Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2312,4,Mod(1,2312)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2312, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("2312.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2312 = 2^{3} \cdot 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2312.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: | \(136.412415933\) |
Analytic rank: | \(1\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 345 x^{16} - 182 x^{15} + 48165 x^{14} + 48078 x^{13} - 3485278 x^{12} - 4881882 x^{11} + 139131876 x^{10} + 239770606 x^{9} - 3013674039 x^{8} + \cdots - 119632152329 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{15}\cdot 3^{2}\cdot 17^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-8.88256\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2312.1 |
$q$-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 | ||||||||
\(3\) | −8.88256 | −1.70945 | −0.854725 | − | 0.519082i | \(-0.826274\pi\) | ||||
−0.854725 | + | 0.519082i | \(0.826274\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.51577 | 0.225017 | 0.112509 | − | 0.993651i | \(-0.464111\pi\) | ||||
0.112509 | + | 0.993651i | \(0.464111\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 10.7880 | 0.582496 | 0.291248 | − | 0.956648i | \(-0.405929\pi\) | ||||
0.291248 | + | 0.956648i | \(0.405929\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 51.8999 | 1.92222 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.61582 | 0.126520 | 0.0632602 | − | 0.997997i | \(-0.479850\pi\) | ||||
0.0632602 | + | 0.997997i | \(0.479850\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 38.1572 | 0.814070 | 0.407035 | − | 0.913413i | \(-0.366563\pi\) | ||||
0.407035 | + | 0.913413i | \(0.366563\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −22.3464 | −0.384655 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 70.4236 | 0.850331 | 0.425166 | − | 0.905116i | \(-0.360216\pi\) | ||||
0.425166 | + | 0.905116i | \(0.360216\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −95.8249 | −0.995748 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −136.987 | −1.24190 | −0.620950 | − | 0.783850i | \(-0.713253\pi\) | ||||
−0.620950 | + | 0.783850i | \(0.713253\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −118.671 | −0.949367 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −221.175 | −1.57648 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −219.743 | −1.40708 | −0.703540 | − | 0.710655i | \(-0.748399\pi\) | ||||
−0.703540 | + | 0.710655i | \(0.748399\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 275.440 | 1.59582 | 0.797912 | − | 0.602774i | \(-0.205938\pi\) | ||||
0.797912 | + | 0.602774i | \(0.205938\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −41.0003 | −0.216280 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 27.1400 | 0.131072 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 128.032 | 0.568873 | 0.284436 | − | 0.958695i | \(-0.408194\pi\) | ||||
0.284436 | + | 0.958695i | \(0.408194\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −338.934 | −1.39161 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −436.505 | −1.66270 | −0.831348 | − | 0.555751i | \(-0.812431\pi\) | ||||
−0.831348 | + | 0.555751i | \(0.812431\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −150.637 | −0.534229 | −0.267115 | − | 0.963665i | \(-0.586070\pi\) | ||||
−0.267115 | + | 0.963665i | \(0.586070\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 130.568 | 0.432532 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 391.842 | 1.21609 | 0.608043 | − | 0.793904i | \(-0.291955\pi\) | ||||
0.608043 | + | 0.793904i | \(0.291955\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −226.619 | −0.660698 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 117.330 | 0.304084 | 0.152042 | − | 0.988374i | \(-0.451415\pi\) | ||||
0.152042 | + | 0.988374i | \(0.451415\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 11.6123 | 0.0284692 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −625.542 | −1.45360 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −31.7994 | −0.0701683 | −0.0350842 | − | 0.999384i | \(-0.511170\pi\) | ||||
−0.0350842 | + | 0.999384i | \(0.511170\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −481.126 | −1.00987 | −0.504933 | − | 0.863158i | \(-0.668483\pi\) | ||||
−0.504933 | + | 0.863158i | \(0.668483\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 559.895 | 1.11968 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 95.9947 | 0.183180 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −722.761 | −1.31790 | −0.658950 | − | 0.752187i | \(-0.728999\pi\) | ||||
−0.658950 | + | 0.752187i | \(0.728999\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1216.79 | 2.12297 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 495.446 | 0.828150 | 0.414075 | − | 0.910243i | \(-0.364105\pi\) | ||||
0.414075 | + | 0.910243i | \(0.364105\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −719.065 | −1.15288 | −0.576440 | − | 0.817140i | \(-0.695558\pi\) | ||||
−0.576440 | + | 0.817140i | \(0.695558\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1054.10 | 1.62290 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 49.7954 | 0.0736976 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 149.298 | 0.212624 | 0.106312 | − | 0.994333i | \(-0.466096\pi\) | ||||
0.106312 | + | 0.994333i | \(0.466096\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 563.300 | 0.772702 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1214.22 | 1.60576 | 0.802879 | − | 0.596142i | \(-0.203301\pi\) | ||||
0.802879 | + | 0.596142i | \(0.203301\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1951.88 | 2.40533 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 602.356 | 0.717411 | 0.358706 | − | 0.933451i | \(-0.383218\pi\) | ||||
0.358706 | + | 0.933451i | \(0.383218\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 411.640 | 0.474193 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2446.62 | −2.72798 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 177.169 | 0.191339 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1773.07 | 1.85596 | 0.927979 | − | 0.372634i | \(-0.121545\pi\) | ||||
