Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [192,12,Mod(1,192)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(192, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("192.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 192 = 2^{6} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 192.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: | \(147.521890667\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 24) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 192.1 |
$q$-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 | ||||||||
\(3\) | −243.000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 7130.00 | 1.02036 | 0.510181 | − | 0.860067i | \(-0.329578\pi\) | ||||
0.510181 | + | 0.860067i | \(0.329578\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 19536.0 | 0.439336 | 0.219668 | − | 0.975575i | \(-0.429503\pi\) | ||||
0.219668 | + | 0.975575i | \(0.429503\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 59049.0 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −196148. | −0.367218 | −0.183609 | − | 0.982999i | \(-0.558778\pi\) | ||||
−0.183609 | + | 0.982999i | \(0.558778\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −361414. | −0.269971 | −0.134985 | − | 0.990848i | \(-0.543099\pi\) | ||||
−0.134985 | + | 0.990848i | \(0.543099\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.73259e6 | −0.589107 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −130942. | −0.0223671 | −0.0111836 | − | 0.999937i | \(-0.503560\pi\) | ||||
−0.0111836 | + | 0.999937i | \(0.503560\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.85167e7 | 1.71561 | 0.857805 | − | 0.513975i | \(-0.171828\pi\) | ||||
0.857805 | + | 0.513975i | \(0.171828\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.74725e6 | −0.253651 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.15609e7 | −0.698495 | −0.349247 | − | 0.937031i | \(-0.613563\pi\) | ||||
−0.349247 | + | 0.937031i | \(0.613563\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.00878e6 | 0.0411397 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.43489e7 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.91664e8 | −1.73521 | −0.867603 | − | 0.497258i | \(-0.834340\pi\) | ||||
−0.867603 | + | 0.497258i | \(0.834340\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.07934e8 | −1.30448 | −0.652238 | − | 0.758015i | \(-0.726170\pi\) | ||||
−0.652238 | + | 0.758015i | \(0.726170\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.76640e7 | 0.212013 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.39292e8 | 0.448282 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.00785e8 | 0.476016 | 0.238008 | − | 0.971263i | \(-0.423506\pi\) | ||||
0.238008 | + | 0.971263i | \(0.423506\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 8.78236e7 | 0.155868 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.43526e9 | −1.93472 | −0.967360 | − | 0.253404i | \(-0.918450\pi\) | ||||
−0.967360 | + | 0.253404i | \(0.918450\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.12703e8 | 0.739319 | 0.369660 | − | 0.929167i | \(-0.379474\pi\) | ||||
0.369660 | + | 0.929167i | \(0.379474\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.21019e8 | 0.340121 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.96082e8 | 0.315512 | 0.157756 | − | 0.987478i | \(-0.449574\pi\) | ||||
0.157756 | + | 0.987478i | \(0.449574\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.59567e9 | −0.806984 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.18189e7 | 0.0129137 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.35011e9 | 1.10038 | 0.550190 | − | 0.835040i | \(-0.314555\pi\) | ||||
0.550190 | + | 0.835040i | \(0.314555\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.39854e9 | −0.374696 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.49956e9 | −0.990508 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.58322e9 | 0.834613 | 0.417306 | − | 0.908766i | \(-0.362974\pi\) | ||||
0.417306 | + | 0.908766i | \(0.362974\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.42750e9 | −0.519593 | −0.259797 | − | 0.965663i | \(-0.583656\pi\) | ||||
−0.259797 | + | 0.965663i | \(0.583656\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.15358e9 | 0.146445 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.57688e9 | −0.275468 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.70794e10 | 1.54547 | 0.772735 | − | 0.634729i | \(-0.218888\pi\) | ||||
0.772735 | + | 0.634729i | \(0.218888\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.23929e9 | 0.403276 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.91508e9 | 0.520636 | 0.260318 | − | 0.965523i | \(-0.416173\pi\) | ||||
0.260318 | + | 0.965523i | \(0.416173\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.15597e10 | 1.78179 | 0.890895 | − | 0.454209i | \(-0.150078\pi\) | ||||
0.890895 | + | 0.454209i | \(0.150078\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.88132e8 | −0.0237520 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.83195e9 | −0.161332 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.10236e10 | −1.49998 | −0.749988 | − | 0.661451i | \(-0.769941\pi\) | ||||
−0.749988 | + | 0.661451i | \(0.769941\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.48678e9 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.99747e10 | −0.556609 | −0.278304 | − | 0.960493i | \(-0.589772\pi\) | ||||
−0.278304 | + | 0.960493i | \(0.589772\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.33616e8 | −0.0228226 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.65743e10 | 1.00182 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.06402e10 | −0.201978 | −0.100989 | − | 0.994888i | \(-0.532201\pi\) | ||||
−0.100989 | + | 0.994888i | \(0.532201\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.06058e9 | −0.118608 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.05279e10 | 0.753139 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.32024e11 | 1.75054 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.44111e9 | 0.0761581 | 0.0380790 | − | 0.999275i | \(-0.487876\pi\) | ||||
0.0380790 | + | 0.999275i | \(0.487876\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.15823e10 | −0.122406 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.06774e11 | −1.01088 | −0.505439 | − | 0.862863i | \(-0.668669\pi\) | ||||
−0.505439 | + | 0.862863i | \(0.668669\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.79038e10 | 0.237169 | 0.118585 | − | 0.992944i | \(-0.462164\pi\) | ||||
0.118585 | + | 0.992944i | \(0.462164\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.38479e10 | −0.258816 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.49670e11 | −1.03163 | −0.515817 | − | 0.856699i | \(-0.672511\pi\) | ||||
