Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [45,12,Mod(1,45)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(45, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("45.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 45 = 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 45.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: | \(34.5754431252\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{151}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 151 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2\cdot 3 \) |
Twist minimal: | no (minimal twist has level 5) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-12.2882\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 45.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −63.7292 | −1.40823 | −0.704115 | − | 0.710086i | \(-0.748656\pi\) | ||||
−0.704115 | + | 0.710086i | \(0.748656\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2013.42 | 0.983113 | ||||||||
\(5\) | 3125.00 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 41926.3 | 0.942861 | 0.471431 | − | 0.881903i | \(-0.343738\pi\) | ||||
0.471431 | + | 0.881903i | \(0.343738\pi\) | |||||||
\(8\) | 2204.06 | 0.0237809 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −199154. | −0.629780 | ||||||||
\(11\) | 957905. | 1.79334 | 0.896670 | − | 0.442699i | \(-0.145979\pi\) | ||||
0.896670 | + | 0.442699i | \(0.145979\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.39098e6 | 1.03904 | 0.519520 | − | 0.854458i | \(-0.326111\pi\) | ||||
0.519520 | + | 0.854458i | \(0.326111\pi\) | |||||||
\(14\) | −2.67193e6 | −1.32777 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.26394e6 | −1.01660 | ||||||||
\(17\) | −3.76857e6 | −0.643736 | −0.321868 | − | 0.946785i | \(-0.604311\pi\) | ||||
−0.321868 | + | 0.946785i | \(0.604311\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 9.41036e6 | 0.871889 | 0.435945 | − | 0.899973i | \(-0.356414\pi\) | ||||
0.435945 | + | 0.899973i | \(0.356414\pi\) | |||||||
\(20\) | 6.29192e6 | 0.439661 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.10466e7 | −2.52544 | ||||||||
\(23\) | −3.02942e7 | −0.981423 | −0.490712 | − | 0.871322i | \(-0.663263\pi\) | ||||
−0.490712 | + | 0.871322i | \(0.663263\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.76562e6 | 0.200000 | ||||||||
\(26\) | −8.86460e7 | −1.46321 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 8.44151e7 | 0.926939 | ||||||||
\(29\) | −1.03553e8 | −0.937502 | −0.468751 | − | 0.883330i | \(-0.655296\pi\) | ||||
−0.468751 | + | 0.883330i | \(0.655296\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.48554e7 | −0.344136 | −0.172068 | − | 0.985085i | \(-0.555045\pi\) | ||||
−0.172068 | + | 0.985085i | \(0.555045\pi\) | |||||||
\(32\) | 2.67224e8 | 1.40783 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.40168e8 | 0.906529 | ||||||||
\(35\) | 1.31020e8 | 0.421660 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.78282e8 | 1.13390 | 0.566950 | − | 0.823752i | \(-0.308123\pi\) | ||||
0.566950 | + | 0.823752i | \(0.308123\pi\) | |||||||
\(38\) | −5.99715e8 | −1.22782 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 6.88767e6 | 0.0106351 | ||||||||
\(41\) | 9.29557e8 | 1.25304 | 0.626520 | − | 0.779406i | \(-0.284479\pi\) | ||||
0.626520 | + | 0.779406i | \(0.284479\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.68608e7 | −0.0278639 | −0.0139320 | − | 0.999903i | \(-0.504435\pi\) | ||||
−0.0139320 | + | 0.999903i | \(0.504435\pi\) | |||||||
\(44\) | 1.92866e9 | 1.76306 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.93063e9 | 1.38207 | ||||||||
\(47\) | 1.20497e9 | 0.766370 | 0.383185 | − | 0.923672i | \(-0.374827\pi\) | ||||
0.383185 | + | 0.923672i | \(0.374827\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.19508e8 | −0.111013 | ||||||||
\(50\) | −6.22356e8 | −0.281646 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.80062e9 | 1.02149 | ||||||||
\(53\) | 4.02058e9 | 1.32060 | 0.660301 | − | 0.751001i | \(-0.270429\pi\) | ||||
0.660301 | + | 0.751001i | \(0.270429\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.99345e9 | 0.802006 | ||||||||
\(56\) | 9.24080e7 | 0.0224221 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 6.59933e9 | 1.32022 | ||||||||
\(59\) | −7.97972e9 | −1.45312 | −0.726560 | − | 0.687103i | \(-0.758882\pi\) | ||||
−0.726560 | + | 0.687103i | \(0.758882\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.07472e9 | −0.314518 | −0.157259 | − | 0.987557i | \(-0.550266\pi\) | ||||
−0.157259 | + | 0.987557i | \(0.550266\pi\) | |||||||
\(62\) | 3.49589e9 | 0.484623 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.29741e9 | −0.965946 | ||||||||
\(65\) | 4.34681e9 | 0.464673 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.61370e9 | 0.507969 | 0.253985 | − | 0.967208i | \(-0.418259\pi\) | ||||
0.253985 | + | 0.967208i | \(0.418259\pi\) | |||||||
\(68\) | −7.58770e9 | −0.632865 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −8.34979e9 | −0.593795 | ||||||||
\(71\) | −1.51224e10 | −0.994714 | −0.497357 | − | 0.867546i | \(-0.665696\pi\) | ||||
−0.497357 | + | 0.867546i | \(0.665696\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.64484e9 | −0.375153 | −0.187577 | − | 0.982250i | \(-0.560063\pi\) | ||||
−0.187577 | + | 0.982250i | \(0.560063\pi\) | |||||||
\(74\) | −3.04806e10 | −1.59679 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.89470e10 | 0.857166 | ||||||||
\(77\) | 4.01615e10 | 1.69087 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.57985e10 | −0.577652 | −0.288826 | − | 0.957382i | \(-0.593265\pi\) | ||||
−0.288826 | + | 0.957382i | \(0.593265\pi\) | |||||||
\(80\) | −1.33248e10 | −0.454638 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −5.92399e10 | −1.76457 | ||||||||
\(83\) | 2.04046e10 | 0.568589 | 0.284295 | − | 0.958737i | \(-0.408241\pi\) | ||||
0.284295 | + | 0.958737i | \(0.408241\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.17768e10 | −0.287888 | ||||||||
\(86\) | 1.71182e9 | 0.0392389 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.11128e9 | 0.0426472 | ||||||||
\(89\) | 4.21030e10 | 0.799223 | 0.399611 | − | 0.916685i | \(-0.369145\pi\) | ||||
0.399611 | + | 0.916685i | \(0.369145\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.83187e10 | 0.979670 | ||||||||
\(92\) | −6.09948e10 | −0.964850 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −7.67919e10 | −1.07923 | ||||||||
\(95\) | 2.94074e10 | 0.389921 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.10181e11 | 1.30275 | 0.651376 | − | 0.758755i | \(-0.274192\pi\) | ||||
0.651376 | + | 0.758755i | \(0.274192\pi\) | |||||||
\(98\) | 1.39891e10 | 0.156331 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.96623e10 | 0.196623 | ||||||||
\(101\) | 3.33271e10 | 0.315522 | 0.157761 | − | 0.987477i | \(-0.449572\pi\) | ||||
0.157761 | + | 0.987477i | \(0.449572\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.49419e10 | 0.721966 | 0.360983 | − | 0.932572i | \(-0.382441\pi\) | ||||
0.360983 | + | 0.932572i | \(0.382441\pi\) | |||||||
