Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [256,4,Mod(129,256)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(256, 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("256.129");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 256 = 2^{8} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 256.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: | \(15.1044889615\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 128) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 129.2 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 256.129 |
Dual form | 256.4.b.b.129.1 |
$q$-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 \(\left(\mathbb{Z}/256\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(255\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.00000i | 0.384900i | 0.981307 | + | 0.192450i | \(0.0616434\pi\) | ||||
−0.981307 | + | 0.192450i | \(0.938357\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 6.00000i | − 0.536656i | −0.963328 | − | 0.268328i | \(-0.913529\pi\) | ||||
0.963328 | − | 0.268328i | \(-0.0864711\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −20.0000 | −1.07990 | −0.539949 | − | 0.841698i | \(-0.681557\pi\) | ||||
−0.539949 | + | 0.841698i | \(0.681557\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 23.0000 | 0.851852 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 14.0000i | − 0.383742i | −0.981420 | − | 0.191871i | \(-0.938545\pi\) | ||||
0.981420 | − | 0.191871i | \(-0.0614555\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 54.0000i | 1.15207i | 0.817425 | + | 0.576035i | \(0.195401\pi\) | ||||
−0.817425 | + | 0.576035i | \(0.804599\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 12.0000 | 0.206559 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −66.0000 | −0.941609 | −0.470804 | − | 0.882238i | \(-0.656036\pi\) | ||||
−0.470804 | + | 0.882238i | \(0.656036\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 162.000i | 1.95607i | 0.208438 | + | 0.978035i | \(0.433162\pi\) | ||||
−0.208438 | + | 0.978035i | \(0.566838\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 40.0000i | − 0.415653i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −172.000 | −1.55933 | −0.779663 | − | 0.626200i | \(-0.784609\pi\) | ||||
−0.779663 | + | 0.626200i | \(0.784609\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 89.0000 | 0.712000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 100.000i | 0.712778i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 2.00000i | − 0.0128066i | −0.999979 | − | 0.00640329i | \(-0.997962\pi\) | ||||
0.999979 | − | 0.00640329i | \(-0.00203824\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −128.000 | −0.741596 | −0.370798 | − | 0.928714i | \(-0.620916\pi\) | ||||
−0.370798 | + | 0.928714i | \(0.620916\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 28.0000 | 0.147702 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 120.000i | 0.579534i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 158.000i | − 0.702028i | −0.936370 | − | 0.351014i | \(-0.885837\pi\) | ||||
0.936370 | − | 0.351014i | \(-0.114163\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −108.000 | −0.443432 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −202.000 | −0.769441 | −0.384721 | − | 0.923033i | \(-0.625702\pi\) | ||||
−0.384721 | + | 0.923033i | \(0.625702\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 298.000i | 1.05685i | 0.848980 | + | 0.528425i | \(0.177217\pi\) | ||||
−0.848980 | + | 0.528425i | \(0.822783\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 138.000i | − 0.457152i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −408.000 | −1.26623 | −0.633116 | − | 0.774057i | \(-0.718224\pi\) | ||||
−0.633116 | + | 0.774057i | \(0.718224\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 57.0000 | 0.166181 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 132.000i | − 0.362425i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 690.000i | 1.78828i | 0.447788 | + | 0.894140i | \(0.352212\pi\) | ||||
−0.447788 | + | 0.894140i | \(0.647788\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −84.0000 | −0.205937 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −324.000 | −0.752892 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 322.000i | 0.710523i | 0.934767 | + | 0.355261i | \(0.115608\pi\) | ||||
−0.934767 | + | 0.355261i | \(0.884392\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 298.000i | − 0.625492i | −0.949837 | − | 0.312746i | \(-0.898751\pi\) | ||||
0.949837 | − | 0.312746i | \(-0.101249\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −460.000 | −0.919914 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 324.000 | 0.618265 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 202.000i | 0.368332i | 0.982895 | + | 0.184166i | \(0.0589584\pi\) | ||||
−0.982895 | + | 0.184166i | \(0.941042\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 344.000i | − 0.600185i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 700.000 | 1.17007 | 0.585033 | − | 0.811009i | \(-0.301081\pi\) | ||||
0.585033 | + | 0.811009i | \(0.301081\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 418.000 | 0.670181 | 0.335090 | − | 0.942186i | \(-0.391233\pi\) | ||||
0.335090 | + | 0.942186i | \(0.391233\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 178.000i | 0.274049i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 280.000i | 0.414402i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 744.000 | 1.05958 | 0.529788 | − | 0.848130i | \(-0.322271\pi\) | ||||
0.529788 | + | 0.848130i | \(0.322271\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 421.000 | 0.577503 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 678.000i | − 0.896629i | −0.893876 | − | 0.448314i | \(-0.852025\pi\) | ||||
0.893876 | − | 0.448314i | \(-0.147975\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 396.000i | 0.505320i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.00000 | 0.00492925 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 82.0000 | 0.0976627 | 0.0488314 | − | 0.998807i | \(-0.484450\pi\) | ||||
0.0488314 | + | 0.998807i | \(0.484450\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 1080.00i | − 1.24412i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 256.000i | − 0.285440i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 972.000 | 1.04974 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1122.00 | −1.17445 | −0.587226 | − | 0.809423i | \(-0.699780\pi\) | ||||
−0.587226 | + | 0.809423i | \(0.699780\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 322.000i | − 0.326891i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 1390.00i | − 1.36941i | −0.728821 | − | 0.684704i | \(-0.759932\pi\) | ||||
