Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2205,4,Mod(1,2205)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2205, 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("2205.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2205.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: | \(130.099211563\) |
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 | \(\chi\) | \(=\) | 2205.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.00000 | 1.76777 | 0.883883 | − | 0.467707i | \(-0.154920\pi\) | ||||
0.883883 | + | 0.467707i | \(0.154920\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 17.0000 | 2.12500 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 45.0000 | 1.98874 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 25.0000 | 0.790569 | ||||||||
\(11\) | 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 | \(-0.431564\pi\) | ||||
0.213346 | + | 0.976977i | \(0.431564\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 89.0000 | 1.39062 | ||||||||
\(17\) | 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 | \(0.414417\pi\) | |||||||
\(20\) | 85.0000 | 0.950329 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 250.000 | 2.42274 | ||||||||
\(23\) | 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 | ||||||||
\(26\) | 100.000 | 0.754293 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −50.0000 | −0.320164 | −0.160082 | − | 0.987104i | \(-0.551176\pi\) | ||||
−0.160082 | + | 0.987104i | \(0.551176\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −108.000 | −0.625722 | −0.312861 | − | 0.949799i | \(-0.601287\pi\) | ||||
−0.312861 | + | 0.949799i | \(0.601287\pi\) | |||||||
\(32\) | 85.0000 | 0.469563 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 50.0000 | 0.252204 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −40.0000 | −0.177729 | −0.0888643 | − | 0.996044i | \(-0.528324\pi\) | ||||
−0.0888643 | + | 0.996044i | \(0.528324\pi\) | |||||||
\(38\) | 220.000 | 0.939177 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 225.000 | 0.889391 | ||||||||
\(41\) | −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 | \(-0.334616\pi\) | ||||
0.496507 | + | 0.868033i | \(0.334616\pi\) | |||||||
\(44\) | 850.000 | 2.91233 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 600.000 | 1.92316 | ||||||||
\(47\) | 280.000 | 0.868983 | 0.434491 | − | 0.900676i | \(-0.356928\pi\) | ||||
0.434491 | + | 0.900676i | \(0.356928\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 125.000 | 0.353553 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 340.000 | 0.906721 | ||||||||
\(53\) | −610.000 | −1.58094 | −0.790471 | − | 0.612499i | \(-0.790164\pi\) | ||||
−0.790471 | + | 0.612499i | \(0.790164\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 250.000 | 0.612909 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −250.000 | −0.565976 | ||||||||
\(59\) | −50.0000 | −0.110330 | −0.0551648 | − | 0.998477i | \(-0.517568\pi\) | ||||
−0.0551648 | + | 0.998477i | \(0.517568\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 518.000 | 1.08726 | 0.543632 | − | 0.839324i | \(-0.317049\pi\) | ||||
0.543632 | + | 0.839324i | \(0.317049\pi\) | |||||||
\(62\) | −540.000 | −1.10613 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −287.000 | −0.560547 | ||||||||
\(65\) | 100.000 | 0.190823 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −180.000 | −0.328216 | −0.164108 | − | 0.986442i | \(-0.552475\pi\) | ||||
−0.164108 | + | 0.986442i | \(0.552475\pi\) | |||||||
\(68\) | 170.000 | 0.303170 | ||||||||
\(69\) | 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 | \(-0.393397\pi\) | ||||
0.328677 | + | 0.944442i | \(0.393397\pi\) | |||||||
\(74\) | −200.000 | −0.314183 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 748.000 | 1.12897 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −516.000 | −0.734868 | −0.367434 | − | 0.930050i | \(-0.619764\pi\) | ||||
−0.367434 | + | 0.930050i | \(0.619764\pi\) | |||||||
\(80\) | 445.000 | 0.621906 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2000.00 | −2.69345 | ||||||||
\(83\) | −660.000 | −0.872824 | −0.436412 | − | 0.899747i | \(-0.643751\pi\) | ||||
−0.436412 | + | 0.899747i | \(0.643751\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 50.0000 | 0.0638031 | ||||||||
\(86\) | 1400.00 | 1.75542 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2250.00 | 2.72558 | ||||||||
\(89\) | 1500.00 | 1.78651 | 0.893257 | − | 0.449547i | \(-0.148415\pi\) | ||||
0.893257 | + | 0.449547i | \(0.148415\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2040.00 | 2.31179 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1400.00 | 1.53616 | ||||||||
\(95\) | 220.000 | 0.237595 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1630.00 | 1.70620 | 0.853100 | − | 0.521747i | \(-0.174720\pi\) | ||||
0.853100 | + | 0.521747i | \(0.174720\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 425.000 | 0.425000 | ||||||||
\(101\) | 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 | \(0.620061\pi\) | |||||||
\(104\) | 900.000 | 0.848579 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3050.00 | −2.79474 | ||||||||
\(107\) | 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 | \(0.219929\pi\) | |||||||
\(110\) | 1250.00 | 1.08348 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −310.000 | −0.258074 | −0.129037 | − | 0.991640i | \(-0.541189\pi\) | ||||
−0.129037 | + | 0.991640i | \(0.541189\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 600.000 | 0.486524 | ||||||||
