Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [16,26,Mod(1,16)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(16, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 26, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("16.1");
S:= CuspForms(chi, 26);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 16 = 2^{4} \) |
Weight: | \( k \) | \(=\) | \( 26 \) |
Character orbit: | \([\chi]\) | \(=\) | 16.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: | \(63.3594847924\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 16.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 195804. | 0.212719 | 0.106359 | − | 0.994328i | \(-0.466081\pi\) | ||||
0.106359 | + | 0.994328i | \(0.466081\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −7.41990e8 | −1.35917 | −0.679584 | − | 0.733598i | \(-0.737840\pi\) | ||||
−0.679584 | + | 0.733598i | \(0.737840\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.90806e10 | −1.06718 | −0.533588 | − | 0.845745i | \(-0.679157\pi\) | ||||
−0.533588 | + | 0.845745i | \(0.679157\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −8.08949e11 | −0.954751 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −8.41952e12 | −0.808870 | −0.404435 | − | 0.914567i | \(-0.632532\pi\) | ||||
−0.404435 | + | 0.914567i | \(0.632532\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −8.16510e13 | −0.972008 | −0.486004 | − | 0.873957i | \(-0.661546\pi\) | ||||
−0.486004 | + | 0.873957i | \(0.661546\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.45285e14 | −0.289120 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.51990e15 | −1.04899 | −0.524496 | − | 0.851413i | \(-0.675746\pi\) | ||||
−0.524496 | + | 0.851413i | \(0.675746\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.08206e15 | 0.630421 | 0.315210 | − | 0.949022i | \(-0.397925\pi\) | ||||
0.315210 | + | 0.949022i | \(0.397925\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −7.65214e15 | −0.227008 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 9.49953e16 | 0.903866 | 0.451933 | − | 0.892052i | \(-0.350735\pi\) | ||||
0.451933 | + | 0.892052i | \(0.350735\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.52526e17 | 0.847336 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.24298e17 | −0.415812 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.71247e17 | −0.142361 | −0.0711803 | − | 0.997463i | \(-0.522677\pi\) | ||||
−0.0711803 | + | 0.997463i | \(0.522677\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.29167e18 | −0.978599 | −0.489299 | − | 0.872116i | \(-0.662747\pi\) | ||||
−0.489299 | + | 0.872116i | \(0.662747\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.64857e18 | −0.172062 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.89974e19 | 1.45047 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.03015e19 | 0.506998 | 0.253499 | − | 0.967336i | \(-0.418419\pi\) | ||||
0.253499 | + | 0.967336i | \(0.418419\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.59876e19 | −0.206764 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.83744e20 | −1.27179 | −0.635895 | − | 0.771775i | \(-0.719369\pi\) | ||||
−0.635895 | + | 0.771775i | \(0.719369\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.00902e20 | −1.14834 | −0.574168 | − | 0.818737i | \(-0.694674\pi\) | ||||
−0.574168 | + | 0.818737i | \(0.694674\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.00232e20 | 1.29767 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.24361e20 | 1.16043 | 0.580214 | − | 0.814464i | \(-0.302969\pi\) | ||||
0.580214 | + | 0.814464i | \(0.302969\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.86224e20 | 0.138863 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.93407e20 | −0.223140 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.90292e20 | −0.276895 | −0.138447 | − | 0.990370i | \(-0.544211\pi\) | ||||
−0.138447 | + | 0.990370i | \(0.544211\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.24719e21 | 1.09939 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.19089e21 | 0.134102 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.30526e22 | −0.955093 | −0.477547 | − | 0.878606i | \(-0.658474\pi\) | ||||
−0.477547 | + | 0.878606i | \(0.658474\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.01545e21 | 0.434875 | 0.217438 | − | 0.976074i | \(-0.430230\pi\) | ||||
0.217438 | + | 0.976074i | \(0.430230\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.16142e22 | 1.01889 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.05842e22 | 1.32112 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.66891e22 | 0.398473 | 0.199236 | − | 0.979951i | \(-0.436154\pi\) | ||||
0.199236 | + | 0.979951i | \(0.436154\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.86005e22 | 0.192269 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.92391e23 | 1.39141 | 0.695704 | − | 0.718329i | \(-0.255093\pi\) | ||||
0.695704 | + | 0.718329i | \(0.255093\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.24046e22 | 0.216709 | 0.108355 | − | 0.994112i | \(-0.465442\pi\) | ||||
0.108355 | + | 0.994112i | \(0.465442\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.94455e22 | 0.180244 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.29040e23 | 0.863206 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.71681e23 | 0.517274 | 0.258637 | − | 0.965975i | \(-0.416727\pi\) | ||||
