Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [80,14,Mod(1,80)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(80, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("80.1");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 80 = 2^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
Character orbit: | \([\chi]\) | \(=\) | 80.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: | \(85.7847431615\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4466x - 18720 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{10}\cdot 5 \) |
Twist minimal: | no (minimal twist has level 5) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(69.3208\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 80.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1125.79 | 0.891601 | 0.445801 | − | 0.895132i | \(-0.352919\pi\) | ||||
0.445801 | + | 0.895132i | \(0.352919\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 15625.0 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −324482. | −1.04245 | −0.521223 | − | 0.853420i | \(-0.674524\pi\) | ||||
−0.521223 | + | 0.853420i | \(0.674524\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −326912. | −0.205047 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.64726e6 | 0.280356 | 0.140178 | − | 0.990126i | \(-0.455232\pi\) | ||||
0.140178 | + | 0.990126i | \(0.455232\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.26700e6 | 0.360104 | 0.180052 | − | 0.983657i | \(-0.442373\pi\) | ||||
0.180052 | + | 0.983657i | \(0.442373\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.75905e7 | 0.398736 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.66481e8 | 1.67281 | 0.836406 | − | 0.548110i | \(-0.184653\pi\) | ||||
0.836406 | + | 0.548110i | \(0.184653\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.12929e8 | −1.52598 | −0.762988 | − | 0.646413i | \(-0.776268\pi\) | ||||
−0.762988 | + | 0.646413i | \(0.776268\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.65300e8 | −0.929447 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.32351e8 | 0.890692 | 0.445346 | − | 0.895359i | \(-0.353081\pi\) | ||||
0.445346 | + | 0.895359i | \(0.353081\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.44141e8 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.16291e9 | −1.07442 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.82750e9 | −0.882704 | −0.441352 | − | 0.897334i | \(-0.645501\pi\) | ||||
−0.441352 | + | 0.897334i | \(0.645501\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.61629e9 | −1.54132 | −0.770659 | − | 0.637247i | \(-0.780073\pi\) | ||||
−0.770659 | + | 0.637247i | \(0.780073\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.85448e9 | 0.249966 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.07004e9 | −0.466196 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.99161e10 | 1.27613 | 0.638063 | − | 0.769984i | \(-0.279736\pi\) | ||||
0.638063 | + | 0.769984i | \(0.279736\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7.05535e9 | 0.321069 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.69877e10 | −1.54486 | −0.772430 | − | 0.635099i | \(-0.780959\pi\) | ||||
−0.772430 | + | 0.635099i | \(0.780959\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.85897e9 | 0.189592 | 0.0947961 | − | 0.995497i | \(-0.469780\pi\) | ||||
0.0947961 | + | 0.995497i | \(0.469780\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.10799e9 | −0.0917000 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.31265e10 | −1.12487 | −0.562437 | − | 0.826840i | \(-0.690136\pi\) | ||||
−0.562437 | + | 0.826840i | \(0.690136\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 8.39984e9 | 0.0866955 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.87423e11 | 1.49148 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.19285e11 | −0.739255 | −0.369628 | − | 0.929180i | \(-0.620515\pi\) | ||||
−0.369628 | + | 0.929180i | \(0.620515\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.57385e10 | 0.125379 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.52294e11 | −1.36056 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.20299e11 | −1.29724 | −0.648620 | − | 0.761112i | \(-0.724654\pi\) | ||||
−0.648620 | + | 0.761112i | \(0.724654\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.15504e11 | 1.03260 | 0.516299 | − | 0.856409i | \(-0.327309\pi\) | ||||
0.516299 | + | 0.856409i | \(0.327309\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.06077e11 | 0.213751 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 9.79220e10 | 0.161044 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.02968e11 | 0.139065 | 0.0695323 | − | 0.997580i | \(-0.477849\pi\) | ||||
0.0695323 | + | 0.997580i | \(0.477849\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.11897e11 | 0.794142 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.00383e11 | 0.370933 | 0.185467 | − | 0.982651i | \(-0.440620\pi\) | ||||
0.185467 | + | 0.982651i | \(0.440620\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.55011e11 | 0.429243 | 0.214621 | − | 0.976697i | \(-0.431148\pi\) | ||||
0.214621 | + | 0.976697i | \(0.431148\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.74852e11 | 0.178320 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.34508e11 | −0.292257 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.60313e12 | −0.741980 | −0.370990 | − | 0.928637i | \(-0.620982\pi\) | ||||
−0.370990 | + | 0.928637i | \(0.620982\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.91379e12 | −0.752908 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.64201e11 | 0.0887005 | 0.0443503 | − | 0.999016i | \(-0.485878\pi\) | ||||
0.0443503 | + | 0.999016i | \(0.485878\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.60127e12 | 0.748104 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.18318e12 | −0.787020 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.69637e12 | −0.788388 | −0.394194 | − | 0.919027i | \(-0.628976\pi\) | ||||
−0.394194 | + | 0.919027i | \(0.628976\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.03353e12 | −0.375390 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.57437e12 | −1.37424 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.88952e12 | −0.682437 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.00920e13 | −1.23016 | −0.615081 | − | 0.788464i | \(-0.710877\pi\) | ||||
−0.615081 | + | 0.788464i | \(0.710877\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.38510e11 | −0.0574863 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.56737e12 | 0.240658 | 0.120329 | − | 0.992734i | \(-0.461605\pi\) | ||||
0.120329 | + | 0.992734i | \(0.461605\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.21037e13 | −0.998791 | −0.499395 | − | 0.866374i | \(-0.666444\pi\) | ||||
