Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2,10,Mod(1,2)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 2.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: | \(1.03007167233\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 2.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 16.0000 | 0.707107 | ||||||||
\(3\) | −156.000 | −1.11193 | −0.555967 | − | 0.831204i | \(-0.687652\pi\) | ||||
−0.555967 | + | 0.831204i | \(0.687652\pi\) | |||||||
\(4\) | 256.000 | 0.500000 | ||||||||
\(5\) | 870.000 | 0.622521 | 0.311261 | − | 0.950325i | \(-0.399249\pi\) | ||||
0.311261 | + | 0.950325i | \(0.399249\pi\) | |||||||
\(6\) | −2496.00 | −0.786256 | ||||||||
\(7\) | −952.000 | −0.149863 | −0.0749317 | − | 0.997189i | \(-0.523874\pi\) | ||||
−0.0749317 | + | 0.997189i | \(0.523874\pi\) | |||||||
\(8\) | 4096.00 | 0.353553 | ||||||||
\(9\) | 4653.00 | 0.236397 | ||||||||
\(10\) | 13920.0 | 0.440189 | ||||||||
\(11\) | −56148.0 | −1.15629 | −0.578146 | − | 0.815934i | \(-0.696223\pi\) | ||||
−0.578146 | + | 0.815934i | \(0.696223\pi\) | |||||||
\(12\) | −39936.0 | −0.555967 | ||||||||
\(13\) | 178094. | 1.72943 | 0.864717 | − | 0.502259i | \(-0.167497\pi\) | ||||
0.864717 | + | 0.502259i | \(0.167497\pi\) | |||||||
\(14\) | −15232.0 | −0.105969 | ||||||||
\(15\) | −135720. | −0.692203 | ||||||||
\(16\) | 65536.0 | 0.250000 | ||||||||
\(17\) | −247662. | −0.719183 | −0.359591 | − | 0.933110i | \(-0.617084\pi\) | ||||
−0.359591 | + | 0.933110i | \(0.617084\pi\) | |||||||
\(18\) | 74448.0 | 0.167158 | ||||||||
\(19\) | 315380. | 0.555192 | 0.277596 | − | 0.960698i | \(-0.410462\pi\) | ||||
0.277596 | + | 0.960698i | \(0.410462\pi\) | |||||||
\(20\) | 222720. | 0.311261 | ||||||||
\(21\) | 148512. | 0.166638 | ||||||||
\(22\) | −898368. | −0.817621 | ||||||||
\(23\) | 204504. | 0.152380 | 0.0761898 | − | 0.997093i | \(-0.475725\pi\) | ||||
0.0761898 | + | 0.997093i | \(0.475725\pi\) | |||||||
\(24\) | −638976. | −0.393128 | ||||||||
\(25\) | −1.19622e6 | −0.612467 | ||||||||
\(26\) | 2.84950e6 | 1.22290 | ||||||||
\(27\) | 2.34468e6 | 0.849076 | ||||||||
\(28\) | −243712. | −0.0749317 | ||||||||
\(29\) | −3.84045e6 | −1.00830 | −0.504152 | − | 0.863615i | \(-0.668195\pi\) | ||||
−0.504152 | + | 0.863615i | \(0.668195\pi\) | |||||||
\(30\) | −2.17152e6 | −0.489461 | ||||||||
\(31\) | −1.30941e6 | −0.254652 | −0.127326 | − | 0.991861i | \(-0.540639\pi\) | ||||
−0.127326 | + | 0.991861i | \(0.540639\pi\) | |||||||
\(32\) | 1.04858e6 | 0.176777 | ||||||||
\(33\) | 8.75909e6 | 1.28572 | ||||||||
\(34\) | −3.96259e6 | −0.508539 | ||||||||
\(35\) | −828240. | −0.0932932 | ||||||||
\(36\) | 1.19117e6 | 0.118198 | ||||||||
\(37\) | 4.30708e6 | 0.377811 | 0.188906 | − | 0.981995i | \(-0.439506\pi\) | ||||
0.188906 | + | 0.981995i | \(0.439506\pi\) | |||||||
\(38\) | 5.04608e6 | 0.392580 | ||||||||
\(39\) | −2.77827e7 | −1.92302 | ||||||||
\(40\) | 3.56352e6 | 0.220095 | ||||||||
\(41\) | 1.51204e6 | 0.0835673 | 0.0417837 | − | 0.999127i | \(-0.486696\pi\) | ||||
0.0417837 | + | 0.999127i | \(0.486696\pi\) | |||||||
\(42\) | 2.37619e6 | 0.117831 | ||||||||
\(43\) | 3.36706e7 | 1.50191 | 0.750953 | − | 0.660355i | \(-0.229594\pi\) | ||||
0.750953 | + | 0.660355i | \(0.229594\pi\) | |||||||
\(44\) | −1.43739e7 | −0.578146 | ||||||||
\(45\) | 4.04811e6 | 0.147162 | ||||||||
\(46\) | 3.27206e6 | 0.107749 | ||||||||
\(47\) | −1.05811e7 | −0.316293 | −0.158146 | − | 0.987416i | \(-0.550552\pi\) | ||||
−0.158146 | + | 0.987416i | \(0.550552\pi\) | |||||||
\(48\) | −1.02236e7 | −0.277983 | ||||||||
\(49\) | −3.94473e7 | −0.977541 | ||||||||
\(50\) | −1.91396e7 | −0.433080 | ||||||||
\(51\) | 3.86353e7 | 0.799684 | ||||||||
\(52\) | 4.55921e7 | 0.864717 | ||||||||
\(53\) | 1.66162e7 | 0.289262 | 0.144631 | − | 0.989486i | \(-0.453801\pi\) | ||||
0.144631 | + | 0.989486i | \(0.453801\pi\) | |||||||
\(54\) | 3.75149e7 | 0.600388 | ||||||||
\(55\) | −4.88488e7 | −0.719816 | ||||||||
\(56\) | −3.89939e6 | −0.0529847 | ||||||||
\(57\) | −4.91993e7 | −0.617336 | ||||||||
\(58\) | −6.14472e7 | −0.712978 | ||||||||
\(59\) | 1.12235e8 | 1.20585 | 0.602927 | − | 0.797796i | \(-0.294001\pi\) | ||||
0.602927 | + | 0.797796i | \(0.294001\pi\) | |||||||
\(60\) | −3.47443e7 | −0.346101 | ||||||||
\(61\) | −3.31972e7 | −0.306985 | −0.153493 | − | 0.988150i | \(-0.549052\pi\) | ||||
−0.153493 | + | 0.988150i | \(0.549052\pi\) | |||||||
\(62\) | −2.09505e7 | −0.180066 | ||||||||
\(63\) | −4.42966e6 | −0.0354273 | ||||||||
\(64\) | 1.67772e7 | 0.125000 | ||||||||
\(65\) | 1.54942e8 | 1.07661 | ||||||||
\(66\) | 1.40145e8 | 0.909141 | ||||||||
\(67\) | −1.21372e8 | −0.735839 | −0.367919 | − | 0.929858i | \(-0.619930\pi\) | ||||
−0.367919 | + | 0.929858i | \(0.619930\pi\) | |||||||
\(68\) | −6.34015e7 | −0.359591 | ||||||||
\(69\) | −3.19026e7 | −0.169436 | ||||||||
\(70\) | −1.32518e7 | −0.0659683 | ||||||||
\(71\) | −3.87173e8 | −1.80818 | −0.904091 | − | 0.427340i | \(-0.859451\pi\) | ||||
−0.904091 | + | 0.427340i | \(0.859451\pi\) | |||||||
\(72\) | 1.90587e7 | 0.0835789 | ||||||||
\(73\) | 2.55240e8 | 1.05195 | 0.525976 | − | 0.850499i | \(-0.323700\pi\) | ||||
0.525976 | + | 0.850499i | \(0.323700\pi\) | |||||||
\(74\) | 6.89132e7 | 0.267153 | ||||||||
\(75\) | 1.86611e8 | 0.681023 | ||||||||
\(76\) | 8.07373e7 | 0.277596 | ||||||||
\(77\) | 5.34529e7 | 0.173286 | ||||||||
\(78\) | −4.44523e8 | −1.35978 | ||||||||
\(79\) | 4.92102e8 | 1.42145 | 0.710727 | − | 0.703467i | \(-0.248366\pi\) | ||||
0.710727 | + | 0.703467i | \(0.248366\pi\) | |||||||
\(80\) | 5.70163e7 | 0.155630 | ||||||||
\(81\) | −4.57355e8 | −1.18051 | ||||||||
\(82\) | 2.41927e7 | 0.0590910 | ||||||||
\(83\) | −4.57420e8 | −1.05795 | −0.528974 | − | 0.848638i | \(-0.677423\pi\) | ||||
−0.528974 | + | 0.848638i | \(0.677423\pi\) | |||||||
\(84\) | 3.80191e7 | 0.0833191 | ||||||||
\(85\) | −2.15466e8 | −0.447707 | ||||||||
\(86\) | 5.38730e8 | 1.06201 | ||||||||
\(87\) | 5.99110e8 | 1.12117 | ||||||||
\(88\) | −2.29982e8 | −0.408811 | ||||||||
\(89\) | −3.18095e7 | −0.0537405 | −0.0268703 | − | 0.999639i | \(-0.508554\pi\) | ||||
−0.0268703 | + | 0.999639i | \(0.508554\pi\) | |||||||
\(90\) | 6.47698e7 | 0.104059 | ||||||||
\(91\) | −1.69545e8 | −0.259179 | ||||||||
\(92\) | 5.23530e7 | 0.0761898 | ||||||||
\(93\) | 2.04268e8 | 0.283156 | ||||||||
\(94\) | −1.69297e8 | −0.223653 | ||||||||
\(95\) | 2.74381e8 | 0.345619 | ||||||||
\(96\) | −1.63578e8 | −0.196564 | ||||||||
\(97\) | −6.73532e8 | −0.772477 | −0.386238 | − | 0.922399i | \(-0.626226\pi\) | ||||
−0.386238 | + | 0.922399i | \(0.626226\pi\) | |||||||
\(98\) | −6.31157e8 | −0.691226 | ||||||||
\(99\) | −2.61257e8 | −0.273344 | ||||||||
\(100\) | −3.06234e8 | −0.306234 | ||||||||
\(101\) | 1.05772e9 | 1.01140 | 0.505701 | − | 0.862709i | \(-0.331234\pi\) | ||||
0.505701 | + | 0.862709i | \(0.331234\pi\) | |||||||
\(102\) | 6.18164e8 | 0.565462 | ||||||||
\(103\) | 7.95866e8 | 0.696743 | 0.348371 | − | 0.937357i | \(-0.386735\pi\) | ||||
0.348371 | + | 0.937357i | \(0.386735\pi\) | |||||||
\(104\) | 7.29473e8 | 0.611448 | ||||||||
\(105\) | 1.29205e8 | 0.103736 | ||||||||
\(106\) | 2.65859e8 | 0.204539 | ||||||||
\(107\) | −1.97413e9 | −1.45596 | −0.727981 | − | 0.685598i | \(-0.759541\pi\) | ||||
−0.727981 | + | 0.685598i | \(0.759541\pi\) | |||||||
\(108\) | 6.00238e8 | 0.424538 | ||||||||
\(109\) | −1.34465e9 | −0.912408 | −0.456204 | − | 0.889875i | \(-0.650791\pi\) | ||||
−0.456204 | + | 0.889875i | \(0.650791\pi\) | |||||||
\(110\) | −7.81580e8 | −0.508987 | ||||||||
\(111\) | −6.71904e8 | −0.420101 | ||||||||
\(112\) | −6.23903e7 | −0.0374659 | ||||||||
\(113\) | 2.70680e9 | 1.56172 | 0.780861 | − | 0.624705i | \(-0.214781\pi\) | ||||
0.780861 | + | 0.624705i | \(0.214781\pi\) | |||||||
\(114\) | −7.87188e8 | −0.436523 | ||||||||
