Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [49,16,Mod(1,49)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(49, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 16, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("49.1");
S:= CuspForms(chi, 16);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 49 = 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 16 \) |
Character orbit: | \([\chi]\) | \(=\) | 49.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(69.9198174990\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 49.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 216.000 | 1.19324 | 0.596621 | − | 0.802523i | \(-0.296509\pi\) | ||||
0.596621 | + | 0.802523i | \(0.296509\pi\) | |||||||
\(3\) | 3348.00 | 0.883845 | 0.441922 | − | 0.897053i | \(-0.354297\pi\) | ||||
0.441922 | + | 0.897053i | \(0.354297\pi\) | |||||||
\(4\) | 13888.0 | 0.423828 | ||||||||
\(5\) | −52110.0 | −0.298295 | −0.149148 | − | 0.988815i | \(-0.547653\pi\) | ||||
−0.149148 | + | 0.988815i | \(0.547653\pi\) | |||||||
\(6\) | 723168. | 1.05464 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −4.07808e6 | −0.687513 | ||||||||
\(9\) | −3.13980e6 | −0.218818 | ||||||||
\(10\) | −1.12558e7 | −0.355938 | ||||||||
\(11\) | 2.05869e7 | 0.318526 | 0.159263 | − | 0.987236i | \(-0.449088\pi\) | ||||
0.159263 | + | 0.987236i | \(0.449088\pi\) | |||||||
\(12\) | 4.64970e7 | 0.374598 | ||||||||
\(13\) | 1.90073e8 | 0.840129 | 0.420065 | − | 0.907494i | \(-0.362007\pi\) | ||||
0.420065 | + | 0.907494i | \(0.362007\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.74464e8 | −0.263647 | ||||||||
\(16\) | −1.33595e9 | −1.24420 | ||||||||
\(17\) | −1.64653e9 | −0.973200 | −0.486600 | − | 0.873625i | \(-0.661763\pi\) | ||||
−0.486600 | + | 0.873625i | \(0.661763\pi\) | |||||||
\(18\) | −6.78197e8 | −0.261103 | ||||||||
\(19\) | −1.56326e9 | −0.401216 | −0.200608 | − | 0.979672i | \(-0.564292\pi\) | ||||
−0.200608 | + | 0.979672i | \(0.564292\pi\) | |||||||
\(20\) | −7.23704e8 | −0.126426 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.44676e9 | 0.380079 | ||||||||
\(23\) | 9.45112e9 | 0.578794 | 0.289397 | − | 0.957209i | \(-0.406545\pi\) | ||||
0.289397 | + | 0.957209i | \(0.406545\pi\) | |||||||
\(24\) | −1.36534e10 | −0.607655 | ||||||||
\(25\) | −2.78021e10 | −0.911020 | ||||||||
\(26\) | 4.10558e10 | 1.00248 | ||||||||
\(27\) | −5.85522e10 | −1.07725 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.69026e10 | −0.397257 | −0.198629 | − | 0.980075i | \(-0.563649\pi\) | ||||
−0.198629 | + | 0.980075i | \(0.563649\pi\) | |||||||
\(30\) | −3.76843e10 | −0.314594 | ||||||||
\(31\) | −7.15885e10 | −0.467337 | −0.233669 | − | 0.972316i | \(-0.575073\pi\) | ||||
−0.233669 | + | 0.972316i | \(0.575073\pi\) | |||||||
\(32\) | −1.54934e11 | −0.797117 | ||||||||
\(33\) | 6.89248e10 | 0.281528 | ||||||||
\(34\) | −3.55650e11 | −1.16126 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −4.36056e10 | −0.0927413 | ||||||||
\(37\) | −1.03365e12 | −1.79003 | −0.895017 | − | 0.446031i | \(-0.852837\pi\) | ||||
−0.895017 | + | 0.446031i | \(0.852837\pi\) | |||||||
\(38\) | −3.37664e11 | −0.478748 | ||||||||
\(39\) | 6.36366e11 | 0.742544 | ||||||||
\(40\) | 2.12509e11 | 0.205082 | ||||||||
\(41\) | −1.64197e12 | −1.31670 | −0.658351 | − | 0.752711i | \(-0.728746\pi\) | ||||
−0.658351 | + | 0.752711i | \(0.728746\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.92403e11 | −0.276253 | −0.138127 | − | 0.990415i | \(-0.544108\pi\) | ||||
−0.138127 | + | 0.990415i | \(0.544108\pi\) | |||||||
\(44\) | 2.85910e11 | 0.135000 | ||||||||
\(45\) | 1.63615e11 | 0.0652724 | ||||||||
\(46\) | 2.04144e12 | 0.690642 | ||||||||
\(47\) | 3.41068e12 | 0.981991 | 0.490996 | − | 0.871162i | \(-0.336633\pi\) | ||||
0.490996 | + | 0.871162i | \(0.336633\pi\) | |||||||
\(48\) | −4.47275e12 | −1.09968 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −6.00526e12 | −1.08707 | ||||||||
\(51\) | −5.51258e12 | −0.860158 | ||||||||
\(52\) | 2.63974e12 | 0.356070 | ||||||||
\(53\) | 6.79715e12 | 0.794800 | 0.397400 | − | 0.917645i | \(-0.369913\pi\) | ||||
0.397400 | + | 0.917645i | \(0.369913\pi\) | |||||||
\(54\) | −1.26473e13 | −1.28542 | ||||||||
\(55\) | −1.07278e12 | −0.0950147 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.23379e12 | −0.354613 | ||||||||
\(58\) | −7.97095e12 | −0.474024 | ||||||||
\(59\) | −9.85886e12 | −0.515747 | −0.257873 | − | 0.966179i | \(-0.583022\pi\) | ||||
−0.257873 | + | 0.966179i | \(0.583022\pi\) | |||||||
\(60\) | −2.42296e12 | −0.111741 | ||||||||
\(61\) | −4.93184e12 | −0.200926 | −0.100463 | − | 0.994941i | \(-0.532032\pi\) | ||||
−0.100463 | + | 0.994941i | \(0.532032\pi\) | |||||||
\(62\) | −1.54631e13 | −0.557647 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.03106e13 | 0.293044 | ||||||||
\(65\) | −9.90472e12 | −0.250606 | ||||||||
\(66\) | 1.48878e13 | 0.335931 | ||||||||
\(67\) | −2.88378e13 | −0.581302 | −0.290651 | − | 0.956829i | \(-0.593872\pi\) | ||||
−0.290651 | + | 0.956829i | \(0.593872\pi\) | |||||||
\(68\) | −2.28670e13 | −0.412470 | ||||||||
\(69\) | 3.16423e13 | 0.511564 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.25050e14 | 1.63172 | 0.815862 | − | 0.578247i | \(-0.196263\pi\) | ||||
0.815862 | + | 0.578247i | \(0.196263\pi\) | |||||||
\(72\) | 1.28044e13 | 0.150440 | ||||||||
\(73\) | 8.21715e13 | 0.870562 | 0.435281 | − | 0.900295i | \(-0.356649\pi\) | ||||
0.435281 | + | 0.900295i | \(0.356649\pi\) | |||||||
\(74\) | −2.23269e14 | −2.13595 | ||||||||
\(75\) | −9.30815e13 | −0.805200 | ||||||||
\(76\) | −2.17105e13 | −0.170047 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.37455e14 | 0.886035 | ||||||||
\(79\) | −2.54131e13 | −0.148886 | −0.0744430 | − | 0.997225i | \(-0.523718\pi\) | ||||
−0.0744430 | + | 0.997225i | \(0.523718\pi\) | |||||||
\(80\) | 6.96162e13 | 0.371138 | ||||||||
\(81\) | −1.50980e14 | −0.733300 | ||||||||
\(82\) | −3.54666e14 | −1.57114 | ||||||||
\(83\) | 2.81737e14 | 1.13961 | 0.569807 | − | 0.821779i | \(-0.307018\pi\) | ||||
0.569807 | + | 0.821779i | \(0.307018\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.58006e13 | 0.290301 | ||||||||
\(86\) | −1.06359e14 | −0.329637 | ||||||||
\(87\) | −1.23550e14 | −0.351114 | ||||||||
\(88\) | −8.39548e13 | −0.218991 | ||||||||
\(89\) | −7.15619e14 | −1.71497 | −0.857485 | − | 0.514509i | \(-0.827974\pi\) | ||||
−0.857485 | + | 0.514509i | \(0.827974\pi\) | |||||||
\(90\) | 3.53409e13 | 0.0778858 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.31257e14 | 0.245309 | ||||||||
\(93\) | −2.39678e14 | −0.413054 | ||||||||
\(94\) | 7.36708e14 | 1.17175 | ||||||||
\(95\) | 8.14613e13 | 0.119681 | ||||||||
\(96\) | −5.18719e14 | −0.704528 | ||||||||
\(97\) | −6.12786e14 | −0.770054 | −0.385027 | − | 0.922905i | \(-0.625808\pi\) | ||||
−0.385027 | + | 0.922905i | \(0.625808\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.46387e13 | −0.0696993 | ||||||||
\(100\) | −3.86116e14 | −0.386116 | ||||||||
\(101\) | 8.17642e14 | 0.758844 | 0.379422 | − | 0.925224i | \(-0.376123\pi\) | ||||
0.379422 | + | 0.925224i | \(0.376123\pi\) | |||||||
\(102\) | −1.19072e15 | −1.02638 | ||||||||
\(103\) | −7.41115e14 | −0.593753 | −0.296877 | − | 0.954916i | \(-0.595945\pi\) | ||||
−0.296877 | + | 0.954916i | \(0.595945\pi\) | |||||||
\(104\) | −7.75134e14 | −0.577600 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.46818e15 | 0.948389 | ||||||||
\(107\) | −2.51430e15 | −1.51370 | −0.756849 | − | 0.653590i | \(-0.773262\pi\) | ||||
