Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,9,Mod(53,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.53");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.bk (of order \(6\), degree \(2\), 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: | \(102.659409735\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(22\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 233.2 | ||
Character | \(\chi\) | \(=\) | 252.233 |
Dual form | 252.9.bk.a.53.2 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1009.83 | − | 583.025i | −1.61573 | − | 0.932840i | −0.988009 | − | 0.154399i | \(-0.950656\pi\) |
−0.627718 | − | 0.778441i | \(-0.716011\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1699.40 | + | 1696.12i | −0.707790 | + | 0.706423i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2949.92 | − | 1703.14i | 0.201484 | − | 0.116327i | −0.395864 | − | 0.918309i | \(-0.629555\pi\) |
0.597347 | + | 0.801983i | \(0.296221\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 21577.4 | 0.755486 | 0.377743 | − | 0.925910i | \(-0.376700\pi\) | ||||
0.377743 | + | 0.925910i | \(0.376700\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3995.22 | − | 2306.64i | 0.0478349 | − | 0.0276175i | −0.475892 | − | 0.879504i | \(-0.657875\pi\) |
0.523727 | + | 0.851886i | \(0.324541\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −67464.5 | + | 116852.i | −0.517679 | + | 0.896647i | 0.482110 | + | 0.876111i | \(0.339871\pi\) |
−0.999789 | + | 0.0205359i | \(0.993463\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −963.083 | − | 556.036i | −0.00344154 | − | 0.00198697i | 0.498278 | − | 0.867017i | \(-0.333966\pi\) |
−0.501720 | + | 0.865030i | \(0.667299\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 484524. | + | 839220.i | 1.24038 | + | 2.14840i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 612721.i | 0.866305i | 0.901321 | + | 0.433153i | \(0.142599\pi\) | ||||
−0.901321 | + | 0.433153i | \(0.857401\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 280802. | + | 486363.i | 0.304056 | + | 0.526640i | 0.977051 | − | 0.213007i | \(-0.0683257\pi\) |
−0.672995 | + | 0.739647i | \(0.734992\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.70499e6 | − | 721998.i | 1.80257 | − | 0.481132i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.43778e6 | + | 2.49032e6i | −0.767162 | + | 1.32876i | 0.171934 | + | 0.985108i | \(0.444998\pi\) |
−0.939096 | + | 0.343655i | \(0.888335\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 3.77743e6i | − | 1.33678i | −0.743809 | − | 0.668392i | \(-0.766983\pi\) | ||
0.743809 | − | 0.668392i | \(-0.233017\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.31458e6 | 0.384515 | 0.192258 | − | 0.981345i | \(-0.438419\pi\) | ||||
0.192258 | + | 0.981345i | \(0.438419\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.88499e6 | + | 2.24300e6i | 0.796156 | + | 0.459661i | 0.842125 | − | 0.539282i | \(-0.181304\pi\) |
−0.0459693 | + | 0.998943i | \(0.514638\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 11142.3 | − | 5.76479e6i | 0.00193281 | − | 0.999998i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −166235. | + | 95976.0i | −0.0210678 | + | 0.0121635i | −0.510497 | − | 0.859880i | \(-0.670539\pi\) |
0.489429 | + | 0.872043i | \(0.337205\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.97189e6 | −0.434057 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.80410e6 | + | 5.08305e6i | −0.726569 | + | 0.419485i | −0.817166 | − | 0.576403i | \(-0.804456\pi\) |
0.0905966 | + | 0.995888i | \(0.471123\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.83072e6 | − | 6.63500e6i | 0.276669 | − | 0.479206i | −0.693886 | − | 0.720085i | \(-0.744103\pi\) |
0.970555 | + | 0.240880i | \(0.0774360\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.17895e7 | − | 1.25802e7i | −1.22066 | − | 0.704748i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.64797e7 | − | 2.85437e7i | −0.817808 | − | 1.41648i | −0.907294 | − | 0.420496i | \(-0.861856\pi\) |
0.0894868 | − | 0.995988i | \(-0.471477\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.07695e6i | 0.121084i | 0.998166 | + | 0.0605420i | \(0.0192829\pi\) | ||||
−0.998166 | + | 0.0605420i | \(0.980717\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.27557e6 | − | 2.20936e6i | −0.0449173 | − | 0.0777990i | 0.842693 | − | 0.538395i | \(-0.180969\pi\) |
−0.887610 | + | 0.460596i | \(0.847636\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.12438e6 | + | 7.89775e6i | −0.0604323 | + | 0.224668i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.67470e6 | + | 2.90067e6i | −0.0429961 | + | 0.0744714i | −0.886723 | − | 0.462302i | \(-0.847024\pi\) |
0.843726 | + | 0.536773i | \(0.180357\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.88063e6i | 0.0606980i | 0.999539 | + | 0.0303490i | \(0.00966187\pi\) | ||||
−0.999539 | + | 0.0303490i | \(0.990338\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.37932e6 | −0.103051 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.18939e7 | − | 4.72815e7i | −1.30524 | − | 0.753583i | −0.323945 | − | 0.946076i | \(-0.605009\pi\) |
−0.981298 | + | 0.192493i | \(0.938343\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.66688e7 | + | 3.65980e7i | −0.534725 | + | 0.533693i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.36255e8 | − | 7.86669e7i | 1.67286 | − | 0.965824i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.14470e7 | 0.694087 | 0.347043 | − | 0.937849i | \(-0.387186\pi\) | ||||
0.347043 | + | 0.937849i | \(0.387186\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.44159e8 | − | 8.32305e7i | 1.38534 | − | 0.799829i | 0.392558 | − | 0.919727i | \(-0.371590\pi\) |
0.992786 | + | 0.119899i | \(0.0382570\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.33527e7 | + | 1.44371e8i | −0.740578 | + | 1.28272i | 0.211655 | + | 0.977345i | \(0.432115\pi\) |
−0.952232 | + | 0.305374i | \(0.901219\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.84702e8 | + | 1.06638e8i | 1.40908 | + | 0.813533i | 0.995300 | − | 0.0968428i | \(-0.0308744\pi\) |