\(115\) | 1.77918e8 | 0.0948595 | ||||||||
\(116\) | −9.83155e8 | −0.504152 | ||||||||
\(117\) | 8.28671e8 | 0.408833 | ||||||||
\(118\) | 1.79576e9 | 0.852667 | ||||||||
\(119\) | 2.35774e8 | 0.107779 | ||||||||
\(120\) | −5.55909e8 | −0.244731 | ||||||||
\(121\) | 7.94650e8 | 0.337009 | ||||||||
\(122\) | −5.31155e8 | −0.217071 | ||||||||
\(123\) | −2.35879e8 | −0.0929213 | ||||||||
\(124\) | −3.35208e8 | −0.127326 | ||||||||
\(125\) | −2.73993e9 | −1.00380 | ||||||||
\(126\) | −7.08745e7 | −0.0250509 | ||||||||
\(127\) | 1.19960e9 | 0.409185 | 0.204593 | − | 0.978847i | \(-0.434413\pi\) | ||||
0.204593 | + | 0.978847i | \(0.434413\pi\) | |||||||
\(128\) | 2.68435e8 | 0.0883883 | ||||||||
\(129\) | −5.25261e9 | −1.67002 | ||||||||
\(130\) | 2.47907e9 | 0.761278 | ||||||||
\(131\) | 2.78615e9 | 0.826576 | 0.413288 | − | 0.910600i | \(-0.364380\pi\) | ||||
0.413288 | + | 0.910600i | \(0.364380\pi\) | |||||||
\(132\) | 2.24233e9 | 0.642860 | ||||||||
\(133\) | −3.00242e8 | −0.0832029 | ||||||||
\(134\) | −1.94196e9 | −0.520317 | ||||||||
\(135\) | 2.03987e9 | 0.528568 | ||||||||
\(136\) | −1.01442e9 | −0.254269 | ||||||||
\(137\) | 2.88233e9 | 0.699039 | 0.349519 | − | 0.936929i | \(-0.386345\pi\) | ||||
0.349519 | + | 0.936929i | \(0.386345\pi\) | |||||||
\(138\) | −5.10442e8 | −0.119809 | ||||||||
\(139\) | 2.15641e9 | 0.489965 | 0.244982 | − | 0.969528i | \(-0.421218\pi\) | ||||
0.244982 | + | 0.969528i | \(0.421218\pi\) | |||||||
\(140\) | −2.12029e8 | −0.0466466 | ||||||||
\(141\) | 1.65065e9 | 0.351697 | ||||||||
\(142\) | −6.19476e9 | −1.27858 | ||||||||
\(143\) | −9.99962e9 | −1.99973 | ||||||||
\(144\) | 3.04939e8 | 0.0590992 | ||||||||
\(145\) | −3.34119e9 | −0.627690 | ||||||||
\(146\) | 4.08384e9 | 0.743843 | ||||||||
\(147\) | 6.15378e9 | 1.08696 | ||||||||
\(148\) | 1.10261e9 | 0.188906 | ||||||||
\(149\) | 7.54548e9 | 1.25415 | 0.627074 | − | 0.778960i | \(-0.284253\pi\) | ||||
0.627074 | + | 0.778960i | \(0.284253\pi\) | |||||||
\(150\) | 2.98578e9 | 0.481556 | ||||||||
\(151\) | −4.31308e9 | −0.675136 | −0.337568 | − | 0.941301i | \(-0.609604\pi\) | ||||
−0.337568 | + | 0.941301i | \(0.609604\pi\) | |||||||
\(152\) | 1.29180e9 | 0.196290 | ||||||||
\(153\) | −1.15237e9 | −0.170013 | ||||||||
\(154\) | 8.55246e8 | 0.122532 | ||||||||
\(155\) | −1.13918e9 | −0.158526 | ||||||||
\(156\) | −7.11236e9 | −0.961509 | ||||||||
\(157\) | −4.23157e9 | −0.555845 | −0.277922 | − | 0.960604i | \(-0.589646\pi\) | ||||
−0.277922 | + | 0.960604i | \(0.589646\pi\) | |||||||
\(158\) | 7.87363e9 | 1.00512 | ||||||||
\(159\) | −2.59213e9 | −0.321640 | ||||||||
\(160\) | 9.12261e8 | 0.110047 | ||||||||
\(161\) | −1.94688e8 | −0.0228361 | ||||||||
\(162\) | −7.31768e9 | −0.834749 | ||||||||
\(163\) | 8.28448e8 | 0.0919223 | 0.0459612 | − | 0.998943i | \(-0.485365\pi\) | ||||
0.0459612 | + | 0.998943i | \(0.485365\pi\) | |||||||
\(164\) | 3.87083e8 | 0.0417837 | ||||||||
\(165\) | 7.62041e9 | 0.800388 | ||||||||
\(166\) | −7.31872e9 | −0.748082 | ||||||||
\(167\) | −2.85500e9 | −0.284041 | −0.142021 | − | 0.989864i | \(-0.545360\pi\) | ||||
−0.142021 | + | 0.989864i | \(0.545360\pi\) | |||||||
\(168\) | 6.08305e8 | 0.0589155 | ||||||||
\(169\) | 2.11130e10 | 1.99094 | ||||||||
\(170\) | −3.44746e9 | −0.316576 | ||||||||
\(171\) | 1.46746e9 | 0.131246 | ||||||||
\(172\) | 8.61967e9 | 0.750953 | ||||||||
\(173\) | −1.76690e10 | −1.49970 | −0.749851 | − | 0.661607i | \(-0.769875\pi\) | ||||
−0.749851 | + | 0.661607i | \(0.769875\pi\) | |||||||
\(174\) | 9.58576e9 | 0.792784 | ||||||||
\(175\) | 1.13881e9 | 0.0917865 | ||||||||
\(176\) | −3.67972e9 | −0.289073 | ||||||||
\(177\) | −1.75087e10 | −1.34083 | ||||||||
\(178\) | −5.08952e8 | −0.0380003 | ||||||||
\(179\) | −5.86732e8 | −0.0427170 | −0.0213585 | − | 0.999772i | \(-0.506799\pi\) | ||||
−0.0213585 | + | 0.999772i | \(0.506799\pi\) | |||||||
\(180\) | 1.03632e9 | 0.0735811 | ||||||||
\(181\) | −5.43396e9 | −0.376325 | −0.188162 | − | 0.982138i | \(-0.560253\pi\) | ||||
−0.188162 | + | 0.982138i | \(0.560253\pi\) | |||||||
\(182\) | −2.71273e9 | −0.183267 | ||||||||
\(183\) | 5.17877e9 | 0.341347 | ||||||||
\(184\) | 8.37648e8 | 0.0538743 | ||||||||
\(185\) | 3.74716e9 | 0.235196 | ||||||||
\(186\) | 3.26828e9 | 0.200222 | ||||||||
\(187\) | 1.39057e10 | 0.831585 | ||||||||
\(188\) | −2.70875e9 | −0.158146 | ||||||||
\(189\) | −2.23214e9 | −0.127245 | ||||||||
\(190\) | 4.39009e9 | 0.244389 | ||||||||
\(191\) | 3.23292e10 | 1.75770 | 0.878851 | − | 0.477096i | \(-0.158311\pi\) | ||||
0.878851 | + | 0.477096i | \(0.158311\pi\) | |||||||
\(192\) | −2.61725e9 | −0.138992 | ||||||||
\(193\) | −1.29399e10 | −0.671311 | −0.335655 | − | 0.941985i | \(-0.608958\pi\) | ||||
−0.335655 | + | 0.941985i | \(0.608958\pi\) | |||||||
\(194\) | −1.07765e10 | −0.546224 | ||||||||
\(195\) | −2.41709e10 | −1.19712 | ||||||||
\(196\) | −1.00985e10 | −0.488770 | ||||||||
\(197\) | 8.81090e9 | 0.416795 | 0.208397 | − | 0.978044i | \(-0.433175\pi\) | ||||
0.208397 | + | 0.978044i | \(0.433175\pi\) | |||||||
\(198\) | −4.18011e9 | −0.193283 | ||||||||
\(199\) | −2.48534e10 | −1.12343 | −0.561716 | − | 0.827330i | \(-0.689859\pi\) | ||||
−0.561716 | + | 0.827330i | \(0.689859\pi\) | |||||||
\(200\) | −4.89974e9 | −0.216540 | ||||||||
\(201\) | 1.89341e10 | 0.818204 | ||||||||
\(202\) | 1.69235e10 | 0.715170 | ||||||||
\(203\) | 3.65611e9 | 0.151108 | ||||||||
\(204\) | 9.89063e9 | 0.399842 | ||||||||
\(205\) | 1.31548e9 | 0.0520224 | ||||||||
\(206\) | 1.27339e10 | 0.492672 | ||||||||
\(207\) | 9.51557e8 | 0.0360220 | ||||||||
\(208\) | 1.16716e10 | 0.432359 | ||||||||
\(209\) | −1.77080e10 | −0.641963 | ||||||||
\(210\) | 2.06729e9 | 0.0733523 | ||||||||
\(211\) | −4.65163e10 | −1.61560 | −0.807801 | − | 0.589456i | \(-0.799342\pi\) | ||||
−0.807801 | + | 0.589456i | \(0.799342\pi\) | |||||||
\(212\) | 4.25375e9 | 0.144631 | ||||||||
\(213\) | 6.03989e10 | 2.01058 | ||||||||
\(214\) | −3.15862e10 | −1.02952 | ||||||||
\(215\) | 2.92934e10 | 0.934969 | ||||||||
\(216\) | 9.60381e9 | 0.300194 | ||||||||
\(217\) | 1.24656e9 | 0.0381631 | ||||||||
\(218\) | −2.15144e10 | −0.645170 | ||||||||
\(219\) | −3.98175e10 | −1.16970 | ||||||||
\(220\) | −1.25053e10 | −0.359908 | ||||||||
\(221\) | −4.41071e10 | −1.24378 | ||||||||
\(222\) | −1.07505e10 | −0.297056 | ||||||||
\(223\) | 4.66347e10 | 1.26281 | 0.631404 | − | 0.775454i | \(-0.282479\pi\) | ||||
0.631404 | + | 0.775454i | \(0.282479\pi\) | |||||||
\(224\) | −9.98244e8 | −0.0264924 | ||||||||
\(225\) | −5.56603e9 | −0.144785 | ||||||||
\(226\) | 4.33088e10 | 1.10430 | ||||||||
\(227\) | 2.65867e10 | 0.664582 | 0.332291 | − | 0.943177i | \(-0.392178\pi\) | ||||
0.332291 | + | 0.943177i | \(0.392178\pi\) | |||||||
\(228\) | −1.25950e10 | −0.308668 | ||||||||
\(229\) | 3.99907e10 | 0.960947 | 0.480474 | − | 0.877009i | \(-0.340465\pi\) | ||||
0.480474 | + | 0.877009i | \(0.340465\pi\) | |||||||
\(230\) | 2.84670e9 | 0.0670758 | ||||||||
\(231\) | −8.33865e9 | −0.192682 | ||||||||
\(232\) | −1.57305e10 | −0.356489 | ||||||||
\(233\) | 6.53338e9 | 0.145223 | 0.0726116 | − | 0.997360i | \(-0.476867\pi\) | ||||
0.0726116 | + | 0.997360i | \(0.476867\pi\) | |||||||
\(234\) | 1.32587e10 | 0.289089 | ||||||||
\(235\) | −9.20553e9 | −0.196899 | ||||||||
\(236\) | 2.87322e10 | 0.602927 | ||||||||
\(237\) | −7.67679e10 | −1.58056 | ||||||||
\(238\) | 3.77239e9 | 0.0762114 | ||||||||
\(239\) | −5.66773e10 | −1.12362 | −0.561809 | − | 0.827267i | \(-0.689894\pi\) | ||||
−0.561809 | + | 0.827267i | \(0.689894\pi\) | |||||||
\(240\) | −8.89455e9 | −0.173051 | ||||||||
\(241\) | 4.61491e9 | 0.0881225 | 0.0440613 | − | 0.999029i | \(-0.485970\pi\) | ||||
0.0440613 | + | 0.999029i | \(0.485970\pi\) | |||||||
\(242\) | 1.27144e10 | 0.238302 | ||||||||
\(243\) | 2.51971e10 | 0.463577 | ||||||||
