Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1400,4,Mod(449,1400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1400, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1400.449");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1400.g (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(82.6026740080\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.7807489600.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 63x^{4} + 1041x^{2} + 1600 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 280) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 449.5 | ||
Root | \(-1.30726i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1400.449 |
Dual form | 1400.4.g.l.449.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times\).
\(n\) | \(351\) | \(701\) | \(801\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 3.45643i | 0.665190i | 0.943070 | + | 0.332595i | \(0.107924\pi\) | ||||
−0.943070 | + | 0.332595i | \(0.892076\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 7.00000i | − 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 15.0531 | 0.557522 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −51.8821 | −1.42210 | −0.711048 | − | 0.703144i | \(-0.751779\pi\) | ||||
−0.711048 | + | 0.703144i | \(0.751779\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 5.91120i | − 0.126113i | −0.998010 | − | 0.0630566i | \(-0.979915\pi\) | ||||
0.998010 | − | 0.0630566i | \(-0.0200849\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 103.850i | 1.48160i | 0.671724 | + | 0.740802i | \(0.265554\pi\) | ||||
−0.671724 | + | 0.740802i | \(0.734446\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −118.470 | −1.43047 | −0.715236 | − | 0.698883i | \(-0.753681\pi\) | ||||
−0.715236 | + | 0.698883i | \(0.753681\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 24.1950 | 0.251418 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 80.7029i | − 0.731640i | −0.930686 | − | 0.365820i | \(-0.880789\pi\) | ||||
0.930686 | − | 0.365820i | \(-0.119211\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 145.354i | 1.03605i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 218.344 | 1.39812 | 0.699058 | − | 0.715065i | \(-0.253603\pi\) | ||||
0.699058 | + | 0.715065i | \(0.253603\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 39.2738 | 0.227541 | 0.113771 | − | 0.993507i | \(-0.463707\pi\) | ||||
0.113771 | + | 0.993507i | \(0.463707\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 179.327i | − 0.945964i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 159.803i | − 0.710040i | −0.934859 | − | 0.355020i | \(-0.884474\pi\) | ||||
0.934859 | − | 0.355020i | \(-0.115526\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 20.4316 | 0.0838892 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 233.322 | 0.888750 | 0.444375 | − | 0.895841i | \(-0.353426\pi\) | ||||
0.444375 | + | 0.895841i | \(0.353426\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 524.515i | − 1.86018i | −0.367329 | − | 0.930091i | \(-0.619728\pi\) | ||||
0.367329 | − | 0.930091i | \(-0.380272\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 210.441i | 0.653105i | 0.945179 | + | 0.326552i | \(0.105887\pi\) | ||||
−0.945179 | + | 0.326552i | \(0.894113\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −49.0000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −358.949 | −0.985548 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 348.028i | 0.901987i | 0.892527 | + | 0.450994i | \(0.148930\pi\) | ||||
−0.892527 | + | 0.450994i | \(0.851070\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 409.485i | − 0.951536i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 85.1752 | 0.187947 | 0.0939735 | − | 0.995575i | \(-0.470043\pi\) | ||||
0.0939735 | + | 0.995575i | \(0.470043\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −801.720 | −1.68278 | −0.841391 | − | 0.540427i | \(-0.818263\pi\) | ||||
−0.841391 | + | 0.540427i | \(0.818263\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 105.372i | − 0.210724i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 716.049i | − 1.30566i | −0.757504 | − | 0.652831i | \(-0.773581\pi\) | ||||
0.757504 | − | 0.652831i | \(-0.226419\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 278.944 | 0.486679 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −520.412 | −0.869880 | −0.434940 | − | 0.900459i | \(-0.643230\pi\) | ||||
−0.434940 | + | 0.900459i | \(0.643230\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 230.005i | 0.368768i | 0.982854 | + | 0.184384i | \(0.0590289\pi\) | ||||
−0.982854 | + | 0.184384i | \(0.940971\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 363.175i | 0.537502i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 970.534 | 1.38220 | 0.691099 | − | 0.722760i | \(-0.257127\pi\) | ||||
0.691099 | + | 0.722760i | \(0.257127\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −95.9705 | −0.131647 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 1109.38i | − 1.46711i | −0.679630 | − | 0.733555i | \(-0.737860\pi\) | ||||
0.679630 | − | 0.733555i | \(-0.262140\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 754.689i | 0.930013i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1127.45 | −1.34280 | −0.671401 | − | 0.741094i | \(-0.734307\pi\) | ||||
−0.671401 | + | 0.741094i | \(0.734307\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −41.3784 | −0.0476663 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 135.747i | 0.151358i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 1136.37i | − 1.18950i | −0.803912 | − | 0.594748i | \(-0.797252\pi\) | ||||
0.803912 | − | 0.594748i | \(-0.202748\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −780.987 | −0.792850 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 858.838 | 0.846115 | 0.423057 | − | 0.906103i | \(-0.360957\pi\) | ||||