0.413782 | + | 0.910376i | \(0.364208\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.62889e7 | − | 1.14816e8i | −0.469607 | − | 0.813383i | 0.529789 | − | 0.848129i | \(-0.322271\pi\) |
−0.999396 | + | 0.0347460i | \(0.988938\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1.93227e8i | − | 1.18510i | −0.805534 | − | 0.592549i | \(-0.798121\pi\) | ||
0.805534 | − | 0.592549i | \(-0.201879\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 648366. | + | 1.12300e6i | 0.00370705 | + | 0.00642080i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.87714e6 | + | 1.06963e7i | −0.0143474 | + | 0.0533391i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.01378e8 | + | 1.75592e8i | −0.472936 | + | 0.819150i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 6.74470e8i | − | 2.76263i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.19073e8 | −0.842121 | −0.421061 | − | 0.907033i | \(-0.638342\pi\) | ||||
−0.421061 | + | 0.907033i | \(0.638342\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.37881e7 | + | 2.52811e7i | 0.148686 | + | 0.0858440i | 0.572497 | − | 0.819907i | \(-0.305975\pi\) |
−0.423811 | + | 0.905751i | \(0.639308\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.35457e7 | − | 3.13006e8i | −0.267004 | − | 1.00034i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.03831e8 | + | 2.33152e8i | −1.14635 | + | 0.661845i | −0.947995 | − | 0.318285i | \(-0.896893\pi\) |
−0.198355 | + | 0.980130i | \(0.563560\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.61399e8 | −0.968116 | −0.484058 | − | 0.875036i | \(-0.660838\pi\) | ||||
−0.484058 | + | 0.875036i | \(0.660838\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.36518e7 | − | 3.67494e7i | 0.152218 | − | 0.0878832i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.57232e8 | − | 6.18744e8i | 0.808124 | − | 1.39971i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.50785e8 | − | 1.44791e8i | −0.508811 | − | 0.293762i | 0.223534 | − | 0.974696i | \(-0.428241\pi\) |
−0.732345 | + | 0.680934i | \(0.761574\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.17031e8 | − | 5.49114e8i | −0.609809 | − | 1.05622i | −0.991272 | − | 0.131836i | \(-0.957913\pi\) |
0.381463 | − | 0.924384i | \(-0.375420\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 6.54858e8i | − | 1.13454i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.47779e8 | − | 4.29165e8i | −0.407817 | − | 0.706360i | 0.586828 | − | 0.809712i | \(-0.300377\pi\) |
−0.994645 | + | 0.103352i | \(0.967043\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.57977e6 | − | 688576.i | 0.00383953 | − | 0.00102482i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.79112e8 | + | 8.29847e8i | −0.678714 | + | 1.17557i | 0.296654 | + | 0.954985i | \(0.404129\pi\) |
−0.975368 | + | 0.220582i | \(0.929204\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 1.42467e9i | − | 1.83168i | −0.401545 | − | 0.915839i | \(-0.631527\pi\) | ||
0.401545 | − | 0.915839i | \(-0.368473\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.50145e8 | −0.429241 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.06210e8 | − | 1.76790e8i | −0.341849 | − | 0.197367i | 0.319240 | − | 0.947674i | \(-0.396572\pi\) |
−0.661089 | + | 0.750307i | \(0.729906\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.24682e9 | − | 6.04362e8i | −2.39561 | − | 0.644384i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.28077e8 | − | 3.62621e8i | 0.611788 | − | 0.353216i | −0.161877 | − | 0.986811i | \(-0.551755\pi\) |
0.773665 | + | 0.633595i | \(0.218421\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.38960e9 | 1.29472 | 0.647360 | − | 0.762184i | \(-0.275873\pi\) | ||||
0.647360 | + | 0.762184i | \(0.275873\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.90383e9 | − | 1.67653e9i | 2.47905 | − | 1.43128i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.85706e6 | − | 1.36088e7i | 0.00642530 | − | 0.0111290i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.01682e9 | + | 1.16441e9i | 1.51542 | + | 0.874928i | 0.999836 | + | 0.0180894i | \(0.00575834\pi\) |
0.515584 | + | 0.856839i | \(0.327575\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.28989e8 | − | 1.43585e9i | −0.597475 | − | 1.03486i | −0.993192 | − | 0.116485i | \(-0.962837\pi\) |
0.395718 | − | 0.918372i | \(-0.370496\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 2.19344e9i | − | 1.45633i | −0.685402 | − | 0.728165i | \(-0.740373\pi\) | ||
0.685402 | − | 0.728165i | \(-0.259627\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.18164e9 | + | 2.04667e9i | 0.753484 | + | 1.30507i | 0.946124 | + | 0.323804i | \(0.104962\pi\) |
−0.192640 | + | 0.981270i | \(0.561705\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.03925e9 | − | 1.04126e9i | −0.611978 | − | 0.613162i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.20234e9 | + | 3.81456e9i | −1.24701 | + | 2.15988i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.59606e8i | 0.240880i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.66470e6 | 0.00336241 | 0.00168121 | − | 0.999999i | \(-0.499465\pi\) | ||||
0.00168121 | + | 0.999999i | \(0.499465\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.32750e9 | − | 7.66433e8i | −0.621271 | − | 0.358691i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.30213e9 | − | 3.50253e8i | −0.587238 | − | 0.157958i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.62066e7 | − | 4.97714e7i | 0.0361386 | − | 0.0208646i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.94033e9 | 1.59336 | 0.796678 | − | 0.604404i | \(-0.206589\pi\) | ||||
0.796678 | + | 0.604404i | \(0.206589\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.38305e9 | + | 7.98507e8i | −0.520878 | + | 0.300729i | −0.737294 | − | 0.675572i | \(-0.763897\pi\) |
0.216416 | + | 0.976301i | \(0.430563\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.67450e8 | − | 4.63238e8i | 0.0972526 | − | 0.168446i | −0.813294 | − | 0.581853i | \(-0.802328\pi\) |