\(244\) | −8.49849e9 | −0.153493 | ||||||||
\(245\) | −3.43192e10 | −0.608540 | ||||||||
\(246\) | −3.77406e9 | −0.0657053 | ||||||||
\(247\) | 5.61673e10 | 0.960168 | ||||||||
\(248\) | −5.36334e9 | −0.0900331 | ||||||||
\(249\) | 7.13576e10 | 1.17637 | ||||||||
\(250\) | −4.38390e10 | −0.709790 | ||||||||
\(251\) | 6.80194e10 | 1.08169 | 0.540843 | − | 0.841124i | \(-0.318105\pi\) | ||||
0.540843 | + | 0.841124i | \(0.318105\pi\) | |||||||
\(252\) | −1.13399e9 | −0.0177136 | ||||||||
\(253\) | −1.14825e10 | −0.176195 | ||||||||
\(254\) | 1.91936e10 | 0.289338 | ||||||||
\(255\) | 3.36127e10 | 0.497820 | ||||||||
\(256\) | 4.29497e9 | 0.0625000 | ||||||||
\(257\) | −9.35958e10 | −1.33831 | −0.669156 | − | 0.743122i | \(-0.733344\pi\) | ||||
−0.669156 | + | 0.743122i | \(0.733344\pi\) | |||||||
\(258\) | −8.40418e10 | −1.18088 | ||||||||
\(259\) | −4.10034e9 | −0.0566201 | ||||||||
\(260\) | 3.96651e10 | 0.538305 | ||||||||
\(261\) | −1.78696e10 | −0.238360 | ||||||||
\(262\) | 4.45783e10 | 0.584478 | ||||||||
\(263\) | −9.40401e10 | −1.21203 | −0.606013 | − | 0.795454i | \(-0.707232\pi\) | ||||
−0.606013 | + | 0.795454i | \(0.707232\pi\) | |||||||
\(264\) | 3.58772e10 | 0.454570 | ||||||||
\(265\) | 1.44561e10 | 0.180071 | ||||||||
\(266\) | −4.80387e9 | −0.0588334 | ||||||||
\(267\) | 4.96228e9 | 0.0597559 | ||||||||
\(268\) | −3.10713e10 | −0.367919 | ||||||||
\(269\) | 1.22724e11 | 1.42904 | 0.714522 | − | 0.699613i | \(-0.246644\pi\) | ||||
0.714522 | + | 0.699613i | \(0.246644\pi\) | |||||||
\(270\) | 3.26379e10 | 0.373754 | ||||||||
\(271\) | −1.64257e11 | −1.84996 | −0.924982 | − | 0.380012i | \(-0.875920\pi\) | ||||
−0.924982 | + | 0.380012i | \(0.875920\pi\) | |||||||
\(272\) | −1.62308e10 | −0.179796 | ||||||||
\(273\) | 2.64491e10 | 0.288190 | ||||||||
\(274\) | 4.61173e10 | 0.494295 | ||||||||
\(275\) | 6.71656e10 | 0.708190 | ||||||||
\(276\) | −8.16707e9 | −0.0847180 | ||||||||
\(277\) | 6.50134e10 | 0.663505 | 0.331752 | − | 0.943367i | \(-0.392360\pi\) | ||||
0.331752 | + | 0.943367i | \(0.392360\pi\) | |||||||
\(278\) | 3.45026e10 | 0.346458 | ||||||||
\(279\) | −6.09268e9 | −0.0601990 | ||||||||
\(280\) | −3.39247e9 | −0.0329841 | ||||||||
\(281\) | 5.20964e10 | 0.498459 | 0.249230 | − | 0.968444i | \(-0.419823\pi\) | ||||
0.249230 | + | 0.968444i | \(0.419823\pi\) | |||||||
\(282\) | 2.64104e10 | 0.248687 | ||||||||
\(283\) | −9.06992e10 | −0.840552 | −0.420276 | − | 0.907396i | \(-0.638067\pi\) | ||||
−0.420276 | + | 0.907396i | \(0.638067\pi\) | |||||||
\(284\) | −9.91162e10 | −0.904091 | ||||||||
\(285\) | −4.28034e10 | −0.384305 | ||||||||
\(286\) | −1.59994e11 | −1.41402 | ||||||||
\(287\) | −1.43946e9 | −0.0125237 | ||||||||
\(288\) | 4.87902e9 | 0.0417895 | ||||||||
\(289\) | −5.72514e10 | −0.482776 | ||||||||
\(290\) | −5.34591e10 | −0.443844 | ||||||||
\(291\) | 1.05071e11 | 0.858943 | ||||||||
\(292\) | 6.53415e10 | 0.525976 | ||||||||
\(293\) | 7.25569e10 | 0.575141 | 0.287571 | − | 0.957759i | \(-0.407152\pi\) | ||||
0.287571 | + | 0.957759i | \(0.407152\pi\) | |||||||
\(294\) | 9.84605e10 | 0.768597 | ||||||||
\(295\) | 9.76445e10 | 0.750670 | ||||||||
\(296\) | 1.76418e10 | 0.133576 | ||||||||
\(297\) | −1.31649e11 | −0.981779 | ||||||||
\(298\) | 1.20728e11 | 0.886816 | ||||||||
\(299\) | 3.64209e10 | 0.263530 | ||||||||
\(300\) | 4.77724e10 | 0.340512 | ||||||||
\(301\) | −3.20544e10 | −0.225081 | ||||||||
\(302\) | −6.90093e10 | −0.477394 | ||||||||
\(303\) | −1.65004e11 | −1.12461 | ||||||||
\(304\) | 2.06687e10 | 0.138798 | ||||||||
\(305\) | −2.88816e10 | −0.191105 | ||||||||
\(306\) | −1.84379e10 | −0.120217 | ||||||||
\(307\) | 1.81977e11 | 1.16921 | 0.584607 | − | 0.811317i | \(-0.301249\pi\) | ||||
0.584607 | + | 0.811317i | \(0.301249\pi\) | |||||||
\(308\) | 1.36839e10 | 0.0866429 | ||||||||
\(309\) | −1.24155e11 | −0.774732 | ||||||||
\(310\) | −1.82270e10 | −0.112095 | ||||||||
\(311\) | −8.98295e10 | −0.544499 | −0.272250 | − | 0.962227i | \(-0.587768\pi\) | ||||
−0.272250 | + | 0.962227i | \(0.587768\pi\) | |||||||
\(312\) | −1.13798e11 | −0.679889 | ||||||||
\(313\) | 5.51394e9 | 0.0324722 | 0.0162361 | − | 0.999868i | \(-0.494832\pi\) | ||||
0.0162361 | + | 0.999868i | \(0.494832\pi\) | |||||||
\(314\) | −6.77052e10 | −0.393041 | ||||||||
\(315\) | −3.85380e9 | −0.0220542 | ||||||||
\(316\) | 1.25978e11 | 0.710727 | ||||||||
\(317\) | −1.94806e10 | −0.108351 | −0.0541757 | − | 0.998531i | \(-0.517253\pi\) | ||||
−0.0541757 | + | 0.998531i | \(0.517253\pi\) | |||||||
\(318\) | −4.14741e10 | −0.227434 | ||||||||
\(319\) | 2.15634e11 | 1.16589 | ||||||||
\(320\) | 1.45962e10 | 0.0778152 | ||||||||
\(321\) | 3.07965e11 | 1.61893 | ||||||||
\(322\) | −3.11500e9 | −0.0161476 | ||||||||
\(323\) | −7.81076e10 | −0.399284 | ||||||||
\(324\) | −1.17083e11 | −0.590257 | ||||||||
\(325\) | −2.13040e11 | −1.05922 | ||||||||
\(326\) | 1.32552e10 | 0.0649989 | ||||||||
\(327\) | 2.09765e11 | 1.01454 | ||||||||
\(328\) | 6.19332e9 | 0.0295455 | ||||||||
\(329\) | 1.00732e10 | 0.0474007 | ||||||||
\(330\) | 1.21927e11 | 0.565960 | ||||||||
\(331\) | −1.06801e11 | −0.489046 | −0.244523 | − | 0.969644i | \(-0.578631\pi\) | ||||
−0.244523 | + | 0.969644i | \(0.578631\pi\) | |||||||
\(332\) | −1.17100e11 | −0.528974 | ||||||||
\(333\) | 2.00408e10 | 0.0893134 | ||||||||
\(334\) | −4.56800e10 | −0.200848 | ||||||||
\(335\) | −1.05594e11 | −0.458075 | ||||||||
\(336\) | 9.73288e9 | 0.0416596 | ||||||||
\(337\) | −1.75776e11 | −0.742380 | −0.371190 | − | 0.928557i | \(-0.621050\pi\) | ||||
−0.371190 | + | 0.928557i | \(0.621050\pi\) | |||||||
\(338\) | 3.37808e11 | 1.40781 | ||||||||
\(339\) | −4.22261e11 | −1.73653 | ||||||||
\(340\) | −5.51593e10 | −0.223853 | ||||||||
\(341\) | 7.35206e10 | 0.294452 | ||||||||
\(342\) | 2.34794e10 | 0.0928046 | ||||||||
\(343\) | 7.59705e10 | 0.296361 | ||||||||
\(344\) | 1.37915e11 | 0.531004 | ||||||||
\(345\) | −2.77553e10 | −0.105477 | ||||||||
\(346\) | −2.82704e11 | −1.06045 | ||||||||
\(347\) | 8.33026e10 | 0.308444 | 0.154222 | − | 0.988036i | \(-0.450713\pi\) | ||||
0.154222 | + | 0.988036i | \(0.450713\pi\) | |||||||
\(348\) | 1.53372e11 | 0.560583 | ||||||||
\(349\) | 3.21368e11 | 1.15955 | 0.579773 | − | 0.814778i | \(-0.303141\pi\) | ||||
0.579773 | + | 0.814778i | \(0.303141\pi\) | |||||||
\(350\) | 1.82209e10 | 0.0649028 | ||||||||
\(351\) | 4.17573e11 | 1.46842 | ||||||||
\(352\) | −5.88754e10 | −0.204405 | ||||||||
\(353\) | 4.07688e11 | 1.39747 | 0.698735 | − | 0.715381i | \(-0.253747\pi\) | ||||
0.698735 | + | 0.715381i | \(0.253747\pi\) | |||||||
\(354\) | −2.80139e11 | −0.948110 | ||||||||
\(355\) | −3.36840e11 | −1.12563 | ||||||||
\(356\) | −8.14323e9 | −0.0268703 | ||||||||
\(357\) | −3.67808e10 | −0.119843 | ||||||||
\(358\) | −9.38771e9 | −0.0302055 | ||||||||
\(359\) | −5.60079e11 | −1.77961 | −0.889804 | − | 0.456343i | \(-0.849159\pi\) | ||||
−0.889804 | + | 0.456343i | \(0.849159\pi\) | |||||||
\(360\) | 1.65811e10 | 0.0520297 | ||||||||
\(361\) | −2.23223e11 | −0.691762 | ||||||||
\(362\) | −8.69433e10 | −0.266102 | ||||||||
\(363\) | −1.23965e11 | −0.374732 | ||||||||
\(364\) | −4.34036e10 | −0.129590 | ||||||||
\(365\) | 2.22059e11 | 0.654863 | ||||||||
\(366\) | 8.28603e10 | 0.241369 | ||||||||
\(367\) | 3.76056e11 | 1.08207 | 0.541036 | − | 0.841000i | \(-0.318032\pi\) | ||||
0.541036 | + | 0.841000i | \(0.318032\pi\) | |||||||
\(368\) | 1.34024e10 | 0.0380949 | ||||||||
\(369\) | 7.03553e9 | 0.0197551 | ||||||||
\(370\) | 5.99545e10 | 0.166308 | ||||||||
\(371\) | −1.58186e10 | −0.0433497 | ||||||||
\(372\) | 5.22925e10 | 0.141578 | ||||||||
\(373\) | −8.12245e10 | −0.217269 | −0.108634 | − | 0.994082i | \(-0.534648\pi\) | ||||
−0.108634 | + | 0.994082i | \(0.534648\pi\) | |||||||
\(374\) | 2.22492e11 | 0.588019 | ||||||||
\(375\) | 4.27430e11 | 1.11615 | ||||||||