−0.756849 | + | 0.653590i | \(0.773262\pi\) | |||||||
\(108\) | −8.13173e14 | −0.456567 | ||||||||
\(109\) | 1.26835e15 | 0.664572 | 0.332286 | − | 0.943179i | \(-0.392180\pi\) | ||||
0.332286 | + | 0.943179i | \(0.392180\pi\) | |||||||
\(110\) | −2.31721e14 | −0.113376 | ||||||||
\(111\) | −3.46067e15 | −1.58211 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.05416e15 | −0.821385 | −0.410692 | − | 0.911774i | \(-0.634713\pi\) | ||||
−0.410692 | + | 0.911774i | \(0.634713\pi\) | |||||||
\(114\) | −1.13050e15 | −0.423139 | ||||||||
\(115\) | −4.92498e14 | −0.172652 | ||||||||
\(116\) | −5.12503e14 | −0.168369 | ||||||||
\(117\) | −5.96793e14 | −0.183836 | ||||||||
\(118\) | −2.12951e15 | −0.615411 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 7.11479e14 | 0.181260 | ||||||||
\(121\) | −3.75343e15 | −0.898541 | ||||||||
\(122\) | −1.06528e15 | −0.239753 | ||||||||
\(123\) | −5.49733e15 | −1.16376 | ||||||||
\(124\) | −9.94221e14 | −0.198071 | ||||||||
\(125\) | 3.03904e15 | 0.570048 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.99068e15 | 0.498014 | 0.249007 | − | 0.968502i | \(-0.419896\pi\) | ||||
0.249007 | + | 0.968502i | \(0.419896\pi\) | |||||||
\(128\) | 7.30396e15 | 1.14679 | ||||||||
\(129\) | −1.64857e15 | −0.244165 | ||||||||
\(130\) | −2.13942e15 | −0.299034 | ||||||||
\(131\) | 1.62623e15 | 0.214608 | 0.107304 | − | 0.994226i | \(-0.465778\pi\) | ||||
0.107304 | + | 0.994226i | \(0.465778\pi\) | |||||||
\(132\) | 9.57227e14 | 0.119319 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −6.22897e15 | −0.693634 | ||||||||
\(135\) | 3.05116e15 | 0.321337 | ||||||||
\(136\) | 6.71467e15 | 0.669088 | ||||||||
\(137\) | 1.05922e16 | 0.999038 | 0.499519 | − | 0.866303i | \(-0.333510\pi\) | ||||
0.499519 | + | 0.866303i | \(0.333510\pi\) | |||||||
\(138\) | 6.83474e15 | 0.610421 | ||||||||
\(139\) | 1.86709e16 | 1.57963 | 0.789813 | − | 0.613347i | \(-0.210177\pi\) | ||||
0.789813 | + | 0.613347i | \(0.210177\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.14190e16 | 0.867928 | ||||||||
\(142\) | 2.70108e16 | 1.94704 | ||||||||
\(143\) | 3.91301e15 | 0.267603 | ||||||||
\(144\) | 4.19461e15 | 0.272253 | ||||||||
\(145\) | 1.92299e15 | 0.118500 | ||||||||
\(146\) | 1.77490e16 | 1.03879 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.43554e16 | −0.758667 | ||||||||
\(149\) | −1.25560e16 | −0.630889 | −0.315444 | − | 0.948944i | \(-0.602154\pi\) | ||||
−0.315444 | + | 0.948944i | \(0.602154\pi\) | |||||||
\(150\) | −2.01056e16 | −0.960799 | ||||||||
\(151\) | 2.87588e16 | 1.30751 | 0.653753 | − | 0.756708i | \(-0.273194\pi\) | ||||
0.653753 | + | 0.756708i | \(0.273194\pi\) | |||||||
\(152\) | 6.37509e15 | 0.275841 | ||||||||
\(153\) | 5.16977e15 | 0.212954 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.73048e15 | 0.139404 | ||||||||
\(156\) | 8.83784e15 | 0.314711 | ||||||||
\(157\) | 1.45276e16 | 0.493114 | 0.246557 | − | 0.969128i | \(-0.420701\pi\) | ||||
0.246557 | + | 0.969128i | \(0.420701\pi\) | |||||||
\(158\) | −5.48922e15 | −0.177657 | ||||||||
\(159\) | 2.27569e16 | 0.702480 | ||||||||
\(160\) | 8.07362e15 | 0.237776 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −3.26117e16 | −0.875005 | ||||||||
\(163\) | 1.67741e16 | 0.429767 | 0.214884 | − | 0.976640i | \(-0.431063\pi\) | ||||
0.214884 | + | 0.976640i | \(0.431063\pi\) | |||||||
\(164\) | −2.28037e16 | −0.558055 | ||||||||
\(165\) | −3.59167e15 | −0.0839783 | ||||||||
\(166\) | 6.08551e16 | 1.35984 | ||||||||
\(167\) | −6.41999e16 | −1.37139 | −0.685695 | − | 0.727889i | \(-0.740502\pi\) | ||||
−0.685695 | + | 0.727889i | \(0.740502\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.50580e16 | −0.294183 | ||||||||
\(170\) | 1.85329e16 | 0.346399 | ||||||||
\(171\) | 4.90832e15 | 0.0877934 | ||||||||
\(172\) | −6.83849e15 | −0.117084 | ||||||||
\(173\) | 7.59860e16 | 1.24563 | 0.622814 | − | 0.782370i | \(-0.285990\pi\) | ||||
0.622814 | + | 0.782370i | \(0.285990\pi\) | |||||||
\(174\) | −2.66868e16 | −0.418964 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.75029e16 | −0.396309 | ||||||||
\(177\) | −3.30075e16 | −0.455840 | ||||||||
\(178\) | −1.54574e17 | −2.04638 | ||||||||
\(179\) | 9.33749e16 | 1.18531 | 0.592655 | − | 0.805456i | \(-0.298080\pi\) | ||||
0.592655 | + | 0.805456i | \(0.298080\pi\) | |||||||
\(180\) | 2.27229e15 | 0.0276643 | ||||||||
\(181\) | −7.43177e16 | −0.867966 | −0.433983 | − | 0.900921i | \(-0.642892\pi\) | ||||
−0.433983 | + | 0.900921i | \(0.642892\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.65118e16 | −0.177587 | ||||||||
\(184\) | −3.85424e16 | −0.397929 | ||||||||
\(185\) | 5.38636e16 | 0.533958 | ||||||||
\(186\) | −5.17705e16 | −0.492873 | ||||||||
\(187\) | −3.38968e16 | −0.309990 | ||||||||
\(188\) | 4.73676e16 | 0.416196 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.75956e16 | 0.142808 | ||||||||
\(191\) | −9.86224e16 | −0.769529 | −0.384765 | − | 0.923015i | \(-0.625717\pi\) | ||||
−0.384765 | + | 0.923015i | \(0.625717\pi\) | |||||||
\(192\) | 3.45197e16 | 0.259005 | ||||||||
\(193\) | −8.91178e15 | −0.0643109 | −0.0321554 | − | 0.999483i | \(-0.510237\pi\) | ||||
−0.0321554 | + | 0.999483i | \(0.510237\pi\) | |||||||
\(194\) | −1.32362e17 | −0.918861 | ||||||||
\(195\) | −3.31610e16 | −0.221497 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.54176e16 | 0.219140 | 0.109570 | − | 0.993979i | \(-0.465053\pi\) | ||||
0.109570 | + | 0.993979i | \(0.465053\pi\) | |||||||
\(198\) | −1.39620e16 | −0.0831682 | ||||||||
\(199\) | 2.86461e17 | 1.64311 | 0.821556 | − | 0.570127i | \(-0.193106\pi\) | ||||
0.821556 | + | 0.570127i | \(0.193106\pi\) | |||||||
\(200\) | 1.13379e17 | 0.626338 | ||||||||
\(201\) | −9.65490e16 | −0.513780 | ||||||||
\(202\) | 1.76611e17 | 0.905485 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −7.65587e16 | −0.364559 | ||||||||
\(205\) | 8.55633e16 | 0.392766 | ||||||||
\(206\) | −1.60081e17 | −0.708492 | ||||||||
\(207\) | −2.96746e16 | −0.126651 | ||||||||
\(208\) | −2.53928e17 | −1.04529 | ||||||||
\(209\) | −3.21825e16 | −0.127798 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.75834e17 | 1.38956 | 0.694780 | − | 0.719222i | \(-0.255502\pi\) | ||||
0.694780 | + | 0.719222i | \(0.255502\pi\) | |||||||
\(212\) | 9.43988e16 | 0.336859 | ||||||||
\(213\) | 4.18668e17 | 1.44219 | ||||||||
\(214\) | −5.43089e17 | −1.80621 | ||||||||
\(215\) | 2.56591e16 | 0.0824050 | ||||||||
\(216\) | 2.38781e17 | 0.740621 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 2.73964e17 | 0.792995 | ||||||||
\(219\) | 2.75110e17 | 0.769441 | ||||||||
\(220\) | −1.48988e16 | −0.0402699 | ||||||||
\(221\) | −3.12961e17 | −0.817614 | ||||||||
\(222\) | −7.47504e17 | −1.88784 | ||||||||
\(223\) | 2.53078e16 | 0.0617970 | 0.0308985 | − | 0.999523i | \(-0.490163\pi\) | ||||
0.0308985 | + | 0.999523i | \(0.490163\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.72932e16 | 0.199348 | ||||||||
\(226\) | −4.43699e17 | −0.980111 | ||||||||
\(227\) | −3.03692e17 | −0.648992 | −0.324496 | − | 0.945887i | \(-0.605195\pi\) | ||||
−0.324496 | + | 0.945887i | \(0.605195\pi\) | |||||||
\(228\) | −7.26868e16 | −0.150295 | ||||||||
\(229\) | −1.07992e17 | −0.216085 | −0.108042 | − | 0.994146i | \(-0.534458\pi\) | ||||
−0.108042 | + | 0.994146i | \(0.534458\pi\) | |||||||
\(230\) | −1.06379e17 | −0.206015 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.50492e17 | 0.273119 | ||||||||
\(233\) | −7.90506e17 | −1.38911 | −0.694554 | − | 0.719441i | \(-0.744398\pi\) | ||||