−0.515817 | + | 0.856699i | \(0.672511\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.05730e11 | −1.28072 | −0.640358 | − | 0.768077i | \(-0.721214\pi\) | ||||
−0.640358 | + | 0.768077i | \(0.721214\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.87907e10 | −0.274828 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.03547e8 | 0.00308163 | 0.00154081 | − | 0.999999i | \(-0.499510\pi\) | ||||
0.00154081 | + | 0.999999i | \(0.499510\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.53729e11 | −0.712718 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.13411e10 | −0.0899902 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.55808e9 | −0.00982667 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.46838e11 | −0.865151 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.48767e11 | 1.11701 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.33822e11 | −0.978385 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.94981e11 | −1.86661 | −0.933303 | − | 0.359090i | \(-0.883087\pi\) | ||||
−0.933303 | + | 0.359090i | \(0.883087\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.73187e11 | −0.426846 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.01509e11 | 1.13576 | 0.567880 | − | 0.823111i | \(-0.307764\pi\) | ||||
0.567880 | + | 0.823111i | \(0.307764\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.61742e11 | 0.753729 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.02308e11 | −0.196369 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.96827e11 | 0.702486 | 0.351243 | − | 0.936284i | \(-0.385759\pi\) | ||||
0.351243 | + | 0.936284i | \(0.385759\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.87790e11 | −0.960817 | −0.480409 | − | 0.877045i | \(-0.659512\pi\) | ||||
−0.480409 | + | 0.877045i | \(0.659512\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.20548e11 | −0.182161 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.08906e10 | 0.0991381 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.36656e12 | −1.77054 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.87748e11 | 0.465913 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.49939e11 | −0.613466 | −0.306733 | − | 0.951796i | \(-0.599236\pi\) | ||||
−0.306733 | + | 0.951796i | \(0.599236\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.09467e10 | −0.0113478 | −0.00567390 | − | 0.999984i | \(-0.501806\pi\) | ||||
−0.00567390 | + | 0.999984i | \(0.501806\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.73199e9 | −0.00745570 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.48257e12 | −1.33104 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.98667e12 | 1.66218 | 0.831088 | − | 0.556141i | \(-0.187718\pi\) | ||||
0.831088 | + | 0.556141i | \(0.187718\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.14078e11 | −0.635304 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.21213e11 | −0.306874 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.08774e11 | 0.346332 | 0.173166 | − | 0.984893i | \(-0.444600\pi\) | ||||
0.173166 | + | 0.984893i | \(0.444600\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.39844e11 | 0.216331 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.66583e12 | 0.992405 | 0.496203 | − | 0.868207i | \(-0.334727\pi\) | ||||
0.496203 | + | 0.868207i | \(0.334727\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.66154e12 | −0.927116 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.09339e12 | 0.571870 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.93849e12 | −1.44169 | −0.720843 | − | 0.693098i | \(-0.756245\pi\) | ||||
−0.720843 | + | 0.693098i | \(0.756245\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.92434e10 | 0.0180741 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.11372e12 | −0.481864 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.48882e11 | 0.345267 | 0.172634 | − | 0.984986i | \(-0.444772\pi\) | ||||
0.172634 | + | 0.984986i | \(0.444772\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.03014e12 | −1.92463 | −0.962317 | − | 0.271932i | \(-0.912338\pi\) | ||||
−0.962317 | + | 0.271932i | \(0.912338\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.32883e11 | 0.299987 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.43160e12 | 0.485709 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.56840e10 | 0.00821361 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.80320e11 | −0.0845502 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.40796e12 | 0.400781 | 0.200390 | − | 0.979716i | \(-0.435779\pi\) | ||||
0.200390 | + | 0.979716i | \(0.435779\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.94985e11 | −0.0524127 | −0.0262063 | − | 0.999657i | \(-0.508343\pi\) | ||||
−0.0262063 | + | 0.999657i | \(0.508343\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.26182e11 | 0.159041 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.16140e12 | −1.23938 | −0.619688 | − | 0.784848i | \(-0.712741\pi\) | ||||
−0.619688 | + | 0.784848i | \(0.712741\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.02078e12 | 0.231867 | 0.115934 | − | 0.993257i | \(-0.463014\pi\) | ||||
0.115934 | + | 0.993257i | \(0.463014\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.15029e12 | −0.892278 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.74434e12 | −0.762338 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.02334e13 | −1.97412 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.27315e12 | −0.232832 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.63201e12 | −0.630003 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.12166e12 | 1.50148 | 0.750742 | − | 0.660596i | \(-0.229696\pi\) | ||||
0.750742 | + | 0.660596i | \(0.229696\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.92336e12 | −0.300589 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.08157e12 | 0.754374 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.06219e12 | −0.573102 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.66900e12 | −1.02872 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.73243e10 | 0.00603846 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.68108e11 | 0.0568419 | 0.0284210 | − | 0.999596i | \(-0.490952\pi\) | ||||
0.0284210 | + | 0.999596i | \(0.490952\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.18616e11 | 0.0137132 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.32196e13 | −1.45571 | −0.727857 | − | 0.685729i | \(-0.759483\pi\) | ||||
−0.727857 | + | 0.685729i | \(0.759483\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.47551e11 | 0.0889346 | 0.0444673 | − | 0.999011i | \(-0.485841\pi\) | ||||