−0.499395 | + | 0.866374i | \(0.666444\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.70782e12 | −0.415661 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.37488e12 | −0.603909 | −0.301954 | − | 0.953322i | \(-0.597639\pi\) | ||||
−0.301954 | + | 0.953322i | \(0.597639\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.49908e13 | −1.42727 | −0.713637 | − | 0.700516i | \(-0.752953\pi\) | ||||
−0.713637 | + | 0.700516i | \(0.752953\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.24214e13 | 1.13779 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.35600e13 | 0.612703 | 0.306352 | − | 0.951918i | \(-0.400892\pi\) | ||||
0.306352 | + | 0.951918i | \(0.400892\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.88049e12 | 0.398330 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.04876e12 | −0.0738384 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.40202e13 | −1.74382 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.18092e13 | −0.921400 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.28985e13 | −1.37740 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.81470e12 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.16836e13 | 0.247088 | 0.123544 | − | 0.992339i | \(-0.460574\pi\) | ||||
0.123544 | + | 0.992339i | \(0.460574\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.84758e12 | 0.169041 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.12734e13 | −0.886398 | −0.443199 | − | 0.896423i | \(-0.646157\pi\) | ||||
−0.443199 | + | 0.896423i | \(0.646157\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.01540e14 | 1.59075 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.37955e13 | −0.480496 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.15579e13 | −0.924642 | −0.462321 | − | 0.886713i | \(-0.652983\pi\) | ||||
−0.462321 | + | 0.886713i | \(0.652983\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.16286e14 | 1.36751 | 0.683754 | − | 0.729712i | \(-0.260346\pi\) | ||||
0.683754 | + | 0.729712i | \(0.260346\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.35833e13 | −1.00294 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.03234e13 | 0.100958 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.41796e13 | −0.394757 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 9.45649e12 | 0.0772978 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.43657e14 | −1.07552 | −0.537758 | − | 0.843099i | \(-0.680729\pi\) | ||||
−0.537758 | + | 0.843099i | \(0.680729\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.99719e13 | 0.137110 | 0.0685551 | − | 0.997647i | \(-0.478161\pi\) | ||||
0.0685551 | + | 0.997647i | \(0.478161\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.44246e13 | −0.343006 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.19005e14 | −0.689299 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.46452e14 | 1.31336 | 0.656682 | − | 0.754168i | \(-0.271959\pi\) | ||||
0.656682 | + | 0.754168i | \(0.271959\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.34291e14 | −0.659121 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.05187e14 | −0.928499 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.33661e14 | −0.558194 | −0.279097 | − | 0.960263i | \(-0.590035\pi\) | ||||
−0.279097 | + | 0.960263i | \(0.590035\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.89762e13 | 0.111788 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.57170e14 | 0.560676 | 0.280338 | − | 0.959901i | \(-0.409553\pi\) | ||||
0.280338 | + | 0.959901i | \(0.409553\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.63600e14 | −0.870325 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.02300e14 | 0.312897 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.32272e14 | 0.942309 | 0.471155 | − | 0.882051i | \(-0.343837\pi\) | ||||
0.471155 | + | 0.882051i | \(0.343837\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.92193e13 | −0.208489 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.73170e14 | −1.15662 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.96701e14 | −1.12863 | −0.564313 | − | 0.825561i | \(-0.690859\pi\) | ||||
−0.564313 | + | 0.825561i | \(0.690859\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.73895e14 | 1.21317 | 0.606585 | − | 0.795019i | \(-0.292539\pi\) | ||||
0.606585 | + | 0.795019i | \(0.292539\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.67771e14 | 0.920665 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.11189e14 | 0.570701 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.74238e14 | 0.468984 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 7.01828e14 | 1.12003 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.21109e14 | 1.37276 | 0.686379 | − | 0.727244i | \(-0.259199\pi\) | ||||
0.686379 | + | 0.727244i | \(0.259199\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.88779e14 | 1.23786 | 0.618929 | − | 0.785447i | \(-0.287567\pi\) | ||||
0.618929 | + | 0.785447i | \(0.287567\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.10240e14 | 0.143587 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.70943e13 | −0.0574035 | −0.0287017 | − | 0.999588i | \(-0.509137\pi\) | ||||
−0.0287017 | + | 0.999588i | \(0.509137\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.94174e14 | −0.564072 | −0.282036 | − | 0.959404i | \(-0.591010\pi\) | ||||
−0.282036 | + | 0.959404i | \(0.591010\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.15921e14 | 0.123990 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.17473e14 | 0.920172 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.34183e14 | −0.690883 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.06723e14 | −0.182634 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.15477e14 | −0.427817 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.22476e15 | 0.955466 | 0.477733 | − | 0.878505i | \(-0.341459\pi\) | ||||
0.477733 | + | 0.878505i | \(0.341459\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.50748e14 | 0.330725 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.22796e14 | 0.0847882 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.47135e15 | 1.60674 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.24828e14 | 0.382713 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.04334e15 | 0.602387 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.23977e15 | 0.675087 | 0.337544 | − | 0.941310i | \(-0.390404\pi\) | ||||
0.337544 | + | 0.941310i | \(0.390404\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −7.98124e13 | −0.0410095 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.31953e14 | 0.161031 | 0.0805154 | − | 0.996753i | \(-0.474343\pi\) | ||||