0.258637 | + | 0.965975i | \(0.416727\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.21915e23 | 0.866300 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.31454e23 | 0.956501 | 0.478251 | − | 0.878223i | \(-0.341271\pi\) | ||||
0.478251 | + | 0.878223i | \(0.341271\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.86974e24 | 1.42575 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.31112e22 | −0.0302828 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.76364e24 | −0.756892 | −0.378446 | − | 0.925623i | \(-0.623541\pi\) | ||||
−0.378446 | + | 0.925623i | \(0.623541\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.19097e24 | 1.03730 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.40325e23 | −0.208166 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.51282e24 | −0.856847 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.82924e24 | 0.414022 | 0.207011 | − | 0.978339i | \(-0.433626\pi\) | ||||
0.207011 | + | 0.978339i | \(0.433626\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.81096e24 | 0.772269 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.86342e24 | 0.164549 | 0.0822744 | − | 0.996610i | \(-0.473782\pi\) | ||||
0.0822744 | + | 0.996610i | \(0.473782\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.85812e24 | −0.335740 | −0.167870 | − | 0.985809i | \(-0.553689\pi\) | ||||
−0.167870 | + | 0.985809i | \(0.553689\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.67781e24 | 0.308542 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.58304e25 | −1.53799 | −0.768997 | − | 0.639252i | \(-0.779244\pi\) | ||||
−0.768997 | + | 0.639252i | \(0.779244\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.77795e25 | −1.62709 | −0.813543 | − | 0.581505i | \(-0.802464\pi\) | ||||
−0.813543 | + | 0.581505i | \(0.802464\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.97511e24 | 0.107848 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.46476e25 | −1.62008 | −0.810038 | − | 0.586378i | \(-0.800553\pi\) | ||||
−0.810038 | + | 0.586378i | \(0.800553\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.04855e25 | −1.22851 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.60516e25 | 0.928025 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 9.84792e25 | 1.11946 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.74588e25 | −0.345730 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.59779e25 | −0.270534 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.37587e25 | 0.207496 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.35905e26 | −1.69305 | −0.846524 | − | 0.532350i | \(-0.821309\pi\) | ||||
−0.846524 | + | 0.532350i | \(0.821309\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.89178e25 | −0.244273 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.74971e26 | 0.598513 | 0.299257 | − | 0.954173i | \(-0.403261\pi\) | ||||
0.299257 | + | 0.954173i | \(0.403261\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.37690e26 | −0.672769 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.40626e26 | 0.565158 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.18313e26 | 1.20837 | 0.604187 | − | 0.796843i | \(-0.293498\pi\) | ||||
0.604187 | + | 0.796843i | \(0.293498\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.84462e26 | 0.789905 | 0.394952 | − | 0.918702i | \(-0.370761\pi\) | ||||
0.394952 | + | 0.918702i | \(0.370761\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.80994e26 | 0.246845 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.87462e26 | 0.786228 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.01262e26 | 0.193492 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.64635e25 | 0.0295387 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.05569e26 | 0.619574 | 0.309787 | − | 0.950806i | \(-0.399742\pi\) | ||||
0.309787 | + | 0.950806i | \(0.399742\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.16190e27 | −0.672907 | −0.336454 | − | 0.941700i | \(-0.609228\pi\) | ||||
−0.336454 | + | 0.941700i | \(0.609228\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.03847e27 | 1.00152 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.18437e27 | 1.33008 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.41505e26 | −0.121521 | −0.0607605 | − | 0.998152i | \(-0.519353\pi\) | ||||
−0.0607605 | + | 0.998152i | \(0.519353\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.93903e26 | −0.0589008 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.71247e27 | −0.964583 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.63202e27 | −1.03140 | −0.515698 | − | 0.856771i | \(-0.672467\pi\) | ||||
−0.515698 | + | 0.856771i | \(0.672467\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.22323e27 | 0.233861 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.26470e27 | 1.35916 | 0.679581 | − | 0.733600i | \(-0.262162\pi\) | ||||
0.679581 | + | 0.733600i | \(0.262162\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.89517e26 | −0.0552004 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.92008e27 | −0.601895 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.02602e27 | −0.637462 | −0.318731 | − | 0.947845i | \(-0.603257\pi\) | ||||