0.910547 | + | 0.413407i | \(0.135661\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.39744e9 | + | 1.38416e9i | 0.813438 | + | 0.469639i | 0.848148 | − | 0.529759i | \(-0.177717\pi\) |
−0.0347102 | + | 0.999397i | \(0.511051\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.61545e9 | − | 4.53009e9i | −0.857580 | − | 1.48537i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 2.18222e9i | − | 0.668815i | −0.942429 | − | 0.334408i | \(-0.891464\pi\) | ||
0.942429 | − | 0.334408i | \(-0.108536\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.88844e8 | − | 1.19311e9i | −0.204199 | − | 0.353682i | 0.745678 | − | 0.666306i | \(-0.232126\pi\) |
−0.949877 | + | 0.312624i | \(0.898792\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.37227e9 | + | 5.81496e9i | −0.935961 | + | 1.61392i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.45571e9 | + | 2.52136e9i | −0.391099 | + | 0.677404i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 6.99940e9i | − | 1.76346i | −0.471753 | − | 0.881731i | \(-0.656379\pi\) | ||
0.471753 | − | 0.881731i | \(-0.343621\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.78803e6 | −0.000924551 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.78534e9 | − | 1.03077e9i | −0.409250 | − | 0.236280i | 0.281218 | − | 0.959644i | \(-0.409262\pi\) |
−0.690467 | + | 0.723364i | \(0.742595\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.78050e9 | − | 6.67071e9i | −0.395680 | − | 1.48243i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.85529e9 | + | 3.95791e9i | −1.43286 | + | 0.827261i | −0.997338 | − | 0.0729182i | \(-0.976769\pi\) |
−0.435520 | + | 0.900179i | \(0.643435\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.23826e8 | 0.0453865 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.73924e8 | − | 5.62295e8i | 0.186001 | − | 0.107388i | −0.404108 | − | 0.914711i | \(-0.632418\pi\) |
0.590109 | + | 0.807323i | \(0.299085\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.82025e9 | − | 8.34893e9i | 0.893702 | − | 1.54794i | 0.0582995 | − | 0.998299i | \(-0.481432\pi\) |
0.835403 | − | 0.549638i | \(-0.185234\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.85862e9 | + | 1.65042e9i | 0.499833 | + | 0.288579i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.97603e8 | + | 1.55469e9i | 0.152463 | + | 0.264074i | 0.932132 | − | 0.362118i | \(-0.117946\pi\) |
−0.779669 | + | 0.626192i | \(0.784613\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.21803e10i | 1.95359i | 0.214172 | + | 0.976796i | \(0.431295\pi\) | ||||
−0.214172 | + | 0.976796i | \(0.568705\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.69485e9 | + | 4.66762e9i | 0.420135 | + | 0.727696i | 0.995952 | − | 0.0898828i | \(-0.0286493\pi\) |
−0.575817 | + | 0.817579i | \(0.695316\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.40699e9 | + | 6.41938e9i | 0.944335 | + | 0.946162i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.47724e9 | + | 6.02275e9i | −0.498475 | + | 0.863383i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 8.85310e9i | − | 1.20123i | −0.799540 | − | 0.600613i | \(-0.794923\pi\) | ||
0.799540 | − | 0.600613i | \(-0.205077\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.18542e10 | 1.56525 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.07809e7 | − | 1.19978e7i | −0.00260003 | − | 0.00150113i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.23400e9 | + | 2.22969e9i | −0.272156 | + | 0.271630i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.73675e9 | + | 4.46681e9i | −0.894044 | + | 0.516177i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.00703e10 | 1.13368 | 0.566839 | − | 0.823828i | \(-0.308166\pi\) | ||||
0.566839 | + | 0.823828i | \(0.308166\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.12022e9 | − | 2.37881e9i | 0.440432 | − | 0.254284i | −0.263349 | − | 0.964701i | \(-0.584827\pi\) |
0.703781 | + | 0.710417i | \(0.251494\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.58428e9 | + | 1.31364e10i | −0.790200 | + | 1.36867i | 0.135643 | + | 0.990758i | \(0.456690\pi\) |
−0.925843 | + | 0.377909i | \(0.876643\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.75984e9 | + | 4.48015e9i | 0.768451 | + | 0.443665i | 0.832322 | − | 0.554293i | \(-0.187011\pi\) |
−0.0638711 | + | 0.997958i | \(0.520345\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.04355e9 | + | 1.80748e9i | 0.100774 | + | 0.174546i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.22465e8i | 0.0571880i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.04548e10 | + | 1.81082e10i | 0.937091 | + | 1.62309i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.04066e10 | + | 2.77765e9i | −0.888226 | + | 0.237080i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.91639e9 | + | 3.31928e9i | −0.159651 | + | 0.276524i | −0.934743 | − | 0.355325i | \(-0.884370\pi\) |
0.775092 | + | 0.631849i | \(0.217704\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.84324e10i | 3.05153i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.70765e9 | 0.597589 | 0.298794 | − | 0.954317i | \(-0.403416\pi\) | ||||
0.298794 | + | 0.954317i | \(0.403416\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.65669e9 | + | 9.56490e8i | 0.122525 | + | 0.0707396i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.75885e9 | + | 9.81560e9i | 0.705054 | + | 0.709154i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.13003e9 | − | 5.27122e9i | 0.629730 | − | 0.363575i | −0.150918 | − | 0.988546i | \(-0.548223\pi\) |
0.780647 | + | 0.624972i | \(0.214889\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.89812e10 | 1.27944 | 0.639722 | − | 0.768606i | \(-0.279049\pi\) | ||||
0.639722 | + | 0.768606i | \(0.279049\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.46772e10 | + | 1.42474e10i | −1.58927 | + | 0.917565i | −0.595841 | + | 0.803103i | \(0.703181\pi\) |
−0.993428 | + | 0.114462i | \(0.963486\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.79394e9 | − | 3.10719e9i | 0.112952 | − | 0.195639i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.23971e10 | − | 7.15748e9i | −0.746350 | − | 0.430906i | 0.0780233 | − | 0.996952i | \(-0.475139\pi\) |
