Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,10,Mod(1,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.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: | \(197.773761087\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2070x^{2} - 13768x + 561570 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{15}\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-34.7879\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.1 |
$q$-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 | ||||||||
\(3\) | 81.0000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2550.24 | −1.82480 | −0.912401 | − | 0.409298i | \(-0.865774\pi\) | ||||
−0.912401 | + | 0.409298i | \(0.865774\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 11484.8 | 1.80793 | 0.903963 | − | 0.427610i | \(-0.140644\pi\) | ||||
0.903963 | + | 0.427610i | \(0.140644\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6561.00 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −17694.9 | −0.364401 | −0.182201 | − | 0.983261i | \(-0.558322\pi\) | ||||
−0.182201 | + | 0.983261i | \(0.558322\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2878.66 | −0.0279541 | −0.0139770 | − | 0.999902i | \(-0.504449\pi\) | ||||
−0.0139770 | + | 0.999902i | \(0.504449\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −206569. | −1.05355 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −465200. | −1.35089 | −0.675444 | − | 0.737411i | \(-0.736048\pi\) | ||||
−0.675444 | + | 0.737411i | \(0.736048\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 409191. | 0.720335 | 0.360168 | − | 0.932888i | \(-0.382719\pi\) | ||||
0.360168 | + | 0.932888i | \(0.382719\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 930265. | 1.04381 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 374507. | 0.279051 | 0.139526 | − | 0.990218i | \(-0.455442\pi\) | ||||
0.139526 | + | 0.990218i | \(0.455442\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.55058e6 | 2.32990 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 531441. | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.81849e6 | −1.00254 | −0.501269 | − | 0.865291i | \(-0.667133\pi\) | ||||
−0.501269 | + | 0.865291i | \(0.667133\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.57794e6 | 0.501355 | 0.250678 | − | 0.968071i | \(-0.419347\pi\) | ||||
0.250678 | + | 0.968071i | \(0.419347\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.43328e6 | −0.210387 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.92889e7 | −3.29911 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.07373e7 | −0.941858 | −0.470929 | − | 0.882171i | \(-0.656081\pi\) | ||||
−0.470929 | + | 0.882171i | \(0.656081\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −233171. | −0.0161393 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.50461e7 | 0.831564 | 0.415782 | − | 0.909464i | \(-0.363508\pi\) | ||||
0.415782 | + | 0.909464i | \(0.363508\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.21149e7 | −0.540394 | −0.270197 | − | 0.962805i | \(-0.587089\pi\) | ||||
−0.270197 | + | 0.962805i | \(0.587089\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.67321e7 | −0.608267 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.65533e7 | −1.39159 | −0.695793 | − | 0.718242i | \(-0.744947\pi\) | ||||
−0.695793 | + | 0.718242i | \(0.744947\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 9.15461e7 | 2.26860 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.76812e7 | −0.779936 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.10710e8 | 1.92728 | 0.963639 | − | 0.267209i | \(-0.0861014\pi\) | ||||
0.963639 | + | 0.267209i | \(0.0861014\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.51261e7 | 0.664960 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.31445e7 | 0.415886 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.19329e7 | −0.987726 | −0.493863 | − | 0.869540i | \(-0.664416\pi\) | ||||
−0.493863 | + | 0.869540i | \(0.664416\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.64770e8 | 1.52368 | 0.761838 | − | 0.647767i | \(-0.224297\pi\) | ||||
0.761838 | + | 0.647767i | \(0.224297\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.53515e7 | 0.602642 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.34126e6 | 0.0510106 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.68898e8 | −1.63024 | −0.815119 | − | 0.579294i | \(-0.803328\pi\) | ||||
−0.815119 | + | 0.579294i | \(0.803328\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.03350e7 | 0.161110 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.57888e8 | 1.67142 | 0.835708 | − | 0.549174i | \(-0.185058\pi\) | ||||
0.835708 | + | 0.549174i | \(0.185058\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.40257e7 | −0.305091 | −0.152546 | − | 0.988296i | \(-0.548747\pi\) | ||||
−0.152546 | + | 0.988296i | \(0.548747\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.68597e8 | 1.34517 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.03221e8 | −0.658811 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.17558e7 | 0.265040 | 0.132520 | − | 0.991180i | \(-0.457693\pi\) | ||||
0.132520 | + | 0.991180i | \(0.457693\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.86443e8 | −0.431215 | −0.215608 | − | 0.976480i | \(-0.569173\pi\) | ||||
−0.215608 | + | 0.976480i | \(0.569173\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.18637e9 | 2.46510 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.09298e8 | −0.578816 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.37166e8 | −1.07646 | −0.538230 | − | 0.842798i | \(-0.680907\pi\) | ||||
−0.538230 | + | 0.842798i | \(0.680907\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.30607e7 | −0.0505389 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.08813e8 | 0.289458 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.04353e9 | −1.31447 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.12367e7 | −0.0587636 | −0.0293818 | − | 0.999568i | \(-0.509354\pi\) | ||||
−0.0293818 | + | 0.999568i | \(0.509354\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.16096e8 | −0.121467 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.28576e8 | −0.314188 | −0.157094 | − | 0.987584i | \(-0.550213\pi\) | ||||
−0.157094 | + | 0.987584i | \(0.550213\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.13814e9 | 1.87184 | 0.935918 | − | 0.352218i | \(-0.114572\pi\) | ||||
0.935918 | + | 0.352218i | \(0.114572\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.37240e9 | −1.90474 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.38054e9 | 1.01817 | 0.509087 | − | 0.860715i | \(-0.329983\pi\) | ||||