0.423057 | + | 0.906103i | \(0.360957\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 348.379i | − 0.333270i | −0.986019 | − | 0.166635i | \(-0.946710\pi\) | ||||
0.986019 | − | 0.166635i | \(-0.0532901\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 1860.54i | − 1.68098i | −0.541828 | − | 0.840490i | \(-0.682267\pi\) | ||||
0.541828 | − | 0.840490i | \(-0.317733\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1213.61 | −1.06645 | −0.533224 | − | 0.845974i | \(-0.679020\pi\) | ||||
−0.533224 | + | 0.845974i | \(0.679020\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 552.349 | 0.472312 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 267.531i | − 0.222718i | −0.993780 | − | 0.111359i | \(-0.964480\pi\) | ||||
0.993780 | − | 0.111359i | \(-0.0355204\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 88.9819i | − 0.0703109i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 726.948 | 0.559994 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1360.76 | 1.02236 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 806.460i | 0.591188i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 712.388i | 0.497750i | 0.968536 | + | 0.248875i | \(0.0800608\pi\) | ||||
−0.968536 | + | 0.248875i | \(0.919939\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1812.95 | 1.23737 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 746.364 | 0.497787 | 0.248894 | − | 0.968531i | \(-0.419933\pi\) | ||||
0.248894 | + | 0.968531i | \(0.419933\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 829.293i | 0.540668i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 2612.55i | − 1.62924i | −0.579996 | − | 0.814619i | \(-0.696946\pi\) | ||||
0.579996 | − | 0.814619i | \(-0.303054\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −637.320 | −0.388898 | −0.194449 | − | 0.980913i | \(-0.562292\pi\) | ||||
−0.194449 | + | 0.980913i | \(0.562292\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −727.373 | −0.434439 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 306.686i | 0.179345i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 169.365i | − 0.0950271i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2151.92 | 1.18317 | 0.591585 | − | 0.806242i | \(-0.298502\pi\) | ||||
0.591585 | + | 0.806242i | \(0.298502\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1685.18 | 0.908201 | 0.454101 | − | 0.890950i | \(-0.349961\pi\) | ||||
0.454101 | + | 0.890950i | \(0.349961\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1563.26i | 0.826027i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 1139.31i | − 0.579150i | −0.957155 | − | 0.289575i | \(-0.906486\pi\) | ||||
0.957155 | − | 0.289575i | \(-0.0935140\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1202.93 | −0.599993 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −564.920 | −0.276534 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 1758.81i | − 0.845156i | −0.906327 | − | 0.422578i | \(-0.861125\pi\) | ||||
0.906327 | − | 0.422578i | \(-0.138875\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 2350.50i | − 1.08915i | −0.838713 | − | 0.544573i | \(-0.816692\pi\) | ||||
0.838713 | − | 0.544573i | \(-0.183308\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2162.06 | 0.984095 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1783.35 | −0.797520 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 2403.94i | − 1.05646i | −0.849100 | − | 0.528231i | \(-0.822855\pi\) | ||||
0.849100 | − | 0.528231i | \(-0.177145\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 294.402i | 0.125020i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3361.51 | 1.40364 | 0.701819 | − | 0.712355i | \(-0.252372\pi\) | ||||
0.701819 | + | 0.712355i | \(0.252372\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4681.04 | −1.92231 | −0.961156 | − | 0.276004i | \(-0.910990\pi\) | ||||
−0.961156 | + | 0.276004i | \(0.910990\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 2771.09i | − 1.11937i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 5387.95i | − 2.10698i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1017.47 | 0.391589 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2375.90 | 0.900075 | 0.450037 | − | 0.893010i | \(-0.351411\pi\) | ||||
0.450037 | + | 0.893010i | \(0.351411\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4940.87i | 1.84275i | 0.388670 | + | 0.921377i | \(0.372935\pi\) | ||||
−0.388670 | + | 0.921377i | \(0.627065\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 1335.30i | − 0.482926i | −0.970410 | − | 0.241463i | \(-0.922373\pi\) | ||||
0.970410 | − | 0.241463i | \(-0.0776272\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2235.61 | 0.796374 | 0.398187 | − | 0.917304i | \(-0.369640\pi\) | ||||
0.398187 | + | 0.917304i | \(0.369640\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2474.97 | 0.868513 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 1528.40i | − 0.528438i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 1214.83i | − 0.407905i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6146.50 | 2.03427 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −875.868 | −0.285769 | −0.142884 | − | 0.989739i | \(-0.545638\pi\) | ||||
−0.142884 | + | 0.989739i | \(0.545638\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 1798.77i | − 0.578636i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 274.917i | − 0.0860025i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −794.995 | −0.245300 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 613.877 | 0.186850 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 3950.23i | − 1.18622i | −0.805122 | − | 0.593110i | \(-0.797900\pi\) | ||||