\(116\) | −850.000 | −0.680349 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −250.000 | −0.195037 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1169.00 | 0.878287 | ||||||||
\(122\) | 2590.00 | 1.92203 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1836.00 | −1.32966 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1070.00 | −0.747615 | −0.373808 | − | 0.927506i | \(-0.621948\pi\) | ||||
−0.373808 | + | 0.927506i | \(0.621948\pi\) | |||||||
\(128\) | −2115.00 | −1.46048 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 500.000 | 0.337330 | ||||||||
\(131\) | −1950.00 | −1.30055 | −0.650276 | − | 0.759698i | \(-0.725347\pi\) | ||||
−0.650276 | + | 0.759698i | \(0.725347\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −900.000 | −0.580210 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 450.000 | 0.283729 | ||||||||
\(137\) | 1050.00 | 0.654800 | 0.327400 | − | 0.944886i | \(-0.393828\pi\) | ||||
0.327400 | + | 0.944886i | \(0.393828\pi\) | |||||||
\(138\) | 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 | ||||||||
\(142\) | 3500.00 | 2.06840 | ||||||||
\(143\) | 1000.00 | 0.584785 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −250.000 | −0.143182 | ||||||||
\(146\) | 2050.00 | 1.16205 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −680.000 | −0.377673 | ||||||||
\(149\) | 2050.00 | 1.12713 | 0.563566 | − | 0.826071i | \(-0.309429\pi\) | ||||
0.563566 | + | 0.826071i | \(0.309429\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 448.000 | 0.241442 | 0.120721 | − | 0.992686i | \(-0.461479\pi\) | ||||
0.120721 | + | 0.992686i | \(0.461479\pi\) | |||||||
\(152\) | 1980.00 | 1.05657 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −540.000 | −0.279831 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 100.000 | 0.0508336 | 0.0254168 | − | 0.999677i | \(-0.491909\pi\) | ||||
0.0254168 | + | 0.999677i | \(0.491909\pi\) | |||||||
\(158\) | −2580.00 | −1.29907 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 425.000 | 0.209995 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1900.00 | −0.913003 | −0.456501 | − | 0.889723i | \(-0.650898\pi\) | ||||
−0.456501 | + | 0.889723i | \(0.650898\pi\) | |||||||
\(164\) | −6800.00 | −3.23775 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3300.00 | −1.54295 | ||||||||
\(167\) | −1920.00 | −0.889665 | −0.444833 | − | 0.895614i | \(-0.646737\pi\) | ||||
−0.444833 | + | 0.895614i | \(0.646737\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1797.00 | −0.817934 | ||||||||
\(170\) | 250.000 | 0.112789 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4760.00 | 2.11015 | ||||||||
\(173\) | −2550.00 | −1.12065 | −0.560326 | − | 0.828272i | \(-0.689324\pi\) | ||||
−0.560326 | + | 0.828272i | \(0.689324\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4450.00 | 1.90586 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 7500.00 | 3.15814 | ||||||||
\(179\) | 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 | \(-0.149624\pi\) | ||||
0.891542 | + | 0.452937i | \(0.149624\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 5400.00 | 2.16355 | ||||||||
\(185\) | −200.000 | −0.0794827 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 500.000 | 0.195527 | ||||||||
\(188\) | 4760.00 | 1.84659 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1100.00 | 0.420013 | ||||||||
\(191\) | −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 | \(0.285217\pi\) | |||||||
\(194\) | 8150.00 | 3.01616 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 90.0000 | 0.0325494 | 0.0162747 | − | 0.999868i | \(-0.494819\pi\) | ||||
0.0162747 | + | 0.999868i | \(0.494819\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3664.00 | −1.30520 | −0.652598 | − | 0.757704i | \(-0.726321\pi\) | ||||
−0.652598 | + | 0.757704i | \(0.726321\pi\) | |||||||
\(200\) | 1125.00 | 0.397748 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2250.00 | 0.783710 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2000.00 | −0.681395 | ||||||||
\(206\) | −3850.00 | −1.30215 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1780.00 | 0.593369 | ||||||||
\(209\) | 2200.00 | 0.728120 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −268.000 | −0.0874402 | −0.0437201 | − | 0.999044i | \(-0.513921\pi\) | ||||
−0.0437201 | + | 0.999044i | \(0.513921\pi\) | |||||||
\(212\) | −10370.0 | −3.35950 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3300.00 | 1.05413 | ||||||||
\(215\) | 1400.00 | 0.444089 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 8770.00 | 2.72468 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4250.00 | 1.30243 | ||||||||
\(221\) | 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 | ||||||||
\(226\) | −1550.00 | −0.456214 | ||||||||
\(227\) | −3760.00 | −1.09938 | −0.549692 | − | 0.835368i | \(-0.685255\pi\) | ||||
−0.549692 | + | 0.835368i | \(0.685255\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1434.00 | 0.413805 | 0.206903 | − | 0.978362i | \(-0.433662\pi\) | ||||
0.206903 | + | 0.978362i | \(0.433662\pi\) | |||||||
\(230\) | 3000.00 | 0.860061 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2250.00 | −0.636723 | ||||||||
\(233\) | −3450.00 | −0.970030 | −0.485015 | − | 0.874506i | \(-0.661186\pi\) | ||||
−0.485015 | + | 0.874506i | \(0.661186\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1400.00 | 0.388621 | ||||||||
\(236\) | −850.000 | −0.234450 | ||||||||
\(237\) | 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 | \(-0.722903\pi\) | ||||
−0.644424 | + | 0.764668i | \(0.722903\pi\) | |||||||