0.509087 | + | 0.860715i | \(0.329983\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.42057e9 | −0.963926 | −0.481963 | − | 0.876192i | \(-0.660076\pi\) | ||||
−0.481963 | + | 0.876192i | \(0.660076\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.69718e8 | −0.543782 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.63697e8 | 0.267535 | 0.133768 | − | 0.991013i | \(-0.457292\pi\) | ||||
0.133768 | + | 0.991013i | \(0.457292\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.55081e8 | −0.509213 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.88869e7 | −0.00931802 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.34271e9 | −2.44231 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.04484e9 | −0.867212 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.21873e9 | 0.480104 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.62414e9 | −2.42680 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.20157e9 | −1.09206 | −0.546029 | − | 0.837766i | \(-0.683861\pi\) | ||||
−0.546029 | + | 0.837766i | \(0.683861\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.81304e8 | −0.311997 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.24459e9 | −1.25926 | −0.629630 | − | 0.776895i | \(-0.716793\pi\) | ||||
−0.629630 | + | 0.776895i | \(0.716793\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.69946e9 | 1.30231 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.35530e9 | −0.351183 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.87982e9 | −0.455905 | −0.227952 | − | 0.973672i | \(-0.573203\pi\) | ||||
−0.227952 | + | 0.973672i | \(0.573203\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.99062e9 | −0.906720 | −0.453360 | − | 0.891327i | \(-0.649775\pi\) | ||||
−0.453360 | + | 0.891327i | \(0.649775\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.77082e9 | −0.803433 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.09374e7 | 0.0101865 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.73807e9 | 1.82943 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.41523e9 | 1.30978 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.67985e9 | −1.44269 | −0.721346 | − | 0.692574i | \(-0.756476\pi\) | ||||
−0.721346 | + | 0.692574i | \(0.756476\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.40680e9 | 0.689806 | 0.344903 | − | 0.938638i | \(-0.387912\pi\) | ||||
0.344903 | + | 0.938638i | \(0.387912\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.05218e9 | −0.450296 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.57436e9 | −0.914874 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.13694e9 | 0.937484 | 0.468742 | − | 0.883335i | \(-0.344707\pi\) | ||||
0.468742 | + | 0.883335i | \(0.344707\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.96748e9 | 1.11271 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.30112e9 | 0.504504 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.33307e8 | −0.103557 | −0.0517786 | − | 0.998659i | \(-0.516489\pi\) | ||||
−0.0517786 | + | 0.998659i | \(0.516489\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.65521e9 | 0.383915 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.62183e10 | −1.61355 | −0.806773 | − | 0.590862i | \(-0.798788\pi\) | ||||
−0.806773 | + | 0.590862i | \(0.798788\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.05962e10 | −0.999219 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.68470e9 | 0.240112 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.78681e9 | 0.576047 | 0.288024 | − | 0.957623i | \(-0.407002\pi\) | ||||
0.288024 | + | 0.957623i | \(0.407002\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.22624e10 | 4.21229 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −7.44656e9 | −0.570264 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.04635e9 | −0.440205 | −0.220102 | − | 0.975477i | \(-0.570639\pi\) | ||||
−0.220102 | + | 0.975477i | \(0.570639\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.73661e10 | 1.20268 | 0.601339 | − | 0.798994i | \(-0.294634\pi\) | ||||
0.601339 | + | 0.798994i | \(0.294634\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.33463e10 | 0.879695 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.73825e10 | 1.71870 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.23165e9 | 0.492266 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 6.10347e9 | 0.347936 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.55901e10 | 0.847616 | 0.423808 | − | 0.905752i | \(-0.360693\pi\) | ||||
0.423808 | + | 0.905752i | \(0.360693\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.58307e10 | −1.34007 | −0.670036 | − | 0.742329i | \(-0.733721\pi\) | ||||
−0.670036 | + | 0.742329i | \(0.733721\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.94642e8 | 0.0294510 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.09030e10 | −1.46185 | −0.730924 | − | 0.682459i | \(-0.760911\pi\) | ||||
−0.730924 | + | 0.682459i | \(0.760911\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.28574e10 | 0.581183 | 0.290592 | − | 0.956847i | \(-0.406148\pi\) | ||||
0.290592 | + | 0.956847i | \(0.406148\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.17807e10 | −0.941218 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.38545e10 | −1.81252 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.83711e10 | −1.51744 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.45714e9 | 0.0930171 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.24058e9 | −0.262491 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.77349e10 | −0.963288 | −0.481644 | − | 0.876367i | \(-0.659960\pi\) | ||||
−0.481644 | + | 0.876367i | \(0.659960\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.89889e10 | 0.964993 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.08958e10 | 0.986112 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.96070e10 | 0.906413 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.99608e9 | −0.176145 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.33915e9 | 0.0377628 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.93029e10 | −1.33506 | −0.667530 | − | 0.744583i | \(-0.732649\pi\) | ||||
−0.667530 | + | 0.744583i | \(0.732649\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.98564e10 | 0.776633 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.66250e10 | −0.665538 | −0.332769 | − | 0.943008i | \(-0.607983\pi\) | ||||
−0.332769 | + | 0.943008i | \(0.607983\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.63083e10 | −1.59334 | −0.796670 | − | 0.604415i | \(-0.793407\pi\) | ||||
−0.796670 | + | 0.604415i | \(0.793407\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.64609e10 | −0.380365 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.24513e10 | 1.16588 | 0.582941 | − | 0.812514i | \(-0.301902\pi\) | ||||
