Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [192,8,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, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("192.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 192 = 2^{6} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
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: | \(59.9779248930\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{6}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 6 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 96) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.44949\) of defining polynomial | ||
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 | ||||||||
\(3\) | −27.0000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 366.727 | 1.31204 | 0.656020 | − | 0.754743i | \(-0.272239\pi\) | ||||
0.656020 | + | 0.754743i | \(0.272239\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 355.029 | 0.391219 | 0.195610 | − | 0.980682i | \(-0.437331\pi\) | ||||
0.195610 | + | 0.980682i | \(0.437331\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −7100.47 | −1.60847 | −0.804235 | − | 0.594312i | \(-0.797425\pi\) | ||||
−0.804235 | + | 0.594312i | \(0.797425\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3599.83 | 0.454444 | 0.227222 | − | 0.973843i | \(-0.427036\pi\) | ||||
0.227222 | + | 0.973843i | \(0.427036\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −9901.62 | −0.757507 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −21326.7 | −1.05282 | −0.526408 | − | 0.850232i | \(-0.676462\pi\) | ||||
−0.526408 | + | 0.850232i | \(0.676462\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 15138.3 | 0.506337 | 0.253169 | − | 0.967422i | \(-0.418527\pi\) | ||||
0.253169 | + | 0.967422i | \(0.418527\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −9585.77 | −0.225871 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −95346.3 | −1.63402 | −0.817008 | − | 0.576626i | \(-0.804369\pi\) | ||||
−0.817008 | + | 0.576626i | \(0.804369\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 56363.3 | 0.721451 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −19683.0 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 194218. | 1.47876 | 0.739378 | − | 0.673291i | \(-0.235120\pi\) | ||||
0.739378 | + | 0.673291i | \(0.235120\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −16519.2 | −0.0995919 | −0.0497959 | − | 0.998759i | \(-0.515857\pi\) | ||||
−0.0497959 | + | 0.998759i | \(0.515857\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 191713. | 0.928650 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 130198. | 0.513295 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −321381. | −1.04307 | −0.521536 | − | 0.853229i | \(-0.674641\pi\) | ||||
−0.521536 | + | 0.853229i | \(0.674641\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −97195.4 | −0.262373 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 159119. | 0.360561 | 0.180281 | − | 0.983615i | \(-0.442299\pi\) | ||||
0.180281 | + | 0.983615i | \(0.442299\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 856303. | 1.64243 | 0.821217 | − | 0.570616i | \(-0.193296\pi\) | ||||
0.821217 | + | 0.570616i | \(0.193296\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 267344. | 0.437347 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −748446. | −1.05152 | −0.525760 | − | 0.850633i | \(-0.676219\pi\) | ||||
−0.525760 | + | 0.850633i | \(0.676219\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −697498. | −0.846948 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 575821. | 0.607844 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 305261. | 0.281648 | 0.140824 | − | 0.990035i | \(-0.455025\pi\) | ||||
0.140824 | + | 0.990035i | \(0.455025\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.60393e6 | −2.11038 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −408735. | −0.292334 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 688982. | 0.436743 | 0.218371 | − | 0.975866i | \(-0.429926\pi\) | ||||
0.218371 | + | 0.975866i | \(0.429926\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.17704e6 | −0.663951 | −0.331976 | − | 0.943288i | \(-0.607715\pi\) | ||||
−0.331976 | + | 0.943288i | \(0.607715\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 258816. | 0.130406 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.32015e6 | 0.596249 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.25969e6 | −1.73028 | −0.865139 | − | 0.501532i | \(-0.832770\pi\) | ||||
−0.865139 | + | 0.501532i | \(0.832770\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.57435e6 | 0.943400 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.43415e6 | −1.47030 | −0.735150 | − | 0.677905i | \(-0.762888\pi\) | ||||
−0.735150 | + | 0.677905i | \(0.762888\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.12132e6 | −0.638228 | −0.319114 | − | 0.947716i | \(-0.603385\pi\) | ||||
−0.319114 | + | 0.947716i | \(0.603385\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.52181e6 | −0.416530 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.52087e6 | −0.629264 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.37842e6 | −0.542742 | −0.271371 | − | 0.962475i | \(-0.587477\pi\) | ||||
−0.271371 | + | 0.962475i | \(0.587477\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.71208e6 | −1.28850 | −0.644249 | − | 0.764816i | \(-0.722830\pi\) | ||||
−0.644249 | + | 0.764816i | \(0.722830\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.82107e6 | −1.38134 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.24389e6 | −0.853760 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.65976e6 | −0.851007 | −0.425504 | − | 0.904957i | \(-0.639903\pi\) | ||||
−0.425504 | + | 0.904957i | \(0.639903\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.27804e6 | 0.177787 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 446019. | 0.0574994 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.55162e6 | 0.664335 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.56487e7 | 1.74092 | 0.870458 | − | 0.492243i | \(-0.163823\pi\) | ||||
0.870458 | + | 0.492243i | \(0.163823\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.17625e6 | −0.536157 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.69363e7 | 1.63566 | 0.817830 | − | 0.575459i | \(-0.195177\pi\) | ||||
0.817830 | + | 0.575459i | \(0.195177\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.07025e7 | 0.965062 | 0.482531 | − | 0.875879i | \(-0.339718\pi\) | ||||
0.482531 | + | 0.875879i | \(0.339718\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.51536e6 | −0.296351 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.82697e7 | −1.44174 | −0.720871 | − | 0.693069i | \(-0.756258\pi\) | ||||