\(242\) | 5845.00 | 1.55261 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 8806.00 | 2.31044 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 880.000 | 0.226693 | ||||||||
\(248\) | −4860.00 | −1.24440 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 625.000 | 0.158114 | ||||||||
\(251\) | 4650.00 | 1.16934 | 0.584672 | − | 0.811270i | \(-0.301223\pi\) | ||||
0.584672 | + | 0.811270i | \(0.301223\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6000.00 | 1.49098 | ||||||||
\(254\) | −5350.00 | −1.32161 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8279.00 | −2.02124 | ||||||||
\(257\) | −5130.00 | −1.24514 | −0.622569 | − | 0.782565i | \(-0.713911\pi\) | ||||
−0.622569 | + | 0.782565i | \(0.713911\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1700.00 | 0.405498 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −9750.00 | −2.29907 | ||||||||
\(263\) | −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 | ||||||||
\(268\) | −3060.00 | −0.697460 | ||||||||
\(269\) | −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 | \(0.711963\pi\) | |||||||
\(272\) | 890.000 | 0.198398 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5250.00 | 1.15753 | ||||||||
\(275\) | 1250.00 | 0.274101 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4920.00 | 1.06720 | 0.533600 | − | 0.845737i | \(-0.320839\pi\) | ||||
0.533600 | + | 0.845737i | \(0.320839\pi\) | |||||||
\(278\) | −8380.00 | −1.80791 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4500.00 | 0.955329 | 0.477665 | − | 0.878542i | \(-0.341483\pi\) | ||||
0.477665 | + | 0.878542i | \(0.341483\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6900.00 | 1.44934 | 0.724669 | − | 0.689098i | \(-0.241993\pi\) | ||||
0.724669 | + | 0.689098i | \(0.241993\pi\) | |||||||
\(284\) | 11900.0 | 2.48639 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5000.00 | 1.03376 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4813.00 | −0.979646 | ||||||||
\(290\) | −1250.00 | −0.253112 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 6970.00 | 1.39688 | ||||||||
\(293\) | −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 | ||||||||
\(296\) | −1800.00 | −0.353456 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 10250.0 | 1.99251 | ||||||||
\(299\) | 2400.00 | 0.464199 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 2240.00 | 0.426813 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3916.00 | 0.738809 | ||||||||
\(305\) | 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 | ||||||||
\(310\) | −2700.00 | −0.494676 | ||||||||
\(311\) | 5700.00 | 1.03928 | 0.519642 | − | 0.854384i | \(-0.326065\pi\) | ||||
0.519642 | + | 0.854384i | \(0.326065\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3110.00 | −0.561622 | −0.280811 | − | 0.959763i | \(-0.590603\pi\) | ||||
−0.280811 | + | 0.959763i | \(0.590603\pi\) | |||||||
\(314\) | 500.000 | 0.0898619 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8772.00 | −1.56159 | ||||||||
\(317\) | −950.000 | −0.168320 | −0.0841598 | − | 0.996452i | \(-0.526821\pi\) | ||||
−0.0841598 | + | 0.996452i | \(0.526821\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2500.00 | −0.438787 | ||||||||
\(320\) | −1435.00 | −0.250684 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 440.000 | 0.0757965 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 500.000 | 0.0853385 | ||||||||
\(326\) | −9500.00 | −1.61398 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −18000.0 | −3.03013 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2292.00 | 0.380603 | 0.190302 | − | 0.981726i | \(-0.439053\pi\) | ||||
0.190302 | + | 0.981726i | \(0.439053\pi\) | |||||||
\(332\) | −11220.0 | −1.85475 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −9600.00 | −1.57272 | ||||||||
\(335\) | −900.000 | −0.146783 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7730.00 | −1.24950 | −0.624748 | − | 0.780827i | \(-0.714798\pi\) | ||||
−0.624748 | + | 0.780827i | \(0.714798\pi\) | |||||||
\(338\) | −8985.00 | −1.44592 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 850.000 | 0.135582 | ||||||||
\(341\) | −5400.00 | −0.857555 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 12600.0 | 1.97484 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −12750.0 | −1.98105 | ||||||||
\(347\) | −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 | \(-0.528991\pi\) | ||||
−0.0909529 | + | 0.995855i | \(0.528991\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4250.00 | 0.643539 | ||||||||
\(353\) | −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 | ||||||||
\(356\) | 25500.0 | 3.79634 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 18250.0 | 2.69425 | ||||||||
\(359\) | −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 | ||||||||
\(362\) | 21710.0 | 3.15208 | ||||||||
\(363\) | 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 | \(0.706339\pi\) | |||||||
\(368\) | 10680.0 | 1.51286 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1000.00 | −0.140507 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 100.000 | 0.0138815 | 0.00694076 | − | 0.999976i | \(-0.497791\pi\) | ||||
0.00694076 | + | 0.999976i | \(0.497791\pi\) | |||||||
\(374\) | 2500.00 | 0.345647 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 12600.0 | 1.72818 | ||||||||
\(377\) | −1000.00 | −0.136612 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8084.00 | −1.09564 | −0.547820 | − | 0.836597i | \(-0.684542\pi\) | ||||
−0.547820 | + | 0.836597i | \(0.684542\pi\) | |||||||
\(380\) | 3740.00 | 0.504889 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −17500.0 | −2.34392 | ||||||||
