Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,4,Mod(199,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.199");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(13.2754297513\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 5 \) |
Twist minimal: | no (minimal twist has level 45) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 199.2 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 225.199 |
Dual form | 225.4.b.b.199.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.00000i | 1.76777i | 0.467707 | + | 0.883883i | \(0.345080\pi\) | ||||
−0.467707 | + | 0.883883i | \(0.654920\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −17.0000 | −2.12500 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 30.0000i | − 1.61985i | −0.586535 | − | 0.809924i | \(-0.699508\pi\) | ||||
0.586535 | − | 0.809924i | \(-0.300492\pi\) | |||||||
\(8\) | − 45.0000i | − 1.98874i | ||||||||
\(9\) | 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 | ||||||||
\(13\) | 20.0000i | 0.426692i | 0.976977 | + | 0.213346i | \(0.0684362\pi\) | ||||
−0.976977 | + | 0.213346i | \(0.931564\pi\) | |||||||
\(14\) | 150.000 | 2.86351 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 89.0000 | 1.39062 | ||||||||
\(17\) | − 10.0000i | − 0.142668i | −0.997452 | − | 0.0713340i | \(-0.977274\pi\) | ||||
0.997452 | − | 0.0713340i | \(-0.0227256\pi\) | |||||||
\(18\) | 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 | ||||||||
\(22\) | 250.000i | 2.42274i | ||||||||
\(23\) | − 120.000i | − 1.08790i | −0.839117 | − | 0.543951i | \(-0.816928\pi\) | ||||
0.839117 | − | 0.543951i | \(-0.183072\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −100.000 | −0.754293 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 510.000i | 3.44218i | ||||||||
\(29\) | 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 | \(-0.398713\pi\) | ||||
0.312861 | + | 0.949799i | \(0.398713\pi\) | |||||||
\(32\) | 85.0000i | 0.469563i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 50.0000 | 0.252204 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 40.0000i | − 0.177729i | −0.996044 | − | 0.0888643i | \(-0.971676\pi\) | ||||
0.996044 | − | 0.0888643i | \(-0.0283238\pi\) | |||||||
\(38\) | 220.000i | 0.939177i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 400.000 | 1.52365 | 0.761823 | − | 0.647785i | \(-0.224304\pi\) | ||||
0.761823 | + | 0.647785i | \(0.224304\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 280.000i | − 0.993014i | −0.868033 | − | 0.496507i | \(-0.834616\pi\) | ||||
0.868033 | − | 0.496507i | \(-0.165384\pi\) | |||||||
\(44\) | −850.000 | −2.91233 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 600.000 | 1.92316 | ||||||||
\(47\) | − 280.000i | − 0.868983i | −0.900676 | − | 0.434491i | \(-0.856928\pi\) | ||||
0.900676 | − | 0.434491i | \(-0.143072\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −557.000 | −1.62391 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − 340.000i | − 0.906721i | ||||||||
\(53\) | 610.000i | 1.58094i | 0.612499 | + | 0.790471i | \(0.290164\pi\) | ||||
−0.612499 | + | 0.790471i | \(0.709836\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1350.00 | −3.22145 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 250.000i | 0.565976i | ||||||||
\(59\) | −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 | \(-0.682951\pi\) | ||||
−0.543632 | + | 0.839324i | \(0.682951\pi\) | |||||||
\(62\) | 540.000i | 1.10613i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 287.000 | 0.560547 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 180.000i | − 0.328216i | −0.986442 | − | 0.164108i | \(-0.947525\pi\) | ||||
0.986442 | − | 0.164108i | \(-0.0524746\pi\) | |||||||
\(68\) | 170.000i | 0.303170i | ||||||||
\(69\) | 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 | ||||||||
\(73\) | 410.000i | 0.657354i | 0.944442 | + | 0.328677i | \(0.106603\pi\) | ||||
−0.944442 | + | 0.328677i | \(0.893397\pi\) | |||||||
\(74\) | 200.000 | 0.314183 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −748.000 | −1.12897 | ||||||||
\(77\) | − 1500.00i | − 2.22001i | ||||||||
\(78\) | 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 | ||||||||
\(82\) | 2000.00i | 2.69345i | ||||||||
\(83\) | − 660.000i | − 0.872824i | −0.899747 | − | 0.436412i | \(-0.856249\pi\) | ||||
0.899747 | − | 0.436412i | \(-0.143751\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1400.00 | 1.75542 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − 2250.00i | − 2.72558i | ||||||||
\(89\) | 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 | ||||||||
\(92\) | 2040.00i | 2.31179i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1400.00 | 1.53616 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 1630.00i | − 1.70620i | −0.521747 | − | 0.853100i | \(-0.674720\pi\) | ||||
0.521747 | − | 0.853100i | \(-0.325280\pi\) | |||||||
\(98\) | − 2785.00i | − 2.87069i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −450.000 | −0.443333 | −0.221667 | − | 0.975122i | \(-0.571150\pi\) | ||||
−0.221667 | + | 0.975122i | \(0.571150\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 770.000i | − 0.736605i | −0.929706 | − | 0.368303i | \(-0.879939\pi\) | ||||
0.929706 | − | 0.368303i | \(-0.120061\pi\) | |||||||
\(104\) | 900.000 | 0.848579 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3050.00 | −2.79474 | ||||||||
\(107\) | 660.000i | 0.596305i | 0.954518 | + | 0.298152i | \(0.0963704\pi\) | ||||
−0.954518 | + | 0.298152i | \(0.903630\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1754.00 | −1.54131 | −0.770655 | − | 0.637253i | \(-0.780071\pi\) | ||||
−0.770655 | + | 0.637253i | \(0.780071\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − 2670.00i | − 2.25260i | ||||||||