−0.720871 | + | 0.693069i | \(0.756258\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −936031. | −0.0692305 | −0.0346153 | − | 0.999401i | \(-0.511021\pi\) | ||||
−0.0346153 | + | 0.999401i | \(0.511021\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.67730e6 | 0.602218 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.92584e7 | −1.25558 | −0.627791 | − | 0.778382i | \(-0.716041\pi\) | ||||
−0.627791 | + | 0.778382i | \(0.716041\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.49660e7 | −2.14390 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.62428e6 | 0.151481 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.57159e6 | −0.411882 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.09296e7 | 1.58718 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.29622e6 | −0.208170 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.98058e6 | −0.365468 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.40542e7 | −1.47522 | −0.737610 | − | 0.675227i | \(-0.764046\pi\) | ||||
−0.737610 | + | 0.675227i | \(0.764046\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.31202e7 | −0.948259 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.61205e6 | −0.179244 | −0.0896220 | − | 0.995976i | \(-0.528566\pi\) | ||||
−0.0896220 | + | 0.995976i | \(0.528566\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.37454e6 | 0.198089 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −7.21828e6 | −0.252502 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.14188e7 | −0.379401 | −0.189701 | − | 0.981842i | \(-0.560752\pi\) | ||||
−0.189701 | + | 0.981842i | \(0.560752\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.97814e6 | −0.315136 | −0.157568 | − | 0.987508i | \(-0.550365\pi\) | ||||
−0.157568 | + | 0.987508i | \(0.550365\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.02080e7 | 0.607096 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.55605e7 | −0.730959 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.12249e7 | 1.94019 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.88324e7 | 0.488985 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.19127e7 | −0.790337 | −0.395168 | − | 0.918609i | \(-0.629314\pi\) | ||||
−0.395168 | + | 0.918609i | \(0.629314\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.56752e6 | −0.0843231 | −0.0421616 | − | 0.999111i | \(-0.513424\pi\) | ||||
−0.0421616 | + | 0.999111i | \(0.513424\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.55472e7 | −0.350939 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.05804e6 | −0.130669 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.56485e7 | −1.14764 | −0.573818 | − | 0.818983i | \(-0.694538\pi\) | ||||
−0.573818 | + | 0.818983i | \(0.694538\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.24206e6 | −0.162609 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.38506e7 | −0.639258 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.68712e7 | 1.20943 | 0.604717 | − | 0.796440i | \(-0.293286\pi\) | ||||
0.604717 | + | 0.796440i | \(0.293286\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.03062e7 | 1.21843 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.58953e7 | 0.430242 | 0.215121 | − | 0.976587i | \(-0.430985\pi\) | ||||
0.215121 | + | 0.976587i | \(0.430985\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.97898e7 | −0.793481 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.10358e7 | 0.168779 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.85506e7 | −0.272394 | −0.136197 | − | 0.990682i | \(-0.543488\pi\) | ||||
−0.136197 | + | 0.990682i | \(0.543488\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.00106e7 | 0.282245 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.86025e7 | −0.252154 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.44092e8 | 1.87783 | 0.938913 | − | 0.344155i | \(-0.111834\pi\) | ||||
0.938913 | + | 0.344155i | \(0.111834\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.97401e7 | −0.999544 | −0.499772 | − | 0.866157i | \(-0.666583\pi\) | ||||
−0.499772 | + | 0.866157i | \(0.666583\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.17800e7 | 0.383333 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.17859e8 | −1.36855 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.51430e8 | 1.69342 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −6.98803e6 | −0.0752902 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.09598e8 | −1.13811 | −0.569057 | − | 0.822298i | \(-0.692692\pi\) | ||||
−0.569057 | + | 0.822298i | \(0.692692\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.79334e8 | 1.79561 | 0.897803 | − | 0.440398i | \(-0.145163\pi\) | ||||
0.897803 | + | 0.440398i | \(0.145163\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.56441e7 | −0.344244 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.26410e8 | 1.17801 | 0.589005 | − | 0.808130i | \(-0.299520\pi\) | ||||
0.589005 | + | 0.808130i | \(0.299520\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.38271e7 | 0.484189 | 0.242095 | − | 0.970253i | \(-0.422166\pi\) | ||||
0.242095 | + | 0.970253i | \(0.422166\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.15012e8 | 0.998977 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.89529e7 | 0.578518 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.83533e7 | 0.473071 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.95074e7 | −0.544672 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.07489e8 | −0.814428 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.40216e7 | 0.176041 | 0.0880204 | − | 0.996119i | \(-0.471946\pi\) | ||||
0.0880204 | + | 0.996119i | \(0.471946\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.19722e8 | 0.848878 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.14029e8 | 2.15494 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.86480e6 | −0.0389622 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.72756e7 | 0.368481 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.67725e7 | −0.478446 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.70788e7 | 0.465445 | 0.232722 | − | 0.972543i | \(-0.425237\pi\) | ||||
0.232722 | + | 0.972543i | \(0.425237\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.10889e7 | 0.240484 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.46115e8 | −1.39652 | −0.698261 | − | 0.715844i | \(-0.746042\pi\) | ||||
−0.698261 | + | 0.715844i | \(0.746042\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.29557e8 | −1.81345 | −0.906725 | − | 0.421722i | \(-0.861426\pi\) | ||||