0.728821 | − | 0.684704i | \(-0.240068\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −788.000 | −0.753825 | −0.376912 | − | 0.926249i | \(-0.623014\pi\) | ||||
−0.376912 | + | 0.926249i | \(0.623014\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −240.000 | −0.223063 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 1614.00i | − 1.45824i | −0.684388 | − | 0.729118i | \(-0.739930\pi\) | ||||
0.684388 | − | 0.729118i | \(-0.260070\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2014.00i | 1.76978i | 0.465798 | + | 0.884891i | \(0.345767\pi\) | ||||
−0.465798 | + | 0.884891i | \(0.654233\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 316.000 | 0.270211 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −542.000 | −0.451213 | −0.225607 | − | 0.974219i | \(-0.572436\pi\) | ||||
−0.225607 | + | 0.974219i | \(0.572436\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1032.00i | 0.836822i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1242.00i | 0.981393i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1320.00 | 1.01684 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1135.00 | 0.852742 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 404.000i | − 0.296158i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 1284.00i | − 0.918756i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1712.00 | 1.19618 | 0.598092 | − | 0.801427i | \(-0.295926\pi\) | ||||
0.598092 | + | 0.801427i | \(0.295926\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −596.000 | −0.406782 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 2118.00i | − 1.41260i | −0.707913 | − | 0.706300i | \(-0.750363\pi\) | ||||
0.707913 | − | 0.706300i | \(-0.249637\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 3240.00i | − 2.11236i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 600.000 | 0.382517 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 486.000 | 0.303079 | 0.151539 | − | 0.988451i | \(-0.451577\pi\) | ||||
0.151539 | + | 0.988451i | \(0.451577\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 1286.00i | − 0.784727i | −0.919810 | − | 0.392364i | \(-0.871657\pi\) | ||||
0.919810 | − | 0.392364i | \(-0.128343\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 816.000i | − 0.487373i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 756.000 | 0.442097 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −12.0000 | −0.00687273 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 114.000i | 0.0639630i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2666.00i | 1.46582i | 0.680325 | + | 0.732910i | \(0.261838\pi\) | ||||
−0.680325 | + | 0.732910i | \(0.738162\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −172.000 | −0.0926964 | −0.0463482 | − | 0.998925i | \(-0.514758\pi\) | ||||
−0.0463482 | + | 0.998925i | \(0.514758\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1518.00 | −0.802111 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 768.000i | 0.397982i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 838.000i | 0.425985i | 0.977054 | + | 0.212993i | \(0.0683210\pi\) | ||||
−0.977054 | + | 0.212993i | \(0.931679\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1380.00 | −0.688309 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3440.00 | 1.68391 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1346.00i | 0.646791i | 0.946264 | + | 0.323395i | \(0.104824\pi\) | ||||
−0.946264 | + | 0.323395i | \(0.895176\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 168.000i | − 0.0792653i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1052.00 | 0.487462 | 0.243731 | − | 0.969843i | \(-0.421629\pi\) | ||||
0.243731 | + | 0.969843i | \(0.421629\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −719.000 | −0.327264 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3726.00i | 1.66628i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 38.0000i | 0.0166999i | 0.999965 | + | 0.00834996i | \(0.00265791\pi\) | ||||
−0.999965 | + | 0.00834996i | \(0.997342\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1780.00 | −0.768888 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −644.000 | −0.273480 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 2790.00i | − 1.16500i | −0.812832 | − | 0.582498i | \(-0.802075\pi\) | ||||
0.812832 | − | 0.582498i | \(-0.197925\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3418.00i | 1.40364i | 0.712357 | + | 0.701818i | \(0.247628\pi\) | ||||
−0.712357 | + | 0.701818i | \(0.752372\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 596.000 | 0.240752 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −948.000 | −0.376748 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 924.000i | 0.361335i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 2000.00i | − 0.769728i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1968.00 | −0.745547 | −0.372774 | − | 0.927922i | \(-0.621593\pi\) | ||||
−0.372774 | + | 0.927922i | \(0.621593\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1058.00 | −0.394593 | −0.197297 | − | 0.980344i | \(-0.563216\pi\) | ||||
−0.197297 | + | 0.980344i | \(0.563216\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 648.000i | 0.237970i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 726.000i | − 0.262565i | −0.991345 | − | 0.131283i | \(-0.958090\pi\) | ||||
0.991345 | − | 0.131283i | \(-0.0419095\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4116.00 | −1.46621 | −0.733104 | − | 0.680116i | \(-0.761929\pi\) | ||||
−0.733104 | + | 0.680116i | \(0.761929\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −404.000 | −0.141771 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 40.0000i | 0.0138298i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1212.00i | 0.412926i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3956.00 | −1.32831 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2268.00 | 0.750626 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1482.00i | 0.483531i | 0.970335 | + | 0.241766i | \(0.0777265\pi\) | ||||
−0.970335 | + | 0.241766i | \(0.922273\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1400.00i | 0.450359i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1788.00 | 0.567166 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2560.00 | 0.800848 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 836.000i | 0.257953i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 3564.00i | − 1.08480i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −896.000 | −0.269061 | −0.134530 | − | 0.990909i | \(-0.542953\pi\) | ||||
−0.134530 | + | 0.990909i | \(0.542953\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2047.00 | 0.606519 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3410.00i | 0.997047i | 0.866876 | + | 0.498523i | \(0.166124\pi\) | ||||