−0.694554 | + | 0.719441i | \(0.744398\pi\) | |||||||
\(234\) | −1.28907e17 | −0.219360 | ||||||||
\(235\) | −1.77731e17 | −0.292923 | ||||||||
\(236\) | −1.36920e17 | −0.218588 | ||||||||
\(237\) | −8.50830e16 | −0.131592 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.52956e17 | 0.512551 | 0.256275 | − | 0.966604i | \(-0.417505\pi\) | ||||
0.256275 | + | 0.966604i | \(0.417505\pi\) | |||||||
\(240\) | 2.33075e17 | 0.328028 | ||||||||
\(241\) | −6.85690e16 | −0.0935405 | −0.0467703 | − | 0.998906i | \(-0.514893\pi\) | ||||
−0.0467703 | + | 0.998906i | \(0.514893\pi\) | |||||||
\(242\) | −8.10741e17 | −1.07218 | ||||||||
\(243\) | 3.34679e17 | 0.429123 | ||||||||
\(244\) | −6.84934e16 | −0.0851580 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.18742e18 | −1.38865 | ||||||||
\(247\) | −2.97134e17 | −0.337073 | ||||||||
\(248\) | 2.91944e17 | 0.321300 | ||||||||
\(249\) | 9.43255e17 | 1.00724 | ||||||||
\(250\) | 6.56433e17 | 0.680205 | ||||||||
\(251\) | −1.58806e18 | −1.59703 | −0.798515 | − | 0.601975i | \(-0.794381\pi\) | ||||
−0.798515 | + | 0.601975i | \(0.794381\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.94569e17 | 0.184361 | ||||||||
\(254\) | 6.45986e17 | 0.594251 | ||||||||
\(255\) | 2.87260e17 | 0.256581 | ||||||||
\(256\) | 1.23980e18 | 1.07535 | ||||||||
\(257\) | 8.28562e17 | 0.697954 | 0.348977 | − | 0.937131i | \(-0.386529\pi\) | ||||
0.348977 | + | 0.937131i | \(0.386529\pi\) | |||||||
\(258\) | −3.56090e17 | −0.291348 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −1.37557e17 | −0.106214 | ||||||||
\(261\) | 1.15867e17 | 0.0869271 | ||||||||
\(262\) | 3.51265e17 | 0.256080 | ||||||||
\(263\) | 1.40445e18 | 0.995038 | 0.497519 | − | 0.867453i | \(-0.334244\pi\) | ||||
0.497519 | + | 0.867453i | \(0.334244\pi\) | |||||||
\(264\) | −2.81081e17 | −0.193554 | ||||||||
\(265\) | −3.54200e17 | −0.237085 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.39589e18 | −1.51577 | ||||||||
\(268\) | −4.00500e17 | −0.246372 | ||||||||
\(269\) | −1.43582e18 | −0.858930 | −0.429465 | − | 0.903083i | \(-0.641298\pi\) | ||||
−0.429465 | + | 0.903083i | \(0.641298\pi\) | |||||||
\(270\) | 6.59050e17 | 0.383433 | ||||||||
\(271\) | −5.09160e17 | −0.288127 | −0.144064 | − | 0.989568i | \(-0.546017\pi\) | ||||
−0.144064 | + | 0.989568i | \(0.546017\pi\) | |||||||
\(272\) | 2.19967e18 | 1.21085 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.28792e18 | 1.19209 | ||||||||
\(275\) | −5.72358e17 | −0.290184 | ||||||||
\(276\) | 4.39449e17 | 0.216815 | ||||||||
\(277\) | 5.68946e17 | 0.273195 | 0.136598 | − | 0.990627i | \(-0.456383\pi\) | ||||
0.136598 | + | 0.990627i | \(0.456383\pi\) | |||||||
\(278\) | 4.03292e18 | 1.88488 | ||||||||
\(279\) | 2.24774e17 | 0.102262 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.06184e18 | −1.75156 | −0.875780 | − | 0.482710i | \(-0.839652\pi\) | ||||
−0.875780 | + | 0.482710i | \(0.839652\pi\) | |||||||
\(282\) | 2.46650e18 | 1.03565 | ||||||||
\(283\) | −2.78506e18 | −1.13877 | −0.569385 | − | 0.822071i | \(-0.692819\pi\) | ||||
−0.569385 | + | 0.822071i | \(0.692819\pi\) | |||||||
\(284\) | 1.73670e18 | 0.691570 | ||||||||
\(285\) | 2.72733e17 | 0.105779 | ||||||||
\(286\) | 8.45211e17 | 0.319315 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 4.86463e17 | 0.174424 | ||||||||
\(289\) | −1.51369e17 | −0.0528813 | ||||||||
\(290\) | 4.15366e17 | 0.141399 | ||||||||
\(291\) | −2.05161e18 | −0.680608 | ||||||||
\(292\) | 1.14120e18 | 0.368969 | ||||||||
\(293\) | 3.63803e18 | 1.14646 | 0.573230 | − | 0.819395i | \(-0.305690\pi\) | ||||
0.573230 | + | 0.819395i | \(0.305690\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.13745e17 | 0.153845 | ||||||||
\(296\) | 4.21532e18 | 1.23067 | ||||||||
\(297\) | −1.20541e18 | −0.343131 | ||||||||
\(298\) | −2.71209e18 | −0.752803 | ||||||||
\(299\) | 1.79641e18 | 0.486262 | ||||||||
\(300\) | −1.29272e18 | −0.341267 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 6.21190e18 | 1.56017 | ||||||||
\(303\) | 2.73746e18 | 0.670701 | ||||||||
\(304\) | 2.08843e18 | 0.499192 | ||||||||
\(305\) | 2.56998e17 | 0.0599351 | ||||||||
\(306\) | 1.11667e18 | 0.254106 | ||||||||
\(307\) | 9.75296e17 | 0.216570 | 0.108285 | − | 0.994120i | \(-0.465464\pi\) | ||||
0.108285 | + | 0.994120i | \(0.465464\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.48125e18 | −0.524786 | ||||||||
\(310\) | 8.05783e17 | 0.166343 | ||||||||
\(311\) | −3.36692e17 | −0.0678468 | −0.0339234 | − | 0.999424i | \(-0.510800\pi\) | ||||
−0.0339234 | + | 0.999424i | \(0.510800\pi\) | |||||||
\(312\) | −2.59515e18 | −0.510508 | ||||||||
\(313\) | −3.65551e18 | −0.702046 | −0.351023 | − | 0.936367i | \(-0.614166\pi\) | ||||
−0.351023 | + | 0.936367i | \(0.614166\pi\) | |||||||
\(314\) | 3.13797e18 | 0.588405 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.52937e17 | −0.0631021 | ||||||||
\(317\) | −7.97380e17 | −0.139226 | −0.0696131 | − | 0.997574i | \(-0.522176\pi\) | ||||
−0.0696131 | + | 0.997574i | \(0.522176\pi\) | |||||||
\(318\) | 4.91548e18 | 0.838229 | ||||||||
\(319\) | −7.59708e17 | −0.126537 | ||||||||
\(320\) | −5.37283e17 | −0.0874135 | ||||||||
\(321\) | −8.41788e18 | −1.33787 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.57395e18 | 0.390464 | ||||||||
\(324\) | −2.09681e18 | −0.310793 | ||||||||
\(325\) | −5.28444e18 | −0.765375 | ||||||||
\(326\) | 3.62321e18 | 0.512816 | ||||||||
\(327\) | 4.24645e18 | 0.587378 | ||||||||
\(328\) | 6.69610e18 | 0.905249 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −7.75801e17 | −0.100206 | ||||||||
\(331\) | −1.01585e19 | −1.28269 | −0.641343 | − | 0.767255i | \(-0.721622\pi\) | ||||
−0.641343 | + | 0.767255i | \(0.721622\pi\) | |||||||
\(332\) | 3.91276e18 | 0.483000 | ||||||||
\(333\) | 3.24546e18 | 0.391692 | ||||||||
\(334\) | −1.38672e19 | −1.63640 | ||||||||
\(335\) | 1.50274e18 | 0.173399 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.81465e18 | −0.531301 | −0.265651 | − | 0.964069i | \(-0.585587\pi\) | ||||
−0.265651 | + | 0.964069i | \(0.585587\pi\) | |||||||
\(338\) | −3.25253e18 | −0.351032 | ||||||||
\(339\) | −6.87734e18 | −0.725977 | ||||||||
\(340\) | 1.19160e18 | 0.123038 | ||||||||
\(341\) | −1.47378e18 | −0.148859 | ||||||||
\(342\) | 1.06020e18 | 0.104759 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2.00806e18 | 0.189928 | ||||||||
\(345\) | −1.64888e18 | −0.152597 | ||||||||
\(346\) | 1.64130e19 | 1.48634 | ||||||||
\(347\) | 4.50275e18 | 0.399031 | 0.199516 | − | 0.979895i | \(-0.436063\pi\) | ||||
0.199516 | + | 0.979895i | \(0.436063\pi\) | |||||||
\(348\) | −1.71586e18 | −0.148812 | ||||||||
\(349\) | −2.24323e19 | −1.90407 | −0.952036 | − | 0.305986i | \(-0.901014\pi\) | ||||
−0.952036 | + | 0.305986i | \(0.901014\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.11292e19 | −0.905026 | ||||||||
\(352\) | −3.18961e18 | −0.253902 | ||||||||
\(353\) | −8.02510e18 | −0.625374 | −0.312687 | − | 0.949856i | \(-0.601229\pi\) | ||||
−0.312687 | + | 0.949856i | \(0.601229\pi\) | |||||||
\(354\) | −7.12961e18 | −0.543928 | ||||||||
\(355\) | −6.51636e18 | −0.486735 | ||||||||
\(356\) | −9.93851e18 | −0.726853 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.01690e19 | 1.41436 | ||||||||
\(359\) | 1.61507e18 | 0.110913 | 0.0554567 | − | 0.998461i | \(-0.482339\pi\) | ||||
0.0554567 | + | 0.998461i | \(0.482339\pi\) | |||||||
\(360\) | −6.67236e17 | −0.0448756 | ||||||||
\(361\) | −1.27374e19 | −0.839026 | ||||||||