\(104\) | 3.06580e9 | 0.0247093 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.56229e11 | −1.85971 | ||||||||
\(107\) | −1.43774e11 | −0.990989 | −0.495494 | − | 0.868611i | \(-0.665013\pi\) | ||||
−0.495494 | + | 0.868611i | \(0.665013\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.01296e11 | −1.87563 | −0.937816 | − | 0.347134i | \(-0.887155\pi\) | ||||
−0.937816 | + | 0.347134i | \(0.887155\pi\) | |||||||
\(110\) | −1.90771e11 | −1.12941 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.78771e11 | −0.958515 | ||||||||
\(113\) | 2.22891e11 | 1.13805 | 0.569026 | − | 0.822320i | \(-0.307320\pi\) | ||||
0.569026 | + | 0.822320i | \(0.307320\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.46694e10 | −0.438906 | ||||||||
\(116\) | −2.08495e11 | −0.921671 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 5.08541e11 | 2.04633 | ||||||||
\(119\) | −1.58003e11 | −0.606954 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.32271e11 | 2.21607 | ||||||||
\(122\) | 1.32220e11 | 0.442914 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.10447e11 | −0.338324 | ||||||||
\(125\) | 3.05176e10 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.79939e11 | −0.483287 | −0.241644 | − | 0.970365i | \(-0.577687\pi\) | ||||
−0.241644 | + | 0.970365i | \(0.577687\pi\) | |||||||
\(128\) | −1.84863e10 | −0.0475549 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.77019e11 | −0.654366 | ||||||||
\(131\) | 5.65153e11 | 1.27989 | 0.639946 | − | 0.768420i | \(-0.278957\pi\) | ||||
0.639946 | + | 0.768420i | \(0.278957\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.94542e11 | 0.822071 | ||||||||
\(134\) | −3.57757e11 | −0.715338 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −8.30615e9 | −0.0153086 | ||||||||
\(137\) | −1.24499e9 | −0.00220396 | −0.00110198 | − | 0.999999i | \(-0.500351\pi\) | ||||
−0.00110198 | + | 0.999999i | \(0.500351\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.68084e11 | 0.765142 | 0.382571 | − | 0.923926i | \(-0.375039\pi\) | ||||
0.382571 | + | 0.923926i | \(0.375039\pi\) | |||||||
\(140\) | 2.63797e11 | 0.414540 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 9.63736e11 | 1.40079 | ||||||||
\(143\) | 1.33243e12 | 1.86335 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.23602e11 | −0.419264 | ||||||||
\(146\) | 4.23470e11 | 0.528302 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 9.62981e11 | 1.11475 | ||||||||
\(149\) | −1.05439e12 | −1.17619 | −0.588096 | − | 0.808791i | \(-0.700122\pi\) | ||||
−0.588096 | + | 0.808791i | \(0.700122\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.91301e11 | 0.509301 | 0.254651 | − | 0.967033i | \(-0.418040\pi\) | ||||
0.254651 | + | 0.967033i | \(0.418040\pi\) | |||||||
\(152\) | 2.07410e10 | 0.0207343 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.55946e12 | −2.38114 | ||||||||
\(155\) | −1.71423e11 | −0.153902 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.17375e11 | 0.516536 | 0.258268 | − | 0.966073i | \(-0.416848\pi\) | ||||
0.258268 | + | 0.966073i | \(0.416848\pi\) | |||||||
\(158\) | 1.00683e12 | 0.813467 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 8.35074e11 | 0.629600 | ||||||||
\(161\) | −1.27013e12 | −0.925346 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.97234e11 | 0.202333 | 0.101166 | − | 0.994870i | \(-0.467743\pi\) | ||||
0.101166 | + | 0.994870i | \(0.467743\pi\) | |||||||
\(164\) | 1.87158e12 | 1.23188 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.30037e12 | −0.800705 | ||||||||
\(167\) | 2.53524e11 | 0.151035 | 0.0755177 | − | 0.997144i | \(-0.475939\pi\) | ||||
0.0755177 | + | 0.997144i | \(0.475939\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.42662e11 | 0.0796035 | ||||||||
\(170\) | 7.50526e11 | 0.405412 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −5.40820e10 | −0.0273934 | ||||||||
\(173\) | −1.80555e12 | −0.885843 | −0.442922 | − | 0.896560i | \(-0.646058\pi\) | ||||
−0.442922 | + | 0.896560i | \(0.646058\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.09437e11 | 0.188572 | ||||||||
\(176\) | −4.08445e12 | −1.82311 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2.68319e12 | −1.12549 | ||||||||
\(179\) | −1.63020e12 | −0.663054 | −0.331527 | − | 0.943446i | \(-0.607564\pi\) | ||||
−0.331527 | + | 0.943446i | \(0.607564\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.16028e12 | −1.59181 | −0.795904 | − | 0.605423i | \(-0.793004\pi\) | ||||
−0.795904 | + | 0.605423i | \(0.793004\pi\) | |||||||
\(182\) | −3.71660e12 | −1.37960 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −6.67701e10 | −0.0233391 | ||||||||
\(185\) | 1.49463e12 | 0.507096 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.60994e12 | −1.15444 | ||||||||
\(188\) | 2.42611e12 | 0.753429 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.87411e12 | −0.549098 | ||||||||
\(191\) | 3.03600e12 | 0.864208 | 0.432104 | − | 0.901824i | \(-0.357771\pi\) | ||||
0.432104 | + | 0.901824i | \(0.357771\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.77397e12 | 1.01445 | 0.507227 | − | 0.861812i | \(-0.330670\pi\) | ||||
0.507227 | + | 0.861812i | \(0.330670\pi\) | |||||||
\(194\) | −7.02174e12 | −1.83457 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.41961e11 | −0.109138 | ||||||||
\(197\) | 1.03079e12 | 0.247518 | 0.123759 | − | 0.992312i | \(-0.460505\pi\) | ||||
0.123759 | + | 0.992312i | \(0.460505\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.14293e12 | 0.259614 | 0.129807 | − | 0.991539i | \(-0.458564\pi\) | ||||
0.129807 | + | 0.991539i | \(0.458564\pi\) | |||||||
\(200\) | 2.15240e10 | 0.00475617 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.12391e12 | −0.444328 | ||||||||
\(203\) | −4.34159e12 | −0.883935 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.90487e12 | 0.560376 | ||||||||
\(206\) | −5.41328e12 | −1.01670 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −5.93105e12 | −1.05629 | ||||||||
\(209\) | 9.01423e12 | 1.56359 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.96492e12 | 1.14647 | 0.573235 | − | 0.819391i | \(-0.305688\pi\) | ||||
0.573235 | + | 0.819391i | \(0.305688\pi\) | |||||||
\(212\) | 8.09510e12 | 1.29830 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 9.16259e12 | 1.39554 | ||||||||
\(215\) | −8.39400e10 | −0.0124611 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.29989e12 | −0.324472 | ||||||||
\(218\) | 1.92014e13 | 2.64132 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 6.02707e12 | 0.788463 | ||||||||
\(221\) | −5.24201e12 | −0.668868 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.80403e12 | 0.826208 | 0.413104 | − | 0.910684i | \(-0.364445\pi\) | ||||
0.413104 | + | 0.910684i | \(0.364445\pi\) | |||||||
\(224\) | 1.12037e13 | 1.32739 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.42047e13 | −1.60264 | ||||||||
\(227\) | −8.00368e12 | −0.881348 | −0.440674 | − | 0.897667i | \(-0.645261\pi\) | ||||
−0.440674 | + | 0.897667i | \(0.645261\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.20624e13 | 1.26572 | 0.632862 | − | 0.774265i | \(-0.281880\pi\) | ||||
0.632862 | + | 0.774265i | \(0.281880\pi\) | |||||||
