Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [50,26,Mod(1,50)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(50, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 26, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("50.1");
S:= CuspForms(chi, 26);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 50 = 2 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 26 \) |
Character orbit: | \([\chi]\) | \(=\) | 50.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(197.998389976\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{5} - 25534923283x^{3} - 31863478542482x^{2} + 141941149085067124800x + 2515032055818200956928000 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{19}\cdot 3^{5}\cdot 5^{12} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-136720.\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 50.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4096.00 | −0.707107 | ||||||||
\(3\) | 1.22241e6 | 1.32801 | 0.664003 | − | 0.747730i | \(-0.268856\pi\) | ||||
0.664003 | + | 0.747730i | \(0.268856\pi\) | |||||||
\(4\) | 1.67772e7 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −5.00697e9 | −0.939041 | ||||||||
\(7\) | −6.80801e10 | −1.85907 | −0.929533 | − | 0.368739i | \(-0.879789\pi\) | ||||
−0.929533 | + | 0.368739i | \(0.879789\pi\) | |||||||
\(8\) | −6.87195e10 | −0.353553 | ||||||||
\(9\) | 6.46987e11 | 0.763597 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.63529e13 | −1.57104 | −0.785519 | − | 0.618838i | \(-0.787604\pi\) | ||||
−0.785519 | + | 0.618838i | \(0.787604\pi\) | |||||||
\(12\) | 2.05086e13 | 0.664003 | ||||||||
\(13\) | −1.23277e14 | −1.46754 | −0.733769 | − | 0.679399i | \(-0.762241\pi\) | ||||
−0.733769 | + | 0.679399i | \(0.762241\pi\) | |||||||
\(14\) | 2.78856e14 | 1.31456 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.81475e14 | 0.250000 | ||||||||
\(17\) | −1.24327e15 | −0.517550 | −0.258775 | − | 0.965938i | \(-0.583319\pi\) | ||||
−0.258775 | + | 0.965938i | \(0.583319\pi\) | |||||||
\(18\) | −2.65006e15 | −0.539945 | ||||||||
\(19\) | 1.08089e16 | 1.12037 | 0.560187 | − | 0.828366i | \(-0.310729\pi\) | ||||
0.560187 | + | 0.828366i | \(0.310729\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −8.32215e16 | −2.46885 | ||||||||
\(22\) | 6.69815e16 | 1.11089 | ||||||||
\(23\) | −1.26942e17 | −1.20784 | −0.603918 | − | 0.797046i | \(-0.706395\pi\) | ||||
−0.603918 | + | 0.797046i | \(0.706395\pi\) | |||||||
\(24\) | −8.40031e16 | −0.469521 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 5.04942e17 | 1.03771 | ||||||||
\(27\) | −2.44849e17 | −0.313944 | ||||||||
\(28\) | −1.14219e18 | −0.929533 | ||||||||
\(29\) | −1.19617e18 | −0.627797 | −0.313898 | − | 0.949457i | \(-0.601635\pi\) | ||||
−0.313898 | + | 0.949457i | \(0.601635\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.33827e18 | 0.761203 | 0.380602 | − | 0.924739i | \(-0.375717\pi\) | ||||
0.380602 | + | 0.924739i | \(0.375717\pi\) | |||||||
\(32\) | −1.15292e18 | −0.176777 | ||||||||
\(33\) | −1.99899e19 | −2.08635 | ||||||||
\(34\) | 5.09242e18 | 0.365963 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.08546e19 | 0.381799 | ||||||||
\(37\) | −5.02410e19 | −1.25469 | −0.627346 | − | 0.778741i | \(-0.715859\pi\) | ||||
−0.627346 | + | 0.778741i | \(0.715859\pi\) | |||||||
\(38\) | −4.42734e19 | −0.792224 | ||||||||
\(39\) | −1.50694e20 | −1.94890 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.63431e20 | −1.82335 | −0.911673 | − | 0.410917i | \(-0.865209\pi\) | ||||
−0.911673 | + | 0.410917i | \(0.865209\pi\) | |||||||
\(42\) | 3.40875e20 | 1.74574 | ||||||||
\(43\) | −1.36754e20 | −0.521895 | −0.260947 | − | 0.965353i | \(-0.584035\pi\) | ||||
−0.260947 | + | 0.965353i | \(0.584035\pi\) | |||||||
\(44\) | −2.74356e20 | −0.785519 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.19955e20 | 0.854069 | ||||||||
\(47\) | 7.03907e20 | 0.883674 | 0.441837 | − | 0.897095i | \(-0.354327\pi\) | ||||
0.441837 | + | 0.897095i | \(0.354327\pi\) | |||||||
\(48\) | 3.44077e20 | 0.332001 | ||||||||
\(49\) | 3.29383e21 | 2.45613 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.51978e21 | −0.687309 | ||||||||
\(52\) | −2.06824e21 | −0.733769 | ||||||||
\(53\) | 3.75972e21 | 1.05125 | 0.525626 | − | 0.850716i | \(-0.323831\pi\) | ||||
0.525626 | + | 0.850716i | \(0.323831\pi\) | |||||||
\(54\) | 1.00290e21 | 0.221992 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.67843e21 | 0.657279 | ||||||||
\(57\) | 1.32129e22 | 1.48786 | ||||||||
\(58\) | 4.89952e21 | 0.443919 | ||||||||
\(59\) | −6.89657e21 | −0.504642 | −0.252321 | − | 0.967644i | \(-0.581194\pi\) | ||||
−0.252321 | + | 0.967644i | \(0.581194\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.54607e22 | 0.745773 | 0.372886 | − | 0.927877i | \(-0.378368\pi\) | ||||
0.372886 | + | 0.927877i | \(0.378368\pi\) | |||||||
\(62\) | −1.36736e22 | −0.538252 | ||||||||
\(63\) | −4.40470e22 | −1.41958 | ||||||||
\(64\) | 4.72237e21 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 8.18786e22 | 1.47527 | ||||||||
\(67\) | 8.66895e22 | 1.29429 | 0.647145 | − | 0.762367i | \(-0.275963\pi\) | ||||
0.647145 | + | 0.762367i | \(0.275963\pi\) | |||||||
\(68\) | −2.08585e22 | −0.258775 | ||||||||
\(69\) | −1.55175e23 | −1.60401 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.41872e22 | 0.319571 | 0.159785 | − | 0.987152i | \(-0.448920\pi\) | ||||
0.159785 | + | 0.987152i | \(0.448920\pi\) | |||||||
\(72\) | −4.44606e22 | −0.269972 | ||||||||
\(73\) | 8.03151e22 | 0.410451 | 0.205226 | − | 0.978715i | \(-0.434207\pi\) | ||||
0.205226 | + | 0.978715i | \(0.434207\pi\) | |||||||
\(74\) | 2.05787e23 | 0.887201 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.81344e23 | 0.560187 | ||||||||
\(77\) | 1.11331e24 | 2.92066 | ||||||||
\(78\) | 6.17244e23 | 1.37808 | ||||||||
\(79\) | −5.07310e23 | −0.965906 | −0.482953 | − | 0.875646i | \(-0.660436\pi\) | ||||
−0.482953 | + | 0.875646i | \(0.660436\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.47490e23 | −1.18052 | ||||||||
\(82\) | 1.07901e24 | 1.28930 | ||||||||
\(83\) | −5.22032e23 | −0.536070 | −0.268035 | − | 0.963409i | \(-0.586374\pi\) | ||||
−0.268035 | + | 0.963409i | \(0.586374\pi\) | |||||||
\(84\) | −1.39623e24 | −1.23442 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 5.60143e23 | 0.369035 | ||||||||
\(87\) | −1.46221e24 | −0.833717 | ||||||||
\(88\) | 1.12376e24 | 0.555446 | ||||||||
\(89\) | −1.15373e24 | −0.495142 | −0.247571 | − | 0.968870i | \(-0.579632\pi\) | ||||
−0.247571 | + | 0.968870i | \(0.579632\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.39270e24 | 2.72825 | ||||||||
\(92\) | −2.12974e24 | −0.603918 | ||||||||
\(93\) | 4.08072e24 | 1.01088 | ||||||||
\(94\) | −2.88320e24 | −0.624852 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.40934e24 | −0.234760 | ||||||||
\(97\) | 4.89110e24 | 0.715748 | 0.357874 | − | 0.933770i | \(-0.383502\pi\) | ||||
0.357874 | + | 0.933770i | \(0.383502\pi\) | |||||||
\(98\) | −1.34915e25 | −1.73674 | ||||||||
\(99\) | −1.05801e25 | −1.19964 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.39348e25 | 1.23051 | 0.615255 | − | 0.788328i | \(-0.289053\pi\) | ||||
0.615255 | + | 0.788328i | \(0.289053\pi\) | |||||||
\(102\) | 6.22500e24 | 0.486001 | ||||||||
