Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,106,Mod(1,1)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 106, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 106);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 106 \) |
Character orbit: | \([\chi]\) | \(=\) | 1.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: | \(69.8187388595\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + \cdots + 48\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | multiple of \( 2^{111}\cdot 3^{44}\cdot 5^{13}\cdot 7^{7}\cdot 11\cdot 13^{3}\cdot 17 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-9.82818e12\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.56214e15 | −0.402279 | −0.201140 | − | 0.979563i | \(-0.564464\pi\) | ||||
−0.201140 | + | 0.979563i | \(0.564464\pi\) | |||||||
\(3\) | 7.24197e24 | 0.647129 | 0.323564 | − | 0.946206i | \(-0.395119\pi\) | ||||
0.323564 | + | 0.946206i | \(0.395119\pi\) | |||||||
\(4\) | −3.40003e31 | −0.838171 | ||||||||
\(5\) | −1.17115e36 | −0.235878 | −0.117939 | − | 0.993021i | \(-0.537629\pi\) | ||||
−0.117939 | + | 0.993021i | \(0.537629\pi\) | |||||||
\(6\) | −1.85549e40 | −0.260326 | ||||||||
\(7\) | −1.82598e44 | −0.783156 | −0.391578 | − | 0.920145i | \(-0.628071\pi\) | ||||
−0.391578 | + | 0.920145i | \(0.628071\pi\) | |||||||
\(8\) | 1.91046e47 | 0.739458 | ||||||||
\(9\) | −7.27906e49 | −0.581224 | ||||||||
\(10\) | 3.00065e51 | 0.0948888 | ||||||||
\(11\) | 6.21211e54 | 1.31863 | 0.659316 | − | 0.751866i | \(-0.270846\pi\) | ||||
0.659316 | + | 0.751866i | \(0.270846\pi\) | |||||||
\(12\) | −2.46229e56 | −0.542405 | ||||||||
\(13\) | 9.87817e57 | 0.325575 | 0.162787 | − | 0.986661i | \(-0.447952\pi\) | ||||
0.162787 | + | 0.986661i | \(0.447952\pi\) | |||||||
\(14\) | 4.67841e59 | 0.315048 | ||||||||
\(15\) | −8.48143e60 | −0.152643 | ||||||||
\(16\) | 8.89729e62 | 0.540703 | ||||||||
\(17\) | 1.10681e64 | 0.278935 | 0.139468 | − | 0.990227i | \(-0.455461\pi\) | ||||
0.139468 | + | 0.990227i | \(0.455461\pi\) | |||||||
\(18\) | 1.86500e65 | 0.233814 | ||||||||
\(19\) | 1.61722e67 | 1.18633 | 0.593165 | − | 0.805081i | \(-0.297878\pi\) | ||||
0.593165 | + | 0.805081i | \(0.297878\pi\) | |||||||
\(20\) | 3.98194e67 | 0.197706 | ||||||||
\(21\) | −1.32237e69 | −0.506803 | ||||||||
\(22\) | −1.59163e70 | −0.530458 | ||||||||
\(23\) | −2.39949e71 | −0.775188 | −0.387594 | − | 0.921830i | \(-0.626694\pi\) | ||||
−0.387594 | + | 0.921830i | \(0.626694\pi\) | |||||||
\(24\) | 1.38355e72 | 0.478525 | ||||||||
\(25\) | −2.32803e73 | −0.944362 | ||||||||
\(26\) | −2.53092e73 | −0.130972 | ||||||||
\(27\) | −1.43411e75 | −1.02326 | ||||||||
\(28\) | 6.20838e75 | 0.656419 | ||||||||
\(29\) | 4.95038e76 | 0.829360 | 0.414680 | − | 0.909967i | \(-0.363893\pi\) | ||||
0.414680 | + | 0.909967i | \(0.363893\pi\) | |||||||
\(30\) | 2.17306e76 | 0.0614053 | ||||||||
\(31\) | 8.41659e76 | 0.0425253 | 0.0212627 | − | 0.999774i | \(-0.493231\pi\) | ||||
0.0212627 | + | 0.999774i | \(0.493231\pi\) | |||||||
\(32\) | −1.00294e79 | −0.956972 | ||||||||
\(33\) | 4.49879e79 | 0.853324 | ||||||||
\(34\) | −2.83579e79 | −0.112210 | ||||||||
\(35\) | 2.13850e80 | 0.184729 | ||||||||
\(36\) | 2.47490e81 | 0.487166 | ||||||||
\(37\) | 2.33838e82 | 1.09226 | 0.546129 | − | 0.837701i | \(-0.316101\pi\) | ||||
0.546129 | + | 0.837701i | \(0.316101\pi\) | |||||||
\(38\) | −4.14355e82 | −0.477236 | ||||||||
\(39\) | 7.15374e82 | 0.210689 | ||||||||
\(40\) | −2.23744e83 | −0.174422 | ||||||||
\(41\) | 3.56271e84 | 0.759676 | 0.379838 | − | 0.925053i | \(-0.375980\pi\) | ||||
0.379838 | + | 0.925053i | \(0.375980\pi\) | |||||||
\(42\) | 3.38809e84 | 0.203876 | ||||||||
\(43\) | −2.88851e85 | −0.505336 | −0.252668 | − | 0.967553i | \(-0.581308\pi\) | ||||
−0.252668 | + | 0.967553i | \(0.581308\pi\) | |||||||
\(44\) | −2.11214e86 | −1.10524 | ||||||||
\(45\) | 8.52488e85 | 0.137098 | ||||||||
\(46\) | 6.14782e86 | 0.311842 | ||||||||
\(47\) | 8.77673e86 | 0.143944 | 0.0719722 | − | 0.997407i | \(-0.477071\pi\) | ||||
0.0719722 | + | 0.997407i | \(0.477071\pi\) | |||||||
\(48\) | 6.44339e87 | 0.349904 | ||||||||
\(49\) | −2.10199e88 | −0.386666 | ||||||||
\(50\) | 5.96474e88 | 0.379897 | ||||||||
\(51\) | 8.01546e88 | 0.180507 | ||||||||
\(52\) | −3.35860e89 | −0.272887 | ||||||||
\(53\) | −1.32848e90 | −0.397074 | −0.198537 | − | 0.980093i | \(-0.563619\pi\) | ||||
−0.198537 | + | 0.980093i | \(0.563619\pi\) | |||||||
\(54\) | 3.67438e90 | 0.411635 | ||||||||
\(55\) | −7.27532e90 | −0.311036 | ||||||||
\(56\) | −3.48846e91 | −0.579111 | ||||||||
\(57\) | 1.17119e92 | 0.767709 | ||||||||
\(58\) | −1.26835e92 | −0.333634 | ||||||||
\(59\) | 9.30110e92 | 0.997250 | 0.498625 | − | 0.866818i | \(-0.333839\pi\) | ||||
0.498625 | + | 0.866818i | \(0.333839\pi\) | |||||||
\(60\) | 2.88371e92 | 0.127941 | ||||||||
\(61\) | −9.36850e93 | −1.74523 | −0.872617 | − | 0.488406i | \(-0.837579\pi\) | ||||
−0.872617 | + | 0.488406i | \(0.837579\pi\) | |||||||
\(62\) | −2.15645e92 | −0.0171070 | ||||||||
\(63\) | 1.32914e94 | 0.455190 | ||||||||
\(64\) | −1.03951e94 | −0.155733 | ||||||||
\(65\) | −1.15688e94 | −0.0767959 | ||||||||
\(66\) | −1.15265e95 | −0.343275 | ||||||||
\(67\) | −4.39312e95 | −0.594081 | −0.297040 | − | 0.954865i | \(-0.596000\pi\) | ||||
−0.297040 | + | 0.954865i | \(0.596000\pi\) | |||||||
\(68\) | −3.76317e95 | −0.233796 | ||||||||
\(69\) | −1.73770e96 | −0.501647 | ||||||||
\(70\) | −5.47912e95 | −0.0743128 | ||||||||
\(71\) | −2.93219e97 | −1.88855 | −0.944276 | − | 0.329154i | \(-0.893236\pi\) | ||||
−0.944276 | + | 0.329154i | \(0.893236\pi\) | |||||||
\(72\) | −1.39064e97 | −0.429791 | ||||||||
\(73\) | −6.72839e97 | −1.00800 | −0.504000 | − | 0.863703i | \(-0.668139\pi\) | ||||
−0.504000 | + | 0.863703i | \(0.668139\pi\) | |||||||
\(74\) | −5.99126e97 | −0.439393 | ||||||||
\(75\) | −1.68595e98 | −0.611124 | ||||||||
\(76\) | −5.49860e98 | −0.994349 | ||||||||
\(77\) | −1.13432e99 | −1.03269 | ||||||||
\(78\) | −1.83289e98 | −0.0847557 | ||||||||
\(79\) | −7.95646e99 | −1.88494 | −0.942470 | − | 0.334290i | \(-0.891503\pi\) | ||||
−0.942470 | + | 0.334290i | \(0.891503\pi\) | |||||||
\(80\) | −1.04201e99 | −0.127540 | ||||||||
\(81\) | −1.26970e99 | −0.0809539 | ||||||||
\(82\) | −9.12816e99 | −0.305602 | ||||||||
\(83\) | 6.25680e100 | 1.10854 | 0.554272 | − | 0.832336i | \(-0.312997\pi\) | ||||
0.554272 | + | 0.832336i | \(0.312997\pi\) | |||||||
\(84\) | 4.49609e100 | 0.424788 | ||||||||
\(85\) | −1.29624e100 | −0.0657947 | ||||||||
\(86\) | 7.40076e100 | 0.203286 | ||||||||
\(87\) | 3.58505e101 | 0.536703 | ||||||||
\(88\) | 1.18680e102 | 0.975073 | ||||||||
\(89\) | 3.11302e102 | 1.41321 | 0.706606 | − | 0.707607i | \(-0.250225\pi\) | ||||
0.706606 | + | 0.707607i | \(0.250225\pi\) | |||||||
\(90\) | −2.18419e101 | −0.0551517 | ||||||||
\(91\) | −1.80373e102 | −0.254976 | ||||||||
\(92\) | 8.15832e102 | 0.649740 | ||||||||
\(93\) | 6.09527e101 | 0.0275193 | ||||||||
\(94\) | −2.24872e102 | −0.0579059 | ||||||||
\(95\) | −1.89401e103 | −0.279829 | ||||||||
\(96\) | −7.26323e103 | −0.619284 | ||||||||
\(97\) | −3.96647e104 | −1.96285 | −0.981427 | − | 0.191838i | \(-0.938555\pi\) | ||||
−0.981427 | + | 0.191838i | \(0.938555\pi\) | |||||||
\(98\) | 5.38558e103 | 0.155548 | ||||||||
\(99\) | −4.52184e104 | −0.766421 | ||||||||
\(100\) | 7.91537e104 | 0.791537 | ||||||||
\(101\) | −1.19764e105 | −0.710319 | −0.355160 | − | 0.934806i | \(-0.615573\pi\) | ||||
−0.355160 | + | 0.934806i | \(0.615573\pi\) | |||||||
\(102\) | −2.05367e104 | −0.0726142 | ||||||||
\(103\) | 1.60564e105 | 0.340169 | 0.170085 | − | 0.985429i | \(-0.445596\pi\) | ||||
0.170085 | + | 0.985429i | \(0.445596\pi\) | |||||||
\(104\) | 1.88718e105 | 0.240749 | ||||||||