\(376\) | −4.33401e10 | −0.111826 | ||||||||
\(377\) | −6.83961e11 | −1.74379 | ||||||||
\(378\) | −3.57142e10 | −0.0899762 | ||||||||
\(379\) | 2.02729e11 | 0.504708 | 0.252354 | − | 0.967635i | \(-0.418795\pi\) | ||||
0.252354 | + | 0.967635i | \(0.418795\pi\) | |||||||
\(380\) | 7.02414e10 | 0.172809 | ||||||||
\(381\) | −1.87138e11 | −0.454987 | ||||||||
\(382\) | 5.17268e11 | 1.24288 | ||||||||
\(383\) | −4.76816e10 | −0.113229 | −0.0566143 | − | 0.998396i | \(-0.518031\pi\) | ||||
−0.0566143 | + | 0.998396i | \(0.518031\pi\) | |||||||
\(384\) | −4.18759e10 | −0.0982820 | ||||||||
\(385\) | 4.65040e10 | 0.107874 | ||||||||
\(386\) | −2.07039e11 | −0.474688 | ||||||||
\(387\) | 1.56669e11 | 0.355046 | ||||||||
\(388\) | −1.72424e11 | −0.386238 | ||||||||
\(389\) | −1.89795e11 | −0.420253 | −0.210126 | − | 0.977674i | \(-0.567388\pi\) | ||||
−0.210126 | + | 0.977674i | \(0.567388\pi\) | |||||||
\(390\) | −3.86735e11 | −0.846491 | ||||||||
\(391\) | −5.06479e10 | −0.109589 | ||||||||
\(392\) | −1.61576e11 | −0.345613 | ||||||||
\(393\) | −4.34639e11 | −0.919098 | ||||||||
\(394\) | 1.40974e11 | 0.294718 | ||||||||
\(395\) | 4.28129e11 | 0.884886 | ||||||||
\(396\) | −6.68817e10 | −0.136672 | ||||||||
\(397\) | 4.00237e11 | 0.808649 | 0.404325 | − | 0.914616i | \(-0.367507\pi\) | ||||
0.404325 | + | 0.914616i | \(0.367507\pi\) | |||||||
\(398\) | −3.97654e11 | −0.794387 | ||||||||
\(399\) | 4.68377e10 | 0.0925162 | ||||||||
\(400\) | −7.83958e10 | −0.153117 | ||||||||
\(401\) | 8.76186e11 | 1.69218 | 0.846090 | − | 0.533040i | \(-0.178951\pi\) | ||||
0.846090 | + | 0.533040i | \(0.178951\pi\) | |||||||
\(402\) | 3.02945e11 | 0.578558 | ||||||||
\(403\) | −2.33198e11 | −0.440404 | ||||||||
\(404\) | 2.70776e11 | 0.505701 | ||||||||
\(405\) | −3.97899e11 | −0.734895 | ||||||||
\(406\) | 5.84977e10 | 0.106849 | ||||||||
\(407\) | −2.41834e11 | −0.436860 | ||||||||
\(408\) | 1.58250e11 | 0.282731 | ||||||||
\(409\) | 5.72300e11 | 1.01127 | 0.505637 | − | 0.862746i | \(-0.331258\pi\) | ||||
0.505637 | + | 0.862746i | \(0.331258\pi\) | |||||||
\(410\) | 2.10476e10 | 0.0367854 | ||||||||
\(411\) | −4.49643e11 | −0.777285 | ||||||||
\(412\) | 2.03742e11 | 0.348371 | ||||||||
\(413\) | −1.06848e11 | −0.180713 | ||||||||
\(414\) | 1.52249e10 | 0.0254714 | ||||||||
\(415\) | −3.97956e11 | −0.658595 | ||||||||
\(416\) | 1.86745e11 | 0.305724 | ||||||||
\(417\) | −3.36400e11 | −0.544809 | ||||||||
\(418\) | −2.83327e11 | −0.453937 | ||||||||
\(419\) | 4.16693e11 | 0.660469 | 0.330235 | − | 0.943899i | \(-0.392872\pi\) | ||||
0.330235 | + | 0.943899i | \(0.392872\pi\) | |||||||
\(420\) | 3.30766e10 | 0.0518679 | ||||||||
\(421\) | −1.19043e12 | −1.84687 | −0.923434 | − | 0.383757i | \(-0.874630\pi\) | ||||
−0.923434 | + | 0.383757i | \(0.874630\pi\) | |||||||
\(422\) | −7.44261e11 | −1.14240 | ||||||||
\(423\) | −4.92337e10 | −0.0747706 | ||||||||
\(424\) | 6.80600e10 | 0.102269 | ||||||||
\(425\) | 2.96259e11 | 0.440476 | ||||||||
\(426\) | 9.66383e11 | 1.42169 | ||||||||
\(427\) | 3.16038e10 | 0.0460059 | ||||||||
\(428\) | −5.05379e11 | −0.727981 | ||||||||
\(429\) | 1.55994e12 | 2.22357 | ||||||||
\(430\) | 4.68695e11 | 0.661123 | ||||||||
\(431\) | −4.36455e11 | −0.609245 | −0.304622 | − | 0.952473i | \(-0.598530\pi\) | ||||
−0.304622 | + | 0.952473i | \(0.598530\pi\) | |||||||
\(432\) | 1.53661e11 | 0.212269 | ||||||||
\(433\) | 4.48430e11 | 0.613055 | 0.306527 | − | 0.951862i | \(-0.400833\pi\) | ||||
0.306527 | + | 0.951862i | \(0.400833\pi\) | |||||||
\(434\) | 1.99449e10 | 0.0269854 | ||||||||
\(435\) | 5.21226e11 | 0.697950 | ||||||||
\(436\) | −3.44230e11 | −0.456204 | ||||||||
\(437\) | 6.44965e10 | 0.0845998 | ||||||||
\(438\) | −6.37079e11 | −0.827104 | ||||||||
\(439\) | −6.59703e11 | −0.847731 | −0.423866 | − | 0.905725i | \(-0.639327\pi\) | ||||
−0.423866 | + | 0.905725i | \(0.639327\pi\) | |||||||
\(440\) | −2.00085e11 | −0.254493 | ||||||||
\(441\) | −1.83548e11 | −0.231088 | ||||||||
\(442\) | −7.05714e11 | −0.879485 | ||||||||
\(443\) | 9.48507e11 | 1.17010 | 0.585051 | − | 0.810997i | \(-0.301075\pi\) | ||||
0.585051 | + | 0.810997i | \(0.301075\pi\) | |||||||
\(444\) | −1.72007e11 | −0.210051 | ||||||||
\(445\) | −2.76743e10 | −0.0334546 | ||||||||
\(446\) | 7.46156e11 | 0.892941 | ||||||||
\(447\) | −1.17709e12 | −1.39453 | ||||||||
\(448\) | −1.59719e10 | −0.0187329 | ||||||||
\(449\) | −6.11763e11 | −0.710354 | −0.355177 | − | 0.934799i | \(-0.615579\pi\) | ||||
−0.355177 | + | 0.934799i | \(0.615579\pi\) | |||||||
\(450\) | −8.90566e10 | −0.102379 | ||||||||
\(451\) | −8.48981e10 | −0.0966282 | ||||||||
\(452\) | 6.92941e11 | 0.780861 | ||||||||
\(453\) | 6.72841e11 | 0.750707 | ||||||||
\(454\) | 4.25388e11 | 0.469930 | ||||||||
\(455\) | −1.47505e11 | −0.161345 | ||||||||
\(456\) | −2.01520e11 | −0.218261 | ||||||||
\(457\) | −3.79033e11 | −0.406494 | −0.203247 | − | 0.979128i | \(-0.565149\pi\) | ||||
−0.203247 | + | 0.979128i | \(0.565149\pi\) | |||||||
\(458\) | 6.39852e11 | 0.679492 | ||||||||
\(459\) | −5.80688e11 | −0.610641 | ||||||||
\(460\) | 4.55471e10 | 0.0474297 | ||||||||
\(461\) | −8.90062e11 | −0.917839 | −0.458919 | − | 0.888478i | \(-0.651763\pi\) | ||||
−0.458919 | + | 0.888478i | \(0.651763\pi\) | |||||||
\(462\) | −1.33418e11 | −0.136247 | ||||||||
\(463\) | 1.32852e12 | 1.34355 | 0.671776 | − | 0.740755i | \(-0.265532\pi\) | ||||
0.671776 | + | 0.740755i | \(0.265532\pi\) | |||||||
\(464\) | −2.51688e11 | −0.252076 | ||||||||
\(465\) | 1.77713e11 | 0.176271 | ||||||||
\(466\) | 1.04534e11 | 0.102688 | ||||||||
\(467\) | 1.65638e12 | 1.61151 | 0.805755 | − | 0.592249i | \(-0.201760\pi\) | ||||
0.805755 | + | 0.592249i | \(0.201760\pi\) | |||||||
\(468\) | 2.12140e11 | 0.204417 | ||||||||
\(469\) | 1.15546e11 | 0.110275 | ||||||||
\(470\) | −1.47289e11 | −0.139229 | ||||||||
\(471\) | 6.60125e11 | 0.618062 | ||||||||
\(472\) | 4.59715e11 | 0.426334 | ||||||||
\(473\) | −1.89054e12 | −1.73664 | ||||||||
\(474\) | −1.22829e12 | −1.11763 | ||||||||
\(475\) | −3.77265e11 | −0.340037 | ||||||||
\(476\) | 6.03582e10 | 0.0538896 | ||||||||
\(477\) | 7.73152e10 | 0.0683805 | ||||||||
\(478\) | −9.06837e11 | −0.794518 | ||||||||
\(479\) | −1.07973e12 | −0.937143 | −0.468571 | − | 0.883426i | \(-0.655231\pi\) | ||||
−0.468571 | + | 0.883426i | \(0.655231\pi\) | |||||||
\(480\) | −1.42313e11 | −0.122365 | ||||||||
\(481\) | 7.67065e11 | 0.653400 | ||||||||
\(482\) | 7.38386e10 | 0.0623120 | ||||||||
\(483\) | 3.03713e10 | 0.0253923 | ||||||||
\(484\) | 2.03430e11 | 0.168505 | ||||||||
\(485\) | −5.85973e11 | −0.480883 | ||||||||
\(486\) | 4.03153e11 | 0.327798 | ||||||||
\(487\) | 1.60549e12 | 1.29338 | 0.646690 | − | 0.762753i | \(-0.276153\pi\) | ||||
0.646690 | + | 0.762753i | \(0.276153\pi\) | |||||||
\(488\) | −1.35976e11 | −0.108536 | ||||||||
\(489\) | −1.29238e11 | −0.102212 | ||||||||
\(490\) | −5.49106e11 | −0.430303 | ||||||||
\(491\) | 7.93629e11 | 0.616242 | 0.308121 | − | 0.951347i | \(-0.400300\pi\) | ||||
0.308121 | + | 0.951347i | \(0.400300\pi\) | |||||||
\(492\) | −6.03849e10 | −0.0464607 | ||||||||
\(493\) | 9.51134e11 | 0.725154 | ||||||||
\(494\) | 8.98677e11 | 0.678941 | ||||||||
\(495\) | −2.27293e11 | −0.170162 | ||||||||
\(496\) | −8.58134e10 | −0.0636630 | ||||||||
\(497\) | 3.68588e11 | 0.270980 | ||||||||
\(498\) | 1.14172e12 | 0.831817 | ||||||||
\(499\) | −1.96951e12 | −1.42202 | −0.711010 | − | 0.703182i | \(-0.751762\pi\) | ||||
−0.711010 | + | 0.703182i | \(0.751762\pi\) | |||||||
\(500\) | −7.01423e11 | −0.501898 | ||||||||
\(501\) | 4.45380e11 | 0.315835 | ||||||||
\(502\) | 1.08831e12 | 0.764867 | ||||||||
\(503\) | −5.42230e11 | −0.377683 | −0.188842 | − | 0.982008i | \(-0.560473\pi\) | ||||
−0.188842 | + | 0.982008i | \(0.560473\pi\) | |||||||
\(504\) | −1.81439e10 | −0.0125254 | ||||||||