\(230\) | 6.03321e12 | 0.618081 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.28236e11 | −0.0222946 | ||||||||
\(233\) | 1.05744e13 | 1.00878 | 0.504390 | − | 0.863476i | \(-0.331717\pi\) | ||||
0.504390 | + | 0.863476i | \(0.331717\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.76554e12 | 0.342731 | ||||||||
\(236\) | −1.60665e13 | −1.42858 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.00694e13 | 0.854731 | ||||||||
\(239\) | 4.81329e12 | 0.399258 | 0.199629 | − | 0.979872i | \(-0.436026\pi\) | ||||
0.199629 | + | 0.979872i | \(0.436026\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.29674e13 | −1.02745 | −0.513724 | − | 0.857956i | \(-0.671734\pi\) | ||||
−0.513724 | + | 0.857956i | \(0.671734\pi\) | |||||||
\(242\) | −4.02941e13 | −3.12074 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −4.17728e12 | −0.309207 | ||||||||
\(245\) | −6.85963e11 | −0.0496464 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.30896e13 | 0.905928 | ||||||||
\(248\) | −1.20904e11 | −0.00818385 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.94486e12 | −0.125956 | ||||||||
\(251\) | −5.10147e12 | −0.323214 | −0.161607 | − | 0.986855i | \(-0.551668\pi\) | ||||
−0.161607 | + | 0.986855i | \(0.551668\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.90190e13 | −1.76003 | ||||||||
\(254\) | 1.14674e13 | 0.680580 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.81712e13 | 1.03291 | ||||||||
\(257\) | 1.20976e13 | 0.673079 | 0.336539 | − | 0.941669i | \(-0.390744\pi\) | ||||
0.336539 | + | 0.941669i | \(0.390744\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.00526e13 | 1.06911 | ||||||||
\(260\) | 8.75193e12 | 0.456826 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.60167e13 | −1.80238 | ||||||||
\(263\) | 1.09431e13 | 0.536271 | 0.268135 | − | 0.963381i | \(-0.413593\pi\) | ||||
0.268135 | + | 0.963381i | \(0.413593\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.25643e13 | 0.590591 | ||||||||
\(266\) | −2.51439e13 | −1.15767 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.13027e13 | 0.499391 | ||||||||
\(269\) | −1.23621e13 | −0.535125 | −0.267562 | − | 0.963541i | \(-0.586218\pi\) | ||||
−0.267562 | + | 0.963541i | \(0.586218\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.34683e13 | 0.559734 | 0.279867 | − | 0.960039i | \(-0.409710\pi\) | ||||
0.279867 | + | 0.960039i | \(0.409710\pi\) | |||||||
\(272\) | 1.60690e13 | 0.654424 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7.93424e10 | 0.00310368 | ||||||||
\(275\) | 9.35454e12 | 0.358668 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.20976e13 | 0.814153 | 0.407077 | − | 0.913394i | \(-0.366548\pi\) | ||||
0.407077 | + | 0.913394i | \(0.366548\pi\) | |||||||
\(278\) | −2.98306e13 | −1.07750 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.88775e11 | 0.0100274 | ||||||||
\(281\) | −7.15247e12 | −0.243541 | −0.121770 | − | 0.992558i | \(-0.538857\pi\) | ||||
−0.121770 | + | 0.992558i | \(0.538857\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.90996e12 | −0.324524 | −0.162262 | − | 0.986748i | \(-0.551879\pi\) | ||||
−0.162262 | + | 0.986748i | \(0.551879\pi\) | |||||||
\(284\) | −3.04476e13 | −0.977917 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −8.49145e13 | −2.62403 | ||||||||
\(287\) | 3.89729e13 | 1.18144 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.00697e13 | −0.585604 | ||||||||
\(290\) | 2.06229e13 | 0.590420 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.33788e13 | −0.368818 | ||||||||
\(293\) | 6.76585e13 | 1.83042 | 0.915209 | − | 0.402980i | \(-0.132026\pi\) | ||||
0.915209 | + | 0.402980i | \(0.132026\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.49366e13 | −0.649855 | ||||||||
\(296\) | 1.05416e12 | 0.0269651 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6.71957e13 | 1.65635 | ||||||||
\(299\) | −4.21386e13 | −1.01974 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.12618e12 | −0.0262718 | ||||||||
\(302\) | −3.13103e13 | −0.717213 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4.01252e13 | −0.886364 | ||||||||
\(305\) | −6.48351e12 | −0.140657 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.76335e13 | −0.578328 | −0.289164 | − | 0.957280i | \(-0.593377\pi\) | ||||
−0.289164 | + | 0.957280i | \(0.593377\pi\) | |||||||
\(308\) | 8.08617e13 | 1.66232 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.09247e13 | 0.216730 | ||||||||
\(311\) | 1.21728e13 | 0.237251 | 0.118626 | − | 0.992939i | \(-0.462151\pi\) | ||||
0.118626 | + | 0.992939i | \(0.462151\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.17271e13 | 1.53770 | 0.768851 | − | 0.639428i | \(-0.220829\pi\) | ||||
0.768851 | + | 0.639428i | \(0.220829\pi\) | |||||||
\(314\) | −3.93448e13 | −0.727402 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.18089e13 | −0.567897 | ||||||||
\(317\) | −7.61714e13 | −1.33649 | −0.668246 | − | 0.743941i | \(-0.732955\pi\) | ||||
−0.668246 | + | 0.743941i | \(0.732955\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.91937e13 | −1.68126 | ||||||||
\(320\) | −2.59294e13 | −0.431984 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 8.09441e13 | 1.30310 | ||||||||
\(323\) | −3.54636e13 | −0.561267 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.35838e13 | 0.207808 | ||||||||
\(326\) | −1.89425e13 | −0.284931 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.04880e12 | 0.0297984 | ||||||||
\(329\) | 5.05201e13 | 0.722581 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.05093e13 | 1.11376 | 0.556881 | − | 0.830592i | \(-0.311998\pi\) | ||||
0.556881 | + | 0.830592i | \(0.311998\pi\) | |||||||
\(332\) | 4.10830e13 | 0.558988 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.61569e13 | −0.212693 | ||||||||
\(335\) | 1.75428e13 | 0.227171 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.90669e13 | −0.990901 | −0.495451 | − | 0.868636i | \(-0.664997\pi\) | ||||
−0.495451 | + | 0.868636i | \(0.664997\pi\) | |||||||
\(338\) | −9.09176e12 | −0.112100 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.37116e13 | −0.283026 | ||||||||
\(341\) | −5.25463e13 | −0.617153 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.21053e13 | −1.04753 | ||||||||
\(344\) | −5.92027e10 | −0.000662629 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.15067e14 | 1.24747 | ||||||||
\(347\) | −1.40156e14 | −1.49554 | −0.747772 | − | 0.663956i | \(-0.768876\pi\) | ||||
−0.747772 | + | 0.663956i | \(0.768876\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.88347e13 | −1.02181 | −0.510905 | − | 0.859637i | \(-0.670689\pi\) | ||||
−0.510905 | + | 0.859637i | \(0.670689\pi\) | |||||||
\(350\) | −2.60931e13 | −0.265553 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.55975e14 | 2.52472 | ||||||||
\(353\) | 2.74254e13 | 0.266313 | 0.133156 | − | 0.991095i | \(-0.457489\pi\) | ||||
0.133156 | + | 0.991095i | \(0.457489\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.72573e13 | −0.444850 | ||||||||
\(356\) | 8.47708e13 | 0.785726 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.03891e14 | 0.933733 | ||||||||