−0.906725 | + | 0.421722i | \(0.861426\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.80635e7 | 0.363306 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.14579e8 | 0.593416 | 0.296708 | − | 0.954968i | \(-0.404111\pi\) | ||||
0.296708 | + | 0.954968i | \(0.404111\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.74475e8 | −1.37964 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.42173e7 | 0.313352 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.39074e8 | 0.658953 | 0.329476 | − | 0.944164i | \(-0.393128\pi\) | ||||
0.329476 | + | 0.944164i | \(0.393128\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.21938e8 | −0.561150 | −0.280575 | − | 0.959832i | \(-0.590525\pi\) | ||||
−0.280575 | + | 0.959832i | \(0.590525\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.43489e7 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.55791e8 | −1.11123 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.44954e7 | 0.230102 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.81226e8 | 0.743915 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.59091e8 | 1.83249 | 0.916243 | − | 0.400622i | \(-0.131206\pi\) | ||||
0.916243 | + | 0.400622i | \(0.131206\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.77004e8 | 2.62827 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.11169e8 | 0.797516 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.44461e8 | −0.898347 | −0.449173 | − | 0.893445i | \(-0.648281\pi\) | ||||
−0.449173 | + | 0.893445i | \(0.648281\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.14100e8 | −0.408070 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.41585e8 | 0.492919 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.17922e7 | 0.141661 | 0.0708305 | − | 0.997488i | \(-0.477435\pi\) | ||||
0.0708305 | + | 0.997488i | \(0.477435\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.11947e8 | 0.369533 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.52814e8 | 0.491329 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.67457e8 | −1.77746 | −0.888730 | − | 0.458431i | \(-0.848412\pi\) | ||||
−0.888730 | + | 0.458431i | \(0.848412\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.17865e8 | 0.970176 | 0.485088 | − | 0.874465i | \(-0.338788\pi\) | ||||
0.485088 | + | 0.874465i | \(0.338788\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.45071e7 | −0.102645 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.00206e8 | −1.16043 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.09683e8 | 1.72355 | 0.861777 | − | 0.507287i | \(-0.169351\pi\) | ||||
0.861777 | + | 0.507287i | \(0.169351\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.20425e7 | −0.0331973 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.74608e8 | −0.469453 | −0.234726 | − | 0.972061i | \(-0.575419\pi\) | ||||
−0.234726 | + | 0.972061i | \(0.575419\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.36563e8 | 1.40724 | 0.703620 | − | 0.710576i | \(-0.251566\pi\) | ||||
0.703620 | + | 0.710576i | \(0.251566\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.49894e8 | −0.383554 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.64919e7 | 0.141059 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.44895e7 | 0.108422 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.22515e8 | −1.00512 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.35688e8 | −1.47641 | −0.738206 | − | 0.674576i | \(-0.764327\pi\) | ||||
−0.738206 | + | 0.674576i | \(0.764327\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.52668e8 | 0.573024 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.39759e8 | 0.309550 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.43230e8 | −0.742568 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.04012e8 | 0.642551 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.57280e8 | −0.944349 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.31651e8 | −0.871131 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.05086e8 | −0.601781 | −0.300890 | − | 0.953659i | \(-0.597284\pi\) | ||||
−0.300890 | + | 0.953659i | \(0.597284\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.88968e8 | −0.557179 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.78228e8 | −0.901517 | −0.450758 | − | 0.892646i | \(-0.648846\pi\) | ||||
−0.450758 | + | 0.892646i | \(0.648846\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.87232e8 | −0.713783 | −0.356891 | − | 0.934146i | \(-0.616163\pi\) | ||||
−0.356891 | + | 0.934146i | \(0.616163\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 9.49146e7 | 0.171098 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.58088e8 | −0.807683 | −0.403842 | − | 0.914829i | \(-0.632325\pi\) | ||||
−0.403842 | + | 0.914829i | \(0.632325\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.37904e9 | −2.37853 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.93281e8 | 0.832391 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.22850e8 | −0.533080 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.02898e8 | 0.327859 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.52728e7 | 0.0399703 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.65720e8 | −0.411375 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.25648e8 | 0.493572 | 0.246786 | − | 0.969070i | \(-0.420626\pi\) | ||||
0.246786 | + | 0.969070i | \(0.420626\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.34287e8 | −0.347691 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.56214e9 | −2.27020 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.38971e8 | 1.05177 | 0.525887 | − | 0.850554i | \(-0.323733\pi\) | ||||
0.525887 | + | 0.850554i | \(0.323733\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.19976e8 | 0.724911 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.17294e8 | 0.160190 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5.40013e8 | −0.722561 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 9.44082e8 | 1.23778 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.79778e8 | 1.25885 | 0.629426 | − | 0.777060i | \(-0.283290\pi\) | ||||
0.629426 | + | 0.777060i | \(0.283290\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.24643e9 | 1.56956 | 0.784780 | − | 0.619775i | \(-0.212776\pi\) | ||||
0.784780 | + | 0.619775i | \(0.212776\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.08554e7 | −0.0874577 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.58065e8 | −0.796264 | −0.398132 | − | 0.917328i | \(-0.630341\pi\) | ||||
−0.398132 | + | 0.917328i | \(0.630341\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.62612e9 | −1.92909 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.04433e8 | 0.237800 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.52591e7 | 0.0516269 | 0.0258134 | − | 0.999667i | \(-0.491782\pi\) | ||||