\(105\) | 1.54869e105 | 0.119544 | ||||||||
\(106\) | 3.40374e105 | 0.159734 | ||||||||
\(107\) | 4.52744e106 | 1.29779 | 0.648895 | − | 0.760878i | \(-0.275231\pi\) | ||||
0.648895 | + | 0.760878i | \(0.275231\pi\) | |||||||
\(108\) | 4.87601e106 | 0.857664 | ||||||||
\(109\) | −1.52154e106 | −0.164965 | −0.0824826 | − | 0.996593i | \(-0.526285\pi\) | ||||
−0.0824826 | + | 0.996593i | \(0.526285\pi\) | |||||||
\(110\) | 1.86404e106 | 0.125123 | ||||||||
\(111\) | 1.69345e107 | 0.706832 | ||||||||
\(112\) | −1.62463e107 | −0.423455 | ||||||||
\(113\) | −9.69099e107 | −1.58398 | −0.791990 | − | 0.610534i | \(-0.790955\pi\) | ||||
−0.791990 | + | 0.610534i | \(0.790955\pi\) | |||||||
\(114\) | −3.00074e107 | −0.308833 | ||||||||
\(115\) | 2.81016e107 | 0.182850 | ||||||||
\(116\) | −1.68314e108 | −0.695146 | ||||||||
\(117\) | −7.19038e107 | −0.189232 | ||||||||
\(118\) | −2.38307e108 | −0.401173 | ||||||||
\(119\) | −2.02101e108 | −0.218450 | ||||||||
\(120\) | −1.62034e108 | −0.112873 | ||||||||
\(121\) | 1.63965e109 | 0.738789 | ||||||||
\(122\) | 2.40034e109 | 0.702071 | ||||||||
\(123\) | 2.58011e109 | 0.491608 | ||||||||
\(124\) | −2.86166e108 | −0.0356435 | ||||||||
\(125\) | 5.61358e109 | 0.458632 | ||||||||
\(126\) | −3.40544e109 | −0.183113 | ||||||||
\(127\) | 9.27636e109 | 0.329369 | 0.164684 | − | 0.986346i | \(-0.447339\pi\) | ||||
0.164684 | + | 0.986346i | \(0.447339\pi\) | |||||||
\(128\) | 4.33473e110 | 1.01962 | ||||||||
\(129\) | −2.09185e110 | −0.327017 | ||||||||
\(130\) | 2.96409e109 | 0.0308934 | ||||||||
\(131\) | −2.18559e111 | −1.52344 | −0.761721 | − | 0.647905i | \(-0.775645\pi\) | ||||
−0.761721 | + | 0.647905i | \(0.775645\pi\) | |||||||
\(132\) | −1.52960e111 | −0.715232 | ||||||||
\(133\) | −2.95301e111 | −0.929083 | ||||||||
\(134\) | 1.12558e111 | 0.238986 | ||||||||
\(135\) | 1.67956e111 | 0.241364 | ||||||||
\(136\) | 2.11451e111 | 0.206261 | ||||||||
\(137\) | −3.76107e111 | −0.249736 | −0.124868 | − | 0.992173i | \(-0.539851\pi\) | ||||
−0.124868 | + | 0.992173i | \(0.539851\pi\) | |||||||
\(138\) | 4.45223e111 | 0.201802 | ||||||||
\(139\) | 3.64309e112 | 1.13030 | 0.565149 | − | 0.824989i | \(-0.308819\pi\) | ||||
0.565149 | + | 0.824989i | \(0.308819\pi\) | |||||||
\(140\) | −7.27094e111 | −0.154835 | ||||||||
\(141\) | 6.35608e111 | 0.0931506 | ||||||||
\(142\) | 7.51268e112 | 0.759725 | ||||||||
\(143\) | 6.13643e112 | 0.429313 | ||||||||
\(144\) | −6.47639e112 | −0.314270 | ||||||||
\(145\) | −5.79763e112 | −0.195628 | ||||||||
\(146\) | 1.72391e113 | 0.405498 | ||||||||
\(147\) | −1.52225e113 | −0.250223 | ||||||||
\(148\) | −7.95057e113 | −0.915500 | ||||||||
\(149\) | −6.94410e113 | −0.561483 | −0.280742 | − | 0.959783i | \(-0.590580\pi\) | ||||
−0.280742 | + | 0.959783i | \(0.590580\pi\) | |||||||
\(150\) | 4.31964e113 | 0.245842 | ||||||||
\(151\) | −4.13611e114 | −1.66074 | −0.830372 | − | 0.557210i | \(-0.811872\pi\) | ||||
−0.830372 | + | 0.557210i | \(0.811872\pi\) | |||||||
\(152\) | 3.08964e114 | 0.877242 | ||||||||
\(153\) | −8.05652e113 | −0.162124 | ||||||||
\(154\) | 2.90628e114 | 0.415432 | ||||||||
\(155\) | −9.85710e112 | −0.0100308 | ||||||||
\(156\) | −2.43229e114 | −0.176593 | ||||||||
\(157\) | 2.62565e115 | 1.36303 | 0.681515 | − | 0.731804i | \(-0.261321\pi\) | ||||
0.681515 | + | 0.731804i | \(0.261321\pi\) | |||||||
\(158\) | 2.03855e115 | 0.758272 | ||||||||
\(159\) | −9.62079e114 | −0.256958 | ||||||||
\(160\) | 1.17459e115 | 0.225729 | ||||||||
\(161\) | 4.38141e115 | 0.607094 | ||||||||
\(162\) | 3.25315e114 | 0.0325661 | ||||||||
\(163\) | −2.06745e116 | −1.49825 | −0.749126 | − | 0.662428i | \(-0.769526\pi\) | ||||
−0.749126 | + | 0.662428i | \(0.769526\pi\) | |||||||
\(164\) | −1.21133e116 | −0.636739 | ||||||||
\(165\) | −5.26876e115 | −0.201280 | ||||||||
\(166\) | −1.60308e116 | −0.445944 | ||||||||
\(167\) | 6.33450e116 | 1.28558 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(168\) | −2.52633e116 | −0.374760 | ||||||||
\(169\) | −8.22982e116 | −0.894001 | ||||||||
\(170\) | 3.32114e115 | 0.0264678 | ||||||||
\(171\) | −1.17719e117 | −0.689524 | ||||||||
\(172\) | 9.82101e116 | 0.423558 | ||||||||
\(173\) | 4.01565e117 | 1.27742 | 0.638712 | − | 0.769446i | \(-0.279468\pi\) | ||||
0.638712 | + | 0.769446i | \(0.279468\pi\) | |||||||
\(174\) | −9.18538e116 | −0.215904 | ||||||||
\(175\) | 4.25093e117 | 0.739583 | ||||||||
\(176\) | 5.52710e117 | 0.712988 | ||||||||
\(177\) | 6.73583e117 | 0.645349 | ||||||||
\(178\) | −7.97600e117 | −0.568506 | ||||||||
\(179\) | −1.42554e118 | −0.757175 | −0.378587 | − | 0.925566i | \(-0.623590\pi\) | ||||
−0.378587 | + | 0.925566i | \(0.623590\pi\) | |||||||
\(180\) | −2.89848e117 | −0.114912 | ||||||||
\(181\) | 1.74104e117 | 0.0516041 | 0.0258021 | − | 0.999667i | \(-0.491786\pi\) | ||||
0.0258021 | + | 0.999667i | \(0.491786\pi\) | |||||||
\(182\) | 4.62141e117 | 0.102571 | ||||||||
\(183\) | −6.78463e118 | −1.12939 | ||||||||
\(184\) | −4.58412e118 | −0.573219 | ||||||||
\(185\) | −2.73860e118 | −0.257640 | ||||||||
\(186\) | −1.56169e117 | −0.0110705 | ||||||||
\(187\) | 6.87561e118 | 0.367813 | ||||||||
\(188\) | −2.98411e118 | −0.120650 | ||||||||
\(189\) | 2.61865e119 | 0.801369 | ||||||||
\(190\) | 4.85272e118 | 0.112570 | ||||||||
\(191\) | 3.92171e119 | 0.690595 | 0.345297 | − | 0.938493i | \(-0.387778\pi\) | ||||
0.345297 | + | 0.938493i | \(0.387778\pi\) | |||||||
\(192\) | −7.52810e118 | −0.100779 | ||||||||
\(193\) | 5.37554e118 | 0.0547852 | 0.0273926 | − | 0.999625i | \(-0.491280\pi\) | ||||
0.0273926 | + | 0.999625i | \(0.491280\pi\) | |||||||
\(194\) | 1.01626e120 | 0.789615 | ||||||||
\(195\) | −8.37810e118 | −0.0496968 | ||||||||
\(196\) | 7.14681e119 | 0.324092 | ||||||||
\(197\) | −4.45142e120 | −1.54533 | −0.772667 | − | 0.634812i | \(-0.781078\pi\) | ||||
−0.772667 | + | 0.634812i | \(0.781078\pi\) | |||||||
\(198\) | 1.15856e120 | 0.308315 | ||||||||
\(199\) | 1.12654e120 | 0.230122 | 0.115061 | − | 0.993358i | \(-0.463294\pi\) | ||||
0.115061 | + | 0.993358i | \(0.463294\pi\) | |||||||
\(200\) | −4.44761e120 | −0.698316 | ||||||||
\(201\) | −3.18148e120 | −0.384447 | ||||||||
\(202\) | 3.06851e120 | 0.285747 | ||||||||
\(203\) | −9.03928e120 | −0.649519 | ||||||||
\(204\) | −2.72528e120 | −0.151296 | ||||||||
\(205\) | −4.17247e120 | −0.179191 | ||||||||
\(206\) | −4.11388e120 | −0.136843 | ||||||||
\(207\) | 1.74660e121 | 0.450558 | ||||||||
\(208\) | 8.78889e120 | 0.176039 | ||||||||
\(209\) | 1.00464e122 | 1.56433 | ||||||||
\(210\) | −3.96796e120 | −0.0480899 | ||||||||
\(211\) | 1.16814e122 | 1.10323 | 0.551615 | − | 0.834099i | \(-0.314012\pi\) | ||||
0.551615 | + | 0.834099i | \(0.314012\pi\) | |||||||
\(212\) | 4.51686e121 | 0.332816 | ||||||||
\(213\) | −2.12348e122 | −1.22214 | ||||||||
\(214\) | −1.15999e122 | −0.522074 | ||||||||
\(215\) | 3.38288e121 | 0.119198 | ||||||||
\(216\) | −2.73981e122 | −0.756655 | ||||||||
\(217\) | −1.53685e121 | −0.0333040 | ||||||||
\(218\) | 3.89839e121 | 0.0663620 | ||||||||
\(219\) | −4.87268e122 | −0.652306 | ||||||||
\(220\) | 2.47363e122 | 0.260702 | ||||||||
\(221\) | 1.09332e122 | 0.0908142 | ||||||||
\(222\) | −4.33885e122 | −0.284344 | ||||||||
\(223\) | −2.12569e123 | −1.10026 | −0.550130 | − | 0.835079i | \(-0.685422\pi\) | ||||
−0.550130 | + | 0.835079i | \(0.685422\pi\) | |||||||
\(224\) | 1.83134e123 | 0.749459 | ||||||||
\(225\) | 1.69459e123 | 0.548886 | ||||||||
\(226\) | 2.48296e123 | 0.637202 | ||||||||
\(227\) | 5.43051e123 | 1.10531 | 0.552654 | − | 0.833411i | \(-0.313615\pi\) | ||||
0.552654 | + | 0.833411i | \(0.313615\pi\) | |||||||
\(228\) | −3.98207e123 | −0.643472 | ||||||||
\(229\) | 3.86165e123 | 0.495919 | 0.247959 | − | 0.968770i | \(-0.420240\pi\) | ||||