\(362\) | −1.60526e19 | −1.03569 | ||||||||
\(363\) | −1.25665e19 | −0.794171 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.28195e18 | −0.259684 | ||||||||
\(366\) | −3.56655e18 | −0.211905 | ||||||||
\(367\) | 9.97799e18 | 0.580828 | 0.290414 | − | 0.956901i | \(-0.406207\pi\) | ||||
0.290414 | + | 0.956901i | \(0.406207\pi\) | |||||||
\(368\) | −1.26262e19 | −0.720135 | ||||||||
\(369\) | 5.15547e18 | 0.288118 | ||||||||
\(370\) | 1.16345e19 | 0.637142 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −3.32865e18 | −0.175064 | ||||||||
\(373\) | −2.36866e19 | −1.22092 | −0.610459 | − | 0.792048i | \(-0.709015\pi\) | ||||
−0.610459 | + | 0.792048i | \(0.709015\pi\) | |||||||
\(374\) | −7.32171e18 | −0.369893 | ||||||||
\(375\) | 1.01747e19 | 0.503834 | ||||||||
\(376\) | −1.39090e19 | −0.675132 | ||||||||
\(377\) | −7.01419e18 | −0.333747 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.86851e19 | 0.854480 | 0.427240 | − | 0.904138i | \(-0.359486\pi\) | ||||
0.427240 | + | 0.904138i | \(0.359486\pi\) | |||||||
\(380\) | 1.13133e18 | 0.0507241 | ||||||||
\(381\) | 1.00128e19 | 0.440167 | ||||||||
\(382\) | −2.13024e19 | −0.918235 | ||||||||
\(383\) | 3.02521e19 | 1.27869 | 0.639343 | − | 0.768921i | \(-0.279206\pi\) | ||||
0.639343 | + | 0.768921i | \(0.279206\pi\) | |||||||
\(384\) | 2.44537e19 | 1.01358 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.92494e18 | −0.0767385 | ||||||||
\(387\) | 1.54605e18 | 0.0604493 | ||||||||
\(388\) | −8.51037e18 | −0.326370 | ||||||||
\(389\) | −1.00714e18 | −0.0378852 | −0.0189426 | − | 0.999821i | \(-0.506030\pi\) | ||||
−0.0189426 | + | 0.999821i | \(0.506030\pi\) | |||||||
\(390\) | −7.16278e18 | −0.264300 | ||||||||
\(391\) | −1.55615e19 | −0.563283 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.44461e18 | 0.189680 | ||||||||
\(394\) | 7.65020e18 | 0.261487 | ||||||||
\(395\) | 1.32428e18 | 0.0444120 | ||||||||
\(396\) | −8.97702e17 | −0.0295405 | ||||||||
\(397\) | −3.56324e19 | −1.15058 | −0.575290 | − | 0.817950i | \(-0.695111\pi\) | ||||
−0.575290 | + | 0.817950i | \(0.695111\pi\) | |||||||
\(398\) | 6.18756e19 | 1.96063 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.71422e19 | 1.13349 | ||||||||
\(401\) | 3.94327e19 | 1.18106 | 0.590532 | − | 0.807014i | \(-0.298918\pi\) | ||||
0.590532 | + | 0.807014i | \(0.298918\pi\) | |||||||
\(402\) | −2.08546e19 | −0.613065 | ||||||||
\(403\) | −1.36071e19 | −0.392624 | ||||||||
\(404\) | 1.13554e19 | 0.321620 | ||||||||
\(405\) | 7.86757e18 | 0.218740 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.12796e19 | −0.570172 | ||||||||
\(408\) | 2.24807e19 | 0.591370 | ||||||||
\(409\) | 5.27823e19 | 1.36321 | 0.681607 | − | 0.731719i | \(-0.261282\pi\) | ||||
0.681607 | + | 0.731719i | \(0.261282\pi\) | |||||||
\(410\) | 1.84817e19 | 0.468665 | ||||||||
\(411\) | 3.54627e19 | 0.882995 | ||||||||
\(412\) | −1.02926e19 | −0.251649 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −6.40972e18 | −0.151125 | ||||||||
\(415\) | −1.46813e19 | −0.339941 | ||||||||
\(416\) | −2.94488e19 | −0.669681 | ||||||||
\(417\) | 6.25102e19 | 1.39615 | ||||||||
\(418\) | −6.95143e18 | −0.152494 | ||||||||
\(419\) | −8.62630e18 | −0.185874 | −0.0929372 | − | 0.995672i | \(-0.529626\pi\) | ||||
−0.0929372 | + | 0.995672i | \(0.529626\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.29249e19 | −0.892469 | −0.446235 | − | 0.894916i | \(-0.647235\pi\) | ||||
−0.446235 | + | 0.894916i | \(0.647235\pi\) | |||||||
\(422\) | 8.11801e19 | 1.65808 | ||||||||
\(423\) | −1.07089e19 | −0.214878 | ||||||||
\(424\) | −2.77193e19 | −0.546435 | ||||||||
\(425\) | 4.57770e19 | 0.886605 | ||||||||
\(426\) | 9.04322e19 | 1.72088 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −3.49186e19 | −0.641547 | ||||||||
\(429\) | 1.31008e19 | 0.236519 | ||||||||
\(430\) | 5.54237e18 | 0.0983291 | ||||||||
\(431\) | 5.04764e19 | 0.880053 | 0.440026 | − | 0.897985i | \(-0.354969\pi\) | ||||
0.440026 | + | 0.897985i | \(0.354969\pi\) | |||||||
\(432\) | 7.82227e19 | 1.34031 | ||||||||
\(433\) | −5.05734e19 | −0.851653 | −0.425827 | − | 0.904805i | \(-0.640017\pi\) | ||||
−0.425827 | + | 0.904805i | \(0.640017\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.43818e18 | 0.104735 | ||||||||
\(436\) | 1.76149e19 | 0.281664 | ||||||||
\(437\) | −1.47745e19 | −0.232222 | ||||||||
\(438\) | 5.94238e19 | 0.918130 | ||||||||
\(439\) | −2.47946e19 | −0.376594 | −0.188297 | − | 0.982112i | \(-0.560297\pi\) | ||||
−0.188297 | + | 0.982112i | \(0.560297\pi\) | |||||||
\(440\) | 4.37489e18 | 0.0653238 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6.75996e19 | −0.975612 | ||||||||
\(443\) | −1.30654e20 | −1.85394 | −0.926970 | − | 0.375135i | \(-0.877596\pi\) | ||||
−0.926970 | + | 0.375135i | \(0.877596\pi\) | |||||||
\(444\) | −4.80617e19 | −0.670544 | ||||||||
\(445\) | 3.72909e19 | 0.511567 | ||||||||
\(446\) | 5.46648e18 | 0.0737389 | ||||||||
\(447\) | −4.20373e19 | −0.557608 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.78280e19 | −0.998363 | −0.499181 | − | 0.866498i | \(-0.666366\pi\) | ||||
−0.499181 | + | 0.866498i | \(0.666366\pi\) | |||||||
\(450\) | 1.88553e19 | 0.237870 | ||||||||
\(451\) | −3.38031e19 | −0.419404 | ||||||||
\(452\) | −2.85282e19 | −0.348126 | ||||||||
\(453\) | 9.62844e19 | 1.15563 | ||||||||
\(454\) | −6.55975e19 | −0.774405 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.13438e19 | 0.243801 | ||||||||
\(457\) | −1.18451e20 | −1.33096 | −0.665482 | − | 0.746414i | \(-0.731774\pi\) | ||||
−0.665482 | + | 0.746414i | \(0.731774\pi\) | |||||||
\(458\) | −2.33262e19 | −0.257841 | ||||||||
\(459\) | 9.64078e19 | 1.04838 | ||||||||
\(460\) | −6.83981e18 | −0.0731746 | ||||||||
\(461\) | −1.38643e20 | −1.45929 | −0.729644 | − | 0.683827i | \(-0.760314\pi\) | ||||
−0.729644 | + | 0.683827i | \(0.760314\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.75645e20 | 1.78969 | 0.894846 | − | 0.446375i | \(-0.147285\pi\) | ||||
0.894846 | + | 0.446375i | \(0.147285\pi\) | |||||||
\(464\) | 4.92999e19 | 0.494266 | ||||||||
\(465\) | 1.24896e19 | 0.123212 | ||||||||
\(466\) | −1.70749e20 | −1.65754 | ||||||||
\(467\) | 1.36631e20 | 1.30519 | 0.652593 | − | 0.757708i | \(-0.273681\pi\) | ||||
0.652593 | + | 0.757708i | \(0.273681\pi\) | |||||||
\(468\) | −8.28826e18 | −0.0779147 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −3.83899e19 | −0.349528 | ||||||||
\(471\) | 4.86385e19 | 0.435837 | ||||||||
\(472\) | 4.02052e19 | 0.354583 | ||||||||
\(473\) | −1.01370e19 | −0.0879938 | ||||||||
\(474\) | −1.83779e19 | −0.157021 | ||||||||
\(475\) | 4.34619e19 | 0.365516 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.13417e19 | −0.173917 | ||||||||
\(478\) | 7.62386e19 | 0.611597 | ||||||||
\(479\) | −6.41058e19 | −0.506269 | −0.253134 | − | 0.967431i | \(-0.581461\pi\) | ||||
−0.253134 | + | 0.967431i | \(0.581461\pi\) | |||||||
\(480\) | 2.70305e19 | 0.210157 | ||||||||
\(481\) | −1.96470e20 | −1.50386 | ||||||||
\(482\) | −1.48109e19 | −0.111617 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.21276e19 | −0.380827 | ||||||||
\(485\) | 3.19323e19 | 0.229703 | ||||||||
\(486\) | 7.22907e19 | 0.512047 | ||||||||
\(487\) | −2.41343e19 | −0.168332 | −0.0841662 | − | 0.996452i | \(-0.526823\pi\) | ||||
−0.0841662 | + | 0.996452i | \(0.526823\pi\) | |||||||
\(488\) | 2.01124e19 | 0.138139 | ||||||||
\(489\) | 5.61598e19 | 0.379847 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.80908e19 | −0.184269 | −0.0921346 | − | 0.995747i | \(-0.529369\pi\) | ||||