\(113\) | 310.000i | 0.258074i | 0.991640 | + | 0.129037i | \(0.0411886\pi\) | ||||
−0.991640 | + | 0.129037i | \(0.958811\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −850.000 | −0.680349 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − 250.000i | − 0.195037i | ||||||||
\(119\) | −300.000 | −0.231100 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1169.00 | 0.878287 | ||||||||
\(122\) | − 2590.00i | − 1.92203i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1836.00 | −1.32966 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 1070.00i | − 0.747615i | −0.927506 | − | 0.373808i | \(-0.878052\pi\) | ||||
0.927506 | − | 0.373808i | \(-0.121948\pi\) | |||||||
\(128\) | 2115.00i | 1.46048i | ||||||||
\(129\) | 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 | ||||||||
\(133\) | − 1320.00i | − 0.860590i | ||||||||
\(134\) | 900.000 | 0.580210 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −450.000 | −0.283729 | ||||||||
\(137\) | 1050.00i | 0.654800i | 0.944886 | + | 0.327400i | \(0.106172\pi\) | ||||
−0.944886 | + | 0.327400i | \(0.893828\pi\) | |||||||
\(138\) | 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 | ||||||||
\(142\) | 3500.00i | 2.06840i | ||||||||
\(143\) | 1000.00i | 0.584785i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2050.00 | −1.16205 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 680.000i | 0.377673i | ||||||||
\(149\) | −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 | \(-0.461479\pi\) | ||||
0.120721 | + | 0.992686i | \(0.461479\pi\) | |||||||
\(152\) | − 1980.00i | − 1.05657i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 7500.00 | 3.92446 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 100.000i | − 0.0508336i | −0.999677 | − | 0.0254168i | \(-0.991909\pi\) | ||||
0.999677 | − | 0.0254168i | \(-0.00809128\pi\) | |||||||
\(158\) | 2580.00i | 1.29907i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3600.00 | −1.76223 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1900.00i | 0.913003i | 0.889723 | + | 0.456501i | \(0.150898\pi\) | ||||
−0.889723 | + | 0.456501i | \(0.849102\pi\) | |||||||
\(164\) | −6800.00 | −3.23775 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3300.00 | 1.54295 | ||||||||
\(167\) | 1920.00i | 0.889665i | 0.895614 | + | 0.444833i | \(0.146737\pi\) | ||||
−0.895614 | + | 0.444833i | \(0.853263\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1797.00 | 0.817934 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4760.00i | 2.11015i | ||||||||
\(173\) | − 2550.00i | − 1.12065i | −0.828272 | − | 0.560326i | \(-0.810676\pi\) | ||||
0.828272 | − | 0.560326i | \(-0.189324\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4450.00 | 1.90586 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 7500.00i | 3.15814i | ||||||||
\(179\) | −3650.00 | −1.52410 | −0.762050 | − | 0.647518i | \(-0.775807\pi\) | ||||
−0.762050 | + | 0.647518i | \(0.775807\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4342.00 | −1.78308 | −0.891542 | − | 0.452937i | \(-0.850376\pi\) | ||||
−0.891542 | + | 0.452937i | \(0.850376\pi\) | |||||||
\(182\) | 3000.00i | 1.22184i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5400.00 | −2.16355 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 500.000i | − 0.195527i | ||||||||
\(188\) | 4760.00i | 1.84659i | ||||||||
\(189\) | 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 | ||||||||
\(193\) | − 3350.00i | − 1.24942i | −0.780856 | − | 0.624711i | \(-0.785217\pi\) | ||||
0.780856 | − | 0.624711i | \(-0.214783\pi\) | |||||||
\(194\) | 8150.00 | 3.01616 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 9469.00 | 3.45080 | ||||||||
\(197\) | 90.0000i | 0.0325494i | 0.999868 | + | 0.0162747i | \(0.00518063\pi\) | ||||
−0.999868 | + | 0.0162747i | \(0.994819\pi\) | |||||||
\(198\) | 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 | ||||||||
\(202\) | − 2250.00i | − 0.783710i | ||||||||
\(203\) | − 1500.00i | − 0.518618i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 3850.00 | 1.30215 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1780.00i | 0.593369i | ||||||||
\(209\) | 2200.00 | 0.728120 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −268.000 | −0.0874402 | −0.0437201 | − | 0.999044i | \(-0.513921\pi\) | ||||
−0.0437201 | + | 0.999044i | \(0.513921\pi\) | |||||||
\(212\) | − 10370.0i | − 3.35950i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3300.00 | −1.05413 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 3240.00i | − 1.01357i | ||||||||
\(218\) | − 8770.00i | − 2.72468i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 200.000 | 0.0608754 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3670.00i | 1.10207i | 0.834482 | + | 0.551034i | \(0.185767\pi\) | ||||
−0.834482 | + | 0.551034i | \(0.814233\pi\) | |||||||
\(224\) | 2550.00 | 0.760621 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1550.00 | −0.456214 | ||||||||
\(227\) | 3760.00i | 1.09938i | 0.835368 | + | 0.549692i | \(0.185255\pi\) | ||||
−0.835368 | + | 0.549692i | \(0.814745\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1434.00 | 0.413805 | 0.206903 | − | 0.978362i | \(-0.433662\pi\) | ||||
0.206903 | + | 0.978362i | \(0.433662\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − 2250.00i | − 0.636723i | ||||||||
\(233\) | 3450.00i | 0.970030i | 0.874506 | + | 0.485015i | \(0.161186\pi\) | ||||
−0.874506 | + | 0.485015i | \(0.838814\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 850.000 | 0.234450 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − 1500.00i | − 0.408532i | ||||||||
\(239\) | 4900.00 | 1.32617 | 0.663085 | − | 0.748544i | \(-0.269247\pi\) | ||||
