.655876 | 0.327938 | − | 0.944699i | \(-0.393646\pi\) | ||||
0.327938 | + | 0.944699i | \(0.393646\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7444.93 | −0.688489 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6338.68 | −0.582608 | −0.291304 | − | 0.956630i | \(-0.594089\pi\) | ||||
−0.291304 | + | 0.956630i | \(0.594089\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9951.89 | −0.909149 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1127.68 | 0.101777 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5402.66 | 0.484682 | 0.242341 | − | 0.970191i | \(-0.422085\pi\) | ||||
0.242341 | + | 0.970191i | \(0.422085\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5713.66 | 0.509516 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7770.85 | −0.688837 | −0.344419 | − | 0.938816i | \(-0.611924\pi\) | ||||
−0.344419 | + | 0.938816i | \(0.611924\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −13957.3 | −1.22261 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 729.019 | 0.0634837 | 0.0317418 | − | 0.999496i | \(-0.489895\pi\) | ||||
0.0317418 | + | 0.999496i | \(0.489895\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8123.91 | −0.703289 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2271.22 | −0.195472 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −28007.6 | −2.38254 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −11366.6 | −0.961349 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14783.8 | 1.24317 | 0.621585 | − | 0.783346i | \(-0.286489\pi\) | ||||
0.621585 | + | 0.783346i | \(0.286489\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 395.434 | 0.0330614 | 0.0165307 | − | 0.999863i | \(-0.494738\pi\) | ||||
0.0165307 | + | 0.999863i | \(0.494738\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7924.36 | 0.655011 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12166.2 | −0.999936 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6381.40 | 0.521524 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8660.29 | −0.703787 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4171.88 | −0.335251 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7418.24 | −0.592813 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16507.9 | −1.31188 | −0.655942 | − | 0.754811i | \(-0.727728\pi\) | ||||
−0.655942 | + | 0.754811i | \(0.727728\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7537.66 | −0.595713 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9242.35 | 0.722440 | 0.361220 | − | 0.932481i | \(-0.382360\pi\) | ||||
0.361220 | + | 0.932481i | \(0.382360\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4234.70 | 0.329203 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8337.86 | −0.644655 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1736.07 | 0.133499 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10449.5 | 0.794898 | 0.397449 | − | 0.917624i | \(-0.369896\pi\) | ||||
0.397449 | + | 0.917624i | \(0.369896\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −19978.8 | −1.51165 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 16458.6 | 1.23865 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −13670.1 | −1.02331 | −0.511656 | − | 0.859191i | \(-0.670968\pi\) | ||||
−0.511656 | + | 0.859191i | \(0.670968\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1772.33 | 0.131271 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13616.7 | 1.00323 | 0.501617 | − | 0.865090i | \(-0.332739\pi\) | ||||
0.501617 | + | 0.865090i | \(0.332739\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11833.4 | 0.867270 | 0.433635 | − | 0.901089i | \(-0.357231\pi\) | ||||
0.433635 | + | 0.901089i | \(0.357231\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8618.47 | 0.628345 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7131.30 | −0.514523 | −0.257262 | − | 0.966342i | \(-0.582820\pi\) | ||||
−0.257262 | + | 0.966342i | \(0.582820\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 12392.4 | 0.889482 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14926.5 | −1.06584 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 15553.4 | 1.10490 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 25214.3 | 1.77292 | 0.886461 | − | 0.462804i | \(-0.153157\pi\) | ||||
0.886461 | + | 0.462804i | \(0.153157\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6639.17 | 0.464452 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6730.57 | 0.468458 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4218.04 | −0.292098 | −0.146049 | − | 0.989277i | \(-0.546656\pi\) | ||||