\(359\) | −1.57856e14 | −1.39715 | −0.698574 | − | 0.715538i | \(-0.746182\pi\) | ||||
−0.698574 | + | 0.715538i | \(0.746182\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.79354e13 | −0.239809 | ||||||||
\(362\) | 2.65132e14 | 2.24163 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.17420e14 | 0.963127 | ||||||||
\(365\) | −2.07651e13 | −0.167774 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.95534e14 | −1.53306 | −0.766529 | − | 0.642210i | \(-0.778018\pi\) | ||||
−0.766529 | + | 0.642210i | \(0.778018\pi\) | |||||||
\(368\) | 1.29173e14 | 0.997717 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −9.52518e13 | −0.714107 | ||||||||
\(371\) | 1.68568e14 | 1.24514 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.35940e13 | 0.599482 | 0.299741 | − | 0.954021i | \(-0.403100\pi\) | ||||
0.299741 | + | 0.954021i | \(0.403100\pi\) | |||||||
\(374\) | 2.30059e14 | 1.62572 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.65583e12 | 0.0182249 | ||||||||
\(377\) | −1.44040e14 | −0.974102 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.81905e14 | 1.85177 | 0.925887 | − | 0.377802i | \(-0.123320\pi\) | ||||
0.925887 | + | 0.377802i | \(0.123320\pi\) | |||||||
\(380\) | 5.92093e13 | 0.383336 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.93482e14 | −1.21700 | ||||||||
\(383\) | −2.51689e13 | −0.156053 | −0.0780264 | − | 0.996951i | \(-0.524862\pi\) | ||||
−0.0780264 | + | 0.996951i | \(0.524862\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.25505e14 | 0.756181 | ||||||||
\(386\) | −2.40512e14 | −1.42859 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.21840e14 | 1.28075 | ||||||||
\(389\) | 1.44036e14 | 0.819879 | 0.409939 | − | 0.912113i | \(-0.365550\pi\) | ||||
0.409939 | + | 0.912113i | \(0.365550\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.14166e14 | 0.631778 | ||||||||
\(392\) | −4.83809e11 | −0.00263998 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −6.56916e13 | −0.348563 | ||||||||
\(395\) | −4.93703e13 | −0.258334 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.78848e13 | 0.192804 | 0.0964021 | − | 0.995342i | \(-0.469267\pi\) | ||||
0.0964021 | + | 0.995342i | \(0.469267\pi\) | |||||||
\(398\) | −7.28380e13 | −0.365596 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.16400e13 | −0.203320 | ||||||||
\(401\) | −1.24111e13 | −0.0597747 | −0.0298874 | − | 0.999553i | \(-0.509515\pi\) | ||||
−0.0298874 | + | 0.999553i | \(0.509515\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.63027e13 | −0.357571 | ||||||||
\(404\) | 6.71012e13 | 0.310194 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.76686e14 | 1.24478 | ||||||||
\(407\) | 4.58149e14 | 2.03347 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.37138e14 | −1.88860 | −0.944301 | − | 0.329082i | \(-0.893261\pi\) | ||||
−0.944301 | + | 0.329082i | \(0.893261\pi\) | |||||||
\(410\) | −1.85125e14 | −0.789139 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.71023e14 | 0.709775 | ||||||||
\(413\) | −3.34560e14 | −1.37009 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.37644e13 | 0.254281 | ||||||||
\(416\) | 3.71702e14 | 1.46279 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −5.74470e14 | −2.20190 | ||||||||
\(419\) | −5.14822e14 | −1.94751 | −0.973755 | − | 0.227598i | \(-0.926913\pi\) | ||||
−0.973755 | + | 0.227598i | \(0.926913\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.90682e14 | −1.43970 | −0.719850 | − | 0.694130i | \(-0.755789\pi\) | ||||
−0.719850 | + | 0.694130i | \(0.755789\pi\) | |||||||
\(422\) | −4.43869e14 | −1.61449 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 8.86159e12 | 0.0314050 | ||||||||
\(425\) | −3.68025e13 | −0.128747 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.69855e13 | −0.296547 | ||||||||
\(428\) | −2.89476e14 | −0.974254 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5.34943e12 | 0.0175482 | ||||||||
\(431\) | 3.29050e14 | 1.06571 | 0.532853 | − | 0.846208i | \(-0.321120\pi\) | ||||
0.532853 | + | 0.846208i | \(0.321120\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.59793e14 | −1.76744 | −0.883718 | − | 0.468019i | \(-0.844968\pi\) | ||||
−0.883718 | + | 0.468019i | \(0.844968\pi\) | |||||||
\(434\) | 1.46570e14 | 0.456932 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6.06634e14 | −1.84396 | ||||||||
\(437\) | −2.85079e14 | −0.855693 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.25752e14 | 0.368095 | 0.184047 | − | 0.982917i | \(-0.441080\pi\) | ||||
0.184047 | + | 0.982917i | \(0.441080\pi\) | |||||||
\(440\) | 6.59774e12 | 0.0190724 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.34069e14 | 0.941920 | ||||||||
\(443\) | −3.33211e14 | −0.927894 | −0.463947 | − | 0.885863i | \(-0.653567\pi\) | ||||
−0.463947 | + | 0.885863i | \(0.653567\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.31572e14 | 0.357423 | ||||||||
\(446\) | −4.33616e14 | −1.16349 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3.47880e14 | −0.910753 | ||||||||
\(449\) | 1.08196e14 | 0.279804 | 0.139902 | − | 0.990165i | \(-0.455321\pi\) | ||||
0.139902 | + | 0.990165i | \(0.455321\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.90427e14 | 2.24713 | ||||||||
\(452\) | 4.48773e14 | 1.11883 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 5.10068e14 | 1.24114 | ||||||||
\(455\) | 1.82246e14 | 0.438122 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.81057e14 | −0.424890 | −0.212445 | − | 0.977173i | \(-0.568143\pi\) | ||||
−0.212445 | + | 0.977173i | \(0.568143\pi\) | |||||||
\(458\) | −7.68728e14 | −1.78243 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.90609e14 | −0.431494 | ||||||||
\(461\) | 3.74610e14 | 0.837962 | 0.418981 | − | 0.907995i | \(-0.362387\pi\) | ||||
0.418981 | + | 0.907995i | \(0.362387\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.33341e13 | 0.0509678 | 0.0254839 | − | 0.999675i | \(-0.491887\pi\) | ||||
0.0254839 | + | 0.999675i | \(0.491887\pi\) | |||||||
\(464\) | 4.41542e14 | 0.953067 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.73896e14 | −1.42060 | ||||||||
\(467\) | 7.37382e14 | 1.53621 | 0.768103 | − | 0.640326i | \(-0.221201\pi\) | ||||
0.768103 | + | 0.640326i | \(0.221201\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.35362e14 | 0.478945 | ||||||||
\(470\) | −2.39975e14 | −0.482645 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.75877e13 | −0.0345564 | ||||||||
\(473\) | −2.57301e13 | −0.0499695 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9.18980e13 | 0.174378 | ||||||||
\(476\) | −3.18125e14 | −0.596704 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3.06747e14 | −0.562247 | ||||||||
\(479\) | 3.39424e14 | 0.615030 | 0.307515 | − | 0.951543i | \(-0.400503\pi\) | ||||
0.307515 | + | 0.951543i | \(0.400503\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.65281e14 | 1.17817 | ||||||||
\(482\) | 8.26404e14 | 1.44688 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.27302e15 | 2.17865 | ||||||||
\(485\) | 3.44315e14 | 0.582608 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.27468e14 | −0.541700 | −0.270850 | − | 0.962622i | \(-0.587305\pi\) | ||||