0.663085 | + | 0.748544i | \(0.269247\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4822.00 | 1.28885 | 0.644424 | − | 0.764668i | \(-0.277097\pi\) | ||||
0.644424 | + | 0.764668i | \(0.277097\pi\) | |||||||
\(242\) | 5845.00i | 1.55261i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 8806.00 | 2.31044 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 880.000i | 0.226693i | ||||||||
\(248\) | − 4860.00i | − 1.24440i | ||||||||
\(249\) | 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 | ||||||||
\(253\) | − 6000.00i | − 1.49098i | ||||||||
\(254\) | 5350.00 | 1.32161 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8279.00 | −2.02124 | ||||||||
\(257\) | 5130.00i | 1.24514i | 0.782565 | + | 0.622569i | \(0.213911\pi\) | ||||
−0.782565 | + | 0.622569i | \(0.786089\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1200.00 | −0.287893 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 9750.00i | 2.29907i | ||||||||
\(263\) | 1280.00i | 0.300107i | 0.988678 | + | 0.150054i | \(0.0479446\pi\) | ||||
−0.988678 | + | 0.150054i | \(0.952055\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 6600.00 | 1.52132 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3060.00i | 0.697460i | ||||||||
\(269\) | −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 | \(-0.288037\pi\) | ||||
0.617768 | + | 0.786361i | \(0.288037\pi\) | |||||||
\(272\) | − 890.000i | − 0.198398i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5250.00 | −1.15753 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4920.00i | 1.06720i | 0.845737 | + | 0.533600i | \(0.179161\pi\) | ||||
−0.845737 | + | 0.533600i | \(0.820839\pi\) | |||||||
\(278\) | − 8380.00i | − 1.80791i | ||||||||
\(279\) | 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 | ||||||||
\(283\) | 6900.00i | 1.44934i | 0.689098 | + | 0.724669i | \(0.258007\pi\) | ||||
−0.689098 | + | 0.724669i | \(0.741993\pi\) | |||||||
\(284\) | −11900.0 | −2.48639 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5000.00 | −1.03376 | ||||||||
\(287\) | − 12000.0i | − 2.46808i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4813.00 | 0.979646 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − 6970.00i | − 1.39688i | ||||||||
\(293\) | − 1530.00i | − 0.305063i | −0.988299 | − | 0.152532i | \(-0.951257\pi\) | ||||
0.988299 | − | 0.152532i | \(-0.0487426\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1800.00 | −0.353456 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − 10250.0i | − 1.99251i | ||||||||
\(299\) | 2400.00 | 0.464199 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8400.00 | −1.60853 | ||||||||
\(302\) | 2240.00i | 0.426813i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3916.00 | 0.738809 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3040.00i | 0.565153i | 0.959245 | + | 0.282576i | \(0.0911891\pi\) | ||||
−0.959245 | + | 0.282576i | \(0.908811\pi\) | |||||||
\(308\) | 25500.0i | 4.71752i | ||||||||
\(309\) | 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 | ||||||||
\(313\) | − 3110.00i | − 0.561622i | −0.959763 | − | 0.280811i | \(-0.909397\pi\) | ||||
0.959763 | − | 0.280811i | \(-0.0906034\pi\) | |||||||
\(314\) | 500.000 | 0.0898619 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8772.00 | −1.56159 | ||||||||
\(317\) | − 950.000i | − 0.168320i | −0.996452 | − | 0.0841598i | \(-0.973179\pi\) | ||||
0.996452 | − | 0.0841598i | \(-0.0268206\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2500.00 | 0.438787 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − 18000.0i | − 3.11522i | ||||||||
\(323\) | − 440.000i | − 0.0757965i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −9500.00 | −1.61398 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − 18000.0i | − 3.03013i | ||||||||
\(329\) | −8400.00 | −1.40762 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2292.00 | 0.380603 | 0.190302 | − | 0.981726i | \(-0.439053\pi\) | ||||
0.190302 | + | 0.981726i | \(0.439053\pi\) | |||||||
\(332\) | 11220.0i | 1.85475i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −9600.00 | −1.57272 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 7730.00i | − 1.24950i | −0.780827 | − | 0.624748i | \(-0.785202\pi\) | ||||
0.780827 | − | 0.624748i | \(-0.214798\pi\) | |||||||
\(338\) | 8985.00i | 1.44592i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5400.00 | 0.857555 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6420.00i | 1.01063i | ||||||||
\(344\) | −12600.0 | −1.97484 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 12750.0 | 1.98105 | ||||||||
\(347\) | − 1120.00i | − 0.173270i | −0.996240 | − | 0.0866351i | \(-0.972389\pi\) | ||||
0.996240 | − | 0.0866351i | \(-0.0276114\pi\) | |||||||
\(348\) | 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 | ||||||||
\(352\) | 4250.00i | 0.643539i | ||||||||
\(353\) | − 3630.00i | − 0.547324i | −0.961826 | − | 0.273662i | \(-0.911765\pi\) | ||||
0.961826 | − | 0.273662i | \(-0.0882350\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −25500.0 | −3.79634 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − 18250.0i | − 2.69425i | ||||||||
\(359\) | 1800.00 | 0.264625 | 0.132312 | − | 0.991208i | \(-0.457760\pi\) | ||||
0.132312 | + | 0.991208i | \(0.457760\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4923.00 | −0.717743 | ||||||||
\(362\) | − 21710.0i | − 3.15208i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −10200.0 | −1.46875 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8490.00i | 1.20756i | 0.797151 | + | 0.603780i | \(0.206339\pi\) | ||||
−0.797151 | + | 0.603780i | \(0.793661\pi\) | |||||||