0.0258134 | + | 0.999667i | \(0.491782\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.64703e8 | −0.743622 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8.35098e8 | −0.916356 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.77944e8 | −0.837382 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.03217e9 | −1.08998 | −0.544991 | − | 0.838442i | \(-0.683467\pi\) | ||||
−0.544991 | + | 0.838442i | \(0.683467\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.15998e8 | 0.120187 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.08377e8 | 0.110186 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.25005e8 | 0.523821 | 0.261910 | − | 0.965092i | \(-0.415647\pi\) | ||||
0.261910 | + | 0.965092i | \(0.415647\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.15476e8 | 0.211003 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.99151e8 | 0.672011 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.22050e8 | 0.775642 | 0.387821 | − | 0.921735i | \(-0.373228\pi\) | ||||
0.387821 | + | 0.921735i | \(0.373228\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.19462e8 | 0.851719 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.99387e8 | 0.272293 | 0.136147 | − | 0.990689i | \(-0.456528\pi\) | ||||
0.136147 | + | 0.990689i | \(0.456528\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.24470e8 | −0.825620 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.24245e8 | 0.547478 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.12130e8 | −0.613389 | −0.306694 | − | 0.951808i | \(-0.599223\pi\) | ||||
−0.306694 | + | 0.951808i | \(0.599223\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.03342e9 | 1.72032 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.24525e8 | 0.103487 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.72229e8 | −0.712099 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.53020e8 | −0.443582 | −0.221791 | − | 0.975094i | \(-0.571190\pi\) | ||||
−0.221791 | + | 0.975094i | \(0.571190\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.45112e8 | −0.114367 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.24965e8 | 0.406561 | 0.203280 | − | 0.979121i | \(-0.434840\pi\) | ||||
0.203280 | + | 0.979121i | \(0.434840\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.94664e7 | −0.0452589 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.94894e8 | 0.145782 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.28196e9 | 1.67775 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.85772e8 | 0.206533 | 0.103266 | − | 0.994654i | \(-0.467071\pi\) | ||||
0.103266 | + | 0.994654i | \(0.467071\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.08308e8 | 0.219047 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.44608e8 | 0.170862 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.46150e9 | −1.69056 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.69410e8 | 0.181944 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.14977e9 | −0.763591 | −0.381796 | − | 0.924247i | \(-0.624694\pi\) | ||||
−0.381796 | + | 0.924247i | \(0.624694\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.46430e7 | −0.0160956 | −0.00804778 | − | 0.999968i | \(-0.502562\pi\) | ||||
−0.00804778 | + | 0.999968i | \(0.502562\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.45617e8 | −0.350507 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.20204e9 | −0.759555 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.17882e8 | −0.259751 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.90133e8 | 0.422019 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.58335e9 | −0.952593 | −0.476297 | − | 0.879285i | \(-0.658021\pi\) | ||||
−0.476297 | + | 0.879285i | \(0.658021\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.36866e8 | −0.495391 | −0.247695 | − | 0.968838i | \(-0.579673\pi\) | ||||
−0.247695 | + | 0.968838i | \(0.579673\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.92307e9 | −1.12017 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.44338e9 | −0.827363 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.08460e9 | 1.74010 | 0.870048 | − | 0.492967i | \(-0.164088\pi\) | ||||
0.870048 | + | 0.492967i | \(0.164088\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.08476e8 | −0.282316 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.35708e8 | 0.511360 | 0.255680 | − | 0.966761i | \(-0.417701\pi\) | ||||
0.255680 | + | 0.966761i | \(0.417701\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.07558e9 | −1.11656 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.61644e8 | 0.456301 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.11014e9 | 1.62150 | 0.810752 | − | 0.585390i | \(-0.199058\pi\) | ||||
0.810752 | + | 0.585390i | \(0.199058\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.12982e9 | −0.579952 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9.63229e7 | 0.0486840 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.68692e8 | 0.233264 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.01909e9 | 0.989577 | 0.494789 | − | 0.869013i | \(-0.335246\pi\) | ||||
0.494789 | + | 0.869013i | \(0.335246\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.19773e8 | 0.202615 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.35152e8 | 0.349481 | 0.174741 | − | 0.984614i | \(-0.444091\pi\) | ||||
0.174741 | + | 0.984614i | \(0.444091\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.98518e9 | 1.39777 | 0.698887 | − | 0.715232i | \(-0.253679\pi\) | ||||
0.698887 | + | 0.715232i | \(0.253679\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.63567e8 | 0.0754415 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.07591e9 | −1.39754 | −0.698769 | − | 0.715347i | \(-0.746269\pi\) | ||||
−0.698769 | + | 0.715347i | \(0.746269\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.51231e9 | −0.676918 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.50251e9 | 0.662588 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.08016e9 | −2.64180 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.53246e8 | 0.365298 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.22536e8 | 0.0938826 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.60321e9 | 0.666523 | 0.333262 | − | 0.942834i | \(-0.391851\pi\) | ||||
0.333262 | + | 0.942834i | \(0.391851\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.15692e9 | −0.474018 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 9.13967e8 | 0.369076 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.73880e9 | 2.28415 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.70605e9 | 0.669331 | 0.334665 | − | 0.942337i | \(-0.391377\pi\) | ||||