\(103\) | −1.11068e25 | −0.767579 | −0.383789 | − | 0.923421i | \(-0.625381\pi\) | ||||
−0.383789 | + | 0.923421i | \(0.625381\pi\) | |||||||
\(104\) | 8.47152e24 | 0.518853 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.53998e25 | −0.743348 | ||||||||
\(107\) | −2.28767e25 | −0.981967 | −0.490983 | − | 0.871169i | \(-0.663362\pi\) | ||||
−0.490983 | + | 0.871169i | \(0.663362\pi\) | |||||||
\(108\) | −4.10789e24 | −0.156972 | ||||||||
\(109\) | 3.92414e25 | 1.33633 | 0.668164 | − | 0.744014i | \(-0.267081\pi\) | ||||
0.668164 | + | 0.744014i | \(0.267081\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.14149e25 | −1.66624 | ||||||||
\(112\) | −1.91628e25 | −0.464766 | ||||||||
\(113\) | −2.95166e25 | −0.640599 | −0.320299 | − | 0.947316i | \(-0.603784\pi\) | ||||
−0.320299 | + | 0.947316i | \(0.603784\pi\) | |||||||
\(114\) | −5.41201e25 | −1.05208 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.00685e25 | −0.313898 | ||||||||
\(117\) | −7.97585e25 | −1.12061 | ||||||||
\(118\) | 2.82484e25 | 0.356835 | ||||||||
\(119\) | 8.46417e25 | 0.962160 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.59071e26 | 1.46816 | ||||||||
\(122\) | −6.33271e25 | −0.527341 | ||||||||
\(123\) | −3.22020e26 | −2.42141 | ||||||||
\(124\) | 5.60069e25 | 0.380602 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.80416e26 | 1.00379 | ||||||||
\(127\) | −3.71288e25 | −0.187139 | −0.0935696 | − | 0.995613i | \(-0.529828\pi\) | ||||
−0.0935696 | + | 0.995613i | \(0.529828\pi\) | |||||||
\(128\) | −1.93428e25 | −0.0883883 | ||||||||
\(129\) | −1.67168e26 | −0.693079 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.02734e26 | −0.693482 | −0.346741 | − | 0.937961i | \(-0.612712\pi\) | ||||
−0.346741 | + | 0.937961i | \(0.612712\pi\) | |||||||
\(132\) | −3.35375e26 | −1.04317 | ||||||||
\(133\) | −7.35874e26 | −2.08285 | ||||||||
\(134\) | −3.55080e26 | −0.915201 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 8.54366e25 | 0.182982 | ||||||||
\(137\) | −4.21478e26 | −0.823697 | −0.411848 | − | 0.911252i | \(-0.635117\pi\) | ||||
−0.411848 | + | 0.911252i | \(0.635117\pi\) | |||||||
\(138\) | 6.35596e26 | 1.13421 | ||||||||
\(139\) | −2.61876e26 | −0.426983 | −0.213491 | − | 0.976945i | \(-0.568484\pi\) | ||||
−0.213491 | + | 0.976945i | \(0.568484\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.60460e26 | 1.17352 | ||||||||
\(142\) | −1.80991e26 | −0.225971 | ||||||||
\(143\) | 2.01593e27 | 2.30556 | ||||||||
\(144\) | 1.82111e26 | 0.190899 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −3.28971e26 | −0.290233 | ||||||||
\(147\) | 4.02640e27 | 3.26175 | ||||||||
\(148\) | −8.42905e26 | −0.627346 | ||||||||
\(149\) | 5.33091e26 | 0.364732 | 0.182366 | − | 0.983231i | \(-0.441625\pi\) | ||||
0.182366 | + | 0.983231i | \(0.441625\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.15195e26 | −0.0667148 | −0.0333574 | − | 0.999443i | \(-0.510620\pi\) | ||||
−0.0333574 | + | 0.999443i | \(0.510620\pi\) | |||||||
\(152\) | −7.42784e26 | −0.396112 | ||||||||
\(153\) | −8.04377e26 | −0.395200 | ||||||||
\(154\) | −4.56011e27 | −2.06522 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.52823e27 | −0.974449 | ||||||||
\(157\) | −7.11181e26 | −0.253066 | −0.126533 | − | 0.991962i | \(-0.540385\pi\) | ||||
−0.126533 | + | 0.991962i | \(0.540385\pi\) | |||||||
\(158\) | 2.07794e27 | 0.682999 | ||||||||
\(159\) | 4.59590e27 | 1.39607 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.64224e27 | 2.24545 | ||||||||
\(162\) | 3.47132e27 | 0.834751 | ||||||||
\(163\) | −4.92749e27 | −1.09719 | −0.548594 | − | 0.836089i | \(-0.684837\pi\) | ||||
−0.548594 | + | 0.836089i | \(0.684837\pi\) | |||||||
\(164\) | −4.41964e27 | −0.911673 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.13825e27 | 0.379059 | ||||||||
\(167\) | −1.54847e26 | −0.0254651 | −0.0127326 | − | 0.999919i | \(-0.504053\pi\) | ||||
−0.0127326 | + | 0.999919i | \(0.504053\pi\) | |||||||
\(168\) | 5.71894e27 | 0.872870 | ||||||||
\(169\) | 8.14076e27 | 1.15367 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.99325e27 | 0.855515 | ||||||||
\(172\) | −2.29434e27 | −0.260947 | ||||||||
\(173\) | 1.24940e28 | 1.32168 | 0.660840 | − | 0.750527i | \(-0.270200\pi\) | ||||
0.660840 | + | 0.750527i | \(0.270200\pi\) | |||||||
\(174\) | 5.98921e27 | 0.589527 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.60293e27 | −0.392759 | ||||||||
\(177\) | −8.43041e27 | −0.670167 | ||||||||
\(178\) | 4.72569e27 | 0.350118 | ||||||||
\(179\) | 1.81393e28 | 1.25302 | 0.626509 | − | 0.779414i | \(-0.284483\pi\) | ||||
0.626509 | + | 0.779414i | \(0.284483\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.28334e28 | −1.37274 | −0.686369 | − | 0.727254i | \(-0.740796\pi\) | ||||
−0.686369 | + | 0.727254i | \(0.740796\pi\) | |||||||
\(182\) | −3.43765e28 | −1.92916 | ||||||||
\(183\) | 1.88993e28 | 0.990390 | ||||||||
\(184\) | 8.72340e27 | 0.427035 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1.67146e28 | −0.714801 | ||||||||
\(187\) | 2.03310e28 | 0.813091 | ||||||||
\(188\) | 1.18096e28 | 0.441837 | ||||||||
\(189\) | 1.66694e28 | 0.583642 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.88305e28 | −1.19195 | −0.595973 | − | 0.803005i | \(-0.703233\pi\) | ||||
−0.595973 | + | 0.803005i | \(0.703233\pi\) | |||||||
\(192\) | 5.77265e27 | 0.166001 | ||||||||
\(193\) | −5.16030e28 | −1.39062 | −0.695310 | − | 0.718710i | \(-0.744733\pi\) | ||||
−0.695310 | + | 0.718710i | \(0.744733\pi\) | |||||||
\(194\) | −2.00340e28 | −0.506110 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.52613e28 | 1.22806 | ||||||||
\(197\) | −4.39578e28 | −0.916659 | −0.458330 | − | 0.888782i | \(-0.651552\pi\) | ||||
−0.458330 | + | 0.888782i | \(0.651552\pi\) | |||||||
\(198\) | 4.33362e28 | 0.848274 | ||||||||
\(199\) | 6.89463e28 | 1.26721 | 0.633604 | − | 0.773658i | \(-0.281575\pi\) | ||||
0.633604 | + | 0.773658i | \(0.281575\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.05970e29 | 1.71882 | ||||||||
\(202\) | −5.70771e28 | −0.870102 | ||||||||
\(203\) | 8.14356e28 | 1.16712 | ||||||||
\(204\) | −2.54976e28 | −0.343655 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 4.54934e28 | 0.542760 | ||||||||
\(207\) | −8.21300e28 | −0.922301 | ||||||||
\(208\) | −3.46993e28 | −0.366885 | ||||||||
\(209\) | −1.76758e29 | −1.76015 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.04578e29 | 1.80854 | 0.904269 | − | 0.426962i | \(-0.140416\pi\) | ||||
0.904269 | + | 0.426962i | \(0.140416\pi\) | |||||||
\(212\) | 6.30776e28 | 0.525626 | ||||||||
\(213\) | 5.40147e28 | 0.424392 | ||||||||
\(214\) | 9.37031e28 | 0.694355 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.68259e28 | 0.110996 | ||||||||
\(217\) | −2.27270e29 | −1.41513 | ||||||||
\(218\) | −1.60733e29 | −0.944926 | ||||||||
\(219\) | 9.81777e28 | 0.545081 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.53266e29 | 0.759525 | ||||||||
\(222\) | 2.51556e29 | 1.17821 | ||||||||
\(223\) | 3.97032e29 | 1.75798 | 0.878991 | − | 0.476839i | \(-0.158217\pi\) | ||||
0.878991 | + | 0.476839i | \(0.158217\pi\) | |||||||
\(224\) | 7.84910e28 | 0.328639 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.20900e29 | 0.452972 | ||||||||
\(227\) | 3.06368e29 | 1.08623 | 0.543113 | − | 0.839660i | \(-0.317246\pi\) | ||||