\(368\) | − 10680.0i | − 1.51286i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 18300.0 | 2.56089 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 100.000i | − 0.0138815i | −0.999976 | − | 0.00694076i | \(-0.997791\pi\) | ||||
0.999976 | − | 0.00694076i | \(-0.00220933\pi\) | |||||||
\(374\) | 2500.00 | 0.345647 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −12600.0 | −1.72818 | ||||||||
\(377\) | 1000.00i | 0.136612i | ||||||||
\(378\) | 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 | ||||||||
\(382\) | − 17500.0i | − 2.34392i | ||||||||
\(383\) | 9480.00i | 1.26477i | 0.774656 | + | 0.632383i | \(0.217923\pi\) | ||||
−0.774656 | + | 0.632383i | \(0.782077\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 16750.0 | 2.20869 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 27710.0i | 3.62568i | ||||||||
\(389\) | 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 | ||||||||
\(392\) | 25065.0i | 3.22952i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −450.000 | −0.0575398 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13840.0i | 1.74965i | 0.484442 | + | 0.874823i | \(0.339023\pi\) | ||||
−0.484442 | + | 0.874823i | \(0.660977\pi\) | |||||||
\(398\) | − 18320.0i | − 2.30728i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9300.00 | 1.15815 | 0.579077 | − | 0.815273i | \(-0.303413\pi\) | ||||
0.579077 | + | 0.815273i | \(0.303413\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2160.00i | 0.266991i | ||||||||
\(404\) | 7650.00 | 0.942083 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7500.00 | 0.916795 | ||||||||
\(407\) | − 2000.00i | − 0.243578i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2854.00 | 0.345040 | 0.172520 | − | 0.985006i | \(-0.444809\pi\) | ||||
0.172520 | + | 0.985006i | \(0.444809\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 13090.0i | 1.56529i | ||||||||
\(413\) | 1500.00i | 0.178717i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1700.00 | −0.200359 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 11000.0i | 1.28715i | ||||||||
\(419\) | −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 | \(0.723594\pi\) | |||||||
\(422\) | − 1340.00i | − 0.154574i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 27450.0 | 3.14408 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 15540.0i | 1.76120i | ||||||||
\(428\) | − 11220.0i | − 1.26715i | ||||||||
\(429\) | 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 | ||||||||
\(433\) | − 1510.00i | − 0.167589i | −0.996483 | − | 0.0837944i | \(-0.973296\pi\) | ||||
0.996483 | − | 0.0837944i | \(-0.0267039\pi\) | |||||||
\(434\) | 16200.0 | 1.79176 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 29818.0 | 3.27528 | ||||||||
\(437\) | − 5280.00i | − 0.577979i | ||||||||
\(438\) | 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 | ||||||||
\(442\) | 1000.00i | 0.107613i | ||||||||
\(443\) | − 12360.0i | − 1.32560i | −0.748796 | − | 0.662801i | \(-0.769368\pi\) | ||||
0.748796 | − | 0.662801i | \(-0.230632\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −18350.0 | −1.94820 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − 8610.00i | − 0.908001i | ||||||||
\(449\) | 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 | ||||||||
\(452\) | − 5270.00i | − 0.548407i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −18800.0 | −1.94345 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 7190.00i | − 0.735961i | −0.929834 | − | 0.367980i | \(-0.880049\pi\) | ||||
0.929834 | − | 0.367980i | \(-0.119951\pi\) | |||||||
\(458\) | 7170.00i | 0.731511i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −150.000 | −0.0151544 | −0.00757722 | − | 0.999971i | \(-0.502412\pi\) | ||||
−0.00757722 | + | 0.999971i | \(0.502412\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 2670.00i | − 0.268003i | −0.990981 | − | 0.134002i | \(-0.957217\pi\) | ||||
0.990981 | − | 0.134002i | \(-0.0427827\pi\) | |||||||
\(464\) | 4450.00 | 0.445229 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −17250.0 | −1.71479 | ||||||||
\(467\) | 1180.00i | 0.116925i | 0.998290 | + | 0.0584624i | \(0.0186198\pi\) | ||||
−0.998290 | + | 0.0584624i | \(0.981380\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5400.00 | −0.531661 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2250.00i | 0.219417i | ||||||||
\(473\) | − 14000.0i | − 1.36093i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 5100.00 | 0.491088 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 24500.0i | 2.34436i | ||||||||
\(479\) | 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 | ||||||||
\(482\) | 24110.0i | 2.27838i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −19873.0 | −1.86636 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 9850.00i | − 0.916522i | −0.888818 | − | 0.458261i | \(-0.848473\pi\) | ||||
0.888818 | − | 0.458261i | \(-0.151527\pi\) | |||||||
\(488\) | 23310.0i | 2.16228i | ||||||||
\(489\) | 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 | ||||||||
\(493\) | − 500.000i | − 0.0456772i | ||||||||
\(494\) | −4400.00 | −0.400740 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9612.00 | 0.870144 | ||||||||
\(497\) | − 21000.0i | − 1.89533i | ||||||||
\(498\) | 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 | ||||||||
\(502\) | − 23250.0i | − 2.06713i | ||||||||
\(503\) | 20600.0i | 1.82606i | 0.407891 | + | 0.913030i | \(0.366264\pi\) | ||||
−0.407891 | + | 0.913030i | \(0.633736\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 30000.0 | 2.63570 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 18190.0i | 1.58868i | ||||||||
\(509\) | −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 | ||||||||