−0.270850 | + | 0.962622i | \(0.587305\pi\) | |||||||
\(488\) | −4.57280e12 | −0.00747952 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 4.37159e13 | 0.0699135 | ||||||||
\(491\) | 3.28187e14 | 0.519006 | 0.259503 | − | 0.965742i | \(-0.416441\pi\) | ||||
0.259503 | + | 0.965742i | \(0.416441\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.90246e14 | 0.603504 | ||||||||
\(494\) | −8.34191e14 | −1.27576 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.33900e14 | 0.349849 | ||||||||
\(497\) | −6.34025e14 | −0.937878 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.84812e14 | 0.412103 | 0.206052 | − | 0.978541i | \(-0.433939\pi\) | ||||
0.206052 | + | 0.978541i | \(0.433939\pi\) | |||||||
\(500\) | 6.14446e13 | 0.0879323 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.25112e14 | 0.455159 | ||||||||
\(503\) | 2.01563e13 | 0.0279117 | 0.0139559 | − | 0.999903i | \(-0.495558\pi\) | ||||
0.0139559 | + | 0.999903i | \(0.495558\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.04147e14 | 0.141106 | ||||||||
\(506\) | 1.84936e15 | 2.47852 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.62292e14 | −0.475126 | ||||||||
\(509\) | 6.91697e14 | 0.897362 | 0.448681 | − | 0.893692i | \(-0.351894\pi\) | ||||
0.448681 | + | 0.893692i | \(0.351894\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.78594e14 | −0.353717 | ||||||||
\(512\) | −1.12018e15 | −1.40703 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −7.70969e14 | −0.947850 | ||||||||
\(515\) | 2.65443e14 | 0.322873 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.15425e15 | 1.37436 | ||||||||
\(518\) | −1.27794e15 | −1.50555 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 9.58061e12 | 0.0110503 | ||||||||
\(521\) | −5.00013e14 | −0.570656 | −0.285328 | − | 0.958430i | \(-0.592102\pi\) | ||||
−0.285328 | + | 0.958430i | \(0.592102\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.89272e14 | −0.323256 | −0.161628 | − | 0.986852i | \(-0.551674\pi\) | ||||
−0.161628 | + | 0.986852i | \(0.551674\pi\) | |||||||
\(524\) | 1.13789e15 | 1.25828 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.97396e14 | −0.755193 | ||||||||
\(527\) | 2.06727e14 | 0.221533 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.50713e13 | −0.0368083 | ||||||||
\(530\) | −8.00715e14 | −0.831688 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 7.94377e14 | 0.808188 | ||||||||
\(533\) | 1.29299e15 | 1.30196 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.49293e14 | −0.443184 | ||||||||
\(536\) | 1.23729e13 | 0.0120800 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 7.87828e14 | 0.753579 | ||||||||
\(539\) | −2.10268e14 | −0.199084 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.20798e15 | 1.12066 | 0.560331 | − | 0.828269i | \(-0.310674\pi\) | ||||
0.560331 | + | 0.828269i | \(0.310674\pi\) | |||||||
\(542\) | −8.58325e14 | −0.788235 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.00705e15 | −0.906271 | ||||||||
\(545\) | −9.41550e14 | −0.838808 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.74686e15 | −1.52521 | −0.762603 | − | 0.646867i | \(-0.776079\pi\) | ||||
−0.762603 | + | 0.646867i | \(0.776079\pi\) | |||||||
\(548\) | −2.50668e12 | −0.00216674 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −5.96158e14 | −0.505087 | ||||||||
\(551\) | −9.74468e14 | −0.817398 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.62373e14 | −0.544646 | ||||||||
\(554\) | −1.40826e15 | −1.14652 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.42447e14 | 0.752221 | ||||||||
\(557\) | −8.14516e14 | −0.643719 | −0.321859 | − | 0.946787i | \(-0.604308\pi\) | ||||
−0.321859 | + | 0.946787i | \(0.604308\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.73628e13 | −0.0289517 | ||||||||
\(560\) | −5.58660e14 | −0.428661 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4.55821e14 | 0.342961 | ||||||||
\(563\) | 8.94179e14 | 0.666237 | 0.333118 | − | 0.942885i | \(-0.391899\pi\) | ||||
0.333118 | + | 0.942885i | \(0.391899\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.96536e14 | 0.508952 | ||||||||
\(566\) | 6.31554e14 | 0.457004 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.33305e13 | −0.0236552 | ||||||||
\(569\) | −5.58478e14 | −0.392544 | −0.196272 | − | 0.980549i | \(-0.562884\pi\) | ||||
−0.196272 | + | 0.980549i | \(0.562884\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.19826e15 | 0.826136 | 0.413068 | − | 0.910700i | \(-0.364457\pi\) | ||||
0.413068 | + | 0.910700i | \(0.364457\pi\) | |||||||
\(572\) | 2.68273e15 | 1.83189 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.48371e15 | −1.66374 | ||||||||
\(575\) | −2.95842e14 | −0.196285 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.70453e15 | −1.10953 | −0.554764 | − | 0.832008i | \(-0.687192\pi\) | ||||
−0.554764 | + | 0.832008i | \(0.687192\pi\) | |||||||
\(578\) | 1.27903e15 | 0.824665 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −6.51545e14 | −0.412184 | ||||||||
\(581\) | 8.55491e14 | 0.536101 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.85134e15 | 2.36829 | ||||||||
\(584\) | −1.46456e13 | −0.00892147 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.31182e15 | −2.57765 | ||||||||
\(587\) | −8.77553e14 | −0.519713 | −0.259857 | − | 0.965647i | \(-0.583675\pi\) | ||||
−0.259857 | + | 0.965647i | \(0.583675\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.16209e14 | −0.300048 | ||||||||
\(590\) | 1.58919e15 | 0.915145 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.03937e15 | −1.15273 | ||||||||
\(593\) | −3.16216e15 | −1.77086 | −0.885428 | − | 0.464776i | \(-0.846135\pi\) | ||||
−0.885428 | + | 0.464776i | \(0.846135\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.93758e14 | −0.271438 | ||||||||
\(596\) | −2.12293e15 | −1.15633 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.68546e15 | 1.43603 | ||||||||
\(599\) | −1.86633e15 | −0.988873 | −0.494437 | − | 0.869214i | \(-0.664626\pi\) | ||||
−0.494437 | + | 0.869214i | \(0.664626\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.57728e14 | 0.446211 | 0.223105 | − | 0.974794i | \(-0.428381\pi\) | ||||
0.223105 | + | 0.974794i | \(0.428381\pi\) | |||||||
\(602\) | 7.17703e13 | 0.0369968 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 9.89193e14 | 0.500701 | ||||||||
\(605\) | 1.97585e15 | 0.991057 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.90938e15 | 1.43306 | 0.716528 | − | 0.697558i | \(-0.245730\pi\) | ||||
0.716528 | + | 0.697558i | \(0.245730\pi\) | |||||||
\(608\) | 2.51467e15 | 1.22747 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.13189e14 | 0.198077 | ||||||||
\(611\) | 1.67609e15 | 0.796289 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.95415e15 | −1.84510 | −0.922551 | − | 0.385875i | \(-0.873900\pi\) | ||||
−0.922551 | + | 0.385875i | \(0.873900\pi\) | |||||||
\(614\) | 1.76106e15 | 0.814419 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 8.85181e13 | 0.0402104 | ||||||||
\(617\) | 1.44545e15 | 0.650778 | 0.325389 | − | 0.945580i | \(-0.394505\pi\) | ||||