0.247959 | + | 0.968770i | \(0.420240\pi\) | |||||||
\(230\) | −7.20002e122 | −0.0735567 | ||||||||
\(231\) | −8.21470e123 | −0.668286 | ||||||||
\(232\) | 9.45749e123 | 0.613277 | ||||||||
\(233\) | −2.50053e123 | −0.129374 | −0.0646868 | − | 0.997906i | \(-0.520605\pi\) | ||||
−0.0646868 | + | 0.997906i | \(0.520605\pi\) | |||||||
\(234\) | 1.84227e123 | 0.0761241 | ||||||||
\(235\) | −1.02789e123 | −0.0339533 | ||||||||
\(236\) | −3.16240e124 | −0.835866 | ||||||||
\(237\) | −5.76204e124 | −1.21980 | ||||||||
\(238\) | 5.17809e123 | 0.0878779 | ||||||||
\(239\) | 2.77950e124 | 0.378509 | 0.189255 | − | 0.981928i | \(-0.439393\pi\) | ||||
0.189255 | + | 0.981928i | \(0.439393\pi\) | |||||||
\(240\) | −7.54617e123 | −0.0825347 | ||||||||
\(241\) | −7.57110e124 | −0.665678 | −0.332839 | − | 0.942984i | \(-0.608007\pi\) | ||||
−0.332839 | + | 0.942984i | \(0.608007\pi\) | |||||||
\(242\) | −4.20102e124 | −0.297199 | ||||||||
\(243\) | 1.70408e125 | 0.970868 | ||||||||
\(244\) | 3.18531e125 | 1.46280 | ||||||||
\(245\) | 2.46174e124 | 0.0912060 | ||||||||
\(246\) | −6.61059e124 | −0.197764 | ||||||||
\(247\) | 1.59752e125 | 0.386239 | ||||||||
\(248\) | 1.60796e124 | 0.0314457 | ||||||||
\(249\) | 4.53116e125 | 0.717370 | ||||||||
\(250\) | −1.43828e125 | −0.184498 | ||||||||
\(251\) | −6.06940e125 | −0.631357 | −0.315679 | − | 0.948866i | \(-0.602232\pi\) | ||||
−0.315679 | + | 0.948866i | \(0.602232\pi\) | |||||||
\(252\) | −4.51912e125 | −0.381527 | ||||||||
\(253\) | −1.49059e126 | −1.02219 | ||||||||
\(254\) | −2.37673e125 | −0.132498 | ||||||||
\(255\) | −9.38731e124 | −0.0425776 | ||||||||
\(256\) | −6.88941e125 | −0.254439 | ||||||||
\(257\) | 2.79612e126 | 0.841525 | 0.420762 | − | 0.907171i | \(-0.361763\pi\) | ||||
0.420762 | + | 0.907171i | \(0.361763\pi\) | |||||||
\(258\) | 5.35961e125 | 0.131552 | ||||||||
\(259\) | −4.26984e126 | −0.855409 | ||||||||
\(260\) | 3.93343e125 | 0.0643681 | ||||||||
\(261\) | −3.60341e126 | −0.482044 | ||||||||
\(262\) | 5.59979e126 | 0.612849 | ||||||||
\(263\) | 2.58860e126 | 0.231946 | 0.115973 | − | 0.993252i | \(-0.463001\pi\) | ||||
0.115973 | + | 0.993252i | \(0.463001\pi\) | |||||||
\(264\) | 8.59476e126 | 0.630998 | ||||||||
\(265\) | 1.55585e126 | 0.0936609 | ||||||||
\(266\) | 7.56603e126 | 0.373751 | ||||||||
\(267\) | 2.25444e127 | 0.914530 | ||||||||
\(268\) | 1.49367e127 | 0.497941 | ||||||||
\(269\) | −3.07299e127 | −0.842493 | −0.421247 | − | 0.906946i | \(-0.638407\pi\) | ||||
−0.421247 | + | 0.906946i | \(0.638407\pi\) | |||||||
\(270\) | −4.30325e126 | −0.0970955 | ||||||||
\(271\) | −6.80647e127 | −1.26484 | −0.632418 | − | 0.774627i | \(-0.717937\pi\) | ||||
−0.632418 | + | 0.774627i | \(0.717937\pi\) | |||||||
\(272\) | 9.84758e126 | 0.150821 | ||||||||
\(273\) | −1.30626e127 | −0.165002 | ||||||||
\(274\) | 9.63637e126 | 0.100464 | ||||||||
\(275\) | −1.44620e128 | −1.24526 | ||||||||
\(276\) | 5.90823e127 | 0.420466 | ||||||||
\(277\) | 4.37682e127 | 0.257615 | 0.128807 | − | 0.991670i | \(-0.458885\pi\) | ||||
0.128807 | + | 0.991670i | \(0.458885\pi\) | |||||||
\(278\) | −9.33409e127 | −0.454695 | ||||||||
\(279\) | −6.12649e126 | −0.0247167 | ||||||||
\(280\) | 4.08551e127 | 0.136600 | ||||||||
\(281\) | 3.24288e127 | 0.0899184 | 0.0449592 | − | 0.998989i | \(-0.485684\pi\) | ||||
0.0449592 | + | 0.998989i | \(0.485684\pi\) | |||||||
\(282\) | −1.62851e127 | −0.0374726 | ||||||||
\(283\) | 5.75459e128 | 1.09958 | 0.549789 | − | 0.835303i | \(-0.314708\pi\) | ||||
0.549789 | + | 0.835303i | \(0.314708\pi\) | |||||||
\(284\) | 9.96953e128 | 1.58293 | ||||||||
\(285\) | −1.37164e128 | −0.181086 | ||||||||
\(286\) | −1.57224e128 | −0.172704 | ||||||||
\(287\) | −6.50544e128 | −0.594945 | ||||||||
\(288\) | 7.30043e128 | 0.556215 | ||||||||
\(289\) | −1.45198e129 | −0.922195 | ||||||||
\(290\) | 1.48543e128 | 0.0786970 | ||||||||
\(291\) | −2.87250e129 | −1.27022 | ||||||||
\(292\) | 2.28767e129 | 0.844878 | ||||||||
\(293\) | −2.15304e129 | −0.664512 | −0.332256 | − | 0.943189i | \(-0.607810\pi\) | ||||
−0.332256 | + | 0.943189i | \(0.607810\pi\) | |||||||
\(294\) | 3.90022e128 | 0.100659 | ||||||||
\(295\) | −1.08930e129 | −0.235229 | ||||||||
\(296\) | 4.46739e129 | 0.807679 | ||||||||
\(297\) | −8.90884e129 | −1.34930 | ||||||||
\(298\) | 1.77917e129 | 0.225873 | ||||||||
\(299\) | −2.37025e129 | −0.252382 | ||||||||
\(300\) | 5.73228e129 | 0.512226 | ||||||||
\(301\) | 5.27436e129 | 0.395757 | ||||||||
\(302\) | 1.05973e130 | 0.668083 | ||||||||
\(303\) | −8.67326e129 | −0.459668 | ||||||||
\(304\) | 1.43889e130 | 0.641452 | ||||||||
\(305\) | 1.09719e130 | 0.411662 | ||||||||
\(306\) | 2.06419e129 | 0.0652191 | ||||||||
\(307\) | −1.55007e130 | −0.412654 | −0.206327 | − | 0.978483i | \(-0.566151\pi\) | ||||
−0.206327 | + | 0.978483i | \(0.566151\pi\) | |||||||
\(308\) | 3.85671e130 | 0.865575 | ||||||||
\(309\) | 1.16280e130 | 0.220133 | ||||||||
\(310\) | 2.52552e128 | 0.00403518 | ||||||||
\(311\) | −1.05354e131 | −1.42145 | −0.710724 | − | 0.703471i | \(-0.751633\pi\) | ||||
−0.710724 | + | 0.703471i | \(0.751633\pi\) | |||||||
\(312\) | 1.36669e130 | 0.155795 | ||||||||
\(313\) | −1.51544e131 | −1.46036 | −0.730181 | − | 0.683253i | \(-0.760564\pi\) | ||||
−0.730181 | + | 0.683253i | \(0.760564\pi\) | |||||||
\(314\) | −6.72729e130 | −0.548319 | ||||||||
\(315\) | −1.55662e130 | −0.107369 | ||||||||
\(316\) | 2.70522e131 | 1.57990 | ||||||||
\(317\) | −3.01876e131 | −1.49354 | −0.746770 | − | 0.665083i | \(-0.768396\pi\) | ||||
−0.746770 | + | 0.665083i | \(0.768396\pi\) | |||||||
\(318\) | 2.46498e130 | 0.103369 | ||||||||
\(319\) | 3.07523e131 | 1.09362 | ||||||||
\(320\) | 1.21742e130 | 0.0367340 | ||||||||
\(321\) | 3.27876e131 | 0.839837 | ||||||||
\(322\) | −1.12258e131 | −0.244221 | ||||||||
\(323\) | 1.78995e131 | 0.330910 | ||||||||
\(324\) | 4.31702e130 | 0.0678532 | ||||||||
\(325\) | −2.29967e131 | −0.307460 | ||||||||
\(326\) | 5.29708e131 | 0.602716 | ||||||||
\(327\) | −1.10189e131 | −0.106754 | ||||||||
\(328\) | 6.80642e131 | 0.561749 | ||||||||
\(329\) | −1.60261e131 | −0.112731 | ||||||||
\(330\) | 1.34993e131 | 0.0809709 | ||||||||
\(331\) | −1.11942e132 | −0.572828 | −0.286414 | − | 0.958106i | \(-0.592463\pi\) | ||||
−0.286414 | + | 0.958106i | \(0.592463\pi\) | |||||||
\(332\) | −2.12733e132 | −0.929150 | ||||||||
\(333\) | −1.70212e132 | −0.634847 | ||||||||
\(334\) | −1.62299e132 | −0.517160 | ||||||||
\(335\) | 5.14500e131 | 0.140131 | ||||||||
\(336\) | −1.17655e132 | −0.274030 | ||||||||
\(337\) | 6.42673e132 | 1.28062 | 0.640310 | − | 0.768117i | \(-0.278806\pi\) | ||||
0.640310 | + | 0.768117i | \(0.278806\pi\) | |||||||
\(338\) | 2.10859e132 | 0.359638 | ||||||||
\(339\) | −7.01818e132 | −1.02504 | ||||||||
\(340\) | 4.40724e131 | 0.0551472 | ||||||||
\(341\) | 5.22848e131 | 0.0560752 | ||||||||
\(342\) | 3.01611e132 | 0.277381 | ||||||||
\(343\) | 1.37645e133 | 1.08598 | ||||||||
\(344\) | −5.51838e132 | −0.373675 | ||||||||
\(345\) | 2.03511e132 | 0.118327 | ||||||||
\(346\) | −1.02886e133 | −0.513881 | ||||||||
\(347\) | 2.99641e133 | 1.28619 | 0.643093 | − | 0.765788i | \(-0.277651\pi\) | ||||
0.643093 | + | 0.765788i | \(0.277651\pi\) | |||||||
\(348\) | −1.21893e133 | −0.449849 | ||||||||
\(349\) | 4.87919e133 | 1.54886 | 0.774431 | − | 0.632659i | \(-0.218036\pi\) | ||||
0.774431 | + | 0.632659i | \(0.218036\pi\) | |||||||
\(350\) | −1.08915e133 | −0.297519 | ||||||||
\(351\) | −1.41664e133 | −0.333146 | ||||||||
\(352\) | −6.23035e133 | −1.26189 | ||||||||
\(353\) | −5.34299e133 | −0.932421 | −0.466210 | − | 0.884674i | \(-0.654381\pi\) | ||||
−0.466210 | + | 0.884674i | \(0.654381\pi\) | |||||||
\(354\) | −1.72581e133 | −0.259611 | ||||||||