0.582941 | + | 0.812514i | \(0.301902\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.18722e11 | 2.53937 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 7.43222e9 | 0.153021 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.83125e10 | −0.561291 | −0.280646 | − | 0.959811i | \(-0.590549\pi\) | ||||
−0.280646 | + | 0.959811i | \(0.590549\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.73233e10 | −1.66745 | −0.833726 | − | 0.552178i | \(-0.813797\pi\) | ||||
−0.833726 | + | 0.552178i | \(0.813797\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3.48678e9 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.33464e11 | −4.13974 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.17792e9 | −0.0201363 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.51019e10 | −0.248962 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.44391e10 | −0.547671 | −0.273836 | − | 0.961776i | \(-0.588292\pi\) | ||||
−0.273836 | + | 0.961776i | \(0.588292\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.62684e9 | −0.101687 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 9.60960e10 | 1.42323 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.18147e11 | −1.68937 | −0.844685 | − | 0.535264i | \(-0.820212\pi\) | ||||
−0.844685 | + | 0.535264i | \(0.820212\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.23315e11 | −1.70281 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.50531e10 | −0.334180 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.09809e9 | 0.0399294 | 0.0199647 | − | 0.999801i | \(-0.493645\pi\) | ||||
0.0199647 | + | 0.999801i | \(0.493645\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.82336e11 | −3.51690 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.16105e10 | −0.621494 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.92323e10 | 1.03905 | 0.519526 | − | 0.854455i | \(-0.326109\pi\) | ||||
0.519526 | + | 0.854455i | \(0.326109\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.33152e11 | −1.49964 | −0.749821 | − | 0.661641i | \(-0.769860\pi\) | ||||
−0.749821 | + | 0.661641i | \(0.769860\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.67792e9 | −0.0291786 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8.05220e10 | −0.849019 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.36458e11 | −1.39264 | −0.696322 | − | 0.717730i | \(-0.745181\pi\) | ||||
−0.696322 | + | 0.717730i | \(0.745181\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.69139e10 | 0.167118 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.62851e10 | 0.538537 | 0.269268 | − | 0.963065i | \(-0.413218\pi\) | ||||
0.269268 | + | 0.963065i | \(0.413218\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.30168e10 | 0.120633 | 0.0603163 | − | 0.998179i | \(-0.480789\pi\) | ||||
0.0603163 | + | 0.998179i | \(0.480789\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8.45262e10 | −0.758909 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.72801e11 | 1.50341 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.78231e10 | 0.824900 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.15017e9 | −0.0339272 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.06089e11 | 1.63362 | 0.816810 | − | 0.576907i | \(-0.195741\pi\) | ||||
0.816810 | + | 0.576907i | \(0.195741\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.34451e11 | 1.80240 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −9.40377e9 | −0.0701291 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.07808e9 | −0.00780062 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.39136e11 | −0.976993 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.66147e10 | −0.181397 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.20202e11 | −2.78041 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.28066e10 | 0.403536 | 0.201768 | − | 0.979433i | \(-0.435331\pi\) | ||||
0.201768 | + | 0.979433i | \(0.435331\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.73189e11 | 1.08071 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.85384e10 | −0.172985 | −0.0864925 | − | 0.996253i | \(-0.527566\pi\) | ||||
−0.0864925 | + | 0.996253i | \(0.527566\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.03679e10 | 0.0610578 | 0.0305289 | − | 0.999534i | \(-0.490281\pi\) | ||||
0.0305289 | + | 0.999534i | \(0.490281\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.92164e11 | −1.09970 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.10284e11 | 0.613400 | 0.306700 | − | 0.951806i | \(-0.400775\pi\) | ||||
0.306700 | + | 0.951806i | \(0.400775\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.75677e10 | 0.365327 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.11824e11 | 0.587844 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.90356e11 | −0.973093 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.30996e10 | −0.0651301 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.15066e11 | −0.556523 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.34654e11 | −2.51589 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.32144e11 | −1.06299 | −0.531497 | − | 0.847060i | \(-0.678370\pi\) | ||||
−0.531497 | + | 0.847060i | \(0.678370\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.04471e10 | −0.313953 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.85753e11 | 2.97486 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.90284e11 | 0.803652 | 0.401826 | − | 0.915716i | \(-0.368376\pi\) | ||||
0.401826 | + | 0.915716i | \(0.368376\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.75595e10 | 0.154462 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.56163e10 | −0.182695 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.87933e11 | 2.29353 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −7.73615e10 | −0.293994 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.80544e11 | −1.03877 | −0.519383 | − | 0.854541i | \(-0.673838\pi\) | ||||
−0.519383 | + | 0.854541i | \(0.673838\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.24413e10 | −0.189217 | −0.0946083 | − | 0.995515i | \(-0.530160\pi\) | ||||
−0.0946083 | + | 0.995515i | \(0.530160\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.52984e9 | −0.00537976 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.36154e11 | 1.83782 | 0.918911 | − | 0.394466i | \(-0.129070\pi\) | ||||
0.918911 | + | 0.394466i | \(0.129070\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.12699e11 | −3.05000 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.32759e11 | −1.41007 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.53244e11 | 0.486920 | 0.243460 | − | 0.969911i | \(-0.421718\pi\) | ||||