\(383\) | 9480.00 | 1.26477 | 0.632383 | − | 0.774656i | \(-0.282077\pi\) | ||||
0.632383 | + | 0.774656i | \(0.282077\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 16750.0 | 2.20869 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 27710.0 | 3.62568 | ||||||||
\(389\) | −10950.0 | −1.42722 | −0.713608 | − | 0.700545i | \(-0.752940\pi\) | ||||
−0.713608 | + | 0.700545i | \(0.752940\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1200.00 | 0.155209 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 450.000 | 0.0575398 | ||||||||
\(395\) | −2580.00 | −0.328643 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13840.0 | −1.74965 | −0.874823 | − | 0.484442i | \(-0.839023\pi\) | ||||
−0.874823 | + | 0.484442i | \(0.839023\pi\) | |||||||
\(398\) | −18320.0 | −2.30728 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2225.00 | 0.278125 | ||||||||
\(401\) | 9300.00 | 1.15815 | 0.579077 | − | 0.815273i | \(-0.303413\pi\) | ||||
0.579077 | + | 0.815273i | \(0.303413\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2160.00 | −0.266991 | ||||||||
\(404\) | 7650.00 | 0.942083 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2000.00 | −0.243578 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2854.00 | 0.345040 | 0.172520 | − | 0.985006i | \(-0.444809\pi\) | ||||
0.172520 | + | 0.985006i | \(0.444809\pi\) | |||||||
\(410\) | −10000.0 | −1.20455 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −13090.0 | −1.56529 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3300.00 | −0.390339 | ||||||||
\(416\) | 1700.00 | 0.200359 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 11000.0 | 1.28715 | ||||||||
\(419\) | −1150.00 | −0.134084 | −0.0670420 | − | 0.997750i | \(-0.521356\pi\) | ||||
−0.0670420 | + | 0.997750i | \(0.521356\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11162.0 | −1.29217 | −0.646084 | − | 0.763266i | \(-0.723594\pi\) | ||||
−0.646084 | + | 0.763266i | \(0.723594\pi\) | |||||||
\(422\) | −1340.00 | −0.154574 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −27450.0 | −3.14408 | ||||||||
\(425\) | 250.000 | 0.0285336 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 11220.0 | 1.26715 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 7000.00 | 0.785046 | ||||||||
\(431\) | −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 | \(-0.526704\pi\) | ||||
−0.0837944 | + | 0.996483i | \(0.526704\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 29818.0 | 3.27528 | ||||||||
\(437\) | 5280.00 | 0.577979 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −424.000 | −0.0460966 | −0.0230483 | − | 0.999734i | \(-0.507337\pi\) | ||||
−0.0230483 | + | 0.999734i | \(0.507337\pi\) | |||||||
\(440\) | 11250.0 | 1.21892 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1000.00 | 0.107613 | ||||||||
\(443\) | 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 | ||||||||
\(446\) | 18350.0 | 1.94820 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1300.00 | −0.136639 | −0.0683194 | − | 0.997664i | \(-0.521764\pi\) | ||||
−0.0683194 | + | 0.997664i | \(0.521764\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −20000.0 | −2.08817 | ||||||||
\(452\) | −5270.00 | −0.548407 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −18800.0 | −1.94345 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7190.00 | −0.735961 | −0.367980 | − | 0.929834i | \(-0.619951\pi\) | ||||
−0.367980 | + | 0.929834i | \(0.619951\pi\) | |||||||
\(458\) | 7170.00 | 0.731511 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 10200.0 | 1.03386 | ||||||||
\(461\) | 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 | \(-0.457217\pi\) | ||||
0.134002 | + | 0.990981i | \(0.457217\pi\) | |||||||
\(464\) | −4450.00 | −0.445229 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −17250.0 | −1.71479 | ||||||||
\(467\) | −1180.00 | −0.116925 | −0.0584624 | − | 0.998290i | \(-0.518620\pi\) | ||||
−0.0584624 | + | 0.998290i | \(0.518620\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 7000.00 | 0.686991 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2250.00 | −0.219417 | ||||||||
\(473\) | 14000.0 | 1.36093 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1100.00 | 0.106256 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −24500.0 | −2.34436 | ||||||||
\(479\) | 14100.0 | 1.34498 | 0.672490 | − | 0.740106i | \(-0.265225\pi\) | ||||
0.672490 | + | 0.740106i | \(0.265225\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −800.000 | −0.0758355 | ||||||||
\(482\) | −24110.0 | −2.27838 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 19873.0 | 1.86636 | ||||||||
\(485\) | 8150.00 | 0.763036 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9850.00 | −0.916522 | −0.458261 | − | 0.888818i | \(-0.651527\pi\) | ||||
−0.458261 | + | 0.888818i | \(0.651527\pi\) | |||||||
\(488\) | 23310.0 | 2.16228 | ||||||||
\(489\) | 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 | ||||||||
\(494\) | 4400.00 | 0.400740 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −9612.00 | −0.870144 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17036.0 | −1.52833 | −0.764164 | − | 0.645021i | \(-0.776848\pi\) | ||||
−0.764164 | + | 0.645021i | \(0.776848\pi\) | |||||||
\(500\) | 2125.00 | 0.190066 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 23250.0 | 2.06713 | ||||||||
\(503\) | 20600.0 | 1.82606 | 0.913030 | − | 0.407891i | \(-0.133736\pi\) | ||||
0.913030 | + | 0.407891i | \(0.133736\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2250.00 | 0.198265 | ||||||||