0.0444673 | + | 0.999011i | \(0.485841\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.31163e11 | 0.0931451 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.77637e13 | −1.69464 | −0.847318 | − | 0.531086i | \(-0.821784\pi\) | ||||
−0.847318 | + | 0.531086i | \(0.821784\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.53707e12 | 0.321936 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 9.96873e12 | 0.866012 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.10633e13 | −0.917690 | −0.458845 | − | 0.888516i | \(-0.651737\pi\) | ||||
−0.458845 | + | 0.888516i | \(0.651737\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.31452e13 | −1.04153 | −0.520765 | − | 0.853700i | \(-0.674353\pi\) | ||||
−0.520765 | + | 0.853700i | \(0.674353\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −8.47289e11 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.13771e13 | −0.823416 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.69219e12 | −0.463164 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.85385e12 | 0.321358 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.49029e13 | 1.57777 | 0.788887 | − | 0.614539i | \(-0.210658\pi\) | ||||
0.788887 | + | 0.614539i | \(0.210658\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.22912e12 | 0.256500 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.26869e11 | 0.0131766 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.90572e13 | −1.06030 | −0.530148 | − | 0.847905i | \(-0.677864\pi\) | ||||
−0.530148 | + | 0.847905i | \(0.677864\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.92253e12 | 0.209131 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.13176e13 | −0.578402 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.58113e13 | −1.26489 | −0.632447 | − | 0.774604i | \(-0.717949\pi\) | ||||
−0.632447 | + | 0.774604i | \(0.717949\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.38863e13 | 1.12279 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.58556e12 | 0.116612 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.60114e13 | 0.693093 | 0.346547 | − | 0.938033i | \(-0.387354\pi\) | ||||
0.346547 | + | 0.938033i | \(0.387354\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.14306e13 | 0.890644 | 0.445322 | − | 0.895371i | \(-0.353089\pi\) | ||||
0.445322 | + | 0.895371i | \(0.353089\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.71572e12 | 0.0684782 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.94017e11 | −0.0151072 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.25644e13 | −0.831352 | −0.415676 | − | 0.909513i | \(-0.636455\pi\) | ||||
−0.415676 | + | 0.909513i | \(0.636455\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.22783e13 | −0.434825 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.45643e13 | 0.495912 | 0.247956 | − | 0.968771i | \(-0.420241\pi\) | ||||
0.247956 | + | 0.968771i | \(0.420241\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.43495e13 | −0.797380 | −0.398690 | − | 0.917086i | \(-0.630535\pi\) | ||||
−0.398690 | + | 0.917086i | \(0.630535\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.20818e13 | −1.01068 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.80392e13 | −0.849992 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.42548e13 | −0.999500 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.56519e12 | −0.0439699 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.32740e11 | 0.0117073 | 0.00585363 | − | 0.999983i | \(-0.498137\pi\) | ||||
0.00585363 | + | 0.999983i | \(0.498137\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.26784e13 | 0.851607 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.81451e12 | 0.0706712 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.79240e12 | 0.188573 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.39234e13 | 0.324809 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.59461e13 | 0.583630 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.44381e13 | −0.530174 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.89356e13 | −1.23344 | −0.616718 | − | 0.787185i | \(-0.711538\pi\) | ||||
−0.616718 | + | 0.787185i | \(0.711538\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.78062e12 | −0.136930 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.29359e13 | −0.252125 | −0.126062 | − | 0.992022i | \(-0.540234\pi\) | ||||
−0.126062 | + | 0.992022i | \(0.540234\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.56949e13 | −0.483452 | −0.241726 | − | 0.970345i | \(-0.577714\pi\) | ||||
−0.241726 | + | 0.970345i | \(0.577714\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 8.22503e12 | 0.149427 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.33665e13 | −0.234527 | −0.117263 | − | 0.993101i | \(-0.537412\pi\) | ||||
−0.117263 | + | 0.993101i | \(0.537412\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.75945e13 | 0.637199 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.63699e13 | 0.595614 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.42461e12 | −0.0383732 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.25999e11 | −0.0111065 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.99925e13 | 0.739422 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 9.69147e12 | 0.138616 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.25245e12 | −0.0864960 | −0.0432480 | − | 0.999064i | \(-0.513771\pi\) | ||||
−0.0432480 | + | 0.999064i | \(0.513771\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.18561e13 | 0.158672 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.21776e14 | 1.57694 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.09170e13 | 0.763439 | 0.381720 | − | 0.924278i | \(-0.375332\pi\) | ||||
0.381720 | + | 0.924278i | \(0.375332\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.46662e11 | −0.00177918 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.07858e13 | 0.479027 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.98021e13 | −0.793873 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.73562e13 | 0.411488 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.85685e13 | 0.411548 | 0.205774 | − | 0.978600i | \(-0.434029\pi\) | ||||
0.205774 | + | 0.978600i | \(0.434029\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.48853e13 | −0.360664 | −0.180332 | − | 0.983606i | \(-0.557717\pi\) | ||||
−0.180332 | + | 0.983606i | \(0.557717\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.18590e12 | 0.0519559 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.67569e13 | 0.939553 | 0.469777 | − | 0.882785i | \(-0.344335\pi\) | ||||
0.469777 | + | 0.882785i | \(0.344335\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.64345e13 | 0.531238 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.21614e11 | 0.00567343 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.64650e14 | −1.45728 | −0.728638 | − | 0.684899i | \(-0.759846\pi\) | ||||