−0.866876 | + | 0.498523i | \(0.833876\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 4502.00i | − 1.29913i | −0.760307 | − | 0.649564i | \(-0.774951\pi\) | ||||
0.760307 | − | 0.649564i | \(-0.225049\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −560.000 | −0.159503 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2302.00 | −0.647249 | −0.323625 | − | 0.946186i | \(-0.604901\pi\) | ||||
−0.323625 | + | 0.946186i | \(0.604901\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2448.00i | 0.679532i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1488.00i | 0.407831i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4024.00 | 1.08908 | 0.544542 | − | 0.838734i | \(-0.316704\pi\) | ||||
0.544542 | + | 0.838734i | \(0.316704\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3586.00 | −0.958484 | −0.479242 | − | 0.877683i | \(-0.659088\pi\) | ||||
−0.479242 | + | 0.877683i | \(0.659088\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3542.00i | 0.935059i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 342.000i | − 0.0891820i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8748.00 | −2.25353 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1356.00 | 0.345112 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1250.00i | 0.314340i | 0.987572 | + | 0.157170i | \(0.0502370\pi\) | ||||
−0.987572 | + | 0.157170i | \(0.949763\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2408.00i | 0.598378i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −792.000 | −0.194498 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6638.00 | −1.61116 | −0.805578 | − | 0.592490i | \(-0.798145\pi\) | ||||
−0.805578 | + | 0.592490i | \(0.798145\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3160.00i | 0.758119i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 46.0000i | − 0.0109093i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1724.00 | 0.404207 | 0.202103 | − | 0.979364i | \(-0.435222\pi\) | ||||
0.202103 | + | 0.979364i | \(0.435222\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4140.00 | 0.959691 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 164.000i | 0.0375904i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4814.00i | 1.09113i | 0.838068 | + | 0.545566i | \(0.183685\pi\) | ||||
−0.838068 | + | 0.545566i | \(0.816315\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1640.00 | −0.367612 | −0.183806 | − | 0.982963i | \(-0.558842\pi\) | ||||
−0.183806 | + | 0.982963i | \(0.558842\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2160.00 | 0.478861 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 1246.00i | − 0.273224i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 3982.00i | − 0.863737i | −0.901937 | − | 0.431869i | \(-0.857854\pi\) | ||||
0.901937 | − | 0.431869i | \(-0.142146\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2944.00 | −0.631730 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4126.00 | −0.875931 | −0.437965 | − | 0.898992i | \(-0.644301\pi\) | ||||
−0.437965 | + | 0.898992i | \(0.644301\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 3446.00i | − 0.723828i | −0.932211 | − | 0.361914i | \(-0.882123\pi\) | ||||
0.932211 | − | 0.361914i | \(-0.117877\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1944.00i | 0.404044i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4040.00 | 0.830919 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −557.000 | −0.113373 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 2244.00i | − 0.452047i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1514.00i | 0.301873i | 0.988543 | + | 0.150937i | \(0.0482289\pi\) | ||||
−0.988543 | + | 0.150937i | \(0.951771\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1932.00 | 0.381306 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1400.00 | 0.273523 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 9288.00i | − 1.79645i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 5960.00i | − 1.14129i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2780.00 | 0.527085 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1788.00 | −0.335674 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5490.00i | 1.02062i | 0.859990 | + | 0.510311i | \(0.170470\pi\) | ||||
−0.859990 | + | 0.510311i | \(0.829530\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 1576.00i | − 0.290147i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5556.00 | 1.01303 | 0.506514 | − | 0.862232i | \(-0.330934\pi\) | ||||
0.506514 | + | 0.862232i | \(0.330934\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2054.00 | 0.370923 | 0.185462 | − | 0.982652i | \(-0.440622\pi\) | ||||
0.185462 | + | 0.982652i | \(0.440622\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2760.00i | 0.493677i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2494.00i | 0.441883i | 0.975287 | + | 0.220942i | \(0.0709130\pi\) | ||||
−0.975287 | + | 0.220942i | \(0.929087\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −28.0000 | −0.00491442 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3228.00 | 0.561275 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 10692.0i | − 1.84185i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4806.00i | 0.820274i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4028.00 | −0.681189 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8160.00 | 1.36740 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2914.00i | 0.483891i | 0.970290 | + | 0.241946i | \(0.0777855\pi\) | ||||
−0.970290 | + | 0.241946i | \(0.922214\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 3634.00i | − 0.598024i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1212.00 | 0.197668 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7186.00 | 1.16156 | 0.580781 | − | 0.814060i | \(-0.302747\pi\) | ||||
0.580781 | + | 0.814060i | \(0.302747\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 1084.00i | − 0.173672i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1792.00i | 0.284581i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5720.00 | 0.900440 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2064.00 | −0.322093 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 4446.00i | − 0.687821i | −0.939002 | − | 0.343910i | \(-0.888248\pi\) | ||||
0.939002 | − | 0.343910i | \(-0.111752\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 430.000i | 0.0659524i | 0.999456 | + | 0.0329762i | \(0.0104985\pi\) | ||||
−0.999456 | + | 0.0329762i | \(0.989501\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5400.00 | −0.821170 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 850.000 | 0.128161 | 0.0640806 | − | 0.997945i | \(-0.479589\pi\) | ||||