0.334665 | + | 0.942337i | \(0.391377\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.80552e9 | −0.698267 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.03396e9 | 1.15671 | 0.578355 | − | 0.815785i | \(-0.303695\pi\) | ||||
0.578355 | + | 0.815785i | \(0.303695\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.14203e9 | −1.55686 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.89827e9 | −0.703459 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.57425e9 | −0.575209 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.91071e9 | 1.04869 | 0.524344 | − | 0.851506i | \(-0.324310\pi\) | ||||
0.524344 | + | 0.851506i | \(0.324310\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.99173e8 | −0.248400 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.61700e9 | 0.566528 | 0.283264 | − | 0.959042i | \(-0.408583\pi\) | ||||
0.283264 | + | 0.959042i | \(0.408583\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.21098e9 | 2.14605 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.34432e9 | 0.458116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.47914e8 | −0.0497163 | −0.0248581 | − | 0.999691i | \(-0.507913\pi\) | ||||
−0.0248581 | + | 0.999691i | \(0.507913\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.53129e8 | −0.249687 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.97968e8 | −0.0974447 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.92489e9 | 1.26620 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.31432e9 | 1.69134 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.00866e8 | 0.157266 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.28069e9 | 0.706536 | 0.353268 | − | 0.935522i | \(-0.385070\pi\) | ||||
0.353268 | + | 0.935522i | \(0.385070\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.70860e9 | 1.13359 | 0.566793 | − | 0.823860i | \(-0.308184\pi\) | ||||
0.566793 | + | 0.823860i | \(0.308184\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5.40286e8 | −0.162954 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.52301e8 | 0.104852 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.68609e9 | 1.67001 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.02268e8 | 0.145581 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.72802e8 | 0.163855 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.69998e9 | −1.89163 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.89049e9 | −1.08416 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.95256e9 | 1.36229 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.43003e8 | −0.0659813 | −0.0329907 | − | 0.999456i | \(-0.510503\pi\) | ||||
−0.0329907 | + | 0.999456i | \(0.510503\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.15298e9 | 0.577087 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.43267e8 | −0.0908333 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.23514e9 | −0.322672 | −0.161336 | − | 0.986900i | \(-0.551580\pi\) | ||||
−0.161336 | + | 0.986900i | \(0.551580\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.58061e8 | −0.221317 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.94013e9 | 0.748749 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.44406e8 | −0.212331 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.18219e9 | 0.790135 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.03766e8 | 0.0990002 | 0.0495001 | − | 0.998774i | \(-0.484237\pi\) | ||||
0.0495001 | + | 0.998774i | \(0.484237\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.08254e9 | 0.746394 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.08860e9 | −0.977698 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.17239e9 | −0.276882 | −0.138441 | − | 0.990371i | \(-0.544209\pi\) | ||||
−0.138441 | + | 0.990371i | \(0.544209\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.06256e9 | −1.64738 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.88677e8 | 0.0434688 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.08771e9 | 0.702658 | 0.351329 | − | 0.936252i | \(-0.385730\pi\) | ||||
0.351329 | + | 0.936252i | \(0.385730\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.26406e9 | 0.284147 | 0.142073 | − | 0.989856i | \(-0.454623\pi\) | ||||
0.142073 | + | 0.989856i | \(0.454623\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.95914e9 | 0.657090 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.37403e9 | −1.17886 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.12237e9 | −0.893371 | −0.446685 | − | 0.894691i | \(-0.647396\pi\) | ||||
−0.446685 | + | 0.894691i | \(0.647396\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.84201e9 | −1.03669 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.38298e9 | −0.504085 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.16750e9 | −0.453022 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 9.62391e8 | 0.198750 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.43332e9 | 0.292489 | 0.146245 | − | 0.989248i | \(-0.453281\pi\) | ||||
0.146245 | + | 0.989248i | \(0.453281\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.50073e8 | −0.0504271 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.41306e9 | −0.680124 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9.06949e9 | 1.78604 | 0.893021 | − | 0.450015i | \(-0.148581\pi\) | ||||
0.893021 | + | 0.450015i | \(0.148581\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.77670e9 | −0.540406 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.45333e9 | −0.279547 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.87038e9 | −1.30613 | −0.653065 | − | 0.757302i | \(-0.726517\pi\) | ||||
−0.653065 | + | 0.757302i | \(0.726517\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.21863e9 | 0.228988 | 0.114494 | − | 0.993424i | \(-0.463475\pi\) | ||||
0.114494 | + | 0.993424i | \(0.463475\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.10531e9 | −0.576759 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.13427e10 | 2.08244 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.23889e8 | 0.0406324 | 0.0203162 | − | 0.999794i | \(-0.493533\pi\) | ||||
0.0203162 | + | 0.999794i | \(0.493533\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.86173e9 | −0.334007 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.69428e9 | −0.477857 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.74524e9 | −0.481359 | −0.240680 | − | 0.970605i | \(-0.577370\pi\) | ||||
−0.240680 | + | 0.970605i | \(0.577370\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.57554e9 | −0.273128 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.52382e7 | 0.00432574 | 0.00216287 | − | 0.999998i | \(-0.499312\pi\) | ||||