−0.824374 | + | 0.566046i | \(0.808472\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.11127e8 | − | 1.05850e9i | −0.0359834 | − | 0.0623251i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.97476e9i | 0.167603i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.31850e10 | − | 2.28370e10i | −0.726799 | − | 1.25885i | −0.958229 | − | 0.286002i | \(-0.907674\pi\) |
0.231430 | − | 0.972852i | \(-0.425660\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.19714e8 | − | 4.45057e8i | 0.00631901 | − | 0.0234920i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.44900e10 | − | 2.50973e10i | 0.748569 | − | 1.29656i | −0.199940 | − | 0.979808i | \(-0.564075\pi\) |
0.948509 | − | 0.316751i | \(-0.102592\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.32210e10i | 0.654482i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.06511e10 | −1.48556 | −0.742778 | − | 0.669538i | \(-0.766492\pi\) | ||||
−0.742778 | + | 0.669538i | \(0.766492\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.96490e9 | + | 4.59854e9i | 0.370156 | + | 0.213710i | 0.673527 | − | 0.739163i | \(-0.264779\pi\) |
−0.303370 | + | 0.952873i | \(0.598112\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.74985e9 | − | 6.73681e9i | 0.307221 | − | 0.306628i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.26837e10 | + | 7.32292e9i | −0.553919 | + | 0.319805i | −0.750701 | − | 0.660642i | \(-0.770284\pi\) |
0.196782 | + | 0.980447i | \(0.436951\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.13030e6 | −0.000219501 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.38232e9 | − | 1.95278e9i | 0.138940 | − | 0.0802169i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.61513e10 | − | 2.79750e10i | 0.650200 | − | 1.12618i | −0.332875 | − | 0.942971i | \(-0.608019\pi\) |
0.983074 | − | 0.183208i | \(-0.0586481\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.70108e10 | − | 9.82121e9i | −0.657882 | − | 0.379829i | 0.133587 | − | 0.991037i | \(-0.457350\pi\) |
−0.791470 | + | 0.611208i | \(0.790684\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.05899e9 | + | 1.04945e10i | 0.229710 | + | 0.397869i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.79499e9i | 0.356966i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.07087e10 | − | 1.85480e10i | −0.382687 | − | 0.662833i | 0.608758 | − | 0.793356i | \(-0.291668\pi\) |
−0.991445 | + | 0.130522i | \(0.958335\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.34025e9 | − | 2.35710e10i | 0.217924 | − | 0.810172i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.67948e9 | − | 2.90894e9i | 0.0566215 | − | 0.0980714i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.84846e10i | 0.599726i | 0.953982 | + | 0.299863i | \(0.0969410\pi\) | ||||
−0.953982 | + | 0.299863i | \(0.903059\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.59856e10 | 0.508861 | 0.254431 | − | 0.967091i | \(-0.418112\pi\) | ||||
0.254431 | + | 0.967091i | \(0.418112\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.87156e9 | + | 2.23524e9i | 0.118667 | + | 0.0685124i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.74383e9 | + | 1.77729e10i | 0.142698 | + | 0.534622i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.12038e9 | − | 2.37890e9i | 0.119407 | − | 0.0689394i | −0.439107 | − | 0.898435i | \(-0.644705\pi\) |
0.558514 | + | 0.829495i | \(0.311372\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.45848e10 | −1.83729 | −0.918647 | − | 0.395078i | \(-0.870717\pi\) | ||||
−0.918647 | + | 0.395078i | \(0.870717\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.29948e8 | − | 7.50254e7i | 0.00356322 | − | 0.00205723i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.95978e10 | + | 5.12649e10i | −0.796895 | + | 1.38026i | 0.124734 | + | 0.992190i | \(0.460192\pi\) |
−0.921629 | + | 0.388072i | \(0.873141\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.68295e10 | − | 1.54900e10i | −0.696624 | − | 0.402196i | 0.109465 | − | 0.993991i | \(-0.465086\pi\) |
−0.806089 | + | 0.591795i | \(0.798420\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.51326e10 | + | 9.54924e10i | 1.40594 | + | 2.43517i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.81243e9i | 0.0445940i | 0.999751 | + | 0.0222970i | \(0.00709794\pi\) | ||||
−0.999751 | + | 0.0222970i | \(0.992902\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.43350e9 | − | 1.11431e10i | −0.155504 | − | 0.269340i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.83667e10 | − | 1.55789e10i | 1.36182 | − | 0.363488i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.87113e10 | − | 4.97295e10i | 0.658247 | − | 1.14012i | −0.322822 | − | 0.946460i | \(-0.604632\pi\) |
0.981069 | − | 0.193657i | \(-0.0620350\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 3.10020e10i | − | 0.686414i | −0.939260 | − | 0.343207i | \(-0.888487\pi\) | ||
0.939260 | − | 0.343207i | \(-0.111513\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.10071e10 | 0.674742 | 0.337371 | − | 0.941372i | \(-0.390462\pi\) | ||||
0.337371 | + | 0.941372i | \(0.390462\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.93878e10 | + | 2.85140e10i | 1.03837 | + | 0.599503i | 0.919371 | − | 0.393392i | \(-0.128698\pi\) |
0.118998 | + | 0.992894i | \(0.462032\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.64194e10 | + | 2.05557e10i | 1.57947 | + | 0.424855i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.87791e9 | − | 2.23891e9i | 0.0774736 | − | 0.0447294i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.30753e11 | −2.56848 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.93970e10 | − | 4.00664e10i | 1.31825 | − | 0.761093i | 0.334805 | − | 0.942287i | \(-0.391330\pi\) |
0.983447 | + | 0.181194i | \(0.0579962\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.10237e10 | + | 5.37346e10i | −0.579580 | + | 1.00386i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.20510e10 | − | 3.58251e10i | −1.12145 | − | 0.647472i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.04785e10 | − | 1.81492e10i | −0.186287 | − | 0.322658i | 0.757723 | − | 0.652577i | \(-0.226312\pi\) |