0.543113 | + | 0.839660i | \(0.317246\pi\) | |||||||
\(228\) | 2.21676e29 | 0.743931 | ||||||||
\(229\) | 2.92488e28 | 0.0929319 | 0.0464660 | − | 0.998920i | \(-0.485204\pi\) | ||||
0.0464660 | + | 0.998920i | \(0.485204\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.36091e30 | 3.87865 | ||||||||
\(232\) | 8.22004e28 | 0.221960 | ||||||||
\(233\) | 3.00032e29 | 0.767748 | 0.383874 | − | 0.923385i | \(-0.374590\pi\) | ||||
0.383874 | + | 0.923385i | \(0.374590\pi\) | |||||||
\(234\) | 3.26691e29 | 0.792390 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.15705e29 | −0.252321 | ||||||||
\(237\) | −6.20139e29 | −1.28273 | ||||||||
\(238\) | −3.46692e29 | −0.680350 | ||||||||
\(239\) | −7.62279e29 | −1.41952 | −0.709758 | − | 0.704445i | \(-0.751196\pi\) | ||||
−0.709758 | + | 0.704445i | \(0.751196\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.68961e29 | −0.954705 | −0.477352 | − | 0.878712i | \(-0.658403\pi\) | ||||
−0.477352 | + | 0.878712i | \(0.658403\pi\) | |||||||
\(242\) | −6.51553e29 | −1.03814 | ||||||||
\(243\) | −8.28519e29 | −1.25379 | ||||||||
\(244\) | 2.59388e29 | 0.372886 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.31899e30 | 1.71220 | ||||||||
\(247\) | −1.33249e30 | −1.64419 | ||||||||
\(248\) | −2.29404e29 | −0.269126 | ||||||||
\(249\) | −6.38136e29 | −0.711903 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.84848e29 | 0.792253 | 0.396127 | − | 0.918196i | \(-0.370354\pi\) | ||||
0.396127 | + | 0.918196i | \(0.370354\pi\) | |||||||
\(252\) | −7.38986e29 | −0.709789 | ||||||||
\(253\) | 2.07587e30 | 1.89756 | ||||||||
\(254\) | 1.52080e29 | 0.132327 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 7.92282e28 | 0.0625000 | ||||||||
\(257\) | −1.93819e30 | −1.45624 | −0.728119 | − | 0.685450i | \(-0.759605\pi\) | ||||
−0.728119 | + | 0.685450i | \(0.759605\pi\) | |||||||
\(258\) | 6.84722e29 | 0.490081 | ||||||||
\(259\) | 3.42041e30 | 2.33255 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.73909e29 | −0.479384 | ||||||||
\(262\) | 8.30399e29 | 0.490366 | ||||||||
\(263\) | −7.76661e29 | −0.437305 | −0.218653 | − | 0.975803i | \(-0.570166\pi\) | ||||
−0.218653 | + | 0.975803i | \(0.570166\pi\) | |||||||
\(264\) | 1.37369e30 | 0.737634 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 3.01414e30 | 1.47280 | ||||||||
\(267\) | −1.41033e30 | −0.657551 | ||||||||
\(268\) | 1.45441e30 | 0.647145 | ||||||||
\(269\) | 1.26958e30 | 0.539209 | 0.269604 | − | 0.962971i | \(-0.413107\pi\) | ||||
0.269604 | + | 0.962971i | \(0.413107\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.59506e29 | −0.100469 | −0.0502344 | − | 0.998737i | \(-0.515997\pi\) | ||||
−0.0502344 | + | 0.998737i | \(0.515997\pi\) | |||||||
\(272\) | −3.49948e29 | −0.129388 | ||||||||
\(273\) | 1.02593e31 | 3.62313 | ||||||||
\(274\) | 1.72637e30 | 0.582442 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2.60340e30 | −0.802006 | ||||||||
\(277\) | −4.20101e30 | −1.23696 | −0.618482 | − | 0.785799i | \(-0.712252\pi\) | ||||
−0.618482 | + | 0.785799i | \(0.712252\pi\) | |||||||
\(278\) | 1.07264e30 | 0.301922 | ||||||||
\(279\) | 2.15982e30 | 0.581253 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.34654e30 | 1.80823 | 0.904115 | − | 0.427290i | \(-0.140532\pi\) | ||||
0.904115 | + | 0.427290i | \(0.140532\pi\) | |||||||
\(282\) | −3.52444e30 | −0.829806 | ||||||||
\(283\) | −7.45011e30 | −1.67816 | −0.839078 | − | 0.544011i | \(-0.816905\pi\) | ||||
−0.839078 | + | 0.544011i | \(0.816905\pi\) | |||||||
\(284\) | 7.41339e29 | 0.159785 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −8.25727e30 | −1.63028 | ||||||||
\(287\) | 1.79344e31 | 3.38972 | ||||||||
\(288\) | −7.45926e29 | −0.134986 | ||||||||
\(289\) | −4.22492e30 | −0.732142 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.97891e30 | 0.950517 | ||||||||
\(292\) | 1.34746e30 | 0.205226 | ||||||||
\(293\) | −3.40180e30 | −0.496436 | −0.248218 | − | 0.968704i | \(-0.579845\pi\) | ||||
−0.248218 | + | 0.968704i | \(0.579845\pi\) | |||||||
\(294\) | −1.64921e31 | −2.30640 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3.45254e30 | 0.443601 | ||||||||
\(297\) | 4.00400e30 | 0.493217 | ||||||||
\(298\) | −2.18354e30 | −0.257904 | ||||||||
\(299\) | 1.56490e31 | 1.77255 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.31020e30 | 0.970237 | ||||||||
\(302\) | 4.71839e29 | 0.0471745 | ||||||||
\(303\) | 1.70340e31 | 1.63412 | ||||||||
\(304\) | 3.04245e30 | 0.280093 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 3.29473e30 | 0.279449 | ||||||||
\(307\) | −2.05490e31 | −1.67325 | −0.836624 | − | 0.547778i | \(-0.815474\pi\) | ||||
−0.836624 | + | 0.547778i | \(0.815474\pi\) | |||||||
\(308\) | 1.86782e31 | 1.46033 | ||||||||
\(309\) | −1.35770e31 | −1.01935 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.23094e28 | −0.00500829 | −0.00250415 | − | 0.999997i | \(-0.500797\pi\) | ||||
−0.00250415 | + | 0.999997i | \(0.500797\pi\) | |||||||
\(312\) | 1.03556e31 | 0.689040 | ||||||||
\(313\) | −1.14602e31 | −0.732635 | −0.366318 | − | 0.930490i | \(-0.619382\pi\) | ||||
−0.366318 | + | 0.930490i | \(0.619382\pi\) | |||||||
\(314\) | 2.91300e30 | 0.178945 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.51125e30 | −0.482953 | ||||||||
\(317\) | 2.43704e31 | 1.32929 | 0.664647 | − | 0.747158i | \(-0.268582\pi\) | ||||
0.664647 | + | 0.747158i | \(0.268582\pi\) | |||||||
\(318\) | −1.88248e31 | −0.987170 | ||||||||
\(319\) | 1.95609e31 | 0.986292 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.79646e31 | −1.30406 | ||||||||
\(322\) | −3.53986e31 | −1.58777 | ||||||||
\(323\) | −1.34384e31 | −0.579850 | ||||||||
\(324\) | −1.42185e31 | −0.590258 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.01830e31 | 0.775828 | ||||||||
\(327\) | 4.79689e31 | 1.77465 | ||||||||
\(328\) | 1.81029e31 | 0.644650 | ||||||||
\(329\) | −4.79220e31 | −1.64281 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.61088e31 | −1.14753 | −0.573764 | − | 0.819021i | \(-0.694517\pi\) | ||||
−0.573764 | + | 0.819021i | \(0.694517\pi\) | |||||||
\(332\) | −8.75825e30 | −0.268035 | ||||||||
\(333\) | −3.25053e31 | −0.958079 | ||||||||
\(334\) | 6.34252e29 | 0.0180066 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2.34248e31 | −0.617212 | ||||||||
\(337\) | −5.01811e31 | −1.27399 | −0.636995 | − | 0.770868i | \(-0.719823\pi\) | ||||
−0.636995 | + | 0.770868i | \(0.719823\pi\) | |||||||
\(338\) | −3.33446e31 | −0.815767 | ||||||||
\(339\) | −3.60813e31 | −0.850718 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.45905e31 | −1.19588 | ||||||||
\(342\) | −2.86443e31 | −0.604940 | ||||||||
\(343\) | −1.32944e32 | −2.70703 | ||||||||
\(344\) | 9.39763e30 | 0.184518 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5.11756e31 | −0.934569 | ||||||||
\(347\) | −2.69651e31 | −0.474988 | −0.237494 | − | 0.971389i | \(-0.576326\pi\) | ||||
−0.237494 | + | 0.971389i | \(0.576326\pi\) | |||||||
\(348\) | −2.45318e31 | −0.416859 | ||||||||
\(349\) | 4.66669e31 | 0.765052 | 0.382526 | − | 0.923945i | \(-0.375054\pi\) | ||||
0.382526 | + | 0.923945i | \(0.375054\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.01842e31 | 0.460725 | ||||||||
\(352\) | 1.88536e31 | 0.277723 | ||||||||
\(353\) | −6.63592e31 | −0.943446 | −0.471723 | − | 0.881747i | \(-0.656368\pi\) | ||||