0.805122 | − | 0.593110i | \(-0.202100\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2254.32i | 0.659138i | 0.944132 | + | 0.329569i | \(0.106903\pi\) | ||||
−0.944132 | + | 0.329569i | \(0.893097\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3680.17 | 1.06198 | 0.530988 | − | 0.847379i | \(-0.321821\pi\) | ||||
0.530988 | + | 0.847379i | \(0.321821\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1255.29 | −0.357541 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 1109.74i | − 0.312024i | −0.987755 | − | 0.156012i | \(-0.950136\pi\) | ||||
0.987755 | − | 0.156012i | \(-0.0498638\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3354.58i | 0.919424i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1079.71 | −0.292220 | −0.146110 | − | 0.989268i | \(-0.546675\pi\) | ||||
−0.146110 | + | 0.989268i | \(0.546675\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 81.1127 | 0.0216802 | 0.0108401 | − | 0.999941i | \(-0.496549\pi\) | ||||
0.0108401 | + | 0.999941i | \(0.496549\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3592.83i | 0.948478i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 700.302i | 0.180402i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3834.49 | 0.975907 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2193.90 | −0.551704 | −0.275852 | − | 0.961200i | \(-0.588960\pi\) | ||||
−0.275852 | + | 0.961200i | \(0.588960\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4187.04i | 1.04046i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3933.07i | 0.954623i | 0.878734 | + | 0.477312i | \(0.158389\pi\) | ||||
−0.878734 | + | 0.477312i | \(0.841611\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1118.62 | −0.268370 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3286.75 | 0.779481 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 497.852i | 0.116726i | 0.998295 | + | 0.0583629i | \(0.0185880\pi\) | ||||
−0.998295 | + | 0.0583629i | \(0.981412\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 3896.95i | − 0.893219i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7672.17 | 1.73896 | 0.869481 | − | 0.493967i | \(-0.164454\pi\) | ||||
0.869481 | + | 0.493967i | \(0.164454\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3392.88 | −0.760526 | −0.380263 | − | 0.924878i | \(-0.624167\pi\) | ||||
−0.380263 | + | 0.924878i | \(0.624167\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − 143.021i | − 0.0317072i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 2314.21i | − 0.501975i | −0.967990 | − | 0.250988i | \(-0.919245\pi\) | ||||
0.967990 | − | 0.250988i | \(-0.0807553\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 591.192 | 0.126859 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3604.79 | −0.765280 | −0.382640 | − | 0.923897i | \(-0.624985\pi\) | ||||
−0.382640 | + | 0.923897i | \(0.624985\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 2304.38i | − 0.484032i | −0.970272 | − | 0.242016i | \(-0.922191\pi\) | ||||
0.970272 | − | 0.242016i | \(-0.0778087\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 1633.25i | − 0.335916i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5871.77 | −1.19515 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3927.79 | 0.791241 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 6680.29i | − 1.33197i | −0.745966 | − | 0.665984i | \(-0.768012\pi\) | ||||
0.745966 | − | 0.665984i | \(-0.231988\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 7541.25i | − 1.47336i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −477.051 | −0.0922694 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3671.61 | −0.703083 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2968.51i | 0.562827i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3532.96i | 0.656798i | 0.944539 | + | 0.328399i | \(0.106509\pi\) | ||||
−0.944539 | + | 0.328399i | \(0.893491\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1204.15 | 0.221688 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7713.50 | −1.40641 | −0.703204 | − | 0.710989i | \(-0.748248\pi\) | ||||
−0.703204 | + | 0.710989i | \(0.748248\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5776.97i | 1.04324i | 0.853178 | + | 0.521619i | \(0.174672\pi\) | ||||
−0.853178 | + | 0.521619i | \(0.825328\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 2879.80i | − 0.510239i | −0.966910 | − | 0.255120i | \(-0.917885\pi\) | ||||
0.966910 | − | 0.255120i | \(-0.0821148\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −11328.1 | −1.98826 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6430.81 | 1.11817 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 12303.1i | − 2.11939i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 4194.76i | − 0.709391i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1473.08 | 0.246850 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2784.80 | −0.462437 | −0.231218 | − | 0.972902i | \(-0.574271\pi\) | ||||
−0.231218 | + | 0.972902i | \(0.574271\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 2405.53i | − 0.395863i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 2009.52i | − 0.324824i | −0.986723 | − | 0.162412i | \(-0.948073\pi\) | ||||
0.986723 | − | 0.162412i | \(-0.0519273\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 924.701 | 0.148150 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2037.61 | −0.323586 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 5117.20i | − 0.791659i | −0.918324 | − | 0.395829i | \(-0.870457\pi\) | ||||
0.918324 | − | 0.395829i | \(-0.129543\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9330.98 | 1.43116 | 0.715581 | − | 0.698530i | \(-0.246162\pi\) | ||||
0.715581 | + | 0.698530i | \(0.246162\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 859.214 | 0.130659 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 1549.68i | − 0.233657i | −0.993152 | − | 0.116829i | \(-0.962727\pi\) | ||||