0.243460 | + | 0.969911i | \(0.421718\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.55250e11 | −0.481117 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.65632e11 | −0.500685 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.88783e11 | 0.556731 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.74040e11 | −1.07627 | −0.538134 | − | 0.842859i | \(-0.680871\pi\) | ||||
−0.538134 | + | 0.842859i | \(0.680871\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9.87173e10 | 0.277188 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.27147e12 | 3.48437 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.01779e11 | 0.539742 | 0.269871 | − | 0.962896i | \(-0.413019\pi\) | ||||
0.269871 | + | 0.962896i | \(0.413019\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.36555e11 | −1.40111 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.09921e10 | 0.0280250 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.79938e11 | −1.69275 | −0.846375 | − | 0.532588i | \(-0.821220\pi\) | ||||
−0.846375 | + | 0.532588i | \(0.821220\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.59327e11 | −0.630500 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.62580e11 | −1.09848 | −0.549240 | − | 0.835664i | \(-0.685083\pi\) | ||||
−0.549240 | + | 0.835664i | \(0.685083\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.18262e11 | 1.20220 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.94857e10 | −0.180131 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5.13044e11 | −1.13601 | −0.568004 | − | 0.823026i | \(-0.692284\pi\) | ||||
−0.568004 | + | 0.823026i | \(0.692284\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.74220e11 | −0.376967 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.43812e11 | −0.727034 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.33999e11 | −0.483646 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.14443e11 | −1.44348 | −0.721739 | − | 0.692165i | \(-0.756657\pi\) | ||||
−0.721739 | + | 0.692165i | \(0.756657\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.80656e11 | 0.751891 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.80010e11 | −0.540785 | −0.270392 | − | 0.962750i | \(-0.587153\pi\) | ||||
−0.270392 | + | 0.962750i | \(0.587153\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.42101e9 | −0.0140149 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.09779e11 | −0.202756 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.89994e11 | 0.343214 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.09398e11 | 0.193309 | 0.0966546 | − | 0.995318i | \(-0.469186\pi\) | ||||
0.0966546 | + | 0.995318i | \(0.469186\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.52266e11 | −0.263217 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.05583e12 | −1.78574 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.75473e11 | 0.786882 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.23240e11 | −0.523495 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.69404e10 | 0.106102 | 0.0530512 | − | 0.998592i | \(-0.483105\pi\) | ||||
0.0530512 | + | 0.998592i | \(0.483105\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.27317e11 | −0.662949 | −0.331475 | − | 0.943464i | \(-0.607546\pi\) | ||||
−0.331475 | + | 0.943464i | \(0.607546\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.05436e11 | −0.463862 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.11693e12 | −3.14743 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.89234e12 | 2.75469 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.12593e9 | 0.00588118 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.00618e11 | 0.559220 | 0.279610 | − | 0.960114i | \(-0.409795\pi\) | ||||
0.279610 | + | 0.960114i | \(0.409795\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.69071e11 | 0.504562 | 0.252281 | − | 0.967654i | \(-0.418819\pi\) | ||||
0.252281 | + | 0.967654i | \(0.418819\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.88783e11 | 1.05622 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.53245e11 | 0.201011 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.02355e12 | 1.31528 | 0.657640 | − | 0.753332i | \(-0.271555\pi\) | ||||
0.657640 | + | 0.753332i | \(0.271555\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.00634e11 | 0.756199 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.64264e11 | −0.326002 | −0.163001 | − | 0.986626i | \(-0.552117\pi\) | ||||
−0.163001 | + | 0.986626i | \(0.552117\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.62493e12 | 1.96432 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −7.03068e11 | −0.832939 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.41761e11 | −0.629070 | −0.314535 | − | 0.949246i | \(-0.601849\pi\) | ||||
−0.314535 | + | 0.949246i | \(0.601849\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.66238e11 | −0.303023 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.56951e11 | 0.398260 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 8.43126e10 | 0.0922234 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.87461e10 | −0.0630022 | −0.0315011 | − | 0.999504i | \(-0.510029\pi\) | ||||
−0.0315011 | + | 0.999504i | \(0.510029\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.47226e11 | −0.259979 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.57233e12 | 1.62139 | 0.810697 | − | 0.585466i | \(-0.199089\pi\) | ||||
0.810697 | + | 0.585466i | \(0.199089\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.14079e11 | −0.924420 | −0.462210 | − | 0.886771i | \(-0.652943\pi\) | ||||
−0.462210 | + | 0.886771i | \(0.652943\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.32523e11 | −0.528202 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.14555e11 | 0.597909 | 0.298954 | − | 0.954267i | \(-0.403362\pi\) | ||||
0.298954 | + | 0.954267i | \(0.403362\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.08823e12 | −2.94735 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.78092e11 | 0.541257 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.14371e11 | 0.196920 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.86206e12 | 1.67831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.26366e11 | 0.642426 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.71639e11 | −0.843325 | −0.421663 | − | 0.906753i | \(-0.638553\pi\) | ||||
−0.421663 | + | 0.906753i | \(0.638553\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.09089e10 | 0.0263288 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.48391e11 | 0.291276 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.30666e11 | 0.107232 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.35678e12 | 1.89862 | 0.949312 | − | 0.314335i | \(-0.101782\pi\) | ||||