\(512\) | − 24475.0i | − 2.11260i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −25650.0 | −2.20111 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 14000.0i | − 1.19095i | ||||||||
\(518\) | − 6000.00i | − 0.508928i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15500.0 | −1.30339 | −0.651696 | − | 0.758480i | \(-0.725942\pi\) | ||||
−0.651696 | + | 0.758480i | \(0.725942\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13940.0i | 1.16549i | 0.812653 | + | 0.582747i | \(0.198022\pi\) | ||||
−0.812653 | + | 0.582747i | \(0.801978\pi\) | |||||||
\(524\) | −33150.0 | −2.76367 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6400.00 | −0.530520 | ||||||||
\(527\) | − 1080.00i | − 0.0892705i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2233.00 | −0.183529 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 22440.0i | 1.82875i | ||||||||
\(533\) | 8000.00i | 0.650128i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −8100.00 | −0.652736 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 16750.0i | − 1.34227i | ||||||||
\(539\) | −27850.0 | −2.22557 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20478.0 | −1.62739 | −0.813695 | − | 0.581292i | \(-0.802547\pi\) | ||||
−0.813695 | + | 0.581292i | \(0.802547\pi\) | |||||||
\(542\) | 27560.0i | 2.18414i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 850.000 | 0.0669916 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12040.0i | 0.941121i | 0.882368 | + | 0.470561i | \(0.155948\pi\) | ||||
−0.882368 | + | 0.470561i | \(0.844052\pi\) | |||||||
\(548\) | − 17850.0i | − 1.39145i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2200.00 | 0.170096 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 15480.0i | − 1.19037i | ||||||||
\(554\) | −24600.0 | −1.88656 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 28492.0 | 2.17326 | ||||||||
\(557\) | 23550.0i | 1.79146i | 0.444594 | + | 0.895732i | \(0.353348\pi\) | ||||
−0.444594 | + | 0.895732i | \(0.646652\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5600.00 | 0.423712 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 22500.0i | 1.68880i | ||||||||
\(563\) | 6120.00i | 0.458130i | 0.973411 | + | 0.229065i | \(0.0735669\pi\) | ||||
−0.973411 | + | 0.229065i | \(0.926433\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −34500.0 | −2.56209 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − 31500.0i | − 2.32696i | ||||||||
\(569\) | 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 | \(-0.597003\pi\) | ||||
−0.300050 | + | 0.953923i | \(0.597003\pi\) | |||||||
\(572\) | − 17000.0i | − 1.24267i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 60000.0 | 4.36298 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11690.0i | 0.843433i | 0.906728 | + | 0.421717i | \(0.138572\pi\) | ||||
−0.906728 | + | 0.421717i | \(0.861428\pi\) | |||||||
\(578\) | 24065.0i | 1.73179i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −19800.0 | −1.41384 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 30500.0i | 2.16669i | ||||||||
\(584\) | 18450.0 | 1.30731 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7650.00 | 0.539281 | ||||||||
\(587\) | 21060.0i | 1.48082i | 0.672157 | + | 0.740408i | \(0.265368\pi\) | ||||
−0.672157 | + | 0.740408i | \(0.734632\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4752.00 | 0.332433 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − 3560.00i | − 0.247154i | ||||||||
\(593\) | 22910.0i | 1.58651i | 0.608889 | + | 0.793255i | \(0.291615\pi\) | ||||
−0.608889 | + | 0.793255i | \(0.708385\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 34850.0 | 2.39515 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 12000.0i | 0.820596i | ||||||||
\(599\) | 1400.00 | 0.0954966 | 0.0477483 | − | 0.998859i | \(-0.484795\pi\) | ||||
0.0477483 | + | 0.998859i | \(0.484795\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11002.0 | −0.746724 | −0.373362 | − | 0.927686i | \(-0.621795\pi\) | ||||
−0.373362 | + | 0.927686i | \(0.621795\pi\) | |||||||
\(602\) | − 42000.0i | − 2.84351i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −7616.00 | −0.513064 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4630.00i | 0.309598i | 0.987946 | + | 0.154799i | \(0.0494730\pi\) | ||||
−0.987946 | + | 0.154799i | \(0.950527\pi\) | |||||||
\(608\) | 3740.00i | 0.249469i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5600.00 | 0.370788 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 24040.0i | − 1.58396i | −0.610548 | − | 0.791979i | \(-0.709051\pi\) | ||||
0.610548 | − | 0.791979i | \(-0.290949\pi\) | |||||||
\(614\) | −15200.0 | −0.999059 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −67500.0 | −4.41502 | ||||||||
\(617\) | − 1890.00i | − 0.123320i | −0.998097 | − | 0.0616601i | \(-0.980361\pi\) | ||||
0.998097 | − | 0.0616601i | \(-0.0196395\pi\) | |||||||
\(618\) | 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 | ||||||||
\(622\) | − 28500.0i | − 1.83721i | ||||||||
\(623\) | − 45000.0i | − 2.89388i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 15550.0 | 0.992816 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1700.00i | 0.108021i | ||||||||
\(629\) | −400.000 | −0.0253562 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15892.0 | 1.00262 | 0.501308 | − | 0.865269i | \(-0.332852\pi\) | ||||
0.501308 | + | 0.865269i | \(0.332852\pi\) | |||||||
\(632\) | − 23220.0i | − 1.46146i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 4750.00 | 0.297550 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 11140.0i | − 0.692909i | ||||||||
\(638\) | 12500.0i | 0.775674i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12600.0 | −0.776396 | −0.388198 | − | 0.921576i | \(-0.626902\pi\) | ||||