\(355\) | 3.43404e133 | 0.445468 | ||||||||
\(356\) | −1.05844e134 | −1.18451 | ||||||||
\(357\) | −1.46361e133 | −0.141365 | ||||||||
\(358\) | 3.65244e133 | 0.304596 | ||||||||
\(359\) | 7.64396e133 | 0.550630 | 0.275315 | − | 0.961354i | \(-0.411218\pi\) | ||||
0.275315 | + | 0.961354i | \(0.411218\pi\) | |||||||
\(360\) | 1.62864e133 | 0.101378 | ||||||||
\(361\) | 7.57057e133 | 0.407381 | ||||||||
\(362\) | −4.46079e132 | −0.0207593 | ||||||||
\(363\) | 1.18743e134 | 0.478091 | ||||||||
\(364\) | 6.13274e133 | 0.213713 | ||||||||
\(365\) | 7.87995e133 | 0.237765 | ||||||||
\(366\) | 1.73832e134 | 0.454330 | ||||||||
\(367\) | 2.15324e134 | 0.487669 | 0.243834 | − | 0.969817i | \(-0.421595\pi\) | ||||
0.243834 | + | 0.969817i | \(0.421595\pi\) | |||||||
\(368\) | −2.13489e134 | −0.419146 | ||||||||
\(369\) | −2.59332e134 | −0.441542 | ||||||||
\(370\) | 7.01667e133 | 0.103643 | ||||||||
\(371\) | 2.42577e134 | 0.310971 | ||||||||
\(372\) | −2.07241e133 | −0.0230659 | ||||||||
\(373\) | −1.48002e135 | −1.43072 | −0.715358 | − | 0.698758i | \(-0.753737\pi\) | ||||
−0.715358 | + | 0.698758i | \(0.753737\pi\) | |||||||
\(374\) | −1.76163e134 | −0.147963 | ||||||||
\(375\) | 4.06534e134 | 0.296794 | ||||||||
\(376\) | 1.67676e134 | 0.106441 | ||||||||
\(377\) | 4.89006e134 | 0.270019 | ||||||||
\(378\) | −6.70934e134 | −0.322374 | ||||||||
\(379\) | −3.14867e135 | −1.31695 | −0.658474 | − | 0.752604i | \(-0.728798\pi\) | ||||
−0.658474 | + | 0.752604i | \(0.728798\pi\) | |||||||
\(380\) | 6.43969e134 | 0.234545 | ||||||||
\(381\) | 6.71791e134 | 0.213144 | ||||||||
\(382\) | −1.00479e135 | −0.277812 | ||||||||
\(383\) | 2.26604e135 | 0.546176 | 0.273088 | − | 0.961989i | \(-0.411955\pi\) | ||||
0.273088 | + | 0.961989i | \(0.411955\pi\) | |||||||
\(384\) | 3.13919e135 | 0.659825 | ||||||||
\(385\) | 1.32846e135 | 0.243590 | ||||||||
\(386\) | −1.37729e134 | −0.0220389 | ||||||||
\(387\) | 2.10256e135 | 0.293713 | ||||||||
\(388\) | 1.34861e136 | 1.64521 | ||||||||
\(389\) | −7.51665e135 | −0.801070 | −0.400535 | − | 0.916281i | \(-0.631176\pi\) | ||||
−0.400535 | + | 0.916281i | \(0.631176\pi\) | |||||||
\(390\) | 2.14659e134 | 0.0199920 | ||||||||
\(391\) | −2.65577e135 | −0.216227 | ||||||||
\(392\) | −4.01576e135 | −0.285923 | ||||||||
\(393\) | −1.58280e136 | −0.985863 | ||||||||
\(394\) | 1.14052e136 | 0.621656 | ||||||||
\(395\) | 9.31821e135 | 0.444616 | ||||||||
\(396\) | 1.53744e136 | 0.642392 | ||||||||
\(397\) | −4.62294e136 | −1.69206 | −0.846031 | − | 0.533133i | \(-0.821014\pi\) | ||||
−0.846031 | + | 0.533133i | \(0.821014\pi\) | |||||||
\(398\) | −2.88634e135 | −0.0925733 | ||||||||
\(399\) | −2.13856e136 | −0.601236 | ||||||||
\(400\) | −2.07132e136 | −0.510619 | ||||||||
\(401\) | −1.12123e136 | −0.242446 | −0.121223 | − | 0.992625i | \(-0.538682\pi\) | ||||
−0.121223 | + | 0.992625i | \(0.538682\pi\) | |||||||
\(402\) | 8.15139e135 | 0.154655 | ||||||||
\(403\) | 8.31405e134 | 0.0138452 | ||||||||
\(404\) | 4.07200e136 | 0.595369 | ||||||||
\(405\) | 1.48701e135 | 0.0190952 | ||||||||
\(406\) | 2.31599e136 | 0.261288 | ||||||||
\(407\) | 1.45263e137 | 1.44029 | ||||||||
\(408\) | 1.53132e136 | 0.133477 | ||||||||
\(409\) | 8.99941e136 | 0.689827 | 0.344914 | − | 0.938634i | \(-0.387908\pi\) | ||||
0.344914 | + | 0.938634i | \(0.387908\pi\) | |||||||
\(410\) | 1.06905e136 | 0.0720848 | ||||||||
\(411\) | −2.72375e136 | −0.161611 | ||||||||
\(412\) | −5.45923e136 | −0.285120 | ||||||||
\(413\) | −1.69836e137 | −0.781003 | ||||||||
\(414\) | −4.47503e136 | −0.181250 | ||||||||
\(415\) | −7.32766e136 | −0.261481 | ||||||||
\(416\) | −9.90717e136 | −0.311566 | ||||||||
\(417\) | 2.63831e137 | 0.731448 | ||||||||
\(418\) | −2.57402e137 | −0.629299 | ||||||||
\(419\) | 2.61797e137 | 0.564584 | 0.282292 | − | 0.959329i | \(-0.408905\pi\) | ||||
0.282292 | + | 0.959329i | \(0.408905\pi\) | |||||||
\(420\) | −5.26559e136 | −0.100198 | ||||||||
\(421\) | −4.32460e137 | −0.726333 | −0.363166 | − | 0.931724i | \(-0.618304\pi\) | ||||
−0.363166 | + | 0.931724i | \(0.618304\pi\) | |||||||
\(422\) | −2.99294e137 | −0.443807 | ||||||||
\(423\) | −6.38864e136 | −0.0836640 | ||||||||
\(424\) | −2.53800e137 | −0.293619 | ||||||||
\(425\) | −2.57668e137 | −0.263416 | ||||||||
\(426\) | 5.44066e137 | 0.491640 | ||||||||
\(427\) | 1.71067e138 | 1.36679 | ||||||||
\(428\) | −1.53934e138 | −1.08777 | ||||||||
\(429\) | 4.44398e137 | 0.277821 | ||||||||
\(430\) | −8.66740e136 | −0.0479507 | ||||||||
\(431\) | 2.80133e138 | 1.37185 | 0.685926 | − | 0.727672i | \(-0.259397\pi\) | ||||
0.685926 | + | 0.727672i | \(0.259397\pi\) | |||||||
\(432\) | −1.27597e138 | −0.553277 | ||||||||
\(433\) | 3.15333e138 | 1.21103 | 0.605516 | − | 0.795833i | \(-0.292967\pi\) | ||||
0.605516 | + | 0.795833i | \(0.292967\pi\) | |||||||
\(434\) | 3.93763e136 | 0.0133975 | ||||||||
\(435\) | −4.19863e137 | −0.126596 | ||||||||
\(436\) | 5.17328e137 | 0.138269 | ||||||||
\(437\) | −3.88051e138 | −0.919630 | ||||||||
\(438\) | 1.24845e138 | 0.262409 | ||||||||
\(439\) | −2.85338e138 | −0.532075 | −0.266037 | − | 0.963963i | \(-0.585714\pi\) | ||||
−0.266037 | + | 0.963963i | \(0.585714\pi\) | |||||||
\(440\) | −1.38992e138 | −0.229998 | ||||||||
\(441\) | 1.53005e138 | 0.224740 | ||||||||
\(442\) | −2.80124e137 | −0.0365327 | ||||||||
\(443\) | −8.53493e138 | −0.988564 | −0.494282 | − | 0.869302i | \(-0.664569\pi\) | ||||
−0.494282 | + | 0.869302i | \(0.664569\pi\) | |||||||
\(444\) | −5.75778e138 | −0.592446 | ||||||||
\(445\) | −3.64582e138 | −0.333346 | ||||||||
\(446\) | 5.44632e138 | 0.442612 | ||||||||
\(447\) | −5.02889e138 | −0.363352 | ||||||||
\(448\) | 1.89812e138 | 0.121963 | ||||||||
\(449\) | 1.33416e139 | 0.762563 | 0.381282 | − | 0.924459i | \(-0.375483\pi\) | ||||
0.381282 | + | 0.924459i | \(0.375483\pi\) | |||||||
\(450\) | −4.34177e138 | −0.220805 | ||||||||
\(451\) | 2.21320e139 | 1.00173 | ||||||||
\(452\) | 3.29496e139 | 1.32765 | ||||||||
\(453\) | −2.99536e139 | −1.07471 | ||||||||
\(454\) | −1.39137e139 | −0.444643 | ||||||||
\(455\) | 2.11244e138 | 0.0601432 | ||||||||
\(456\) | 2.23751e139 | 0.567689 | ||||||||
\(457\) | 5.91284e139 | 1.33720 | 0.668599 | − | 0.743623i | \(-0.266894\pi\) | ||||
0.668599 | + | 0.743623i | \(0.266894\pi\) | |||||||
\(458\) | −9.89409e138 | −0.199498 | ||||||||
\(459\) | −1.58728e139 | −0.285422 | ||||||||
\(460\) | −9.55462e138 | −0.153259 | ||||||||
\(461\) | −3.82087e139 | −0.546844 | −0.273422 | − | 0.961894i | \(-0.588155\pi\) | ||||
−0.273422 | + | 0.961894i | \(0.588155\pi\) | |||||||
\(462\) | 2.10472e139 | 0.268838 | ||||||||
\(463\) | −1.58389e140 | −1.80602 | −0.903012 | − | 0.429616i | \(-0.858649\pi\) | ||||
−0.903012 | + | 0.429616i | \(0.858649\pi\) | |||||||
\(464\) | 4.40449e139 | 0.448437 | ||||||||
\(465\) | −7.13848e137 | −0.00649121 | ||||||||
\(466\) | 6.40669e138 | 0.0520443 | ||||||||
\(467\) | −1.90647e140 | −1.38386 | −0.691932 | − | 0.721962i | \(-0.743240\pi\) | ||||
−0.691932 | + | 0.721962i | \(0.743240\pi\) | |||||||
\(468\) | 2.44475e139 | 0.158609 | ||||||||
\(469\) | 8.02173e139 | 0.465258 | ||||||||
\(470\) | 2.63359e138 | 0.0136587 | ||||||||
\(471\) | 1.90149e140 | 0.882056 | ||||||||
\(472\) | 1.77694e140 | 0.737425 | ||||||||
\(473\) | −1.79438e140 | −0.666351 | ||||||||
\(474\) | 1.47631e140 | 0.490700 | ||||||||
\(475\) | −3.76495e140 | −1.12033 | ||||||||
\(476\) | 6.87147e139 | 0.183099 | ||||||||
\(477\) | 9.67007e139 | 0.230789 | ||||||||
\(478\) | −7.12146e139 | −0.152266 | ||||||||
\(479\) | 6.06845e140 | 1.16269 | 0.581344 | − | 0.813658i | \(-0.302527\pi\) | ||||
0.581344 | + | 0.813658i | \(0.302527\pi\) | |||||||
\(480\) | 8.50633e139 | 0.146075 | ||||||||
\(481\) | 2.30990e140 | 0.355611 | ||||||||