0.00216287 | + | 0.999998i | \(0.499312\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.17398e9 | 0.707347 | 0.353674 | − | 0.935369i | \(-0.384932\pi\) | ||||
0.353674 | + | 0.935369i | \(0.384932\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.87670e9 | 0.314467 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.00938e9 | −0.332930 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.33008e9 | −1.20096 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.90221e9 | 0.470210 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.85400e9 | 1.09816 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.64464e9 | 0.260596 | 0.130298 | − | 0.991475i | \(-0.458407\pi\) | ||||
0.130298 | + | 0.991475i | \(0.458407\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.48583e8 | −0.101637 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.24886e10 | −1.93555 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.51087e9 | −0.384890 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.23249e9 | −0.490100 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.21295e8 | 0.108171 | 0.0540854 | − | 0.998536i | \(-0.482776\pi\) | ||||
0.0540854 | + | 0.998536i | \(0.482776\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.90611e8 | 0.146948 | 0.0734741 | − | 0.997297i | \(-0.476591\pi\) | ||||
0.0734741 | + | 0.997297i | \(0.476591\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.47878e9 | −1.24415 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.87612e9 | 0.998110 | 0.499055 | − | 0.866570i | \(-0.333681\pi\) | ||||
0.499055 | + | 0.866570i | \(0.333681\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.89210e9 | −0.702488 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.58350e8 | 0.0224949 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.58692e9 | −0.925734 | −0.462867 | − | 0.886428i | \(-0.653179\pi\) | ||||
−0.462867 | + | 0.886428i | \(0.653179\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.69136e9 | −0.235175 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.54644e9 | −0.212743 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.21929e9 | −0.165961 | −0.0829806 | − | 0.996551i | \(-0.526444\pi\) | ||||
−0.0829806 | + | 0.996551i | \(0.526444\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.93235e9 | −0.260244 | −0.130122 | − | 0.991498i | \(-0.541537\pi\) | ||||
−0.130122 | + | 0.991498i | \(0.541537\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.07286e9 | 0.276231 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.97098e9 | 0.259901 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.85180e10 | −2.41631 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.08113e9 | −0.268725 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.35753e9 | 1.06795 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.47851e9 | −1.19864 | −0.599318 | − | 0.800511i | \(-0.704561\pi\) | ||||
−0.599318 | + | 0.800511i | \(0.704561\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.10940e9 | −0.138843 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.46353e9 | 0.924452 | 0.462226 | − | 0.886762i | \(-0.347051\pi\) | ||||
0.462226 | + | 0.886762i | \(0.347051\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.55574e9 | 0.681079 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.64511e9 | 0.806282 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.79020e9 | −0.214995 | −0.107498 | − | 0.994205i | \(-0.534284\pi\) | ||||
−0.107498 | + | 0.994205i | \(0.534284\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.18758e9 | −0.497790 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.89803e9 | 1.04700 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.09889e9 | 0.127993 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.44397e9 | −0.858285 | −0.429142 | − | 0.903237i | \(-0.641184\pi\) | ||||
−0.429142 | + | 0.903237i | \(0.641184\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.83771e9 | −0.209755 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.65925e9 | −0.413471 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.39349e9 | −0.379605 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.09363e9 | −0.342609 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.28971e9 | 0.141410 | 0.0707050 | − | 0.997497i | \(-0.477475\pi\) | ||||
0.0707050 | + | 0.997497i | \(0.477475\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.86517e9 | −0.528147 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7.41082e9 | 0.796534 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.01286e9 | 0.639902 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.13464e9 | −0.330313 | −0.165157 | − | 0.986267i | \(-0.552813\pi\) | ||||
−0.165157 | + | 0.986267i | \(0.552813\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.73387e9 | −0.180914 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.57505e9 | 0.162735 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.37371e9 | −0.959048 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.75501e9 | −0.380447 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.98384e9 | −0.801052 | −0.400526 | − | 0.916285i | \(-0.631173\pi\) | ||||
−0.400526 | + | 0.916285i | \(0.631173\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.79969e9 | 0.377551 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.29232e9 | 0.323980 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.09468e10 | 1.06685 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.62828e9 | −0.350212 | −0.175106 | − | 0.984550i | \(-0.556027\pi\) | ||||
−0.175106 | + | 0.984550i | \(0.556027\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.82621e10 | −1.72918 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.42705e10 | 1.33837 | 0.669183 | − | 0.743098i | \(-0.266644\pi\) | ||||
0.669183 | + | 0.743098i | \(0.266644\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6.90635e9 | 0.641569 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.02458e10 | 2.78310 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.65044e10 | 1.50434 | 0.752168 | − | 0.658971i | \(-0.229008\pi\) | ||||
0.752168 | + | 0.658971i | \(0.229008\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.47137e9 | −0.132849 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −9.34147e9 | −0.835516 | −0.417758 | − | 0.908558i | \(-0.637184\pi\) | ||||
−0.417758 | + | 0.908558i | \(0.637184\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.17032e10 | −1.03695 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.89311e9 | −0.429499 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.48626e9 | −0.564037 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.36465e10 | −1.17566 | −0.587829 | − | 0.808986i | \(-0.700017\pi\) | ||||