−0.471723 | + | 0.881747i | \(0.656368\pi\) | |||||||
\(354\) | 3.45310e31 | 0.473879 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.93564e31 | −0.247571 | ||||||||
\(357\) | 1.03466e32 | 1.27775 | ||||||||
\(358\) | −7.42985e31 | −0.886017 | ||||||||
\(359\) | −7.18124e31 | −0.827025 | −0.413513 | − | 0.910498i | \(-0.635698\pi\) | ||||
−0.413513 | + | 0.910498i | \(0.635698\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.37566e31 | 0.255238 | ||||||||
\(362\) | 9.35254e31 | 0.970672 | ||||||||
\(363\) | 1.94449e32 | 1.94972 | ||||||||
\(364\) | 1.40806e32 | 1.36413 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −7.74114e31 | −0.700311 | ||||||||
\(367\) | 8.09654e31 | 0.707903 | 0.353951 | − | 0.935264i | \(-0.384838\pi\) | ||||
0.353951 | + | 0.935264i | \(0.384838\pi\) | |||||||
\(368\) | −3.57310e31 | −0.301959 | ||||||||
\(369\) | −1.70437e32 | −1.39230 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.55962e32 | −1.95435 | ||||||||
\(372\) | 6.84632e31 | 0.505441 | ||||||||
\(373\) | 1.63975e32 | 1.17063 | 0.585313 | − | 0.810807i | \(-0.300972\pi\) | ||||
0.585313 | + | 0.810807i | \(0.300972\pi\) | |||||||
\(374\) | −8.32758e31 | −0.574942 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.83721e31 | −0.312426 | ||||||||
\(377\) | 1.47460e32 | 0.921316 | ||||||||
\(378\) | −6.82777e31 | −0.412697 | ||||||||
\(379\) | −5.11219e31 | −0.298963 | −0.149481 | − | 0.988765i | \(-0.547760\pi\) | ||||
−0.149481 | + | 0.988765i | \(0.547760\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.53865e31 | −0.248522 | ||||||||
\(382\) | 1.59050e32 | 0.842833 | ||||||||
\(383\) | 2.90570e32 | 1.49028 | 0.745138 | − | 0.666911i | \(-0.232384\pi\) | ||||
0.745138 | + | 0.666911i | \(0.232384\pi\) | |||||||
\(384\) | −2.36448e31 | −0.117380 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.11366e32 | 0.983317 | ||||||||
\(387\) | −8.84778e31 | −0.398518 | ||||||||
\(388\) | 8.20591e31 | 0.357874 | ||||||||
\(389\) | 9.70428e31 | 0.409820 | 0.204910 | − | 0.978781i | \(-0.434310\pi\) | ||||
0.204910 | + | 0.978781i | \(0.434310\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.57823e32 | 0.625116 | ||||||||
\(392\) | −2.26350e32 | −0.868371 | ||||||||
\(393\) | −2.47823e32 | −0.920948 | ||||||||
\(394\) | 1.80051e32 | 0.648176 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.77505e32 | −0.599820 | ||||||||
\(397\) | 4.94379e32 | 1.61875 | 0.809373 | − | 0.587295i | \(-0.199807\pi\) | ||||
0.809373 | + | 0.587295i | \(0.199807\pi\) | |||||||
\(398\) | −2.82404e32 | −0.896051 | ||||||||
\(399\) | −8.99536e32 | −2.76603 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.47162e31 | 0.129170 | 0.0645848 | − | 0.997912i | \(-0.479428\pi\) | ||||
0.0645848 | + | 0.997912i | \(0.479428\pi\) | |||||||
\(402\) | −4.34052e32 | −1.21539 | ||||||||
\(403\) | −4.11531e32 | −1.11709 | ||||||||
\(404\) | 2.33788e32 | 0.615255 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.33560e32 | −0.825275 | ||||||||
\(407\) | 8.21587e32 | 1.97117 | ||||||||
\(408\) | 1.04438e32 | 0.243001 | ||||||||
\(409\) | 3.47804e32 | 0.784863 | 0.392431 | − | 0.919781i | \(-0.371634\pi\) | ||||
0.392431 | + | 0.919781i | \(0.371634\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.15217e32 | −1.09387 | ||||||||
\(412\) | −1.86341e32 | −0.383789 | ||||||||
\(413\) | 4.69519e32 | 0.938162 | ||||||||
\(414\) | 3.36404e32 | 0.652165 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.42128e32 | 0.259427 | ||||||||
\(417\) | −3.20119e32 | −0.567035 | ||||||||
\(418\) | 7.23999e32 | 1.24461 | ||||||||
\(419\) | −1.64856e32 | −0.275061 | −0.137531 | − | 0.990498i | \(-0.543917\pi\) | ||||
−0.137531 | + | 0.990498i | \(0.543917\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.59846e32 | 0.722914 | 0.361457 | − | 0.932389i | \(-0.382279\pi\) | ||||
0.361457 | + | 0.932389i | \(0.382279\pi\) | |||||||
\(422\) | −8.37951e32 | −1.27883 | ||||||||
\(423\) | 4.55419e32 | 0.674771 | ||||||||
\(424\) | −2.58366e32 | −0.371674 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −2.21244e32 | −0.300090 | ||||||||
\(427\) | −1.05257e33 | −1.38644 | ||||||||
\(428\) | −3.83808e32 | −0.490983 | ||||||||
\(429\) | 2.46429e33 | 3.06179 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.08014e32 | 0.829996 | 0.414998 | − | 0.909822i | \(-0.363782\pi\) | ||||
0.414998 | + | 0.909822i | \(0.363782\pi\) | |||||||
\(432\) | −6.89190e31 | −0.0784860 | ||||||||
\(433\) | 1.74438e32 | 0.192993 | 0.0964964 | − | 0.995333i | \(-0.469236\pi\) | ||||
0.0964964 | + | 0.995333i | \(0.469236\pi\) | |||||||
\(434\) | 9.30898e32 | 1.00065 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.58361e32 | 0.668164 | ||||||||
\(437\) | −1.37211e33 | −1.35323 | ||||||||
\(438\) | −4.02136e32 | −0.385431 | ||||||||
\(439\) | −9.83917e32 | −0.916541 | −0.458271 | − | 0.888813i | \(-0.651531\pi\) | ||||
−0.458271 | + | 0.888813i | \(0.651531\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.13107e33 | 1.87549 | ||||||||
\(442\) | −6.27777e32 | −0.537065 | ||||||||
\(443\) | −9.66613e32 | −0.803908 | −0.401954 | − | 0.915660i | \(-0.631669\pi\) | ||||
−0.401954 | + | 0.915660i | \(0.631669\pi\) | |||||||
\(444\) | −1.03037e33 | −0.833118 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.62624e33 | −1.24308 | ||||||||
\(447\) | 6.51654e32 | 0.484365 | ||||||||
\(448\) | −3.21499e32 | −0.232383 | ||||||||
\(449\) | 5.74227e32 | 0.403650 | 0.201825 | − | 0.979422i | \(-0.435313\pi\) | ||||
0.201825 | + | 0.979422i | \(0.435313\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.30787e33 | 2.86454 | ||||||||
\(452\) | −4.95207e32 | −0.320299 | ||||||||
\(453\) | −1.40815e32 | −0.0885977 | ||||||||
\(454\) | −1.25488e33 | −0.768078 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −9.07984e32 | −0.526039 | ||||||||
\(457\) | 3.19404e33 | 1.80048 | 0.900238 | − | 0.435398i | \(-0.143392\pi\) | ||||
0.900238 | + | 0.435398i | \(0.143392\pi\) | |||||||
\(458\) | −1.19803e32 | −0.0657128 | ||||||||
\(459\) | 3.04413e32 | 0.162482 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.15114e33 | 1.08745 | 0.543723 | − | 0.839264i | \(-0.317014\pi\) | ||||
0.543723 | + | 0.839264i | \(0.317014\pi\) | |||||||
\(462\) | −5.57430e33 | −2.74262 | ||||||||
\(463\) | 6.57140e32 | 0.314699 | 0.157350 | − | 0.987543i | \(-0.449705\pi\) | ||||
0.157350 | + | 0.987543i | \(0.449705\pi\) | |||||||
\(464\) | −3.36693e32 | −0.156949 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.22893e33 | −0.542880 | ||||||||
\(467\) | 1.92599e32 | 0.0828312 | 0.0414156 | − | 0.999142i | \(-0.486813\pi\) | ||||
0.0414156 | + | 0.999142i | \(0.486813\pi\) | |||||||
\(468\) | −1.33813e33 | −0.560304 | ||||||||
\(469\) | −5.90183e33 | −2.40617 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.69352e32 | −0.336074 | ||||||||
\(472\) | 4.73929e32 | 0.178418 | ||||||||
\(473\) | 2.23632e33 | 0.819916 | ||||||||
\(474\) | 2.54009e33 | 0.907026 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.42005e33 | 0.481080 | ||||||||
\(477\) | 2.43249e33 | 0.802734 | ||||||||
\(478\) | 3.12230e33 | 1.00375 | ||||||||
\(479\) | 3.90669e33 | 1.22353 | 0.611766 | − | 0.791039i | \(-0.290459\pi\) | ||||
0.611766 | + | 0.791039i | \(0.290459\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.19355e33 | 1.84131 | ||||||||