0.927979 | + | 0.372634i | \(0.121545\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 239.561 | 0.243200 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1480.23 | 1.45830 | 0.729148 | − | 0.684356i | \(-0.239916\pi\) | ||||
0.729148 | + | 0.684356i | \(0.239916\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 948.709 | 0.907564 | 0.453782 | − | 0.891113i | \(-0.350075\pi\) | ||||
0.453782 | + | 0.891113i | \(0.350075\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −241.073 | −0.224060 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1089.50 | −0.984353 | −0.492177 | − | 0.870495i | \(-0.663799\pi\) | ||||
−0.492177 | + | 0.870495i | \(0.663799\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1676.91 | −1.47356 | −0.736782 | − | 0.676131i | \(-0.763656\pi\) | ||||
−0.736782 | + | 0.676131i | \(0.763656\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1137.25 | −0.972459 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −112.895 | −0.0939846 | −0.0469923 | − | 0.998895i | \(-0.514964\pi\) | ||||
−0.0469923 | + | 0.998895i | \(0.514964\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −344.627 | −0.279449 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1980.36 | 1.56482 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1309.69 | −0.983993 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3877.28 | 2.84230 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −613.019 | −0.438641 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1023.09 | −0.714842 | −0.357421 | − | 0.933943i | \(-0.616344\pi\) | ||||
−0.357421 | + | 0.933943i | \(0.616344\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1338.04 | 0.913238 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2415.30 | 1.61088 | 0.805441 | − | 0.592676i | \(-0.201929\pi\) | ||||
0.805441 | + | 0.592676i | \(0.201929\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 759.729 | 0.495315 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −556.424 | −0.354736 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 994.871 | 0.620420 | 0.310210 | − | 0.950668i | \(-0.399601\pi\) | ||||
0.310210 | + | 0.950668i | \(0.399601\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1363.31 | −0.831904 | −0.415952 | − | 0.909387i | \(-0.636551\pi\) | ||||
−0.415952 | + | 0.909387i | \(0.636551\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3480.56 | −2.07884 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 176.127 | 0.102996 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −552.823 | −0.316617 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2012.96 | 1.12943 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1720.70 | 0.946073 | 0.473036 | − | 0.881043i | \(-0.343158\pi\) | ||||
0.473036 | + | 0.881043i | \(0.343158\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −128.263 | −0.0691250 | −0.0345625 | − | 0.999403i | \(-0.511004\pi\) | ||||
−0.0345625 | + | 0.999403i | \(0.511004\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 692.944 | 0.359088 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −726.645 | −0.369380 | −0.184690 | − | 0.982797i | \(-0.559128\pi\) | ||||
−0.184690 | + | 0.982797i | \(0.559128\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1042.19 | −0.519817 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1477.81 | −0.723402 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3372.62 | −1.62064 | −0.810320 | − | 0.585987i | \(-0.800707\pi\) | ||||
−0.810320 | + | 0.585987i | \(0.800707\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −103.147 | −0.0486667 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3078.11 | −1.42629 | −0.713147 | − | 0.701015i | \(-0.752731\pi\) | ||||
−0.713147 | + | 0.701015i | \(0.752731\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −741.026 | −0.337290 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3654.98 | 1.63452 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1060.40 | 0.466014 | 0.233007 | − | 0.972475i | \(-0.425144\pi\) | ||||
0.233007 | + | 0.972475i | \(0.425144\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1280.22 | −0.553003 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 282.460 | 0.119949 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2972.05 | 1.24102 | 0.620508 | − | 0.784200i | \(-0.286927\pi\) | ||||
0.620508 | + | 0.784200i | \(0.286927\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −170.006 | −0.0698148 | −0.0349074 | − | 0.999391i | \(-0.511114\pi\) | ||||
−0.0349074 | + | 0.999391i | \(0.511114\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4273.63 | 1.72632 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 322.098 | 0.128006 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2386.03 | −0.918296 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3586.29 | 1.35861 | 0.679306 | − | 0.733856i | \(-0.262281\pi\) | ||||
0.679306 | + | 0.733856i | \(0.262281\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3831.91 | −1.42915 | −0.714577 | − | 0.699557i | \(-0.753381\pi\) | ||||
−0.714577 | + | 0.699557i | \(0.753381\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −852.679 | −0.313136 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1958.63 | 0.708360 | 0.354180 | − | 0.935177i | \(-0.384760\pi\) | ||||
0.354180 | + | 0.935177i | \(0.384760\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5257.05 | −1.87267 | −0.936337 | − | 0.351102i | \(-0.885807\pi\) | ||||
−0.936337 | + | 0.351102i | \(0.885807\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6419.96 | 2.25288 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2370.59 | −0.819619 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1098.14 | −0.374135 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7109.59 | −2.38720 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 325.063 | 0.107584 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1549.01 | 0.505394 | 0.252697 | − | 0.967545i | \(-0.418682\pi\) | ||||
0.252697 | + | 0.967545i | \(0.418682\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4400.83 | −1.41568 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −378.967 | −0.120211 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2971.45 | 0.929562 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6387.14 | 1.97079 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2166.71 | 0.650643 | 0.325321 | − | 0.945603i | \(-0.394527\pi\) | ||||