−0.944009 | + | 0.329919i | \(0.892979\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 6.95951e10i | − | 1.19744i | −0.800959 | − | 0.598719i | \(-0.795677\pi\) | ||
0.800959 | − | 0.598719i | \(-0.204323\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.41333e9 | + | 2.44796e9i | 0.0239252 | + | 0.0414396i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.21888e9 | − | 5.22897e9i | −0.0855365 | − | 0.0857020i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.47908e10 | − | 4.29389e10i | 0.399842 | − | 0.692547i | −0.593864 | − | 0.804565i | \(-0.702398\pi\) |
0.993706 | + | 0.112019i | \(0.0357316\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 1.02162e10i | − | 0.159594i | −0.996811 | − | 0.0797968i | \(-0.974573\pi\) | ||
0.996811 | − | 0.0797968i | \(-0.0254271\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.94102e11 | −2.98445 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.83594e10 | − | 3.94673e10i | −1.01842 | − | 0.587985i | −0.104774 | − | 0.994496i | \(-0.533412\pi\) |
−0.913646 | + | 0.406511i | \(0.866745\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.91505e9 | + | 1.59106e9i | 0.0867510 | + | 0.0233347i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.68344e11 | − | 9.71934e10i | 2.39314 | − | 1.38168i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.52806e10 | 0.213883 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.38907e10 | + | 8.01978e9i | −0.188526 | + | 0.108846i | −0.591293 | − | 0.806457i | \(-0.701382\pi\) |
0.402766 | + | 0.915303i | \(0.368049\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.37134e10 | − | 9.30343e10i | 0.717919 | − | 1.24347i | −0.243903 | − | 0.969800i | \(-0.578428\pi\) |
0.961823 | − | 0.273673i | \(-0.0882387\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.24373e9 | + | 1.29542e9i | 0.0290890 | + | 0.0167945i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.91549e10 | − | 6.78182e10i | −0.499992 | − | 0.866012i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 8.15074e10i | − | 1.00992i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.24345e11 | − | 2.15372e11i | −1.51779 | − | 2.62889i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −9.78537e9 | − | 1.70247e10i | −0.115937 | − | 0.201708i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.07445e10 | − | 1.86100e10i | 0.125429 | − | 0.217249i | −0.796472 | − | 0.604676i | \(-0.793303\pi\) |
0.921900 | + | 0.387427i | \(0.126636\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.54592e11i | 1.75227i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.60994e10 | 0.514927 | 0.257464 | − | 0.966288i | \(-0.417113\pi\) | ||||
0.257464 | + | 0.966288i | \(0.417113\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.15976e10 | − | 4.13369e10i | −0.776770 | − | 0.448468i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.07389e9 | − | 7.76990e9i | −0.0221761 | − | 0.0830835i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.55361e10 | − | 2.62903e10i | 0.473081 | − | 0.273133i | −0.244448 | − | 0.969662i | \(-0.578607\pi\) |
0.717529 | + | 0.696529i | \(0.245273\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.83653e10 | 0.290496 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.52554e10 | + | 2.03547e10i | −0.350907 | + | 0.202596i | −0.665085 | − | 0.746768i | \(-0.731605\pi\) |
0.314178 | + | 0.949364i | \(0.398271\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.12656e11 | + | 1.95126e11i | −1.10551 | + | 1.91480i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.62872e11 | − | 9.40342e10i | −1.55381 | − | 0.897092i | −0.997826 | − | 0.0658981i | \(-0.979009\pi\) |
−0.555983 | − | 0.831194i | \(-0.687658\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.60776e10 | − | 7.98087e10i | −0.433456 | − | 0.750768i | 0.563712 | − | 0.825971i | \(-0.309373\pi\) |
−0.997168 | + | 0.0752031i | \(0.976039\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 1.07765e9i | − | 0.00985841i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.84010e10 | + | 3.18714e10i | 0.166011 | + | 0.287540i | 0.937014 | − | 0.349292i | \(-0.113578\pi\) |
−0.771003 | + | 0.636832i | \(0.780245\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.88589e9 | − | 4.89535e9i | −0.0428785 | − | 0.0429614i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.26921e8 | + | 5.66244e8i | −0.00282988 | + | 0.00490150i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 1.39975e11i | − | 1.17896i | −0.807784 | − | 0.589478i | \(-0.799333\pi\) | ||
0.807784 | − | 0.589478i | \(-0.200667\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.57766e10 | −0.629614 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.26526e10 | − | 1.30785e10i | −0.183189 | − | 0.105764i | 0.405601 | − | 0.914050i | \(-0.367062\pi\) |
−0.588790 | + | 0.808286i | \(0.700396\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.14163e9 | − | 9.12398e9i | 0.0729383 | − | 0.0727975i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.84894e10 | + | 3.37689e10i | −0.454328 | + | 0.262307i | −0.709656 | − | 0.704548i | \(-0.751150\pi\) |
0.255328 | + | 0.966854i | \(0.417817\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.55575e10 | 0.272542 | 0.136271 | − | 0.990672i | \(-0.456488\pi\) | ||||
0.136271 | + | 0.990672i | \(0.456488\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.04749e11 | − | 1.18212e11i | 1.52827 | − | 0.882348i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.08790e10 | − | 1.05445e11i | 0.448448 | − | 0.776735i | −0.549837 | − | 0.835272i | \(-0.685310\pi\) |
0.998285 | + | 0.0585368i | \(0.0186435\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.38281e10 | + | 4.83982e10i | 0.601485 | + | 0.347267i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.00334e11 | + | 1.73783e11i | 0.710567 | + | 1.23074i | 0.964645 | + | 0.263554i | \(0.0848948\pi\) |
−0.254077 | + | 0.967184i | \(0.581772\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.45362e11i | 1.00302i | 0.865152 | + | 0.501509i | \(0.167222\pi\) | ||||