−0.728638 | + | 0.684899i | \(0.759846\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.26378e14 | 1.94332 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.99815e13 | 0.499495 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.25020e14 | 1.81807 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.19183e14 | −0.934435 | −0.467218 | − | 0.884142i | \(-0.654744\pi\) | ||||
−0.467218 | + | 0.884142i | \(0.654744\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.47505e13 | −0.644907 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.54478e13 | 0.483436 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.61183e14 | 1.15590 | 0.577949 | − | 0.816073i | \(-0.303853\pi\) | ||||
0.577949 | + | 0.816073i | \(0.303853\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 8.11187e13 | 0.564871 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.92700e13 | 0.468455 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.33388e14 | 0.876195 | 0.438098 | − | 0.898927i | \(-0.355652\pi\) | ||||
0.438098 | + | 0.898927i | \(0.355652\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.68880e14 | 1.07769 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.38158e13 | 0.395671 | 0.197836 | − | 0.980235i | \(-0.436609\pi\) | ||||
0.197836 | + | 0.980235i | \(0.436609\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.73218e13 | −0.164617 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.20844e13 | 0.246440 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.85909e13 | 0.219665 | 0.109833 | − | 0.993950i | \(-0.464968\pi\) | ||||
0.109833 | + | 0.993950i | \(0.464968\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.82322e12 | 0.0156233 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.21867e14 | −0.655731 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.92498e14 | −1.53052 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.64317e13 | 0.134517 | 0.0672585 | − | 0.997736i | \(-0.478575\pi\) | ||||
0.0672585 | + | 0.997736i | \(0.478575\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −8.79033e13 | −0.435165 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.59354e13 | 0.221235 | 0.110617 | − | 0.993863i | \(-0.464717\pi\) | ||||
0.110617 | + | 0.993863i | \(0.464717\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.51502e13 | 0.352170 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.48608e13 | 0.113374 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.93836e13 | −0.174802 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.23890e13 | 0.183136 | 0.0915682 | − | 0.995799i | \(-0.470812\pi\) | ||||
0.0915682 | + | 0.995799i | \(0.470812\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.64289e13 | −0.405581 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.95378e13 | 0.366675 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.42419e14 | −0.567943 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.42833e14 | 0.554728 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.41929e14 | −1.67177 | −0.835883 | − | 0.548907i | \(-0.815044\pi\) | ||||
−0.835883 | + | 0.548907i | \(0.815044\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.10369e14 | 1.14374 | 0.571870 | − | 0.820344i | \(-0.306218\pi\) | ||||
0.571870 | + | 0.820344i | \(0.306218\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.92932e13 | 0.105171 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.63033e11 | −0.000920177 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.69597e13 | −0.228276 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.72264e13 | −0.0572374 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.06558e13 | −0.0992860 | −0.0496430 | − | 0.998767i | \(-0.515808\pi\) | ||||
−0.0496430 | + | 0.998767i | \(0.515808\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.06583e14 | −0.652245 | −0.326122 | − | 0.945328i | \(-0.605742\pi\) | ||||
−0.326122 | + | 0.945328i | \(0.605742\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.32075e14 | 1.02222 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.99236e14 | −1.19834 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.97201e14 | 0.577238 | 0.288619 | − | 0.957444i | \(-0.406804\pi\) | ||||
0.288619 | + | 0.957444i | \(0.406804\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −9.42228e13 | −0.268995 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.98874e14 | −0.553805 | −0.276903 | − | 0.960898i | \(-0.589308\pi\) | ||||
−0.276903 | + | 0.960898i | \(0.589308\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.58644e13 | −0.206090 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.33635e14 | 0.354185 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.87389e14 | 1.77766 | 0.888828 | − | 0.458240i | \(-0.151520\pi\) | ||||
0.888828 | + | 0.458240i | \(0.151520\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.81523e14 | 0.710465 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.66006e12 | 0.00655166 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.03420e13 | −0.121023 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.89942e14 | 0.915085 | 0.457543 | − | 0.889188i | \(-0.348730\pi\) | ||||
0.457543 | + | 0.889188i | \(0.348730\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.87887e12 | 0.00430455 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.08640e14 | −1.58515 | −0.792576 | − | 0.609774i | \(-0.791260\pi\) | ||||
−0.792576 | + | 0.609774i | \(0.791260\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.00543e14 | 1.31174 | 0.655871 | − | 0.754873i | \(-0.272301\pi\) | ||||
0.655871 | + | 0.754873i | \(0.272301\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.60264e14 | 0.768475 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.95277e13 | −0.0615159 | −0.0307579 | − | 0.999527i | \(-0.509792\pi\) | ||||
−0.0307579 | + | 0.999527i | \(0.509792\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.33663e14 | 0.678980 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.82760e14 | −0.959658 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.39795e14 | −0.271492 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.71959e13 | 0.0705797 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.97821e14 | 0.366793 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.00961e15 | −1.82940 | −0.914702 | − | 0.404128i | \(-0.867575\pi\) | ||||
−0.914702 | + | 0.404128i | \(0.867575\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.25665e13 | −0.128510 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.02355e14 | 0.177174 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.59251e13 | 0.0777088 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.21837e14 | 1.35949 | 0.679745 | − | 0.733448i | \(-0.262090\pi\) | ||||
