Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [720,4,Mod(1,720)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(720, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("720.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 720.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: | \(42.4813752041\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 45) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 720.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 30.0000 | 1.61985 | 0.809924 | − | 0.586535i | \(-0.199508\pi\) | ||||
0.809924 | + | 0.586535i | \(0.199508\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 50.0000 | 1.37051 | 0.685253 | − | 0.728305i | \(-0.259692\pi\) | ||||
0.685253 | + | 0.728305i | \(0.259692\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −20.0000 | −0.426692 | −0.213346 | − | 0.976977i | \(-0.568436\pi\) | ||||
−0.213346 | + | 0.976977i | \(0.568436\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 10.0000 | 0.142668 | 0.0713340 | − | 0.997452i | \(-0.477274\pi\) | ||||
0.0713340 | + | 0.997452i | \(0.477274\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 44.0000 | 0.531279 | 0.265639 | − | 0.964072i | \(-0.414417\pi\) | ||||
0.265639 | + | 0.964072i | \(0.414417\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 120.000 | 1.08790 | 0.543951 | − | 0.839117i | \(-0.316928\pi\) | ||||
0.543951 | + | 0.839117i | \(0.316928\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 50.0000 | 0.320164 | 0.160082 | − | 0.987104i | \(-0.448824\pi\) | ||||
0.160082 | + | 0.987104i | \(0.448824\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −108.000 | −0.625722 | −0.312861 | − | 0.949799i | \(-0.601287\pi\) | ||||
−0.312861 | + | 0.949799i | \(0.601287\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 150.000 | 0.724418 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −40.0000 | −0.177729 | −0.0888643 | − | 0.996044i | \(-0.528324\pi\) | ||||
−0.0888643 | + | 0.996044i | \(0.528324\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −400.000 | −1.52365 | −0.761823 | − | 0.647785i | \(-0.775696\pi\) | ||||
−0.761823 | + | 0.647785i | \(0.775696\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −280.000 | −0.993014 | −0.496507 | − | 0.868033i | \(-0.665384\pi\) | ||||
−0.496507 | + | 0.868033i | \(0.665384\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −280.000 | −0.868983 | −0.434491 | − | 0.900676i | \(-0.643072\pi\) | ||||
−0.434491 | + | 0.900676i | \(0.643072\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 557.000 | 1.62391 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 610.000 | 1.58094 | 0.790471 | − | 0.612499i | \(-0.209836\pi\) | ||||
0.790471 | + | 0.612499i | \(0.209836\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 250.000 | 0.612909 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 50.0000 | 0.110330 | 0.0551648 | − | 0.998477i | \(-0.482432\pi\) | ||||
0.0551648 | + | 0.998477i | \(0.482432\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −518.000 | −1.08726 | −0.543632 | − | 0.839324i | \(-0.682951\pi\) | ||||
−0.543632 | + | 0.839324i | \(0.682951\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −100.000 | −0.190823 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 180.000 | 0.328216 | 0.164108 | − | 0.986442i | \(-0.447525\pi\) | ||||
0.164108 | + | 0.986442i | \(0.447525\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 700.000 | 1.17007 | 0.585033 | − | 0.811009i | \(-0.301081\pi\) | ||||
0.585033 | + | 0.811009i | \(0.301081\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −410.000 | −0.657354 | −0.328677 | − | 0.944442i | \(-0.606603\pi\) | ||||
−0.328677 | + | 0.944442i | \(0.606603\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1500.00 | 2.22001 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 516.000 | 0.734868 | 0.367434 | − | 0.930050i | \(-0.380236\pi\) | ||||
0.367434 | + | 0.930050i | \(0.380236\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 660.000 | 0.872824 | 0.436412 | − | 0.899747i | \(-0.356249\pi\) | ||||
0.436412 | + | 0.899747i | \(0.356249\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 50.0000 | 0.0638031 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1500.00 | 1.78651 | 0.893257 | − | 0.449547i | \(-0.148415\pi\) | ||||
0.893257 | + | 0.449547i | \(0.148415\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −600.000 | −0.691177 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 220.000 | 0.237595 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1630.00 | −1.70620 | −0.853100 | − | 0.521747i | \(-0.825280\pi\) | ||||
−0.853100 | + | 0.521747i | \(0.825280\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 450.000 | 0.443333 | 0.221667 | − | 0.975122i | \(-0.428850\pi\) | ||||
0.221667 | + | 0.975122i | \(0.428850\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −770.000 | −0.736605 | −0.368303 | − | 0.929706i | \(-0.620061\pi\) | ||||
−0.368303 | + | 0.929706i | \(0.620061\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 660.000 | 0.596305 | 0.298152 | − | 0.954518i | \(-0.403630\pi\) | ||||