−0.146049 | + | 0.989277i | \(0.546656\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3333.85 | 0.228552 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5956.57 | −0.406308 | −0.203154 | − | 0.979147i | \(-0.565119\pi\) | ||||
−0.203154 | + | 0.979147i | \(0.565119\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5182.29 | −0.351731 | −0.175865 | − | 0.984414i | \(-0.556272\pi\) | ||||
−0.175865 | + | 0.984414i | \(0.556272\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6008.24 | −0.405762 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10142.0 | 0.678171 | 0.339086 | − | 0.940755i | \(-0.389882\pi\) | ||||
0.339086 | + | 0.940755i | \(0.389882\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6506.38 | 0.432926 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −42420.7 | −2.80877 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4022.95 | 0.265066 | 0.132533 | − | 0.991179i | \(-0.457689\pi\) | ||||
0.132533 | + | 0.991179i | \(0.457689\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 27074.4 | 1.76657 | 0.883285 | − | 0.468837i | \(-0.155327\pi\) | ||||
0.883285 | + | 0.468837i | \(0.155327\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17245.7 | 1.11981 | 0.559905 | − | 0.828557i | \(-0.310838\pi\) | ||||
0.559905 | + | 0.828557i | \(0.310838\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 23.7766 | 0.00153643 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 13751.5 | 0.884336 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 13789.3 | 0.878297 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −39238.1 | −2.48732 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14254.4 | 0.899302 | 0.449651 | − | 0.893204i | \(-0.351548\pi\) | ||||
0.449651 | + | 0.893204i | \(0.351548\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −13639.9 | −0.856456 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −11235.8 | −0.698865 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 463.840 | 0.0287155 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2611.61 | 0.160924 | 0.0804621 | − | 0.996758i | \(-0.474360\pi\) | ||||
0.0804621 | + | 0.996758i | \(0.474360\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −27414.4 | −1.68136 | −0.840682 | − | 0.541529i | \(-0.817846\pi\) | ||||
−0.840682 | + | 0.541529i | \(0.817846\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12820.8 | 0.779041 | 0.389521 | − | 0.921018i | \(-0.372641\pi\) | ||||
0.389521 | + | 0.921018i | \(0.372641\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −38743.5 | −2.34332 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5180.82 | −0.311908 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15786.4 | 0.946049 | 0.473025 | − | 0.881049i | \(-0.343162\pi\) | ||||
0.473025 | + | 0.881049i | \(0.343162\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3341.55 | −0.198427 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4822.61 | −0.285072 | −0.142536 | − | 0.989790i | \(-0.545526\pi\) | ||||
−0.142536 | + | 0.989790i | \(0.545526\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23624.9 | −1.39017 | −0.695084 | − | 0.718929i | \(-0.744633\pi\) | ||||
−0.695084 | + | 0.718929i | \(0.744633\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 24928.4 | 1.46024 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 87.2858 | 0.00506705 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9038.78 | −0.522361 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −25710.2 | −1.47918 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8903.65 | 0.509971 | 0.254985 | − | 0.966945i | \(-0.417929\pi\) | ||||
0.254985 | + | 0.966945i | \(0.417929\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9034.56 | 0.512890 | 0.256445 | − | 0.966559i | \(-0.417449\pi\) | ||||
0.256445 | + | 0.966559i | \(0.417449\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −33238.6 | −1.87862 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4545.81 | −0.255794 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 28676.8 | 1.60657 | 0.803284 | − | 0.595596i | \(-0.203084\pi\) | ||||
0.803284 | + | 0.595596i | \(0.203084\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7619.95 | −0.423172 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 23557.3 | 1.30256 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20653.1 | 1.13702 | 0.568509 | − | 0.822677i | \(-0.307520\pi\) | ||||
0.568509 | + | 0.822677i | \(0.307520\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −10760.4 | −0.589831 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10506.4 | 0.570957 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −14318.7 | −0.774799 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −11000.1 | −0.592678 | −0.296339 | − | 0.955083i | \(-0.595766\pi\) | ||||