−0.0921346 | + | 0.995747i | \(0.529369\pi\) | |||||||
\(492\) | −7.63469e19 | −0.493234 | ||||||||
\(493\) | 6.07611e19 | 0.386611 | ||||||||
\(494\) | −6.41808e19 | −0.402210 | ||||||||
\(495\) | 3.36832e18 | 0.0207910 | ||||||||
\(496\) | 9.56384e19 | 0.581460 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 2.03743e20 | 1.20188 | ||||||||
\(499\) | −1.71994e20 | −0.999443 | −0.499722 | − | 0.866186i | \(-0.666564\pi\) | ||||
−0.499722 | + | 0.866186i | \(0.666564\pi\) | |||||||
\(500\) | 4.22062e19 | 0.241602 | ||||||||
\(501\) | −2.14941e20 | −1.21210 | ||||||||
\(502\) | −3.43020e20 | −1.90564 | ||||||||
\(503\) | 1.83497e20 | 1.00431 | 0.502155 | − | 0.864778i | \(-0.332541\pi\) | ||||
0.502155 | + | 0.864778i | \(0.332541\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.26073e19 | −0.226359 | ||||||||
\(506\) | 4.20268e19 | 0.219987 | ||||||||
\(507\) | −5.04142e19 | −0.260012 | ||||||||
\(508\) | 4.15345e19 | 0.211072 | ||||||||
\(509\) | −2.67204e20 | −1.33801 | −0.669004 | − | 0.743258i | \(-0.733279\pi\) | ||||
−0.669004 | + | 0.743258i | \(0.733279\pi\) | |||||||
\(510\) | 6.20482e19 | 0.306163 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 2.84604e19 | 0.136369 | ||||||||
\(513\) | 9.15321e19 | 0.432209 | ||||||||
\(514\) | 1.78969e20 | 0.832828 | ||||||||
\(515\) | 3.86195e19 | 0.177114 | ||||||||
\(516\) | −2.28953e19 | −0.103484 | ||||||||
\(517\) | 7.02153e19 | 0.312790 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.54401e20 | 1.10094 | ||||||||
\(520\) | 4.03922e19 | 0.172295 | ||||||||
\(521\) | 2.01468e20 | 0.847076 | 0.423538 | − | 0.905878i | \(-0.360788\pi\) | ||||
0.423538 | + | 0.905878i | \(0.360788\pi\) | |||||||
\(522\) | 2.50272e19 | 0.103725 | ||||||||
\(523\) | −3.58989e20 | −1.46662 | −0.733311 | − | 0.679894i | \(-0.762026\pi\) | ||||
−0.733311 | + | 0.679894i | \(0.762026\pi\) | |||||||
\(524\) | 2.25850e19 | 0.0909570 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.03362e20 | 1.18732 | ||||||||
\(527\) | 1.17872e20 | 0.454813 | ||||||||
\(528\) | −9.20799e19 | −0.350276 | ||||||||
\(529\) | −1.77312e20 | −0.664997 | ||||||||
\(530\) | −7.65071e19 | −0.282900 | ||||||||
\(531\) | 3.09549e19 | 0.112855 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.12095e20 | −1.10620 | ||||||||
\(534\) | −5.17512e20 | −1.80868 | ||||||||
\(535\) | 1.31020e20 | 0.451528 | ||||||||
\(536\) | 1.17603e20 | 0.399652 | ||||||||
\(537\) | 3.12619e20 | 1.04763 | ||||||||
\(538\) | −3.10137e20 | −1.02491 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 4.23744e19 | 0.136192 | ||||||||
\(541\) | 2.02328e20 | 0.641323 | 0.320662 | − | 0.947194i | \(-0.396095\pi\) | ||||
0.320662 | + | 0.947194i | \(0.396095\pi\) | |||||||
\(542\) | −1.09979e20 | −0.343806 | ||||||||
\(543\) | −2.48816e20 | −0.767147 | ||||||||
\(544\) | 2.55103e20 | 0.775755 | ||||||||
\(545\) | −6.60939e19 | −0.198238 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.40963e19 | 0.216218 | 0.108109 | − | 0.994139i | \(-0.465520\pi\) | ||||
0.108109 | + | 0.994139i | \(0.465520\pi\) | |||||||
\(548\) | 1.47104e20 | 0.423420 | ||||||||
\(549\) | 1.54850e19 | 0.0439662 | ||||||||
\(550\) | −1.23629e20 | −0.346259 | ||||||||
\(551\) | 5.76882e19 | 0.159386 | ||||||||
\(552\) | −1.29040e20 | −0.351707 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 1.22892e20 | 0.325988 | ||||||||
\(555\) | 1.80335e20 | 0.471936 | ||||||||
\(556\) | 2.59302e20 | 0.669490 | ||||||||
\(557\) | 2.09626e18 | 0.00533987 | 0.00266994 | − | 0.999996i | \(-0.499150\pi\) | ||||
0.00266994 | + | 0.999996i | \(0.499150\pi\) | |||||||
\(558\) | 4.85511e19 | 0.122023 | ||||||||
\(559\) | −9.35927e19 | −0.232088 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.13487e20 | −0.273983 | ||||||||
\(562\) | −8.77357e20 | −2.09004 | ||||||||
\(563\) | −6.87353e20 | −1.61572 | −0.807861 | − | 0.589373i | \(-0.799375\pi\) | ||||
−0.807861 | + | 0.589373i | \(0.799375\pi\) | |||||||
\(564\) | 1.58587e20 | 0.367852 | ||||||||
\(565\) | 1.07042e20 | 0.245015 | ||||||||
\(566\) | −6.01573e20 | −1.35883 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.09964e20 | −1.12183 | ||||||||
\(569\) | −9.05218e19 | −0.196522 | −0.0982610 | − | 0.995161i | \(-0.531328\pi\) | ||||
−0.0982610 | + | 0.995161i | \(0.531328\pi\) | |||||||
\(570\) | 5.89102e19 | 0.126220 | ||||||||
\(571\) | 2.05774e20 | 0.435130 | 0.217565 | − | 0.976046i | \(-0.430189\pi\) | ||||
0.217565 | + | 0.976046i | \(0.430189\pi\) | |||||||
\(572\) | 5.43439e19 | 0.113418 | ||||||||
\(573\) | −3.30188e20 | −0.680145 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.62761e20 | −0.527293 | ||||||||
\(576\) | −3.23731e19 | −0.0641233 | ||||||||
\(577\) | −5.70778e20 | −1.11596 | −0.557980 | − | 0.829854i | \(-0.688424\pi\) | ||||
−0.557980 | + | 0.829854i | \(0.688424\pi\) | |||||||
\(578\) | −3.26956e19 | −0.0631002 | ||||||||
\(579\) | −2.98366e19 | −0.0568408 | ||||||||
\(580\) | 2.67065e19 | 0.0502236 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −4.43147e20 | −0.812130 | ||||||||
\(583\) | 1.39932e20 | 0.253164 | ||||||||
\(584\) | −3.35102e20 | −0.598522 | ||||||||
\(585\) | 3.10989e19 | 0.0548373 | ||||||||
\(586\) | 7.85814e20 | 1.36800 | ||||||||
\(587\) | 9.30363e20 | 1.59907 | 0.799534 | − | 0.600621i | \(-0.205080\pi\) | ||||
0.799534 | + | 0.600621i | \(0.205080\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.11911e20 | 0.187503 | ||||||||
\(590\) | 1.10969e20 | 0.183574 | ||||||||
\(591\) | 1.18578e20 | 0.193686 | ||||||||
\(592\) | 1.38090e21 | 2.22716 | ||||||||
\(593\) | −3.54225e20 | −0.564116 | −0.282058 | − | 0.959397i | \(-0.591017\pi\) | ||||
−0.282058 | + | 0.959397i | \(0.591017\pi\) | |||||||
\(594\) | −2.60368e20 | −0.409438 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.74377e20 | −0.267388 | ||||||||
\(597\) | 9.59071e20 | 1.45226 | ||||||||
\(598\) | 3.88024e20 | 0.580229 | ||||||||
\(599\) | −3.30045e20 | −0.487385 | −0.243693 | − | 0.969853i | \(-0.578359\pi\) | ||||
−0.243693 | + | 0.969853i | \(0.578359\pi\) | |||||||
\(600\) | 3.79594e20 | 0.553586 | ||||||||
\(601\) | 3.35884e20 | 0.483761 | 0.241880 | − | 0.970306i | \(-0.422236\pi\) | ||||
0.241880 | + | 0.970306i | \(0.422236\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.05451e19 | 0.127199 | ||||||||
\(604\) | 3.99402e20 | 0.554158 | ||||||||
\(605\) | 1.95591e20 | 0.268030 | ||||||||
\(606\) | 5.91292e20 | 0.800309 | ||||||||
\(607\) | 1.33438e21 | 1.78387 | 0.891934 | − | 0.452165i | \(-0.149348\pi\) | ||||
0.891934 | + | 0.452165i | \(0.149348\pi\) | |||||||
\(608\) | 2.42202e20 | 0.319816 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 5.55116e19 | 0.0715172 | ||||||||
\(611\) | 6.48280e20 | 0.825000 | ||||||||
\(612\) | 7.17978e19 | 0.0902559 | ||||||||
\(613\) | 5.68844e18 | 0.00706381 | 0.00353191 | − | 0.999994i | \(-0.498876\pi\) | ||||
0.00353191 | + | 0.999994i | \(0.498876\pi\) | |||||||
\(614\) | 2.10664e20 | 0.258421 | ||||||||
\(615\) | 2.86466e20 | 0.347144 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.98915e20 | 0.471783 | 0.235891 | − | 0.971779i | \(-0.424199\pi\) | ||||
0.235891 | + | 0.971779i | \(0.424199\pi\) | |||||||
\(618\) | −5.35950e20 | −0.626197 | ||||||||
\(619\) | 5.40017e20 | 0.623343 | 0.311672 | − | 0.950190i | \(-0.399111\pi\) | ||||
0.311672 | + | 0.950190i | \(0.399111\pi\) | |||||||
\(620\) | 5.18088e19 | 0.0590835 | ||||||||
\(621\) | −5.53384e20 | −0.623504 | ||||||||