0.325389 | + | 0.945580i | \(0.394505\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.27132e15 | −1.88914 | −0.944569 | − | 0.328314i | \(-0.893519\pi\) | ||||
−0.944569 | + | 0.328314i | \(0.893519\pi\) | |||||||
\(620\) | −3.45146e14 | −0.151303 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −7.75764e14 | −0.334105 | ||||||||
\(623\) | 1.76522e15 | 0.753556 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.53674e13 | 0.0400000 | ||||||||
\(626\) | −5.20840e15 | −2.16544 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.24303e15 | 0.507813 | ||||||||
\(629\) | −1.80244e15 | −0.729933 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.19799e15 | 0.874711 | 0.437355 | − | 0.899289i | \(-0.355915\pi\) | ||||
0.437355 | + | 0.899289i | \(0.355915\pi\) | |||||||
\(632\) | −3.48207e13 | −0.0137371 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 4.85435e15 | 1.88209 | ||||||||
\(635\) | −5.62310e14 | −0.216133 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.05331e14 | −0.115347 | ||||||||
\(638\) | 6.32154e15 | 2.36760 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −5.77698e13 | −0.0212672 | ||||||||
\(641\) | 6.69744e14 | 0.244450 | 0.122225 | − | 0.992502i | \(-0.460997\pi\) | ||||
0.122225 | + | 0.992502i | \(0.460997\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.43086e15 | 1.23096 | 0.615478 | − | 0.788154i | \(-0.288963\pi\) | ||||
0.615478 | + | 0.788154i | \(0.288963\pi\) | |||||||
\(644\) | −2.55729e15 | −0.909720 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.26007e15 | 0.790393 | ||||||||
\(647\) | 2.12502e15 | 0.736869 | 0.368435 | − | 0.929654i | \(-0.379894\pi\) | ||||
0.368435 | + | 0.929654i | \(0.379894\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.64381e15 | −2.60594 | ||||||||
\(650\) | −8.65684e14 | −0.292641 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5.98455e14 | 0.198916 | ||||||||
\(653\) | −4.76025e15 | −1.56894 | −0.784471 | − | 0.620166i | \(-0.787065\pi\) | ||||
−0.784471 | + | 0.620166i | \(0.787065\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.76610e15 | 0.572385 | ||||||||
\(656\) | −3.96357e15 | −1.27384 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −3.21961e15 | −1.01756 | ||||||||
\(659\) | −1.31734e15 | −0.412886 | −0.206443 | − | 0.978459i | \(-0.566189\pi\) | ||||
−0.206443 | + | 0.978459i | \(0.566189\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.45528e15 | −0.756822 | −0.378411 | − | 0.925638i | \(-0.623529\pi\) | ||||
−0.378411 | + | 0.925638i | \(0.623529\pi\) | |||||||
\(662\) | −5.13080e15 | −1.56843 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4.49729e13 | 0.0135215 | ||||||||
\(665\) | 1.23294e15 | 0.367641 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.13705e15 | 0.920087 | ||||||||
\(668\) | 5.10449e14 | 0.148485 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.11799e15 | −0.319909 | ||||||||
\(671\) | −1.98739e15 | −0.564038 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.60705e14 | −0.240310 | −0.120155 | − | 0.992755i | \(-0.538339\pi\) | ||||
−0.120155 | + | 0.992755i | \(0.538339\pi\) | |||||||
\(674\) | 5.03888e15 | 1.39542 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.87238e14 | 0.0782593 | ||||||||
\(677\) | −1.90003e15 | −0.513479 | −0.256739 | − | 0.966481i | \(-0.582648\pi\) | ||||
−0.256739 | + | 0.966481i | \(0.582648\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.61948e15 | 1.22831 | ||||||||
\(680\) | −2.59567e13 | −0.00684622 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 3.34873e15 | 0.869093 | ||||||||
\(683\) | 2.35084e15 | 0.605214 | 0.302607 | − | 0.953115i | \(-0.402143\pi\) | ||||
0.302607 | + | 0.953115i | \(0.402143\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.89060e12 | −0.000985640 0 | ||||||||
\(686\) | 5.86980e15 | 1.47516 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.14533e14 | 0.0283265 | ||||||||
\(689\) | 5.59255e15 | 1.37216 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.60668e15 | −1.59534 | −0.797672 | − | 0.603092i | \(-0.793935\pi\) | ||||
−0.797672 | + | 0.603092i | \(0.793935\pi\) | |||||||
\(692\) | −3.63533e15 | −0.870884 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 8.93203e15 | 2.10607 | ||||||||
\(695\) | 1.46276e15 | 0.342182 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.50310e15 | −0.806627 | ||||||||
\(698\) | 6.29866e15 | 1.43894 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 8.24367e14 | 0.185388 | ||||||||
\(701\) | 8.01300e14 | 0.178791 | 0.0893956 | − | 0.995996i | \(-0.471506\pi\) | ||||
0.0893956 | + | 0.995996i | \(0.471506\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.50081e15 | 0.988636 | ||||||||
\(704\) | −7.94813e15 | −1.73227 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.74780e15 | −0.375030 | ||||||||
\(707\) | 1.39728e15 | 0.297493 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.10789e15 | 0.861121 | 0.430560 | − | 0.902562i | \(-0.358316\pi\) | ||||
0.430560 | + | 0.902562i | \(0.358316\pi\) | |||||||
\(710\) | 3.01167e15 | 0.626451 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 9.27973e13 | 0.0190062 | ||||||||
\(713\) | 1.66180e15 | 0.337743 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.16383e15 | 0.833316 | ||||||||
\(716\) | −3.28227e15 | −0.651857 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.00601e16 | 1.96751 | ||||||||
\(719\) | −2.12875e15 | −0.413157 | −0.206578 | − | 0.978430i | \(-0.566233\pi\) | ||||
−0.206578 | + | 0.978430i | \(0.566233\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.56130e15 | 0.680714 | ||||||||
\(722\) | 1.78030e15 | 0.337706 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −8.37637e15 | −1.56493 | ||||||||
\(725\) | −1.01126e15 | −0.187500 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.60450e15 | −0.840898 | −0.420449 | − | 0.907316i | \(-0.638127\pi\) | ||||
−0.420449 | + | 0.907316i | \(0.638127\pi\) | |||||||
\(728\) | 1.28538e14 | 0.0232974 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.32334e15 | 0.236264 | ||||||||
\(731\) | 1.01227e14 | 0.0179370 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.94830e15 | −0.689190 | −0.344595 | − | 0.938752i | \(-0.611984\pi\) | ||||
−0.344595 | + | 0.938752i | \(0.611984\pi\) | |||||||
\(734\) | 1.24612e16 | 2.15890 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8.09532e15 | −1.38168 | ||||||||
\(737\) | 5.37739e15 | 0.910962 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.01640e15 | 0.336537 | 0.168269 | − | 0.985741i | \(-0.446182\pi\) | ||||
0.168269 | + | 0.985741i | \(0.446182\pi\) | |||||||
\(740\) | 3.00932e15 | 0.498532 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.07427e16 | −1.75345 | ||||||||
\(743\) | 7.15627e15 | 1.15944 | 0.579720 | − | 0.814816i | \(-0.303162\pi\) | ||||
0.579720 | + | 0.814816i | \(0.303162\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.29498e15 | −0.526009 | ||||||||
\(746\) | −5.32738e15 | −0.844209 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −7.26830e15 | −1.13494 | ||||||||