0.949312 | + | 0.314335i | \(0.101782\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.55979e10 | −0.0597888 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.35095e11 | 0.570791 | 0.285395 | − | 0.958410i | \(-0.407875\pi\) | ||||
0.285395 | + | 0.958410i | \(0.407875\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.77636e12 | 1.35432 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.96072e11 | 0.221653 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.11026e12 | 3.02180 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.92617e11 | 0.211275 | 0.105637 | − | 0.994405i | \(-0.466312\pi\) | ||||
0.105637 | + | 0.994405i | \(0.466312\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.31368e12 | −0.931581 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.02398e12 | −1.40978 | −0.704890 | − | 0.709317i | \(-0.749004\pi\) | ||||
−0.704890 | + | 0.709317i | \(0.749004\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.37948e11 | 0.573332 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8.58293e11 | −0.576899 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.65483e11 | 0.505482 | 0.252741 | − | 0.967534i | \(-0.418668\pi\) | ||||
0.252741 | + | 0.967534i | \(0.418668\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.50168e11 | −0.551583 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.17461e11 | 0.138629 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.45275e12 | −3.41573 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.23755e11 | 0.507096 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.49731e11 | 0.332581 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.50936e12 | 1.49208 | 0.746041 | − | 0.665900i | \(-0.231952\pi\) | ||||
0.746041 | + | 0.665900i | \(0.231952\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.38072e10 | 0.0548250 | 0.0274125 | − | 0.999624i | \(-0.491273\pi\) | ||||
0.0274125 | + | 0.999624i | \(0.491273\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.23325e12 | 2.43196 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.19926e12 | −0.677275 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.66090e12 | −0.922130 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.03171e11 | −0.329242 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.33125e10 | −0.0232456 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.52071e12 | −1.85797 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.89755e11 | −0.254152 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.61990e12 | −0.826680 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.38883e12 | 0.697044 | 0.348522 | − | 0.937301i | \(-0.386684\pi\) | ||||
0.348522 | + | 0.937301i | \(0.386684\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.40666e12 | 0.694366 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.62279e12 | 1.75897 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.50687e11 | 0.119726 | 0.0598631 | − | 0.998207i | \(-0.480934\pi\) | ||||
0.0598631 | + | 0.998207i | \(0.480934\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.08105e12 | 0.507892 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.56249e12 | −0.722164 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.05379e12 | 0.479173 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.21799e12 | 0.992294 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.07853e11 | −0.0914973 | −0.0457487 | − | 0.998953i | \(-0.514567\pi\) | ||||
−0.0457487 | + | 0.998953i | \(0.514567\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.48746e10 | 0.0151062 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.66764e11 | 0.284210 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.85431e12 | 0.777850 | 0.388925 | − | 0.921269i | \(-0.372847\pi\) | ||||
0.388925 | + | 0.921269i | \(0.372847\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.18254e12 | −0.488199 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.94381e11 | 0.200881 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.99208e12 | −0.796712 | −0.398356 | − | 0.917231i | \(-0.630419\pi\) | ||||
−0.398356 | + | 0.917231i | \(0.630419\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.49143e12 | −0.587139 | −0.293570 | − | 0.955938i | \(-0.594843\pi\) | ||||
−0.293570 | + | 0.955938i | \(0.594843\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.26280e12 | 0.489372 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.70422e12 | 0.650162 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.82633e12 | 0.685942 | 0.342971 | − | 0.939346i | \(-0.388567\pi\) | ||||
0.342971 | + | 0.939346i | \(0.388567\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.09229e12 | −0.773691 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.14125e12 | −0.779605 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.95899e12 | −0.702303 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.81660e10 | 0.0170035 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.12345e12 | −0.738193 | −0.369096 | − | 0.929391i | \(-0.620333\pi\) | ||||
−0.369096 | + | 0.929391i | \(0.620333\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.05487e12 | 0.361144 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.50314e12 | −0.843998 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.09754e12 | 0.696569 | 0.348284 | − | 0.937389i | \(-0.386764\pi\) | ||||
0.348284 | + | 0.937389i | \(0.386764\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.36252e13 | 4.45672 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.04145e12 | 0.335546 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.89930e12 | −0.920178 | −0.460089 | − | 0.887873i | \(-0.652182\pi\) | ||||
−0.460089 | + | 0.887873i | \(0.652182\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.36479e12 | −1.36467 | −0.682337 | − | 0.731038i | \(-0.739036\pi\) | ||||
−0.682337 | + | 0.731038i | \(0.739036\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.76424e12 | −0.543412 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.21483e12 | 1.58249 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.16703e12 | 0.647913 | 0.323956 | − | 0.946072i | \(-0.394987\pi\) | ||||
0.323956 | + | 0.946072i | \(0.394987\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.55221e12 | −1.04646 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.34011e11 | 0.0389005 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.83561e12 | −0.525058 | −0.262529 | − | 0.964924i | \(-0.584557\pi\) | ||||