−0.388198 | + | 0.921576i | \(0.626902\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 7260.00i | − 0.445267i | −0.974902 | − | 0.222633i | \(-0.928535\pi\) | ||||
0.974902 | − | 0.222633i | \(-0.0714653\pi\) | |||||||
\(644\) | 61200.0 | 3.74475 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2200.00 | 0.133990 | ||||||||
\(647\) | 7400.00i | 0.449651i | 0.974399 | + | 0.224825i | \(0.0721812\pi\) | ||||
−0.974399 | + | 0.224825i | \(0.927819\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2500.00 | −0.151207 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − 32300.0i | − 1.94013i | ||||||||
\(653\) | 4790.00i | 0.287055i | 0.989646 | + | 0.143528i | \(0.0458446\pi\) | ||||
−0.989646 | + | 0.143528i | \(0.954155\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 35600.0 | 2.11882 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − 42000.0i | − 2.48834i | ||||||||
\(659\) | 1450.00 | 0.0857117 | 0.0428558 | − | 0.999081i | \(-0.486354\pi\) | ||||
0.0428558 | + | 0.999081i | \(0.486354\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11818.0 | 0.695411 | 0.347706 | − | 0.937604i | \(-0.386961\pi\) | ||||
0.347706 | + | 0.937604i | \(0.386961\pi\) | |||||||
\(662\) | 11460.0i | 0.672818i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −29700.0 | −1.73582 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 6000.00i | − 0.348307i | ||||||||
\(668\) | − 32640.0i | − 1.89054i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −25900.0 | −1.49010 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 5550.00i | − 0.317885i | −0.987288 | − | 0.158943i | \(-0.949192\pi\) | ||||
0.987288 | − | 0.158943i | \(-0.0508085\pi\) | |||||||
\(674\) | 38650.0 | 2.20882 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −30549.0 | −1.73811 | ||||||||
\(677\) | 12930.0i | 0.734033i | 0.930214 | + | 0.367016i | \(0.119621\pi\) | ||||
−0.930214 | + | 0.367016i | \(0.880379\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −48900.0 | −2.76378 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 27000.0i | 1.51596i | ||||||||
\(683\) | − 32580.0i | − 1.82524i | −0.408809 | − | 0.912620i | \(-0.634056\pi\) | ||||
0.408809 | − | 0.912620i | \(-0.365944\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −32100.0 | −1.78657 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − 24920.0i | − 1.38091i | ||||||||
\(689\) | −12200.0 | −0.674576 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10228.0 | 0.563085 | 0.281542 | − | 0.959549i | \(-0.409154\pi\) | ||||
0.281542 | + | 0.959549i | \(0.409154\pi\) | |||||||
\(692\) | 43350.0i | 2.38139i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5600.00 | 0.306301 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 4000.00i | − 0.217376i | ||||||||
\(698\) | − 5930.00i | − 0.321567i | ||||||||
\(699\) | 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 | ||||||||
\(703\) | − 1760.00i | − 0.0944234i | ||||||||
\(704\) | 14350.0 | 0.768233 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 18150.0 | 0.967541 | ||||||||
\(707\) | 13500.0i | 0.718133i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14954.0 | 0.792115 | 0.396057 | − | 0.918226i | \(-0.370378\pi\) | ||||
0.396057 | + | 0.918226i | \(0.370378\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 67500.0i | − 3.55291i | ||||||||
\(713\) | − 12960.0i | − 0.680723i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 62050.0 | 3.23871 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 9000.00i | 0.467795i | ||||||||
\(719\) | −29400.0 | −1.52494 | −0.762472 | − | 0.647021i | \(-0.776015\pi\) | ||||
−0.762472 | + | 0.647021i | \(0.776015\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −23100.0 | −1.19319 | ||||||||
\(722\) | − 24615.0i | − 1.26880i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 73814.0 | 3.78905 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 16330.0i | − 0.833076i | −0.909118 | − | 0.416538i | \(-0.863243\pi\) | ||||
0.909118 | − | 0.416538i | \(-0.136757\pi\) | |||||||
\(728\) | − 27000.0i | − 1.37457i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2800.00 | −0.141671 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 30800.0i | − 1.55201i | −0.630726 | − | 0.776005i | \(-0.717243\pi\) | ||||
0.630726 | − | 0.776005i | \(-0.282757\pi\) | |||||||
\(734\) | −42450.0 | −2.13468 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 10200.0 | 0.510838 | ||||||||
\(737\) | − 9000.00i | − 0.449823i | ||||||||
\(738\) | 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 | ||||||||
\(742\) | 91500.0i | 4.52705i | ||||||||
\(743\) | 28600.0i | 1.41216i | 0.708134 | + | 0.706078i | \(0.249537\pi\) | ||||
−0.708134 | + | 0.706078i | \(0.750463\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 500.000 | 0.0245393 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 8500.00i | 0.415496i | ||||||||
\(749\) | 19800.0 | 0.965923 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8252.00 | −0.400958 | −0.200479 | − | 0.979698i | \(-0.564250\pi\) | ||||
−0.200479 | + | 0.979698i | \(0.564250\pi\) | |||||||
\(752\) | − 24920.0i | − 1.20843i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −5000.00 | −0.241498 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 24920.0i | − 1.19648i | −0.801318 | − | 0.598238i | \(-0.795868\pi\) | ||||
0.801318 | − | 0.598238i | \(-0.204132\pi\) | |||||||
\(758\) | 40420.0i | 1.93683i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 27900.0 | 1.32901 | 0.664503 | − | 0.747285i | \(-0.268643\pi\) | ||||
0.664503 | + | 0.747285i | \(0.268643\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 52620.0i | 2.49669i | ||||||||