\(482\) | 1.93982e140 | 0.267788 | ||||||||
\(483\) | 3.17300e140 | 0.392868 | ||||||||
\(484\) | −5.57487e140 | −0.619232 | ||||||||
\(485\) | 4.64533e140 | 0.462994 | ||||||||
\(486\) | −4.36608e140 | −0.390560 | ||||||||
\(487\) | −6.06707e140 | −0.487201 | −0.243601 | − | 0.969876i | \(-0.578329\pi\) | ||||
−0.243601 | + | 0.969876i | \(0.578329\pi\) | |||||||
\(488\) | −1.78981e141 | −1.29053 | ||||||||
\(489\) | −1.49724e141 | −0.969562 | ||||||||
\(490\) | −6.30732e139 | −0.0366903 | ||||||||
\(491\) | 8.94476e140 | 0.467509 | 0.233755 | − | 0.972296i | \(-0.424899\pi\) | ||||
0.233755 | + | 0.972296i | \(0.424899\pi\) | |||||||
\(492\) | −8.77243e140 | −0.412052 | ||||||||
\(493\) | 5.47911e140 | 0.231338 | ||||||||
\(494\) | −4.09307e140 | −0.155376 | ||||||||
\(495\) | 5.29575e140 | 0.180782 | ||||||||
\(496\) | 7.48849e139 | 0.0229935 | ||||||||
\(497\) | 5.35412e141 | 1.47903 | ||||||||
\(498\) | −1.16094e141 | −0.288583 | ||||||||
\(499\) | 6.99369e140 | 0.156469 | 0.0782344 | − | 0.996935i | \(-0.475072\pi\) | ||||
0.0782344 | + | 0.996935i | \(0.475072\pi\) | |||||||
\(500\) | −1.90863e141 | −0.384412 | ||||||||
\(501\) | 4.58742e141 | 0.831933 | ||||||||
\(502\) | 1.55506e141 | 0.253982 | ||||||||
\(503\) | −9.78558e140 | −0.143968 | −0.0719842 | − | 0.997406i | \(-0.522933\pi\) | ||||
−0.0719842 | + | 0.997406i | \(0.522933\pi\) | |||||||
\(504\) | 2.53927e141 | 0.336594 | ||||||||
\(505\) | 1.40261e141 | 0.167549 | ||||||||
\(506\) | 3.81909e141 | 0.411205 | ||||||||
\(507\) | −5.96001e141 | −0.578534 | ||||||||
\(508\) | −3.15399e141 | −0.276067 | ||||||||
\(509\) | −6.84286e141 | −0.540199 | −0.270100 | − | 0.962832i | \(-0.587057\pi\) | ||||
−0.270100 | + | 0.962832i | \(0.587057\pi\) | |||||||
\(510\) | 2.40516e140 | 0.0171281 | ||||||||
\(511\) | 1.22859e142 | 0.789422 | ||||||||
\(512\) | −1.58186e142 | −0.917264 | ||||||||
\(513\) | −2.31927e142 | −1.21392 | ||||||||
\(514\) | −7.16404e141 | −0.338528 | ||||||||
\(515\) | −1.88045e141 | −0.0802384 | ||||||||
\(516\) | 7.11235e141 | 0.274096 | ||||||||
\(517\) | 5.45220e141 | 0.189810 | ||||||||
\(518\) | 1.09399e142 | 0.344113 | ||||||||
\(519\) | 2.90812e142 | 0.826658 | ||||||||
\(520\) | −2.21018e141 | −0.0567873 | ||||||||
\(521\) | −6.61502e142 | −1.53656 | −0.768282 | − | 0.640111i | \(-0.778888\pi\) | ||||
−0.768282 | + | 0.640111i | \(0.778888\pi\) | |||||||
\(522\) | 9.23243e141 | 0.193916 | ||||||||
\(523\) | 2.02789e142 | 0.385218 | 0.192609 | − | 0.981276i | \(-0.438305\pi\) | ||||
0.192609 | + | 0.981276i | \(0.438305\pi\) | |||||||
\(524\) | 7.43107e142 | 1.27691 | ||||||||
\(525\) | 3.07851e142 | 0.478605 | ||||||||
\(526\) | −6.63234e141 | −0.0933072 | ||||||||
\(527\) | 9.31554e140 | 0.0118618 | ||||||||
\(528\) | 4.00271e142 | 0.461395 | ||||||||
\(529\) | −3.82372e142 | −0.399083 | ||||||||
\(530\) | −3.98629e141 | −0.0376778 | ||||||||
\(531\) | −6.77033e142 | −0.579626 | ||||||||
\(532\) | 1.00403e143 | 0.778731 | ||||||||
\(533\) | 3.51931e142 | 0.247331 | ||||||||
\(534\) | −5.77619e142 | −0.367896 | ||||||||
\(535\) | −5.30231e142 | −0.306120 | ||||||||
\(536\) | −8.39287e142 | −0.439298 | ||||||||
\(537\) | −1.03237e143 | −0.489990 | ||||||||
\(538\) | 7.87342e142 | 0.338918 | ||||||||
\(539\) | −1.30578e143 | −0.509870 | ||||||||
\(540\) | −5.71054e142 | −0.202304 | ||||||||
\(541\) | −2.71630e143 | −0.873214 | −0.436607 | − | 0.899652i | \(-0.643820\pi\) | ||||
−0.436607 | + | 0.899652i | \(0.643820\pi\) | |||||||
\(542\) | 1.74391e143 | 0.508817 | ||||||||
\(543\) | 1.26086e142 | 0.0333945 | ||||||||
\(544\) | −1.11006e143 | −0.266933 | ||||||||
\(545\) | 1.78195e142 | 0.0389116 | ||||||||
\(546\) | 3.34681e142 | 0.0663770 | ||||||||
\(547\) | −1.10405e142 | −0.0198909 | −0.00994546 | − | 0.999951i | \(-0.503166\pi\) | ||||
−0.00994546 | + | 0.999951i | \(0.503166\pi\) | |||||||
\(548\) | 1.27877e143 | 0.209322 | ||||||||
\(549\) | 6.81939e143 | 1.01437 | ||||||||
\(550\) | 3.70536e143 | 0.500944 | ||||||||
\(551\) | 8.00586e143 | 0.983896 | ||||||||
\(552\) | −3.31981e143 | −0.370947 | ||||||||
\(553\) | 1.45283e144 | 1.47620 | ||||||||
\(554\) | −1.12140e143 | −0.103633 | ||||||||
\(555\) | −1.98328e143 | −0.166726 | ||||||||
\(556\) | −1.23866e144 | −0.947383 | ||||||||
\(557\) | −2.49231e144 | −1.73462 | −0.867308 | − | 0.497771i | \(-0.834152\pi\) | ||||
−0.867308 | + | 0.497771i | \(0.834152\pi\) | |||||||
\(558\) | 1.56969e142 | 0.00994303 | ||||||||
\(559\) | −2.85332e143 | −0.164524 | ||||||||
\(560\) | 1.90268e143 | 0.0998837 | ||||||||
\(561\) | 4.97929e143 | 0.238022 | ||||||||
\(562\) | −8.30869e142 | −0.0361723 | ||||||||
\(563\) | −5.67998e143 | −0.225245 | −0.112623 | − | 0.993638i | \(-0.535925\pi\) | ||||
−0.112623 | + | 0.993638i | \(0.535925\pi\) | |||||||
\(564\) | −2.16108e143 | −0.0780762 | ||||||||
\(565\) | 1.13496e144 | 0.373626 | ||||||||
\(566\) | −1.47440e144 | −0.442338 | ||||||||
\(567\) | 2.31845e143 | 0.0633996 | ||||||||
\(568\) | −5.60184e144 | −1.39651 | ||||||||
\(569\) | 5.71338e144 | 1.29867 | 0.649336 | − | 0.760502i | \(-0.275047\pi\) | ||||
0.649336 | + | 0.760502i | \(0.275047\pi\) | |||||||
\(570\) | 3.51432e143 | 0.0728470 | ||||||||
\(571\) | −1.15237e144 | −0.217869 | −0.108934 | − | 0.994049i | \(-0.534744\pi\) | ||||
−0.108934 | + | 0.994049i | \(0.534744\pi\) | |||||||
\(572\) | −2.08640e144 | −0.359838 | ||||||||
\(573\) | 2.84009e144 | 0.446904 | ||||||||
\(574\) | 1.66678e144 | 0.239334 | ||||||||
\(575\) | 5.58608e144 | 0.732058 | ||||||||
\(576\) | 7.56666e143 | 0.0905157 | ||||||||
\(577\) | 6.44279e144 | 0.703629 | 0.351815 | − | 0.936070i | \(-0.385565\pi\) | ||||
0.351815 | + | 0.936070i | \(0.385565\pi\) | |||||||
\(578\) | 3.72016e144 | 0.370980 | ||||||||
\(579\) | 3.89295e143 | 0.0354531 | ||||||||
\(580\) | 1.97121e144 | 0.163970 | ||||||||
\(581\) | −1.14248e145 | −0.868163 | ||||||||
\(582\) | 7.35975e144 | 0.510983 | ||||||||
\(583\) | −8.25265e144 | −0.523594 | ||||||||
\(584\) | −1.28543e145 | −0.745375 | ||||||||
\(585\) | 8.42102e143 | 0.0446356 | ||||||||
\(586\) | 5.51639e144 | 0.267319 | ||||||||
\(587\) | −1.50682e145 | −0.667670 | −0.333835 | − | 0.942632i | \(-0.608343\pi\) | ||||
−0.333835 | + | 0.942632i | \(0.608343\pi\) | |||||||
\(588\) | 5.17570e144 | 0.209729 | ||||||||
\(589\) | 1.36115e144 | 0.0504491 | ||||||||
\(590\) | 2.79093e144 | 0.0946278 | ||||||||
\(591\) | −3.22371e145 | −1.00003 | ||||||||
\(592\) | 2.08053e145 | 0.590587 | ||||||||
\(593\) | −6.35659e145 | −1.65140 | −0.825702 | − | 0.564107i | \(-0.809220\pi\) | ||||
−0.825702 | + | 0.564107i | \(0.809220\pi\) | |||||||
\(594\) | 2.28257e145 | 0.542794 | ||||||||
\(595\) | 2.36690e144 | 0.0515275 | ||||||||
\(596\) | 2.36101e145 | 0.470619 | ||||||||
\(597\) | 8.15833e144 | 0.148919 | ||||||||
\(598\) | 6.07292e144 | 0.101528 | ||||||||
\(599\) | 4.32195e145 | 0.661868 | 0.330934 | − | 0.943654i | \(-0.392636\pi\) | ||||
0.330934 | + | 0.943654i | \(0.392636\pi\) | |||||||
\(600\) | −3.22094e145 | −0.451900 | ||||||||
\(601\) | 6.55679e145 | 0.842910 | 0.421455 | − | 0.906849i | \(-0.361519\pi\) | ||||
0.421455 | + | 0.906849i | \(0.361519\pi\) | |||||||
\(602\) | −1.35136e145 | −0.159205 | ||||||||
\(603\) | 3.19778e145 | 0.345294 | ||||||||
\(604\) | 1.40629e146 | 1.39199 | ||||||||
\(605\) | −1.92028e145 | −0.174264 | ||||||||
\(606\) | 2.22221e145 | 0.184915 | ||||||||
\(607\) | 2.18967e145 | 0.167098 | 0.0835492 | − | 0.996504i | \(-0.473374\pi\) | ||||
0.0835492 | + | 0.996504i | \(0.473374\pi\) | |||||||
\(608\) | −1.62197e146 | −1.13529 | ||||||||
\(609\) | −6.54622e145 | −0.420322 | ||||||||
\(610\) | −2.81116e145 | −0.165603 | ||||||||
\(611\) | 8.66980e144 | 0.0468647 | ||||||||