0.0640806 | + | 0.997945i | \(0.479589\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 4200.00i | − 0.627924i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2640.00i | 0.391383i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10988.0 | 1.61539 | 0.807694 | − | 0.589602i | \(-0.200715\pi\) | ||||
0.807694 | + | 0.589602i | \(0.200715\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19385.0 | −2.82621 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2270.00i | 0.328221i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 2508.00i | − 0.359657i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 872.000 | 0.124027 | 0.0620137 | − | 0.998075i | \(-0.480248\pi\) | ||||
0.0620137 | + | 0.998075i | \(0.480248\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4646.00 | −0.655450 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 13800.0i | − 1.93116i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 3454.00i | − 0.479467i | −0.970839 | − | 0.239734i | \(-0.922940\pi\) | ||||
0.970839 | − | 0.239734i | \(-0.0770601\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2568.00 | 0.353629 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 108.000 | 0.0147541 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1490.00i | 0.201942i | 0.994889 | + | 0.100971i | \(0.0321950\pi\) | ||||
−0.994889 | + | 0.100971i | \(0.967805\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3424.00i | 0.460412i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10240.0 | 1.36616 | 0.683080 | − | 0.730343i | \(-0.260640\pi\) | ||||
0.683080 | + | 0.730343i | \(0.260640\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1680.00 | 0.222392 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6854.00i | 0.900280i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7458.00i | 0.972071i | 0.873939 | + | 0.486035i | \(0.161557\pi\) | ||||
−0.873939 | + | 0.486035i | \(0.838443\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11352.0 | 1.46827 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4236.00 | 0.543710 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 4464.00i | − 0.568628i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 4706.00i | − 0.594930i | −0.954733 | − | 0.297465i | \(-0.903859\pi\) | ||||
0.954733 | − | 0.297465i | \(-0.0961412\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6480.00 | 0.813047 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5598.00 | 0.697134 | 0.348567 | − | 0.937284i | \(-0.386668\pi\) | ||||
0.348567 | + | 0.937284i | \(0.386668\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 6912.00i | − 0.854370i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 2526.00i | − 0.309921i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2212.00 | −0.269397 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 838.000 | 0.101312 | 0.0506558 | − | 0.998716i | \(-0.483869\pi\) | ||||
0.0506558 | + | 0.998716i | \(0.483869\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 972.000i | 0.116655i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 6440.00i | − 0.767292i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4068.00 | −0.481181 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2572.00 | 0.302042 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 26.0000i | 0.00303146i | 0.999999 | + | 0.00151573i | \(0.000482473\pi\) | ||||
−0.999999 | + | 0.00151573i | \(0.999518\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15578.0i | 1.80339i | 0.432377 | + | 0.901693i | \(0.357675\pi\) | ||||
−0.432377 | + | 0.901693i | \(0.642325\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9384.00 | −1.07864 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5874.00 | −0.670426 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5960.00i | 0.675467i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1512.00i | 0.170163i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6792.00 | −0.759070 | −0.379535 | − | 0.925177i | \(-0.623916\pi\) | ||||
−0.379535 | + | 0.925177i | \(0.623916\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9314.00 | −1.03372 | −0.516862 | − | 0.856069i | \(-0.672900\pi\) | ||||
−0.516862 | + | 0.856069i | \(0.672900\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 24.0000i | − 0.00264531i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 27864.0i | − 3.05015i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3828.00 | 0.416174 | 0.208087 | − | 0.978110i | \(-0.433276\pi\) | ||||
0.208087 | + | 0.978110i | \(0.433276\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1311.00 | 0.141561 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 15414.0i | − 1.65314i | −0.562834 | − | 0.826570i | \(-0.690289\pi\) | ||||
0.562834 | − | 0.826570i | \(-0.309711\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 492.000i | − 0.0524113i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5332.00 | −0.564195 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3650.00 | −0.383640 | −0.191820 | − | 0.981430i | \(-0.561439\pi\) | ||||
−0.191820 | + | 0.981430i | \(0.561439\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2828.00i | 0.295267i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 344.000i | − 0.0356789i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6480.00 | −0.667664 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15862.0 | 1.62362 | 0.811809 | − | 0.583924i | \(-0.198483\pi\) | ||||
0.811809 | + | 0.583924i | \(0.198483\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 6600.00i | − 0.671158i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 78.0000i | 0.00788031i | 0.999992 | + | 0.00394015i | \(0.00125419\pi\) | ||||
−0.999992 | + | 0.00394015i | \(0.998746\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4376.00 | −0.439244 | −0.219622 | − | 0.975585i | \(-0.570482\pi\) | ||||
−0.219622 | + | 0.975585i | \(0.570482\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1536.00 | −0.153183 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13714.0i | 1.35890i | 0.733720 | + | 0.679452i | \(0.237782\pi\) | ||||
−0.733720 | + | 0.679452i | \(0.762218\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 4040.00i | − 0.397761i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1676.00 | −0.163962 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4172.00 | 0.405558 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14418.0i | 1.39272i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 15870.0i | 1.52335i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 19072.0 | 1.81925 | 0.909626 | − | 0.415428i | \(-0.136368\pi\) | ||||
0.909626 | + | 0.415428i | \(0.136368\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8532.00 | 0.808785 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6880.00i | 0.648138i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6732.00i | 0.630277i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −19428.0 | −1.80773 | −0.903867 | − | 0.427813i | \(-0.859284\pi\) | ||||