\(764\) | 59500.0 | 2.81758 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −47400.0 | −2.23581 | ||||||||
\(767\) | − 1000.00i | − 0.0470768i | ||||||||
\(768\) | 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 | ||||||||
\(772\) | 56950.0i | 2.65502i | ||||||||
\(773\) | 12510.0i | 0.582087i | 0.956710 | + | 0.291044i | \(0.0940025\pi\) | ||||
−0.956710 | + | 0.291044i | \(0.905998\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −73350.0 | −3.39318 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 54750.0i | 2.52299i | ||||||||
\(779\) | 17600.0 | 0.809481 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 35000.0 | 1.60358 | ||||||||
\(782\) | − 6000.00i | − 0.274373i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −49573.0 | −2.25825 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 1100.00i | − 0.0498231i | −0.999690 | − | 0.0249115i | \(-0.992070\pi\) | ||||
0.999690 | − | 0.0249115i | \(-0.00793041\pi\) | |||||||
\(788\) | − 1530.00i | − 0.0691675i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9300.00 | 0.418040 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 10360.0i | − 0.463927i | ||||||||
\(794\) | −69200.0 | −3.09297 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 62288.0 | 2.77354 | ||||||||
\(797\) | − 4490.00i | − 0.199553i | −0.995010 | − | 0.0997766i | \(-0.968187\pi\) | ||||
0.995010 | − | 0.0997766i | \(-0.0318128\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2800.00 | −0.123976 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 46500.0i | 2.04735i | ||||||||
\(803\) | 20500.0i | 0.900908i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −10800.0 | −0.471977 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 20250.0i | 0.881674i | ||||||||
\(809\) | −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 | \(-0.430059\pi\) | ||||
0.217963 | + | 0.975957i | \(0.430059\pi\) | |||||||
\(812\) | 25500.0i | 1.10206i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 10000.0 | 0.430589 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 12320.0i | − 0.527567i | ||||||||
\(818\) | 14270.0i | 0.609950i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −14250.0 | −0.605759 | −0.302880 | − | 0.953029i | \(-0.597948\pi\) | ||||
−0.302880 | + | 0.953029i | \(0.597948\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 6830.00i | − 0.289282i | −0.989484 | − | 0.144641i | \(-0.953797\pi\) | ||||
0.989484 | − | 0.144641i | \(-0.0462027\pi\) | |||||||
\(824\) | −34650.0 | −1.46491 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7500.00 | −0.315930 | ||||||||
\(827\) | − 8920.00i | − 0.375065i | −0.982258 | − | 0.187533i | \(-0.939951\pi\) | ||||
0.982258 | − | 0.187533i | \(-0.0600490\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3534.00 | 0.148059 | 0.0740295 | − | 0.997256i | \(-0.476414\pi\) | ||||
0.0740295 | + | 0.997256i | \(0.476414\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5740.00i | 0.239181i | ||||||||
\(833\) | 5570.00i | 0.231680i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −37400.0 | −1.54726 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − 5750.00i | − 0.237029i | ||||||||
\(839\) | 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 | ||||||||
\(842\) | − 55810.0i | − 2.28425i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4556.00 | 0.185810 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 35070.0i | − 1.42269i | ||||||||
\(848\) | 54290.0i | 2.19850i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4800.00 | −0.193351 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 5160.00i | − 0.207122i | −0.994623 | − | 0.103561i | \(-0.966976\pi\) | ||||
0.994623 | − | 0.103561i | \(-0.0330237\pi\) | |||||||
\(854\) | −77700.0 | −3.11339 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 29700.0 | 1.18589 | ||||||||
\(857\) | 7670.00i | 0.305720i | 0.988248 | + | 0.152860i | \(0.0488484\pi\) | ||||
−0.988248 | + | 0.152860i | \(0.951152\pi\) | |||||||
\(858\) | 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 | ||||||||
\(862\) | − 6000.00i | − 0.237078i | ||||||||
\(863\) | − 400.000i | − 0.0157777i | −0.999969 | − | 0.00788885i | \(-0.997489\pi\) | ||||
0.999969 | − | 0.00788885i | \(-0.00251113\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 7550.00 | 0.296258 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 55080.0i | 2.15384i | ||||||||
\(869\) | 25800.0 | 1.00714 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3600.00 | 0.140047 | ||||||||
\(872\) | 78930.0i | 3.06526i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 26400.0 | 1.02173 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 35100.0i | − 1.35147i | −0.737143 | − | 0.675737i | \(-0.763825\pi\) | ||||
0.737143 | − | 0.675737i | \(-0.236175\pi\) | |||||||
\(878\) | − 2120.00i | − 0.0814881i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18700.0 | −0.715118 | −0.357559 | − | 0.933891i | \(-0.616391\pi\) | ||||
−0.357559 | + | 0.933891i | \(0.616391\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2980.00i | 0.113573i | 0.998386 | + | 0.0567865i | \(0.0180854\pi\) | ||||
−0.998386 | + | 0.0567865i | \(0.981915\pi\) | |||||||
\(884\) | −3400.00 | −0.129360 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 61800.0 | 2.34335 | ||||||||
\(887\) | − 35880.0i | − 1.35821i | −0.734041 | − | 0.679105i | \(-0.762368\pi\) | ||||
0.734041 | − | 0.679105i | \(-0.237632\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −32100.0 | −1.21102 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − 62390.0i | − 2.34190i | ||||||||
\(893\) | − 12320.0i | − 0.461672i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 63450.0 | 2.36575 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 6500.00i | 0.241545i | ||||||||