−0.296339 | + | 0.955083i | \(0.595766\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −32874.4 | −1.76370 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 21394.4 | 1.13807 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −372.560 | −0.0197345 | −0.00986725 | − | 0.999951i | \(-0.503141\pi\) | ||||
−0.00986725 | + | 0.999951i | \(0.503141\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 714.086 | 0.0376657 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −69.5028 | −0.00365063 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 733.032 | 0.0381807 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7207.32 | 0.373835 | 0.186918 | − | 0.982376i | \(-0.440150\pi\) | ||||
0.186918 | + | 0.982376i | \(0.440150\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16611.6 | 0.858043 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −16719.5 | −0.860036 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −23423.6 | −1.19496 | −0.597479 | − | 0.801885i | \(-0.703831\pi\) | ||||
−0.597479 | + | 0.801885i | \(0.703831\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 24237.6 | 1.22635 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20368.0 | 1.02634 | 0.513172 | − | 0.858286i | \(-0.328470\pi\) | ||||
0.513172 | + | 0.858286i | \(0.328470\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 36477.9 | 1.82318 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2603.64 | −0.129603 | −0.0648014 | − | 0.997898i | \(-0.520641\pi\) | ||||
−0.0648014 | + | 0.997898i | \(0.520641\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 20885.5 | 1.03542 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8627.83 | 0.426009 | 0.213004 | − | 0.977051i | \(-0.431675\pi\) | ||||
0.213004 | + | 0.977051i | \(0.431675\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6139.62 | −0.300719 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 20687.0 | 1.00919 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18735.5 | 0.910343 | 0.455172 | − | 0.890404i | \(-0.349578\pi\) | ||||
0.455172 | + | 0.890404i | \(0.349578\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −17360.3 | −0.840167 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10787.3 | −0.517926 | −0.258963 | − | 0.965887i | \(-0.583381\pi\) | ||||
−0.258963 | + | 0.965887i | \(0.583381\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −144.355 | −0.00690349 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2175.95 | −0.103651 | −0.0518253 | − | 0.998656i | \(-0.516504\pi\) | ||||
−0.0518253 | + | 0.998656i | \(0.516504\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15060.7 | −0.714594 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −58681.4 | −2.76253 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18705.8 | 0.877176 | 0.438588 | − | 0.898688i | \(-0.355479\pi\) | ||||
0.438588 | + | 0.898688i | \(0.355479\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −23342.2 | −1.09034 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −8243.60 | −0.383573 | −0.191786 | − | 0.981437i | \(-0.561428\pi\) | ||||
−0.191786 | + | 0.981437i | \(0.561428\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 25653.2 | 1.18443 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8802.41 | 0.404851 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2816.12 | −0.129025 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2676.22 | 0.122146 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −29442.1 | −1.33354 | −0.666770 | − | 0.745263i | \(-0.732324\pi\) | ||||
−0.666770 | + | 0.745263i | \(0.732324\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 15367.8 | 0.693422 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7677.15 | 0.345092 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −38941.0 | −1.74380 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −42045.4 | −1.86866 | −0.934332 | − | 0.356403i | \(-0.884003\pi\) | ||||
−0.934332 | + | 0.356403i | \(0.884003\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 51463.3 | 2.27865 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5656.30 | 0.249507 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 20287.6 | 0.891575 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −21375.4 | −0.932402 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 43757.6 | 1.90165 | 0.950825 | − | 0.309727i | \(-0.100238\pi\) | ||||
0.950825 | + | 0.309727i | \(0.100238\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3273.00 | −0.141715 | −0.0708574 | − | 0.997486i | \(-0.522574\pi\) | ||||