−0.903867 | + | 0.427813i | \(0.859284\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2692.00 | −0.248950 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2490.00i | 0.228864i | 0.993431 | + | 0.114432i | \(0.0365048\pi\) | ||||
−0.993431 | + | 0.114432i | \(0.963495\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 132.000i | 0.0120588i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1932.00 | −0.175428 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −14000.0 | −1.26355 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2826.00i | 0.253525i | 0.991933 | + | 0.126763i | \(0.0404587\pi\) | ||||
−0.991933 | + | 0.126763i | \(0.959541\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2104.00i | 0.187624i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2268.00 | −0.201044 | −0.100522 | − | 0.994935i | \(-0.532051\pi\) | ||||
−0.100522 | + | 0.994935i | \(0.532051\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8340.00 | −0.734901 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 1438.00i | − 0.125964i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10534.0i | 0.917311i | 0.888614 | + | 0.458656i | \(0.151669\pi\) | ||||
−0.888614 | + | 0.458656i | \(0.848331\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8360.00 | −0.723727 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −16200.0 | −1.39424 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4728.00i | 0.404545i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5712.00i | 0.485906i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −76.0000 | −0.00642780 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9478.00 | 0.797003 | 0.398502 | − | 0.917168i | \(-0.369530\pi\) | ||||
0.398502 | + | 0.917168i | \(0.369530\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5858.00i | 0.489775i | 0.969551 | + | 0.244888i | \(0.0787511\pi\) | ||||
−0.969551 | + | 0.244888i | \(0.921249\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 3560.00i | − 0.295945i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8448.00 | 0.698293 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17417.0 | 1.43150 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7406.00i | 0.605260i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 10908.0i | − 0.886450i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9684.00 | −0.782572 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5580.00 | 0.448407 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 798.000i | − 0.0637705i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1910.00i | 0.151788i | 0.997116 | + | 0.0758940i | \(0.0241811\pi\) | ||||
−0.997116 | + | 0.0758940i | \(0.975819\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6836.00 | −0.540259 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12084.0 | 0.949765 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1754.00i | 0.137104i | 0.997648 | + | 0.0685518i | \(0.0218378\pi\) | ||||
−0.997648 | + | 0.0685518i | \(0.978162\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 6854.00i | − 0.532826i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 324.000 | 0.0250506 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −14880.0 | −1.14424 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 1896.00i | − 0.145010i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2294.00i | 0.174506i | 0.996186 | + | 0.0872531i | \(0.0278089\pi\) | ||||
−0.996186 | + | 0.0872531i | \(0.972191\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −16092.0 | −1.21757 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1848.00 | −0.139078 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 16242.0i | 1.21584i | 0.793998 | + | 0.607921i | \(0.207996\pi\) | ||||
−0.793998 | + | 0.607921i | \(0.792004\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3252.00i | 0.242146i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −8420.00 | −0.623645 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15990.0 | 1.17809 | 0.589047 | − | 0.808099i | \(-0.299503\pi\) | ||||
0.589047 | + | 0.808099i | \(0.299503\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21674.0i | 1.58849i | 0.607597 | + | 0.794246i | \(0.292134\pi\) | ||||
−0.607597 | + | 0.794246i | \(0.707866\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 3936.00i | − 0.286961i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −15308.0 | −1.11024 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12542.0 | −0.904905 | −0.452453 | − | 0.891788i | \(-0.649451\pi\) | ||||
−0.452453 | + | 0.891788i | \(0.649451\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 2116.00i | − 0.151879i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13560.0i | 0.968268i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9660.00 | 0.686237 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 7452.00 | 0.526671 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 18578.0i | 1.30630i | 0.757230 | + | 0.653148i | \(0.226552\pi\) | ||||
−0.757230 | + | 0.653148i | \(0.773448\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 20736.0i | − 1.45061i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1452.00 | 0.101061 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 14514.0 | 1.00509 | 0.502545 | − | 0.864551i | \(-0.332397\pi\) | ||||
0.502545 | + | 0.864551i | \(0.332397\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 7920.00i | − 0.545695i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 8232.00i | − 0.564344i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3460.00 | 0.236013 | 0.118006 | − | 0.993013i | \(-0.462350\pi\) | ||||
0.118006 | + | 0.993013i | \(0.462350\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20686.0 | −1.40399 | −0.701996 | − | 0.712181i | \(-0.747708\pi\) | ||||
−0.701996 | + | 0.712181i | \(0.747708\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4646.00i | 0.313764i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 6810.00i | − 0.457630i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9776.00 | −0.653700 | −0.326850 | − | 0.945076i | \(-0.605987\pi\) | ||||
−0.326850 | + | 0.945076i | \(0.605987\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −80.0000 | −0.00532309 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 22032.0i | − 1.45879i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8794.00i | 0.579423i | 0.957114 | + | 0.289712i | \(0.0935594\pi\) | ||||
−0.957114 | + | 0.289712i | \(0.906441\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2424.00 | −0.158935 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16398.0 | −1.06995 | −0.534975 | − | 0.844868i | \(-0.679679\pi\) | ||||
−0.534975 | + | 0.844868i | \(0.679679\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 21374.0i | − 1.38787i | −0.720036 | − | 0.693937i | \(-0.755875\pi\) | ||||