0.298152 | + | 0.954518i | \(0.403630\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1754.00 | 1.54131 | 0.770655 | − | 0.637253i | \(-0.219929\pi\) | ||||
0.770655 | + | 0.637253i | \(0.219929\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 310.000 | 0.258074 | 0.129037 | − | 0.991640i | \(-0.458811\pi\) | ||||
0.129037 | + | 0.991640i | \(0.458811\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 600.000 | 0.486524 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 300.000 | 0.231100 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1169.00 | 0.878287 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1070.00 | 0.747615 | 0.373808 | − | 0.927506i | \(-0.378052\pi\) | ||||
0.373808 | + | 0.927506i | \(0.378052\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1950.00 | 1.30055 | 0.650276 | − | 0.759698i | \(-0.274653\pi\) | ||||
0.650276 | + | 0.759698i | \(0.274653\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1320.00 | 0.860590 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1050.00 | −0.654800 | −0.327400 | − | 0.944886i | \(-0.606172\pi\) | ||||
−0.327400 | + | 0.944886i | \(0.606172\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1676.00 | −1.02271 | −0.511354 | − | 0.859370i | \(-0.670856\pi\) | ||||
−0.511354 | + | 0.859370i | \(0.670856\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1000.00 | −0.584785 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 250.000 | 0.143182 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2050.00 | −1.12713 | −0.563566 | − | 0.826071i | \(-0.690571\pi\) | ||||
−0.563566 | + | 0.826071i | \(0.690571\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −448.000 | −0.241442 | −0.120721 | − | 0.992686i | \(-0.538521\pi\) | ||||
−0.120721 | + | 0.992686i | \(0.538521\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −540.000 | −0.279831 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −100.000 | −0.0508336 | −0.0254168 | − | 0.999677i | \(-0.508091\pi\) | ||||
−0.0254168 | + | 0.999677i | \(0.508091\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3600.00 | 1.76223 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1900.00 | 0.913003 | 0.456501 | − | 0.889723i | \(-0.349102\pi\) | ||||
0.456501 | + | 0.889723i | \(0.349102\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1920.00 | 0.889665 | 0.444833 | − | 0.895614i | \(-0.353263\pi\) | ||||
0.444833 | + | 0.895614i | \(0.353263\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1797.00 | −0.817934 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2550.00 | −1.12065 | −0.560326 | − | 0.828272i | \(-0.689324\pi\) | ||||
−0.560326 | + | 0.828272i | \(0.689324\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 750.000 | 0.323970 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3650.00 | 1.52410 | 0.762050 | − | 0.647518i | \(-0.224193\pi\) | ||||
0.762050 | + | 0.647518i | \(0.224193\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4342.00 | −1.78308 | −0.891542 | − | 0.452937i | \(-0.850376\pi\) | ||||
−0.891542 | + | 0.452937i | \(0.850376\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −200.000 | −0.0794827 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 500.000 | 0.195527 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3500.00 | −1.32592 | −0.662961 | − | 0.748654i | \(-0.730701\pi\) | ||||
−0.662961 | + | 0.748654i | \(0.730701\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3350.00 | 1.24942 | 0.624711 | − | 0.780856i | \(-0.285217\pi\) | ||||
0.624711 | + | 0.780856i | \(0.285217\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −90.0000 | −0.0325494 | −0.0162747 | − | 0.999868i | \(-0.505181\pi\) | ||||
−0.0162747 | + | 0.999868i | \(0.505181\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3664.00 | −1.30520 | −0.652598 | − | 0.757704i | \(-0.726321\pi\) | ||||
−0.652598 | + | 0.757704i | \(0.726321\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1500.00 | 0.518618 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2000.00 | −0.681395 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2200.00 | 0.728120 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 268.000 | 0.0874402 | 0.0437201 | − | 0.999044i | \(-0.486079\pi\) | ||||
0.0437201 | + | 0.999044i | \(0.486079\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1400.00 | −0.444089 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3240.00 | −1.01357 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −200.000 | −0.0608754 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3670.00 | 1.10207 | 0.551034 | − | 0.834482i | \(-0.314233\pi\) | ||||
0.551034 | + | 0.834482i | \(0.314233\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3760.00 | 1.09938 | 0.549692 | − | 0.835368i | \(-0.314745\pi\) | ||||
0.549692 | + | 0.835368i | \(0.314745\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1434.00 | −0.413805 | −0.206903 | − | 0.978362i | \(-0.566338\pi\) | ||||
−0.206903 | + | 0.978362i | \(0.566338\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3450.00 | 0.970030 | 0.485015 | − | 0.874506i | \(-0.338814\pi\) | ||||