0.0805154 | + | 0.996753i | \(0.474343\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.92799e15 | −0.883433 | −0.441717 | − | 0.897155i | \(-0.645630\pi\) | ||||
−0.441717 | + | 0.897155i | \(0.645630\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.01746e14 | −0.260576 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.12721e15 | −0.461522 | −0.230761 | − | 0.973010i | \(-0.574122\pi\) | ||||
−0.230761 | + | 0.973010i | \(0.574122\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.29885e15 | −0.503059 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.80479e15 | −0.661550 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.13044e15 | 0.739405 | 0.369703 | − | 0.929150i | \(-0.379460\pi\) | ||||
0.369703 | + | 0.929150i | \(0.379460\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.70709e15 | 1.21877 | 0.609386 | − | 0.792874i | \(-0.291416\pi\) | ||||
0.609386 | + | 0.792874i | \(0.291416\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.29385e15 | 0.403128 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.31248e14 | 0.0387714 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.96113e15 | −0.549510 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.97435e14 | 0.0790855 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.69706e15 | −0.428368 | −0.214184 | − | 0.976793i | \(-0.568709\pi\) | ||||
−0.214184 | + | 0.976793i | \(0.568709\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.04165e15 | 0.249711 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.92849e15 | 0.667011 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.42768e14 | −0.0742053 | −0.0371027 | − | 0.999311i | \(-0.511813\pi\) | ||||
−0.0371027 | + | 0.999311i | \(0.511813\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.46243e15 | −1.33029 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.24342e14 | 0.180996 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.63399e15 | −0.863460 | −0.431730 | − | 0.902003i | \(-0.642097\pi\) | ||||
−0.431730 | + | 0.902003i | \(0.642097\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.86384e15 | −0.330605 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.16134e15 | −0.702927 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.38103e15 | −0.865915 | −0.432957 | − | 0.901414i | \(-0.642530\pi\) | ||||
−0.432957 | + | 0.901414i | \(0.642530\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.17255e15 | −1.25331 | −0.626653 | − | 0.779298i | \(-0.715576\pi\) | ||||
−0.626653 | + | 0.779298i | \(0.715576\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.28934e15 | −0.334698 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.02164e14 | 0.0560713 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.61841e14 | −0.101332 | −0.0506659 | − | 0.998716i | \(-0.516134\pi\) | ||||
−0.0506659 | + | 0.998716i | \(0.516134\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.48985e15 | 0.316043 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.73851e15 | −1.18005 | −0.590027 | − | 0.807384i | \(-0.700883\pi\) | ||||
−0.590027 | + | 0.807384i | \(0.700883\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.30296e16 | 1.50771 | 0.753857 | − | 0.657038i | \(-0.228191\pi\) | ||||
0.753857 | + | 0.657038i | \(0.228191\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.50459e15 | −0.608461 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.52467e16 | 1.61044 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.78114e16 | 1.79830 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.13615e16 | −1.09681 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.27472e15 | −0.394701 | −0.197351 | − | 0.980333i | \(-0.563234\pi\) | ||||
−0.197351 | + | 0.980333i | \(0.563234\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.56718e15 | −0.580144 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.56289e15 | −0.301221 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.96295e15 | 0.320742 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.55010e15 | −0.197640 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.89033e15 | 0.214571 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.49224e15 | 0.461791 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.84450e16 | −1.25742 | −0.628709 | − | 0.777640i | \(-0.716417\pi\) | ||||
−0.628709 | + | 0.777640i | \(0.716417\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.36262e16 | −0.890523 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.21772e16 | 1.38984 | 0.694918 | − | 0.719089i | \(-0.255441\pi\) | ||||
0.694918 | + | 0.719089i | \(0.255441\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.02883e16 | −1.21957 | −0.609785 | − | 0.792567i | \(-0.708744\pi\) | ||||
−0.609785 | + | 0.792567i | \(0.708744\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.65745e15 | 0.0955923 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.93347e16 | 1.07017 | 0.535085 | − | 0.844798i | \(-0.320280\pi\) | ||||
0.535085 | + | 0.844798i | \(0.320280\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.65763e15 | −0.247472 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.05542e16 | −0.538446 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.20968e16 | −2.55267 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.53003e15 | 0.0720208 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.81344e16 | −1.27256 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.69731e16 | 1.17262 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.61159e15 | −0.192739 | −0.0963693 | − | 0.995346i | \(-0.530723\pi\) | ||||
−0.0963693 | + | 0.995346i | \(0.530723\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.51081e15 | −0.261666 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.60888e15 | 0.0621916 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.91103e16 | −1.45444 | −0.727222 | − | 0.686402i | \(-0.759189\pi\) | ||||
−0.727222 | + | 0.686402i | \(0.759189\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.52658e16 | 0.546287 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.25460e16 | −0.432119 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.87132e16 | 0.952071 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.11234e16 | 0.355151 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.96375e15 | −0.183391 | −0.0916955 | − | 0.995787i | \(-0.529229\pi\) | ||||
−0.0916955 | + | 0.995787i | \(0.529229\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.76636e15 | 0.0819490 | 0.0409745 | − | 0.999160i | \(-0.486954\pi\) | ||||
0.0409745 | + | 0.999160i | \(0.486954\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.35550e16 | −0.386904 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.98418e16 | 0.545816 | 0.272908 | − | 0.962040i | \(-0.412015\pi\) | ||||