\(506\) | 30000.0 | 2.63570 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −18190.0 | −1.58868 | ||||||||
\(509\) | −5750.00 | −0.500716 | −0.250358 | − | 0.968153i | \(-0.580548\pi\) | ||||
−0.250358 | + | 0.968153i | \(0.580548\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −24475.0 | −2.11260 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −25650.0 | −2.20111 | ||||||||
\(515\) | −3850.00 | −0.329420 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14000.0 | 1.19095 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 4500.00 | 0.379496 | ||||||||
\(521\) | 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 | \(0.301978\pi\) | |||||||
\(524\) | −33150.0 | −2.76367 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6400.00 | −0.530520 | ||||||||
\(527\) | −1080.00 | −0.0892705 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2233.00 | 0.183529 | ||||||||
\(530\) | −15250.0 | −1.24984 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8000.00 | −0.650128 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3300.00 | 0.266676 | ||||||||
\(536\) | −8100.00 | −0.652736 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −16750.0 | −1.34227 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20478.0 | −1.62739 | −0.813695 | − | 0.581292i | \(-0.802547\pi\) | ||||
−0.813695 | + | 0.581292i | \(0.802547\pi\) | |||||||
\(542\) | −27560.0 | −2.18414 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 850.000 | 0.0669916 | ||||||||
\(545\) | 8770.00 | 0.689295 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12040.0 | 0.941121 | 0.470561 | − | 0.882368i | \(-0.344052\pi\) | ||||
0.470561 | + | 0.882368i | \(0.344052\pi\) | |||||||
\(548\) | 17850.0 | 1.39145 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 6250.00 | 0.484547 | ||||||||
\(551\) | −2200.00 | −0.170096 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 24600.0 | 1.88656 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −28492.0 | −2.17326 | ||||||||
\(557\) | 23550.0 | 1.79146 | 0.895732 | − | 0.444594i | \(-0.146652\pi\) | ||||
0.895732 | + | 0.444594i | \(0.146652\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5600.00 | 0.423712 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 22500.0 | 1.68880 | ||||||||
\(563\) | 6120.00 | 0.458130 | 0.229065 | − | 0.973411i | \(-0.426433\pi\) | ||||
0.229065 | + | 0.973411i | \(0.426433\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1550.00 | −0.115414 | ||||||||
\(566\) | 34500.0 | 2.56209 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 31500.0 | 2.32696 | ||||||||
\(569\) | −11700.0 | −0.862020 | −0.431010 | − | 0.902347i | \(-0.641843\pi\) | ||||
−0.431010 | + | 0.902347i | \(0.641843\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8188.00 | −0.600100 | −0.300050 | − | 0.953923i | \(-0.597003\pi\) | ||||
−0.300050 | + | 0.953923i | \(0.597003\pi\) | |||||||
\(572\) | 17000.0 | 1.24267 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3000.00 | 0.217580 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11690.0 | −0.843433 | −0.421717 | − | 0.906728i | \(-0.638572\pi\) | ||||
−0.421717 | + | 0.906728i | \(0.638572\pi\) | |||||||
\(578\) | −24065.0 | −1.73179 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −4250.00 | −0.304261 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −30500.0 | −2.16669 | ||||||||
\(584\) | 18450.0 | 1.30731 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7650.00 | −0.539281 | ||||||||
\(587\) | −21060.0 | −1.48082 | −0.740408 | − | 0.672157i | \(-0.765368\pi\) | ||||
−0.740408 | + | 0.672157i | \(0.765368\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4752.00 | −0.332433 | ||||||||
\(590\) | −1250.00 | −0.0872232 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3560.00 | −0.247154 | ||||||||
\(593\) | 22910.0 | 1.58651 | 0.793255 | − | 0.608889i | \(-0.208385\pi\) | ||||
0.793255 | + | 0.608889i | \(0.208385\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 34850.0 | 2.39515 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 12000.0 | 0.820596 | ||||||||
\(599\) | −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 | \(-0.378205\pi\) | ||||
0.373362 | + | 0.927686i | \(0.378205\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 7616.00 | 0.513064 | ||||||||
\(605\) | 5845.00 | 0.392782 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4630.00 | −0.309598 | −0.154799 | − | 0.987946i | \(-0.549473\pi\) | ||||
−0.154799 | + | 0.987946i | \(0.549473\pi\) | |||||||
\(608\) | 3740.00 | 0.249469 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 12950.0 | 0.859558 | ||||||||
\(611\) | 5600.00 | 0.370788 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24040.0 | 1.58396 | 0.791979 | − | 0.610548i | \(-0.209051\pi\) | ||||
0.791979 | + | 0.610548i | \(0.209051\pi\) | |||||||
\(614\) | −15200.0 | −0.999059 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1890.00 | −0.123320 | −0.0616601 | − | 0.998097i | \(-0.519639\pi\) | ||||
−0.0616601 | + | 0.998097i | \(0.519639\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19244.0 | −1.24957 | −0.624783 | − | 0.780798i | \(-0.714813\pi\) | ||||
−0.624783 | + | 0.780798i | \(0.714813\pi\) | |||||||
\(620\) | −9180.00 | −0.594641 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 28500.0 | 1.83721 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | −15550.0 | −0.992816 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1700.00 | 0.108021 | ||||||||
\(629\) | −400.000 | −0.0253562 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15892.0 | 1.00262 | 0.501308 | − | 0.865269i | \(-0.332852\pi\) | ||||