0.325321 | + | 0.945603i | \(0.394527\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6159.00 | −1.82489 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2421.62 | −0.708056 | −0.354028 | − | 0.935235i | \(-0.615188\pi\) | ||||
−0.354028 | + | 0.935235i | \(0.615188\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4358.00 | 1.25757 | 0.628787 | − | 0.777578i | \(-0.283552\pi\) | ||||
0.628787 | + | 0.777578i | \(0.283552\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −442.311 | −0.125982 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2416.05 | −0.679316 | −0.339658 | − | 0.940549i | \(-0.610311\pi\) | ||||
−0.339658 | + | 0.940549i | \(0.610311\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 985.783 | 0.273640 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1326.15 | −0.363470 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2512.23 | −0.679928 | −0.339964 | − | 0.940438i | \(-0.610415\pi\) | ||||
−0.339964 | + | 0.940438i | \(0.610415\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −737.205 | −0.197044 | −0.0985219 | − | 0.995135i | \(-0.531411\pi\) | ||||
−0.0985219 | + | 0.995135i | \(0.531411\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 968.169 | 0.255589 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −570.122 | −0.148668 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2687.17 | 0.692229 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −10785.4 | −2.74496 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4620.18 | −1.16185 | −0.580923 | − | 0.813958i | \(-0.697308\pi\) | ||||
−0.580923 | + | 0.813958i | \(0.697308\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −632.307 | −0.157126 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6573.88 | −1.59559 | −0.797797 | − | 0.602926i | \(-0.794001\pi\) | ||||
−0.797797 | + | 0.602926i | \(0.794001\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1381.20 | 0.331366 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −11404.7 | −2.70471 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1382.15 | −0.324057 | −0.162029 | − | 0.986786i | \(-0.551804\pi\) | ||||
−0.162029 | + | 0.986786i | \(0.551804\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 295.174 | 0.0684241 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5350.46 | −1.22638 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3193.92 | 0.723929 | 0.361965 | − | 0.932192i | \(-0.382106\pi\) | ||||
0.361965 | + | 0.932192i | \(0.382106\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1506.54 | −0.337696 | −0.168848 | − | 0.985642i | \(-0.554005\pi\) | ||||
−0.168848 | + | 0.985642i | \(0.554005\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3656.41 | −0.810609 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −547.764 | −0.120114 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4911.09 | −1.06527 | −0.532633 | − | 0.846346i | \(-0.678797\pi\) | ||||
−0.532633 | + | 0.846346i | \(0.678797\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 14295.3 | 3.06752 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7198.28 | −1.52816 | −0.764081 | − | 0.645120i | \(-0.776807\pi\) | ||||
−0.764081 | + | 0.645120i | \(0.776807\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4315.91 | 0.906553 | 0.453276 | − | 0.891370i | \(-0.350255\pi\) | ||||
0.453276 | + | 0.891370i | \(0.350255\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1573.72 | −0.327084 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4709.00 | −0.968515 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −15749.4 | −3.17266 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3086.04 | −0.615320 | −0.307660 | − | 0.951496i | \(-0.599546\pi\) | ||||
−0.307660 | + | 0.951496i | \(0.599546\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −79.9999 | −0.0157891 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1020.90 | −0.199457 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5227.03 | −1.01099 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1625.07 | −0.311187 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −13148.2 | −2.49288 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1210.40 | −0.227237 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2132.90 | −0.396518 | −0.198259 | − | 0.980150i | \(-0.563529\pi\) | ||||
−0.198259 | + | 0.980150i | \(0.563529\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8426.96 | −1.55143 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5896.43 | 1.07510 | 0.537550 | − | 0.843232i | \(-0.319350\pi\) | ||||
0.537550 | + | 0.843232i | \(0.319350\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2976.48 | 0.537510 | 0.268755 | − | 0.963209i | \(-0.413388\pi\) | ||||
0.268755 | + | 0.963209i | \(0.413388\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1408.56 | 0.251948 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2742.33 | 0.485882 | 0.242941 | − | 0.970041i | \(-0.421888\pi\) | ||||
0.242941 | + | 0.970041i | \(0.421888\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1014.30 | −0.178024 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9677.54 | 1.68270 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4528.15 | −0.772852 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 14895.2 | 2.51898 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4227.19 | 0.708366 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4210.57 | 0.699196 | 0.349598 | − | 0.936900i | \(-0.386318\pi\) | ||||
0.349598 | + | 0.936900i | \(0.386318\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6644.83 | 1.09350 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1818.30 | −0.296550 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6629.30 | −1.07158 | −0.535788 | − | 0.844352i | \(-0.679985\pi\) | ||||
−0.535788 | + | 0.844352i | \(0.679985\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1002.80 | 0.160662 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1271.38 | 0.201904 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6145.04 | −0.967350 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3061.17 | 0.477703 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10327.2 | 1.59768 | 0.798838 | − | 0.601546i | \(-0.205448\pi\) | ||||
0.798838 | + | 0.601546i | \(0.205448\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1403.59 | −0.215279 | −0.107640 | − | 0.994190i | \(-0.534329\pi\) | ||||