−0.587829 | + | 0.808986i | \(0.700017\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.23955e10 | −1.05799 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.30830e9 | −0.110635 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.63373e9 | 0.555804 | 0.277902 | − | 0.960609i | \(-0.410361\pi\) | ||||
0.277902 | + | 0.960609i | \(0.410361\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.82791e10 | −1.51743 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.32467e10 | 1.08958 | 0.544792 | − | 0.838571i | \(-0.316609\pi\) | ||||
0.544792 | + | 0.838571i | \(0.316609\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.32318e8 | −0.0270843 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.70156e9 | −0.460446 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.48022e9 | 0.198475 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.73702e10 | −1.37741 | −0.688706 | − | 0.725041i | \(-0.741821\pi\) | ||||
−0.688706 | + | 0.725041i | \(0.741821\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.60045e9 | 0.518661 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −8.20862e9 | −0.639207 | −0.319604 | − | 0.947551i | \(-0.603550\pi\) | ||||
−0.319604 | + | 0.947551i | \(0.603550\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.31079e8 | −0.0718506 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.08069e9 | 0.235599 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.40880e9 | 0.182566 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.14845e10 | 2.36493 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.82279e9 | −0.284587 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.04078e10 | −1.50575 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.20336e9 | −0.380516 | −0.190258 | − | 0.981734i | \(-0.560932\pi\) | ||||
−0.190258 | + | 0.981734i | \(0.560932\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.12839e9 | −0.0817881 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.83728e9 | −0.491208 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.23714e9 | −0.301729 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.02258e9 | −0.213350 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.74511e10 | −1.22101 | −0.610504 | − | 0.792013i | \(-0.709033\pi\) | ||||
−0.610504 | + | 0.792013i | \(0.709033\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.59619e10 | 1.10706 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.12597e9 | −0.283669 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.50624e10 | 1.02657 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.24139e10 | −0.838733 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.53213e10 | 1.02622 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.67781e8 | 0.0377017 | 0.0188509 | − | 0.999822i | \(-0.493999\pi\) | ||||
0.0188509 | + | 0.999822i | \(0.493999\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.26569e10 | 1.49151 | 0.745756 | − | 0.666219i | \(-0.232088\pi\) | ||||
0.745756 | + | 0.666219i | \(0.232088\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.58236e9 | −0.560131 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.45234e10 | 1.58683 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.29630e10 | 0.831626 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 9.31693e8 | 0.0592624 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.43924e9 | 0.343034 | 0.171517 | − | 0.985181i | \(-0.445133\pi\) | ||||
0.171517 | + | 0.985181i | \(0.445133\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.81390e9 | −0.238490 | −0.119245 | − | 0.992865i | \(-0.538047\pi\) | ||||
−0.119245 | + | 0.992865i | \(0.538047\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.08056e10 | 0.669976 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.04027e10 | 1.25435 | 0.627176 | − | 0.778878i | \(-0.284211\pi\) | ||||
0.627176 | + | 0.778878i | \(0.284211\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.09133e10 | 1.27492 | 0.637458 | − | 0.770485i | \(-0.279986\pi\) | ||||
0.637458 | + | 0.770485i | \(0.279986\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.64614e10 | −0.995095 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.48753e10 | 0.891680 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.49649e9 | 0.564495 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.25148e8 | 0.0191665 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.29188e10 | −1.33975 | −0.669876 | − | 0.742473i | \(-0.733653\pi\) | ||||
−0.669876 | + | 0.742473i | \(0.733653\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.04707e10 | 1.18672 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.71442e9 | 0.271039 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.82592e10 | −1.04108 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.09809e10 | 0.620933 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.44872e10 | −0.812471 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.06425e10 | 1.70440 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.12228e9 | −0.172247 | −0.0861233 | − | 0.996284i | \(-0.527448\pi\) | ||||
−0.0861233 | + | 0.996284i | \(0.527448\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.04713e9 | 0.221445 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.39835e10 | −1.84431 | −0.922157 | − | 0.386817i | \(-0.873575\pi\) | ||||
−0.922157 | + | 0.386817i | \(0.873575\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.07390e10 | 1.11638 | 0.558190 | − | 0.829713i | \(-0.311496\pi\) | ||||
0.558190 | + | 0.829713i | \(0.311496\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.52528e9 | −0.0814402 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.13047e10 | 0.598719 | 0.299360 | − | 0.954140i | \(-0.403227\pi\) | ||||
0.299360 | + | 0.954140i | \(0.403227\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.80300e9 | −0.357391 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.20122e9 | −0.0625972 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.68879e10 | 0.872984 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.53341e10 | −0.786314 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.14079e10 | 0.580305 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.83333e9 | −0.142978 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.41724e10 | −0.709486 | −0.354743 | − | 0.934964i | \(-0.615432\pi\) | ||||
−0.354743 | + | 0.934964i | \(0.615432\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.71636e10 | 0.852407 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.71670e8 | 0.0183123 | 0.00915614 | − | 0.999958i | \(-0.497085\pi\) | ||||