0.485015 | + | 0.874506i | \(0.338814\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1400.00 | −0.388621 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4900.00 | −1.32617 | −0.663085 | − | 0.748544i | \(-0.730753\pi\) | ||||
−0.663085 | + | 0.748544i | \(0.730753\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4822.00 | 1.28885 | 0.644424 | − | 0.764668i | \(-0.277097\pi\) | ||||
0.644424 | + | 0.764668i | \(0.277097\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2785.00 | 0.726233 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −880.000 | −0.226693 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4650.00 | −1.16934 | −0.584672 | − | 0.811270i | \(-0.698777\pi\) | ||||
−0.584672 | + | 0.811270i | \(0.698777\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6000.00 | 1.49098 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5130.00 | −1.24514 | −0.622569 | − | 0.782565i | \(-0.713911\pi\) | ||||
−0.622569 | + | 0.782565i | \(0.713911\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1200.00 | −0.287893 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1280.00 | −0.300107 | −0.150054 | − | 0.988678i | \(-0.547945\pi\) | ||||
−0.150054 | + | 0.988678i | \(0.547945\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3050.00 | 0.707019 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3350.00 | −0.759305 | −0.379653 | − | 0.925129i | \(-0.623956\pi\) | ||||
−0.379653 | + | 0.925129i | \(0.623956\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5512.00 | −1.23554 | −0.617768 | − | 0.786361i | \(-0.711963\pi\) | ||||
−0.617768 | + | 0.786361i | \(0.711963\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1250.00 | 0.274101 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4920.00 | 1.06720 | 0.533600 | − | 0.845737i | \(-0.320839\pi\) | ||||
0.533600 | + | 0.845737i | \(0.320839\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4500.00 | −0.955329 | −0.477665 | − | 0.878542i | \(-0.658517\pi\) | ||||
−0.477665 | + | 0.878542i | \(0.658517\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6900.00 | 1.44934 | 0.724669 | − | 0.689098i | \(-0.241993\pi\) | ||||
0.724669 | + | 0.689098i | \(0.241993\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12000.0 | −2.46808 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4813.00 | −0.979646 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1530.00 | −0.305063 | −0.152532 | − | 0.988299i | \(-0.548743\pi\) | ||||
−0.152532 | + | 0.988299i | \(0.548743\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 250.000 | 0.0493409 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2400.00 | −0.464199 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8400.00 | −1.60853 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2590.00 | −0.486239 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3040.00 | −0.565153 | −0.282576 | − | 0.959245i | \(-0.591189\pi\) | ||||
−0.282576 | + | 0.959245i | \(0.591189\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5700.00 | −1.03928 | −0.519642 | − | 0.854384i | \(-0.673935\pi\) | ||||
−0.519642 | + | 0.854384i | \(0.673935\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3110.00 | 0.561622 | 0.280811 | − | 0.959763i | \(-0.409397\pi\) | ||||
0.280811 | + | 0.959763i | \(0.409397\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 950.000 | 0.168320 | 0.0841598 | − | 0.996452i | \(-0.473179\pi\) | ||||
0.0841598 | + | 0.996452i | \(0.473179\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2500.00 | 0.438787 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 440.000 | 0.0757965 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −500.000 | −0.0853385 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8400.00 | −1.40762 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2292.00 | −0.380603 | −0.190302 | − | 0.981726i | \(-0.560947\pi\) | ||||
−0.190302 | + | 0.981726i | \(0.560947\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 900.000 | 0.146783 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7730.00 | −1.24950 | −0.624748 | − | 0.780827i | \(-0.714798\pi\) | ||||
−0.624748 | + | 0.780827i | \(0.714798\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5400.00 | −0.857555 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6420.00 | 1.01063 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1120.00 | −0.173270 | −0.0866351 | − | 0.996240i | \(-0.527611\pi\) | ||||
−0.0866351 | + | 0.996240i | \(0.527611\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1186.00 | 0.181906 | 0.0909529 | − | 0.995855i | \(-0.471009\pi\) | ||||
0.0909529 | + | 0.995855i | \(0.471009\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3630.00 | −0.547324 | −0.273662 | − | 0.961826i | \(-0.588235\pi\) | ||||
−0.273662 | + | 0.961826i | \(0.588235\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3500.00 | 0.523270 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1800.00 | −0.264625 | −0.132312 | − | 0.991208i | \(-0.542240\pi\) | ||||
−0.132312 | + | 0.991208i | \(0.542240\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4923.00 | −0.717743 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2050.00 | −0.293978 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8490.00 | −1.20756 | −0.603780 | − | 0.797151i | \(-0.706339\pi\) | ||||