0.720036 | − | 0.693937i | \(-0.244125\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 17200.0i | − 1.11145i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1640.00 | −0.105466 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3421.00 | 0.218944 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4536.00i | 0.288916i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10428.0i | 0.661036i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18916.0 | 1.19340 | 0.596699 | − | 0.802465i | \(-0.296479\pi\) | ||||
0.596699 | + | 0.802465i | \(0.296479\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2964.00 | −0.186111 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 10272.0i | − 0.641940i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3078.00i | 0.191452i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 16100.0 | 0.996723 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5250.00 | −0.323498 | −0.161749 | − | 0.986832i | \(-0.551714\pi\) | ||||
−0.161749 | + | 0.986832i | \(0.551714\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 4502.00i | − 0.276114i | −0.990424 | − | 0.138057i | \(-0.955914\pi\) | ||||
0.990424 | − | 0.138057i | \(-0.0440858\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3576.00i | 0.218302i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −11076.0 | −0.673018 | −0.336509 | − | 0.941680i | \(-0.609246\pi\) | ||||
−0.336509 | + | 0.941680i | \(0.609246\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4508.00 | 0.272657 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5120.00i | 0.308247i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 30766.0i | 1.84375i | 0.387491 | + | 0.921873i | \(0.373342\pi\) | ||||
−0.387491 | + | 0.921873i | \(0.626658\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12708.0 | −0.758080 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9614.00 | 0.570895 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 20518.0i | − 1.21285i | −0.795141 | − | 0.606425i | \(-0.792603\pi\) | ||||
0.795141 | − | 0.606425i | \(-0.207397\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 70.0000i | − 0.00411904i | −0.999998 | − | 0.00205952i | \(-0.999344\pi\) | ||||
0.999998 | − | 0.00205952i | \(-0.000655566\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 7128.00 | 0.417539 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −19440.0 | −1.13361 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 344.000i | 0.0199696i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 1792.00i | − 0.103562i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4172.00 | −0.240027 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23070.0 | 1.32137 | 0.660686 | − | 0.750663i | \(-0.270266\pi\) | ||||
0.660686 | + | 0.750663i | \(0.270266\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 8900.00i | 0.507498i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 2622.00i | − 0.148850i | −0.997227 | − | 0.0744251i | \(-0.976288\pi\) | ||||
0.997227 | − | 0.0744251i | \(-0.0237122\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 22440.0 | 1.26829 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6820.00 | −0.383764 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 14682.0i | 0.822535i | 0.911515 | + | 0.411267i | \(0.134914\pi\) | ||||
−0.911515 | + | 0.411267i | \(0.865086\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 2916.00i | − 0.162649i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9004.00 | 0.500035 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −37260.0 | −2.06022 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 23270.0i | − 1.28109i | −0.767921 | − | 0.640545i | \(-0.778709\pi\) | ||||
0.767921 | − | 0.640545i | \(-0.221291\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6440.00i | 0.353009i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7716.00 | −0.421129 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13332.0 | 0.724513 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 4604.00i | − 0.249126i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 31530.0i | − 1.69882i | −0.527735 | − | 0.849409i | \(-0.676959\pi\) | ||||
0.527735 | − | 0.849409i | \(-0.323041\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 25596.0 | 1.37322 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4896.00 | −0.261552 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 27800.0i | 1.47882i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 22014.0i | − 1.16608i | −0.812442 | − | 0.583042i | \(-0.801862\pi\) | ||||
0.812442 | − | 0.583042i | \(-0.198138\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 17112.0 | 0.902602 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 22016.0 | 1.15639 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 4536.00i | − 0.237254i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8048.00i | 0.419188i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 19016.0 | 0.986338 | 0.493169 | − | 0.869933i | \(-0.335838\pi\) | ||||
0.493169 | + | 0.869933i | \(0.335838\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15760.0 | 0.814054 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 7172.00i | − 0.368921i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 178.000i | − 0.00911828i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −15996.0 | −0.816037 | −0.408018 | − | 0.912974i | \(-0.633780\pi\) | ||||
−0.408018 | + | 0.912974i | \(0.633780\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4283.00 | 0.217599 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 19668.0i | − 0.995140i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10622.0i | 0.535242i | 0.963524 | + | 0.267621i | \(0.0862375\pi\) | ||||
−0.963524 | + | 0.267621i | \(0.913762\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 684.000 | 0.0343261 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2828.00 | 0.141344 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 8878.00i | − 0.441925i | −0.975282 | − | 0.220962i | \(-0.929080\pi\) | ||||
0.975282 | − | 0.220962i | \(-0.0709198\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 17496.0i | − 0.867384i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21852.0 | 1.07897 | 0.539483 | − | 0.841996i | \(-0.318620\pi\) | ||||
0.539483 | + | 0.841996i | \(0.318620\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15996.0 | 0.786642 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 15594.0i | − 0.763795i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 32280.0i | 1.57475i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 32024.0 | 1.55602 | 0.778011 | − | 0.628251i | \(-0.216229\pi\) | ||||