0.501308 | + | 0.865269i | \(0.332852\pi\) | |||||||
\(632\) | −23220.0 | −1.46146 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −4750.00 | −0.297550 | ||||||||
\(635\) | −5350.00 | −0.334344 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −12500.0 | −0.775674 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −10575.0 | −0.653146 | ||||||||
\(641\) | −12600.0 | −0.776396 | −0.388198 | − | 0.921576i | \(-0.626902\pi\) | ||||
−0.388198 | + | 0.921576i | \(0.626902\pi\) | |||||||
\(642\) | 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 | ||||||||
\(646\) | 2200.00 | 0.133990 | ||||||||
\(647\) | −7400.00 | −0.449651 | −0.224825 | − | 0.974399i | \(-0.572181\pi\) | ||||
−0.224825 | + | 0.974399i | \(0.572181\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2500.00 | −0.151207 | ||||||||
\(650\) | 2500.00 | 0.150859 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −32300.0 | −1.94013 | ||||||||
\(653\) | −4790.00 | −0.287055 | −0.143528 | − | 0.989646i | \(-0.545845\pi\) | ||||
−0.143528 | + | 0.989646i | \(0.545845\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9750.00 | −0.581624 | ||||||||
\(656\) | −35600.0 | −2.11882 | ||||||||
\(657\) | 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 | \(-0.613039\pi\) | ||||
−0.347706 | + | 0.937604i | \(0.613039\pi\) | |||||||
\(662\) | 11460.0 | 0.672818 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −29700.0 | −1.73582 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6000.00 | −0.348307 | ||||||||
\(668\) | −32640.0 | −1.89054 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −4500.00 | −0.259478 | ||||||||
\(671\) | 25900.0 | 1.49010 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5550.00 | 0.317885 | 0.158943 | − | 0.987288i | \(-0.449192\pi\) | ||||
0.158943 | + | 0.987288i | \(0.449192\pi\) | |||||||
\(674\) | −38650.0 | −2.20882 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −30549.0 | −1.73811 | ||||||||
\(677\) | −12930.0 | −0.734033 | −0.367016 | − | 0.930214i | \(-0.619621\pi\) | ||||
−0.367016 | + | 0.930214i | \(0.619621\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 2250.00 | 0.126888 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −27000.0 | −1.51596 | ||||||||
\(683\) | 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 | ||||||||
\(688\) | 24920.0 | 1.38091 | ||||||||
\(689\) | −12200.0 | −0.674576 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10228.0 | −0.563085 | −0.281542 | − | 0.959549i | \(-0.590846\pi\) | ||||
−0.281542 | + | 0.959549i | \(0.590846\pi\) | |||||||
\(692\) | −43350.0 | −2.38139 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −5600.00 | −0.306301 | ||||||||
\(695\) | −8380.00 | −0.457369 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4000.00 | −0.217376 | ||||||||
\(698\) | −5930.00 | −0.321567 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8350.00 | 0.449893 | 0.224947 | − | 0.974371i | \(-0.427779\pi\) | ||||
0.224947 | + | 0.974371i | \(0.427779\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1760.00 | −0.0944234 | ||||||||
\(704\) | −14350.0 | −0.768233 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −18150.0 | −0.967541 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14954.0 | −0.792115 | −0.396057 | − | 0.918226i | \(-0.629622\pi\) | ||||
−0.396057 | + | 0.918226i | \(0.629622\pi\) | |||||||
\(710\) | 17500.0 | 0.925019 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 67500.0 | 3.55291 | ||||||||
\(713\) | −12960.0 | −0.680723 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5000.00 | 0.261524 | ||||||||
\(716\) | 62050.0 | 3.23871 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −9000.00 | −0.467795 | ||||||||
\(719\) | −29400.0 | −1.52494 | −0.762472 | − | 0.647021i | \(-0.776015\pi\) | ||||
−0.762472 | + | 0.647021i | \(0.776015\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −24615.0 | −1.26880 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 73814.0 | 3.78905 | ||||||||
\(725\) | −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 | ||||||||
\(730\) | 10250.0 | 0.519684 | ||||||||
\(731\) | 2800.00 | 0.141671 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −30800.0 | −1.55201 | −0.776005 | − | 0.630726i | \(-0.782757\pi\) | ||||
−0.776005 | + | 0.630726i | \(0.782757\pi\) | |||||||
\(734\) | −42450.0 | −2.13468 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 10200.0 | 0.510838 | ||||||||
\(737\) | −9000.00 | −0.449823 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9524.00 | −0.474081 | −0.237041 | − | 0.971500i | \(-0.576177\pi\) | ||||
−0.237041 | + | 0.971500i | \(0.576177\pi\) | |||||||
\(740\) | −3400.00 | −0.168901 | ||||||||
\(741\) | 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 | ||||||||
\(746\) | 500.000 | 0.0245393 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 8500.00 | 0.415496 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8252.00 | −0.400958 | −0.200479 | − | 0.979698i | \(-0.564250\pi\) | ||||
−0.200479 | + | 0.979698i | \(0.564250\pi\) | |||||||
\(752\) | 24920.0 | 1.20843 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −5000.00 | −0.241498 | ||||||||
\(755\) | 2240.00 | 0.107976 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −24920.0 | −1.19648 | −0.598238 | − | 0.801318i | \(-0.704132\pi\) | ||||
−0.598238 | + | 0.801318i | \(0.704132\pi\) | |||||||
\(758\) | −40420.0 | −1.93683 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 9900.00 | 0.472514 | ||||||||