−0.603780 | + | 0.797151i | \(0.706339\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 18300.0 | 2.56089 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 100.000 | 0.0138815 | 0.00694076 | − | 0.999976i | \(-0.497791\pi\) | ||||
0.00694076 | + | 0.999976i | \(0.497791\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1000.00 | −0.136612 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8084.00 | 1.09564 | 0.547820 | − | 0.836597i | \(-0.315458\pi\) | ||||
0.547820 | + | 0.836597i | \(0.315458\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9480.00 | −1.26477 | −0.632383 | − | 0.774656i | \(-0.717923\pi\) | ||||
−0.632383 | + | 0.774656i | \(0.717923\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7500.00 | 0.992819 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10950.0 | 1.42722 | 0.713608 | − | 0.700545i | \(-0.247060\pi\) | ||||
0.713608 | + | 0.700545i | \(0.247060\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1200.00 | 0.155209 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2580.00 | 0.328643 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13840.0 | 1.74965 | 0.874823 | − | 0.484442i | \(-0.160977\pi\) | ||||
0.874823 | + | 0.484442i | \(0.160977\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9300.00 | −1.15815 | −0.579077 | − | 0.815273i | \(-0.696587\pi\) | ||||
−0.579077 | + | 0.815273i | \(0.696587\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2160.00 | 0.266991 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2000.00 | −0.243578 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2854.00 | −0.345040 | −0.172520 | − | 0.985006i | \(-0.555191\pi\) | ||||
−0.172520 | + | 0.985006i | \(0.555191\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1500.00 | 0.178717 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3300.00 | 0.390339 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1150.00 | 0.134084 | 0.0670420 | − | 0.997750i | \(-0.478644\pi\) | ||||
0.0670420 | + | 0.997750i | \(0.478644\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11162.0 | −1.29217 | −0.646084 | − | 0.763266i | \(-0.723594\pi\) | ||||
−0.646084 | + | 0.763266i | \(0.723594\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 250.000 | 0.0285336 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −15540.0 | −1.76120 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1200.00 | −0.134111 | −0.0670556 | − | 0.997749i | \(-0.521361\pi\) | ||||
−0.0670556 | + | 0.997749i | \(0.521361\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1510.00 | 0.167589 | 0.0837944 | − | 0.996483i | \(-0.473296\pi\) | ||||
0.0837944 | + | 0.996483i | \(0.473296\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5280.00 | 0.577979 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −424.000 | −0.0460966 | −0.0230483 | − | 0.999734i | \(-0.507337\pi\) | ||||
−0.0230483 | + | 0.999734i | \(0.507337\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12360.0 | 1.32560 | 0.662801 | − | 0.748796i | \(-0.269368\pi\) | ||||
0.662801 | + | 0.748796i | \(0.269368\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7500.00 | 0.798953 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1300.00 | 0.136639 | 0.0683194 | − | 0.997664i | \(-0.478236\pi\) | ||||
0.0683194 | + | 0.997664i | \(0.478236\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −20000.0 | −2.08817 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3000.00 | −0.309104 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7190.00 | −0.735961 | −0.367980 | − | 0.929834i | \(-0.619951\pi\) | ||||
−0.367980 | + | 0.929834i | \(0.619951\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 150.000 | 0.0151544 | 0.00757722 | − | 0.999971i | \(-0.497588\pi\) | ||||
0.00757722 | + | 0.999971i | \(0.497588\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2670.00 | −0.268003 | −0.134002 | − | 0.990981i | \(-0.542783\pi\) | ||||
−0.134002 | + | 0.990981i | \(0.542783\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1180.00 | 0.116925 | 0.0584624 | − | 0.998290i | \(-0.481380\pi\) | ||||
0.0584624 | + | 0.998290i | \(0.481380\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5400.00 | 0.531661 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −14000.0 | −1.36093 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1100.00 | 0.106256 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14100.0 | −1.34498 | −0.672490 | − | 0.740106i | \(-0.734775\pi\) | ||||
−0.672490 | + | 0.740106i | \(0.734775\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 800.000 | 0.0758355 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8150.00 | −0.763036 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9850.00 | 0.916522 | 0.458261 | − | 0.888818i | \(-0.348473\pi\) | ||||
0.458261 | + | 0.888818i | \(0.348473\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2450.00 | −0.225187 | −0.112594 | − | 0.993641i | \(-0.535916\pi\) | ||||