0.272908 | + | 0.962040i | \(0.412015\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.25598e15 | 0.165887 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.08156e16 | −1.55479 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.22798e16 | 0.795824 | 0.397912 | − | 0.917424i | \(-0.369735\pi\) | ||||
0.397912 | + | 0.917424i | \(0.369735\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.58716e16 | 1.32860 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.58106e16 | −0.821522 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.67204e15 | 0.191963 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.42436e16 | 0.945194 | 0.472597 | − | 0.881279i | \(-0.343317\pi\) | ||||
0.472597 | + | 0.881279i | \(0.343317\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.53608e16 | 0.316770 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.87060e16 | 0.770634 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.26267e16 | 1.78086 | 0.890428 | − | 0.455125i | \(-0.150405\pi\) | ||||
0.890428 | + | 0.455125i | \(0.150405\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.29456e15 | 0.0797472 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.77199e16 | −0.317865 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.71415e16 | 0.643732 | 0.321866 | − | 0.946785i | \(-0.395690\pi\) | ||||
0.321866 | + | 0.946785i | \(0.395690\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.31533e16 | 0.220304 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.22127e16 | 0.197706 | 0.0988532 | − | 0.995102i | \(-0.468483\pi\) | ||||
0.0988532 | + | 0.995102i | \(0.468483\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.35169e15 | −0.130701 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.56919e15 | −0.0388754 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.53716e16 | 1.10290 | 0.551449 | − | 0.834209i | \(-0.314075\pi\) | ||||
0.551449 | + | 0.834209i | \(0.314075\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.05275e17 | 1.48996 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.77233e16 | −0.790314 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.50489e16 | −0.331824 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.59809e16 | 1.10221 | 0.551104 | − | 0.834437i | \(-0.314207\pi\) | ||||
0.551104 | + | 0.834437i | \(0.314207\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.14313e17 | 1.41831 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.13598e17 | −1.36437 | −0.682186 | − | 0.731178i | \(-0.738971\pi\) | ||||
−0.682186 | + | 0.731178i | \(0.738971\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.77313e16 | −0.555035 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.99030e16 | −0.336711 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.28071e16 | 0.357770 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.50572e16 | −0.370318 | −0.185159 | − | 0.982709i | \(-0.559280\pi\) | ||||
−0.185159 | + | 0.982709i | \(0.559280\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.05594e16 | −0.824412 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.36380e17 | 1.35230 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.12813e15 | 0.0396681 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.30914e17 | 1.21927 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.82535e15 | 0.0255083 | 0.0127541 | − | 0.999919i | \(-0.495940\pi\) | ||||
0.0127541 | + | 0.999919i | \(0.495940\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.17054e16 | 0.715183 | 0.357591 | − | 0.933878i | \(-0.383598\pi\) | ||||
0.357591 | + | 0.933878i | \(0.383598\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.71750e16 | 0.230652 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.06448e16 | 0.334562 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.34824e17 | −1.07643 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.16220e16 | 0.0900139 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.31353e16 | −0.324139 | −0.162069 | − | 0.986779i | \(-0.551817\pi\) | ||||
−0.162069 | + | 0.986779i | \(0.551817\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.25222e16 | −0.455893 | −0.227947 | − | 0.973674i | \(-0.573201\pi\) | ||||
−0.227947 | + | 0.973674i | \(0.573201\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.97371e16 | −0.351966 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.97881e17 | −1.35917 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.25265e16 | 0.483590 | 0.241795 | − | 0.970327i | \(-0.422264\pi\) | ||||
0.241795 | + | 0.970327i | \(0.422264\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.74601e15 | −0.0177767 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.76459e17 | 1.73783 | 0.868914 | − | 0.494962i | \(-0.164818\pi\) | ||||
0.868914 | + | 0.494962i | \(0.164818\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.77557e16 | −0.352578 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.61728e17 | −0.958931 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.46120e17 | 1.41757 | 0.708786 | − | 0.705424i | \(-0.249243\pi\) | ||||
0.708786 | + | 0.705424i | \(0.249243\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.74012e16 | −0.433112 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.24843e16 | 0.122248 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.17740e16 | −0.167879 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.45983e17 | −1.77664 | −0.888319 | − | 0.459226i | \(-0.848127\pi\) | ||||
−0.888319 | + | 0.459226i | \(0.848127\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.60084e17 | −1.79731 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.04114e17 | −0.505188 | −0.252594 | − | 0.967572i | \(-0.581284\pi\) | ||||
−0.252594 | + | 0.967572i | \(0.581284\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.70140e17 | 0.802656 | 0.401328 | − | 0.915934i | \(-0.368549\pi\) | ||||
0.401328 | + | 0.915934i | \(0.368549\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.33975e17 | −0.614579 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.84060e17 | −0.821106 | −0.410553 | − | 0.911837i | \(-0.634664\pi\) | ||||
−0.410553 | + | 0.911837i | \(0.634664\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.34114e16 | −0.144968 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.77454e17 | 1.17100 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.29458e16 | 0.0531534 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.63987e16 | −0.305195 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.89958e16 | 0.151582 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.13215e17 | 0.806562 | 0.403281 | − | 0.915076i | \(-0.367870\pi\) | ||||