\(612\) | 2.73924e145 | 0.135888 | ||||||||
\(613\) | −2.25524e146 | −1.02688 | −0.513438 | − | 0.858127i | \(-0.671628\pi\) | ||||
−0.513438 | + | 0.858127i | \(0.671628\pi\) | |||||||
\(614\) | 3.97148e145 | 0.166002 | ||||||||
\(615\) | −3.02169e145 | −0.115960 | ||||||||
\(616\) | −2.16707e146 | −0.763635 | ||||||||
\(617\) | −2.13544e146 | −0.691060 | −0.345530 | − | 0.938408i | \(-0.612301\pi\) | ||||
−0.345530 | + | 0.938408i | \(0.612301\pi\) | |||||||
\(618\) | −2.97926e145 | −0.0885550 | ||||||||
\(619\) | 2.66610e146 | 0.727977 | 0.363989 | − | 0.931403i | \(-0.381415\pi\) | ||||
0.363989 | + | 0.931403i | \(0.381415\pi\) | |||||||
\(620\) | 3.35144e144 | 0.00840752 | ||||||||
\(621\) | 3.44112e146 | 0.793216 | ||||||||
\(622\) | 2.69932e146 | 0.571819 | ||||||||
\(623\) | −5.68432e146 | −1.10677 | ||||||||
\(624\) | 6.36489e145 | 0.113920 | ||||||||
\(625\) | 5.08160e146 | 0.836180 | ||||||||
\(626\) | 3.88276e146 | 0.587474 | ||||||||
\(627\) | 7.27555e146 | 1.01232 | ||||||||
\(628\) | −8.92729e146 | −1.14245 | ||||||||
\(629\) | 2.58814e146 | 0.304669 | ||||||||
\(630\) | 3.98829e145 | 0.0431924 | ||||||||
\(631\) | 1.72070e146 | 0.171460 | 0.0857302 | − | 0.996318i | \(-0.472678\pi\) | ||||
0.0857302 | + | 0.996318i | \(0.472678\pi\) | |||||||
\(632\) | −1.52005e147 | −1.39383 | ||||||||
\(633\) | 8.45964e146 | 0.713932 | ||||||||
\(634\) | 7.73447e146 | 0.600820 | ||||||||
\(635\) | −1.08640e146 | −0.0776908 | ||||||||
\(636\) | 3.27110e146 | 0.215375 | ||||||||
\(637\) | −2.07638e146 | −0.125889 | ||||||||
\(638\) | −7.87916e146 | −0.439941 | ||||||||
\(639\) | 2.13436e147 | 1.09767 | ||||||||
\(640\) | −5.07662e146 | −0.240506 | ||||||||
\(641\) | −4.25546e147 | −1.85738 | −0.928689 | − | 0.370859i | \(-0.879063\pi\) | ||||
−0.928689 | + | 0.370859i | \(0.879063\pi\) | |||||||
\(642\) | −8.40063e146 | −0.337849 | ||||||||
\(643\) | 3.00504e146 | 0.111372 | 0.0556858 | − | 0.998448i | \(-0.482265\pi\) | ||||
0.0556858 | + | 0.998448i | \(0.482265\pi\) | |||||||
\(644\) | −1.48969e147 | −0.508848 | ||||||||
\(645\) | 2.44987e146 | 0.0771362 | ||||||||
\(646\) | −4.58611e146 | −0.133118 | ||||||||
\(647\) | −2.99856e147 | −0.802486 | −0.401243 | − | 0.915972i | \(-0.631422\pi\) | ||||
−0.401243 | + | 0.915972i | \(0.631422\pi\) | |||||||
\(648\) | −2.42571e146 | −0.0598620 | ||||||||
\(649\) | 5.77795e147 | 1.31500 | ||||||||
\(650\) | 5.89207e146 | 0.123685 | ||||||||
\(651\) | −1.11298e146 | −0.0215520 | ||||||||
\(652\) | 7.02937e147 | 1.25579 | ||||||||
\(653\) | −6.59787e146 | −0.108758 | −0.0543791 | − | 0.998520i | \(-0.517318\pi\) | ||||
−0.0543791 | + | 0.998520i | \(0.517318\pi\) | |||||||
\(654\) | 2.82320e146 | 0.0429448 | ||||||||
\(655\) | 2.55966e147 | 0.359346 | ||||||||
\(656\) | 3.16985e147 | 0.410759 | ||||||||
\(657\) | 4.89764e147 | 0.585875 | ||||||||
\(658\) | 4.10611e146 | 0.0453494 | ||||||||
\(659\) | −1.06461e148 | −1.08569 | −0.542844 | − | 0.839834i | \(-0.682652\pi\) | ||||
−0.542844 | + | 0.839834i | \(0.682652\pi\) | |||||||
\(660\) | 1.79139e147 | 0.168707 | ||||||||
\(661\) | −1.04052e148 | −0.905051 | −0.452526 | − | 0.891751i | \(-0.649477\pi\) | ||||
−0.452526 | + | 0.891751i | \(0.649477\pi\) | |||||||
\(662\) | 2.86811e147 | 0.230437 | ||||||||
\(663\) | 7.91781e146 | 0.0587685 | ||||||||
\(664\) | 1.19534e148 | 0.819722 | ||||||||
\(665\) | 3.45842e147 | 0.219150 | ||||||||
\(666\) | 4.36108e147 | 0.255386 | ||||||||
\(667\) | −1.18784e148 | −0.642910 | ||||||||
\(668\) | −2.15375e148 | −1.07753 | ||||||||
\(669\) | −1.53942e148 | −0.712010 | ||||||||
\(670\) | −1.31822e147 | −0.0563716 | ||||||||
\(671\) | −5.81982e148 | −2.30132 | ||||||||
\(672\) | 1.32625e148 | 0.484996 | ||||||||
\(673\) | 4.95268e148 | 1.67513 | 0.837567 | − | 0.546335i | \(-0.183977\pi\) | ||||
0.837567 | + | 0.546335i | \(0.183977\pi\) | |||||||
\(674\) | −1.64662e148 | −0.515167 | ||||||||
\(675\) | 3.33865e148 | 0.966323 | ||||||||
\(676\) | 2.79816e148 | 0.749326 | ||||||||
\(677\) | −6.34338e148 | −1.57187 | −0.785934 | − | 0.618311i | \(-0.787817\pi\) | ||||
−0.785934 | + | 0.618311i | \(0.787817\pi\) | |||||||
\(678\) | 1.79815e148 | 0.412352 | ||||||||
\(679\) | 7.24268e148 | 1.53722 | ||||||||
\(680\) | −2.47641e147 | −0.0486524 | ||||||||
\(681\) | 3.93276e148 | 0.715277 | ||||||||
\(682\) | −1.33961e147 | −0.0225579 | ||||||||
\(683\) | −4.16276e148 | −0.649074 | −0.324537 | − | 0.945873i | \(-0.605209\pi\) | ||||
−0.324537 | + | 0.945873i | \(0.605209\pi\) | |||||||
\(684\) | 4.00247e148 | 0.577940 | ||||||||
\(685\) | 4.40478e147 | 0.0589073 | ||||||||
\(686\) | −3.52666e148 | −0.436866 | ||||||||
\(687\) | 2.79660e148 | 0.320923 | ||||||||
\(688\) | −2.56999e148 | −0.273236 | ||||||||
\(689\) | −1.31229e148 | −0.129277 | ||||||||
\(690\) | −5.21423e147 | −0.0476006 | ||||||||
\(691\) | 3.41789e148 | 0.289175 | 0.144587 | − | 0.989492i | \(-0.453815\pi\) | ||||
0.144587 | + | 0.989492i | \(0.453815\pi\) | |||||||
\(692\) | −1.36533e149 | −1.07070 | ||||||||
\(693\) | 8.25678e148 | 0.600227 | ||||||||
\(694\) | −7.67721e148 | −0.517406 | ||||||||
\(695\) | −4.26660e148 | −0.266612 | ||||||||
\(696\) | 6.84909e148 | 0.396869 | ||||||||
\(697\) | 3.94324e148 | 0.211901 | ||||||||
\(698\) | −1.25011e149 | −0.623075 | ||||||||
\(699\) | −1.81087e148 | −0.0837214 | ||||||||
\(700\) | −1.44533e149 | −0.619897 | ||||||||
\(701\) | −2.33245e149 | −0.928146 | −0.464073 | − | 0.885797i | \(-0.653612\pi\) | ||||
−0.464073 | + | 0.885797i | \(0.653612\pi\) | |||||||
\(702\) | 3.62962e148 | 0.134018 | ||||||||
\(703\) | 3.78169e149 | 1.29578 | ||||||||
\(704\) | −6.45756e148 | −0.205354 | ||||||||
\(705\) | −7.44392e147 | −0.0219722 | ||||||||
\(706\) | 1.36895e149 | 0.375094 | ||||||||
\(707\) | 2.18686e149 | 0.556291 | ||||||||
\(708\) | −2.29020e149 | −0.540913 | ||||||||
\(709\) | −3.10165e148 | −0.0680244 | −0.0340122 | − | 0.999421i | \(-0.510829\pi\) | ||||
−0.0340122 | + | 0.999421i | \(0.510829\pi\) | |||||||
\(710\) | −8.79847e148 | −0.179203 | ||||||||
\(711\) | 5.79156e149 | 1.09557 | ||||||||
\(712\) | 5.94731e149 | 1.04501 | ||||||||
\(713\) | −2.01955e148 | −0.0329651 | ||||||||
\(714\) | 3.74996e148 | 0.0568683 | ||||||||
\(715\) | −7.18668e148 | −0.101265 | ||||||||
\(716\) | 4.84688e149 | 0.634642 | ||||||||
\(717\) | 2.01290e149 | 0.244944 | ||||||||
\(718\) | −1.95849e149 | −0.221507 | ||||||||
\(719\) | −1.69695e150 | −1.78403 | −0.892015 | − | 0.452005i | \(-0.850709\pi\) | ||||
−0.892015 | + | 0.452005i | \(0.850709\pi\) | |||||||
\(720\) | 7.58483e148 | 0.0741293 | ||||||||
\(721\) | −2.93187e149 | −0.266406 | ||||||||
\(722\) | −1.93969e149 | −0.163881 | ||||||||
\(723\) | −5.48297e149 | −0.430779 | ||||||||
\(724\) | −5.91959e148 | −0.0432531 | ||||||||
\(725\) | −1.15246e150 | −0.783216 | ||||||||
\(726\) | −3.04236e149 | −0.192326 | ||||||||
\(727\) | −8.19359e148 | −0.0481856 | −0.0240928 | − | 0.999710i | \(-0.507670\pi\) | ||||
−0.0240928 | + | 0.999710i | \(0.507670\pi\) | |||||||
\(728\) | −3.44596e149 | −0.188544 | ||||||||
\(729\) | 1.39310e150 | 0.709231 | ||||||||
\(730\) | −2.01895e149 | −0.0956480 | ||||||||
\(731\) | −3.19702e149 | −0.140956 | ||||||||
\(732\) | 2.30679e150 | 0.946623 | ||||||||
\(733\) | 1.32500e150 | 0.506126 | 0.253063 | − | 0.967450i | \(-0.418562\pi\) | ||||
0.253063 | + | 0.967450i | \(0.418562\pi\) | |||||||
\(734\) | −5.51691e149 | −0.196179 | ||||||||
\(735\) | 1.78279e149 | 0.0590220 | ||||||||
\(736\) | 2.40653e150 | 0.741833 | ||||||||
\(737\) | −2.72905e150 | −0.783373 | ||||||||
\(738\) | 6.64445e149 | 0.177623 | ||||||||
\(739\) | 5.43053e149 | 0.135210 | 0.0676051 | − | 0.997712i | \(-0.478464\pi\) | ||||
0.0676051 | + | 0.997712i | \(0.478464\pi\) | |||||||