0.679745 | + | 0.733448i | \(0.262090\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.23632e14 | −0.199955 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.64714e14 | −1.36749 | −0.683745 | − | 0.729721i | \(-0.739650\pi\) | ||||
−0.683745 | + | 0.729721i | \(0.739650\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.50968e13 | 0.0388115 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8.25821e13 | −0.124899 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.54629e14 | 0.228734 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.07789e14 | 0.879427 | 0.439714 | − | 0.898138i | \(-0.355080\pi\) | ||||
0.439714 | + | 0.898138i | \(0.355080\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.04796e14 | −0.572965 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.90522e14 | 0.679257 | 0.339629 | − | 0.940560i | \(-0.389699\pi\) | ||||
0.339629 | + | 0.940560i | \(0.389699\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.61299e14 | −1.03146 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.03754e14 | 0.535271 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.07479e15 | 1.39436 | 0.697179 | − | 0.716897i | \(-0.254438\pi\) | ||||
0.697179 | + | 0.716897i | \(0.254438\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.16549e14 | 0.782804 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.65694e14 | −0.330169 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.98954e14 | 0.241999 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.73056e13 | −0.115862 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.14053e14 | 0.832358 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.25510e13 | −0.0942139 | −0.0471069 | − | 0.998890i | \(-0.515000\pi\) | ||||
−0.0471069 | + | 0.998890i | \(0.515000\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.87128e14 | −0.767854 | −0.383927 | − | 0.923363i | \(-0.625429\pi\) | ||||
−0.383927 | + | 0.923363i | \(0.625429\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −9.53615e12 | −0.0104351 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.72273e13 | 0.0291773 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.87939e14 | −0.512105 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.70635e14 | 0.278204 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.18722e14 | 0.522318 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.06715e15 | −1.05264 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.06278e14 | −0.199340 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.12988e14 | 0.296339 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.39934e15 | −1.29819 | −0.649093 | − | 0.760709i | \(-0.724851\pi\) | ||||
−0.649093 | + | 0.760709i | \(0.724851\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.22232e15 | 1.11119 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.46686e15 | −1.30679 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.41257e15 | 1.23333 | 0.616667 | − | 0.787224i | \(-0.288483\pi\) | ||||
0.616667 | + | 0.787224i | \(0.288483\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.02391e14 | −0.173198 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.54898e15 | −2.97694 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.01437e14 | −0.658993 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.47878e14 | −0.280424 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.02686e15 | −0.811539 | −0.405769 | − | 0.913975i | \(-0.632996\pi\) | ||||
−0.405769 | + | 0.913975i | \(0.632996\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.57581e14 | −0.199595 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.24121e12 | −0.00474213 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.08846e15 | −0.810992 | −0.405496 | − | 0.914097i | \(-0.632901\pi\) | ||||
−0.405496 | + | 0.914097i | \(0.632901\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.30329e12 | 0.00314438 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 6.81178e13 | 0.0488151 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.95900e15 | −1.37695 | −0.688474 | − | 0.725261i | \(-0.741719\pi\) | ||||
−0.688474 | + | 0.725261i | \(0.741719\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.58327e15 | 1.09158 | 0.545791 | − | 0.837921i | \(-0.316229\pi\) | ||||
0.545791 | + | 0.837921i | \(0.316229\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.42134e14 | −0.231391 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.33109e13 | −0.0287359 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.69378e14 | 0.175346 | 0.0876728 | − | 0.996149i | \(-0.472057\pi\) | ||||
0.0876728 | + | 0.996149i | \(0.472057\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.73814e13 | 0.0302605 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.90225e14 | −0.244538 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.57118e14 | −0.404079 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.52162e14 | −0.0918226 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7.20364e14 | −0.426621 | −0.213311 | − | 0.976984i | \(-0.568425\pi\) | ||||
−0.213311 | + | 0.976984i | \(0.568425\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.85025e15 | −2.23797 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.25422e15 | 0.715554 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.27192e15 | −0.712294 | −0.356147 | − | 0.934430i | \(-0.615910\pi\) | ||||
−0.356147 | + | 0.934430i | \(0.615910\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.82391e13 | −0.0100268 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.48049e14 | −0.133869 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.83469e14 | −0.256166 | −0.128083 | − | 0.991763i | \(-0.540882\pi\) | ||||
−0.128083 | + | 0.991763i | \(0.540882\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.68175e15 | 1.91533 | 0.957667 | − | 0.287880i | \(-0.0929503\pi\) | ||||
0.957667 | + | 0.287880i | \(0.0929503\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.00852e15 | 0.515157 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.75995e15 | −0.882768 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.30279e15 | 1.13427 | 0.567135 | − | 0.823625i | \(-0.308052\pi\) | ||||
0.567135 | + | 0.823625i | \(0.308052\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 9.09875e14 | 0.440136 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.79291e14 | −0.0851789 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.23428e14 | −0.0575947 | −0.0287973 | − | 0.999585i | \(-0.509168\pi\) | ||||