0.993152 | − | 0.116829i | \(-0.0372728\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2512.64i | 0.372502i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9513.09 | −1.39856 | −0.699278 | − | 0.714850i | \(-0.746495\pi\) | ||||
−0.699278 | + | 0.714850i | \(0.746495\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7176.25 | 1.04625 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4703.35i | 0.680061i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6441.14i | 0.916144i | 0.888915 | + | 0.458072i | \(0.151460\pi\) | ||||
−0.888915 | + | 0.458072i | \(0.848540\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3512.22 | 0.495498 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2436.20 | 0.340919 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 7428.14i | − 1.03114i | −0.856848 | − | 0.515569i | \(-0.827581\pi\) | ||||
0.856848 | − | 0.515569i | \(-0.172419\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 1290.67i | − 0.176321i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10369.5 | 1.40539 | 0.702696 | − | 0.711491i | \(-0.251980\pi\) | ||||
0.702696 | + | 0.711491i | \(0.251980\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2462.32 | −0.331098 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5924.21i | 0.790374i | 0.918601 | + | 0.395187i | \(0.129320\pi\) | ||||
−0.918601 | + | 0.395187i | \(0.870680\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 7895.58i | − 1.03709i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1330.48 | −0.173413 | −0.0867067 | − | 0.996234i | \(-0.527634\pi\) | ||||
−0.0867067 | + | 0.996234i | \(0.527634\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8380.97 | 1.08400 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2579.75i | 0.331123i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 10355.1i | − 1.30909i | −0.756023 | − | 0.654544i | \(-0.772860\pi\) | ||||
0.756023 | − | 0.654544i | \(-0.227140\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2866.39 | −0.359647 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3844.38 | 0.478751 | 0.239376 | − | 0.970927i | \(-0.423057\pi\) | ||||
0.239376 | + | 0.970927i | \(0.423057\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 232.155i | − 0.0286960i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8290.93i | 1.00975i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8351.01 | −1.00961 | −0.504805 | − | 0.863233i | \(-0.668436\pi\) | ||||
−0.504805 | + | 0.863233i | \(0.668436\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9030.11 | 1.08375 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 596.227i | − 0.0710373i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − 2202.85i | − 0.258691i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1966.13 | 0.229240 | 0.114620 | − | 0.993409i | \(-0.463435\pi\) | ||||
0.114620 | + | 0.993409i | \(0.463435\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12154.0 | 1.40700 | 0.703501 | − | 0.710694i | \(-0.251619\pi\) | ||||
0.703501 | + | 0.710694i | \(0.251619\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3167.78i | 0.364120i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5612.04i | 0.636032i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1060.04 | −0.119299 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15045.0 | −1.68143 | −0.840713 | − | 0.541481i | \(-0.817864\pi\) | ||||
−0.840713 | + | 0.541481i | \(0.817864\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1945.75i | 0.215950i | 0.994154 | + | 0.107975i | \(0.0344367\pi\) | ||||
−0.994154 | + | 0.107975i | \(0.965563\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9560.91i | 1.04659i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8484.35 | −0.922405 | −0.461203 | − | 0.887295i | \(-0.652582\pi\) | ||||
−0.461203 | + | 0.887295i | \(0.652582\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −737.602 | −0.0796460 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 14875.3i | − 1.59537i | −0.603078 | − | 0.797683i | \(-0.706059\pi\) | ||||
0.603078 | − | 0.797683i | \(-0.293941\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7437.97i | 0.787033i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17995.8 | −1.89148 | −0.945742 | − | 0.324918i | \(-0.894663\pi\) | ||||
−0.945742 | + | 0.324918i | \(0.894663\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12105.2 | −1.26389 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5824.72i | 0.604126i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 4243.31i | − 0.434340i | −0.976134 | − | 0.217170i | \(-0.930317\pi\) | ||||
0.976134 | − | 0.217170i | \(-0.0696827\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −15094.9 | −1.53501 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11234.8 | −1.13504 | −0.567522 | − | 0.823358i | \(-0.692098\pi\) | ||||
−0.567522 | + | 0.823358i | \(0.692098\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 226.775i | − 0.0227627i | −0.999935 | − | 0.0113814i | \(-0.996377\pi\) | ||||
0.999935 | − | 0.0113814i | \(-0.00362288\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11886.0i | 1.17777i | 0.808217 | + | 0.588885i | \(0.200433\pi\) | ||||
−0.808217 | + | 0.588885i | \(0.799567\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5012.35 | −0.493494 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3937.93 | 0.385245 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 27213.0i | 2.64536i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5238.90i | 0.502878i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5052.68 | −0.481969 | −0.240984 | − | 0.970529i | \(-0.577470\pi\) | ||||