−0.262529 | + | 0.964924i | \(0.584557\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.10806e12 | −0.876094 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.04193e11 | −0.195618 | −0.0978089 | − | 0.995205i | \(-0.531183\pi\) | ||||
−0.0978089 | + | 0.995205i | \(0.531183\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.20869e12 | 1.69978 | 0.849889 | − | 0.526962i | \(-0.176669\pi\) | ||||
0.849889 | + | 0.526962i | \(0.176669\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.99028e11 | 0.0537035 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7.31770e12 | −1.94616 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.00526e12 | 2.09853 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.86487e11 | −0.151549 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.99497e12 | 1.27235 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.83096e12 | −0.459776 | −0.229888 | − | 0.973217i | \(-0.573836\pi\) | ||||
−0.229888 | + | 0.973217i | \(0.573836\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.24653e12 | −0.556155 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8.16475e12 | 1.99279 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.63530e11 | −0.0634165 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.34810e12 | 0.557139 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.57030e11 | 0.223905 | 0.111953 | − | 0.993714i | \(-0.464290\pi\) | ||||
0.111953 | + | 0.993714i | \(0.464290\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.17043e12 | 0.270019 | 0.135010 | − | 0.990844i | \(-0.456893\pi\) | ||||
0.135010 | + | 0.990844i | \(0.456893\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.50256e12 | 0.569332 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7.13180e12 | −1.60004 | −0.800018 | − | 0.599976i | \(-0.795177\pi\) | ||||
−0.800018 | + | 0.599976i | \(0.795177\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.62674e12 | 0.359929 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.39817e12 | 0.523318 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.45995e12 | −0.314217 | −0.157108 | − | 0.987581i | \(-0.550217\pi\) | ||||
−0.157108 | + | 0.987581i | \(0.550217\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.08247e13 | 2.29790 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.85683e11 | −0.101697 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.16319e12 | 0.653343 | 0.326672 | − | 0.945138i | \(-0.394073\pi\) | ||||
0.326672 | + | 0.945138i | \(0.394073\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.94931e12 | −1.21216 | −0.606080 | − | 0.795404i | \(-0.707259\pi\) | ||||
−0.606080 | + | 0.795404i | \(0.707259\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.08471e11 | 0.0218024 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.19847e13 | −2.37646 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.43005e12 | −0.279760 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.99354e12 | −0.770798 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.91558e12 | −0.555230 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.63233e12 | 1.24623 | 0.623115 | − | 0.782130i | \(-0.285867\pi\) | ||||
0.623115 | + | 0.782130i | \(0.285867\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.41837e12 | 0.448389 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.68780e12 | 0.491754 | 0.245877 | − | 0.969301i | \(-0.420924\pi\) | ||||
0.245877 | + | 0.969301i | \(0.420924\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.88441e11 | −0.106240 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.15662e12 | −0.384249 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.14691e11 | −0.0377503 | −0.0188751 | − | 0.999822i | \(-0.506008\pi\) | ||||
−0.0188751 | + | 0.999822i | \(0.506008\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.79399e12 | 0.831935 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.37097e12 | −0.919915 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.18695e11 | −0.0538752 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.18271e12 | −0.864780 | −0.432390 | − | 0.901687i | \(-0.642330\pi\) | ||||
−0.432390 | + | 0.901687i | \(0.642330\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.33333e12 | −0.219604 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.01770e13 | 1.65458 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.99943e12 | −1.12335 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.24856e12 | 0.673122 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.92911e12 | 0.927381 | 0.463691 | − | 0.885997i | \(-0.346525\pi\) | ||||
0.463691 | + | 0.885997i | \(0.346525\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.39359e12 | −0.678454 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 9.61648e12 | 1.46611 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.77362e12 | −0.568030 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.63915e12 | 0.689493 | 0.344747 | − | 0.938696i | \(-0.387965\pi\) | ||||
0.344747 | + | 0.938696i | \(0.387965\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.02010e11 | 0.0883467 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.65456e11 | 0.139904 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.29903e11 | −0.0185883 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2.29332e12 | −0.324062 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.00203e12 | 0.418924 | 0.209462 | − | 0.977817i | \(-0.432829\pi\) | ||||
0.209462 | + | 0.977817i | \(0.432829\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.45560e13 | 3.38414 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −7.07319e12 | −0.962704 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.73764e13 | −2.33581 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.19643e11 | 0.122100 | 0.0610498 | − | 0.998135i | \(-0.480555\pi\) | ||||
0.0610498 | + | 0.998135i | \(0.480555\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.82430e11 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.63584e12 | 0.730012 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.03255e13 | −1.32113 | −0.660564 | − | 0.750769i | \(-0.729683\pi\) | ||||
−0.660564 | + | 0.750769i | \(0.729683\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.89106e13 | −2.39008 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.75811e12 | 0.594061 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.25490e12 | 0.401456 | 0.200728 | − | 0.979647i | \(-0.435669\pi\) | ||||
0.200728 | + | 0.979647i | \(0.435669\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −9.54116e10 | −0.0116257 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.84135e12 | 0.462418 | 0.231209 | − | 0.972904i | \(-0.425732\pi\) | ||||