\(505\) | 9.20216e11 | 0.629620 | ||||||||
\(506\) | −1.83720e11 | −0.124589 | ||||||||
\(507\) | −3.29362e12 | −2.21380 | ||||||||
\(508\) | 3.07098e11 | 0.204593 | ||||||||
\(509\) | −1.69215e12 | −1.11740 | −0.558699 | − | 0.829370i | \(-0.688699\pi\) | ||||
−0.558699 | + | 0.829370i | \(0.688699\pi\) | |||||||
\(510\) | 5.37803e11 | 0.352012 | ||||||||
\(511\) | −2.42989e11 | −0.157649 | ||||||||
\(512\) | 6.87195e10 | 0.0441942 | ||||||||
\(513\) | 7.39465e11 | 0.471400 | ||||||||
\(514\) | −1.49753e12 | −0.946329 | ||||||||
\(515\) | 6.92403e11 | 0.433737 | ||||||||
\(516\) | −1.34467e12 | −0.835010 | ||||||||
\(517\) | 5.94106e11 | 0.365727 | ||||||||
\(518\) | −6.56054e10 | −0.0400365 | ||||||||
\(519\) | 2.75637e12 | 1.66757 | ||||||||
\(520\) | 6.34642e11 | 0.380639 | ||||||||
\(521\) | 2.97596e12 | 1.76953 | 0.884764 | − | 0.466040i | \(-0.154320\pi\) | ||||
0.884764 | + | 0.466040i | \(0.154320\pi\) | |||||||
\(522\) | −2.85914e11 | −0.168546 | ||||||||
\(523\) | −1.07989e12 | −0.631137 | −0.315568 | − | 0.948903i | \(-0.602195\pi\) | ||||
−0.315568 | + | 0.948903i | \(0.602195\pi\) | |||||||
\(524\) | 7.13253e11 | 0.413288 | ||||||||
\(525\) | −1.77654e11 | −0.102060 | ||||||||
\(526\) | −1.50464e12 | −0.857032 | ||||||||
\(527\) | 3.24291e11 | 0.183141 | ||||||||
\(528\) | 5.74036e11 | 0.321430 | ||||||||
\(529\) | −1.75933e12 | −0.976780 | ||||||||
\(530\) | 2.31298e11 | 0.127330 | ||||||||
\(531\) | 5.22230e11 | 0.285060 | ||||||||
\(532\) | −7.68619e10 | −0.0416015 | ||||||||
\(533\) | 2.69286e11 | 0.144524 | ||||||||
\(534\) | 7.93965e10 | 0.0422538 | ||||||||
\(535\) | −1.71750e12 | −0.906367 | ||||||||
\(536\) | −4.97141e11 | −0.260158 | ||||||||
\(537\) | 9.15302e10 | 0.0474985 | ||||||||
\(538\) | 1.96359e12 | 1.01049 | ||||||||
\(539\) | 2.21489e12 | 1.13032 | ||||||||
\(540\) | 5.22207e11 | 0.264284 | ||||||||
\(541\) | −2.02167e12 | −1.01467 | −0.507333 | − | 0.861750i | \(-0.669369\pi\) | ||||
−0.507333 | + | 0.861750i | \(0.669369\pi\) | |||||||
\(542\) | −2.62812e12 | −1.30812 | ||||||||
\(543\) | 8.47697e11 | 0.418448 | ||||||||
\(544\) | −2.59692e11 | −0.127135 | ||||||||
\(545\) | −1.16984e12 | −0.567994 | ||||||||
\(546\) | 4.23186e11 | 0.203781 | ||||||||
\(547\) | −2.62612e12 | −1.25421 | −0.627107 | − | 0.778933i | \(-0.715761\pi\) | ||||
−0.627107 | + | 0.778933i | \(0.715761\pi\) | |||||||
\(548\) | 7.37876e11 | 0.349519 | ||||||||
\(549\) | −1.54467e11 | −0.0725703 | ||||||||
\(550\) | 1.07465e12 | 0.500766 | ||||||||
\(551\) | −1.21120e12 | −0.559802 | ||||||||
\(552\) | −1.30673e11 | −0.0599046 | ||||||||
\(553\) | −4.68481e11 | −0.213024 | ||||||||
\(554\) | 1.04021e12 | 0.469169 | ||||||||
\(555\) | −5.84557e11 | −0.261522 | ||||||||
\(556\) | 5.52041e11 | 0.244982 | ||||||||
\(557\) | 3.48482e12 | 1.53402 | 0.767012 | − | 0.641633i | \(-0.221743\pi\) | ||||
0.767012 | + | 0.641633i | \(0.221743\pi\) | |||||||
\(558\) | −9.74828e10 | −0.0425671 | ||||||||
\(559\) | 5.99653e12 | 2.59745 | ||||||||
\(560\) | −5.42795e10 | −0.0233233 | ||||||||
\(561\) | −2.16929e12 | −0.924667 | ||||||||
\(562\) | 8.33543e11 | 0.352464 | ||||||||
\(563\) | −2.77091e12 | −1.16235 | −0.581173 | − | 0.813780i | \(-0.697406\pi\) | ||||
−0.581173 | + | 0.813780i | \(0.697406\pi\) | |||||||
\(564\) | 4.22566e11 | 0.175848 | ||||||||
\(565\) | 2.35492e12 | 0.972205 | ||||||||
\(566\) | −1.45119e12 | −0.594360 | ||||||||
\(567\) | 4.35402e11 | 0.176916 | ||||||||
\(568\) | −1.58586e12 | −0.639289 | ||||||||
\(569\) | −6.70382e11 | −0.268113 | −0.134056 | − | 0.990974i | \(-0.542800\pi\) | ||||
−0.134056 | + | 0.990974i | \(0.542800\pi\) | |||||||
\(570\) | −6.84854e11 | −0.271745 | ||||||||
\(571\) | 2.67123e12 | 1.05160 | 0.525798 | − | 0.850609i | \(-0.323767\pi\) | ||||
0.525798 | + | 0.850609i | \(0.323767\pi\) | |||||||
\(572\) | −2.55990e12 | −0.999865 | ||||||||
\(573\) | −5.04336e12 | −1.95445 | ||||||||
\(574\) | −2.30314e10 | −0.00885559 | ||||||||
\(575\) | −2.44633e11 | −0.0933274 | ||||||||
\(576\) | 7.80644e10 | 0.0295496 | ||||||||
\(577\) | −6.59284e11 | −0.247618 | −0.123809 | − | 0.992306i | \(-0.539511\pi\) | ||||
−0.123809 | + | 0.992306i | \(0.539511\pi\) | |||||||
\(578\) | −9.16023e11 | −0.341374 | ||||||||
\(579\) | 2.01863e12 | 0.746453 | ||||||||
\(580\) | −8.55345e11 | −0.313845 | ||||||||
\(581\) | 4.35464e11 | 0.158548 | ||||||||
\(582\) | 1.68114e12 | 0.607365 | ||||||||
\(583\) | −9.32967e11 | −0.334471 | ||||||||
\(584\) | 1.04546e12 | 0.371921 | ||||||||
\(585\) | 7.20944e11 | 0.254507 | ||||||||
\(586\) | 1.16091e12 | 0.406686 | ||||||||
\(587\) | 1.04947e12 | 0.364835 | 0.182418 | − | 0.983221i | \(-0.441608\pi\) | ||||
0.182418 | + | 0.983221i | \(0.441608\pi\) | |||||||
\(588\) | 1.57537e12 | 0.543480 | ||||||||
\(589\) | −4.12961e11 | −0.141381 | ||||||||
\(590\) | 1.56231e12 | 0.530804 | ||||||||
\(591\) | −1.37450e12 | −0.463448 | ||||||||
\(592\) | 2.82269e11 | 0.0944528 | ||||||||
\(593\) | −1.31188e12 | −0.435662 | −0.217831 | − | 0.975987i | \(-0.569898\pi\) | ||||
−0.217831 | + | 0.975987i | \(0.569898\pi\) | |||||||
\(594\) | −2.10639e12 | −0.694223 | ||||||||
\(595\) | 2.05124e11 | 0.0670949 | ||||||||
\(596\) | 1.93164e12 | 0.627074 | ||||||||
\(597\) | 3.87713e12 | 1.24918 | ||||||||
\(598\) | 5.82735e11 | 0.186344 | ||||||||
\(599\) | −3.37603e12 | −1.07148 | −0.535742 | − | 0.844382i | \(-0.679968\pi\) | ||||
−0.535742 | + | 0.844382i | \(0.679968\pi\) | |||||||
\(600\) | 7.64359e11 | 0.240778 | ||||||||
\(601\) | 2.63880e12 | 0.825034 | 0.412517 | − | 0.910950i | \(-0.364650\pi\) | ||||
0.412517 | + | 0.910950i | \(0.364650\pi\) | |||||||
\(602\) | −5.12871e11 | −0.159156 | ||||||||
\(603\) | −5.64745e11 | −0.173950 | ||||||||
\(604\) | −1.10415e12 | −0.337568 | ||||||||
\(605\) | 6.91346e11 | 0.209795 | ||||||||
\(606\) | −2.64007e12 | −0.795221 | ||||||||
\(607\) | −5.15939e12 | −1.54259 | −0.771293 | − | 0.636481i | \(-0.780390\pi\) | ||||
−0.771293 | + | 0.636481i | \(0.780390\pi\) | |||||||
\(608\) | 3.30700e11 | 0.0981449 | ||||||||
\(609\) | −5.70353e11 | −0.168022 | ||||||||
\(610\) | −4.62105e11 | −0.135132 | ||||||||
\(611\) | −1.88443e12 | −0.547008 | ||||||||
\(612\) | −2.95007e11 | −0.0850063 | ||||||||
\(613\) | −5.37354e11 | −0.153705 | −0.0768525 | − | 0.997042i | \(-0.524487\pi\) | ||||
−0.0768525 | + | 0.997042i | \(0.524487\pi\) | |||||||
\(614\) | 2.91163e12 | 0.826759 | ||||||||
\(615\) | −2.05214e11 | −0.0578455 | ||||||||
\(616\) | 2.18943e11 | 0.0612658 | ||||||||
\(617\) | 4.63358e12 | 1.28716 | 0.643582 | − | 0.765378i | \(-0.277448\pi\) | ||||
0.643582 | + | 0.765378i | \(0.277448\pi\) | |||||||
\(618\) | −1.98648e12 | −0.547818 | ||||||||
\(619\) | 3.06267e12 | 0.838480 | 0.419240 | − | 0.907876i | \(-0.362297\pi\) | ||||
0.419240 | + | 0.907876i | \(0.362297\pi\) | |||||||
\(620\) | −2.91631e11 | −0.0792632 | ||||||||
\(621\) | 4.79496e11 | 0.129382 | ||||||||
\(622\) | −1.43727e12 | −0.385019 | ||||||||
\(623\) | 3.02827e10 | 0.00805374 | ||||||||
\(624\) | −1.82076e12 | −0.480754 | ||||||||
\(625\) | −4.73661e10 | −0.0124167 | ||||||||
\(626\) | 8.82230e10 | 0.0229613 | ||||||||
\(627\) | 2.76244e12 | 0.713821 | ||||||||
\(628\) | −1.08328e12 | −0.277922 | ||||||||
\(629\) | −1.06670e12 | −0.271715 | ||||||||
\(630\) | −6.16608e10 | −0.0155947 | ||||||||
\(631\) | −5.46928e10 | −0.0137340 | −0.00686702 | − | 0.999976i | \(-0.502186\pi\) | ||||
−0.00686702 | + | 0.999976i | \(0.502186\pi\) | |||||||
\(632\) | 2.01565e12 | 0.502560 | ||||||||
\(633\) | 7.25654e12 | 1.79644 | ||||||||
\(634\) | −3.11689e11 | −0.0766160 | ||||||||
\(635\) | 1.04365e12 | 0.254727 | ||||||||
\(636\) | −6.63585e11 | −0.160820 | ||||||||
\(637\) | −7.02533e12 | −1.69059 | ||||||||
\(638\) | 3.45014e12 | 0.824410 | ||||||||
\(639\) | −1.80151e12 | −0.427449 | ||||||||