−0.107640 | + | 0.994190i | \(0.534329\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8439.41 | −1.28337 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3518.63 | −0.530532 | −0.265266 | − | 0.964175i | \(-0.585460\pi\) | ||||
−0.265266 | + | 0.964175i | \(0.585460\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1246.43 | 0.186348 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4829.92 | −0.710066 | −0.355033 | − | 0.934854i | \(-0.615530\pi\) | ||||
−0.355033 | + | 0.934854i | \(0.615530\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1899.51 | −0.276937 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 11633.4 | 1.68209 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1809.00 | −0.259418 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13511.1 | 1.92173 | 0.960863 | − | 0.277023i | \(-0.0893477\pi\) | ||||
0.960863 | + | 0.277023i | \(0.0893477\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −22654.5 | −3.19606 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1265.75 | 0.177128 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4797.04 | 0.665902 | 0.332951 | − | 0.942944i | \(-0.391956\pi\) | ||||
0.332951 | + | 0.942944i | \(0.391956\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5445.18 | 0.749834 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8384.80 | −1.14546 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5901.75 | 0.799875 | 0.399937 | − | 0.916543i | \(-0.369032\pi\) | ||||
0.399937 | + | 0.916543i | \(0.369032\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9087.69 | 1.22199 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13587.9 | −1.81282 | −0.906409 | − | 0.422401i | \(-0.861188\pi\) | ||||
−0.906409 | + | 0.422401i | \(0.861188\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 125.274 | 0.0165832 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7818.02 | −1.02691 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4100.95 | 0.534516 | 0.267258 | − | 0.963625i | \(-0.413882\pi\) | ||||
0.267258 | + | 0.963625i | \(0.413882\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −21454.0 | −2.75372 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 375.598 | 0.0478440 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12231.2 | −1.54626 | −0.773130 | − | 0.634248i | \(-0.781310\pi\) | ||||
−0.773130 | + | 0.634248i | \(0.781310\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6748.34 | −0.846716 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 284.483 | 0.0354275 | 0.0177137 | − | 0.999843i | \(-0.494361\pi\) | ||||
0.0177137 | + | 0.999843i | \(0.494361\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10510.0 | 1.29911 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1417.13 | 0.173871 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 590.972 | 0.0719739 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10841.1 | −1.31066 | −0.655329 | − | 0.755343i | \(-0.727470\pi\) | ||||
−0.655329 | + | 0.755343i | \(0.727470\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8837.00 | −1.06058 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −343.052 | −0.0408728 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3054.69 | 0.361323 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12109.7 | 1.42210 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2502.89 | −0.291824 | −0.145912 | − | 0.989298i | \(-0.546612\pi\) | ||||
−0.145912 | + | 0.989298i | \(0.546612\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7379.41 | −0.854277 | −0.427138 | − | 0.904186i | \(-0.640478\pi\) | ||||
−0.427138 | + | 0.904186i | \(0.640478\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 20336.6 | 2.33758 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5190.38 | −0.588243 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1564.46 | −0.176067 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2269.80 | −0.253671 | −0.126836 | − | 0.991924i | \(-0.540482\pi\) | ||||
−0.126836 | + | 0.991924i | \(0.540482\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10132.3 | −1.12454 | −0.562272 | − | 0.826952i | \(-0.690073\pi\) | ||||
−0.562272 | + | 0.826952i | \(0.690073\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4910.49 | 0.541241 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −9647.10 | −1.05603 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12762.1 | −1.38747 | −0.693737 | − | 0.720228i | \(-0.744037\pi\) | ||||
−0.693737 | + | 0.720228i | \(0.744037\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −11761.5 | −1.27001 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8883.68 | −0.952768 | −0.476384 | − | 0.879237i | \(-0.658053\pi\) | ||||
−0.476384 | + | 0.879237i | \(0.658053\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1515.39 | 0.161430 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −15284.2 | −1.61726 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12729.0 | −1.33790 | −0.668949 | − | 0.743308i | \(-0.733256\pi\) | ||||
−0.668949 | + | 0.743308i | \(0.733256\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2014.83 | −0.210365 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1139.30 | 0.118166 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1035.59 | 0.106701 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15299.0 | −1.56599 | −0.782993 | − | 0.622030i | \(-0.786308\pi\) | ||||
−0.782993 | + | 0.622030i | \(0.786308\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2186.66 | 0.220917 | 0.110459 | − | 0.993881i | \(-0.464768\pi\) | ||||
0.110459 | + | 0.993881i | \(0.464768\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1074.21 | −0.107825 | −0.0539123 | − | 0.998546i | \(-0.517169\pi\) | ||||
−0.0539123 | + | 0.998546i | \(0.517169\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6155.11 | −0.613842 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3439.93 | 0.340859 | 0.170430 | − | 0.985370i | \(-0.445484\pi\) | ||||
0.170430 | + | 0.985370i | \(0.445484\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7797.13 | −0.767671 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6454.47 | 0.631436 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −695.312 | −0.0675909 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8357.24 | −0.807277 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6089.39 | 0.584516 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2397.04 | 0.228650 | 0.114325 | − | 0.993443i | \(-0.463529\pi\) | ||||