\(622\) | −7.27254e19 | −0.0809577 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −8.50151e20 | −0.923871 | ||||||||
\(625\) | 6.90089e20 | 0.740978 | ||||||||
\(626\) | −7.89591e20 | −0.837711 | ||||||||
\(627\) | −1.07747e20 | −0.112953 | ||||||||
\(628\) | 2.01760e20 | 0.208996 | ||||||||
\(629\) | 1.70194e21 | 1.74206 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.59111e20 | 0.958625 | 0.479312 | − | 0.877644i | \(-0.340886\pi\) | ||||
0.479312 | + | 0.877644i | \(0.340886\pi\) | |||||||
\(632\) | 1.03637e20 | 0.102361 | ||||||||
\(633\) | 1.25829e21 | 1.22816 | ||||||||
\(634\) | −1.72234e20 | −0.166131 | ||||||||
\(635\) | −1.55844e20 | −0.148555 | ||||||||
\(636\) | 3.16047e20 | 0.297731 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.64097e20 | −0.150989 | ||||||||
\(639\) | −3.92633e20 | −0.357051 | ||||||||
\(640\) | −3.80609e20 | −0.342082 | ||||||||
\(641\) | −9.25925e20 | −0.822509 | −0.411255 | − | 0.911521i | \(-0.634909\pi\) | ||||
−0.411255 | + | 0.911521i | \(0.634909\pi\) | |||||||
\(642\) | −1.81826e21 | −1.59641 | ||||||||
\(643\) | 7.65928e20 | 0.664669 | 0.332335 | − | 0.943162i | \(-0.392164\pi\) | ||||
0.332335 | + | 0.943162i | \(0.392164\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.59068e19 | 0.0728332 | ||||||||
\(646\) | 5.55972e20 | 0.465918 | ||||||||
\(647\) | −1.36075e21 | −1.12719 | −0.563596 | − | 0.826051i | \(-0.690582\pi\) | ||||
−0.563596 | + | 0.826051i | \(0.690582\pi\) | |||||||
\(648\) | 6.15709e20 | 0.504153 | ||||||||
\(649\) | −2.02963e20 | −0.164279 | ||||||||
\(650\) | −1.14144e21 | −0.913278 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.32959e20 | 0.182147 | ||||||||
\(653\) | −2.71809e20 | −0.210094 | −0.105047 | − | 0.994467i | \(-0.533499\pi\) | ||||
−0.105047 | + | 0.994467i | \(0.533499\pi\) | |||||||
\(654\) | 9.17233e20 | 0.700885 | ||||||||
\(655\) | −8.47427e19 | −0.0640166 | ||||||||
\(656\) | 2.19359e21 | 1.63824 | ||||||||
\(657\) | −2.58002e20 | −0.190495 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.74316e20 | 0.486657 | 0.243329 | − | 0.969944i | \(-0.421761\pi\) | ||||
0.243329 | + | 0.969944i | \(0.421761\pi\) | |||||||
\(660\) | −4.98811e19 | −0.0355923 | ||||||||
\(661\) | −1.26727e21 | −0.894042 | −0.447021 | − | 0.894524i | \(-0.647515\pi\) | ||||
−0.447021 | + | 0.894524i | \(0.647515\pi\) | |||||||
\(662\) | −2.19424e21 | −1.53056 | ||||||||
\(663\) | −1.04779e21 | −0.722644 | ||||||||
\(664\) | −1.14894e21 | −0.783499 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 7.01020e20 | 0.467384 | ||||||||
\(667\) | −3.48770e20 | −0.229930 | ||||||||
\(668\) | −8.91609e20 | −0.581234 | ||||||||
\(669\) | 8.47305e19 | 0.0546190 | ||||||||
\(670\) | 3.24592e20 | 0.206908 | ||||||||
\(671\) | −1.01531e20 | −0.0640000 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.13945e21 | −0.702394 | −0.351197 | − | 0.936302i | \(-0.614225\pi\) | ||||
−0.351197 | + | 0.936302i | \(0.614225\pi\) | |||||||
\(674\) | −1.03997e21 | −0.633971 | ||||||||
\(675\) | 1.62788e21 | 0.981393 | ||||||||
\(676\) | −2.09126e20 | −0.124683 | ||||||||
\(677\) | −1.74431e21 | −1.02851 | −0.514256 | − | 0.857637i | \(-0.671932\pi\) | ||||
−0.514256 | + | 0.857637i | \(0.671932\pi\) | |||||||
\(678\) | −1.48550e21 | −0.866266 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −3.49902e20 | −0.199586 | ||||||||
\(681\) | −1.01676e21 | −0.573608 | ||||||||
\(682\) | −3.18337e20 | −0.177625 | ||||||||
\(683\) | −1.43739e21 | −0.793267 | −0.396634 | − | 0.917977i | \(-0.629822\pi\) | ||||
−0.396634 | + | 0.917977i | \(0.629822\pi\) | |||||||
\(684\) | 6.81667e19 | 0.0372093 | ||||||||
\(685\) | −5.51960e20 | −0.298008 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.61556e20 | −0.190985 | ||||||||
\(688\) | 6.57825e20 | 0.343714 | ||||||||
\(689\) | 1.29196e21 | 0.667735 | ||||||||
\(690\) | −3.56159e20 | −0.182085 | ||||||||
\(691\) | 1.77548e21 | 0.897903 | 0.448951 | − | 0.893556i | \(-0.351798\pi\) | ||||
0.448951 | + | 0.893556i | \(0.351798\pi\) | |||||||
\(692\) | 1.05529e21 | 0.527932 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 9.72594e20 | 0.476141 | ||||||||
\(695\) | −9.72941e20 | −0.471195 | ||||||||
\(696\) | 5.03846e20 | 0.241395 | ||||||||
\(697\) | 2.70356e21 | 1.28141 | ||||||||
\(698\) | −4.84538e21 | −2.27202 | ||||||||
\(699\) | −2.64661e21 | −1.22776 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.43100e21 | 0.649764 | 0.324882 | − | 0.945755i | \(-0.394675\pi\) | ||||
0.324882 | + | 0.945755i | \(0.394675\pi\) | |||||||
\(702\) | −2.40391e21 | −1.07992 | ||||||||
\(703\) | 1.61586e21 | 0.718191 | ||||||||
\(704\) | 2.12262e20 | 0.0933420 | ||||||||
\(705\) | −5.95043e20 | −0.258899 | ||||||||
\(706\) | −1.73342e21 | −0.746223 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −4.58408e20 | −0.193198 | ||||||||
\(709\) | −2.41840e21 | −1.00851 | −0.504257 | − | 0.863554i | \(-0.668234\pi\) | ||||
−0.504257 | + | 0.863554i | \(0.668234\pi\) | |||||||
\(710\) | −1.40753e21 | −0.580793 | ||||||||
\(711\) | 7.97921e19 | 0.0325790 | ||||||||
\(712\) | 2.91835e21 | 1.17906 | ||||||||
\(713\) | −6.76591e20 | −0.270492 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.03907e20 | −0.0798246 | ||||||||
\(716\) | 1.29679e21 | 0.502368 | ||||||||
\(717\) | 1.18170e21 | 0.453015 | ||||||||
\(718\) | 3.48856e20 | 0.132347 | ||||||||
\(719\) | −4.74444e21 | −1.78122 | −0.890611 | − | 0.454766i | \(-0.849723\pi\) | ||||
−0.890611 | + | 0.454766i | \(0.849723\pi\) | |||||||
\(720\) | −2.18581e20 | −0.0812118 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −2.75127e21 | −1.00116 | ||||||||
\(723\) | −2.29569e20 | −0.0826753 | ||||||||
\(724\) | −1.03212e21 | −0.367868 | ||||||||
\(725\) | 1.02597e21 | 0.361909 | ||||||||
\(726\) | −2.71436e21 | −0.947639 | ||||||||
\(727\) | 3.59265e21 | 1.24138 | 0.620692 | − | 0.784054i | \(-0.286852\pi\) | ||||
0.620692 | + | 0.784054i | \(0.286852\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.28690e21 | 1.11258 | ||||||||
\(730\) | −9.24902e20 | −0.309866 | ||||||||
\(731\) | 8.10755e20 | 0.268850 | ||||||||
\(732\) | −2.29316e20 | −0.0752664 | ||||||||
\(733\) | 2.76824e21 | 0.899339 | 0.449669 | − | 0.893195i | \(-0.351542\pi\) | ||||
0.449669 | + | 0.893195i | \(0.351542\pi\) | |||||||
\(734\) | 2.15525e21 | 0.693069 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.46430e21 | −0.461367 | ||||||||
\(737\) | −5.93680e20 | −0.185160 | ||||||||
\(738\) | 1.11358e21 | 0.343795 | ||||||||
\(739\) | 3.55824e21 | 1.08743 | 0.543716 | − | 0.839269i | \(-0.317017\pi\) | ||||
0.543716 | + | 0.839269i | \(0.317017\pi\) | |||||||
\(740\) | 7.48058e20 | 0.226307 | ||||||||
\(741\) | −9.94803e20 | −0.297921 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.94092e21 | −0.569628 | −0.284814 | − | 0.958583i | \(-0.591932\pi\) | ||||
−0.284814 | + | 0.958583i | \(0.591932\pi\) | |||||||
\(744\) | 9.77427e20 | 0.283980 | ||||||||
\(745\) | 6.54291e20 | 0.188191 | ||||||||
\(746\) | −5.11630e21 | −1.45685 | ||||||||
\(747\) | −8.84598e20 | −0.249368 | ||||||||
\(748\) | −4.70759e20 | −0.131382 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 2.19774e21 | 0.601196 | ||||||||
\(751\) | 4.75565e21 | 1.28798 | 0.643992 | − | 0.765032i | \(-0.277277\pi\) | ||||
0.643992 | + | 0.765032i | \(0.277277\pi\) | |||||||
\(752\) | −4.55650e21 | −1.22179 | ||||||||
\(753\) | −5.31681e21 | −1.41153 | ||||||||
\(754\) | −1.51507e21 | −0.398241 | ||||||||