\(761\) | −27900.0 | −1.32901 | −0.664503 | − | 0.747285i | \(-0.731357\pi\) | ||||
−0.664503 | + | 0.747285i | \(0.731357\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −59500.0 | −2.81758 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 47400.0 | 2.23581 | ||||||||
\(767\) | −1000.00 | −0.0470768 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11506.0 | 0.539554 | 0.269777 | − | 0.962923i | \(-0.413050\pi\) | ||||
0.269777 | + | 0.962923i | \(0.413050\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 56950.0 | 2.65502 | ||||||||
\(773\) | 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 | ||||||||
\(776\) | 73350.0 | 3.39318 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −54750.0 | −2.52299 | ||||||||
\(779\) | −17600.0 | −0.809481 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 35000.0 | 1.60358 | ||||||||
\(782\) | 6000.00 | 0.274373 | ||||||||
\(783\) | 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 | \(0.492070\pi\) | |||||||
\(788\) | 1530.00 | 0.0691675 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −12900.0 | −0.580964 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10360.0 | 0.463927 | ||||||||
\(794\) | −69200.0 | −3.09297 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −62288.0 | −2.77354 | ||||||||
\(797\) | 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 | ||||||||
\(800\) | 2125.00 | 0.0939126 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 46500.0 | 2.04735 | ||||||||
\(803\) | 20500.0 | 0.900908 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −10800.0 | −0.471977 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 20250.0 | 0.881674 | ||||||||
\(809\) | 28600.0 | 1.24292 | 0.621460 | − | 0.783446i | \(-0.286540\pi\) | ||||
0.621460 | + | 0.783446i | \(0.286540\pi\) | |||||||
\(810\) | 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 | ||||||||
\(814\) | −10000.0 | −0.430589 | ||||||||
\(815\) | −9500.00 | −0.408307 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12320.0 | 0.527567 | ||||||||
\(818\) | 14270.0 | 0.609950 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −34000.0 | −1.44797 | ||||||||
\(821\) | −14250.0 | −0.605759 | −0.302880 | − | 0.953029i | \(-0.597948\pi\) | ||||
−0.302880 | + | 0.953029i | \(0.597948\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6830.00 | 0.289282 | 0.144641 | − | 0.989484i | \(-0.453797\pi\) | ||||
0.144641 | + | 0.989484i | \(0.453797\pi\) | |||||||
\(824\) | −34650.0 | −1.46491 | ||||||||
\(825\) | 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 | \(-0.476414\pi\) | ||||
0.0740295 | + | 0.997256i | \(0.476414\pi\) | |||||||
\(830\) | −16500.0 | −0.690028 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −5740.00 | −0.239181 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9600.00 | −0.397870 | ||||||||
\(836\) | 37400.0 | 1.54726 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −5750.00 | −0.237029 | ||||||||
\(839\) | 8000.00 | 0.329190 | 0.164595 | − | 0.986361i | \(-0.447368\pi\) | ||||
0.164595 | + | 0.986361i | \(0.447368\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21889.0 | −0.897495 | ||||||||
\(842\) | −55810.0 | −2.28425 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −4556.00 | −0.185810 | ||||||||
\(845\) | −8985.00 | −0.365791 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −54290.0 | −2.19850 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1250.00 | 0.0504408 | ||||||||
\(851\) | −4800.00 | −0.193351 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5160.00 | −0.207122 | −0.103561 | − | 0.994623i | \(-0.533024\pi\) | ||||
−0.103561 | + | 0.994623i | \(0.533024\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 29700.0 | 1.18589 | ||||||||
\(857\) | −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 | \(0.671269\pi\) | |||||||
\(860\) | 23800.0 | 0.943690 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −6000.00 | −0.237078 | ||||||||
\(863\) | 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 | ||||||||
\(866\) | −7550.00 | −0.296258 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −25800.0 | −1.00714 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3600.00 | −0.140047 | ||||||||
\(872\) | 78930.0 | 3.06526 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 26400.0 | 1.02173 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −35100.0 | −1.35147 | −0.675737 | − | 0.737143i | \(-0.736175\pi\) | ||||
−0.675737 | + | 0.737143i | \(0.736175\pi\) | |||||||
\(878\) | −2120.00 | −0.0814881 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 22250.0 | 0.852327 | ||||||||
\(881\) | 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 | \(-0.518085\pi\) | ||||
−0.0567865 | + | 0.998386i | \(0.518085\pi\) | |||||||
\(884\) | 3400.00 | 0.129360 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 61800.0 | 2.34335 | ||||||||
\(887\) | 35880.0 | 1.35821 | 0.679105 | − | 0.734041i | \(-0.262368\pi\) | ||||
0.679105 | + | 0.734041i | \(0.262368\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 37500.0 | 1.41236 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 62390.0 | 2.34190 | ||||||||
\(893\) | 12320.0 | 0.461672 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18250.0 | 0.681598 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −6500.00 | −0.241545 | ||||||||
\(899\) | 5400.00 | 0.200334 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6100.00 | −0.225550 | ||||||||
\(902\) | −100000. | −3.69139 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −13950.0 | −0.513241 | ||||||||