\(740\) | 9.31131e149 | 0.215946 | ||||||||
\(741\) | 1.15692e150 | 0.249946 | ||||||||
\(742\) | −6.21516e149 | −0.125097 | ||||||||
\(743\) | 3.72400e150 | 0.698388 | 0.349194 | − | 0.937051i | \(-0.386455\pi\) | ||||
0.349194 | + | 0.937051i | \(0.386455\pi\) | |||||||
\(744\) | 1.16448e149 | 0.0203494 | ||||||||
\(745\) | 8.13258e149 | 0.132441 | ||||||||
\(746\) | 3.79201e150 | 0.575548 | ||||||||
\(747\) | −4.55437e150 | −0.644313 | ||||||||
\(748\) | −2.33773e150 | −0.308290 | ||||||||
\(749\) | −8.26701e150 | −1.01637 | ||||||||
\(750\) | −1.04160e150 | −0.119394 | ||||||||
\(751\) | −7.26582e150 | −0.776583 | −0.388292 | − | 0.921537i | \(-0.626935\pi\) | ||||
−0.388292 | + | 0.921537i | \(0.626935\pi\) | |||||||
\(752\) | 7.80891e149 | 0.0778312 | ||||||||
\(753\) | −4.39544e150 | −0.408569 | ||||||||
\(754\) | −1.25290e150 | −0.108623 | ||||||||
\(755\) | 4.84401e150 | 0.391733 | ||||||||
\(756\) | −8.90348e150 | −0.671685 | ||||||||
\(757\) | 6.80097e150 | 0.478671 | 0.239336 | − | 0.970937i | \(-0.423070\pi\) | ||||
0.239336 | + | 0.970937i | \(0.423070\pi\) | |||||||
\(758\) | 8.06732e150 | 0.529781 | ||||||||
\(759\) | −1.07948e151 | −0.661487 | ||||||||
\(760\) | −3.61843e150 | −0.206922 | ||||||||
\(761\) | 3.21674e151 | 1.71681 | 0.858405 | − | 0.512973i | \(-0.171456\pi\) | ||||
0.858405 | + | 0.512973i | \(0.171456\pi\) | |||||||
\(762\) | −1.72122e150 | −0.0857434 | ||||||||
\(763\) | 2.77830e150 | 0.129194 | ||||||||
\(764\) | −1.33339e151 | −0.578837 | ||||||||
\(765\) | 9.43539e149 | 0.0382415 | ||||||||
\(766\) | −5.80591e150 | −0.219715 | ||||||||
\(767\) | 9.18779e150 | 0.324679 | ||||||||
\(768\) | −4.98929e150 | −0.164655 | ||||||||
\(769\) | 1.66173e151 | 0.512185 | 0.256093 | − | 0.966652i | \(-0.417565\pi\) | ||||
0.256093 | + | 0.966652i | \(0.417565\pi\) | |||||||
\(770\) | −3.40369e150 | −0.0979912 | ||||||||
\(771\) | 2.02494e151 | 0.544575 | ||||||||
\(772\) | −1.82770e150 | −0.0459194 | ||||||||
\(773\) | 7.47787e151 | 1.75531 | 0.877656 | − | 0.479291i | \(-0.159106\pi\) | ||||
0.877656 | + | 0.479291i | \(0.159106\pi\) | |||||||
\(774\) | −5.38706e150 | −0.118155 | ||||||||
\(775\) | −1.95941e150 | −0.0401593 | ||||||||
\(776\) | −7.57778e151 | −1.45145 | ||||||||
\(777\) | −3.09220e151 | −0.553560 | ||||||||
\(778\) | 1.92587e151 | 0.322254 | ||||||||
\(779\) | 5.76170e151 | 0.901227 | ||||||||
\(780\) | 2.84858e150 | 0.0416545 | ||||||||
\(781\) | −1.82151e152 | −2.49030 | ||||||||
\(782\) | 6.80445e150 | 0.0869838 | ||||||||
\(783\) | −7.09937e151 | −0.848648 | ||||||||
\(784\) | −1.87020e151 | −0.209071 | ||||||||
\(785\) | −3.07503e151 | −0.321509 | ||||||||
\(786\) | 4.05535e151 | 0.396592 | ||||||||
\(787\) | −2.94929e151 | −0.269801 | −0.134900 | − | 0.990859i | \(-0.543071\pi\) | ||||
−0.134900 | + | 0.990859i | \(0.543071\pi\) | |||||||
\(788\) | 1.51350e152 | 1.29525 | ||||||||
\(789\) | 1.87465e151 | 0.150099 | ||||||||
\(790\) | −2.38745e151 | −0.178860 | ||||||||
\(791\) | 1.76955e152 | 1.24050 | ||||||||
\(792\) | −8.63879e151 | −0.566736 | ||||||||
\(793\) | −9.25436e151 | −0.568204 | ||||||||
\(794\) | 1.18446e152 | 0.680682 | ||||||||
\(795\) | 1.12674e151 | 0.0606107 | ||||||||
\(796\) | −3.83025e151 | −0.192882 | ||||||||
\(797\) | 3.01507e152 | 1.42146 | 0.710731 | − | 0.703464i | \(-0.248364\pi\) | ||||
0.710731 | + | 0.703464i | \(0.248364\pi\) | |||||||
\(798\) | 5.47929e151 | 0.241865 | ||||||||
\(799\) | 9.71414e150 | 0.0401512 | ||||||||
\(800\) | 2.33486e152 | 0.903727 | ||||||||
\(801\) | −2.26599e152 | −0.821393 | ||||||||
\(802\) | 2.87275e151 | 0.0975310 | ||||||||
\(803\) | −4.17975e152 | −1.32918 | ||||||||
\(804\) | 1.08171e152 | 0.322232 | ||||||||
\(805\) | −5.13129e151 | −0.143200 | ||||||||
\(806\) | −2.13017e150 | −0.00556962 | ||||||||
\(807\) | −2.22545e152 | −0.545202 | ||||||||
\(808\) | −2.28804e152 | −0.525251 | ||||||||
\(809\) | 4.42609e151 | 0.0952188 | 0.0476094 | − | 0.998866i | \(-0.484840\pi\) | ||||
0.0476094 | + | 0.998866i | \(0.484840\pi\) | |||||||
\(810\) | −3.80992e150 | −0.00768162 | ||||||||
\(811\) | 1.17673e152 | 0.222373 | 0.111186 | − | 0.993800i | \(-0.464535\pi\) | ||||
0.111186 | + | 0.993800i | \(0.464535\pi\) | |||||||
\(812\) | 3.07338e152 | 0.544408 | ||||||||
\(813\) | −4.92922e152 | −0.818512 | ||||||||
\(814\) | −3.72184e152 | −0.579397 | ||||||||
\(815\) | 2.42129e152 | 0.353405 | ||||||||
\(816\) | 7.13159e151 | 0.0976007 | ||||||||
\(817\) | −4.67136e152 | −0.599495 | ||||||||
\(818\) | −2.30577e152 | −0.277503 | ||||||||
\(819\) | 1.31295e152 | 0.148198 | ||||||||
\(820\) | 1.41865e152 | 0.150193 | ||||||||
\(821\) | 9.52380e152 | 0.945789 | 0.472895 | − | 0.881119i | \(-0.343209\pi\) | ||||
0.472895 | + | 0.881119i | \(0.343209\pi\) | |||||||
\(822\) | 6.97863e151 | 0.0650129 | ||||||||
\(823\) | 2.93577e152 | 0.256585 | 0.128292 | − | 0.991736i | \(-0.459050\pi\) | ||||
0.128292 | + | 0.991736i | \(0.459050\pi\) | |||||||
\(824\) | 3.06752e152 | 0.251541 | ||||||||
\(825\) | −1.04733e153 | −0.805847 | ||||||||
\(826\) | 4.35144e152 | 0.314181 | ||||||||
\(827\) | 4.85556e152 | 0.329003 | 0.164502 | − | 0.986377i | \(-0.447398\pi\) | ||||
0.164502 | + | 0.986377i | \(0.447398\pi\) | |||||||
\(828\) | −5.93850e152 | −0.377645 | ||||||||
\(829\) | 3.22510e153 | 1.92500 | 0.962500 | − | 0.271282i | \(-0.0874477\pi\) | ||||
0.962500 | + | 0.271282i | \(0.0874477\pi\) | |||||||
\(830\) | 1.87745e152 | 0.105188 | ||||||||
\(831\) | 3.16968e152 | 0.166710 | ||||||||
\(832\) | −1.02685e152 | −0.0507027 | ||||||||
\(833\) | −2.32649e152 | −0.107855 | ||||||||
\(834\) | −6.75972e152 | −0.294246 | ||||||||
\(835\) | −7.41865e152 | −0.303239 | ||||||||
\(836\) | −3.41579e153 | −1.31118 | ||||||||
\(837\) | −1.20703e152 | −0.0435143 | ||||||||
\(838\) | −6.70760e152 | −0.227120 | ||||||||
\(839\) | 4.24065e152 | 0.134874 | 0.0674372 | − | 0.997724i | \(-0.478518\pi\) | ||||
0.0674372 | + | 0.997724i | \(0.478518\pi\) | |||||||
\(840\) | 2.95871e152 | 0.0883976 | ||||||||
\(841\) | −1.11216e153 | −0.312162 | ||||||||
\(842\) | 1.10802e153 | 0.292189 | ||||||||
\(843\) | 2.34848e152 | 0.0581888 | ||||||||
\(844\) | −3.97171e153 | −0.924696 | ||||||||
\(845\) | 9.63835e152 | 0.210875 | ||||||||
\(846\) | 1.63686e152 | 0.0336563 | ||||||||
\(847\) | −2.99397e153 | −0.578587 | ||||||||
\(848\) | −1.18198e153 | −0.214699 | ||||||||
\(849\) | 4.16745e153 | 0.711569 | ||||||||
\(850\) | 6.60181e152 | 0.105967 | ||||||||
\(851\) | −5.61092e153 | −0.846705 | ||||||||
\(852\) | 7.21990e153 | 1.02436 | ||||||||
\(853\) | −2.26454e152 | −0.0302103 | −0.0151052 | − | 0.999886i | \(-0.504808\pi\) | ||||
−0.0151052 | + | 0.999886i | \(0.504808\pi\) | |||||||
\(854\) | −4.38296e153 | −0.549832 | ||||||||
\(855\) | 1.37866e153 | 0.162644 | ||||||||
\(856\) | 8.64949e153 | 0.959661 | ||||||||
\(857\) | 1.27702e154 | 1.33262 | 0.666309 | − | 0.745675i | \(-0.267873\pi\) | ||||
0.666309 | + | 0.745675i | \(0.267873\pi\) | |||||||
\(858\) | −1.13861e153 | −0.111762 | ||||||||
\(859\) | 1.34385e154 | 1.24083 | 0.620414 | − | 0.784275i | \(-0.286965\pi\) | ||||
0.620414 | + | 0.784275i | \(0.286965\pi\) | |||||||
\(860\) | −1.15019e153 | −0.0999080 | ||||||||
\(861\) | −4.71122e153 | −0.385006 | ||||||||
\(862\) | −7.17738e153 | −0.551867 | ||||||||
\(863\) | −3.76062e153 | −0.272078 | −0.136039 | − | 0.990703i | \(-0.543437\pi\) | ||||
−0.136039 | + | 0.990703i | \(0.543437\pi\) | |||||||
\(864\) | 1.43832e154 | 0.979227 | ||||||||
\(865\) | −4.70293e153 | −0.301316 | ||||||||
\(866\) | −8.07928e153 | −0.487173 | ||||||||
\(867\) | −1.05152e154 | −0.596779 | ||||||||
\(868\) | 5.22534e152 | 0.0279144 | ||||||||
\(869\) | −4.94264e154 | −2.48554 | ||||||||
\(870\) | 1.07575e153 | 0.0509271 | ||||||||