0.114325 | + | 0.993443i | \(0.463529\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4885.34 | 0.463102 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 13126.7 | 1.23662 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4460.63 | 0.417622 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11064.2 | −1.02950 | −0.514751 | − | 0.857339i | \(-0.672116\pi\) | ||||
−0.514751 | + | 0.857339i | \(0.672116\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 29957.5 | 2.77040 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12258.8 | 1.12674 | 0.563371 | − | 0.826204i | \(-0.309504\pi\) | ||||
0.563371 | + | 0.826204i | \(0.309504\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 602.679 | 0.0547240 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5344.86 | 0.482394 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13076.1 | −1.17308 | −0.586541 | − | 0.809920i | \(-0.699511\pi\) | ||||
−0.586541 | + | 0.809920i | \(0.699511\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 27341.5 | 2.43818 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3204.51 | 0.284060 | 0.142030 | − | 0.989862i | \(-0.454637\pi\) | ||||
0.142030 | + | 0.989862i | \(0.454637\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3723.90 | 0.328142 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6582.21 | 0.576580 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5752.67 | 0.500948 | 0.250474 | − | 0.968123i | \(-0.419413\pi\) | ||||
0.250474 | + | 0.968123i | \(0.419413\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7757.26 | −0.671548 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −15575.9 | −1.34053 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2386.73 | 0.204217 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1808.67 | 0.153860 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9419.02 | −0.796627 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10333.6 | 0.868954 | 0.434477 | − | 0.900683i | \(-0.356933\pi\) | ||||
0.434477 | + | 0.900683i | \(0.356933\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9797.30 | 0.819132 | 0.409566 | − | 0.912281i | \(-0.365680\pi\) | ||||
0.409566 | + | 0.912281i | \(0.365680\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 11371.6 | 0.945331 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6598.35 | 0.542315 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1650.39 | −0.134879 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −16655.8 | −1.35355 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2740.92 | −0.221496 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −26399.4 | −2.12145 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1046.04 | −0.0835917 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12700.1 | 1.00928 | 0.504638 | − | 0.863331i | \(-0.331626\pi\) | ||||
0.504638 | + | 0.863331i | \(0.331626\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1510.09 | 0.119345 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4218.70 | −0.331577 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −144.879 | −0.0113246 | −0.00566232 | − | 0.999984i | \(-0.501802\pi\) | ||||
−0.00566232 | + | 0.999984i | \(0.501802\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −24970.4 | −1.94118 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −15475.1 | −1.19648 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1610.62 | 0.123853 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2861.05 | −0.218820 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 22211.3 | 1.68963 | 0.844814 | − | 0.535061i | \(-0.179711\pi\) | ||||
0.844814 | + | 0.535061i | \(0.179711\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5747.88 | −0.434900 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3615.69 | −0.270663 | −0.135331 | − | 0.990800i | \(-0.543210\pi\) | ||||
−0.135331 | + | 0.990800i | \(0.543210\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −284.017 | −0.0211481 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 6076.87 | 0.450096 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −428.770 | −0.0315905 | −0.0157952 | − | 0.999875i | \(-0.505028\pi\) | ||||
−0.0157952 | + | 0.999875i | \(0.505028\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1806.75 | 0.132417 | 0.0662086 | − | 0.997806i | \(-0.478910\pi\) | ||||
0.0662086 | + | 0.997806i | \(0.478910\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −31855.4 | −2.32248 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 16256.3 | 1.17902 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22101.9 | −1.59465 | −0.797324 | − | 0.603551i | \(-0.793752\pi\) | ||||
−0.797324 | + | 0.603551i | \(0.793752\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 34037.1 | 2.44307 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13099.0 | 0.935348 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 541.573 | 0.0384728 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4982.11 | 0.352111 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −23557.8 | −1.65645 | −0.828225 | − | 0.560396i | \(-0.810649\pi\) | ||||
−0.828225 | + | 0.560396i | \(0.810649\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 19397.5 | 1.35698 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −17397.7 | −1.21091 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −13400.6 | −0.927989 | −0.463995 | − | 0.885838i | \(-0.653584\pi\) | ||||
−0.463995 | + | 0.885838i | \(0.653584\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 46696.0 | 3.20124 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3641.89 | −0.248420 | −0.124210 | − | 0.992256i | \(-0.539640\pi\) | ||||
−0.124210 | + | 0.992256i | \(0.539640\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4853.99 | 0.329448 | 0.164724 | − | 0.986340i | \(-0.447327\pi\) | ||||
0.164724 | + | 0.986340i | \(0.447327\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −37511.2 | −2.53329 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3294.89 | −0.221415 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15241.7 | 1.01918 | 0.509589 | − | 0.860418i | \(-0.329798\pi\) | ||||