0.403281 | + | 0.915076i | \(0.367870\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.24814e17 | 0.459538 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.30998e17 | −0.827851 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.57688e17 | −0.550145 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.74978e17 | 1.27370 | 0.636851 | − | 0.770987i | \(-0.280237\pi\) | ||||
0.636851 | + | 0.770987i | \(0.280237\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.50475e17 | −0.497687 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.11003e17 | −1.32378 | −0.661889 | − | 0.749602i | \(-0.730245\pi\) | ||||
−0.661889 | + | 0.749602i | \(0.730245\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.70725e17 | −1.47660 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8.41421e15 | −0.0257087 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.29917e17 | −0.386678 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.73839e17 | −0.504072 | −0.252036 | − | 0.967718i | \(-0.581100\pi\) | ||||
−0.252036 | + | 0.967718i | \(0.581100\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.76941e17 | 0.499899 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.28753e17 | 0.905062 | 0.452531 | − | 0.891749i | \(-0.350521\pi\) | ||||
0.452531 | + | 0.891749i | \(0.350521\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.01152e16 | 0.107625 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.96759e17 | −0.775983 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.89978e16 | 0.175861 | 0.0879305 | − | 0.996127i | \(-0.471975\pi\) | ||||
0.0879305 | + | 0.996127i | \(0.471975\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.80091e17 | −0.447463 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.76839e17 | 1.63954 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.89120e17 | −0.446673 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.36931e17 | −0.315365 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.74069e17 | 0.840164 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.38335e17 | 1.83642 | 0.918211 | − | 0.396092i | \(-0.129634\pi\) | ||||
0.918211 | + | 0.396092i | \(0.129634\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.91687e17 | 0.409573 | 0.204786 | − | 0.978807i | \(-0.434350\pi\) | ||||
0.204786 | + | 0.978807i | \(0.434350\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −8.91846e16 | −0.185889 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.26797e18 | −2.57834 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.04168e17 | −0.206668 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.37401e17 | 0.265996 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.94472e17 | −0.556311 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.46483e17 | −0.270076 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.59183e17 | −1.00628 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.38368e16 | 0.0243056 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.65938e17 | −1.48492 | −0.742462 | − | 0.669888i | \(-0.766342\pi\) | ||||
−0.742462 | + | 0.669888i | \(0.766342\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.46087e17 | 1.08166 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.90481e17 | −0.638296 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.16237e18 | −1.85536 | −0.927678 | − | 0.373382i | \(-0.878198\pi\) | ||||
−0.927678 | + | 0.373382i | \(0.878198\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.35833e17 | −0.211731 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.84806e17 | 1.34698 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.20187e17 | 0.773475 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.50335e17 | 0.508837 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.02746e17 | −0.145783 | −0.0728917 | − | 0.997340i | \(-0.523223\pi\) | ||||
−0.0728917 | + | 0.997340i | \(0.523223\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.92522e16 | 0.0682730 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.08736e17 | 0.418146 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7.17343e17 | −0.949341 | −0.474671 | − | 0.880164i | \(-0.657433\pi\) | ||||
−0.474671 | + | 0.880164i | \(0.657433\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.11875e17 | 0.274009 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 6.20992e17 | 0.784867 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.25353e17 | −0.154848 | −0.0774238 | − | 0.996998i | \(-0.524669\pi\) | ||||
−0.0774238 | + | 0.996998i | \(0.524669\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.00269e17 | 0.121069 | 0.0605344 | − | 0.998166i | \(-0.480720\pi\) | ||||
0.0605344 | + | 0.998166i | \(0.480720\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.03698e18 | 1.22395 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.54383e17 | 0.178138 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.36098e18 | −1.53535 | −0.767675 | − | 0.640839i | \(-0.778587\pi\) | ||||
−0.767675 | + | 0.640839i | \(0.778587\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.00058e18 | 1.10368 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.57285e16 | −0.0924656 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.96495e17 | −0.207255 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.20118e16 | −0.0330215 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.87785e16 | 0.0693913 | 0.0346956 | − | 0.999398i | \(-0.488954\pi\) | ||||
0.0346956 | + | 0.999398i | \(0.488954\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.38336e18 | 2.35201 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.30185e16 | −0.0511810 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.46338e17 | −0.327073 | −0.163536 | − | 0.986537i | \(-0.552290\pi\) | ||||
−0.163536 | + | 0.986537i | \(0.552290\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.44066e17 | −0.779859 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.56338e17 | −0.502928 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.08982e18 | 0.964004 | 0.482002 | − | 0.876170i | \(-0.339910\pi\) | ||||
0.482002 | + | 0.876170i | \(0.339910\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.73058e17 | 0.236358 | 0.118179 | − | 0.992992i | \(-0.462294\pi\) | ||||
0.118179 | + | 0.992992i | \(0.462294\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.36615e16 | −0.0285148 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.97019e17 | −0.412063 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.19160e18 | 0.966951 | 0.483476 | − | 0.875358i | \(-0.339374\pi\) | ||||
0.483476 | + | 0.875358i | \(0.339374\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.03289e18 | 0.820426 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.20954e17 | −0.405072 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.63023e17 | 0.276338 | 0.138169 | − | 0.990409i | \(-0.455878\pi\) | ||||