\(871\) | −4.33959e153 | −0.193418 | ||||||||
\(872\) | −2.90684e153 | −0.121985 | ||||||||
\(873\) | 2.88722e154 | 1.14086 | ||||||||
\(874\) | 9.94239e153 | 0.369948 | ||||||||
\(875\) | −1.02503e154 | −0.359181 | ||||||||
\(876\) | 1.65672e154 | 0.546745 | ||||||||
\(877\) | 4.57524e153 | 0.142212 | 0.0711058 | − | 0.997469i | \(-0.477347\pi\) | ||||
0.0711058 | + | 0.997469i | \(0.477347\pi\) | |||||||
\(878\) | 7.31076e153 | 0.214043 | ||||||||
\(879\) | −1.55923e154 | −0.430025 | ||||||||
\(880\) | −6.47306e153 | −0.168178 | ||||||||
\(881\) | −3.46430e154 | −0.847969 | −0.423985 | − | 0.905669i | \(-0.639369\pi\) | ||||
−0.423985 | + | 0.905669i | \(0.639369\pi\) | |||||||
\(882\) | −3.92020e153 | −0.0904081 | ||||||||
\(883\) | 7.08435e154 | 1.53944 | 0.769720 | − | 0.638381i | \(-0.220396\pi\) | ||||
0.769720 | + | 0.638381i | \(0.220396\pi\) | |||||||
\(884\) | −3.71733e153 | −0.0761179 | ||||||||
\(885\) | −7.88867e153 | −0.152224 | ||||||||
\(886\) | 2.18677e154 | 0.397679 | ||||||||
\(887\) | −3.38114e153 | −0.0579525 | −0.0289763 | − | 0.999580i | \(-0.509225\pi\) | ||||
−0.0289763 | + | 0.999580i | \(0.509225\pi\) | |||||||
\(888\) | 3.23527e154 | 0.522672 | ||||||||
\(889\) | −1.69384e154 | −0.257947 | ||||||||
\(890\) | 9.34109e153 | 0.134098 | ||||||||
\(891\) | −7.88752e153 | −0.106748 | ||||||||
\(892\) | 7.22741e154 | 0.922206 | ||||||||
\(893\) | 1.41939e154 | 0.170766 | ||||||||
\(894\) | 1.28847e154 | 0.146169 | ||||||||
\(895\) | 1.66952e154 | 0.178601 | ||||||||
\(896\) | −7.91512e154 | −0.798522 | ||||||||
\(897\) | −1.71653e154 | −0.163323 | ||||||||
\(898\) | −3.41831e154 | −0.306763 | ||||||||
\(899\) | 4.16653e153 | 0.0352688 | ||||||||
\(900\) | −5.76165e154 | −0.460061 | ||||||||
\(901\) | −1.47037e154 | −0.110758 | ||||||||
\(902\) | −5.67052e154 | −0.402976 | ||||||||
\(903\) | 3.81967e154 | 0.256106 | ||||||||
\(904\) | −1.85142e155 | −1.17129 | ||||||||
\(905\) | −2.03902e153 | −0.0121723 | ||||||||
\(906\) | 7.67452e154 | 0.432335 | ||||||||
\(907\) | 7.45945e154 | 0.396574 | 0.198287 | − | 0.980144i | \(-0.436462\pi\) | ||||
0.198287 | + | 0.980144i | \(0.436462\pi\) | |||||||
\(908\) | −1.84639e155 | −0.926438 | ||||||||
\(909\) | 8.71768e154 | 0.412855 | ||||||||
\(910\) | −5.41237e153 | −0.0241944 | ||||||||
\(911\) | −2.85703e155 | −1.20559 | −0.602796 | − | 0.797895i | \(-0.705947\pi\) | ||||
−0.602796 | + | 0.797895i | \(0.705947\pi\) | |||||||
\(912\) | 1.04204e155 | 0.415102 | ||||||||
\(913\) | 3.88680e155 | 1.46176 | ||||||||
\(914\) | −1.51495e155 | −0.537927 | ||||||||
\(915\) | 7.94583e154 | 0.266398 | ||||||||
\(916\) | −1.31297e155 | −0.415665 | ||||||||
\(917\) | 3.99084e155 | 1.19309 | ||||||||
\(918\) | 4.06683e154 | 0.114819 | ||||||||
\(919\) | 5.08138e155 | 1.35493 | 0.677465 | − | 0.735555i | \(-0.263078\pi\) | ||||
0.677465 | + | 0.735555i | \(0.263078\pi\) | |||||||
\(920\) | 5.36870e154 | 0.135210 | ||||||||
\(921\) | −1.12255e155 | −0.267040 | ||||||||
\(922\) | 9.78958e154 | 0.219984 | ||||||||
\(923\) | −2.89647e155 | −0.614865 | ||||||||
\(924\) | 2.79302e155 | 0.560139 | ||||||||
\(925\) | −5.44383e155 | −1.03149 | ||||||||
\(926\) | 4.05815e155 | 0.726526 | ||||||||
\(927\) | −1.16876e155 | −0.197715 | ||||||||
\(928\) | −4.96491e155 | −0.793674 | ||||||||
\(929\) | 1.26997e155 | 0.191853 | 0.0959267 | − | 0.995388i | \(-0.469419\pi\) | ||||
0.0959267 | + | 0.995388i | \(0.469419\pi\) | |||||||
\(930\) | 1.82898e153 | 0.00261128 | ||||||||
\(931\) | −3.39938e155 | −0.458714 | ||||||||
\(932\) | 8.50186e154 | 0.108437 | ||||||||
\(933\) | −7.62971e155 | −0.919860 | ||||||||
\(934\) | 4.88464e155 | 0.556700 | ||||||||
\(935\) | −8.05237e154 | −0.0867590 | ||||||||
\(936\) | −1.37369e155 | −0.139929 | ||||||||
\(937\) | −6.80517e155 | −0.655406 | −0.327703 | − | 0.944781i | \(-0.606275\pi\) | ||||
−0.327703 | + | 0.944781i | \(0.606275\pi\) | |||||||
\(938\) | −2.05528e155 | −0.187164 | ||||||||
\(939\) | −1.09748e156 | −0.945043 | ||||||||
\(940\) | 3.49484e154 | 0.0284587 | ||||||||
\(941\) | 1.63427e156 | 1.25855 | 0.629274 | − | 0.777184i | \(-0.283352\pi\) | ||||
0.629274 | + | 0.777184i | \(0.283352\pi\) | |||||||
\(942\) | −4.87188e155 | −0.354833 | ||||||||
\(943\) | −8.54869e155 | −0.588892 | ||||||||
\(944\) | 8.27546e155 | 0.539216 | ||||||||
\(945\) | −3.06683e155 | −0.189025 | ||||||||
\(946\) | 4.59744e155 | 0.268059 | ||||||||
\(947\) | 3.35162e156 | 1.84876 | 0.924380 | − | 0.381472i | \(-0.124583\pi\) | ||||
0.924380 | + | 0.381472i | \(0.124583\pi\) | |||||||
\(948\) | 1.95911e156 | 1.02240 | ||||||||
\(949\) | −6.64642e155 | −0.328179 | ||||||||
\(950\) | 9.64631e155 | 0.450684 | ||||||||
\(951\) | −2.18617e156 | −0.966513 | ||||||||
\(952\) | −3.86105e155 | −0.161535 | ||||||||
\(953\) | 1.15047e156 | 0.455508 | 0.227754 | − | 0.973719i | \(-0.426862\pi\) | ||||
0.227754 | + | 0.973719i | \(0.426862\pi\) | |||||||
\(954\) | −2.47761e155 | −0.0928416 | ||||||||
\(955\) | −4.59291e155 | −0.162896 | ||||||||
\(956\) | −9.45037e155 | −0.317256 | ||||||||
\(957\) | 2.22707e156 | 0.707713 | ||||||||
\(958\) | −1.55482e156 | −0.467725 | ||||||||
\(959\) | 6.86763e155 | 0.195583 | ||||||||
\(960\) | 8.81654e154 | 0.0237716 | ||||||||
\(961\) | −3.91014e156 | −0.998192 | ||||||||
\(962\) | −5.91827e155 | −0.143055 | ||||||||
\(963\) | −3.29555e156 | −0.754307 | ||||||||
\(964\) | 2.57419e156 | 0.557952 | ||||||||
\(965\) | −6.29556e154 | −0.0129226 | ||||||||
\(966\) | −8.12967e155 | −0.158043 | ||||||||
\(967\) | 2.29280e156 | 0.422159 | 0.211079 | − | 0.977469i | \(-0.432302\pi\) | ||||
0.211079 | + | 0.977469i | \(0.432302\pi\) | |||||||
\(968\) | 3.13249e156 | 0.546303 | ||||||||
\(969\) | 1.29628e156 | 0.214141 | ||||||||
\(970\) | −1.19020e156 | −0.186253 | ||||||||
\(971\) | −4.42509e156 | −0.656013 | −0.328006 | − | 0.944676i | \(-0.606377\pi\) | ||||
−0.328006 | + | 0.944676i | \(0.606377\pi\) | |||||||
\(972\) | −5.79391e156 | −0.813754 | ||||||||
\(973\) | −6.65220e156 | −0.885199 | ||||||||
\(974\) | 1.55447e156 | 0.195991 | ||||||||
\(975\) | −1.66541e156 | −0.198966 | ||||||||
\(976\) | −8.33542e156 | −0.943652 | ||||||||
\(977\) | 5.67880e156 | 0.609244 | 0.304622 | − | 0.952473i | \(-0.401470\pi\) | ||||
0.304622 | + | 0.952473i | \(0.401470\pi\) | |||||||
\(978\) | 3.83613e156 | 0.390035 | ||||||||
\(979\) | 1.93385e157 | 1.86351 | ||||||||
\(980\) | −8.36999e155 | −0.0764462 | ||||||||
\(981\) | 1.10754e156 | 0.0958817 | ||||||||
\(982\) | −2.29177e156 | −0.188069 | ||||||||
\(983\) | 1.60539e157 | 1.24888 | 0.624441 | − | 0.781072i | \(-0.285327\pi\) | ||||
0.624441 | + | 0.781072i | \(0.285327\pi\) | |||||||
\(984\) | 4.92919e156 | 0.363524 | ||||||||
\(985\) | 5.21329e156 | 0.364510 | ||||||||
\(986\) | −1.40382e156 | −0.0930624 | ||||||||
\(987\) | −1.16061e156 | −0.0729515 | ||||||||
\(988\) | −5.43161e156 | −0.323735 | ||||||||
\(989\) | 6.93094e156 | 0.391730 | ||||||||
\(990\) | −1.35684e156 | −0.0727247 | ||||||||
\(991\) | −1.04972e157 | −0.533591 | −0.266795 | − | 0.963753i | \(-0.585965\pi\) | ||||
−0.266795 | + | 0.963753i | \(0.585965\pi\) | |||||||
\(992\) | −8.44130e155 | −0.0406955 | ||||||||
\(993\) | −8.10682e156 | −0.370693 | ||||||||
\(994\) | −1.37180e157 | −0.594984 | ||||||||
\(995\) | −1.31934e156 | −0.0542807 | ||||||||
\(996\) | −1.54061e157 | −0.601279 | ||||||||
\(997\) | 1.20849e157 | 0.447451 | 0.223726 | − | 0.974652i | \(-0.428178\pi\) | ||||
0.223726 | + | 0.974652i | \(0.428178\pi\) | |||||||
\(998\) | −1.79188e156 | −0.0629441 | ||||||||
\(999\) | −3.35349e157 | −1.11766 |
(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 | 1.106.a.a.1.4 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.106.a.a.1.4 | ✓ | 8 | 1.1 | even | 1 | trivial |