\(640\) | 2.33539e11 | 0.0550236 | ||||||||
\(641\) | −4.78068e12 | −1.11848 | −0.559240 | − | 0.829006i | \(-0.688907\pi\) | ||||
−0.559240 | + | 0.829006i | \(0.688907\pi\) | |||||||
\(642\) | 4.92744e12 | 1.14476 | ||||||||
\(643\) | 4.10484e12 | 0.946994 | 0.473497 | − | 0.880795i | \(-0.342992\pi\) | ||||
0.473497 | + | 0.880795i | \(0.342992\pi\) | |||||||
\(644\) | −4.98401e10 | −0.0114181 | ||||||||
\(645\) | −4.56977e12 | −1.03962 | ||||||||
\(646\) | −1.24972e12 | −0.282337 | ||||||||
\(647\) | −5.49263e12 | −1.23228 | −0.616142 | − | 0.787635i | \(-0.711305\pi\) | ||||
−0.616142 | + | 0.787635i | \(0.711305\pi\) | |||||||
\(648\) | −1.87333e12 | −0.417375 | ||||||||
\(649\) | −6.30178e12 | −1.39432 | ||||||||
\(650\) | −3.40865e12 | −0.748983 | ||||||||
\(651\) | −1.94463e11 | −0.0424348 | ||||||||
\(652\) | 2.12083e11 | 0.0459612 | ||||||||
\(653\) | 4.15994e12 | 0.895320 | 0.447660 | − | 0.894204i | \(-0.352258\pi\) | ||||
0.447660 | + | 0.894204i | \(0.352258\pi\) | |||||||
\(654\) | 3.35624e12 | 0.717386 | ||||||||
\(655\) | 2.42395e12 | 0.514561 | ||||||||
\(656\) | 9.90932e10 | 0.0208918 | ||||||||
\(657\) | 1.18763e12 | 0.248678 | ||||||||
\(658\) | 1.61171e11 | 0.0335174 | ||||||||
\(659\) | 2.15295e12 | 0.444681 | 0.222341 | − | 0.974969i | \(-0.428630\pi\) | ||||
0.222341 | + | 0.974969i | \(0.428630\pi\) | |||||||
\(660\) | 1.95082e12 | 0.400194 | ||||||||
\(661\) | 8.63978e12 | 1.76034 | 0.880169 | − | 0.474660i | \(-0.157429\pi\) | ||||
0.880169 | + | 0.474660i | \(0.157429\pi\) | |||||||
\(662\) | −1.70882e12 | −0.345807 | ||||||||
\(663\) | 6.88071e12 | 1.38300 | ||||||||
\(664\) | −1.87359e12 | −0.374041 | ||||||||
\(665\) | −2.61210e11 | −0.0517956 | ||||||||
\(666\) | 3.20653e11 | 0.0631541 | ||||||||
\(667\) | −7.85387e11 | −0.153645 | ||||||||
\(668\) | −7.30880e11 | −0.142021 | ||||||||
\(669\) | −7.27502e12 | −1.40416 | ||||||||
\(670\) | −1.68950e12 | −0.323908 | ||||||||
\(671\) | 1.86396e12 | 0.354964 | ||||||||
\(672\) | 1.55726e11 | 0.0294578 | ||||||||
\(673\) | −2.90788e12 | −0.546398 | −0.273199 | − | 0.961957i | \(-0.588082\pi\) | ||||
−0.273199 | + | 0.961957i | \(0.588082\pi\) | |||||||
\(674\) | −2.81242e12 | −0.524942 | ||||||||
\(675\) | −2.80476e12 | −0.520031 | ||||||||
\(676\) | 5.40492e12 | 0.995472 | ||||||||
\(677\) | 4.26822e12 | 0.780904 | 0.390452 | − | 0.920623i | \(-0.372319\pi\) | ||||
0.390452 | + | 0.920623i | \(0.372319\pi\) | |||||||
\(678\) | −6.75618e12 | −1.22791 | ||||||||
\(679\) | 6.41203e11 | 0.115766 | ||||||||
\(680\) | −8.82548e11 | −0.158288 | ||||||||
\(681\) | −4.14753e12 | −0.738971 | ||||||||
\(682\) | 1.17633e12 | 0.208209 | ||||||||
\(683\) | −7.69165e11 | −0.135247 | −0.0676233 | − | 0.997711i | \(-0.521542\pi\) | ||||
−0.0676233 | + | 0.997711i | \(0.521542\pi\) | |||||||
\(684\) | 3.75671e11 | 0.0656228 | ||||||||
\(685\) | 2.50763e12 | 0.435166 | ||||||||
\(686\) | 1.21553e12 | 0.209559 | ||||||||
\(687\) | −6.23855e12 | −1.06851 | ||||||||
\(688\) | 2.20664e12 | 0.375477 | ||||||||
\(689\) | 2.95925e12 | 0.500259 | ||||||||
\(690\) | −4.44085e11 | −0.0745838 | ||||||||
\(691\) | 1.38648e12 | 0.231347 | 0.115673 | − | 0.993287i | \(-0.463097\pi\) | ||||
0.115673 | + | 0.993287i | \(0.463097\pi\) | |||||||
\(692\) | −4.52327e12 | −0.749851 | ||||||||
\(693\) | 2.48716e11 | 0.0409642 | ||||||||
\(694\) | 1.33284e12 | 0.218103 | ||||||||
\(695\) | 1.87608e12 | 0.305014 | ||||||||
\(696\) | 2.45396e12 | 0.396392 | ||||||||
\(697\) | −3.74475e11 | −0.0601002 | ||||||||
\(698\) | 5.14189e12 | 0.819923 | ||||||||
\(699\) | −1.01921e12 | −0.161479 | ||||||||
\(700\) | 2.91534e11 | 0.0458932 | ||||||||
\(701\) | −5.51186e12 | −0.862119 | −0.431059 | − | 0.902324i | \(-0.641860\pi\) | ||||
−0.431059 | + | 0.902324i | \(0.641860\pi\) | |||||||
\(702\) | 6.68118e12 | 1.03833 | ||||||||
\(703\) | 1.35837e12 | 0.209758 | ||||||||
\(704\) | −9.42007e11 | −0.144536 | ||||||||
\(705\) | 1.43606e12 | 0.218939 | ||||||||
\(706\) | 6.52302e12 | 0.988160 | ||||||||
\(707\) | −1.00695e12 | −0.151572 | ||||||||
\(708\) | −4.48222e12 | −0.670415 | ||||||||
\(709\) | 2.43152e12 | 0.361385 | 0.180693 | − | 0.983540i | \(-0.442166\pi\) | ||||
0.180693 | + | 0.983540i | \(0.442166\pi\) | |||||||
\(710\) | −5.38944e12 | −0.795942 | ||||||||
\(711\) | 2.28975e12 | 0.336028 | ||||||||
\(712\) | −1.30292e11 | −0.0190001 | ||||||||
\(713\) | −2.67779e11 | −0.0388038 | ||||||||
\(714\) | −5.88492e11 | −0.0847420 | ||||||||
\(715\) | −8.69967e12 | −1.24487 | ||||||||
\(716\) | −1.50203e11 | −0.0213585 | ||||||||
\(717\) | 8.84166e12 | 1.24939 | ||||||||
\(718\) | −8.96126e12 | −1.25837 | ||||||||
\(719\) | −2.70890e12 | −0.378018 | −0.189009 | − | 0.981975i | \(-0.560528\pi\) | ||||
−0.189009 | + | 0.981975i | \(0.560528\pi\) | |||||||
\(720\) | 2.65297e11 | 0.0367905 | ||||||||
\(721\) | −7.57664e11 | −0.104416 | ||||||||
\(722\) | −3.57157e12 | −0.489150 | ||||||||
\(723\) | −7.19927e11 | −0.0979864 | ||||||||
\(724\) | −1.39109e12 | −0.188162 | ||||||||
\(725\) | 4.59404e12 | 0.617553 | ||||||||
\(726\) | −1.98345e12 | −0.264976 | ||||||||
\(727\) | 5.26647e11 | 0.0699221 | 0.0349611 | − | 0.999389i | \(-0.488869\pi\) | ||||
0.0349611 | + | 0.999389i | \(0.488869\pi\) | |||||||
\(728\) | −6.94458e11 | −0.0916336 | ||||||||
\(729\) | 5.07138e12 | 0.665047 | ||||||||
\(730\) | 3.55294e12 | 0.463058 | ||||||||
\(731\) | −8.33893e12 | −1.08015 | ||||||||
\(732\) | 1.32576e12 | 0.170674 | ||||||||
\(733\) | −2.78009e12 | −0.355706 | −0.177853 | − | 0.984057i | \(-0.556915\pi\) | ||||
−0.177853 | + | 0.984057i | \(0.556915\pi\) | |||||||
\(734\) | 6.01690e12 | 0.765140 | ||||||||
\(735\) | 5.35379e12 | 0.676656 | ||||||||
\(736\) | 2.14438e11 | 0.0269371 | ||||||||
\(737\) | 6.81481e12 | 0.850844 | ||||||||
\(738\) | 1.12569e11 | 0.0139689 | ||||||||
\(739\) | −2.36558e12 | −0.291768 | −0.145884 | − | 0.989302i | \(-0.546603\pi\) | ||||
−0.145884 | + | 0.989302i | \(0.546603\pi\) | |||||||
\(740\) | 9.59272e11 | 0.117598 | ||||||||
\(741\) | −8.76210e12 | −1.06764 | ||||||||
\(742\) | −2.53098e11 | −0.0306529 | ||||||||
\(743\) | 1.31398e13 | 1.58175 | 0.790876 | − | 0.611977i | \(-0.209625\pi\) | ||||
0.790876 | + | 0.611977i | \(0.209625\pi\) | |||||||
\(744\) | 8.36680e11 | 0.100111 | ||||||||
\(745\) | 6.56457e12 | 0.780733 | ||||||||
\(746\) | −1.29959e12 | −0.153632 | ||||||||
\(747\) | −2.12838e12 | −0.250095 | ||||||||
\(748\) | 3.55987e12 | 0.415792 | ||||||||
\(749\) | 1.87938e12 | 0.218195 | ||||||||
\(750\) | 6.83888e12 | 0.789240 | ||||||||
\(751\) | −7.29436e12 | −0.836773 | −0.418387 | − | 0.908269i | \(-0.637404\pi\) | ||||
−0.418387 | + | 0.908269i | \(0.637404\pi\) | |||||||
\(752\) | −6.93441e11 | −0.0790732 | ||||||||
\(753\) | −1.06110e13 | −1.20276 | ||||||||
\(754\) | −1.09434e13 | −1.23305 | ||||||||
\(755\) | −3.75238e12 | −0.420287 | ||||||||
\(756\) | −5.71427e11 | −0.0636227 | ||||||||
\(757\) | −1.63020e13 | −1.80430 | −0.902150 | − | 0.431423i | \(-0.858012\pi\) | ||||
−0.902150 | + | 0.431423i | \(0.858012\pi\) | |||||||
\(758\) | 3.24367e12 | 0.356882 | ||||||||
\(759\) | 1.79127e12 | 0.195917 | ||||||||
\(760\) | 1.12386e12 | 0.122195 | ||||||||
\(761\) | −9.68945e12 | −1.04729 | −0.523646 | − | 0.851936i | \(-0.675429\pi\) | ||||
−0.523646 | + | 0.851936i | \(0.675429\pi\) | |||||||
\(762\) | −2.99420e12 | −0.321724 | ||||||||
\(763\) | 1.28010e12 | 0.136737 | ||||||||
\(764\) | 8.27629e12 | 0.878851 | ||||||||
\(765\) | −1.00256e12 | −0.105836 | ||||||||
\(766\) | −7.62906e11 | −0.0800648 | ||||||||
\(767\) | 1.99884e13 | 2.08545 | ||||||||
\(768\) | −6.70015e11 | −0.0694959 | ||||||||
\(769\) | 1.21329e13 | 1.25111 | 0.625554 | − | 0.780180i | \(-0.284873\pi\) | ||||
0.625554 | + | 0.780180i | \(0.284873\pi\) | |||||||
\(770\) | 7.44064e11 | 0.0762785 | ||||||||