\(482\) | 2.33046e33 | 0.675078 | ||||||||
\(483\) | 1.05643e34 | 2.98196 | ||||||||
\(484\) | 2.66876e33 | 0.734079 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 3.39361e33 | 0.886562 | ||||||||
\(487\) | 4.17680e33 | 1.06349 | 0.531743 | − | 0.846906i | \(-0.321537\pi\) | ||||
0.531743 | + | 0.846906i | \(0.321537\pi\) | |||||||
\(488\) | −1.06245e33 | −0.263670 | ||||||||
\(489\) | −6.02339e33 | −1.45707 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.40550e33 | −0.323083 | −0.161541 | − | 0.986866i | \(-0.551647\pi\) | ||||
−0.161541 | + | 0.986866i | \(0.551647\pi\) | |||||||
\(492\) | −5.40260e33 | −1.21071 | ||||||||
\(493\) | 1.48716e33 | 0.324916 | ||||||||
\(494\) | 5.45788e33 | 1.16262 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9.39640e32 | 0.190301 | ||||||||
\(497\) | −3.00827e33 | −0.594103 | ||||||||
\(498\) | 2.61380e33 | 0.503392 | ||||||||
\(499\) | 8.69572e32 | 0.163323 | 0.0816617 | − | 0.996660i | \(-0.473977\pi\) | ||||
0.0816617 | + | 0.996660i | \(0.473977\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.89285e32 | −0.0338178 | ||||||||
\(502\) | −3.21474e33 | −0.560208 | ||||||||
\(503\) | −7.81824e33 | −1.32895 | −0.664476 | − | 0.747310i | \(-0.731345\pi\) | ||||
−0.664476 | + | 0.747310i | \(0.731345\pi\) | |||||||
\(504\) | 3.02688e33 | 0.501897 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −8.50278e33 | −1.34177 | ||||||||
\(507\) | 9.95131e33 | 1.53208 | ||||||||
\(508\) | −6.22918e32 | −0.0935696 | ||||||||
\(509\) | −7.92846e33 | −1.16203 | −0.581014 | − | 0.813894i | \(-0.697344\pi\) | ||||
−0.581014 | + | 0.813894i | \(0.697344\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.46786e33 | −0.763056 | ||||||||
\(512\) | −3.24519e32 | −0.0441942 | ||||||||
\(513\) | −2.64656e33 | −0.351734 | ||||||||
\(514\) | 7.93883e33 | 1.02972 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2.80462e33 | −0.346539 | ||||||||
\(517\) | −1.15109e34 | −1.38828 | ||||||||
\(518\) | −1.40100e34 | −1.64936 | ||||||||
\(519\) | 1.52728e34 | 1.75520 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.29787e33 | −0.361212 | −0.180606 | − | 0.983556i | \(-0.557806\pi\) | ||||
−0.180606 | + | 0.983556i | \(0.557806\pi\) | |||||||
\(522\) | 3.16993e33 | 0.338976 | ||||||||
\(523\) | −1.60818e33 | −0.167905 | −0.0839524 | − | 0.996470i | \(-0.526754\pi\) | ||||
−0.0839524 | + | 0.996470i | \(0.526754\pi\) | |||||||
\(524\) | −3.40131e33 | −0.346741 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.18120e33 | 0.309221 | ||||||||
\(527\) | −4.15036e33 | −0.393961 | ||||||||
\(528\) | −5.62665e33 | −0.521586 | ||||||||
\(529\) | 5.06855e33 | 0.458868 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.46199e33 | −0.385343 | ||||||||
\(532\) | −1.23459e34 | −1.04142 | ||||||||
\(533\) | 3.24750e34 | 2.67583 | ||||||||
\(534\) | 5.77671e33 | 0.464959 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −5.95726e33 | −0.457601 | ||||||||
\(537\) | 2.21736e34 | 1.66401 | ||||||||
\(538\) | −5.20020e33 | −0.381278 | ||||||||
\(539\) | −5.38637e34 | −3.85866 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.05559e34 | −0.721990 | −0.360995 | − | 0.932568i | \(-0.617563\pi\) | ||||
−0.360995 | + | 0.932568i | \(0.617563\pi\) | |||||||
\(542\) | 1.06294e33 | 0.0710422 | ||||||||
\(543\) | −2.79116e34 | −1.82300 | ||||||||
\(544\) | 1.43339e33 | 0.0914908 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −4.20220e34 | −2.56194 | ||||||||
\(547\) | 2.41768e34 | 1.44065 | 0.720324 | − | 0.693638i | \(-0.243993\pi\) | ||||
0.720324 | + | 0.693638i | \(0.243993\pi\) | |||||||
\(548\) | −7.07122e33 | −0.411848 | ||||||||
\(549\) | 1.00029e34 | 0.569470 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.29294e34 | −0.703367 | ||||||||
\(552\) | 1.06635e34 | 0.567104 | ||||||||
\(553\) | 3.45377e34 | 1.79568 | ||||||||
\(554\) | 1.72073e34 | 0.874665 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.39355e33 | −0.213491 | ||||||||
\(557\) | −1.98926e34 | −0.945153 | −0.472576 | − | 0.881290i | \(-0.656676\pi\) | ||||
−0.472576 | + | 0.881290i | \(0.656676\pi\) | |||||||
\(558\) | −8.84662e33 | −0.411008 | ||||||||
\(559\) | 1.68585e34 | 0.765901 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.48527e34 | 1.07979 | ||||||||
\(562\) | −3.00914e34 | −1.27861 | ||||||||
\(563\) | −3.43624e34 | −1.42800 | −0.714001 | − | 0.700145i | \(-0.753119\pi\) | ||||
−0.714001 | + | 0.700145i | \(0.753119\pi\) | |||||||
\(564\) | 1.44361e34 | 0.586762 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 3.05157e34 | 1.18664 | ||||||||
\(567\) | 5.76972e34 | 2.19466 | ||||||||
\(568\) | −3.03652e33 | −0.112985 | ||||||||
\(569\) | −4.74393e34 | −1.72677 | −0.863386 | − | 0.504544i | \(-0.831661\pi\) | ||||
−0.863386 | + | 0.504544i | \(0.831661\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.26964e33 | −0.148744 | −0.0743721 | − | 0.997231i | \(-0.523695\pi\) | ||||
−0.0743721 | + | 0.997231i | \(0.523695\pi\) | |||||||
\(572\) | 3.38218e34 | 1.15278 | ||||||||
\(573\) | −4.74667e34 | −1.58291 | ||||||||
\(574\) | −7.34594e34 | −2.39689 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 3.05531e33 | 0.0954497 | ||||||||
\(577\) | −1.96194e34 | −0.599775 | −0.299887 | − | 0.953975i | \(-0.596949\pi\) | ||||
−0.299887 | + | 0.953975i | \(0.596949\pi\) | |||||||
\(578\) | 1.73053e34 | 0.517702 | ||||||||
\(579\) | −6.30798e34 | −1.84675 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.55400e34 | 0.996589 | ||||||||
\(582\) | −2.44896e34 | −0.672117 | ||||||||
\(583\) | −6.14824e34 | −1.65156 | ||||||||
\(584\) | −5.51921e33 | −0.145116 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.39338e34 | 0.351033 | ||||||||
\(587\) | 4.23298e34 | 1.04393 | 0.521963 | − | 0.852968i | \(-0.325200\pi\) | ||||
0.521963 | + | 0.852968i | \(0.325200\pi\) | |||||||
\(588\) | 6.75518e34 | 1.63087 | ||||||||
\(589\) | 3.60832e34 | 0.852832 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.37343e34 | −1.21733 | ||||||||
\(592\) | −1.41416e34 | −0.313673 | ||||||||
\(593\) | −2.29135e34 | −0.497631 | −0.248816 | − | 0.968551i | \(-0.580041\pi\) | ||||
−0.248816 | + | 0.968551i | \(0.580041\pi\) | |||||||
\(594\) | −1.64004e34 | −0.348757 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 8.94379e33 | 0.182366 | ||||||||
\(597\) | 8.42804e34 | 1.68286 | ||||||||
\(598\) | −6.40984e34 | −1.25338 | ||||||||
\(599\) | 1.21937e34 | 0.233508 | 0.116754 | − | 0.993161i | \(-0.462751\pi\) | ||||
0.116754 | + | 0.993161i | \(0.462751\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.38798e33 | −0.0438631 | −0.0219315 | − | 0.999759i | \(-0.506982\pi\) | ||||
−0.0219315 | + | 0.999759i | \(0.506982\pi\) | |||||||
\(602\) | −3.81346e34 | −0.686061 | ||||||||
\(603\) | 5.60870e34 | 0.988317 | ||||||||
\(604\) | −1.93265e33 | −0.0333574 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −6.97714e34 | −1.15550 | ||||||||
\(607\) | 2.92481e34 | 0.474504 | 0.237252 | − | 0.971448i | \(-0.423753\pi\) | ||||
0.237252 | + | 0.971448i | \(0.423753\pi\) | |||||||
\(608\) | −1.24619e34 | −0.198056 | ||||||||
\(609\) | 9.95473e34 | 1.54993 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.67754e34 | −1.29682 | ||||||||
\(612\) | −1.34952e34 | −0.197600 | ||||||||