\(749\) | −6.02791e15 | −0.934365 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.55257e14 | −0.0389904 | −0.0194952 | − | 0.999810i | \(-0.506206\pi\) | ||||
−0.0194952 | + | 0.999810i | \(0.506206\pi\) | |||||||
\(752\) | −5.13792e15 | −0.779094 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 9.17953e15 | 1.37176 | ||||||||
\(755\) | 1.53532e15 | 0.227766 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.67357e15 | −0.829524 | −0.414762 | − | 0.909930i | \(-0.636135\pi\) | ||||
−0.414762 | + | 0.909930i | \(0.636135\pi\) | |||||||
\(758\) | −1.79656e16 | −2.60772 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6.48155e13 | 0.00927265 | ||||||||
\(761\) | −8.59220e15 | −1.22036 | −0.610181 | − | 0.792262i | \(-0.708903\pi\) | ||||
−0.610181 | + | 0.792262i | \(0.708903\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.26322e16 | −1.76846 | ||||||||
\(764\) | 6.11273e15 | 0.849614 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.60400e15 | 0.219758 | ||||||||
\(767\) | −1.10996e16 | −1.50985 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.23682e16 | 1.65849 | 0.829243 | − | 0.558888i | \(-0.188772\pi\) | ||||
0.829243 | + | 0.558888i | \(0.188772\pi\) | |||||||
\(770\) | −7.99831e15 | −1.06488 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 7.59856e15 | 0.997324 | ||||||||
\(773\) | −8.62674e15 | −1.12424 | −0.562120 | − | 0.827055i | \(-0.690014\pi\) | ||||
−0.562120 | + | 0.827055i | \(0.690014\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.35697e14 | −0.0688272 | ||||||||
\(776\) | 2.42845e14 | 0.0309806 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −9.17933e15 | −1.15458 | ||||||||
\(779\) | 8.74746e15 | 1.09251 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.44858e16 | −1.78386 | ||||||||
\(782\) | −7.27571e15 | −0.889689 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 9.35970e14 | 0.112856 | ||||||||
\(785\) | 1.92930e15 | 0.231002 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.18931e16 | 1.40421 | 0.702106 | − | 0.712073i | \(-0.252243\pi\) | ||||
0.702106 | + | 0.712073i | \(0.252243\pi\) | |||||||
\(788\) | 2.07541e15 | 0.243338 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3.14633e15 | 0.363794 | ||||||||
\(791\) | 9.34502e15 | 1.07302 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.88589e15 | −0.326797 | ||||||||
\(794\) | −2.41437e15 | −0.271513 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.30119e15 | 0.255230 | ||||||||
\(797\) | 6.33100e15 | 0.697351 | 0.348676 | − | 0.937243i | \(-0.386631\pi\) | ||||
0.348676 | + | 0.937243i | \(0.386631\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.54103e15 | −0.493340 | ||||||||
\(800\) | 2.60961e15 | 0.281566 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 7.90952e14 | 0.0841766 | ||||||||
\(803\) | −6.36512e15 | −0.672777 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.96914e15 | −0.413827 | ||||||||
\(806\) | 4.86271e15 | 0.503542 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 7.34547e13 | 0.00750339 | ||||||||
\(809\) | −1.06496e16 | −1.08048 | −0.540238 | − | 0.841512i | \(-0.681666\pi\) | ||||
−0.540238 | + | 0.841512i | \(0.681666\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.79444e15 | 0.680047 | 0.340024 | − | 0.940417i | \(-0.389565\pi\) | ||||
0.340024 | + | 0.940417i | \(0.389565\pi\) | |||||||
\(812\) | −8.74141e15 | −0.869008 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2.91975e16 | −2.86359 | ||||||||
\(815\) | 9.28855e14 | 0.0904860 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.52770e14 | −0.0242943 | ||||||||
\(818\) | 2.78585e16 | 2.65959 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5.84870e15 | 0.550913 | ||||||||
\(821\) | −2.03099e16 | −1.90029 | −0.950145 | − | 0.311807i | \(-0.899066\pi\) | ||||
−0.950145 | + | 0.311807i | \(0.899066\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.88821e15 | −0.174322 | −0.0871609 | − | 0.996194i | \(-0.527779\pi\) | ||||
−0.0871609 | + | 0.996194i | \(0.527779\pi\) | |||||||
\(824\) | 1.87217e14 | 0.0171690 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.13213e16 | 1.92940 | ||||||||
\(827\) | 1.10204e16 | 0.990644 | 0.495322 | − | 0.868710i | \(-0.335050\pi\) | ||||
0.495322 | + | 0.868710i | \(0.335050\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.45180e15 | −0.749720 | −0.374860 | − | 0.927081i | \(-0.622309\pi\) | ||||
−0.374860 | + | 0.927081i | \(0.622309\pi\) | |||||||
\(830\) | −4.06366e15 | −0.358086 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.15415e16 | −1.00366 | ||||||||
\(833\) | 8.27233e14 | 0.0714629 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.92263e14 | 0.0675451 | ||||||||
\(836\) | 1.81494e16 | 1.53719 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.28092e16 | 2.74254 | ||||||||
\(839\) | −5.30367e15 | −0.440439 | −0.220219 | − | 0.975450i | \(-0.570677\pi\) | ||||
−0.220219 | + | 0.975450i | \(0.570677\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.47735e15 | −0.121089 | ||||||||
\(842\) | 2.48979e16 | 2.02743 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.40233e16 | 1.12711 | ||||||||
\(845\) | 4.45820e14 | 0.0355998 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.65088e16 | 2.08945 | ||||||||
\(848\) | −1.71435e16 | −1.34253 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.34539e15 | 0.181306 | ||||||||
\(851\) | −1.44892e16 | −1.11284 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.43767e15 | −0.336462 | −0.168231 | − | 0.985748i | \(-0.553805\pi\) | ||||
−0.168231 | + | 0.985748i | \(0.553805\pi\) | |||||||
\(854\) | 5.54352e15 | 0.417607 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.16885e14 | −0.0235666 | ||||||||
\(857\) | 2.12803e16 | 1.57247 | 0.786236 | − | 0.617926i | \(-0.212027\pi\) | ||||
0.786236 | + | 0.617926i | \(0.212027\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.61602e15 | −0.336748 | −0.168374 | − | 0.985723i | \(-0.553852\pi\) | ||||
−0.168374 | + | 0.985723i | \(0.553852\pi\) | |||||||
\(860\) | −1.69006e14 | −0.0122507 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.09701e16 | −1.50076 | ||||||||
\(863\) | −6.10081e15 | −0.433839 | −0.216919 | − | 0.976190i | \(-0.569601\pi\) | ||||
−0.216919 | + | 0.976190i | \(0.569601\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.64235e15 | −0.396161 | ||||||||
\(866\) | 3.56752e16 | 2.48896 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4.63062e15 | −0.318993 | ||||||||
\(869\) | −1.51334e16 | −1.03593 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.80854e15 | 0.527800 | ||||||||
\(872\) | −6.64073e14 | −0.0446041 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.81679e16 | 1.20501 | ||||||||
\(875\) | 1.27949e15 | 0.0843321 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.32501e14 | 0.0606948 | 0.0303474 | − | 0.999539i | \(-0.490339\pi\) | ||||
0.0303474 | + | 0.999539i | \(0.490339\pi\) | |||||||
\(878\) | −8.01407e15 | −0.518362 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.27639e16 | −0.815321 | ||||||||
\(881\) | 1.26049e16 | 0.800150 | 0.400075 | − | 0.916482i | \(-0.368984\pi\) | ||||