0.00915614 | + | 0.999958i | \(0.497085\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.28024e10 | 1.11460 | 0.557299 | − | 0.830312i | \(-0.311838\pi\) | ||||
0.557299 | + | 0.830312i | \(0.311838\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.82203e9 | −0.330836 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4.09283e9 | −0.196920 | −0.0984602 | − | 0.995141i | \(-0.531392\pi\) | ||||
−0.0984602 | + | 0.995141i | \(0.531392\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.20902e10 | −0.577135 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.77348e9 | −0.178719 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.13302e10 | −0.532424 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.28425e10 | 2.46378 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.26722e9 | 0.428722 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.20833e9 | −0.147272 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.51022e9 | −0.296523 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.20832e9 | −0.370977 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.92428e10 | −1.31144 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.93238e10 | −1.74997 | −0.874983 | − | 0.484153i | \(-0.839128\pi\) | ||||
−0.874983 | + | 0.484153i | \(0.839128\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.23465e10 | 0.545220 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.39548e10 | 1.04973 | 0.524866 | − | 0.851185i | \(-0.324115\pi\) | ||||
0.524866 | + | 0.851185i | \(0.324115\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.76589e10 | 2.07251 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.16546e10 | 0.502948 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.63741e9 | −0.0701237 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.48503e10 | −1.48116 | −0.740580 | − | 0.671968i | \(-0.765449\pi\) | ||||
−0.740580 | + | 0.671968i | \(0.765449\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.23733e9 | 0.347438 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.59622e10 | −0.668168 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.81141e10 | −0.752526 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7.80213e9 | 0.321687 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.68507e9 | −0.0689547 | −0.0344774 | − | 0.999405i | \(-0.510977\pi\) | ||||
−0.0344774 | + | 0.999405i | \(0.510977\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.05589e10 | −0.428841 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.29122e10 | 0.520491 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.55333e10 | 2.22184 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.83372e10 | −0.728189 | −0.364094 | − | 0.931362i | \(-0.618621\pi\) | ||||
−0.364094 | + | 0.931362i | \(0.618621\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.04553e10 | 0.412103 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.09477e9 | 0.121078 | 0.0605390 | − | 0.998166i | \(-0.480718\pi\) | ||||
0.0605390 | + | 0.998166i | \(0.480718\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.51714e10 | −0.589163 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.56269e9 | −0.0987838 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.46943e10 | −1.71012 | −0.855061 | − | 0.518527i | \(-0.826481\pi\) | ||||
−0.855061 | + | 0.518527i | \(0.826481\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.63639e9 | −0.290039 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.23684e10 | 0.466316 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.13357e10 | −0.798514 | −0.399257 | − | 0.916839i | \(-0.630732\pi\) | ||||
−0.399257 | + | 0.916839i | \(0.630732\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.01925e10 | −1.49325 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.72341e10 | 1.37325 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.05400e9 | −0.148429 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.72397e10 | −0.990081 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.33186e10 | −0.480581 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.57664e10 | 2.35591 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.55906e10 | 0.554461 | 0.277231 | − | 0.960803i | \(-0.410583\pi\) | ||||
0.277231 | + | 0.960803i | \(0.410583\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.71696e9 | 0.307774 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.00913e9 | 0.245695 | 0.122848 | − | 0.992426i | \(-0.460797\pi\) | ||||
0.122848 | + | 0.992426i | \(0.460797\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.54252e9 | −0.123287 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5.47826e9 | −0.189289 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.94015e10 | 0.665587 | 0.332794 | − | 0.943000i | \(-0.392009\pi\) | ||||
0.332794 | + | 0.943000i | \(0.392009\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.01870e10 | 1.36882 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.82367e8 | −0.0230768 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.00668e10 | −1.68117 | −0.840587 | − | 0.541677i | \(-0.817790\pi\) | ||||
−0.840587 | + | 0.541677i | \(0.817790\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.63578e10 | 1.54560 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 7.17443e9 | 0.237507 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.16453e10 | −2.68376 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.16083e10 | 1.68446 | 0.842232 | − | 0.539115i | \(-0.181241\pi\) | ||||
0.842232 | + | 0.539115i | \(0.181241\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −8.79249e9 | −0.284964 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.97398e10 | 0.635276 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.60890e9 | −0.179244 | −0.0896221 | − | 0.995976i | \(-0.528566\pi\) | ||||
−0.0896221 | + | 0.995976i | \(0.528566\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.32575e9 | 0.200739 |
(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 | 192.8.a.s.1.2 | 2 | ||
3.2 | odd | 2 | 576.8.a.bg.1.1 | 2 | |||
4.3 | odd | 2 | 192.8.a.v.1.2 | 2 | |||
8.3 | odd | 2 | 96.8.a.c.1.1 | ✓ | 2 | ||
8.5 | even | 2 | 96.8.a.f.1.1 | yes | 2 | ||
12.11 | even | 2 | 576.8.a.bh.1.1 | 2 | |||
24.5 | odd | 2 | 288.8.a.l.1.2 | 2 | |||
24.11 | even | 2 | 288.8.a.m.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
96.8.a.c.1.1 | ✓ | 2 | 8.3 | odd | 2 | ||
96.8.a.f.1.1 | yes | 2 | 8.5 | even | 2 | ||
192.8.a.s.1.2 | 2 | 1.1 | even | 1 | trivial | ||
192.8.a.v.1.2 | 2 | 4.3 | odd | 2 | |||
288.8.a.l.1.2 | 2 | 24.5 | odd | 2 | |||
288.8.a.m.1.2 | 2 | 24.11 | even | 2 | |||
576.8.a.bg.1.1 | 2 | 3.2 | odd | 2 | |||
576.8.a.bh.1.1 | 2 | 12.11 | even | 2 |