−0.240984 | + | 0.970529i | \(0.577470\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −944.629 | −0.0895455 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 1952.61i | − 0.183948i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 3987.21i | − 0.371001i | −0.982644 | − | 0.185501i | \(-0.940609\pi\) | ||||
0.982644 | − | 0.185501i | \(-0.0593907\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6079.19 | 0.562189 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4969.66 | −0.456777 | −0.228389 | − | 0.973570i | \(-0.573346\pi\) | ||||
−0.228389 | + | 0.973570i | \(0.573346\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 22674.9i | 2.07145i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3642.88i | 0.328784i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11651.2 | −1.04525 | −0.522625 | − | 0.852562i | \(-0.675047\pi\) | ||||
−0.522625 | + | 0.852562i | \(0.675047\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8124.35 | 0.724490 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1024.77i | 0.0908398i | 0.998968 | + | 0.0454199i | \(0.0144626\pi\) | ||||
−0.998968 | + | 0.0454199i | \(0.985537\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7473.00i | 0.654610i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6350.40 | 0.552999 | 0.276500 | − | 0.961014i | \(-0.410826\pi\) | ||||
0.276500 | + | 0.961014i | \(0.410826\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1610.03 | 0.139381 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − 17220.1i | − 1.48204i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 10918.1i | − 0.928778i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8309.04 | 0.702749 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11664.5 | 0.980864 | 0.490432 | − | 0.871479i | \(-0.336839\pi\) | ||||
0.490432 | + | 0.871479i | \(0.336839\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2475.61i | 0.206980i | 0.994630 | + | 0.103490i | \(0.0330011\pi\) | ||||
−0.994630 | + | 0.103490i | \(0.966999\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4078.57i | 0.337126i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5654.05 | 0.464703 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1282.15 | 0.104785 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 1379.21i | − 0.112083i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 11618.8i | 0.933686i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2542.22 | 0.203157 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5689.60 | −0.452153 | −0.226077 | − | 0.974110i | \(-0.572590\pi\) | ||||
−0.226077 | + | 0.974110i | \(0.572590\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 16179.7i | − 1.27870i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13796.6i | 1.07843i | 0.842169 | + | 0.539213i | \(0.181278\pi\) | ||||
−0.842169 | + | 0.539213i | \(0.818722\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −12068.4 | −0.938188 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −25867.3 | −1.99997 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 6793.74i | − 0.522422i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14995.2i | 1.14069i | 0.821404 | + | 0.570347i | \(0.193191\pi\) | ||||
−0.821404 | + | 0.570347i | \(0.806809\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3100.51 | −0.234593 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 18623.1 | 1.40154 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 7110.77i | − 0.532297i | −0.963932 | − | 0.266149i | \(-0.914249\pi\) | ||||
0.963932 | − | 0.266149i | \(-0.0857512\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 671.793i | 0.0497578i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 19858.3 | 1.46310 | 0.731549 | − | 0.681789i | \(-0.238798\pi\) | ||||
0.731549 | + | 0.681789i | \(0.238798\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8680.50 | −0.636196 | −0.318098 | − | 0.948058i | \(-0.603044\pi\) | ||||
−0.318098 | + | 0.948058i | \(0.603044\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8212.14i | 0.598721i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4639.54i | 0.334743i | 0.985894 | + | 0.167372i | \(0.0535279\pi\) | ||||
−0.985894 | + | 0.167372i | \(0.946472\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −17077.8 | −1.22578 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7765.65 | −0.554516 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 18056.4i | − 1.28271i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 11286.4i | − 0.793597i | −0.917906 | − | 0.396799i | \(-0.870121\pi\) | ||||
0.917906 | − | 0.396799i | \(-0.129879\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4652.78 | −0.325492 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4615.38 | 0.321237 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 2434.90i | − 0.168616i | −0.996440 | − | 0.0843082i | \(-0.973132\pi\) | ||||
0.996440 | − | 0.0843082i | \(-0.0268680\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7727.24i | 0.529740i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5668.75 | 0.386676 | 0.193338 | − | 0.981132i | \(-0.438069\pi\) | ||||
0.193338 | + | 0.981132i | \(0.438069\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22312.6 | 1.51439 | 0.757195 | − | 0.653189i | \(-0.226569\pi\) | ||||
0.757195 | + | 0.653189i | \(0.226569\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 10778.8i | − 0.727936i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13583.7i | 0.908314i | 0.890922 | + | 0.454157i | \(0.150059\pi\) | ||||
−0.890922 | + | 0.454157i | \(0.849941\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5282.82 | 0.351512 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1243.96 | 0.0823651 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6448.94i | 0.424911i | 0.977171 | + | 0.212455i | \(0.0681460\pi\) | ||||