−0.112594 | + | 0.993641i | \(0.535916\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 500.000 | 0.0456772 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 21000.0 | 1.89533 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17036.0 | 1.52833 | 0.764164 | − | 0.645021i | \(-0.223152\pi\) | ||||
0.764164 | + | 0.645021i | \(0.223152\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −20600.0 | −1.82606 | −0.913030 | − | 0.407891i | \(-0.866264\pi\) | ||||
−0.913030 | + | 0.407891i | \(0.866264\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2250.00 | 0.198265 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5750.00 | −0.500716 | −0.250358 | − | 0.968153i | \(-0.580548\pi\) | ||||
−0.250358 | + | 0.968153i | \(0.580548\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12300.0 | −1.06481 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3850.00 | −0.329420 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −14000.0 | −1.19095 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15500.0 | 1.30339 | 0.651696 | − | 0.758480i | \(-0.274058\pi\) | ||||
0.651696 | + | 0.758480i | \(0.274058\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13940.0 | 1.16549 | 0.582747 | − | 0.812653i | \(-0.301978\pi\) | ||||
0.582747 | + | 0.812653i | \(0.301978\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1080.00 | −0.0892705 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2233.00 | 0.183529 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8000.00 | 0.650128 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3300.00 | 0.266676 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 27850.0 | 2.22557 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20478.0 | −1.62739 | −0.813695 | − | 0.581292i | \(-0.802547\pi\) | ||||
−0.813695 | + | 0.581292i | \(0.802547\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8770.00 | 0.689295 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12040.0 | −0.941121 | −0.470561 | − | 0.882368i | \(-0.655948\pi\) | ||||
−0.470561 | + | 0.882368i | \(0.655948\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2200.00 | 0.170096 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15480.0 | 1.19037 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −23550.0 | −1.79146 | −0.895732 | − | 0.444594i | \(-0.853348\pi\) | ||||
−0.895732 | + | 0.444594i | \(0.853348\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5600.00 | 0.423712 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6120.00 | −0.458130 | −0.229065 | − | 0.973411i | \(-0.573567\pi\) | ||||
−0.229065 | + | 0.973411i | \(0.573567\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1550.00 | 0.115414 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11700.0 | 0.862020 | 0.431010 | − | 0.902347i | \(-0.358157\pi\) | ||||
0.431010 | + | 0.902347i | \(0.358157\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8188.00 | 0.600100 | 0.300050 | − | 0.953923i | \(-0.402997\pi\) | ||||
0.300050 | + | 0.953923i | \(0.402997\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3000.00 | 0.217580 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11690.0 | 0.843433 | 0.421717 | − | 0.906728i | \(-0.361428\pi\) | ||||
0.421717 | + | 0.906728i | \(0.361428\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 19800.0 | 1.41384 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 30500.0 | 2.16669 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 21060.0 | 1.48082 | 0.740408 | − | 0.672157i | \(-0.234632\pi\) | ||||
0.740408 | + | 0.672157i | \(0.234632\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4752.00 | −0.332433 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 22910.0 | 1.58651 | 0.793255 | − | 0.608889i | \(-0.208385\pi\) | ||||
0.793255 | + | 0.608889i | \(0.208385\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1500.00 | 0.103351 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1400.00 | −0.0954966 | −0.0477483 | − | 0.998859i | \(-0.515205\pi\) | ||||
−0.0477483 | + | 0.998859i | \(0.515205\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11002.0 | −0.746724 | −0.373362 | − | 0.927686i | \(-0.621795\pi\) | ||||
−0.373362 | + | 0.927686i | \(0.621795\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5845.00 | 0.392782 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4630.00 | −0.309598 | −0.154799 | − | 0.987946i | \(-0.549473\pi\) | ||||
−0.154799 | + | 0.987946i | \(0.549473\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5600.00 | 0.370788 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24040.0 | 1.58396 | 0.791979 | − | 0.610548i | \(-0.209051\pi\) | ||||
0.791979 | + | 0.610548i | \(0.209051\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1890.00 | 0.123320 | 0.0616601 | − | 0.998097i | \(-0.480361\pi\) | ||||
0.0616601 | + | 0.998097i | \(0.480361\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19244.0 | −1.24957 | −0.624783 | − | 0.780798i | \(-0.714813\pi\) | ||||
−0.624783 | + | 0.780798i | \(0.714813\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 45000.0 | 2.89388 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −400.000 | −0.0253562 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15892.0 | −1.00262 | −0.501308 | − | 0.865269i | \(-0.667148\pi\) | ||||