\(771\) | 1.46009e13 | 1.48811 | ||||||||
\(772\) | −3.31262e12 | −0.335655 | ||||||||
\(773\) | −1.68647e13 | −1.69891 | −0.849454 | − | 0.527663i | \(-0.823068\pi\) | ||||
−0.849454 | + | 0.527663i | \(0.823068\pi\) | |||||||
\(774\) | 2.50671e12 | 0.251055 | ||||||||
\(775\) | 1.56635e12 | 0.155966 | ||||||||
\(776\) | −2.75879e12 | −0.273112 | ||||||||
\(777\) | 6.39653e11 | 0.0629578 | ||||||||
\(778\) | −3.03671e12 | −0.297164 | ||||||||
\(779\) | 4.76868e11 | 0.0463959 | ||||||||
\(780\) | −6.18775e12 | −0.598560 | ||||||||
\(781\) | 2.17390e13 | 2.09079 | ||||||||
\(782\) | −8.10366e11 | −0.0774909 | ||||||||
\(783\) | −9.00463e12 | −0.856126 | ||||||||
\(784\) | −2.58522e12 | −0.244385 | ||||||||
\(785\) | −3.68147e12 | −0.346025 | ||||||||
\(786\) | −6.95422e12 | −0.649901 | ||||||||
\(787\) | −6.00116e12 | −0.557634 | −0.278817 | − | 0.960344i | \(-0.589942\pi\) | ||||
−0.278817 | + | 0.960344i | \(0.589942\pi\) | |||||||
\(788\) | 2.25559e12 | 0.208397 | ||||||||
\(789\) | 1.46703e13 | 1.34769 | ||||||||
\(790\) | 6.85006e12 | 0.625709 | ||||||||
\(791\) | −2.57688e12 | −0.234045 | ||||||||
\(792\) | −1.07011e12 | −0.0966416 | ||||||||
\(793\) | −5.91223e12 | −0.530911 | ||||||||
\(794\) | 6.40380e12 | 0.571801 | ||||||||
\(795\) | −2.25515e12 | −0.200228 | ||||||||
\(796\) | −6.36247e12 | −0.561716 | ||||||||
\(797\) | −1.43155e13 | −1.25674 | −0.628368 | − | 0.777916i | \(-0.716277\pi\) | ||||
−0.628368 | + | 0.777916i | \(0.716277\pi\) | |||||||
\(798\) | 7.49403e11 | 0.0654188 | ||||||||
\(799\) | 2.62053e12 | 0.227472 | ||||||||
\(800\) | −1.25433e12 | −0.108270 | ||||||||
\(801\) | −1.48010e11 | −0.0127041 | ||||||||
\(802\) | 1.40190e13 | 1.19655 | ||||||||
\(803\) | −1.43312e13 | −1.21636 | ||||||||
\(804\) | 4.84712e12 | 0.409102 | ||||||||
\(805\) | −1.69378e11 | −0.0142160 | ||||||||
\(806\) | −3.73116e12 | −0.311413 | ||||||||
\(807\) | −1.91450e13 | −1.58900 | ||||||||
\(808\) | 4.33242e12 | 0.357585 | ||||||||
\(809\) | −1.09893e13 | −0.901992 | −0.450996 | − | 0.892526i | \(-0.648931\pi\) | ||||
−0.450996 | + | 0.892526i | \(0.648931\pi\) | |||||||
\(810\) | −6.36638e12 | −0.519649 | ||||||||
\(811\) | 2.15444e13 | 1.74880 | 0.874399 | − | 0.485207i | \(-0.161256\pi\) | ||||
0.874399 | + | 0.485207i | \(0.161256\pi\) | |||||||
\(812\) | 9.35964e11 | 0.0755539 | ||||||||
\(813\) | 2.56242e13 | 2.05704 | ||||||||
\(814\) | −3.86934e12 | −0.308907 | ||||||||
\(815\) | 7.20750e11 | 0.0572236 | ||||||||
\(816\) | 2.53200e12 | 0.199921 | ||||||||
\(817\) | 1.06190e13 | 0.833846 | ||||||||
\(818\) | 9.15680e12 | 0.715079 | ||||||||
\(819\) | −7.88895e11 | −0.0612691 | ||||||||
\(820\) | 3.36762e11 | 0.0260112 | ||||||||
\(821\) | 5.71748e12 | 0.439198 | 0.219599 | − | 0.975590i | \(-0.429525\pi\) | ||||
0.219599 | + | 0.975590i | \(0.429525\pi\) | |||||||
\(822\) | −7.19430e12 | −0.549623 | ||||||||
\(823\) | −1.00524e13 | −0.763787 | −0.381893 | − | 0.924206i | \(-0.624728\pi\) | ||||
−0.381893 | + | 0.924206i | \(0.624728\pi\) | |||||||
\(824\) | 3.25987e12 | 0.246336 | ||||||||
\(825\) | −1.04778e13 | −0.787461 | ||||||||
\(826\) | −1.70957e12 | −0.127784 | ||||||||
\(827\) | 2.29581e13 | 1.70672 | 0.853359 | − | 0.521324i | \(-0.174562\pi\) | ||||
0.853359 | + | 0.521324i | \(0.174562\pi\) | |||||||
\(828\) | 2.43599e11 | 0.0180110 | ||||||||
\(829\) | −1.57277e13 | −1.15657 | −0.578283 | − | 0.815836i | \(-0.696277\pi\) | ||||
−0.578283 | + | 0.815836i | \(0.696277\pi\) | |||||||
\(830\) | −6.36729e12 | −0.465697 | ||||||||
\(831\) | −1.01421e13 | −0.737773 | ||||||||
\(832\) | 2.98792e12 | 0.216179 | ||||||||
\(833\) | 9.76960e12 | 0.703031 | ||||||||
\(834\) | −5.38240e12 | −0.385238 | ||||||||
\(835\) | −2.48385e12 | −0.176822 | ||||||||
\(836\) | −4.53324e12 | −0.320982 | ||||||||
\(837\) | −3.07014e12 | −0.216219 | ||||||||
\(838\) | 6.66708e12 | 0.467022 | ||||||||
\(839\) | −8.52168e12 | −0.593740 | −0.296870 | − | 0.954918i | \(-0.595943\pi\) | ||||
−0.296870 | + | 0.954918i | \(0.595943\pi\) | |||||||
\(840\) | 5.29225e11 | 0.0366762 | ||||||||
\(841\) | 2.41910e11 | 0.0166752 | ||||||||
\(842\) | −1.90469e13 | −1.30593 | ||||||||
\(843\) | −8.12705e12 | −0.554254 | ||||||||
\(844\) | −1.19082e13 | −0.807801 | ||||||||
\(845\) | 1.83683e13 | 1.23941 | ||||||||
\(846\) | −7.87740e11 | −0.0528708 | ||||||||
\(847\) | −7.56507e11 | −0.0505054 | ||||||||
\(848\) | 1.08896e12 | 0.0723154 | ||||||||
\(849\) | 1.41491e13 | 0.934638 | ||||||||
\(850\) | 4.74015e12 | 0.311463 | ||||||||
\(851\) | 8.80815e11 | 0.0575707 | ||||||||
\(852\) | 1.54621e13 | 1.00529 | ||||||||
\(853\) | −1.83160e12 | −0.118457 | −0.0592285 | − | 0.998244i | \(-0.518864\pi\) | ||||
−0.0592285 | + | 0.998244i | \(0.518864\pi\) | |||||||
\(854\) | 5.05660e11 | 0.0325311 | ||||||||
\(855\) | 1.27669e12 | 0.0817032 | ||||||||
\(856\) | −8.08606e12 | −0.514760 | ||||||||
\(857\) | −6.20072e11 | −0.0392671 | −0.0196335 | − | 0.999807i | \(-0.506250\pi\) | ||||
−0.0196335 | + | 0.999807i | \(0.506250\pi\) | |||||||
\(858\) | 2.49591e13 | 1.57230 | ||||||||
\(859\) | −5.71581e12 | −0.358186 | −0.179093 | − | 0.983832i | \(-0.557316\pi\) | ||||
−0.179093 | + | 0.983832i | \(0.557316\pi\) | |||||||
\(860\) | 7.49912e12 | 0.467484 | ||||||||
\(861\) | 2.24556e11 | 0.0139255 | ||||||||
\(862\) | −6.98328e12 | −0.430801 | ||||||||
\(863\) | 2.02596e13 | 1.24332 | 0.621658 | − | 0.783289i | \(-0.286460\pi\) | ||||
0.621658 | + | 0.783289i | \(0.286460\pi\) | |||||||
\(864\) | 2.45858e12 | 0.150097 | ||||||||
\(865\) | −1.53720e13 | −0.933596 | ||||||||
\(866\) | 7.17488e12 | 0.433495 | ||||||||
\(867\) | 8.93122e12 | 0.536815 | ||||||||
\(868\) | 3.19118e11 | 0.0190815 | ||||||||
\(869\) | −2.76305e13 | −1.64362 | ||||||||
\(870\) | 8.33961e12 | 0.493525 | ||||||||
\(871\) | −2.16157e13 | −1.27259 | ||||||||
\(872\) | −5.50768e12 | −0.322585 | ||||||||
\(873\) | −3.13394e12 | −0.182611 | ||||||||
\(874\) | 1.03194e12 | 0.0598211 | ||||||||
\(875\) | 2.60842e12 | 0.150432 | ||||||||
\(876\) | −1.01933e13 | −0.584851 | ||||||||
\(877\) | −9.14573e10 | −0.00522059 | −0.00261030 | − | 0.999997i | \(-0.500831\pi\) | ||||
−0.00261030 | + | 0.999997i | \(0.500831\pi\) | |||||||
\(878\) | −1.05552e13 | −0.599436 | ||||||||
\(879\) | −1.13189e13 | −0.639519 | ||||||||
\(880\) | −3.20135e12 | −0.179954 | ||||||||
\(881\) | 1.73150e13 | 0.968347 | 0.484174 | − | 0.874972i | \(-0.339120\pi\) | ||||
0.484174 | + | 0.874972i | \(0.339120\pi\) | |||||||
\(882\) | −2.93677e12 | −0.163404 | ||||||||
\(883\) | 1.38781e13 | 0.768259 | 0.384130 | − | 0.923279i | \(-0.374502\pi\) | ||||
0.384130 | + | 0.923279i | \(0.374502\pi\) | |||||||
\(884\) | −1.12914e13 | −0.621890 | ||||||||
\(885\) | −1.52325e13 | −0.834695 | ||||||||
\(886\) | 1.51761e13 | 0.827387 | ||||||||
\(887\) | 1.76586e13 | 0.957853 | 0.478926 | − | 0.877855i | \(-0.341026\pi\) | ||||
0.478926 | + | 0.877855i | \(0.341026\pi\) | |||||||
\(888\) | −2.75212e12 | −0.148528 | ||||||||
\(889\) | −1.14202e12 | −0.0613219 | ||||||||
\(890\) | −4.42788e11 | −0.0236560 | ||||||||
\(891\) | 2.56796e13 | 1.36502 | ||||||||
\(892\) | 1.19385e13 | 0.631404 | ||||||||
\(893\) | −3.33706e12 | −0.175603 | ||||||||
\(894\) | −1.88335e13 | −0.986081 | ||||||||
\(895\) | −5.10457e11 | −0.0265923 | ||||||||
\(896\) | −2.55551e11 | −0.0132462 | ||||||||
\(897\) | −5.68167e12 | −0.293028 | ||||||||
\(898\) | −9.78821e12 | −0.502296 | ||||||||
\(899\) | 5.02872e12 | 0.256767 | ||||||||
\(900\) | −1.42490e12 | −0.0723927 | ||||||||
\(901\) | −4.11520e12 | −0.208032 | ||||||||
\(902\) | −1.35837e12 | −0.0683264 | ||||||||
\(903\) | 5.00049e12 | 0.250275 | ||||||||
\(904\) | 1.10871e13 | 0.552152 | ||||||||
\(905\) | −4.72754e12 | −0.234270 | ||||||||
\(906\) | 1.07655e13 | 0.530830 | ||||||||
\(907\) | 1.23924e13 | 0.608025 | 0.304013 | − | 0.952668i | \(-0.401673\pi\) | ||||