0.509589 | + | 0.860418i | \(0.329798\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 21056.9 | 1.40110 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 14951.6 | 0.989979 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8519.26 | 0.561321 | 0.280660 | − | 0.959807i | \(-0.409447\pi\) | ||||
0.280660 | + | 0.959807i | \(0.409447\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 9754.33 | 0.639565 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13044.7 | −0.851154 | −0.425577 | − | 0.904922i | \(-0.639929\pi\) | ||||
−0.425577 | + | 0.904922i | \(0.639929\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11591.6 | −0.752674 | −0.376337 | − | 0.926483i | \(-0.622816\pi\) | ||||
−0.376337 | + | 0.926483i | \(0.622816\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 30298.0 | 1.95784 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6498.20 | 0.417889 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13291.7 | 0.850666 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2887.39 | −0.183910 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20451.8 | −1.29029 | −0.645145 | − | 0.764060i | \(-0.723203\pi\) | ||||
−0.645145 | + | 0.764060i | \(0.723203\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −13759.2 | −0.863946 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2573.87 | −0.160852 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8647.17 | −0.537855 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 25713.6 | 1.59188 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 29696.1 | 1.82984 | 0.914919 | − | 0.403637i | \(-0.132254\pi\) | ||||
0.914919 | + | 0.403637i | \(0.132254\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1806.65 | 0.110804 | 0.0554022 | − | 0.998464i | \(-0.482356\pi\) | ||||
0.0554022 | + | 0.998464i | \(0.482356\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3366.19 | 0.205494 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 14664.2 | 0.891052 | 0.445526 | − | 0.895269i | \(-0.353017\pi\) | ||||
0.445526 | + | 0.895269i | \(0.353017\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −146.781 | −0.00887772 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −26394.0 | −1.58904 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4054.25 | 0.242963 | 0.121482 | − | 0.992594i | \(-0.461235\pi\) | ||||
0.121482 | + | 0.992594i | \(0.461235\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6076.32 | 0.362476 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −37319.4 | −2.21609 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9241.66 | −0.546288 | −0.273144 | − | 0.961973i | \(-0.588064\pi\) | ||||
−0.273144 | + | 0.961973i | \(0.588064\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22727.1 | 1.33734 | 0.668671 | − | 0.743559i | \(-0.266864\pi\) | ||||
0.668671 | + | 0.743559i | \(0.266864\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1911.30 | 0.111454 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 30101.9 | 1.74745 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −19245.9 | −1.11224 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2220.79 | −0.127769 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25575.9 | −1.46490 | −0.732451 | − | 0.680819i | \(-0.761624\pi\) | ||||
−0.732451 | + | 0.680819i | \(0.761624\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 26247.0 | 1.49666 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −25301.6 | −1.43636 | −0.718182 | − | 0.695855i | \(-0.755026\pi\) | ||||
−0.718182 | + | 0.695855i | \(0.755026\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 19127.8 | 1.08109 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 21510.2 | 1.21039 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6633.48 | 0.371630 | 0.185815 | − | 0.982585i | \(-0.440508\pi\) | ||||
0.185815 | + | 0.982585i | \(0.440508\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2502.86 | 0.139605 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −38710.2 | −2.14976 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4476.97 | 0.247546 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21211.2 | 1.16775 | 0.583874 | − | 0.811844i | \(-0.301536\pi\) | ||||
0.583874 | + | 0.811844i | \(0.301536\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2584.38 | 0.141663 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3429.77 | −0.187192 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 21460.7 | 1.16126 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 31524.7 | 1.69853 | 0.849267 | − | 0.527963i | \(-0.177044\pi\) | ||||
0.849267 | + | 0.527963i | \(0.177044\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9016.46 | 0.483730 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −8756.28 | −0.467774 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 15968.6 | 0.849452 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 23585.3 | 1.24931 | 0.624657 | − | 0.780899i | \(-0.285239\pi\) | ||||
0.624657 | + | 0.780899i | \(0.285239\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7748.53 | 0.408710 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −37731.7 | −1.98185 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 443.095 | 0.0231759 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 22315.1 | 1.16230 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5515.05 | 0.286060 | 0.143030 | − | 0.989718i | \(-0.454316\pi\) | ||||
0.143030 | + | 0.989718i | \(0.454316\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10234.7 | 0.528653 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6548.27 | 0.336836 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 26077.2 | 1.33584 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −32407.1 | −1.65325 | −0.826625 | − | 0.562754i | \(-0.809742\pi\) | ||||
−0.826625 | + | 0.562754i | \(0.809742\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23808.9 | −1.20962 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 32710.6 | 1.64828 | 0.824142 | − | 0.566383i | \(-0.191658\pi\) | ||||
0.824142 | + | 0.566383i | \(0.191658\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5064.14 | 0.254141 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3336.14 | −0.166741 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −33363.0 | −1.66073 | −0.830364 | − | 0.557221i | \(-0.811868\pi\) | ||||