0.778011 | + | 0.628251i | \(0.216229\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2500.00 | −0.120989 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1032.00i | 0.0497461i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26602.0i | 1.27723i | 0.769525 | + | 0.638617i | \(0.220493\pi\) | ||||
−0.769525 | + | 0.638617i | \(0.779507\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4816.00 | −0.230316 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13958.0 | 0.664885 | 0.332442 | − | 0.943124i | \(-0.392127\pi\) | ||||
0.332442 | + | 0.943124i | \(0.392127\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 40280.0i | − 1.91118i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9108.00i | 0.430458i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −17388.0 | −0.818571 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11970.0 | −0.561312 | −0.280656 | − | 0.959808i | \(-0.590552\pi\) | ||||
−0.280656 | + | 0.959808i | \(0.590552\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 13276.0i | − 0.620134i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 12318.0i | − 0.573154i | −0.958057 | − | 0.286577i | \(-0.907483\pi\) | ||||
0.958057 | − | 0.286577i | \(-0.0925173\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −11392.0 | −0.528016 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6320.00 | −0.291800 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 32724.0i | − 1.50508i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 9800.00i | − 0.449003i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 200.000 | 0.00912825 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5028.00 | 0.228608 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26698.0i | 1.20925i | 0.796510 | + | 0.604626i | \(0.206677\pi\) | ||||
−0.796510 | + | 0.604626i | \(0.793323\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3448.00i | 0.155579i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10840.0 | 0.487264 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16092.0 | 0.720610 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 8280.00i | 0.369385i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 4794.00i | − 0.213064i | −0.994309 | − | 0.106532i | \(-0.966025\pi\) | ||||
0.994309 | − | 0.106532i | \(-0.0339747\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 26928.0 | 1.19230 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1886.00 | 0.0831942 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 5852.00i | − 0.257176i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 20640.0i | − 0.903683i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −9628.00 | −0.419977 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −39114.0 | −1.69985 | −0.849923 | − | 0.526907i | \(-0.823351\pi\) | ||||
−0.849923 | + | 0.526907i | \(0.823351\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1090.00i | 0.0471949i | 0.999722 | + | 0.0235975i | \(0.00751200\pi\) | ||||
−0.999722 | + | 0.0235975i | \(0.992488\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 3280.00i | − 0.141494i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8076.00 | 0.347104 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −48276.0 | −2.06727 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 24840.0i | − 1.05980i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9730.00i | 0.413617i | 0.978381 | + | 0.206808i | \(0.0663077\pi\) | ||||
−0.978381 | + | 0.206808i | \(0.933692\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1100.00 | −0.0465900 | −0.0232950 | − | 0.999729i | \(-0.507416\pi\) | ||||
−0.0232950 | + | 0.999729i | \(0.507416\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2492.00 | 0.105164 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 38074.0i | 1.60092i | 0.599385 | + | 0.800461i | \(0.295412\pi\) | ||||
−0.599385 | + | 0.800461i | \(0.704588\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 24230.0i | 1.01513i | 0.861613 | + | 0.507565i | \(0.169454\pi\) | ||||
−0.861613 | + | 0.507565i | \(0.830546\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7964.00 | 0.332453 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3762.00 | −0.156477 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 6312.00i | − 0.261600i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 12800.0i | − 0.528593i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −16820.0 | −0.692123 | −0.346061 | − | 0.938212i | \(-0.612481\pi\) | ||||
−0.346061 | + | 0.938212i | \(0.612481\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24385.0 | 0.999836 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 8252.00i | − 0.337146i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4314.00i | 0.175629i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −22700.0 | −0.920875 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6892.00 | 0.278602 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 27176.0i | 1.09469i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22162.0i | 0.889581i | 0.895635 | + | 0.444790i | \(0.146722\pi\) | ||||
−0.895635 | + | 0.444790i | \(0.853278\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 22356.0 | 0.894221 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 8790.00 | 0.350363 | 0.175181 | − | 0.984536i | \(-0.443949\pi\) | ||||
0.175181 | + | 0.984536i | \(0.443949\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 10558.0i | − 0.419365i | −0.977770 | − | 0.209682i | \(-0.932757\pi\) | ||||
0.977770 | − | 0.209682i | \(-0.0672430\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8080.00i | 0.319821i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7392.00 | −0.291572 | −0.145786 | − | 0.989316i | \(-0.546571\pi\) | ||||
−0.145786 | + | 0.989316i | \(0.546571\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 228.000 | 0.00896212 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 1114.00i | − 0.0436372i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 10416.0i | − 0.406604i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10908.0 | −0.424344 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −25806.0 | −1.00046 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 25680.0i | 0.992163i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6574.00i | 0.253122i | 0.991959 | + | 0.126561i | \(0.0403940\pi\) | ||||
−0.991959 | + | 0.126561i | \(0.959606\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3028.00 | −0.116191 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 47154.0 | 1.80324 | 0.901622 | − | 0.432524i | \(-0.142377\pi\) | ||||
0.901622 | + | 0.432524i | \(0.142377\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 642.000i | 0.0244677i | 0.999925 | + | 0.0122339i | \(0.00389426\pi\) | ||||