−0.977171 | + | 0.212455i | \(0.931854\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 4075.91i | − 0.265948i | −0.991120 | − | 0.132974i | \(-0.957547\pi\) | ||||
0.991120 | − | 0.132974i | \(-0.0424526\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17730.9 | 1.15131 | 0.575657 | − | 0.817691i | \(-0.304746\pi\) | ||||
0.575657 | + | 0.817691i | \(0.304746\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 11730.4 | 0.758014 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7892.14i | 0.507531i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 21244.9i | 1.35318i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 16595.5 | 1.05200 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24687.2 | −1.55750 | −0.778748 | − | 0.627337i | \(-0.784145\pi\) | ||||
−0.778748 | + | 0.627337i | \(0.784145\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 3027.38i | − 0.190091i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 289.649i | 0.0180162i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7833.81 | −0.484977 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3640.27 | −0.224309 | −0.112154 | − | 0.993691i | \(-0.535775\pi\) | ||||
−0.112154 | + | 0.993691i | \(0.535775\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18809.9i | 1.15364i | 0.816871 | + | 0.576821i | \(0.195707\pi\) | ||||
−0.816871 | + | 0.576821i | \(0.804293\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 7914.91i | − 0.480939i | −0.970657 | − | 0.240469i | \(-0.922699\pi\) | ||||
0.970657 | − | 0.240469i | \(-0.0773014\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4419.07 | −0.267279 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 950.229 | 0.0572080 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 20629.9i | 1.23631i | 0.786056 | + | 0.618155i | \(0.212120\pi\) | ||||
−0.786056 | + | 0.618155i | \(0.787880\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3462.29i | 0.205596i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −20033.4 | −1.18420 | −0.592101 | − | 0.805864i | \(-0.701701\pi\) | ||||
−0.592101 | + | 0.805864i | \(0.701701\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −33181.9 | −1.95254 | −0.976268 | − | 0.216565i | \(-0.930515\pi\) | ||||
−0.976268 | + | 0.216565i | \(0.930515\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2121.82i | 0.124291i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 17621.0i | − 1.02292i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 13653.7 | 0.789061 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 41594.9 | 2.39308 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9881.92i | 0.566003i | 0.959119 | + | 0.283001i | \(0.0913301\pi\) | ||||
−0.959119 | + | 0.283001i | \(0.908670\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2059.42i | 0.116913i | 0.998290 | + | 0.0584563i | \(0.0186178\pi\) | ||||
−0.998290 | + | 0.0584563i | \(0.981382\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7954.61 | −0.449587 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7791.89 | −0.438452 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 29350.2i | 1.64429i | 0.569275 | + | 0.822147i | \(0.307224\pi\) | ||||
−0.569275 | + | 0.822147i | \(0.692776\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 12720.3i | 0.706416i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2057.26 | 0.113753 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11343.4 | −0.624491 | −0.312246 | − | 0.950001i | \(-0.601081\pi\) | ||||
−0.312246 | + | 0.950001i | \(0.601081\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5466.91i | 0.299669i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 24230.4i | 1.31678i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3835.74 | 0.207555 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16939.1 | −0.912667 | −0.456334 | − | 0.889809i | \(-0.650838\pi\) | ||||
−0.456334 | + | 0.889809i | \(0.650838\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18932.0i | 1.01569i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 6011.87i | − 0.319801i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −20813.0 | −1.10247 | −0.551233 | − | 0.834351i | \(-0.685843\pi\) | ||||
−0.551233 | + | 0.834351i | \(0.685843\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14609.5 | 0.770606 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 3169.51i | − 0.166478i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 3731.94i | − 0.194382i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −15526.6 | −0.805348 | −0.402674 | − | 0.915344i | \(-0.631919\pi\) | ||||
−0.402674 | + | 0.915344i | \(0.631919\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2438.65 | −0.125964 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 280.360i | 0.0144214i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18301.0i | 0.933628i | 0.884356 | + | 0.466814i | \(0.154598\pi\) | ||||
−0.884356 | + | 0.466814i | \(0.845402\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −15009.6 | −0.762565 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 54470.8 | 2.75605 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 31175.7i | − 1.57094i | −0.618897 | − | 0.785472i | \(-0.712420\pi\) | ||||
0.618897 | − | 0.785472i | \(-0.287580\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 37150.2i | 1.85678i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 38874.4 | 1.93507 | 0.967537 | − | 0.252730i | \(-0.0813284\pi\) | ||||
0.967537 | + | 0.252730i | \(0.0813284\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2420.55 | −0.120001 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 15899.8i | − 0.785071i | −0.919737 | − | 0.392536i | \(-0.871598\pi\) | ||||
0.919737 | − | 0.392536i | \(-0.128402\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 16699.6i | − 0.817947i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −13023.7 | −0.635350 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20419.5 | 0.992168 | 0.496084 | − | 0.868275i | \(-0.334771\pi\) | ||||