−0.0287973 | + | 0.999585i | \(0.509168\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.48671e15 | 1.13976 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.94167e15 | −1.32442 | −0.662210 | − | 0.749318i | \(-0.730381\pi\) | ||||
−0.662210 | + | 0.749318i | \(0.730381\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.62405e15 | −1.60286 | −0.801430 | − | 0.598088i | \(-0.795927\pi\) | ||||
−0.801430 | + | 0.598088i | \(0.795927\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.09375e14 | 0.134425 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.07866e14 | −0.0887360 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.47824e15 | −1.03945 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8.82579e14 | 0.363732 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.62912e13 | −0.0106471 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.12294e15 | −0.446884 | −0.223442 | − | 0.974717i | \(-0.571729\pi\) | ||||
−0.223442 | + | 0.974717i | \(0.571729\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.21656e15 | −0.866882 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.95522e15 | −1.90461 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.76698e14 | 0.217862 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.67377e14 | 0.173545 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.60734e15 | 1.31664 | 0.658321 | − | 0.752738i | \(-0.271267\pi\) | ||||
0.658321 | + | 0.752738i | \(0.271267\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.13436e15 | −1.48337 | −0.741683 | − | 0.670751i | \(-0.765972\pi\) | ||||
−0.741683 | + | 0.670751i | \(0.765972\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.23482e15 | −0.435538 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.00765e15 | −1.73644 | −0.868221 | − | 0.496177i | \(-0.834737\pi\) | ||||
−0.868221 | + | 0.496177i | \(0.834737\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.98990e14 | −0.306485 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.87113e14 | 0.330881 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.80675e15 | 1.91386 | 0.956931 | − | 0.290314i | \(-0.0937598\pi\) | ||||
0.956931 | + | 0.290314i | \(0.0937598\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.57576e15 | 1.15889 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.86357e15 | 0.593930 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.09336e15 | 0.969529 | 0.484765 | − | 0.874645i | \(-0.338905\pi\) | ||||
0.484765 | + | 0.874645i | \(0.338905\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.99504e14 | 0.123144 | 0.0615719 | − | 0.998103i | \(-0.480389\pi\) | ||||
0.0615719 | + | 0.998103i | \(0.480389\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.14998e13 | −0.00348631 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.57922e15 | 0.769076 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.13244e15 | 1.21203 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.13750e14 | −0.0328177 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.72298e14 | 0.190804 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.16111e15 | −0.603384 | −0.301692 | − | 0.953405i | \(-0.597551\pi\) | ||||
−0.301692 | + | 0.953405i | \(0.597551\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.88237e13 | −0.00791734 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.72622e15 | −1.27725 | −0.638626 | − | 0.769518i | \(-0.720497\pi\) | ||||
−0.638626 | + | 0.769518i | \(0.720497\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.25833e14 | 0.0334590 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.21236e15 | 0.840456 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.37911e15 | −1.12738 | −0.563692 | − | 0.825985i | \(-0.690620\pi\) | ||||
−0.563692 | + | 0.825985i | \(0.690620\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.82938e15 | 0.716791 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.05955e14 | −0.0513464 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.21078e15 | −0.297070 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.37871e15 | 1.78177 | 0.890884 | − | 0.454230i | \(-0.150086\pi\) | ||||
0.890884 | + | 0.454230i | \(0.150086\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.26273e14 | −0.0537773 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.19094e15 | −0.980382 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.87935e14 | 0.0432741 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.31659e15 | 0.978399 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.97202e15 | −0.663136 | −0.331568 | − | 0.943431i | \(-0.607578\pi\) | ||||
−0.331568 | + | 0.943431i | \(0.607578\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.71787e15 | 0.816658 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −8.59507e14 | −0.185870 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.08594e15 | −0.444114 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.84420e15 | 0.805845 | 0.402923 | − | 0.915234i | \(-0.367994\pi\) | ||||
0.402923 | + | 0.915234i | \(0.367994\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.42240e15 | −0.499992 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.48323e15 | 0.911169 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.05450e14 | 0.101157 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.68838e15 | 0.529829 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.49014e15 | −0.677383 | −0.338691 | − | 0.940898i | \(-0.609984\pi\) | ||||
−0.338691 | + | 0.940898i | \(0.609984\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.45128e14 | 0.104197 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.19427e15 | 0.601328 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.85009e14 | −0.0713859 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.26477e15 | −0.230978 | −0.115489 | − | 0.993309i | \(-0.536844\pi\) | ||||
−0.115489 | + | 0.993309i | \(0.536844\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.05891e14 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.33228e13 | −0.0165364 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.50679e15 | 1.31033 | 0.655167 | − | 0.755484i | \(-0.272598\pi\) | ||||
0.655167 | + | 0.755484i | \(0.272598\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.76464e15 | 0.475400 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.35009e15 | −0.567525 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.20650e15 | 1.20276 | 0.601381 | − | 0.798962i | \(-0.294617\pi\) | ||||
0.601381 | + | 0.798962i | \(0.294617\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.62620e15 | 0.267408 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.39426e15 | 0.225894 | 0.112947 | − | 0.993601i | \(-0.463971\pi\) | ||||