0.304013 | + | 0.952668i | \(0.401673\pi\) | |||||||
\(908\) | 6.80620e12 | 0.332291 | ||||||||
\(909\) | 4.92157e12 | 0.239092 | ||||||||
\(910\) | −2.36007e12 | −0.114088 | ||||||||
\(911\) | −1.38104e13 | −0.664313 | −0.332157 | − | 0.943224i | \(-0.607776\pi\) | ||||
−0.332157 | + | 0.943224i | \(0.607776\pi\) | |||||||
\(912\) | −3.22432e12 | −0.154334 | ||||||||
\(913\) | 2.56832e13 | 1.22329 | ||||||||
\(914\) | −6.06452e12 | −0.287434 | ||||||||
\(915\) | 4.50553e12 | 0.212496 | ||||||||
\(916\) | 1.02376e13 | 0.480474 | ||||||||
\(917\) | −2.65241e12 | −0.123874 | ||||||||
\(918\) | −9.29101e12 | −0.431788 | ||||||||
\(919\) | 8.56606e11 | 0.0396152 | 0.0198076 | − | 0.999804i | \(-0.493695\pi\) | ||||
0.0198076 | + | 0.999804i | \(0.493695\pi\) | |||||||
\(920\) | 7.28754e11 | 0.0335379 | ||||||||
\(921\) | −2.83884e13 | −1.30009 | ||||||||
\(922\) | −1.42410e13 | −0.649010 | ||||||||
\(923\) | −6.89531e13 | −3.12713 | ||||||||
\(924\) | −2.13469e12 | −0.0963412 | ||||||||
\(925\) | −5.15223e12 | −0.231397 | ||||||||
\(926\) | 2.12563e13 | 0.950034 | ||||||||
\(927\) | 3.70316e12 | 0.164708 | ||||||||
\(928\) | −4.02700e12 | −0.178244 | ||||||||
\(929\) | 1.29169e13 | 0.568968 | 0.284484 | − | 0.958681i | \(-0.408178\pi\) | ||||
0.284484 | + | 0.958681i | \(0.408178\pi\) | |||||||
\(930\) | 2.84341e12 | 0.124642 | ||||||||
\(931\) | −1.24409e13 | −0.542723 | ||||||||
\(932\) | 1.67254e12 | 0.0726116 | ||||||||
\(933\) | 1.40134e13 | 0.605447 | ||||||||
\(934\) | 2.65020e13 | 1.13951 | ||||||||
\(935\) | 1.20980e13 | 0.517679 | ||||||||
\(936\) | 3.39424e12 | 0.144544 | ||||||||
\(937\) | −3.67867e12 | −0.155906 | −0.0779530 | − | 0.996957i | \(-0.524838\pi\) | ||||
−0.0779530 | + | 0.996957i | \(0.524838\pi\) | |||||||
\(938\) | 1.84874e12 | 0.0779765 | ||||||||
\(939\) | −8.60174e11 | −0.0361070 | ||||||||
\(940\) | −2.35662e12 | −0.0984495 | ||||||||
\(941\) | 4.45145e13 | 1.85075 | 0.925376 | − | 0.379051i | \(-0.123749\pi\) | ||||
0.925376 | + | 0.379051i | \(0.123749\pi\) | |||||||
\(942\) | 1.05620e13 | 0.437036 | ||||||||
\(943\) | 3.09219e11 | 0.0127339 | ||||||||
\(944\) | 7.35544e12 | 0.301463 | ||||||||
\(945\) | −1.94196e12 | −0.0792130 | ||||||||
\(946\) | −3.02486e13 | −1.22799 | ||||||||
\(947\) | −1.99543e13 | −0.806236 | −0.403118 | − | 0.915148i | \(-0.632074\pi\) | ||||
−0.403118 | + | 0.915148i | \(0.632074\pi\) | |||||||
\(948\) | −1.96526e13 | −0.790282 | ||||||||
\(949\) | 4.54567e13 | 1.81928 | ||||||||
\(950\) | −6.03625e12 | −0.240442 | ||||||||
\(951\) | 3.03897e12 | 0.120480 | ||||||||
\(952\) | 9.65731e11 | 0.0381057 | ||||||||
\(953\) | 7.13202e12 | 0.280088 | 0.140044 | − | 0.990145i | \(-0.455276\pi\) | ||||
0.140044 | + | 0.990145i | \(0.455276\pi\) | |||||||
\(954\) | 1.23704e12 | 0.0483523 | ||||||||
\(955\) | 2.81264e13 | 1.09421 | ||||||||
\(956\) | −1.45094e13 | −0.561809 | ||||||||
\(957\) | −3.36388e13 | −1.29639 | ||||||||
\(958\) | −1.72757e13 | −0.662660 | ||||||||
\(959\) | −2.74398e12 | −0.104760 | ||||||||
\(960\) | −2.27700e12 | −0.0865253 | ||||||||
\(961\) | −2.47251e13 | −0.935152 | ||||||||
\(962\) | 1.22730e13 | 0.462024 | ||||||||
\(963\) | −9.18565e12 | −0.344185 | ||||||||
\(964\) | 1.18142e12 | 0.0440613 | ||||||||
\(965\) | −1.12577e13 | −0.417905 | ||||||||
\(966\) | 4.85941e11 | 0.0179550 | ||||||||
\(967\) | 2.84176e12 | 0.104512 | 0.0522562 | − | 0.998634i | \(-0.483359\pi\) | ||||
0.0522562 | + | 0.998634i | \(0.483359\pi\) | |||||||
\(968\) | 3.25489e12 | 0.119151 | ||||||||
\(969\) | 1.21848e13 | 0.443978 | ||||||||
\(970\) | −9.37557e12 | −0.340036 | ||||||||
\(971\) | −3.90309e13 | −1.40903 | −0.704517 | − | 0.709687i | \(-0.748836\pi\) | ||||
−0.704517 | + | 0.709687i | \(0.748836\pi\) | |||||||
\(972\) | 6.45045e12 | 0.231788 | ||||||||
\(973\) | −2.05290e12 | −0.0734278 | ||||||||
\(974\) | 2.56878e13 | 0.914558 | ||||||||
\(975\) | 3.32343e13 | 1.17778 | ||||||||
\(976\) | −2.17561e12 | −0.0767463 | ||||||||
\(977\) | −2.17556e13 | −0.763915 | −0.381958 | − | 0.924180i | \(-0.624750\pi\) | ||||
−0.381958 | + | 0.924180i | \(0.624750\pi\) | |||||||
\(978\) | −2.06781e12 | −0.0722745 | ||||||||
\(979\) | 1.78604e12 | 0.0621397 | ||||||||
\(980\) | −8.78570e12 | −0.304270 | ||||||||
\(981\) | −6.25664e12 | −0.215690 | ||||||||
\(982\) | 1.26981e13 | 0.435749 | ||||||||
\(983\) | 4.64998e13 | 1.58840 | 0.794201 | − | 0.607655i | \(-0.207890\pi\) | ||||
0.794201 | + | 0.607655i | \(0.207890\pi\) | |||||||
\(984\) | −9.66159e11 | −0.0328527 | ||||||||
\(985\) | 7.66548e12 | 0.259464 | ||||||||
\(986\) | 1.52181e13 | 0.512761 | ||||||||
\(987\) | −1.57142e12 | −0.0527065 | ||||||||
\(988\) | 1.43788e13 | 0.480084 | ||||||||
\(989\) | 6.88577e12 | 0.228860 | ||||||||
\(990\) | −3.63669e12 | −0.120323 | ||||||||
\(991\) | −1.55209e13 | −0.511194 | −0.255597 | − | 0.966783i | \(-0.582272\pi\) | ||||
−0.255597 | + | 0.966783i | \(0.582272\pi\) | |||||||
\(992\) | −1.37301e12 | −0.0450166 | ||||||||
\(993\) | 1.66610e13 | 0.543786 | ||||||||
\(994\) | 5.89741e12 | 0.191612 | ||||||||
\(995\) | −2.16225e13 | −0.699361 | ||||||||
\(996\) | 1.82675e13 | 0.588184 | ||||||||
\(997\) | −4.26334e13 | −1.36654 | −0.683268 | − | 0.730167i | \(-0.739442\pi\) | ||||
−0.683268 | + | 0.730167i | \(0.739442\pi\) | |||||||
\(998\) | −3.15121e13 | −1.00552 | ||||||||
\(999\) | 1.00987e13 | 0.320791 |
(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 | 2.10.a.a.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 18.10.a.a.1.1 | 1 | |||
4.3 | odd | 2 | 16.10.a.d.1.1 | 1 | |||
5.2 | odd | 4 | 50.10.b.a.49.2 | 2 | |||
5.3 | odd | 4 | 50.10.b.a.49.1 | 2 | |||
5.4 | even | 2 | 50.10.a.c.1.1 | 1 | |||
7.2 | even | 3 | 98.10.c.c.67.1 | 2 | |||
7.3 | odd | 6 | 98.10.c.b.79.1 | 2 | |||
7.4 | even | 3 | 98.10.c.c.79.1 | 2 | |||
7.5 | odd | 6 | 98.10.c.b.67.1 | 2 | |||
7.6 | odd | 2 | 98.10.a.c.1.1 | 1 | |||
8.3 | odd | 2 | 64.10.a.b.1.1 | 1 | |||
8.5 | even | 2 | 64.10.a.h.1.1 | 1 | |||
9.2 | odd | 6 | 162.10.c.i.109.1 | 2 | |||
9.4 | even | 3 | 162.10.c.b.55.1 | 2 | |||
9.5 | odd | 6 | 162.10.c.i.55.1 | 2 | |||
9.7 | even | 3 | 162.10.c.b.109.1 | 2 | |||
11.10 | odd | 2 | 242.10.a.a.1.1 | 1 | |||
12.11 | even | 2 | 144.10.a.d.1.1 | 1 | |||
13.12 | even | 2 | 338.10.a.a.1.1 | 1 | |||
16.3 | odd | 4 | 256.10.b.e.129.2 | 2 | |||
16.5 | even | 4 | 256.10.b.g.129.2 | 2 | |||
16.11 | odd | 4 | 256.10.b.e.129.1 | 2 | |||
16.13 | even | 4 | 256.10.b.g.129.1 | 2 | |||
20.3 | even | 4 | 400.10.c.d.49.2 | 2 | |||
20.7 | even | 4 | 400.10.c.d.49.1 | 2 | |||
20.19 | odd | 2 | 400.10.a.b.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2.10.a.a.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
16.10.a.d.1.1 | 1 | 4.3 | odd | 2 | |||
18.10.a.a.1.1 | 1 | 3.2 | odd | 2 | |||
50.10.a.c.1.1 | 1 | 5.4 | even | 2 | |||
50.10.b.a.49.1 | 2 | 5.3 | odd | 4 | |||
50.10.b.a.49.2 | 2 | 5.2 | odd | 4 | |||
64.10.a.b.1.1 | 1 | 8.3 | odd | 2 | |||
64.10.a.h.1.1 | 1 | 8.5 | even | 2 | |||
98.10.a.c.1.1 | 1 | 7.6 | odd | 2 | |||
98.10.c.b.67.1 | 2 | 7.5 | odd | 6 | |||
98.10.c.b.79.1 | 2 | 7.3 | odd | 6 | |||
98.10.c.c.67.1 | 2 | 7.2 | even | 3 | |||
98.10.c.c.79.1 | 2 | 7.4 | even | 3 | |||
144.10.a.d.1.1 | 1 | 12.11 | even | 2 | |||
162.10.c.b.55.1 | 2 | 9.4 | even | 3 | |||
162.10.c.b.109.1 | 2 | 9.7 | even | 3 | |||
162.10.c.i.55.1 | 2 | 9.5 | odd | 6 | |||
162.10.c.i.109.1 | 2 | 9.2 | odd | 6 | |||
242.10.a.a.1.1 | 1 | 11.10 | odd | 2 | |||
256.10.b.e.129.1 | 2 | 16.11 | odd | 4 | |||
256.10.b.e.129.2 | 2 | 16.3 | odd | 4 | |||
256.10.b.g.129.1 | 2 | 16.13 | even | 4 | |||
256.10.b.g.129.2 | 2 | 16.5 | even | 4 | |||
338.10.a.a.1.1 | 1 | 13.12 | even | 2 | |||
400.10.a.b.1.1 | 1 | 20.19 | odd | 2 | |||
400.10.c.d.49.1 | 2 | 20.7 | even | 4 | |||
400.10.c.d.49.2 | 2 | 20.3 | even | 4 |