\(755\) | −1.49862e21 | −0.390022 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.62137e21 | 0.923960 | 0.461980 | − | 0.886890i | \(-0.347139\pi\) | ||||
0.461980 | + | 0.886890i | \(0.347139\pi\) | |||||||
\(758\) | 4.03599e21 | 1.01960 | ||||||||
\(759\) | 6.51416e20 | 0.162947 | ||||||||
\(760\) | −3.32206e20 | −0.0822821 | ||||||||
\(761\) | 3.86361e21 | 0.947564 | 0.473782 | − | 0.880642i | \(-0.342888\pi\) | ||||
0.473782 | + | 0.880642i | \(0.342888\pi\) | |||||||
\(762\) | 2.16276e21 | 0.525226 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −1.36967e21 | −0.326148 | ||||||||
\(765\) | −2.69397e20 | −0.0635231 | ||||||||
\(766\) | 6.53445e21 | 1.52578 | ||||||||
\(767\) | −1.87391e21 | −0.433294 | ||||||||
\(768\) | 4.15085e21 | 0.950446 | ||||||||
\(769\) | 5.39327e21 | 1.22294 | 0.611469 | − | 0.791268i | \(-0.290579\pi\) | ||||
0.611469 | + | 0.791268i | \(0.290579\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.77403e21 | 0.616883 | ||||||||
\(772\) | −1.23767e20 | −0.0272568 | ||||||||
\(773\) | −6.57037e21 | −1.43299 | −0.716496 | − | 0.697591i | \(-0.754255\pi\) | ||||
−0.716496 | + | 0.697591i | \(0.754255\pi\) | |||||||
\(774\) | 3.33947e20 | 0.0721306 | ||||||||
\(775\) | 1.99031e21 | 0.425754 | ||||||||
\(776\) | 2.49899e21 | 0.529422 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.17543e20 | −0.0452062 | ||||||||
\(779\) | 2.56683e21 | 0.528282 | ||||||||
\(780\) | −4.60540e20 | −0.0938767 | ||||||||
\(781\) | 2.57439e21 | 0.519746 | ||||||||
\(782\) | −3.36129e21 | −0.672133 | ||||||||
\(783\) | 2.16073e21 | 0.427944 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.57035e20 | −0.147094 | ||||||||
\(786\) | 1.17604e21 | 0.226335 | ||||||||
\(787\) | 3.72074e20 | 0.0709281 | 0.0354641 | − | 0.999371i | \(-0.488709\pi\) | ||||
0.0354641 | + | 0.999371i | \(0.488709\pi\) | |||||||
\(788\) | 4.91879e20 | 0.0928778 | ||||||||
\(789\) | 4.70211e21 | 0.879459 | ||||||||
\(790\) | 2.86044e20 | 0.0529943 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 2.63602e20 | 0.0479192 | ||||||||
\(793\) | −9.37412e20 | −0.168804 | ||||||||
\(794\) | −7.69660e21 | −1.37292 | ||||||||
\(795\) | −1.18586e21 | −0.209546 | ||||||||
\(796\) | 3.97837e21 | 0.696397 | ||||||||
\(797\) | −2.61511e21 | −0.453474 | −0.226737 | − | 0.973956i | \(-0.572806\pi\) | ||||
−0.226737 | + | 0.973956i | \(0.572806\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.61579e21 | −0.955674 | ||||||||
\(800\) | 4.30750e21 | 0.726190 | ||||||||
\(801\) | 2.24690e21 | 0.375267 | ||||||||
\(802\) | 8.51746e21 | 1.40930 | ||||||||
\(803\) | 1.69165e21 | 0.277296 | ||||||||
\(804\) | −1.34087e21 | −0.217755 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.93913e21 | −0.468495 | ||||||||
\(807\) | −4.80713e21 | −0.759161 | ||||||||
\(808\) | −3.33441e21 | −0.521715 | ||||||||
\(809\) | 5.34899e21 | 0.829198 | 0.414599 | − | 0.910004i | \(-0.363922\pi\) | ||||
0.414599 | + | 0.910004i | \(0.363922\pi\) | |||||||
\(810\) | 1.69939e21 | 0.261010 | ||||||||
\(811\) | −8.46492e21 | −1.28815 | −0.644075 | − | 0.764962i | \(-0.722758\pi\) | ||||
−0.644075 | + | 0.764962i | \(0.722758\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.70467e21 | −0.254660 | ||||||||
\(814\) | −4.59640e21 | −0.680354 | ||||||||
\(815\) | −8.74100e20 | −0.128197 | ||||||||
\(816\) | 7.36451e21 | 1.07021 | ||||||||
\(817\) | 7.69753e20 | 0.110837 | ||||||||
\(818\) | 1.14010e22 | 1.62664 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.18830e21 | 0.166465 | ||||||||
\(821\) | 7.99397e21 | 1.10966 | 0.554829 | − | 0.831965i | \(-0.312784\pi\) | ||||
0.554829 | + | 0.831965i | \(0.312784\pi\) | |||||||
\(822\) | 7.65994e21 | 1.05363 | ||||||||
\(823\) | 1.96841e21 | 0.268297 | 0.134148 | − | 0.990961i | \(-0.457170\pi\) | ||||
0.134148 | + | 0.990961i | \(0.457170\pi\) | |||||||
\(824\) | 3.02232e21 | 0.408213 | ||||||||
\(825\) | −1.91626e21 | −0.256477 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.43539e22 | −1.88659 | −0.943296 | − | 0.331954i | \(-0.892292\pi\) | ||||
−0.943296 | + | 0.331954i | \(0.892292\pi\) | |||||||
\(828\) | −4.12121e20 | −0.0536782 | ||||||||
\(829\) | 8.83327e21 | 1.14015 | 0.570076 | − | 0.821592i | \(-0.306914\pi\) | ||||
0.570076 | + | 0.821592i | \(0.306914\pi\) | |||||||
\(830\) | −3.17116e21 | −0.405632 | ||||||||
\(831\) | 1.90483e21 | 0.241462 | ||||||||
\(832\) | 1.95976e21 | 0.246195 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 1.35022e22 | 1.66594 | ||||||||
\(835\) | 3.34546e21 | 0.409079 | ||||||||
\(836\) | −4.46951e20 | −0.0541643 | ||||||||
\(837\) | 4.19166e21 | 0.503437 | ||||||||
\(838\) | −1.86328e21 | −0.221793 | ||||||||
\(839\) | −1.26696e22 | −1.49469 | −0.747343 | − | 0.664439i | \(-0.768671\pi\) | ||||
−0.747343 | + | 0.664439i | \(0.768671\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.26739e21 | −0.842187 | ||||||||
\(842\) | −9.27177e21 | −1.06493 | ||||||||
\(843\) | −1.35990e22 | −1.54811 | ||||||||
\(844\) | 5.21958e21 | 0.588935 | ||||||||
\(845\) | 7.84673e20 | 0.0877533 | ||||||||
\(846\) | −2.31312e21 | −0.256401 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −9.08064e21 | −0.988889 | ||||||||
\(849\) | −9.32438e21 | −1.00650 | ||||||||
\(850\) | 9.88783e21 | 1.05793 | ||||||||
\(851\) | −9.76917e21 | −1.03606 | ||||||||
\(852\) | 5.81446e21 | 0.611241 | ||||||||
\(853\) | −6.00532e21 | −0.625776 | −0.312888 | − | 0.949790i | \(-0.601296\pi\) | ||||
−0.312888 | + | 0.949790i | \(0.601296\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.55773e20 | −0.0261883 | ||||||||
\(856\) | 1.02535e22 | 1.04069 | ||||||||
\(857\) | −1.47589e22 | −1.48491 | −0.742453 | − | 0.669898i | \(-0.766338\pi\) | ||||
−0.742453 | + | 0.669898i | \(0.766338\pi\) | |||||||
\(858\) | 2.82976e21 | 0.282225 | ||||||||
\(859\) | −9.64956e20 | −0.0954023 | −0.0477012 | − | 0.998862i | \(-0.515190\pi\) | ||||
−0.0477012 | + | 0.998862i | \(0.515190\pi\) | |||||||
\(860\) | 3.56354e20 | 0.0349255 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.09029e22 | 1.05012 | ||||||||
\(863\) | 3.44391e21 | 0.328829 | 0.164415 | − | 0.986391i | \(-0.447426\pi\) | ||||
0.164415 | + | 0.986391i | \(0.447426\pi\) | |||||||
\(864\) | 9.07173e21 | 0.858691 | ||||||||
\(865\) | −3.95963e21 | −0.371564 | ||||||||
\(866\) | −1.09239e22 | −1.01623 | ||||||||
\(867\) | −5.06782e20 | −0.0467389 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.23175e20 | −0.0474241 | ||||||||
\(870\) | 1.39065e21 | 0.124975 | ||||||||
\(871\) | −5.48130e21 | −0.488368 | ||||||||
\(872\) | −5.17245e21 | −0.456901 | ||||||||
\(873\) | 1.92403e21 | 0.168502 | ||||||||
\(874\) | −3.19130e21 | −0.277097 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 3.82073e21 | 0.326111 | ||||||||
\(877\) | −1.09850e22 | −0.929617 | −0.464808 | − | 0.885411i | \(-0.653877\pi\) | ||||
−0.464808 | + | 0.885411i | \(0.653877\pi\) | |||||||
\(878\) | −5.35564e21 | −0.449368 | ||||||||
\(879\) | 1.21801e22 | 1.01329 | ||||||||
\(880\) | 1.43318e21 | 0.118217 | ||||||||
\(881\) | 7.98462e21 | 0.653033 | 0.326516 | − | 0.945192i | \(-0.394125\pi\) | ||||
0.326516 | + | 0.945192i | \(0.394125\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.45236e21 | 0.438409 | 0.219204 | − | 0.975679i | \(-0.429654\pi\) | ||||
0.219204 | + | 0.975679i | \(0.429654\pi\) | |||||||
\(884\) | −4.34640e21 | −0.346528 | ||||||||
\(885\) | 1.72002e21 | 0.135975 | ||||||||
\(886\) | −2.82213e22 | −2.21220 | ||||||||
\(887\) | −1.67127e22 | −1.29903 | −0.649517 | − | 0.760347i | \(-0.725029\pi\) | ||||