−0.865152 | + | 0.501509i | \(0.832778\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.44346e10 | + | 7.69630e10i | 0.302663 | + | 0.524227i | 0.976738 | − | 0.214435i | \(-0.0687912\pi\) |
−0.674076 | + | 0.738662i | \(0.735458\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.19366e11 | − | 5.85518e10i | 1.45619 | − | 0.388676i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.03966e11 | + | 3.53279e11i | −1.33671 | + | 2.31525i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.32658e10i | 0.0847483i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.04238e11 | 1.28831 | 0.644153 | − | 0.764897i | \(-0.277210\pi\) | ||||
0.644153 | + | 0.764897i | \(0.277210\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.21227e11 | + | 1.27725e11i | 1.36064 | + | 0.785564i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.40421e8 | − | 1.24389e11i | 0.00146021 | − | 0.755485i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.25369e11 | + | 1.30117e11i | −1.33494 | + | 0.770728i | −0.986052 | − | 0.166437i | \(-0.946774\pi\) |
−0.348887 | + | 0.937165i | \(0.613440\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.30462e10 | −0.193321 | −0.0966603 | − | 0.995317i | \(-0.530816\pi\) | ||||
−0.0966603 | + | 0.995317i | \(0.530816\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.42517e11 | − | 8.22825e10i | 0.813300 | − | 0.469559i | −0.0348006 | − | 0.999394i | \(-0.511080\pi\) |
0.848101 | + | 0.529835i | \(0.177746\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.73143e10 | + | 2.99892e10i | −0.0975946 | + | 0.169039i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.41617e11 | − | 8.17624e10i | −0.778864 | − | 0.449677i | 0.0571638 | − | 0.998365i | \(-0.481794\pi\) |
−0.836027 | + | 0.548688i | \(0.815128\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.94790e10 | − | 5.10591e10i | −0.160157 | − | 0.277401i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 3.20888e11i | − | 1.70142i | −0.525636 | − | 0.850710i | \(-0.676173\pi\) | ||
0.525636 | − | 0.850710i | \(-0.323827\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.20326e10 | + | 1.59405e11i | 0.482098 | + | 0.835019i | 0.999789 | − | 0.0205490i | \(-0.00654140\pi\) |
−0.517690 | + | 0.855568i | \(0.673208\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −9.81237e10 | + | 3.64792e11i | −0.501750 | + | 1.86534i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.40695e8 | − | 5.90101e8i | 0.00172132 | − | 0.00298142i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 2.60970e10i | − | 0.128736i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.05964e11 | −0.516533 | −0.258267 | − | 0.966074i | \(-0.583151\pi\) | ||||
−0.258267 | + | 0.966074i | \(0.583151\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.22227e10 | + | 2.43773e10i | 0.200998 | + | 0.116046i | 0.597121 | − | 0.802151i | \(-0.296311\pi\) |
−0.396123 | + | 0.918197i | \(0.629645\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.04423e11 | + | 1.04222e11i | −0.491268 | + | 0.490319i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.95366e11 | + | 1.12795e11i | −0.897772 | + | 0.518329i | −0.876477 | − | 0.481444i | \(-0.840112\pi\) |
−0.0212953 | + | 0.999773i | \(0.506779\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.43733e11 | 2.46958 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.58693e9 | + | 2.07092e9i | −0.0159165 | + | 0.00918937i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.83584e11 | − | 3.17977e11i | 0.805234 | − | 1.39471i | −0.110898 | − | 0.993832i | \(-0.535373\pi\) |
0.916133 | − | 0.400875i | \(-0.131294\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.64951e11 | + | 2.10705e11i | 1.56421 | + | 0.903098i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.71318e9 | − | 1.50917e10i | −0.0369186 | − | 0.0639449i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.11417e11i | 0.461401i | 0.973025 | + | 0.230700i | \(0.0741017\pi\) | ||||
−0.973025 | + | 0.230700i | \(0.925898\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.93999e11 | − | 3.36016e11i | −0.794287 | − | 1.37575i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.03816e11 | + | 3.85954e11i | −0.415515 | + | 1.54475i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.89166e10 | + | 1.19367e11i | −0.272734 | + | 0.472389i | −0.969561 | − | 0.244850i | \(-0.921261\pi\) |
0.696827 | + | 0.717239i | \(0.254595\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 6.24544e8i | − | 0.00241660i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.57033e10 | −0.327924 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.99704e11 | − | 2.30769e11i | −1.49563 | − | 0.863500i | −0.495638 | − | 0.868529i | \(-0.665066\pi\) |
−0.999987 | + | 0.00502965i | \(0.998399\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.03221e11 | − | 3.86721e11i | −0.381969 | − | 1.43106i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.14208e11 | + | 2.96878e11i | −1.86117 | + | 1.07455i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.63902e11 | 1.30271 | 0.651354 | − | 0.758774i | \(-0.274201\pi\) | ||||
0.651354 | + | 0.758774i | \(0.274201\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.25204e9 | − | 3.03227e9i | 0.0183932 | − | 0.0106193i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.02143e11 | − | 1.76917e11i | 0.353829 | − | 0.612850i | −0.633088 | − | 0.774080i | \(-0.718213\pi\) |
0.986917 | + | 0.161230i | \(0.0515460\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.72279e10 | − | 5.61346e10i | −0.329550 | − | 0.190266i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.11913e10 | − | 1.23307e11i | −0.238698 | − | 0.413438i | 0.721643 | − | 0.692266i | \(-0.243387\pi\) |
−0.960341 | + | 0.278828i | \(0.910054\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 8.97957e10i | − | 0.294646i | −0.989088 | − | 0.147323i | \(-0.952934\pi\) | ||