0.496084 | + | 0.868275i | \(0.334771\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 7583.05i | − 0.366988i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 33358.9i | − 1.60165i | −0.598897 | − | 0.800826i | \(-0.704394\pi\) | ||||
0.598897 | − | 0.800826i | \(-0.295606\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −14472.2 | −0.692105 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7773.61 | −0.370293 | −0.185147 | − | 0.982711i | \(-0.559276\pi\) | ||||
−0.185147 | + | 0.982711i | \(0.559276\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8495.28i | 0.403080i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 503.488i | − 0.0237026i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −30704.0 | −1.43981 | −0.719906 | − | 0.694072i | \(-0.755815\pi\) | ||||
−0.719906 | + | 0.694072i | \(0.755815\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13594.4 | −0.635006 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 31749.5i | 1.47730i | 0.674091 | + | 0.738648i | \(0.264536\pi\) | ||||
−0.674091 | + | 0.738648i | \(0.735464\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 3866.44i | − 0.178517i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −27641.7 | −1.27133 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 27000.1 | 1.23705 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 31737.0i | 1.44852i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 4536.07i | − 0.205455i | −0.994710 | − | 0.102728i | \(-0.967243\pi\) | ||||
0.994710 | − | 0.102728i | \(-0.0327570\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1720.79 | −0.0776448 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1872.71 | −0.0841796 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4739.13i | 0.212221i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 237.980i | 0.0105768i | 0.999986 | + | 0.00528840i | \(0.00168336\pi\) | ||||
−0.999986 | + | 0.00528840i | \(0.998317\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −21854.2 | −0.967643 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −16971.6 | −0.748642 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 11933.1i | − 0.524423i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 26518.3i | 1.15674i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 33008.4 | 1.43450 | 0.717251 | − | 0.696815i | \(-0.245400\pi\) | ||||
0.717251 | + | 0.696815i | \(0.245400\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16028.1 | −0.693988 | −0.346994 | − | 0.937867i | \(-0.612798\pi\) | ||||
−0.346994 | + | 0.937867i | \(0.612798\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 11727.2i | − 0.505894i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 62139.6i | 2.66094i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −622.873 | −0.0265750 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6121.99 | 0.260242 | 0.130121 | − | 0.991498i | \(-0.458463\pi\) | ||||
0.130121 | + | 0.991498i | \(0.458463\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10372.7i | 0.439331i | 0.975575 | + | 0.219666i | \(0.0704966\pi\) | ||||
−0.975575 | + | 0.219666i | \(0.929503\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5018.82i | 0.211030i | 0.994418 | + | 0.105515i | \(0.0336491\pi\) | ||||
−0.994418 | + | 0.105515i | \(0.966351\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13231.4 | 0.554336 | 0.277168 | − | 0.960822i | \(-0.410604\pi\) | ||||
0.277168 | + | 0.960822i | \(0.410604\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7998.89 | 0.333909 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 5088.64i | − 0.211658i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5708.59i | 0.235744i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9522.56 | 0.391842 | 0.195921 | − | 0.980620i | \(-0.437230\pi\) | ||||
0.195921 | + | 0.980620i | \(0.437230\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23284.9 | 0.954730 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 12459.7i | − 0.509057i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 9525.29i | − 0.386414i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7964.92 | 0.321973 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −12896.6 | −0.519494 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 43594.1i | 1.74986i | 0.484245 | + | 0.874932i | \(0.339094\pi\) | ||||
−0.484245 | + | 0.874932i | \(0.660906\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 31892.6i | − 1.27122i | −0.772012 | − | 0.635608i | \(-0.780749\pi\) | ||||
0.772012 | − | 0.635608i | \(-0.219251\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13058.6 | −0.518689 | −0.259345 | − | 0.965785i | \(-0.583507\pi\) | ||||
−0.259345 | + | 0.965785i | \(0.583507\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5645.22 | 0.223448 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 21487.2i | − 0.847548i | −0.905768 | − | 0.423774i | \(-0.860705\pi\) | ||||
0.905768 | − | 0.423774i | \(-0.139295\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 20295.4i | − 0.795002i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −50353.4 | −1.96562 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4232.71 | −0.164661 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 17105.9i | − 0.663171i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2743.60i | 0.105638i | 0.998604 | + | 0.0528192i | \(0.0168207\pi\) | ||||
−0.998604 | + | 0.0528192i | \(0.983179\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 23089.9 | 0.886012 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −12554.8 | −0.480115 | −0.240057 | − | 0.970759i | \(-0.577166\pi\) | ||||