0.231209 | + | 0.972904i | \(0.425732\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.21357e13 | 2.63263 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.22325e12 | −0.143738 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.58552e13 | 1.84078 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.42668e13 | 1.63662 | 0.818311 | − | 0.574776i | \(-0.194911\pi\) | ||||
0.818311 | + | 0.574776i | \(0.194911\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.78957e12 | −0.316198 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.12384e13 | −1.25876 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.85396e12 | −0.315876 | −0.157938 | − | 0.987449i | \(-0.550485\pi\) | ||||
−0.157938 | + | 0.987449i | \(0.550485\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5.36774e11 | −0.0587089 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.19569e12 | −0.237323 | −0.118662 | − | 0.992935i | \(-0.537860\pi\) | ||||
−0.118662 | + | 0.992935i | \(0.537860\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.63149e13 | −1.74271 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 7.78378e12 | 0.821701 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.64643e11 | 0.0276110 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.45095e12 | 0.562087 | 0.281044 | − | 0.959695i | \(-0.409319\pi\) | ||||
0.281044 | + | 0.959695i | \(0.409319\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.56993e12 | −0.975358 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.19087e12 | 0.623654 | 0.311827 | − | 0.950139i | \(-0.399059\pi\) | ||||
0.311827 | + | 0.950139i | \(0.399059\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.17311e13 | 1.16811 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −9.98850e12 | −0.983118 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.15672e12 | 0.599005 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.33278e12 | −0.609066 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.02930e12 | −0.192939 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.82009e13 | −1.71072 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.77687e12 | 0.165109 | 0.0825543 | − | 0.996587i | \(-0.473692\pi\) | ||||
0.0825543 | + | 0.996587i | \(0.473692\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.50945e11 | 0.0230533 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.32545e12 | 0.483684 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.74315e11 | −0.0425929 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.28692e13 | −2.03048 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9.53311e12 | 0.836898 | 0.418449 | − | 0.908240i | \(-0.362574\pi\) | ||||
0.418449 | + | 0.908240i | \(0.362574\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.16566e13 | 1.87988 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.18045e12 | −0.358820 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.30988e12 | 0.111176 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.09689e13 | −0.920620 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.22782e12 | 0.599897 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4.71178e12 | −0.386738 | −0.193369 | − | 0.981126i | \(-0.561941\pi\) | ||||
−0.193369 | + | 0.981126i | \(0.561941\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.33679e12 | −0.757885 | −0.378943 | − | 0.925420i | \(-0.623712\pi\) | ||||
−0.378943 | + | 0.925420i | \(0.623712\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.07854e13 | −0.865818 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.38015e12 | 0.188971 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.95729e12 | −0.389265 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.16911e11 | −0.0168463 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.62688e11 | −0.0739505 | −0.0369753 | − | 0.999316i | \(-0.511772\pi\) | ||||
−0.0369753 | + | 0.999316i | \(0.511772\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.35265e12 | 0.178755 | 0.0893774 | − | 0.995998i | \(-0.471512\pi\) | ||||
0.0893774 | + | 0.995998i | \(0.471512\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6.52228e12 | −0.490181 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.49308e13 | 1.85337 | 0.926685 | − | 0.375838i | \(-0.122645\pi\) | ||||
0.926685 | + | 0.375838i | \(0.122645\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.92371e12 | −0.362073 | −0.181037 | − | 0.983476i | \(-0.557945\pi\) | ||||
−0.181037 | + | 0.983476i | \(0.557945\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.10531e13 | −0.804043 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.25872e13 | −3.06462 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.13605e13 | 2.94440 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.37002e12 | 0.0964858 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.58161e13 | 1.10197 | 0.550987 | − | 0.834514i | \(-0.314252\pi\) | ||||
0.550987 | + | 0.834514i | \(0.314252\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.37525e10 | 0.00508388 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.55910e12 | 0.310924 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.70229e13 | 1.82338 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.34845e13 | −1.56785 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.05436e12 | 0.0696473 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.02117e12 | −0.262827 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.37094e13 | −1.53338 | −0.766690 | − | 0.642017i | \(-0.778098\pi\) | ||||
−0.766690 | + | 0.642017i | \(0.778098\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.84663e12 | −0.438156 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.88590e13 | 1.19427 | 0.597137 | − | 0.802139i | \(-0.296305\pi\) | ||||
0.597137 | + | 0.802139i | \(0.296305\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.73506e13 | 1.71395 | 0.856974 | − | 0.515360i | \(-0.172342\pi\) | ||||
0.856974 | + | 0.515360i | \(0.172342\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.39968e13 | 0.867992 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5.40502e12 | −0.331703 | −0.165851 | − | 0.986151i | \(-0.553037\pi\) | ||||
−0.165851 | + | 0.986151i | \(0.553037\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.73080e13 | −1.05117 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7.92367e12 | 0.476256 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.62361e12 | −0.0965810 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.74065e11 | 0.0455718 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.36164e11 | −0.0195879 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −7.60766e13 | −4.38748 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.41805e12 | 0.309275 | 0.154638 | − | 0.987971i | \(-0.450579\pi\) | ||||