\(613\) | −6.94539e34 | −0.996416 | −0.498208 | − | 0.867057i | \(-0.666008\pi\) | ||||
−0.498208 | + | 0.867057i | \(0.666008\pi\) | |||||||
\(614\) | 8.41686e34 | 1.18316 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7.65059e34 | −1.03261 | ||||||||
\(617\) | 4.20916e34 | 0.556713 | 0.278356 | − | 0.960478i | \(-0.410210\pi\) | ||||
0.278356 | + | 0.960478i | \(0.410210\pi\) | |||||||
\(618\) | 5.56114e34 | 0.720788 | ||||||||
\(619\) | 5.93194e34 | 0.753466 | 0.376733 | − | 0.926322i | \(-0.377047\pi\) | ||||
0.376733 | + | 0.926322i | \(0.377047\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.10817e34 | 0.379193 | ||||||||
\(622\) | 2.96179e32 | 0.00354140 | ||||||||
\(623\) | 7.85462e34 | 0.920502 | ||||||||
\(624\) | −4.24167e34 | −0.487225 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 4.69410e34 | 0.518051 | ||||||||
\(627\) | −2.16069e35 | −2.33749 | ||||||||
\(628\) | −1.19316e34 | −0.126533 | ||||||||
\(629\) | 6.24630e34 | 0.649366 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.46762e35 | 1.46638 | 0.733192 | − | 0.680022i | \(-0.238030\pi\) | ||||
0.733192 | + | 0.680022i | \(0.238030\pi\) | |||||||
\(632\) | 3.48621e34 | 0.341499 | ||||||||
\(633\) | 2.50077e35 | 2.40175 | ||||||||
\(634\) | −9.98210e34 | −0.939953 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 7.71065e34 | 0.698034 | ||||||||
\(637\) | −4.06053e35 | −3.60446 | ||||||||
\(638\) | −8.01215e34 | −0.697414 | ||||||||
\(639\) | 2.85886e34 | 0.244024 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.22792e35 | 1.00796 | 0.503982 | − | 0.863714i | \(-0.331868\pi\) | ||||
0.503982 | + | 0.863714i | \(0.331868\pi\) | |||||||
\(642\) | 1.14543e35 | 0.922107 | ||||||||
\(643\) | −1.26806e34 | −0.100116 | −0.0500579 | − | 0.998746i | \(-0.515941\pi\) | ||||
−0.0500579 | + | 0.998746i | \(0.515941\pi\) | |||||||
\(644\) | 1.44993e35 | 1.12272 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.50436e34 | 0.410016 | ||||||||
\(647\) | −3.01852e34 | −0.220541 | −0.110271 | − | 0.993902i | \(-0.535172\pi\) | ||||
−0.110271 | + | 0.993902i | \(0.535172\pi\) | |||||||
\(648\) | 5.82391e34 | 0.417376 | ||||||||
\(649\) | 1.12779e35 | 0.792811 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.77816e35 | −1.87930 | ||||||||
\(652\) | −8.26696e34 | −0.548594 | ||||||||
\(653\) | −1.81062e35 | −1.17872 | −0.589361 | − | 0.807870i | \(-0.700620\pi\) | ||||
−0.589361 | + | 0.807870i | \(0.700620\pi\) | |||||||
\(654\) | −1.96481e35 | −1.25487 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −7.41493e34 | −0.455836 | ||||||||
\(657\) | 5.19629e34 | 0.313420 | ||||||||
\(658\) | 1.96289e35 | 1.16164 | ||||||||
\(659\) | −2.69289e35 | −1.56369 | −0.781847 | − | 0.623471i | \(-0.785722\pi\) | ||||
−0.781847 | + | 0.623471i | \(0.785722\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.11605e35 | 1.74215 | 0.871075 | − | 0.491150i | \(-0.163423\pi\) | ||||
0.871075 | + | 0.491150i | \(0.163423\pi\) | |||||||
\(662\) | 1.47902e35 | 0.811424 | ||||||||
\(663\) | 1.87353e35 | 1.00865 | ||||||||
\(664\) | 3.58738e34 | 0.189529 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.33142e35 | 0.677464 | ||||||||
\(667\) | 1.51845e35 | 0.758276 | ||||||||
\(668\) | −2.59789e33 | −0.0127326 | ||||||||
\(669\) | 4.85334e35 | 2.33461 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.52828e35 | −1.17164 | ||||||||
\(672\) | 9.59479e34 | 0.436435 | ||||||||
\(673\) | 1.24919e35 | 0.557752 | 0.278876 | − | 0.960327i | \(-0.410038\pi\) | ||||
0.278876 | + | 0.960327i | \(0.410038\pi\) | |||||||
\(674\) | 2.05542e35 | 0.900848 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.36579e35 | 0.576834 | ||||||||
\(677\) | −2.88499e35 | −1.19615 | −0.598075 | − | 0.801440i | \(-0.704067\pi\) | ||||
−0.598075 | + | 0.801440i | \(0.704067\pi\) | |||||||
\(678\) | 1.47789e35 | 0.601549 | ||||||||
\(679\) | −3.32987e35 | −1.33062 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.74506e35 | 1.44251 | ||||||||
\(682\) | 2.23603e35 | 0.845614 | ||||||||
\(683\) | −3.81708e34 | −0.141733 | −0.0708667 | − | 0.997486i | \(-0.522577\pi\) | ||||
−0.0708667 | + | 0.997486i | \(0.522577\pi\) | |||||||
\(684\) | 1.17327e35 | 0.427757 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 5.44540e35 | 1.91416 | ||||||||
\(687\) | 3.57539e34 | 0.123414 | ||||||||
\(688\) | −3.84927e34 | −0.130474 | ||||||||
\(689\) | −4.63486e35 | −1.54275 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.01041e35 | −0.645372 | −0.322686 | − | 0.946506i | \(-0.604586\pi\) | ||||
−0.322686 | + | 0.946506i | \(0.604586\pi\) | |||||||
\(692\) | 2.09615e35 | 0.660840 | ||||||||
\(693\) | 7.20296e35 | 2.23021 | ||||||||
\(694\) | 1.10449e35 | 0.335867 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.00482e35 | 0.294764 | ||||||||
\(697\) | 3.27515e35 | 0.943673 | ||||||||
\(698\) | −1.91148e35 | −0.540974 | ||||||||
\(699\) | 3.66761e35 | 1.01957 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.78724e35 | 0.479411 | 0.239705 | − | 0.970846i | \(-0.422949\pi\) | ||||
0.239705 | + | 0.970846i | \(0.422949\pi\) | |||||||
\(702\) | −1.23635e35 | −0.325781 | ||||||||
\(703\) | −5.43052e35 | −1.40572 | ||||||||
\(704\) | −7.72244e34 | −0.196380 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.71807e35 | 0.667117 | ||||||||
\(707\) | −9.48686e35 | −2.28760 | ||||||||
\(708\) | −1.41439e35 | −0.335083 | ||||||||
\(709\) | 5.59205e33 | 0.0130165 | 0.00650824 | − | 0.999979i | \(-0.497928\pi\) | ||||
0.00650824 | + | 0.999979i | \(0.497928\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.28223e35 | −0.737564 | ||||||||
\(712\) | 7.92839e34 | 0.175059 | ||||||||
\(713\) | −4.23768e35 | −0.919409 | ||||||||
\(714\) | −4.23799e35 | −0.903508 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.04327e35 | 0.626509 | ||||||||
\(717\) | −9.31815e35 | −1.88512 | ||||||||
\(718\) | 2.94144e35 | 0.584795 | ||||||||
\(719\) | 3.90750e35 | 0.763463 | 0.381732 | − | 0.924273i | \(-0.375328\pi\) | ||||
0.381732 | + | 0.924273i | \(0.375328\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.56151e35 | 1.42698 | ||||||||
\(722\) | −9.73071e34 | −0.180480 | ||||||||
\(723\) | −6.95501e35 | −1.26785 | ||||||||
\(724\) | −3.83080e35 | −0.686369 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −7.96462e35 | −1.37866 | ||||||||
\(727\) | 9.31579e35 | 1.58504 | 0.792518 | − | 0.609848i | \(-0.208770\pi\) | ||||
0.792518 | + | 0.609848i | \(0.208770\pi\) | |||||||
\(728\) | −5.76742e35 | −0.964582 | ||||||||
\(729\) | −2.94718e35 | −0.484520 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.70021e35 | 0.270107 | ||||||||
\(732\) | 3.17077e35 | 0.495195 | ||||||||
\(733\) | −2.49884e35 | −0.383653 | −0.191826 | − | 0.981429i | \(-0.561441\pi\) | ||||
−0.191826 | + | 0.981429i | \(0.561441\pi\) | |||||||
\(734\) | −3.31634e35 | −0.500563 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.46354e35 | 0.213517 | ||||||||
\(737\) | −1.41763e36 | −2.03338 | ||||||||
\(738\) | 6.98109e35 | 0.984506 | ||||||||
\(739\) | −1.12909e35 | −0.156558 | −0.0782788 | − | 0.996932i | \(-0.524942\pi\) | ||||
−0.0782788 | + | 0.996932i | \(0.524942\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.62885e36 | −2.18349 | ||||||||
\(742\) | 1.04842e36 | 1.38193 | ||||||||