−0.318731 | + | 0.947845i | \(0.603257\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.86886e27 | −0.904256 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.55575e27 | −0.203166 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.41023e28 | −1.66493 | −0.832463 | − | 0.554081i | \(-0.813070\pi\) | ||||
−0.832463 | + | 0.554081i | \(0.813070\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.19193e27 | −0.492498 | −0.246249 | − | 0.969207i | \(-0.579198\pi\) | ||||
−0.246249 | + | 0.969207i | \(0.579198\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.76526e27 | 0.0925061 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.50635e28 | −0.689095 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.12163e28 | 0.848497 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.26738e28 | 0.443744 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.50602e27 | −0.169013 | −0.0845066 | − | 0.996423i | \(-0.526931\pi\) | ||||
−0.0845066 | + | 0.996423i | \(0.526931\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.08716e28 | 0.562457 | 0.281228 | − | 0.959641i | \(-0.409258\pi\) | ||||
0.281228 | + | 0.959641i | \(0.409258\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.18626e28 | 0.281027 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.99370e28 | −1.24988 | −0.624938 | − | 0.780674i | \(-0.714876\pi\) | ||||
−0.624938 | + | 0.780674i | \(0.714876\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.24042e27 | −0.0411782 | −0.0205891 | − | 0.999788i | \(-0.506554\pi\) | ||||
−0.0205891 | + | 0.999788i | \(0.506554\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.22583e27 | 0.0847626 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.06005e28 | 0.151924 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.36336e29 | 1.72858 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7.68464e28 | −0.862967 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.12080e28 | −0.509928 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.52475e28 | 0.665214 | 0.332607 | − | 0.943066i | \(-0.392072\pi\) | ||||
0.332607 | + | 0.943066i | \(0.392072\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.76708e28 | 0.295979 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.23266e29 | 1.56078 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.67721e29 | 1.04434 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.30299e27 | 0.0460981 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.05752e29 | 1.01963 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.16696e29 | 1.40227 | 0.701135 | − | 0.713029i | \(-0.252677\pi\) | ||||
0.701135 | + | 0.713029i | \(0.252677\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.04281e29 | −0.808994 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.85094e29 | −1.36535 | −0.682674 | − | 0.730723i | \(-0.739183\pi\) | ||||
−0.682674 | + | 0.730723i | \(0.739183\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.68261e29 | −1.80553 | −0.902765 | − | 0.430134i | \(-0.858466\pi\) | ||||
−0.902765 | + | 0.430134i | \(0.858466\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.44273e28 | 0.183620 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.95586e29 | 1.26815 | 0.634075 | − | 0.773272i | \(-0.281381\pi\) | ||||
0.634075 | + | 0.773272i | \(0.281381\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.85867e29 | −1.57722 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.31962e28 | 0.110034 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.44023e29 | 0.268200 | 0.134100 | − | 0.990968i | \(-0.457186\pi\) | ||||
0.134100 | + | 0.990968i | \(0.457186\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.19456e29 | −0.536041 | −0.268020 | − | 0.963413i | \(-0.586369\pi\) | ||||
−0.268020 | + | 0.963413i | \(0.586369\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3.96547e29 | 0.600090 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.38177e29 | −0.188738 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.96606e29 | −0.612774 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.82383e29 | 0.203466 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.21677e29 | −0.627543 | −0.313771 | − | 0.949499i | \(-0.601593\pi\) | ||||
−0.313771 | + | 0.949499i | \(0.601593\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.99814e29 | −0.731110 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.66103e29 | 0.303285 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.29446e30 | −1.72392 | −0.861960 | − | 0.506977i | \(-0.830763\pi\) | ||||
−0.861960 | + | 0.506977i | \(0.830763\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.93394e29 | −0.541056 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.19425e29 | 0.135919 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.73316e29 | −0.435422 | −0.217711 | − | 0.976013i | \(-0.569859\pi\) | ||||
−0.217711 | + | 0.976013i | \(0.569859\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.34787e29 | 0.376347 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.45327e29 | −0.161005 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.62259e30 | 1.53856 | 0.769282 | − | 0.638910i | \(-0.220614\pi\) | ||||
0.769282 | + | 0.638910i | \(0.220614\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.62767e30 | 1.40447 | 0.702234 | − | 0.711946i | \(-0.252186\pi\) | ||||