\(899\) | 5400.00 | 0.200334 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6100.00 | 0.225550 | ||||||||
\(902\) | 100000.i | 3.69139i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 13950.0 | 0.513241 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 45240.0i | 1.65620i | 0.560584 | + | 0.828098i | \(0.310577\pi\) | ||||
−0.560584 | + | 0.828098i | \(0.689423\pi\) | |||||||
\(908\) | − 63920.0i | − 2.33619i | ||||||||
\(909\) | 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 | ||||||||
\(913\) | − 33000.0i | − 1.19621i | ||||||||
\(914\) | 35950.0 | 1.30101 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −24378.0 | −0.879336 | ||||||||
\(917\) | − 58500.0i | − 2.10670i | ||||||||
\(918\) | 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 | ||||||||
\(922\) | − 750.000i | − 0.0267895i | ||||||||
\(923\) | 14000.0i | 0.499259i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 13350.0 | 0.473767 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4250.00i | 0.150337i | ||||||||
\(929\) | 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 | ||||||||
\(932\) | − 58650.0i | − 2.06131i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −5900.00 | −0.206696 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 52890.0i | 1.84401i | 0.387173 | + | 0.922007i | \(0.373451\pi\) | ||||
−0.387173 | + | 0.922007i | \(0.626549\pi\) | |||||||
\(938\) | − 27000.0i | − 0.939852i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 38050.0 | 1.31817 | 0.659083 | − | 0.752070i | \(-0.270945\pi\) | ||||
0.659083 | + | 0.752070i | \(0.270945\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 48000.0i | − 1.65758i | ||||||||
\(944\) | −4450.00 | −0.153427 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 70000.0 | 2.40581 | ||||||||
\(947\) | − 29640.0i | − 1.01708i | −0.861040 | − | 0.508538i | \(-0.830186\pi\) | ||||
0.861040 | − | 0.508538i | \(-0.169814\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8200.00 | −0.280488 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 13500.0i | 0.459598i | ||||||||
\(953\) | − 15170.0i | − 0.515640i | −0.966193 | − | 0.257820i | \(-0.916996\pi\) | ||||
0.966193 | − | 0.257820i | \(-0.0830041\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −83300.0 | −2.81811 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 70500.0i | 2.37761i | ||||||||
\(959\) | 31500.0 | 1.06068 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −18127.0 | −0.608472 | ||||||||
\(962\) | 4000.00i | 0.134059i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −81974.0 | −2.73880 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 5470.00i | − 0.181906i | −0.995855 | − | 0.0909531i | \(-0.971009\pi\) | ||||
0.995855 | − | 0.0909531i | \(-0.0289913\pi\) | |||||||
\(968\) | − 52605.0i | − 1.74668i | ||||||||
\(969\) | 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 | ||||||||
\(973\) | 50280.0i | 1.65663i | ||||||||
\(974\) | 49250.0 | 1.62020 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −46102.0 | −1.51198 | ||||||||
\(977\) | 31190.0i | 1.02135i | 0.859775 | + | 0.510674i | \(0.170604\pi\) | ||||
−0.859775 | + | 0.510674i | \(0.829396\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 75000.0 | 2.44843 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − 12250.0i | − 0.398079i | ||||||||
\(983\) | 7560.00i | 0.245297i | 0.992450 | + | 0.122648i | \(0.0391387\pi\) | ||||
−0.992450 | + | 0.122648i | \(0.960861\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 2500.00 | 0.0807467 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − 14960.0i | − 0.481722i | ||||||||
\(989\) | −33600.0 | −1.08030 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 32672.0 | 1.04729 | 0.523643 | − | 0.851938i | \(-0.324573\pi\) | ||||
0.523643 | + | 0.851938i | \(0.324573\pi\) | |||||||
\(992\) | 9180.00i | 0.293816i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 105000. | 3.35050 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 4740.00i | − 0.150569i | −0.997162 | − | 0.0752845i | \(-0.976014\pi\) | ||||
0.997162 | − | 0.0752845i | \(-0.0239865\pi\) | |||||||
\(998\) | 85180.0i | 2.70173i | ||||||||
\(999\) | 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 | 225.4.b.b.199.2 | 2 | ||
3.2 | odd | 2 | 225.4.b.a.199.1 | 2 | |||
5.2 | odd | 4 | 225.4.a.a.1.1 | 1 | |||
5.3 | odd | 4 | 45.4.a.e.1.1 | yes | 1 | ||
5.4 | even | 2 | inner | 225.4.b.b.199.1 | 2 | ||
15.2 | even | 4 | 225.4.a.h.1.1 | 1 | |||
15.8 | even | 4 | 45.4.a.a.1.1 | ✓ | 1 | ||
15.14 | odd | 2 | 225.4.b.a.199.2 | 2 | |||
20.3 | even | 4 | 720.4.a.o.1.1 | 1 | |||
35.13 | even | 4 | 2205.4.a.t.1.1 | 1 | |||
45.13 | odd | 12 | 405.4.e.b.136.1 | 2 | |||
45.23 | even | 12 | 405.4.e.n.136.1 | 2 | |||
45.38 | even | 12 | 405.4.e.n.271.1 | 2 | |||
45.43 | odd | 12 | 405.4.e.b.271.1 | 2 | |||
60.23 | odd | 4 | 720.4.a.bc.1.1 | 1 | |||
105.83 | odd | 4 | 2205.4.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.4.a.a.1.1 | ✓ | 1 | 15.8 | even | 4 | ||
45.4.a.e.1.1 | yes | 1 | 5.3 | odd | 4 | ||
225.4.a.a.1.1 | 1 | 5.2 | odd | 4 | |||
225.4.a.h.1.1 | 1 | 15.2 | even | 4 | |||
225.4.b.a.199.1 | 2 | 3.2 | odd | 2 | |||
225.4.b.a.199.2 | 2 | 15.14 | odd | 2 | |||
225.4.b.b.199.1 | 2 | 5.4 | even | 2 | inner | ||
225.4.b.b.199.2 | 2 | 1.1 | even | 1 | trivial | ||
405.4.e.b.136.1 | 2 | 45.13 | odd | 12 | |||
405.4.e.b.271.1 | 2 | 45.43 | odd | 12 | |||
405.4.e.n.136.1 | 2 | 45.23 | even | 12 | |||
405.4.e.n.271.1 | 2 | 45.38 | even | 12 | |||
720.4.a.o.1.1 | 1 | 20.3 | even | 4 | |||
720.4.a.bc.1.1 | 1 | 60.23 | odd | 4 | |||
2205.4.a.a.1.1 | 1 | 105.83 | odd | 4 | |||
2205.4.a.t.1.1 | 1 | 35.13 | even | 4 |