−0.240057 | + | 0.970759i | \(0.577166\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26353.2i | 1.00437i | 0.864761 | + | 0.502184i | \(0.167470\pi\) | ||||
−0.864761 | + | 0.502184i | \(0.832530\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 14016.6i | − 0.530587i | −0.964168 | − | 0.265293i | \(-0.914531\pi\) | ||||
0.964168 | − | 0.265293i | \(-0.0854688\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4986.72 | 0.188132 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4979.15 | 0.187214 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 24931.0i | − 0.934249i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 1648.89i | − 0.0613767i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8575.18 | 0.318129 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −36142.6 | −1.33639 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 12690.6i | − 0.467684i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 30710.0i | − 1.12427i | −0.827047 | − | 0.562134i | \(-0.809981\pi\) | ||||
0.827047 | − | 0.562134i | \(-0.190019\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 12928.2 | 0.471728 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 47099.3 | 1.71292 | 0.856459 | − | 0.516215i | \(-0.172659\pi\) | ||||
0.856459 | + | 0.516215i | \(0.172659\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 57556.9i | 2.08637i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 5224.55i | − 0.188146i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7922.89 | −0.284387 | −0.142194 | − | 0.989839i | \(-0.545416\pi\) | ||||
−0.142194 | + | 0.989839i | \(0.545416\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12211.4 | −0.436895 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3076.26i | 0.109703i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 5244.18i | − 0.185805i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −22388.1 | −0.790668 | −0.395334 | − | 0.918537i | \(-0.629371\pi\) | ||||
−0.395334 | + | 0.918537i | \(0.629371\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5805.05 | 0.204353 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 26661.2i | − 0.935528i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15161.4i | 0.528603i | 0.964440 | + | 0.264302i | \(0.0851414\pi\) | ||||
−0.964440 | + | 0.264302i | \(0.914859\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −19967.7 | −0.693952 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 32547.3 | 1.12754 | 0.563768 | − | 0.825933i | \(-0.309351\pi\) | ||||
0.563768 | + | 0.825933i | \(0.309351\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 18829.7i | − 0.650245i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 16496.7i | − 0.566072i | −0.959109 | − | 0.283036i | \(-0.908658\pi\) | ||||
0.959109 | − | 0.283036i | \(-0.0913416\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1359.60 | 0.0465065 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9953.83 | 0.339406 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 42608.4i | − 1.44829i | −0.689647 | − | 0.724146i | \(-0.742234\pi\) | ||||
0.689647 | − | 0.724146i | \(-0.257766\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 39154.9i | − 1.32257i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −18287.9 | −0.615794 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28248.6 | −0.948225 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 28006.8i | − 0.937183i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25980.4i | 0.863983i | 0.901878 | + | 0.431992i | \(0.142189\pi\) | ||||
−0.901878 | + | 0.431992i | \(0.857811\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 42524.9 | 1.40980 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 475.566 | 0.0157174 | 0.00785872 | − | 0.999969i | \(-0.497498\pi\) | ||||
0.00785872 | + | 0.999969i | \(0.497498\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4461.24i | 0.146990i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 17562.9i | − 0.575115i | −0.957763 | − | 0.287557i | \(-0.907157\pi\) | ||||
0.957763 | − | 0.287557i | \(-0.0928432\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 58494.5 | 1.90959 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −18268.6 | −0.594569 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 20943.8i | − 0.679557i | −0.940505 | − | 0.339779i | \(-0.889648\pi\) | ||||
0.940505 | − | 0.339779i | \(-0.110352\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5091.61i | 0.164202i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −42329.9 | −1.36098 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −55297.8 | −1.77254 | −0.886272 | − | 0.463164i | \(-0.846714\pi\) | ||||
−0.886272 | + | 0.463164i | \(0.846714\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 9625.47i | − 0.307608i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1485.25i | 0.0471800i | 0.999722 | + | 0.0235900i | \(0.00750963\pi\) | ||||
−0.999722 | + | 0.0235900i | \(0.992490\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 23228.0 | 0.735636 |
(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 | 1400.4.g.l.449.5 | 6 | ||
5.2 | odd | 4 | 280.4.a.f.1.3 | ✓ | 3 | ||
5.3 | odd | 4 | 1400.4.a.m.1.1 | 3 | |||
5.4 | even | 2 | inner | 1400.4.g.l.449.2 | 6 | ||
20.7 | even | 4 | 560.4.a.w.1.1 | 3 | |||
35.27 | even | 4 | 1960.4.a.r.1.1 | 3 | |||
40.27 | even | 4 | 2240.4.a.br.1.3 | 3 | |||
40.37 | odd | 4 | 2240.4.a.bz.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.4.a.f.1.3 | ✓ | 3 | 5.2 | odd | 4 | ||
560.4.a.w.1.1 | 3 | 20.7 | even | 4 | |||
1400.4.a.m.1.1 | 3 | 5.3 | odd | 4 | |||
1400.4.g.l.449.2 | 6 | 5.4 | even | 2 | inner | ||
1400.4.g.l.449.5 | 6 | 1.1 | even | 1 | trivial | ||
1960.4.a.r.1.1 | 3 | 35.27 | even | 4 | |||
2240.4.a.br.1.3 | 3 | 40.27 | even | 4 | |||
2240.4.a.bz.1.1 | 3 | 40.37 | odd | 4 |