0.702234 | + | 0.711946i | \(0.252186\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.24805e29 | 0.220654 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.12614e30 | −0.685384 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.54808e30 | −0.750266 | −0.375133 | − | 0.926971i | \(-0.622403\pi\) | ||||
−0.375133 | + | 0.926971i | \(0.622403\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.47174e30 | 0.934318 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.59817e30 | 0.885631 | 0.442816 | − | 0.896613i | \(-0.353980\pi\) | ||||
0.442816 | + | 0.896613i | \(0.353980\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.82265e30 | −0.861061 | −0.430530 | − | 0.902576i | \(-0.641673\pi\) | ||||
−0.430530 | + | 0.902576i | \(0.641673\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8.83629e29 | −0.182267 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.18084e30 | 1.35722 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.79269e29 | 0.100382 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.53977e29 | 0.0880702 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.30007e29 | 0.0189723 | 0.00948615 | − | 0.999955i | \(-0.496980\pi\) | ||||
0.00948615 | + | 0.999955i | \(0.496980\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.68487e30 | 1.29813 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.73043e30 | 0.336338 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −7.75646e30 | −0.878565 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.17594e31 | 1.22548 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.64866e29 | 0.0350026 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.68937e30 | −0.591068 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.43602e31 | −1.16931 | −0.584657 | − | 0.811281i | \(-0.698771\pi\) | ||||
−0.584657 | + | 0.811281i | \(0.698771\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.51239e29 | −0.0714182 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.24630e31 | 1.55584 | 0.777918 | − | 0.628366i | \(-0.216276\pi\) | ||||
0.777918 | + | 0.628366i | \(0.216276\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.37956e30 | −0.0881934 | −0.0440967 | − | 0.999027i | \(-0.514041\pi\) | ||||
−0.0440967 | + | 0.999027i | \(0.514041\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.34574e31 | −1.38484 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.02787e31 | −0.560655 | −0.280327 | − | 0.959904i | \(-0.590443\pi\) | ||||
−0.280327 | + | 0.959904i | \(0.590443\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.28377e30 | 0.115151 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.01574e30 | −0.327160 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.53262e31 | −0.661306 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.06190e31 | −0.823617 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.35542e30 | −0.346112 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.61246e31 | −1.23838 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.75356e30 | 0.182847 | 0.0914233 | − | 0.995812i | \(-0.470858\pi\) | ||||
0.0914233 | + | 0.995812i | \(0.470858\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.64229e31 | −0.484057 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.98030e31 | −0.541591 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.69268e31 | 1.69913 | 0.849564 | − | 0.527485i | \(-0.176865\pi\) | ||||
0.849564 | + | 0.527485i | \(0.176865\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.46163e31 | −0.344621 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.61337e31 | 0.791559 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.51320e31 | 0.918984 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.38013e31 | −0.261326 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.41781e29 | −0.0165894 | −0.00829472 | − | 0.999966i | \(-0.502640\pi\) | ||||
−0.00829472 | + | 0.999966i | \(0.502640\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.39081e31 | −0.555886 | −0.277943 | − | 0.960598i | \(-0.589653\pi\) | ||||
−0.277943 | + | 0.960598i | \(0.589653\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.64793e31 | 0.404173 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.30313e31 | 0.185269 | 0.0926346 | − | 0.995700i | \(-0.470471\pi\) | ||||
0.0926346 | + | 0.995700i | \(0.470471\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.42752e32 | −1.89116 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.92826e31 | 0.238130 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.30336e32 | 1.50101 | 0.750506 | − | 0.660864i | \(-0.229810\pi\) | ||||
0.750506 | + | 0.660864i | \(0.229810\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.60851e31 | −0.602570 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −7.33459e30 | −0.0735433 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.14638e31 | −0.294544 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.06294e32 | 1.80369 | 0.901844 | − | 0.432061i | \(-0.142214\pi\) | ||||
0.901844 | + | 0.432061i | \(0.142214\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.48640e32 | 1.21424 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.87012e31 | 0.295495 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.46051e32 | 1.75657 | 0.878283 | − | 0.478142i | \(-0.158689\pi\) | ||||