−0.830364 | + | 0.557221i | \(0.811868\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −23869.0 | −1.18333 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24474.4 | 1.20845 | 0.604226 | − | 0.796813i | \(-0.293482\pi\) | ||||
0.604226 | + | 0.796813i | \(0.293482\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4328.87 | 0.212882 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 63017.8 | 3.08661 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11753.5 | −0.573382 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3172.55 | −0.154152 | −0.0770759 | − | 0.997025i | \(-0.524558\pi\) | ||||
−0.0770759 | + | 0.997025i | \(0.524558\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 41039.1 | 1.98612 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −322.679 | −0.0155543 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −36897.8 | −1.77156 | −0.885782 | − | 0.464102i | \(-0.846377\pi\) | ||||
−0.885782 | + | 0.464102i | \(0.846377\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5616.50 | 0.268598 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15071.2 | 0.717913 | 0.358957 | − | 0.933354i | \(-0.383133\pi\) | ||||
0.358957 | + | 0.933354i | \(0.383133\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −18090.4 | −0.858345 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1213.38 | −0.0571219 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 25033.3 | 1.17389 | 0.586947 | − | 0.809626i | \(-0.300330\pi\) | ||||
0.586947 | + | 0.809626i | \(0.300330\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 58392.9 | 2.72759 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 26899.1 | 1.25161 | 0.625803 | − | 0.779981i | \(-0.284771\pi\) | ||||
0.625803 | + | 0.779981i | \(0.284771\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −32686.8 | −1.51502 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −12268.6 | −0.566454 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −30740.3 | −1.41384 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2286.89 | 0.104778 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 48601.7 | 2.21824 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1828.07 | −0.0831167 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15295.4 | −0.692787 | −0.346394 | − | 0.938089i | \(-0.612594\pi\) | ||||
−0.346394 | + | 0.938089i | \(0.612594\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 12277.0 | 0.553960 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1217.91 | −0.0547457 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −18358.4 | −0.822102 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2621.90 | −0.116968 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4866.05 | −0.216267 | −0.108133 | − | 0.994136i | \(-0.534487\pi\) | ||||
−0.108133 | + | 0.994136i | \(0.534487\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 31262.2 | 1.37902 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3319.08 | −0.145863 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3717.83 | −0.162778 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −28370.2 | −1.23752 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −11297.5 | −0.490973 | −0.245487 | − | 0.969400i | \(-0.578948\pi\) | ||||
−0.245487 | + | 0.969400i | \(0.578948\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22072.6 | 0.955700 | 0.477850 | − | 0.878441i | \(-0.341416\pi\) | ||||
0.477850 | + | 0.878441i | \(0.341416\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 13381.9 | 0.577274 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8484.74 | −0.364672 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10608.4 | −0.454272 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 21364.0 | 0.911502 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12329.0 | −0.524097 | −0.262048 | − | 0.965055i | \(-0.584398\pi\) | ||||
−0.262048 | + | 0.965055i | \(0.584398\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14234.2 | −0.602885 | −0.301442 | − | 0.953484i | \(-0.597468\pi\) | ||||
−0.301442 | + | 0.953484i | \(0.597468\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4865.55 | 0.205329 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −16569.6 | −0.696713 | −0.348357 | − | 0.937362i | \(-0.613260\pi\) | ||||
−0.348357 | + | 0.937362i | \(0.613260\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −26164.3 | −1.09617 | −0.548085 | − | 0.836423i | \(-0.684643\pi\) | ||||
−0.548085 | + | 0.836423i | \(0.684643\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 43623.0 | 1.82102 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7743.80 | −0.320940 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −60920.4 | −2.51579 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −7683.47 | −0.316165 | −0.158083 | − | 0.987426i | \(-0.550531\pi\) | ||||
−0.158083 | + | 0.987426i | \(0.550531\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23898.2 | 0.979876 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 63939.2 | 2.61232 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1864.25 | −0.0758960 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −14129.0 | −0.573172 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −38336.4 | −1.54971 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −17538.6 | −0.706483 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5850.34 | −0.234832 | −0.117416 | − | 0.993083i | \(-0.537461\pi\) | ||||
−0.117416 | + | 0.993083i | \(0.537461\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9195.07 | 0.367795 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −33338.3 | −1.32884 | −0.664420 | − | 0.747360i | \(-0.731321\pi\) | ||||
−0.664420 | + | 0.747360i | \(0.731321\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −27448.7 | −1.09027 | −0.545133 | − | 0.838350i | \(-0.683521\pi\) | ||||
−0.545133 | + | 0.838350i | \(0.683521\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 41828.0 | 1.65563 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4907.37 | 0.193568 | 0.0967838 | − | 0.995305i | \(-0.469144\pi\) | ||||
0.0967838 | + | 0.995305i | \(0.469144\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2667.71 | 0.104861 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 689.132 | 0.0269013 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −27578.5 | −1.07286 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 92022.0 | 3.56755 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6613.24 | −0.255507 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27586.7 | 1.06219 | 0.531093 | − | 0.847313i | \(-0.321781\pi\) | ||||