0.138169 | + | 0.990409i | \(0.455878\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.26539e17 | −0.615992 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.06720e17 | 0.442726 | 0.221363 | − | 0.975192i | \(-0.428949\pi\) | ||||
0.221363 | + | 0.975192i | \(0.428949\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.29300e18 | 1.63838 | 0.819190 | − | 0.573523i | \(-0.194424\pi\) | ||||
0.819190 | + | 0.573523i | \(0.194424\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.36772e18 | −0.956979 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.19941e18 | 0.821852 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.96046e16 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.80320e17 | −0.381442 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.31566e18 | 2.13472 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.33398e17 | −0.210268 | −0.105134 | − | 0.994458i | \(-0.533527\pi\) | ||||
−0.105134 | + | 0.994458i | \(0.533527\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.37883e18 | 0.851895 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.82556e17 | 0.110501 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.26418e16 | 0.0312194 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.30890e17 | −0.0760589 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.91188e17 | −0.507449 | −0.253724 | − | 0.967277i | \(-0.581656\pi\) | ||||
−0.253724 | + | 0.967277i | \(0.581656\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.58943e17 | −0.311886 | −0.155943 | − | 0.987766i | \(-0.549842\pi\) | ||||
−0.155943 | + | 0.987766i | \(0.549842\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.38243e17 | 0.0755973 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.62698e18 | −0.871973 | −0.435987 | − | 0.899953i | \(-0.643601\pi\) | ||||
−0.435987 | + | 0.899953i | \(0.643601\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.92344e17 | −0.363690 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.78223e18 | 1.43257 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.71206e17 | −0.338782 | −0.169391 | − | 0.985549i | \(-0.554180\pi\) | ||||
−0.169391 | + | 0.985549i | \(0.554180\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.01147e17 | −0.396409 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.81439e17 | −0.0880150 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.08505e18 | 0.516053 | 0.258027 | − | 0.966138i | \(-0.416928\pi\) | ||||
0.258027 | + | 0.966138i | \(0.416928\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.34214e18 | 1.09220 | 0.546100 | − | 0.837720i | \(-0.316112\pi\) | ||||
0.546100 | + | 0.837720i | \(0.316112\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.17458e18 | 0.537089 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.58656e18 | 0.711404 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.78797e18 | −0.786217 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.39573e18 | 0.601909 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.84444e17 | 0.289495 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.92495e17 | 0.328775 | 0.164387 | − | 0.986396i | \(-0.447435\pi\) | ||||
0.164387 | + | 0.986396i | \(0.447435\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.28055e17 | −0.214884 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.35105e18 | −0.938503 | −0.469251 | − | 0.883065i | \(-0.655476\pi\) | ||||
−0.469251 | + | 0.883065i | \(0.655476\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.27469e18 | 1.28238 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.73711e17 | 0.143575 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.22912e17 | 0.121717 | 0.0608583 | − | 0.998146i | \(-0.480616\pi\) | ||||
0.0608583 | + | 0.998146i | \(0.480616\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.11809e18 | −0.413513 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.17052e18 | −0.787670 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7.47563e17 | −0.266209 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.36976e18 | −1.17758 | −0.588792 | − | 0.808284i | \(-0.700396\pi\) | ||||
−0.588792 | + | 0.808284i | \(0.700396\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.74737e17 | 0.0599265 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.81696e18 | 0.611568 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.82257e18 | −2.58426 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.26901e18 | −0.411494 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.38800e18 | −1.71499 | −0.857493 | − | 0.514495i | \(-0.827979\pi\) | ||||
−0.857493 | + | 0.514495i | \(0.827979\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.23233e18 | −1.94734 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.46224e18 | −0.448528 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8.33067e17 | −0.250873 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.40376e18 | −0.415044 | −0.207522 | − | 0.978230i | \(-0.566540\pi\) | ||||
−0.207522 | + | 0.978230i | \(0.566540\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.24082e17 | 0.152141 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.81617e18 | −1.37284 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.61303e17 | 0.0451496 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.39843e18 | 0.659254 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.38614e18 | 0.374170 | 0.187085 | − | 0.982344i | \(-0.440096\pi\) | ||||
0.187085 | + | 0.982344i | \(0.440096\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.92742e18 | 1.04119 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.17342e18 | 1.08666 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.90307e17 | −0.176541 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.20824e18 | −1.05712 | −0.528562 | − | 0.848894i | \(-0.677269\pi\) | ||||
−0.528562 | + | 0.848894i | \(0.677269\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4.50781e18 | 1.11234 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.30837e18 | 0.317152 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.61043e17 | 0.181231 | 0.0906156 | − | 0.995886i | \(-0.471117\pi\) | ||||
0.0906156 | + | 0.995886i | \(0.471117\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.47758e17 | 0.0345686 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.69616e17 | 0.0389877 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.25215e18 | −1.41202 | −0.706010 | − | 0.708202i | \(-0.749507\pi\) | ||||
−0.706010 | + | 0.708202i | \(0.749507\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.20783e18 | −0.489944 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.60504e18 | −1.22223 | −0.611113 | − | 0.791543i | \(-0.709278\pi\) | ||||