0.112947 | + | 0.993601i | \(0.463971\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.92107e15 | −0.625958 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.17948e15 | −0.185536 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.92396e15 | −0.453233 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.66385e15 | 1.17065 | 0.585326 | − | 0.810798i | \(-0.300967\pi\) | ||||
0.585326 | + | 0.810798i | \(0.300967\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6.05141e15 | −0.910928 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.80503e13 | −0.0115789 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.12920e15 | −0.311307 | −0.155654 | − | 0.987812i | \(-0.549748\pi\) | ||||
−0.155654 | + | 0.987812i | \(0.549748\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.02768e15 | −0.148090 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.44003e14 | 0.0346561 | 0.0173280 | − | 0.999850i | \(-0.494484\pi\) | ||||
0.0173280 | + | 0.999850i | \(0.494484\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.01915e15 | −0.562664 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.51291e13 | −0.00760752 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.65644e15 | −0.225321 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.87277e15 | 1.05568 | 0.527840 | − | 0.849344i | \(-0.323002\pi\) | ||||
0.527840 | + | 0.849344i | \(0.323002\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.63090e15 | 0.612162 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.12137e16 | 1.46138 | 0.730691 | − | 0.682709i | \(-0.239198\pi\) | ||||
0.730691 | + | 0.682709i | \(0.239198\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.17692e14 | −0.0536657 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −9.53176e14 | −0.120742 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.65762e16 | −3.31923 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.55253e15 | −0.191187 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.75017e15 | 0.333940 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.41649e16 | 1.69602 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.34408e16 | 1.58695 | 0.793475 | − | 0.608603i | \(-0.208270\pi\) | ||||
0.793475 | + | 0.608603i | \(0.208270\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.27215e15 | 0.730286 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.17909e13 | 0.00135387 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.23875e15 | 0.140275 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.80437e15 | −0.648241 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.64398e16 | 1.81082 | 0.905408 | − | 0.424542i | \(-0.139565\pi\) | ||||
0.905408 | + | 0.424542i | \(0.139565\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.49580e13 | −0.00705709 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.28291e14 | −0.0673259 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.19036e15 | −0.654306 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.00325e15 | −0.313122 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.89077e15 | −0.400158 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.37074e16 | 1.39072 | 0.695358 | − | 0.718664i | \(-0.255246\pi\) | ||||
0.695358 | + | 0.718664i | \(0.255246\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.58825e15 | −0.459232 | −0.229616 | − | 0.973281i | \(-0.573747\pi\) | ||||
−0.229616 | + | 0.973281i | \(0.573747\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.20764e15 | −0.514213 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.62756e15 | 0.353385 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.31969e16 | 1.26838 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.16920e14 | −0.0395359 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.03921e16 | −0.972331 | −0.486165 | − | 0.873867i | \(-0.661605\pi\) | ||||
−0.486165 | + | 0.873867i | \(0.661605\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.90788e15 | −0.545422 | −0.272711 | − | 0.962096i | \(-0.587920\pi\) | ||||
−0.272711 | + | 0.962096i | \(0.587920\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 9.57462e13 | 0.00872217 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.40538e15 | 0.575791 | 0.287895 | − | 0.957662i | \(-0.407044\pi\) | ||||
0.287895 | + | 0.957662i | \(0.407044\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.31696e15 | 0.560348 | 0.280174 | − | 0.959949i | \(-0.409608\pi\) | ||||
0.280174 | + | 0.959949i | \(0.409608\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.48315e15 | 0.479981 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.08940e14 | 0.0180499 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.18773e16 | 1.01261 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.98362e15 | 0.251046 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.09652e16 | −0.910598 | −0.455299 | − | 0.890339i | \(-0.650468\pi\) | ||||
−0.455299 | + | 0.890339i | \(0.650468\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.45345e16 | 2.01094 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.53912e15 | −0.286315 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.18468e16 | −0.945994 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.82222e15 | −0.380092 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.91694e15 | 0.460368 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.32910e15 | −0.332495 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.39896e15 | −0.257707 | −0.128854 | − | 0.991664i | \(-0.541130\pi\) | ||||
−0.128854 | + | 0.991664i | \(0.541130\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.79589e15 | 0.583515 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.05370e16 | 0.778614 | 0.389307 | − | 0.921108i | \(-0.372715\pi\) | ||||
0.389307 | + | 0.921108i | \(0.372715\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.29250e16 | −0.942903 | −0.471451 | − | 0.881892i | \(-0.656270\pi\) | ||||
−0.471451 | + | 0.881892i | \(0.656270\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.81352e15 | 0.490743 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.45598e16 | 1.03537 | 0.517685 | − | 0.855571i | \(-0.326794\pi\) | ||||
0.517685 | + | 0.855571i | \(0.326794\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.09514e16 | −1.47104 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8.32390e15 | 0.577061 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.04669e15 | 0.550819 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.17273e15 | −0.417232 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.80341e14 | 0.0253860 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.52155e15 | −0.429839 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.57548e15 | 0.427986 | 0.213993 | − | 0.976835i | \(-0.431353\pi\) | ||||