−0.501308 | + | 0.865269i | \(0.667148\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5350.00 | 0.334344 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −11140.0 | −0.692909 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12600.0 | 0.776396 | 0.388198 | − | 0.921576i | \(-0.373098\pi\) | ||||
0.388198 | + | 0.921576i | \(0.373098\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7260.00 | −0.445267 | −0.222633 | − | 0.974902i | \(-0.571465\pi\) | ||||
−0.222633 | + | 0.974902i | \(0.571465\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7400.00 | 0.449651 | 0.224825 | − | 0.974399i | \(-0.427819\pi\) | ||||
0.224825 | + | 0.974399i | \(0.427819\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2500.00 | 0.151207 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4790.00 | 0.287055 | 0.143528 | − | 0.989646i | \(-0.454155\pi\) | ||||
0.143528 | + | 0.989646i | \(0.454155\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9750.00 | 0.581624 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1450.00 | −0.0857117 | −0.0428558 | − | 0.999081i | \(-0.513646\pi\) | ||||
−0.0428558 | + | 0.999081i | \(0.513646\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11818.0 | 0.695411 | 0.347706 | − | 0.937604i | \(-0.386961\pi\) | ||||
0.347706 | + | 0.937604i | \(0.386961\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6600.00 | 0.384868 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6000.00 | 0.348307 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −25900.0 | −1.49010 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5550.00 | 0.317885 | 0.158943 | − | 0.987288i | \(-0.449192\pi\) | ||||
0.158943 | + | 0.987288i | \(0.449192\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −12930.0 | −0.734033 | −0.367016 | − | 0.930214i | \(-0.619621\pi\) | ||||
−0.367016 | + | 0.930214i | \(0.619621\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −48900.0 | −2.76378 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 32580.0 | 1.82524 | 0.912620 | − | 0.408809i | \(-0.134056\pi\) | ||||
0.912620 | + | 0.408809i | \(0.134056\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5250.00 | −0.292835 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −12200.0 | −0.674576 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10228.0 | −0.563085 | −0.281542 | − | 0.959549i | \(-0.590846\pi\) | ||||
−0.281542 | + | 0.959549i | \(0.590846\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8380.00 | −0.457369 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4000.00 | −0.217376 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8350.00 | −0.449893 | −0.224947 | − | 0.974371i | \(-0.572221\pi\) | ||||
−0.224947 | + | 0.974371i | \(0.572221\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1760.00 | −0.0944234 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 13500.0 | 0.718133 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14954.0 | −0.792115 | −0.396057 | − | 0.918226i | \(-0.629622\pi\) | ||||
−0.396057 | + | 0.918226i | \(0.629622\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −12960.0 | −0.680723 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5000.00 | −0.261524 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 29400.0 | 1.52494 | 0.762472 | − | 0.647021i | \(-0.223985\pi\) | ||||
0.762472 | + | 0.647021i | \(0.223985\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −23100.0 | −1.19319 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1250.00 | 0.0640329 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16330.0 | 0.833076 | 0.416538 | − | 0.909118i | \(-0.363243\pi\) | ||||
0.416538 | + | 0.909118i | \(0.363243\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2800.00 | −0.141671 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 30800.0 | 1.55201 | 0.776005 | − | 0.630726i | \(-0.217243\pi\) | ||||
0.776005 | + | 0.630726i | \(0.217243\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9000.00 | 0.449823 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9524.00 | 0.474081 | 0.237041 | − | 0.971500i | \(-0.423823\pi\) | ||||
0.237041 | + | 0.971500i | \(0.423823\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −28600.0 | −1.41216 | −0.706078 | − | 0.708134i | \(-0.749537\pi\) | ||||
−0.706078 | + | 0.708134i | \(0.749537\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10250.0 | −0.504068 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 19800.0 | 0.965923 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8252.00 | 0.400958 | 0.200479 | − | 0.979698i | \(-0.435750\pi\) | ||||
0.200479 | + | 0.979698i | \(0.435750\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2240.00 | −0.107976 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −24920.0 | −1.19648 | −0.598238 | − | 0.801318i | \(-0.704132\pi\) | ||||
−0.598238 | + | 0.801318i | \(0.704132\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −27900.0 | −1.32901 | −0.664503 | − | 0.747285i | \(-0.731357\pi\) | ||||