−0.611113 | + | 0.791543i | \(0.709278\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.24464e18 | −0.480985 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.63703e16 | −0.0181878 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.04199e18 | 0.629543 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.79388e18 | −0.975053 | −0.487526 | − | 0.873108i | \(-0.662101\pi\) | ||||
−0.487526 | + | 0.873108i | \(0.662101\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.91053e18 | −0.381933 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.12061e17 | 0.0613175 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.47656e18 | 0.478328 | 0.239164 | − | 0.970979i | \(-0.423127\pi\) | ||||
0.239164 | + | 0.970979i | \(0.423127\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.17268e18 | 0.222643 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.02209e19 | 1.90761 | 0.953804 | − | 0.300430i | \(-0.0971301\pi\) | ||||
0.953804 | + | 0.300430i | \(0.0971301\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.10906e18 | 1.48786 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −8.50385e17 | −0.153397 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.63402e18 | −0.467142 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.71765e18 | −1.69449 | −0.847247 | − | 0.531199i | \(-0.821742\pi\) | ||||
−0.847247 | + | 0.531199i | \(0.821742\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.85886e17 | −0.0661616 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.33996e18 | 1.06886 | 0.534429 | − | 0.845213i | \(-0.320527\pi\) | ||||
0.534429 | + | 0.845213i | \(0.320527\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.85945e18 | −0.308264 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −7.27536e18 | −1.18609 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.47038e19 | 2.35742 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.59536e17 | 0.103994 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.11563e18 | 0.948396 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.85082e18 | 0.587354 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.11756e17 | −0.0917789 | −0.0458894 | − | 0.998947i | \(-0.514612\pi\) | ||||
−0.0458894 | + | 0.998947i | \(0.514612\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5.21691e18 | −0.769862 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.39999e18 | −0.638711 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.60396e18 | 0.371843 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.09829e18 | −0.294768 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.19147e18 | 0.164665 | 0.0823327 | − | 0.996605i | \(-0.473763\pi\) | ||||
0.0823327 | + | 0.996605i | \(0.473763\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.38390e19 | −1.88170 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.20839e18 | 0.161657 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.14249e17 | 0.120341 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.20605e18 | −0.415237 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.05792e18 | −0.772051 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.74613e18 | 0.971447 | 0.485724 | − | 0.874112i | \(-0.338556\pi\) | ||||
0.485724 | + | 0.874112i | \(0.338556\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.31453e18 | 0.532474 | 0.266237 | − | 0.963908i | \(-0.414220\pi\) | ||||
0.266237 | + | 0.963908i | \(0.414220\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9.20061e18 | −1.11745 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.08845e18 | −0.249632 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.45930e18 | −0.289313 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.64786e17 | 0.0769726 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.32454e19 | −1.50950 | −0.754752 | − | 0.656011i | \(-0.772243\pi\) | ||||
−0.754752 | + | 0.656011i | \(0.772243\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.59982e19 | 1.79461 | 0.897307 | − | 0.441407i | \(-0.145520\pi\) | ||||
0.897307 | + | 0.441407i | \(0.145520\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.52754e17 | 0.0499932 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7.72194e18 | 0.839345 | 0.419672 | − | 0.907676i | \(-0.362145\pi\) | ||||
0.419672 | + | 0.907676i | \(0.362145\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.75341e18 | −0.936640 | −0.468320 | − | 0.883559i | \(-0.655141\pi\) | ||||
−0.468320 | + | 0.883559i | \(0.655141\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.57676e17 | −0.0903476 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.39842e18 | 0.145025 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.45578e18 | 0.250742 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.64734e19 | 1.65603 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.14368e19 | −1.13201 | −0.566007 | − | 0.824400i | \(-0.691513\pi\) | ||||
−0.566007 | + | 0.824400i | \(0.691513\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.26589e18 | −0.220834 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.09636e19 | −1.05214 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.11875e18 | −0.389221 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.03215e19 | 0.960511 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.46686e19 | 1.34428 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.25940e19 | 1.13663 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9.31629e17 | −0.0828084 | −0.0414042 | − | 0.999142i | \(-0.513183\pi\) | ||||
−0.0414042 | + | 0.999142i | \(0.513183\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.59844e18 | 0.139932 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.56376e18 | 0.824619 | 0.412309 | − | 0.911044i | \(-0.364722\pi\) | ||||
0.412309 | + | 0.911044i | \(0.364722\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.17114e18 | −0.609022 | −0.304511 | − | 0.952509i | \(-0.598493\pi\) | ||||
−0.304511 | + | 0.952509i | \(0.598493\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.71646e19 | 1.43587 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.34010e19 | −1.10425 | −0.552125 | − | 0.833761i | \(-0.686183\pi\) | ||||
−0.552125 | + | 0.833761i | \(0.686183\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.19174e18 | 0.421414 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.00520e19 | 1.60337 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.64078e18 | −0.208019 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.45302e17 | 0.0500778 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.29920e18 | 0.252241 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.23780e18 | −0.0932393 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8.23622e18 | −0.611266 | −0.305633 | − | 0.952149i | \(-0.598868\pi\) | ||||