−0.0708574 | + | 0.997486i | \(0.522574\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5284.74 | 0.227976 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20306.7 | 0.869572 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −16297.8 | −0.695349 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −40442.6 | −1.71919 | −0.859595 | − | 0.510976i | \(-0.829284\pi\) | ||||
−0.859595 | + | 0.510976i | \(0.829284\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −27236.8 | −1.15360 | −0.576802 | − | 0.816884i | \(-0.695700\pi\) | ||||
−0.576802 | + | 0.816884i | \(0.695700\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −33344.5 | −1.40206 | −0.701028 | − | 0.713133i | \(-0.747275\pi\) | ||||
−0.701028 | + | 0.713133i | \(0.747275\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −32085.0 | −1.34422 | −0.672110 | − | 0.740452i | \(-0.734612\pi\) | ||||
−0.672110 | + | 0.740452i | \(0.734612\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 17431.2 | 0.727656 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 13630.8 | 0.566964 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2130.99 | −0.0880021 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7072.24 | 0.291014 | 0.145507 | − | 0.989357i | \(-0.453519\pi\) | ||||
0.145507 | + | 0.989357i | \(0.453519\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14564.3 | −0.597169 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 12378.6 | 0.505743 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 36206.5 | 1.46880 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2154.99 | −0.0871131 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 344.149 | 0.0138628 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10225.0 | 0.410431 | 0.205215 | − | 0.978717i | \(-0.434211\pi\) | ||||
0.205215 | + | 0.978717i | \(0.434211\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9783.87 | −0.389977 | −0.194989 | − | 0.980805i | \(-0.562467\pi\) | ||||
−0.194989 | + | 0.980805i | \(0.562467\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22931.8 | 0.910853 | 0.455427 | − | 0.890273i | \(-0.349487\pi\) | ||||
0.455427 | + | 0.890273i | \(0.349487\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6868.88 | −0.271883 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −23506.0 | −0.927175 | −0.463588 | − | 0.886051i | \(-0.653438\pi\) | ||||
−0.463588 | + | 0.886051i | \(0.653438\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −15503.3 | −0.607290 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4335.44 | −0.169240 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 55250.0 | 2.14934 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −13671.8 | −0.530035 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −34672.0 | −1.33499 | −0.667497 | − | 0.744613i | \(-0.732634\pi\) | ||||
−0.667497 | + | 0.744613i | \(0.732634\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −11268.6 | −0.432402 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2920.92 | −0.111701 | −0.0558504 | − | 0.998439i | \(-0.517787\pi\) | ||||
−0.0558504 | + | 0.998439i | \(0.517787\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7123.74 | 0.271498 | 0.135749 | − | 0.990743i | \(-0.456656\pi\) | ||||
0.135749 | + | 0.990743i | \(0.456656\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −7923.42 | −0.299935 | −0.149968 | − | 0.988691i | \(-0.547917\pi\) | ||||
−0.149968 | + | 0.988691i | \(0.547917\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 34751.0 | 1.31104 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4425.99 | −0.166415 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 43116.9 | 1.61573 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −218.642 | −0.00813850 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7823.05 | −0.290226 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −28578.9 | −1.05672 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −15846.1 | −0.583972 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 19771.7 | 0.723825 | 0.361912 | − | 0.932212i | \(-0.382124\pi\) | ||||
0.361912 | + | 0.932212i | \(0.382124\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8799.99 | 0.321097 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −38222.7 | −1.39009 | −0.695046 | − | 0.718966i | \(-0.744616\pi\) | ||||
−0.695046 | + | 0.718966i | \(0.744616\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 37275.5 | 1.35119 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 47174.9 | 1.69886 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −39237.3 | −1.40840 | −0.704199 | − | 0.710003i | \(-0.748694\pi\) | ||||