−0.664503 | + | 0.747285i | \(0.731357\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 52620.0 | 2.49669 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1000.00 | −0.0470768 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11506.0 | −0.539554 | −0.269777 | − | 0.962923i | \(-0.586950\pi\) | ||||
−0.269777 | + | 0.962923i | \(0.586950\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12510.0 | 0.582087 | 0.291044 | − | 0.956710i | \(-0.405998\pi\) | ||||
0.291044 | + | 0.956710i | \(0.405998\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2700.00 | −0.125144 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −17600.0 | −0.809481 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 35000.0 | 1.60358 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −500.000 | −0.0227335 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1100.00 | 0.0498231 | 0.0249115 | − | 0.999690i | \(-0.492070\pi\) | ||||
0.0249115 | + | 0.999690i | \(0.492070\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9300.00 | 0.418040 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10360.0 | 0.463927 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4490.00 | 0.199553 | 0.0997766 | − | 0.995010i | \(-0.468187\pi\) | ||||
0.0997766 | + | 0.995010i | \(0.468187\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2800.00 | −0.123976 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −20500.0 | −0.900908 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 18000.0 | 0.788095 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −28600.0 | −1.24292 | −0.621460 | − | 0.783446i | \(-0.713460\pi\) | ||||
−0.621460 | + | 0.783446i | \(0.713460\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10068.0 | −0.435925 | −0.217963 | − | 0.975957i | \(-0.569941\pi\) | ||||
−0.217963 | + | 0.975957i | \(0.569941\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9500.00 | 0.408307 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −12320.0 | −0.527567 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 14250.0 | 0.605759 | 0.302880 | − | 0.953029i | \(-0.402052\pi\) | ||||
0.302880 | + | 0.953029i | \(0.402052\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6830.00 | −0.289282 | −0.144641 | − | 0.989484i | \(-0.546203\pi\) | ||||
−0.144641 | + | 0.989484i | \(0.546203\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8920.00 | −0.375065 | −0.187533 | − | 0.982258i | \(-0.560049\pi\) | ||||
−0.187533 | + | 0.982258i | \(0.560049\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3534.00 | −0.148059 | −0.0740295 | − | 0.997256i | \(-0.523586\pi\) | ||||
−0.0740295 | + | 0.997256i | \(0.523586\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5570.00 | 0.231680 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9600.00 | 0.397870 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8000.00 | −0.329190 | −0.164595 | − | 0.986361i | \(-0.552632\pi\) | ||||
−0.164595 | + | 0.986361i | \(0.552632\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21889.0 | −0.897495 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −8985.00 | −0.365791 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 35070.0 | 1.42269 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4800.00 | −0.193351 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5160.00 | 0.207122 | 0.103561 | − | 0.994623i | \(-0.466976\pi\) | ||||
0.103561 | + | 0.994623i | \(0.466976\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −7670.00 | −0.305720 | −0.152860 | − | 0.988248i | \(-0.548848\pi\) | ||||
−0.152860 | + | 0.988248i | \(0.548848\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −25804.0 | −1.02494 | −0.512469 | − | 0.858706i | \(-0.671269\pi\) | ||||
−0.512469 | + | 0.858706i | \(0.671269\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 400.000 | 0.0157777 | 0.00788885 | − | 0.999969i | \(-0.497489\pi\) | ||||
0.00788885 | + | 0.999969i | \(0.497489\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12750.0 | −0.501171 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 25800.0 | 1.00714 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3600.00 | −0.140047 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3750.00 | 0.144884 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −35100.0 | −1.35147 | −0.675737 | − | 0.737143i | \(-0.736175\pi\) | ||||
−0.675737 | + | 0.737143i | \(0.736175\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18700.0 | 0.715118 | 0.357559 | − | 0.933891i | \(-0.383609\pi\) | ||||
0.357559 | + | 0.933891i | \(0.383609\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2980.00 | 0.113573 | 0.0567865 | − | 0.998386i | \(-0.481915\pi\) | ||||
0.0567865 | + | 0.998386i | \(0.481915\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −35880.0 | −1.35821 | −0.679105 | − | 0.734041i | \(-0.737632\pi\) | ||||
−0.679105 | + | 0.734041i | \(0.737632\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 32100.0 | 1.21102 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −12320.0 | −0.461672 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18250.0 | 0.681598 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5400.00 | −0.200334 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6100.00 | 0.225550 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −21710.0 | −0.797420 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −45240.0 | −1.65620 | −0.828098 | − | 0.560584i | \(-0.810577\pi\) | ||||