\(743\) | −3.71494e35 | −0.481495 | −0.240748 | − | 0.970588i | \(-0.577393\pi\) | ||||
−0.240748 | + | 0.970588i | \(0.577393\pi\) | |||||||
\(744\) | −2.80425e35 | −0.357401 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −6.71643e35 | −0.827758 | ||||||||
\(747\) | −3.37748e35 | −0.409342 | ||||||||
\(748\) | 3.41098e35 | 0.406545 | ||||||||
\(749\) | 1.55745e36 | 1.82554 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.99646e35 | −0.793194 | −0.396597 | − | 0.917993i | \(-0.629809\pi\) | ||||
−0.396597 | + | 0.917993i | \(0.629809\pi\) | |||||||
\(752\) | 1.98132e35 | 0.220918 | ||||||||
\(753\) | 9.59403e35 | 1.05212 | ||||||||
\(754\) | −6.03998e35 | −0.651469 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.79666e35 | 0.291821 | ||||||||
\(757\) | −7.64525e35 | −0.784681 | −0.392341 | − | 0.919820i | \(-0.628335\pi\) | ||||
−0.392341 | + | 0.919820i | \(0.628335\pi\) | |||||||
\(758\) | 2.09395e35 | 0.211399 | ||||||||
\(759\) | 2.53756e36 | 2.51996 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.74903e35 | −0.744628 | −0.372314 | − | 0.928107i | \(-0.621436\pi\) | ||||
−0.372314 | + | 0.928107i | \(0.621436\pi\) | |||||||
\(762\) | 1.85903e35 | 0.175731 | ||||||||
\(763\) | −2.67156e36 | −2.48432 | ||||||||
\(764\) | −6.51468e35 | −0.595973 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.19018e36 | −1.05378 | ||||||||
\(767\) | 8.50187e35 | 0.740581 | ||||||||
\(768\) | 9.68490e34 | 0.0830003 | ||||||||
\(769\) | −1.04301e36 | −0.879447 | −0.439723 | − | 0.898133i | \(-0.644923\pi\) | ||||
−0.439723 | + | 0.898133i | \(0.644923\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.36926e36 | −1.93389 | ||||||||
\(772\) | −8.65755e35 | −0.695310 | ||||||||
\(773\) | 1.42237e36 | 1.12400 | 0.562002 | − | 0.827136i | \(-0.310031\pi\) | ||||
0.562002 | + | 0.827136i | \(0.310031\pi\) | |||||||
\(774\) | 3.62405e35 | 0.281794 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −3.36114e35 | −0.253055 | ||||||||
\(777\) | 4.18114e36 | 3.09764 | ||||||||
\(778\) | −3.97487e35 | −0.289786 | ||||||||
\(779\) | −2.84741e36 | −2.04283 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.22590e35 | −0.502058 | ||||||||
\(782\) | −6.46443e35 | −0.442024 | ||||||||
\(783\) | 2.92882e35 | 0.197093 | ||||||||
\(784\) | 9.27131e35 | 0.614031 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.01508e36 | 0.651209 | ||||||||
\(787\) | 2.40737e36 | 1.52005 | 0.760026 | − | 0.649892i | \(-0.225186\pi\) | ||||
0.760026 | + | 0.649892i | \(0.225186\pi\) | |||||||
\(788\) | −7.37489e35 | −0.458330 | ||||||||
\(789\) | −9.49395e35 | −0.580743 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.00949e36 | 1.19092 | ||||||||
\(792\) | 7.27061e35 | 0.424137 | ||||||||
\(793\) | −1.90595e36 | −1.09445 | ||||||||
\(794\) | −2.02498e36 | −1.14463 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.15673e36 | 0.633604 | ||||||||
\(797\) | −9.73330e35 | −0.524845 | −0.262423 | − | 0.964953i | \(-0.584521\pi\) | ||||
−0.262423 | + | 0.964953i | \(0.584521\pi\) | |||||||
\(798\) | 3.68450e36 | 1.95588 | ||||||||
\(799\) | −8.75143e35 | −0.457345 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.46450e35 | −0.378089 | ||||||||
\(802\) | −1.83158e35 | −0.0913368 | ||||||||
\(803\) | −1.31339e36 | −0.644834 | ||||||||
\(804\) | 1.77788e36 | 0.859412 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.68563e36 | 0.789905 | ||||||||
\(807\) | 1.55194e36 | 0.716072 | ||||||||
\(808\) | −9.57595e35 | −0.435051 | ||||||||
\(809\) | 3.20638e36 | 1.43436 | 0.717179 | − | 0.696889i | \(-0.245433\pi\) | ||||
0.717179 | + | 0.696889i | \(0.245433\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.99227e36 | 1.29790 | 0.648948 | − | 0.760833i | \(-0.275209\pi\) | ||||
0.648948 | + | 0.760833i | \(0.275209\pi\) | |||||||
\(812\) | 1.36626e36 | 0.583558 | ||||||||
\(813\) | −3.17222e35 | −0.133423 | ||||||||
\(814\) | −3.36522e36 | −1.39383 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −4.27779e35 | −0.171827 | ||||||||
\(817\) | −1.47816e36 | −0.584717 | ||||||||
\(818\) | −1.42461e36 | −0.554982 | ||||||||
\(819\) | 5.42997e36 | 2.08328 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.26235e36 | −1.58621 | −0.793103 | − | 0.609087i | \(-0.791536\pi\) | ||||
−0.793103 | + | 0.609087i | \(0.791536\pi\) | |||||||
\(822\) | 2.11033e36 | 0.773485 | ||||||||
\(823\) | 5.35214e36 | 1.93210 | 0.966051 | − | 0.258352i | \(-0.0831796\pi\) | ||||
0.966051 | + | 0.258352i | \(0.0831796\pi\) | |||||||
\(824\) | 7.63252e35 | 0.271380 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.92315e36 | −0.663381 | ||||||||
\(827\) | 3.57743e36 | 1.21549 | 0.607747 | − | 0.794131i | \(-0.292074\pi\) | ||||
0.607747 | + | 0.794131i | \(0.292074\pi\) | |||||||
\(828\) | −1.37791e36 | −0.461150 | ||||||||
\(829\) | −4.26555e36 | −1.40619 | −0.703095 | − | 0.711096i | \(-0.748199\pi\) | ||||
−0.703095 | + | 0.711096i | \(0.748199\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.13534e36 | −1.64269 | ||||||||
\(832\) | −5.82158e35 | −0.183442 | ||||||||
\(833\) | −4.09511e36 | −1.27117 | ||||||||
\(834\) | 1.31121e36 | 0.400955 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2.96550e36 | −0.880075 | ||||||||
\(837\) | −8.17374e35 | −0.238975 | ||||||||
\(838\) | 6.75250e35 | 0.194498 | ||||||||
\(839\) | −5.62994e36 | −1.59764 | −0.798820 | − | 0.601570i | \(-0.794542\pi\) | ||||
−0.798820 | + | 0.601570i | \(0.794542\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.19953e36 | −0.605871 | ||||||||
\(842\) | −1.88353e36 | −0.511177 | ||||||||
\(843\) | 8.98045e36 | 2.40134 | ||||||||
\(844\) | 3.43225e36 | 0.904269 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.86540e36 | −0.477135 | ||||||||
\(847\) | −1.08295e37 | −2.72940 | ||||||||
\(848\) | 1.05827e36 | 0.262813 | ||||||||
\(849\) | −9.10706e36 | −2.22860 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.37771e36 | 1.51546 | ||||||||
\(852\) | 9.06217e35 | 0.212196 | ||||||||
\(853\) | −4.55647e36 | −1.05139 | −0.525697 | − | 0.850672i | \(-0.676195\pi\) | ||||
−0.525697 | + | 0.850672i | \(0.676195\pi\) | |||||||
\(854\) | 4.31131e36 | 0.980361 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.57208e36 | 0.347178 | ||||||||
\(857\) | 7.95266e35 | 0.173082 | 0.0865411 | − | 0.996248i | \(-0.472419\pi\) | ||||
0.0865411 | + | 0.996248i | \(0.472419\pi\) | |||||||
\(858\) | −1.00937e37 | −2.16501 | ||||||||
\(859\) | 1.26545e36 | 0.267505 | 0.133752 | − | 0.991015i | \(-0.457297\pi\) | ||||
0.133752 | + | 0.991015i | \(0.457297\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.19231e37 | 4.50156 | ||||||||
\(862\) | −2.90003e36 | −0.586896 | ||||||||
\(863\) | −3.32635e36 | −0.663487 | −0.331744 | − | 0.943370i | \(-0.607637\pi\) | ||||
−0.331744 | + | 0.943370i | \(0.607637\pi\) | |||||||
\(864\) | 2.82292e35 | 0.0554979 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −7.14496e35 | −0.136467 | ||||||||
\(867\) | −5.16456e36 | −0.972288 | ||||||||
\(868\) | −3.81296e36 | −0.707563 | ||||||||
\(869\) | 8.29600e36 | 1.51747 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.06868e37 | −1.89942 | ||||||||
\(872\) | −2.69665e36 | −0.472463 | ||||||||
\(873\) | 3.16448e36 | 0.546543 | ||||||||
\(874\) | 5.62016e36 | 0.956877 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.64715e36 | 0.272541 | ||||||||