−0.999925 | + | 0.0122339i | \(0.996106\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3864.00i | 0.146765i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −23308.0 | −0.882307 | −0.441153 | − | 0.897432i | \(-0.645431\pi\) | ||||
−0.441153 | + | 0.897432i | \(0.645431\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −34240.0 | −1.29176 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 5894.00i | − 0.221612i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 66096.0i | − 2.47684i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −16740.0 | −0.625203 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 18576.0 | 0.691454 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 256.000i | 0.00949731i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 45540.0i | − 1.68386i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 11920.0 | 0.439283 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 20508.0 | 0.753270 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21450.0i | 0.785265i | 0.919695 | + | 0.392633i | \(0.128436\pi\) | ||||
−0.919695 | + | 0.392633i | \(0.871564\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 31970.0i | − 1.16653i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −40904.0 | −1.48761 | −0.743804 | − | 0.668398i | \(-0.766980\pi\) | ||||
−0.743804 | + | 0.668398i | \(0.766980\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9492.00 | −0.344074 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 3576.00i | − 0.129201i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 42360.0i | 1.52546i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 27380.0 | 0.982789 | 0.491394 | − | 0.870937i | \(-0.336487\pi\) | ||||
0.491394 | + | 0.870937i | \(0.336487\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10980.0 | −0.392837 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 37800.0i | 1.34800i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 14062.0i | − 0.499844i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −18124.0 | −0.642147 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 10302.0 | 0.363830 | 0.181915 | − | 0.983314i | \(-0.441770\pi\) | ||||
0.181915 | + | 0.983314i | \(0.441770\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9234.00i | 0.325061i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 11112.0i | 0.389915i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5544.00 | 0.193912 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5054.00 | −0.176208 | −0.0881040 | − | 0.996111i | \(-0.528081\pi\) | ||||
−0.0881040 | + | 0.996111i | \(0.528081\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4108.00i | 0.142768i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 30462.0i | 1.05530i | 0.849463 | + | 0.527648i | \(0.176926\pi\) | ||||
−0.849463 | + | 0.527648i | \(0.823074\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 34744.0 | 1.19981 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −12000.0 | −0.413079 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 32082.0i | 1.10087i | 0.834878 | + | 0.550436i | \(0.185538\pi\) | ||||
−0.834878 | + | 0.550436i | \(0.814462\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 22572.0i | 0.772095i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4988.00 | −0.170081 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −12970.0 | −0.440860 | −0.220430 | − | 0.975403i | \(-0.570746\pi\) | ||||
−0.220430 | + | 0.975403i | \(0.570746\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 11808.0i | 0.400103i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 56.0000i | − 0.00189156i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9720.00 | −0.327294 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13407.0 | −0.450035 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 37122.0i | − 1.24220i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6348.00i | 0.211761i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1652.00 | −0.0549377 | −0.0274688 | − | 0.999623i | \(-0.508745\pi\) | ||||
−0.0274688 | + | 0.999623i | \(0.508745\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 21384.0 | 0.708930 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 24650.0i | 0.814682i | 0.913276 | + | 0.407341i | \(0.133544\pi\) | ||||
−0.913276 | + | 0.407341i | \(0.866456\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 25720.0i | 0.847426i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −9612.00 | −0.315723 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 23646.0 | 0.774312 | 0.387156 | − | 0.922014i | \(-0.373458\pi\) | ||||
0.387156 | + | 0.922014i | \(0.373458\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 1148.00i | − 0.0374773i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 46322.0i | 1.50759i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −38108.0 | −1.23648 | −0.618238 | − | 0.785991i | \(-0.712153\pi\) | ||||
−0.618238 | + | 0.785991i | \(0.712153\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4356.00 | −0.140907 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 16320.0i | 0.526313i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 51256.0i | − 1.64797i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18640.0 | −0.597497 | −0.298748 | − | 0.954332i | \(-0.596569\pi\) | ||||
−0.298748 | + | 0.954332i | \(0.596569\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −5828.00 | −0.186250 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 24696.0i | 0.786850i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 29022.0i | − 0.921902i | −0.887426 | − | 0.460951i | \(-0.847508\pi\) | ||||
0.887426 | − | 0.460951i | \(-0.152492\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 15800.0 | 0.500390 |
(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 | 256.4.b.b.129.2 | 2 | ||
4.3 | odd | 2 | 256.4.b.f.129.1 | 2 | |||
8.3 | odd | 2 | 256.4.b.f.129.2 | 2 | |||
8.5 | even | 2 | inner | 256.4.b.b.129.1 | 2 | ||
16.3 | odd | 4 | 128.4.a.c.1.1 | yes | 1 | ||
16.5 | even | 4 | 128.4.a.d.1.1 | yes | 1 | ||
16.11 | odd | 4 | 128.4.a.b.1.1 | yes | 1 | ||
16.13 | even | 4 | 128.4.a.a.1.1 | ✓ | 1 | ||
48.5 | odd | 4 | 1152.4.a.d.1.1 | 1 | |||
48.11 | even | 4 | 1152.4.a.c.1.1 | 1 | |||
48.29 | odd | 4 | 1152.4.a.j.1.1 | 1 | |||
48.35 | even | 4 | 1152.4.a.i.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
128.4.a.a.1.1 | ✓ | 1 | 16.13 | even | 4 | ||
128.4.a.b.1.1 | yes | 1 | 16.11 | odd | 4 | ||
128.4.a.c.1.1 | yes | 1 | 16.3 | odd | 4 | ||
128.4.a.d.1.1 | yes | 1 | 16.5 | even | 4 | ||
256.4.b.b.129.1 | 2 | 8.5 | even | 2 | inner | ||
256.4.b.b.129.2 | 2 | 1.1 | even | 1 | trivial | ||
256.4.b.f.129.1 | 2 | 4.3 | odd | 2 | |||
256.4.b.f.129.2 | 2 | 8.3 | odd | 2 | |||
1152.4.a.c.1.1 | 1 | 48.11 | even | 4 | |||
1152.4.a.d.1.1 | 1 | 48.5 | odd | 4 | |||
1152.4.a.i.1.1 | 1 | 48.35 | even | 4 | |||
1152.4.a.j.1.1 | 1 | 48.29 | odd | 4 |