−0.828098 | + | 0.560584i | \(0.810577\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 33200.0 | 1.20743 | 0.603713 | − | 0.797202i | \(-0.293687\pi\) | ||||
0.603713 | + | 0.797202i | \(0.293687\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 33000.0 | 1.19621 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 58500.0 | 2.10670 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −35356.0 | −1.26908 | −0.634541 | − | 0.772889i | \(-0.718811\pi\) | ||||
−0.634541 | + | 0.772889i | \(0.718811\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −14000.0 | −0.499259 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1000.00 | −0.0355457 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 25700.0 | 0.907631 | 0.453816 | − | 0.891096i | \(-0.350062\pi\) | ||||
0.453816 | + | 0.891096i | \(0.350062\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 24508.0 | 0.862747 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2500.00 | 0.0874425 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 52890.0 | 1.84401 | 0.922007 | − | 0.387173i | \(-0.126549\pi\) | ||||
0.922007 | + | 0.387173i | \(0.126549\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −38050.0 | −1.31817 | −0.659083 | − | 0.752070i | \(-0.729055\pi\) | ||||
−0.659083 | + | 0.752070i | \(0.729055\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −48000.0 | −1.65758 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −29640.0 | −1.01708 | −0.508538 | − | 0.861040i | \(-0.669814\pi\) | ||||
−0.508538 | + | 0.861040i | \(0.669814\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8200.00 | 0.280488 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −15170.0 | −0.515640 | −0.257820 | − | 0.966193i | \(-0.583004\pi\) | ||||
−0.257820 | + | 0.966193i | \(0.583004\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −17500.0 | −0.592970 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −31500.0 | −1.06068 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −18127.0 | −0.608472 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 16750.0 | 0.558758 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5470.00 | 0.181906 | 0.0909531 | − | 0.995855i | \(-0.471009\pi\) | ||||
0.0909531 | + | 0.995855i | \(0.471009\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15150.0 | 0.500707 | 0.250354 | − | 0.968154i | \(-0.419453\pi\) | ||||
0.250354 | + | 0.968154i | \(0.419453\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −50280.0 | −1.65663 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −31190.0 | −1.02135 | −0.510674 | − | 0.859775i | \(-0.670604\pi\) | ||||
−0.510674 | + | 0.859775i | \(0.670604\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 75000.0 | 2.44843 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7560.00 | −0.245297 | −0.122648 | − | 0.992450i | \(-0.539139\pi\) | ||||
−0.122648 | + | 0.992450i | \(0.539139\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −450.000 | −0.0145565 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −33600.0 | −1.08030 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −32672.0 | −1.04729 | −0.523643 | − | 0.851938i | \(-0.675427\pi\) | ||||
−0.523643 | + | 0.851938i | \(0.675427\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −18320.0 | −0.583702 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4740.00 | −0.150569 | −0.0752845 | − | 0.997162i | \(-0.523986\pi\) | ||||
−0.0752845 | + | 0.997162i | \(0.523986\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 720.4.a.bc.1.1 | 1 | ||
3.2 | odd | 2 | 720.4.a.o.1.1 | 1 | |||
4.3 | odd | 2 | 45.4.a.a.1.1 | ✓ | 1 | ||
12.11 | even | 2 | 45.4.a.e.1.1 | yes | 1 | ||
20.3 | even | 4 | 225.4.b.a.199.2 | 2 | |||
20.7 | even | 4 | 225.4.b.a.199.1 | 2 | |||
20.19 | odd | 2 | 225.4.a.h.1.1 | 1 | |||
28.27 | even | 2 | 2205.4.a.a.1.1 | 1 | |||
36.7 | odd | 6 | 405.4.e.n.271.1 | 2 | |||
36.11 | even | 6 | 405.4.e.b.271.1 | 2 | |||
36.23 | even | 6 | 405.4.e.b.136.1 | 2 | |||
36.31 | odd | 6 | 405.4.e.n.136.1 | 2 | |||
60.23 | odd | 4 | 225.4.b.b.199.1 | 2 | |||
60.47 | odd | 4 | 225.4.b.b.199.2 | 2 | |||
60.59 | even | 2 | 225.4.a.a.1.1 | 1 | |||
84.83 | odd | 2 | 2205.4.a.t.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.4.a.a.1.1 | ✓ | 1 | 4.3 | odd | 2 | ||
45.4.a.e.1.1 | yes | 1 | 12.11 | even | 2 | ||
225.4.a.a.1.1 | 1 | 60.59 | even | 2 | |||
225.4.a.h.1.1 | 1 | 20.19 | odd | 2 | |||
225.4.b.a.199.1 | 2 | 20.7 | even | 4 | |||
225.4.b.a.199.2 | 2 | 20.3 | even | 4 | |||
225.4.b.b.199.1 | 2 | 60.23 | odd | 4 | |||
225.4.b.b.199.2 | 2 | 60.47 | odd | 4 | |||
405.4.e.b.136.1 | 2 | 36.23 | even | 6 | |||
405.4.e.b.271.1 | 2 | 36.11 | even | 6 | |||
405.4.e.n.136.1 | 2 | 36.31 | odd | 6 | |||
405.4.e.n.271.1 | 2 | 36.7 | odd | 6 | |||
720.4.a.o.1.1 | 1 | 3.2 | odd | 2 | |||
720.4.a.bc.1.1 | 1 | 1.1 | even | 1 | trivial | ||
2205.4.a.a.1.1 | 1 | 28.27 | even | 2 | |||
2205.4.a.t.1.1 | 1 | 84.83 | odd | 2 |