−0.305633 | + | 0.952149i | \(0.598868\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.81246e18 | −0.351916 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.58214e18 | 0.546322 | 0.273161 | − | 0.961968i | \(-0.411931\pi\) | ||||
0.273161 | + | 0.961968i | \(0.411931\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.22388e19 | 0.868946 | 0.434473 | − | 0.900685i | \(-0.356935\pi\) | ||||
0.434473 | + | 0.900685i | \(0.356935\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7.39328e18 | −0.517257 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.48370e18 | −0.171236 | −0.0856182 | − | 0.996328i | \(-0.527287\pi\) | ||||
−0.0856182 | + | 0.996328i | \(0.527287\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.79112e18 | −0.257576 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.15252e18 | −0.211083 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.60127e19 | 1.71653 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.76095e18 | −0.504737 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.46146e18 | 0.285974 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.15350e19 | 1.36053 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.98588e19 | −1.23664 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.87088e18 | −0.176216 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8.96710e18 | 0.542546 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.93837e18 | 0.413819 | 0.206909 | − | 0.978360i | \(-0.433659\pi\) | ||||
0.206909 | + | 0.978360i | \(0.433659\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8.39303e17 | −0.0493462 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.63486e18 | 0.268638 | 0.134319 | − | 0.990938i | \(-0.457115\pi\) | ||||
0.134319 | + | 0.990938i | \(0.457115\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.35208e17 | 0.0248678 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 7.30893e18 | 0.411734 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.66373e19 | 0.924023 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.92534e18 | 0.269703 | 0.134851 | − | 0.990866i | \(-0.456944\pi\) | ||||
0.134851 | + | 0.990866i | \(0.456944\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.07653e19 | −1.12112 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.50920e18 | 0.133575 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.86233e18 | 0.255225 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.95683e18 | 0.204799 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.91203e19 | −0.975870 | −0.487935 | − | 0.872880i | \(-0.662250\pi\) | ||||
−0.487935 | + | 0.872880i | \(0.662250\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.62855e18 | −0.132295 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.49669e19 | 1.23918 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.28497e18 | 0.209736 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.30002e18 | 0.207569 | 0.103785 | − | 0.994600i | \(-0.466905\pi\) | ||||
0.103785 | + | 0.994600i | \(0.466905\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.28404e19 | −1.08737 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.18107e18 | 0.243269 | 0.121635 | − | 0.992575i | \(-0.461186\pi\) | ||||
0.121635 | + | 0.992575i | \(0.461186\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.97128e19 | −1.37600 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.09661e19 | 0.500892 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.94885e19 | −0.878020 | −0.439010 | − | 0.898482i | \(-0.644671\pi\) | ||||
−0.439010 | + | 0.898482i | \(0.644671\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.47825e18 | 0.154572 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.17669e19 | 0.954165 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.96510e19 | −1.28214 | −0.641070 | − | 0.767483i | \(-0.721509\pi\) | ||||
−0.641070 | + | 0.767483i | \(0.721509\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.43923e19 | 0.613916 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5.24353e18 | −0.220646 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.32193e19 | 0.963890 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.35903e19 | 1.37566 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.06476e18 | 0.123830 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.38872e19 | 0.553587 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.25349e18 | −0.0493004 | −0.0246502 | − | 0.999696i | \(-0.507847\pi\) | ||||
−0.0246502 | + | 0.999696i | \(0.507847\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.86502e19 | −2.27596 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.17263e19 | 0.831879 | 0.415940 | − | 0.909392i | \(-0.363453\pi\) | ||||
0.415940 | + | 0.909392i | \(0.363453\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.77327e19 | −1.42555 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.72250e18 | 0.0642139 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.56555e19 | −0.943768 | −0.471884 | − | 0.881661i | \(-0.656426\pi\) | ||||
−0.471884 | + | 0.881661i | \(0.656426\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.08889e18 | −0.221030 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.16977e18 | 0.292659 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.02856e19 | −0.363608 | −0.181804 | − | 0.983335i | \(-0.558194\pi\) | ||||
−0.181804 | + | 0.983335i | \(0.558194\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.35849e17 | −0.0256716 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.03661e19 | 1.04551 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.96963e18 | 0.168868 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.91892e19 | −1.31428 | −0.657140 | − | 0.753769i | \(-0.728234\pi\) | ||||
−0.657140 | + | 0.753769i | \(0.728234\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −5.19170e18 | −0.171846 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.72147e18 | −0.252261 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.60895e19 | 0.518829 | 0.259414 | − | 0.965766i | \(-0.416470\pi\) | ||||
0.259414 | + | 0.965766i | \(0.416470\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.30768e19 | −1.37110 |
(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 | 80.14.a.g.1.3 | 3 | ||
4.3 | odd | 2 | 5.14.a.b.1.1 | ✓ | 3 | ||
12.11 | even | 2 | 45.14.a.e.1.3 | 3 | |||
20.3 | even | 4 | 25.14.b.b.24.5 | 6 | |||
20.7 | even | 4 | 25.14.b.b.24.2 | 6 | |||
20.19 | odd | 2 | 25.14.a.b.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.14.a.b.1.1 | ✓ | 3 | 4.3 | odd | 2 | ||
25.14.a.b.1.3 | 3 | 20.19 | odd | 2 | |||
25.14.b.b.24.2 | 6 | 20.7 | even | 4 | |||
25.14.b.b.24.5 | 6 | 20.3 | even | 4 | |||
45.14.a.e.1.3 | 3 | 12.11 | even | 2 | |||
80.14.a.g.1.3 | 3 | 1.1 | even | 1 | trivial |