0.989088 | − | 0.147323i | \(-0.0470656\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.68833e11 | + | 2.92428e11i | 0.548066 | + | 0.949279i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.94753e11 | + | 1.32056e11i | −1.57203 | + | 0.419597i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.87615e11 | + | 4.98163e11i | −0.904173 | + | 1.56607i | −0.0821491 | + | 0.996620i | \(0.526178\pi\) |
−0.822024 | + | 0.569453i | \(0.807155\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.39348e11i | 2.27542i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.01398e11 | 0.917818 | 0.458909 | − | 0.888483i | \(-0.348240\pi\) | ||||
0.458909 | + | 0.888483i | \(0.348240\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.22959e11 | − | 1.28725e11i | −0.664792 | − | 0.383818i | 0.129308 | − | 0.991604i | \(-0.458724\pi\) |
−0.794100 | + | 0.607787i | \(0.792058\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.07393e11 | + | 8.26842e10i | 0.906976 | + | 0.243963i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.89970e11 | + | 1.09679e11i | −0.548913 | + | 0.316915i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.81746e11 | 1.66352 | 0.831760 | − | 0.555136i | \(-0.187334\pi\) | ||||
0.831760 | + | 0.555136i | \(0.187334\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.05653e11 | − | 6.09988e10i | 0.295913 | − | 0.170845i | −0.344692 | − | 0.938716i | \(-0.612017\pi\) |
0.640605 | + | 0.767870i | \(0.278683\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.72111e11 | + | 4.71309e11i | −0.754290 | + | 1.30647i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.41400e11 | + | 2.54843e11i | 1.19862 | + | 0.692025i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.24047e9 | + | 9.07676e9i | 0.0140853 | + | 0.0243965i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.77845e11i | 1.52171i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.60415e11 | − | 2.77846e11i | −0.418162 | − | 0.724279i | 0.577592 | − | 0.816325i | \(-0.303992\pi\) |
−0.995755 | + | 0.0920468i | \(0.970659\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.27737e11 | + | 3.28371e11i | 0.837181 | + | 0.838801i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.26572e10 | − | 1.43166e11i | 0.209020 | − | 0.362033i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7.09316e10i | 0.175795i | 0.996130 | + | 0.0878975i | \(0.0280148\pi\) | ||||
−0.996130 | + | 0.0878975i | \(0.971985\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.06952e10 | 0.0507787 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.52568e9 | − | 4.34495e9i | −0.0181002 | − | 0.0104502i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.00658e9 | − | 8.08727e8i | −0.00715962 | − | 0.00192583i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.54587e11 | − | 2.04721e11i | 0.827805 | − | 0.477934i | −0.0252952 | − | 0.999680i | \(-0.508053\pi\) |
0.853101 | + | 0.521746i | \(0.174719\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.26321e11 | 1.21665 | 0.608327 | − | 0.793687i | \(-0.291841\pi\) | ||||
0.608327 | + | 0.793687i | \(0.291841\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9.67643e11 | − | 5.58669e11i | 2.19323 | − | 1.26626i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.86875e10 | + | 1.53611e11i | −0.199055 | + | 0.344774i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.86513e11 | − | 2.80889e11i | −1.07083 | − | 0.618246i | −0.142425 | − | 0.989806i | \(-0.545490\pi\) |
−0.928409 | + | 0.371559i | \(0.878823\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.54562e10 | − | 7.87325e10i | −0.0990818 | − | 0.171615i | 0.812223 | − | 0.583347i | \(-0.198257\pi\) |
−0.911305 | + | 0.411732i | \(0.864924\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 7.64100e11i | − | 1.63353i | −0.576968 | − | 0.816767i | \(-0.695764\pi\) | ||
0.576968 | − | 0.816767i | \(-0.304236\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.85984e11 | + | 4.95339e11i | 0.605513 | + | 1.04878i | 0.991970 | + | 0.126472i | \(0.0403655\pi\) |
−0.386457 | + | 0.922307i | \(0.626301\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.32528e10 | − | 2.30573e10i | −0.0275250 | − | 0.0478882i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.30620e11 | + | 1.43868e12i | −1.70866 | + | 2.95949i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.14915e11i | 0.635545i | 0.948167 | + | 0.317772i | \(0.102935\pi\) | ||||
−0.948167 | + | 0.317772i | \(0.897065\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.24819e11 | 0.249515 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.53586e11 | + | 2.04143e11i | 0.693535 | + | 0.400413i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.25543e11 | − | 4.70351e11i | −0.243927 | − | 0.913879i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.76941e9 | − | 1.59892e9i | 0.00528043 | − | 0.00304866i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.25638e11 | −0.237315 | −0.118658 | − | 0.992935i | \(-0.537859\pi\) | ||||
−0.118658 | + | 0.992935i | \(0.537859\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.49878e10 | − | 3.17472e10i | 0.101940 | − | 0.0588548i | −0.448164 | − | 0.893952i | \(-0.647922\pi\) |
0.550103 | + | 0.835097i | \(0.314588\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.59865e11 | − | 6.23304e11i | 0.660947 | − | 1.14479i | −0.319420 | − | 0.947613i | \(-0.603488\pi\) |
0.980367 | − | 0.197181i | \(-0.0631787\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5.04334e11 | − | 2.91177e11i | −0.909233 | − | 0.524946i | −0.0290488 | − | 0.999578i | \(-0.509248\pi\) |
−0.880184 | + | 0.474632i | \(0.842581\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.06146e11 | + | 3.57056e11i | 0.368223 | + | 0.637781i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.14090e10i | 0.0200064i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.55591e11 | − | 6.15901e11i | −0.617842 | − | 1.07013i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.14398e12 | + | 1.14620e12i | 1.95158 | + | 1.95536i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.80524e8 | − | 8.32292e8i | 0.000812301 | − | 0.00140695i | −0.865619 | − | 0.500703i | \(-0.833075\pi\) |