\(877\) | −5.26043e36 | −0.858078 | −0.429039 | − | 0.903286i | \(-0.641148\pi\) | ||||
−0.429039 | + | 0.903286i | \(0.641148\pi\) | |||||||
\(878\) | 4.03012e36 | 0.648093 | ||||||||
\(879\) | −4.15838e36 | −0.659269 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.34809e36 | 0.824137 | 0.412069 | − | 0.911153i | \(-0.364806\pi\) | ||||
0.412069 | + | 0.911153i | \(0.364806\pi\) | |||||||
\(882\) | −8.72885e36 | −1.32617 | ||||||||
\(883\) | −3.32166e36 | −0.497560 | −0.248780 | − | 0.968560i | \(-0.580030\pi\) | ||||
−0.248780 | + | 0.968560i | \(0.580030\pi\) | |||||||
\(884\) | 2.57137e36 | 0.379762 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.95925e36 | 0.568449 | ||||||||
\(887\) | −8.17924e36 | −1.15789 | −0.578945 | − | 0.815366i | \(-0.696536\pi\) | ||||
−0.578945 | + | 0.815366i | \(0.696536\pi\) | |||||||
\(888\) | 4.22040e36 | 0.589104 | ||||||||
\(889\) | 2.52773e36 | 0.347904 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.38589e37 | 1.85464 | ||||||||
\(892\) | 6.66109e36 | 0.878991 | ||||||||
\(893\) | 7.60848e36 | 0.990045 | ||||||||
\(894\) | −2.66917e36 | −0.342498 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.31686e36 | 0.164320 | ||||||||
\(897\) | 1.91295e37 | 2.35395 | ||||||||
\(898\) | −2.35204e36 | −0.285423 | ||||||||
\(899\) | −3.99315e36 | −0.477881 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.67433e36 | −0.544076 | ||||||||
\(902\) | −1.76450e37 | −2.02554 | ||||||||
\(903\) | 1.13808e37 | 1.28848 | ||||||||
\(904\) | 2.02837e36 | 0.226486 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 5.76779e35 | 0.0626480 | ||||||||
\(907\) | 1.71298e37 | 1.83511 | 0.917553 | − | 0.397615i | \(-0.130162\pi\) | ||||
0.917553 | + | 0.397615i | \(0.130162\pi\) | |||||||
\(908\) | 5.14000e36 | 0.543113 | ||||||||
\(909\) | 9.01567e36 | 0.939614 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.12131e36 | 0.620676 | 0.310338 | − | 0.950626i | \(-0.399558\pi\) | ||||
0.310338 | + | 0.950626i | \(0.399558\pi\) | |||||||
\(912\) | 3.71910e36 | 0.371966 | ||||||||
\(913\) | 8.53675e36 | 0.842186 | ||||||||
\(914\) | −1.30828e37 | −1.27313 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.90714e35 | 0.0464660 | ||||||||
\(917\) | 1.38022e37 | 1.28923 | ||||||||
\(918\) | −1.24687e36 | −0.114892 | ||||||||
\(919\) | −1.52693e36 | −0.138795 | −0.0693977 | − | 0.997589i | \(-0.522108\pi\) | ||||
−0.0693977 | + | 0.997589i | \(0.522108\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.51192e37 | −2.22208 | ||||||||
\(922\) | −8.81109e36 | −0.768941 | ||||||||
\(923\) | −5.44726e36 | −0.468983 | ||||||||
\(924\) | 2.28323e37 | 1.93933 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −2.69165e36 | −0.222526 | ||||||||
\(927\) | −7.18595e36 | −0.586121 | ||||||||
\(928\) | 1.37909e36 | 0.110980 | ||||||||
\(929\) | 1.93910e36 | 0.153959 | 0.0769793 | − | 0.997033i | \(-0.475472\pi\) | ||||
0.0769793 | + | 0.997033i | \(0.475472\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.56028e37 | 2.75178 | ||||||||
\(932\) | 5.03370e36 | 0.383874 | ||||||||
\(933\) | −8.83914e34 | −0.00665104 | ||||||||
\(934\) | −7.88887e35 | −0.0585705 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 5.48097e36 | 0.396195 | ||||||||
\(937\) | 1.01514e37 | 0.724069 | 0.362035 | − | 0.932165i | \(-0.382082\pi\) | ||||
0.362035 | + | 0.932165i | \(0.382082\pi\) | |||||||
\(938\) | 2.41739e37 | 1.70142 | ||||||||
\(939\) | −1.40090e37 | −0.972944 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.58463e36 | 0.310051 | 0.155026 | − | 0.987910i | \(-0.450454\pi\) | ||||
0.155026 | + | 0.987910i | \(0.450454\pi\) | |||||||
\(942\) | 3.56087e36 | 0.237640 | ||||||||
\(943\) | 3.34405e37 | 2.20230 | ||||||||
\(944\) | −1.94121e36 | −0.126160 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.15996e36 | −0.579768 | ||||||||
\(947\) | −2.00468e37 | −1.25219 | −0.626094 | − | 0.779748i | \(-0.715347\pi\) | ||||
−0.626094 | + | 0.779748i | \(0.715347\pi\) | |||||||
\(948\) | −1.04042e37 | −0.641364 | ||||||||
\(949\) | −9.90099e36 | −0.602353 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.97905e37 | 1.76531 | ||||||||
\(952\) | −5.81653e36 | −0.340175 | ||||||||
\(953\) | −2.53894e37 | −1.46552 | −0.732758 | − | 0.680489i | \(-0.761767\pi\) | ||||
−0.732758 | + | 0.680489i | \(0.761767\pi\) | |||||||
\(954\) | −9.96348e36 | −0.567619 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.27889e37 | −0.709758 | ||||||||
\(957\) | 2.39114e37 | 1.30980 | ||||||||
\(958\) | −1.60018e37 | −0.865168 | ||||||||
\(959\) | 2.86942e37 | 1.53131 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.08873e36 | −0.420570 | ||||||||
\(962\) | −2.53688e37 | −1.30200 | ||||||||
\(963\) | −1.48010e37 | −0.749827 | ||||||||
\(964\) | −9.54557e36 | −0.477352 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −4.32715e37 | −2.10857 | ||||||||
\(967\) | 3.53299e37 | 1.69946 | 0.849731 | − | 0.527216i | \(-0.176764\pi\) | ||||
0.849731 | + | 0.527216i | \(0.176764\pi\) | |||||||
\(968\) | −1.09312e37 | −0.519072 | ||||||||
\(969\) | −1.64272e37 | −0.770043 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.42162e37 | −1.10628 | −0.553141 | − | 0.833088i | \(-0.686571\pi\) | ||||
−0.553141 | + | 0.833088i | \(0.686571\pi\) | |||||||
\(972\) | −1.39002e37 | −0.626894 | ||||||||
\(973\) | 1.78285e37 | 0.793789 | ||||||||
\(974\) | −1.71082e37 | −0.751998 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.35180e36 | 0.186443 | ||||||||
\(977\) | −2.74750e36 | −0.116213 | −0.0581066 | − | 0.998310i | \(-0.518506\pi\) | ||||
−0.0581066 | + | 0.998310i | \(0.518506\pi\) | |||||||
\(978\) | 2.46718e37 | 1.03030 | ||||||||
\(979\) | 1.88669e37 | 0.777887 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.53887e37 | 1.02042 | ||||||||
\(982\) | 5.75695e36 | 0.228454 | ||||||||
\(983\) | 2.03235e37 | 0.796303 | 0.398152 | − | 0.917320i | \(-0.369652\pi\) | ||||
0.398152 | + | 0.917320i | \(0.369652\pi\) | |||||||
\(984\) | 2.21290e37 | 0.856099 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −6.09141e36 | −0.229751 | ||||||||
\(987\) | −5.85802e37 | −2.18166 | ||||||||
\(988\) | −2.23555e37 | −0.822096 | ||||||||
\(989\) | 1.73598e37 | 0.630363 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.72765e37 | 0.611695 | 0.305847 | − | 0.952081i | \(-0.401060\pi\) | ||||
0.305847 | + | 0.952081i | \(0.401060\pi\) | |||||||
\(992\) | −3.84877e36 | −0.134563 | ||||||||
\(993\) | −4.41396e37 | −1.52392 | ||||||||
\(994\) | 1.23219e37 | 0.420095 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.07061e37 | −0.355952 | ||||||||
\(997\) | −7.90582e36 | −0.259572 | −0.129786 | − | 0.991542i | \(-0.541429\pi\) | ||||
−0.129786 | + | 0.991542i | \(0.541429\pi\) | |||||||
\(998\) | −3.56177e36 | −0.115487 | ||||||||
\(999\) | 1.23015e37 | 0.393903 |
(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 | 50.26.a.i.1.5 | ✓ | 5 | |
5.2 | odd | 4 | 50.26.b.h.49.1 | 10 | |||
5.3 | odd | 4 | 50.26.b.h.49.10 | 10 | |||
5.4 | even | 2 | 50.26.a.j.1.1 | yes | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
50.26.a.i.1.5 | ✓ | 5 | 1.1 | even | 1 | trivial | |
50.26.a.j.1.1 | yes | 5 | 5.4 | even | 2 | ||
50.26.b.h.49.1 | 10 | 5.2 | odd | 4 | |||
50.26.b.h.49.10 | 10 | 5.3 | odd | 4 |