0.213993 | + | 0.976835i | \(0.431353\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.05156e14 | −0.00675919 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.17457e16 | −1.38040 | −0.690202 | − | 0.723617i | \(-0.742478\pi\) | ||||
−0.690202 | + | 0.723617i | \(0.742478\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.89298e15 | 0.118676 | 0.0593378 | − | 0.998238i | \(-0.481101\pi\) | ||||
0.0593378 | + | 0.998238i | \(0.481101\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7.94085e15 | −0.491676 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.03579e16 | −1.24495 | −0.622475 | − | 0.782639i | \(-0.713873\pi\) | ||||
−0.622475 | + | 0.782639i | \(0.713873\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.35772e16 | −0.820066 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.83926e14 | −0.0408020 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9.18581e15 | 0.541295 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.05253e15 | 0.352298 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.89355e15 | −0.108873 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.98534e16 | 2.26353 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.38671e14 | −0.0246123 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.38338e15 | −0.187529 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.58649e16 | −1.96382 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.08169e16 | −1.12610 | −0.563049 | − | 0.826424i | \(-0.690372\pi\) | ||||
−0.563049 | + | 0.826424i | \(0.690372\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.30490e15 | −0.336959 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.56740e15 | −0.0827616 | −0.0413808 | − | 0.999143i | \(-0.513176\pi\) | ||||
−0.0413808 | + | 0.999143i | \(0.513176\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.91799e15 | 0.204397 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.93846e15 | 0.306096 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9.79748e15 | 0.498980 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.45715e15 | 0.0733278 | 0.0366639 | − | 0.999328i | \(-0.488327\pi\) | ||||
0.0366639 | + | 0.999328i | \(0.488327\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.43213e16 | 0.712124 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.86062e15 | −0.140556 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.03332e14 | 0.0195832 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.64769e15 | 0.0790564 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.70074e16 | −0.806400 | −0.403200 | − | 0.915112i | \(-0.632102\pi\) | ||||
−0.403200 | + | 0.915112i | \(0.632102\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.95466e16 | −1.38447 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.14343e15 | 0.145564 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.83127e14 | 0.00838086 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.71528e16 | −1.68044 | −0.840222 | − | 0.542242i | \(-0.817576\pi\) | ||||
−0.840222 | + | 0.542242i | \(0.817576\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.24387e15 | 0.279121 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.09136e16 | −0.924031 | −0.462016 | − | 0.886872i | \(-0.652874\pi\) | ||||
−0.462016 | + | 0.886872i | \(0.652874\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.09454e16 | 1.35139 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.99868e15 | −0.0862718 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.53699e16 | 1.50907 | 0.754533 | − | 0.656262i | \(-0.227863\pi\) | ||||
0.754533 | + | 0.656262i | \(0.227863\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.14061e16 | −0.481031 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.24807e15 | 0.135404 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.45761e16 | 0.600661 | 0.300331 | − | 0.953835i | \(-0.402903\pi\) | ||||
0.300331 | + | 0.953835i | \(0.402903\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.00388e16 | 0.408941 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −9.13545e15 | −0.367887 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.75241e15 | 0.308627 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.78280e16 | 0.701655 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8.83789e15 | −0.343878 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.39024e15 | −0.0534800 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.57202e16 | −0.597878 | −0.298939 | − | 0.954272i | \(-0.596633\pi\) | ||||
−0.298939 | + | 0.954272i | \(0.596633\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.89181e14 | 0.0221548 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.34980e16 | 0.501837 | 0.250918 | − | 0.968008i | \(-0.419267\pi\) | ||||
0.250918 | + | 0.968008i | \(0.419267\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.14831e16 | −0.422121 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.76418e14 | 0.00641235 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.80905e15 | −0.136898 | −0.0684489 | − | 0.997655i | \(-0.521805\pi\) | ||||
−0.0684489 | + | 0.997655i | \(0.521805\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.08705e15 | 0.0741698 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.21482e16 | −0.426905 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.42344e16 | −1.88465 | −0.942325 | − | 0.334698i | \(-0.891366\pi\) | ||||
−0.942325 | + | 0.334698i | \(0.891366\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.68008e16 | −1.26461 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.35503e15 | −0.0800297 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.53665e16 | −0.516411 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.20030e16 | −0.398919 | −0.199459 | − | 0.979906i | \(-0.563919\pi\) | ||||
−0.199459 | + | 0.979906i | \(0.563919\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.51934e15 | 0.0499385 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.27815e15 | 0.236589 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.90012e15 | −0.0932379 | −0.0466189 | − | 0.998913i | \(-0.514845\pi\) | ||||
−0.0466189 | + | 0.998913i | \(0.514845\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.88104e15 | −0.0916093 |
(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 | 192.12.a.i.1.1 | 1 | ||
4.3 | odd | 2 | 192.12.a.s.1.1 | 1 | |||
8.3 | odd | 2 | 24.12.a.a.1.1 | ✓ | 1 | ||
8.5 | even | 2 | 48.12.a.e.1.1 | 1 | |||
24.5 | odd | 2 | 144.12.a.m.1.1 | 1 | |||
24.11 | even | 2 | 72.12.a.d.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
24.12.a.a.1.1 | ✓ | 1 | 8.3 | odd | 2 | ||
48.12.a.e.1.1 | 1 | 8.5 | even | 2 | |||
72.12.a.d.1.1 | 1 | 24.11 | even | 2 | |||
144.12.a.m.1.1 | 1 | 24.5 | odd | 2 | |||
192.12.a.i.1.1 | 1 | 1.1 | even | 1 | trivial | ||
192.12.a.s.1.1 | 1 | 4.3 | odd | 2 |