−0.704199 | + | 0.710003i | \(0.748694\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 22798.6 | 0.815677 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4265.33 | −0.152107 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6832.74 | 0.242089 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 20024.5 | 0.707194 | 0.353597 | − | 0.935398i | \(-0.384958\pi\) | ||||
0.353597 | + | 0.935398i | \(0.384958\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11420.2 | 0.402020 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8550.09 | 0.300019 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8717.10 | 0.303922 | 0.151961 | − | 0.988386i | \(-0.451441\pi\) | ||||
0.151961 | + | 0.988386i | \(0.451441\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2399.05 | 0.0833760 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 39276.2 | 1.36065 | 0.680323 | − | 0.732913i | \(-0.261840\pi\) | ||||
0.680323 | + | 0.732913i | \(0.261840\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −92.1490 | −0.00318217 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −20080.8 | −0.689060 | −0.344530 | − | 0.938775i | \(-0.611962\pi\) | ||||
−0.344530 | + | 0.938775i | \(0.611962\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 30727.9 | 1.05107 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3011.37 | −0.102682 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −38549.9 | −1.31034 | −0.655170 | − | 0.755481i | \(-0.727403\pi\) | ||||
−0.655170 | + | 0.755481i | \(0.727403\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −16248.2 | −0.548829 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6929.95 | −0.233347 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23561.8 | −0.790902 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8509.03 | 0.284735 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24108.2 | −0.801724 | −0.400862 | − | 0.916138i | \(-0.631289\pi\) | ||||
−0.400862 | + | 0.916138i | \(0.631289\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −25337.5 | −0.839999 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 41760.1 | 1.38017 | 0.690084 | − | 0.723729i | \(-0.257573\pi\) | ||||
0.690084 | + | 0.723729i | \(0.257573\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 57433.7 | 1.89233 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4532.52 | −0.148422 | −0.0742109 | − | 0.997243i | \(-0.523644\pi\) | ||||
−0.0742109 | + | 0.997243i | \(0.523644\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −34341.2 | −1.12109 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6194.83 | −0.201616 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −48822.8 | −1.58414 | −0.792068 | − | 0.610432i | \(-0.790996\pi\) | ||||
−0.792068 | + | 0.610432i | \(0.790996\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −33645.9 | −1.08507 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −212.583 | −0.00683492 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26937.6 | 0.863473 | 0.431737 | − | 0.902000i | \(-0.357901\pi\) | ||||
0.431737 | + | 0.902000i | \(0.357901\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 25103.0 | 0.802236 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9191.03 | 0.291959 | 0.145979 | − | 0.989288i | \(-0.453367\pi\) | ||||
0.145979 | + | 0.989288i | \(0.453367\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 10551.8 | 0.334177 |
(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 | 1200.4.a.bp.1.2 | 2 | ||
4.3 | odd | 2 | 600.4.a.u.1.1 | yes | 2 | ||
5.2 | odd | 4 | 1200.4.f.x.49.4 | 4 | |||
5.3 | odd | 4 | 1200.4.f.x.49.1 | 4 | |||
5.4 | even | 2 | 1200.4.a.br.1.1 | 2 | |||
12.11 | even | 2 | 1800.4.a.bm.1.1 | 2 | |||
20.3 | even | 4 | 600.4.f.j.49.4 | 4 | |||
20.7 | even | 4 | 600.4.f.j.49.1 | 4 | |||
20.19 | odd | 2 | 600.4.a.s.1.2 | ✓ | 2 | ||
60.23 | odd | 4 | 1800.4.f.z.649.4 | 4 | |||
60.47 | odd | 4 | 1800.4.f.z.649.1 | 4 | |||
60.59 | even | 2 | 1800.4.a.bo.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
600.4.a.s.1.2 | ✓ | 2 | 20.19 | odd | 2 | ||
600.4.a.u.1.1 | yes | 2 | 4.3 | odd | 2 | ||
600.4.f.j.49.1 | 4 | 20.7 | even | 4 | |||
600.4.f.j.49.4 | 4 | 20.3 | even | 4 | |||
1200.4.a.bp.1.2 | 2 | 1.1 | even | 1 | trivial | ||
1200.4.a.br.1.1 | 2 | 5.4 | even | 2 | |||
1200.4.f.x.49.1 | 4 | 5.3 | odd | 4 | |||
1200.4.f.x.49.4 | 4 | 5.2 | odd | 4 | |||
1800.4.a.bm.1.1 | 2 | 12.11 | even | 2 | |||
1800.4.a.bo.1.2 | 2 | 60.59 | even | 2 | |||
1800.4.f.z.649.1 | 4 | 60.47 | odd | 4 | |||
1800.4.f.z.649.4 | 4 | 60.23 | odd | 4 |