0.400075 | + | 0.916482i | \(0.368984\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.18236e16 | 1.36818 | 0.684090 | − | 0.729397i | \(-0.260199\pi\) | ||||
0.684090 | + | 0.729397i | \(0.260199\pi\) | |||||||
\(884\) | −1.05543e16 | −0.657572 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.12353e16 | 1.30669 | ||||||||
\(887\) | 2.71175e16 | 1.65832 | 0.829162 | − | 0.559008i | \(-0.188818\pi\) | ||||
0.829162 | + | 0.559008i | \(0.188818\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.54420e15 | −0.455673 | ||||||||
\(890\) | −8.38497e15 | −0.503334 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.36993e16 | 0.812256 | ||||||||
\(893\) | 1.13392e16 | 0.668190 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.09437e15 | −0.296527 | ||||||||
\(896\) | −7.75064e14 | −0.0448377 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −6.89522e15 | −0.394029 | ||||||||
\(899\) | 5.68042e15 | 0.322628 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.51519e16 | −0.850119 | ||||||||
\(902\) | −5.67463e16 | −3.16447 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.91265e14 | 0.0270638 | ||||||||
\(905\) | −1.30009e16 | −0.711878 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.41689e16 | 1.30742 | 0.653712 | − | 0.756744i | \(-0.273211\pi\) | ||||
0.653712 | + | 0.756744i | \(0.273211\pi\) | |||||||
\(908\) | −1.61147e16 | −0.866465 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.16144e16 | −0.616977 | ||||||||
\(911\) | 2.08024e16 | 1.09841 | 0.549203 | − | 0.835689i | \(-0.314931\pi\) | ||||
0.549203 | + | 0.835689i | \(0.314931\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.95457e16 | 1.01967 | ||||||||
\(914\) | 1.15386e16 | 0.598342 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.42866e16 | 1.24435 | ||||||||
\(917\) | 2.36948e16 | 1.20676 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.27606e16 | −0.642151 | −0.321076 | − | 0.947054i | \(-0.604044\pi\) | ||||
−0.321076 | + | 0.947054i | \(0.604044\pi\) | |||||||
\(920\) | −2.08657e14 | −0.0104376 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2.38736e16 | −1.18004 | ||||||||
\(923\) | −2.10349e16 | −1.03355 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.67073e15 | 0.226780 | ||||||||
\(926\) | −1.48707e15 | −0.0717744 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.76717e16 | −1.31984 | ||||||||
\(929\) | −2.66057e16 | −1.26150 | −0.630751 | − | 0.775985i | \(-0.717253\pi\) | ||||
−0.630751 | + | 0.775985i | \(0.717253\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.06565e15 | −0.0967908 | ||||||||
\(932\) | 2.12906e16 | 0.991745 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −4.69928e16 | −2.16333 | ||||||||
\(935\) | −1.12811e16 | −0.516281 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.35312e16 | −0.612023 | −0.306012 | − | 0.952028i | \(-0.598995\pi\) | ||||
−0.306012 | + | 0.952028i | \(0.598995\pi\) | |||||||
\(938\) | −1.49994e16 | −0.674465 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 7.58159e15 | 0.336944 | ||||||||
\(941\) | −2.75735e16 | −1.21829 | −0.609143 | − | 0.793061i | \(-0.708486\pi\) | ||||
−0.609143 | + | 0.793061i | \(0.708486\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.81602e16 | −1.22976 | ||||||||
\(944\) | 3.40250e16 | 1.47724 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.63976e15 | 0.0703686 | ||||||||
\(947\) | −4.64018e16 | −1.97975 | −0.989873 | − | 0.141955i | \(-0.954661\pi\) | ||||
−0.989873 | + | 0.141955i | \(0.954661\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.24283e15 | −0.389799 | ||||||||
\(950\) | −5.85659e15 | −0.245564 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.48246e14 | −0.0144339 | ||||||||
\(953\) | −5.27189e15 | −0.217248 | −0.108624 | − | 0.994083i | \(-0.534644\pi\) | ||||
−0.108624 | + | 0.994083i | \(0.534644\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.48750e15 | 0.386485 | ||||||||
\(956\) | 9.69115e15 | 0.392516 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2.16312e16 | −0.866105 | ||||||||
\(959\) | −5.21979e13 | −0.00207803 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.23994e16 | −0.881571 | ||||||||
\(962\) | −4.23978e16 | −1.65913 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.61088e16 | −1.01010 | ||||||||
\(965\) | 1.17936e16 | 0.453678 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.13722e16 | 1.19316 | 0.596581 | − | 0.802553i | \(-0.296526\pi\) | ||||
0.596581 | + | 0.802553i | \(0.296526\pi\) | |||||||
\(968\) | 1.39356e15 | 0.0527001 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.19429e16 | −0.820446 | ||||||||
\(971\) | 4.02261e16 | 1.49555 | 0.747776 | − | 0.663951i | \(-0.231122\pi\) | ||||
0.747776 | + | 0.663951i | \(0.231122\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.96250e16 | 0.721423 | ||||||||
\(974\) | 2.08693e16 | 0.762839 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.84648e15 | 0.319740 | ||||||||
\(977\) | 1.61108e16 | 0.579025 | 0.289513 | − | 0.957174i | \(-0.406507\pi\) | ||||
0.289513 | + | 0.957174i | \(0.406507\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.03307e16 | 1.43328 | ||||||||
\(980\) | −1.38113e15 | −0.0488080 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −2.09151e16 | −0.730880 | ||||||||
\(983\) | 3.39027e16 | 1.17812 | 0.589060 | − | 0.808089i | \(-0.299498\pi\) | ||||
0.589060 | + | 0.808089i | \(0.299498\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.22123e15 | 0.110694 | ||||||||
\(986\) | −2.48701e16 | −0.849873 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.63548e16 | 0.890629 | ||||||||
\(989\) | 8.13727e14 | 0.0273463 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.18340e16 | −1.39035 | −0.695174 | − | 0.718841i | \(-0.744673\pi\) | ||||
−0.695174 | + | 0.718841i | \(0.744673\pi\) | |||||||
\(992\) | −1.46586e16 | −0.484484 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 4.04059e16 | 1.32075 | ||||||||
\(995\) | 3.57166e15 | 0.116103 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.94947e16 | 1.26974 | 0.634871 | − | 0.772618i | \(-0.281053\pi\) | ||||
0.634871 | + | 0.772618i | \(0.281053\pi\) | |||||||
\(998\) | −1.81509e16 | −0.580336 | ||||||||
\(999\) | 0 | 0 |
(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 | 45.12.a.d.1.1 | 2 | ||
3.2 | odd | 2 | 5.12.a.b.1.2 | ✓ | 2 | ||
5.2 | odd | 4 | 225.12.b.f.199.2 | 4 | |||
5.3 | odd | 4 | 225.12.b.f.199.3 | 4 | |||
5.4 | even | 2 | 225.12.a.h.1.2 | 2 | |||
12.11 | even | 2 | 80.12.a.j.1.1 | 2 | |||
15.2 | even | 4 | 25.12.b.c.24.3 | 4 | |||
15.8 | even | 4 | 25.12.b.c.24.2 | 4 | |||
15.14 | odd | 2 | 25.12.a.c.1.1 | 2 | |||
21.20 | even | 2 | 245.12.a.b.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.12.a.b.1.2 | ✓ | 2 | 3.2 | odd | 2 | ||
25.12.a.c.1.1 | 2 | 15.14 | odd | 2 | |||
25.12.b.c.24.2 | 4 | 15.8 | even | 4 | |||
25.12.b.c.24.3 | 4 | 15.2 | even | 4 | |||
45.12.a.d.1.1 | 2 | 1.1 | even | 1 | trivial | ||
80.12.a.j.1.1 | 2 | 12.11 | even | 2 | |||
225.12.a.h.1.2 | 2 | 5.4 | even | 2 | |||
225.12.b.f.199.2 | 4 | 5.2 | odd | 4 | |||
225.12.b.f.199.3 | 4 | 5.3 | odd | 4 | |||
245.12.a.b.1.2 | 2 | 21.20 | even | 2 |