0.531093 | + | 0.847313i | \(0.321781\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 27412.0 | 1.05186 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 45088.4 | 1.72425 | 0.862126 | − | 0.506693i | \(-0.169132\pi\) | ||||
0.862126 | + | 0.506693i | \(0.169132\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 15927.0 | 0.607005 | 0.303502 | − | 0.952831i | \(-0.401844\pi\) | ||||
0.303502 | + | 0.952831i | \(0.401844\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 710.604 | 0.0269906 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 37913.5 | 1.43519 | 0.717593 | − | 0.696463i | \(-0.245244\pi\) | ||||
0.717593 | + | 0.696463i | \(0.245244\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −11037.1 | −0.416393 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2600.09 | 0.0977625 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 27595.0 | 1.03408 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7477.00 | 0.279250 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 46429.4 | 1.72824 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −60526.2 | −2.24545 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 14434.7 | 0.531958 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −427.697 | −0.0157095 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −25256.3 | −0.924611 | −0.462305 | − | 0.886721i | \(-0.652978\pi\) | ||||
−0.462305 | + | 0.886721i | \(0.652978\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 76823.5 | 2.80316 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11135.6 | −0.404983 | −0.202491 | − | 0.979284i | \(-0.564904\pi\) | ||||
−0.202491 | + | 0.979284i | \(0.564904\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5604.62 | 0.203161 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 10751.5 | 0.388450 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 26056.2 | 0.938333 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −45609.6 | −1.63713 | −0.818565 | − | 0.574414i | \(-0.805230\pi\) | ||||
−0.818565 | + | 0.574414i | \(0.805230\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 18945.6 | 0.677827 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 18904.8 | 0.674172 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15193.6 | −0.540069 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 49237.9 | 1.74453 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −23419.6 | −0.827097 | −0.413548 | − | 0.910482i | \(-0.635711\pi\) | ||||
−0.413548 | + | 0.910482i | \(0.635711\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15959.4 | −0.561812 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −52375.4 | −1.83783 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14729.0 | 0.513527 | 0.256764 | − | 0.966474i | \(-0.417344\pi\) | ||||
0.256764 | + | 0.966474i | \(0.417344\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −26438.7 | −0.918845 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −53609.0 | −1.85718 | −0.928589 | − | 0.371110i | \(-0.878977\pi\) | ||||
−0.928589 | + | 0.371110i | \(0.878977\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 59795.3 | 2.06490 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −6002.69 | −0.206632 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −44343.7 | −1.52162 | −0.760811 | − | 0.648973i | \(-0.775199\pi\) | ||||
−0.760811 | + | 0.648973i | \(0.775199\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −27437.5 | −0.938525 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −24358.9 | −0.830591 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −32953.0 | −1.12010 | −0.560049 | − | 0.828460i | \(-0.689218\pi\) | ||||
−0.560049 | + | 0.828460i | \(0.689218\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9022.26 | 0.305711 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9009.56 | 0.304324 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 10732.7 | 0.361393 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 46076.4 | 1.54666 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −56544.8 | −1.89214 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9640.19 | −0.321584 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15193.2 | 0.505254 | 0.252627 | − | 0.967564i | \(-0.418705\pi\) | ||||
0.252627 | + | 0.967564i | \(0.418705\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −27985.5 | −0.924920 | −0.462460 | − | 0.886640i | \(-0.653033\pi\) | ||||
−0.462460 | + | 0.886640i | \(0.653033\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −14707.4 | −0.484581 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 40221.6 | 1.32115 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −54353.9 | −1.77987 | −0.889936 | − | 0.456086i | \(-0.849251\pi\) | ||||
−0.889936 | + | 0.456086i | \(0.849251\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2780.37 | 0.0907671 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −87031.2 | −2.83251 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2179.36 | 0.0707130 | 0.0353565 | − | 0.999375i | \(-0.488743\pi\) | ||||
0.0353565 | + | 0.999375i | \(0.488743\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4927.47 | 0.159393 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −37548.2 | −1.21092 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 20635.2 | 0.663460 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 60236.3 | 1.93085 | 0.965423 | − | 0.260688i | \(-0.0839493\pi\) | ||||
0.965423 | + | 0.260688i | \(0.0839493\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −37400.7 | −1.19524 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −13225.5 | −0.421384 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 38415.9 | 1.22031 | 0.610153 | − | 0.792284i | \(-0.291108\pi\) | ||||
0.610153 | + | 0.792284i | \(0.291108\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −28317.4 | −0.896819 |
(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 | 2312.4.a.o.1.2 | ✓ | 18 | |
17.16 | even | 2 | 2312.4.a.p.1.17 | yes | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2312.4.a.o.1.2 | ✓ | 18 | 1.1 | even | 1 | trivial | |
2312.4.a.p.1.17 | yes | 18 | 17.16 | even | 2 |