0.866431 | + | 0.499296i | \(0.166408\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 6.80681e11i | − | 1.12990i | −0.825125 | − | 0.564950i | \(-0.808896\pi\) | ||
0.825125 | − | 0.564950i | \(-0.191104\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.28883e11 | 0.869996 | 0.434998 | − | 0.900431i | \(-0.356749\pi\) | ||||
0.434998 | + | 0.900431i | \(0.356749\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.55778e9 | + | 4.36349e9i | 0.0122096 | + | 0.00704919i | 0.506092 | − | 0.862479i | \(-0.331089\pi\) |
−0.493883 | + | 0.869528i | \(0.664423\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.72294e11 | − | 3.71575e11i | 0.596045 | − | 0.594894i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.24197e11 | + | 3.02645e11i | −0.824307 | + | 0.475914i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.45668e11 | −1.31798 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.98005e11 | + | 1.72053e11i | −0.456231 | + | 0.263405i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.42764e8 | + | 7.66890e8i | −0.000671852 | + | 0.00116368i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.40326e12 | − | 8.10173e11i | −2.09191 | − | 1.20777i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.21235e10 | + | 5.56395e10i | 0.0474672 | + | 0.0822156i | 0.888783 | − | 0.458329i | \(-0.151552\pi\) |
−0.841316 | + | 0.540544i | \(0.818218\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 4.11062e10i | − | 0.0596807i | −0.999555 | − | 0.0298404i | \(-0.990500\pi\) | ||
0.999555 | − | 0.0298404i | \(-0.00949989\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.90611e9 | + | 8.49763e9i | 0.00706080 | + | 0.0122297i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.17293e11 | + | 3.13072e10i | −0.165881 | + | 0.0442758i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.53663e11 | − | 7.85768e11i | 0.636021 | − | 1.10162i | −0.350277 | − | 0.936646i | \(-0.613912\pi\) |
0.986298 | − | 0.164975i | \(-0.0527543\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.63927e10i | 0.0914773i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.78656e12 | −3.80629 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −7.00845e11 | − | 4.04633e11i | −0.940934 | − | 0.543249i | −0.0506811 | − | 0.998715i | \(-0.516139\pi\) |
−0.890253 | + | 0.455466i | \(0.849473\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.72875e11 | + | 3.90220e11i | 0.895644 | + | 0.519411i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.58686e10 | + | 9.16173e9i | −0.0207631 | + | 0.0119876i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.76135e10 | 0.0487962 | 0.0243981 | − | 0.999702i | \(-0.492233\pi\) | ||||
0.0243981 | + | 0.999702i | \(0.492233\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.12869e12 | − | 6.51647e11i | 1.43951 | − | 0.831101i | 0.441694 | − | 0.897166i | \(-0.354378\pi\) |
0.997815 | + | 0.0660642i | \(0.0210442\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.10039e9 | + | 3.63798e9i | −0.00265615 | + | 0.00460059i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6.36835e11 | − | 3.67677e11i | −0.791821 | − | 0.457158i | 0.0487819 | − | 0.998809i | \(-0.484466\pi\) |
−0.840603 | + | 0.541651i | \(0.817799\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.75236e10 | − | 4.76722e10i | −0.0339344 | − | 0.0587761i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 5.13996e11i | − | 0.623143i | −0.950223 | − | 0.311572i | \(-0.899145\pi\) | ||
0.950223 | − | 0.311572i | \(-0.100855\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.35776e12 | − | 2.35171e12i | −1.63234 | − | 2.82729i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.90818e11 | − | 1.08117e12i | 0.343832 | − | 1.27826i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.68746e11 | − | 4.65482e11i | 0.315100 | − | 0.545769i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.93329e12i | 2.22939i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.00071e12 | 1.14446 | 0.572231 | − | 0.820092i | \(-0.306078\pi\) | ||||
0.572231 | + | 0.820092i | \(0.306078\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.62328e11 | − | 2.66925e11i | −0.520084 | − | 0.300270i | 0.216885 | − | 0.976197i | \(-0.430410\pi\) |
−0.736969 | + | 0.675927i | \(0.763744\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.14162e11 | − | 6.12976e11i | 0.685223 | − | 0.683900i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 5.95841e11 | − | 3.44009e11i | 0.653961 | − | 0.377564i | −0.136011 | − | 0.990707i | \(-0.543428\pi\) |
0.789972 | + | 0.613143i | \(0.210095\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.22108e11 | −0.350647 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.61355e11 | − | 3.24098e11i | 0.601206 | − | 0.347106i | −0.168310 | − | 0.985734i | \(-0.553831\pi\) |
0.769516 | + | 0.638628i | \(0.220498\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.27883e12 | + | 2.21499e12i | −1.35852 | + | 2.35303i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.26605e9 | − | 7.30954e8i | −0.00132332 | − | 0.000764021i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.01433e10 | + | 5.22098e10i | 0.0312534 | + | 0.0541324i | 0.881229 | − | 0.472690i | \(-0.156717\pi\) |
−0.849976 | + | 0.526822i | \(0.823383\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 2.75571e12i | − | 2.81152i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.31592e11 | − | 1.26715e12i | −0.740437 | − | 1.28247i | −0.952296 | − | 0.305175i | \(-0.901285\pi\) |
0.211859 | − | 0.977300i | \(-0.432048\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 252.9.bk.a.233.2 | yes | 44 | |
3.2 | odd | 2 | inner | 252.9.bk.a.233.21 | yes | 44 | |
7.4 | even | 3 | inner | 252.9.bk.a.53.21 | yes | 44 | |
21.11 | odd | 6 | inner | 252.9.bk.a.53.2 | ✓ | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.9.bk.a.53.2 | ✓ | 44 | 21.11 | odd | 6 | inner | |
252.9.bk.a.53.21 | yes | 44 | 7.4 | even | 3 | inner | |
252.9.bk.a.233.2 | yes | 44 | 1.1 | even | 1 | trivial | |
252.9.bk.a.233.21 | yes | 44 | 3.2 | odd | 2 | inner |