−0.649517 | + | 0.760347i | \(0.725029\pi\) | |||||||
\(888\) | 1.41129e22 | 1.08772 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 8.05483e21 | 0.610424 | ||||||||
\(891\) | −3.10820e21 | −0.233575 | ||||||||
\(892\) | 3.51475e20 | 0.0261913 | ||||||||
\(893\) | −5.33178e21 | −0.393991 | ||||||||
\(894\) | −9.08007e21 | −0.665361 | ||||||||
\(895\) | −4.86576e21 | −0.353572 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.01436e21 | 0.429780 | ||||||||
\(898\) | −1.68108e22 | −1.19129 | ||||||||
\(899\) | 2.64180e21 | 0.185653 | ||||||||
\(900\) | 1.21233e21 | 0.0844892 | ||||||||
\(901\) | −1.11917e22 | −0.773500 | ||||||||
\(902\) | −7.30146e21 | −0.500450 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.37704e21 | 0.564712 | ||||||||
\(905\) | 3.87269e21 | 0.258910 | ||||||||
\(906\) | 2.07974e22 | 1.37895 | ||||||||
\(907\) | −1.53384e22 | −1.00862 | −0.504309 | − | 0.863523i | \(-0.668253\pi\) | ||||
−0.504309 | + | 0.863523i | \(0.668253\pi\) | |||||||
\(908\) | −4.21767e21 | −0.275061 | ||||||||
\(909\) | −2.56723e21 | −0.166049 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.49134e22 | −0.948829 | −0.474415 | − | 0.880302i | \(-0.657340\pi\) | ||||
−0.474415 | + | 0.880302i | \(0.657340\pi\) | |||||||
\(912\) | 6.99206e21 | 0.441209 | ||||||||
\(913\) | 5.80007e21 | 0.362997 | ||||||||
\(914\) | −2.55854e22 | −1.58816 | ||||||||
\(915\) | 8.60430e20 | 0.0529734 | ||||||||
\(916\) | −1.49979e21 | −0.0915827 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 2.08241e22 | 1.25097 | ||||||||
\(919\) | −5.86667e21 | −0.349563 | −0.174782 | − | 0.984607i | \(-0.555922\pi\) | ||||
−0.174782 | + | 0.984607i | \(0.555922\pi\) | |||||||
\(920\) | 2.00844e21 | 0.118700 | ||||||||
\(921\) | 3.26529e21 | 0.191414 | ||||||||
\(922\) | −2.99469e22 | −1.74129 | ||||||||
\(923\) | 2.37687e22 | 1.37086 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.87377e22 | 1.63076 | ||||||||
\(926\) | 3.79393e22 | 2.13554 | ||||||||
\(927\) | 2.32695e21 | 0.129924 | ||||||||
\(928\) | 5.71747e21 | 0.316660 | ||||||||
\(929\) | 1.67946e22 | 0.922684 | 0.461342 | − | 0.887222i | \(-0.347368\pi\) | ||||
0.461342 | + | 0.887222i | \(0.347368\pi\) | |||||||
\(930\) | 2.69776e21 | 0.147022 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1.09786e22 | −0.588743 | ||||||||
\(933\) | −1.12724e21 | −0.0599661 | ||||||||
\(934\) | 2.95123e22 | 1.55740 | ||||||||
\(935\) | 1.76636e21 | 0.0924683 | ||||||||
\(936\) | 2.43377e21 | 0.126389 | ||||||||
\(937\) | −5.04466e21 | −0.259887 | −0.129944 | − | 0.991521i | \(-0.541480\pi\) | ||||
−0.129944 | + | 0.991521i | \(0.541480\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.22387e22 | −0.620500 | ||||||||
\(940\) | −2.46833e21 | −0.124149 | ||||||||
\(941\) | −1.65425e22 | −0.825430 | −0.412715 | − | 0.910860i | \(-0.635419\pi\) | ||||
−0.412715 | + | 0.910860i | \(0.635419\pi\) | |||||||
\(942\) | 1.05059e22 | 0.520059 | ||||||||
\(943\) | −1.55185e22 | −0.762100 | ||||||||
\(944\) | 1.31709e22 | 0.641691 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.18960e21 | −0.104998 | ||||||||
\(947\) | −9.81583e21 | −0.466984 | −0.233492 | − | 0.972359i | \(-0.575015\pi\) | ||||
−0.233492 | + | 0.972359i | \(0.575015\pi\) | |||||||
\(948\) | −1.18163e21 | −0.0557725 | ||||||||
\(949\) | 1.56186e22 | 0.731384 | ||||||||
\(950\) | 9.38776e21 | 0.436149 | ||||||||
\(951\) | −2.66963e21 | −0.123054 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.97914e21 | −0.271295 | −0.135648 | − | 0.990757i | \(-0.543311\pi\) | ||||
−0.135648 | + | 0.990757i | \(0.543311\pi\) | |||||||
\(954\) | −4.60981e21 | −0.207525 | ||||||||
\(955\) | 5.13921e21 | 0.229547 | ||||||||
\(956\) | 4.90186e21 | 0.217233 | ||||||||
\(957\) | −2.54350e21 | −0.111839 | ||||||||
\(958\) | −1.38469e22 | −0.604101 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.79882e21 | −0.0772600 | ||||||||
\(961\) | −1.83404e22 | −0.781596 | ||||||||
\(962\) | −4.24375e22 | −1.79447 | ||||||||
\(963\) | 7.89441e21 | 0.331225 | ||||||||
\(964\) | −9.52286e20 | −0.0396451 | ||||||||
\(965\) | 4.64393e20 | 0.0191836 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.44757e22 | −0.588764 | −0.294382 | − | 0.955688i | \(-0.595114\pi\) | ||||
−0.294382 | + | 0.955688i | \(0.595114\pi\) | |||||||
\(968\) | 1.53068e22 | 0.617759 | ||||||||
\(969\) | 8.61757e21 | 0.345109 | ||||||||
\(970\) | 6.89737e21 | 0.274092 | ||||||||
\(971\) | −1.77921e21 | −0.0701590 | −0.0350795 | − | 0.999385i | \(-0.511168\pi\) | ||||
−0.0350795 | + | 0.999385i | \(0.511168\pi\) | |||||||
\(972\) | 4.64802e21 | 0.181874 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −5.21301e21 | −0.200861 | ||||||||
\(975\) | −1.76923e22 | −0.676472 | ||||||||
\(976\) | 6.58868e21 | 0.249991 | ||||||||
\(977\) | 1.04088e22 | 0.391913 | 0.195957 | − | 0.980613i | \(-0.437219\pi\) | ||||
0.195957 | + | 0.980613i | \(0.437219\pi\) | |||||||
\(978\) | 1.21305e22 | 0.453250 | ||||||||
\(979\) | −1.47323e22 | −0.546262 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.98238e21 | −0.145420 | ||||||||
\(982\) | −6.06761e21 | −0.219878 | ||||||||
\(983\) | −3.26461e22 | −1.17403 | −0.587017 | − | 0.809575i | \(-0.699698\pi\) | ||||
−0.587017 | + | 0.809575i | \(0.699698\pi\) | |||||||
\(984\) | 2.24185e22 | 0.800100 | ||||||||
\(985\) | −1.84561e21 | −0.0653684 | ||||||||
\(986\) | 1.31244e22 | 0.461320 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.12659e21 | −0.142861 | ||||||||
\(989\) | −4.65376e21 | −0.159894 | ||||||||
\(990\) | 7.27557e20 | 0.0248087 | ||||||||
\(991\) | −7.47327e21 | −0.252906 | −0.126453 | − | 0.991973i | \(-0.540359\pi\) | ||||
−0.126453 | + | 0.991973i | \(0.540359\pi\) | |||||||
\(992\) | 1.10915e22 | 0.372523 | ||||||||
\(993\) | −3.40107e22 | −1.13369 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.49275e22 | −0.490132 | ||||||||
\(996\) | 1.30999e22 | 0.426897 | ||||||||
\(997\) | 3.10809e22 | 1.00526 | 0.502632 | − | 0.864500i | \(-0.332365\pi\) | ||||
0.502632 | + | 0.864500i | \(0.332365\pi\) | |||||||
\(998\) | −3.71506e22 | −1.19258 | ||||||||
\(999\) | 6.05226e22 | 1.92831 |
(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 | 49.16.a.a.1.1 | 1 | ||
7.2 | even | 3 | 49.16.c.b.18.1 | 2 | |||
7.3 | odd | 6 | 49.16.c.c.30.1 | 2 | |||
7.4 | even | 3 | 49.16.c.b.30.1 | 2 | |||
7.5 | odd | 6 | 49.16.c.c.18.1 | 2 | |||
7.6 | odd | 2 | 1.16.a.a.1.1 | ✓ | 1 | ||
21.20 | even | 2 | 9.16.a.a.1.1 | 1 | |||
28.27 | even | 2 | 16.16.a.d.1.1 | 1 | |||
35.13 | even | 4 | 25.16.b.a.24.1 | 2 | |||
35.27 | even | 4 | 25.16.b.a.24.2 | 2 | |||
35.34 | odd | 2 | 25.16.a.a.1.1 | 1 | |||
56.13 | odd | 2 | 64.16.a.i.1.1 | 1 | |||
56.27 | even | 2 | 64.16.a.c.1.1 | 1 | |||
77.76 | even | 2 | 121.16.a.a.1.1 | 1 | |||
84.83 | odd | 2 | 144.16.a.f.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.16.a.a.1.1 | ✓ | 1 | 7.6 | odd | 2 | ||
9.16.a.a.1.1 | 1 | 21.20 | even | 2 | |||
16.16.a.d.1.1 | 1 | 28.27 | even | 2 | |||
25.16.a.a.1.1 | 1 | 35.34 | odd | 2 | |||
25.16.b.a.24.1 | 2 | 35.13 | even | 4 | |||
25.16.b.a.24.2 | 2 | 35.27 | even | 4 | |||
49.16.a.a.1.1 | 1 | 1.1 | even | 1 | trivial | ||
49.16.c.b.18.1 | 2 | 7.2 | even | 3 | |||
49.16.c.b.30.1 | 2 | 7.4 | even | 3 | |||
49.16.c.c.18.1 | 2 | 7.5 | odd | 6 | |||
49.16.c.c.30.1 | 2 | 7.3 | odd | 6 | |||
64.16.a.c.1.1 | 1 | 56.27 | even | 2 | |||
64.16.a.i.1.1 | 1 | 56.13 | odd | 2 | |||
121.16.a.a.1.1 | 1 | 77.76 | even | 2 | |||
144.16.a.f.1.1 | 1 | 84.83 | odd | 2 |