0.154638 | + | 0.987971i | \(0.450579\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.66932e13 | 0.943171 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.92850e12 | −0.443404 | −0.221702 | − | 0.975114i | \(-0.571161\pi\) | ||||
−0.221702 | + | 0.975114i | \(0.571161\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.68918e13 | −1.48866 | −0.744331 | − | 0.667811i | \(-0.767231\pi\) | ||||
−0.744331 | + | 0.667811i | \(0.767231\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.89905e13 | 1.04062 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.82440e13 | −1.53204 | −0.766020 | − | 0.642817i | \(-0.777766\pi\) | ||||
−0.766020 | + | 0.642817i | \(0.777766\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.67692e13 | −1.97436 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7.61706e11 | −0.0404890 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.90492e13 | −1.00241 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.54196e13 | 0.803286 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.73242e10 | −0.00450369 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.84386e12 | −0.502628 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.15021e13 | −2.60354 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.12700e13 | −0.564067 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.42877e13 | −2.19465 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.28245e13 | 0.629226 | 0.314613 | − | 0.949220i | \(-0.398125\pi\) | ||||
0.314613 | + | 0.949220i | \(0.398125\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.15579e12 | −0.104729 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.36953e12 | 0.450697 | 0.225349 | − | 0.974278i | \(-0.427648\pi\) | ||||
0.225349 | + | 0.974278i | \(0.427648\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.29908e12 | 0.157135 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.40363e13 | −1.60527 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.87481e13 | −2.27665 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.04580e12 | 0.418338 | 0.209169 | − | 0.977880i | \(-0.432924\pi\) | ||||
0.209169 | + | 0.977880i | \(0.432924\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.08734e12 | 0.232982 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.03024e12 | −0.0467229 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.88608e13 | −2.19443 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.40283e13 | 0.623945 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.59777e13 | 0.703789 | 0.351895 | − | 0.936040i | \(-0.385538\pi\) | ||||
0.351895 | + | 0.936040i | \(0.385538\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.74598e13 | 1.63415 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.31161e12 | −0.0998729 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.09927e13 | −0.898287 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5.20573e12 | −0.220624 | −0.110312 | − | 0.993897i | \(-0.535185\pi\) | ||||
−0.110312 | + | 0.993897i | \(0.535185\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 8.39800e11 | 0.0352517 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.35801e13 | −0.564612 | −0.282306 | − | 0.959324i | \(-0.591099\pi\) | ||||
−0.282306 | + | 0.959324i | \(0.591099\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.63485e12 | 0.232049 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.55653e13 | −0.634913 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.11344e13 | −0.449874 | −0.224937 | − | 0.974373i | \(-0.572218\pi\) | ||||
−0.224937 | + | 0.974373i | \(0.572218\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.13095e11 | 0.00852854 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.93297e12 | 0.354147 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.70642e13 | 1.45558 | 0.727791 | − | 0.685799i | \(-0.240547\pi\) | ||||
0.727791 | + | 0.685799i | \(0.240547\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.97585e13 | −1.54673 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.47299e12 | 0.210921 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.15893e13 | −0.824242 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.97938e13 | −0.748643 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.05773e12 | 0.339392 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.58744e13 | 2.44537 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.56420e13 | 0.943047 | 0.471524 | − | 0.881853i | \(-0.343704\pi\) | ||||
0.471524 | + | 0.881853i | \(0.343704\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.54188e13 | −0.561815 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.47900e13 | −1.61694 | −0.808471 | − | 0.588536i | \(-0.799704\pi\) | ||||
−0.808471 | + | 0.588536i | \(0.799704\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.58313e13 | −1.63928 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.06107e12 | −0.0376029 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.70660e12 | −0.165265 | −0.0826326 | − | 0.996580i | \(-0.526333\pi\) | ||||
−0.0826326 | + | 0.996580i | \(0.526333\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.12746e13 | 0.392263 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.32036e12 | −0.321309 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.45816e12 | −0.152288 | −0.0761438 | − | 0.997097i | \(-0.524261\pi\) | ||||
−0.0761438 | + | 0.997097i | \(0.524261\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.88099e13 | 2.66758 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.33069e13 | −1.45255 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.53710e12 | −0.150798 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.02988e13 | 0.339201 | 0.169600 | − | 0.985513i | \(-0.445752\pi\) | ||||
0.169600 | + | 0.985513i | \(0.445752\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.88036e13 | −0.613720 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.27893e13 | −1.06054 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.40551e13 | 1.41211 | 0.706054 | − | 0.708158i | \(-0.250474\pi\) | ||||
0.706054 | + | 0.708158i | \(0.250474\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.70622e12 | −0.181261 |
(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 | 384.10.a.f.1.1 | yes | 4 | |
4.3 | odd | 2 | 384.10.a.b.1.1 | ✓ | 4 | ||
8.3 | odd | 2 | 384.10.a.g.1.4 | yes | 4 | ||
8.5 | even | 2 | 384.10.a.c.1.4 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.10.a.b.1.1 | ✓ | 4 | 4.3 | odd | 2 | ||
384.10.a.c.1.4 | yes | 4 | 8.5 | even | 2 | ||
384.10.a.f.1.1 | yes | 4 | 1.1 | even | 1 | trivial | |
384.10.a.g.1.4 | yes | 4 | 8.3 | odd | 2 |