\(905\) | 21710.0 | 0.797420 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 45240.0 | 1.65620 | 0.828098 | − | 0.560584i | \(-0.189423\pi\) | ||||
0.828098 | + | 0.560584i | \(0.189423\pi\) | |||||||
\(908\) | −63920.0 | −2.33619 | ||||||||
\(909\) | 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 | ||||||||
\(914\) | −35950.0 | −1.30101 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 24378.0 | 0.879336 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 35356.0 | 1.26908 | 0.634541 | − | 0.772889i | \(-0.281189\pi\) | ||||
0.634541 | + | 0.772889i | \(0.281189\pi\) | |||||||
\(920\) | 27000.0 | 0.967569 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 750.000 | 0.0267895 | ||||||||
\(923\) | 14000.0 | 0.499259 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1000.00 | −0.0355457 | ||||||||
\(926\) | 13350.0 | 0.473767 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4250.00 | −0.150337 | ||||||||
\(929\) | 25700.0 | 0.907631 | 0.453816 | − | 0.891096i | \(-0.350062\pi\) | ||||
0.453816 | + | 0.891096i | \(0.350062\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −58650.0 | −2.06131 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −5900.00 | −0.206696 | ||||||||
\(935\) | 2500.00 | 0.0874425 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −52890.0 | −1.84401 | −0.922007 | − | 0.387173i | \(-0.873451\pi\) | ||||
−0.922007 | + | 0.387173i | \(0.873451\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 23800.0 | 0.825820 | ||||||||
\(941\) | −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 | ||||||||
\(944\) | −4450.00 | −0.153427 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 70000.0 | 2.40581 | ||||||||
\(947\) | −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 | ||||||||
\(950\) | 5500.00 | 0.187835 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 15170.0 | 0.515640 | 0.257820 | − | 0.966193i | \(-0.416996\pi\) | ||||
0.257820 | + | 0.966193i | \(0.416996\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −17500.0 | −0.592970 | ||||||||
\(956\) | −83300.0 | −2.81811 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 70500.0 | 2.37761 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −18127.0 | −0.608472 | ||||||||
\(962\) | −4000.00 | −0.134059 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −81974.0 | −2.73880 | ||||||||
\(965\) | 16750.0 | 0.558758 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5470.00 | −0.181906 | −0.0909531 | − | 0.995855i | \(-0.528991\pi\) | ||||
−0.0909531 | + | 0.995855i | \(0.528991\pi\) | |||||||
\(968\) | 52605.0 | 1.74668 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 40750.0 | 1.34887 | ||||||||
\(971\) | −15150.0 | −0.500707 | −0.250354 | − | 0.968154i | \(-0.580547\pi\) | ||||
−0.250354 | + | 0.968154i | \(0.580547\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −49250.0 | −1.62020 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 46102.0 | 1.51198 | ||||||||
\(977\) | 31190.0 | 1.02135 | 0.510674 | − | 0.859775i | \(-0.329396\pi\) | ||||
0.510674 | + | 0.859775i | \(0.329396\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 75000.0 | 2.44843 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −12250.0 | −0.398079 | ||||||||
\(983\) | 7560.00 | 0.245297 | 0.122648 | − | 0.992450i | \(-0.460861\pi\) | ||||
0.122648 | + | 0.992450i | \(0.460861\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 450.000 | 0.0145565 | ||||||||
\(986\) | −2500.00 | −0.0807467 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 14960.0 | 0.481722 | ||||||||
\(989\) | 33600.0 | 1.08030 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 32672.0 | 1.04729 | 0.523643 | − | 0.851938i | \(-0.324573\pi\) | ||||
0.523643 | + | 0.851938i | \(0.324573\pi\) | |||||||
\(992\) | −9180.00 | −0.293816 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −18320.0 | −0.583702 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4740.00 | 0.150569 | 0.0752845 | − | 0.997162i | \(-0.476014\pi\) | ||||
0.0752845 | + | 0.997162i | \(0.476014\pi\) | |||||||
\(998\) | −85180.0 | −2.70173 | ||||||||
\(999\) | 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 | 2205.4.a.t.1.1 | 1 | ||
3.2 | odd | 2 | 2205.4.a.a.1.1 | 1 | |||
7.6 | odd | 2 | 45.4.a.e.1.1 | yes | 1 | ||
21.20 | even | 2 | 45.4.a.a.1.1 | ✓ | 1 | ||
28.27 | even | 2 | 720.4.a.o.1.1 | 1 | |||
35.13 | even | 4 | 225.4.b.b.199.1 | 2 | |||
35.27 | even | 4 | 225.4.b.b.199.2 | 2 | |||
35.34 | odd | 2 | 225.4.a.a.1.1 | 1 | |||
63.13 | odd | 6 | 405.4.e.b.136.1 | 2 | |||
63.20 | even | 6 | 405.4.e.n.271.1 | 2 | |||
63.34 | odd | 6 | 405.4.e.b.271.1 | 2 | |||
63.41 | even | 6 | 405.4.e.n.136.1 | 2 | |||
84.83 | odd | 2 | 720.4.a.bc.1.1 | 1 | |||
105.62 | odd | 4 | 225.4.b.a.199.1 | 2 | |||
105.83 | odd | 4 | 225.4.b.a.199.2 | 2 | |||
105.104 | even | 2 | 225.4.a.h.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.4.a.a.1.1 | ✓ | 1 | 21.20 | even | 2 | ||
45.4.a.e.1.1 | yes | 1 | 7.6 | odd | 2 | ||
225.4.a.a.1.1 | 1 | 35.34 | odd | 2 | |||
225.4.a.h.1.1 | 1 | 105.104 | even | 2 | |||
225.4.b.a.199.1 | 2 | 105.62 | odd | 4 | |||
225.4.b.a.199.2 | 2 | 105.83 | odd | 4 | |||
225.4.b.b.199.1 | 2 | 35.13 | even | 4 | |||
225.4.b.b.199.2 | 2 | 35.27 | even | 4 | |||
405.4.e.b.136.1 | 2 | 63.13 | odd | 6 | |||
405.4.e.b.271.1 | 2 | 63.34 | odd | 6 | |||
405.4.e.n.136.1 | 2 | 63.41 | even | 6 | |||
405.4.e.n.271.1 | 2 | 63.20 | even | 6 | |||
720.4.a.o.1.1 | 1 | 28.27 | even | 2 | |||
720.4.a.bc.1.1 | 1 | 84.83 | odd | 2 | |||
2205.4.a.a.1.1 | 1 | 3.2 | odd | 2 | |||
2205.4.a.t.1.1 | 1 | 1.1 | even | 1 | trivial |