0.878283 | + | 0.478142i | \(0.158689\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6.61009e30 | 0.0441384 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.21476e31 | 0.138376 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.12743e31 | −0.416815 | −0.208407 | − | 0.978042i | \(-0.566828\pi\) | ||||
−0.208407 | + | 0.978042i | \(0.566828\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.57715e31 | −0.360143 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.33051e32 | −0.682393 | −0.341196 | − | 0.939992i | \(-0.610832\pi\) | ||||
−0.341196 | + | 0.939992i | \(0.610832\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.44144e32 | −1.17324 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.43414e32 | 1.09637 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.40509e32 | 1.01569 | 0.507844 | − | 0.861449i | \(-0.330443\pi\) | ||||
0.507844 | + | 0.861449i | \(0.330443\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.39379e32 | −0.948147 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.42599e31 | 0.127315 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.01585e32 | −0.703062 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.12137e32 | −1.34946 | −0.674730 | − | 0.738065i | \(-0.735740\pi\) | ||||
−0.674730 | + | 0.738065i | \(0.735740\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.65407e31 | −0.143111 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.16647e31 | −0.207014 | −0.103507 | − | 0.994629i | \(-0.533006\pi\) | ||||
−0.103507 | + | 0.994629i | \(0.533006\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.50419e32 | 0.951206 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.61454e32 | −1.17745 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.70929e32 | −0.410095 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.34430e32 | 0.303358 | 0.151679 | − | 0.988430i | \(-0.451532\pi\) | ||||
0.151679 | + | 0.988430i | \(0.451532\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.21068e32 | 0.257044 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.10102e32 | 1.01925 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.91130e32 | −1.30004 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.48596e31 | 0.168028 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.71876e32 | 0.286774 | 0.143387 | − | 0.989667i | \(-0.454201\pi\) | ||||
0.143387 | + | 0.989667i | \(0.454201\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.27664e32 | −1.30115 | −0.650576 | − | 0.759441i | \(-0.725472\pi\) | ||||
−0.650576 | + | 0.759441i | \(0.725472\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7.47761e32 | −1.10792 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.36340e32 | −0.888848 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.52329e32 | −0.464088 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.34608e32 | 0.167245 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.83836e31 | 0.0918881 | 0.0459441 | − | 0.998944i | \(-0.485370\pi\) | ||||
0.0459441 | + | 0.998944i | \(0.485370\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.33273e32 | 0.700635 | 0.350318 | − | 0.936631i | \(-0.386074\pi\) | ||||
0.350318 | + | 0.936631i | \(0.386074\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.94080e31 | 0.0411594 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.77767e32 | 0.569816 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.48299e33 | 1.38144 | 0.690718 | − | 0.723124i | \(-0.257295\pi\) | ||||
0.690718 | + | 0.723124i | \(0.257295\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.50646e32 | −0.132579 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.20901e33 | 1.00551 | 0.502753 | − | 0.864430i | \(-0.332321\pi\) | ||||
0.502753 | + | 0.864430i | \(0.332321\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.30860e33 | 1.02874 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.77314e32 | 0.131795 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.48861e32 | −0.666996 | −0.333498 | − | 0.942751i | \(-0.608229\pi\) | ||||
−0.333498 | + | 0.942751i | \(0.608229\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.54704e33 | 1.02871 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.27504e32 | −0.143140 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.36767e33 | −1.40987 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.90644e33 | 1.07466 | 0.537329 | − | 0.843373i | \(-0.319433\pi\) | ||||
0.537329 | + | 0.843373i | \(0.319433\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 8.17199e32 | 0.436183 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.56270e31 | −0.0230653 | −0.0115327 | − | 0.999933i | \(-0.503671\pi\) | ||||
−0.0115327 | + | 0.999933i | \(0.503671\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.13521e33 | −1.02254 | −0.511269 | − | 0.859421i | \(-0.670824\pi\) | ||||
−0.511269 | + | 0.859421i | \(0.670824\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.23513e32 | 0.282933 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.67225e33 | 1.14926 | 0.574628 | − | 0.818415i | \(-0.305147\pi\) | ||||
0.574628 | + | 0.818415i | \(0.305147\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.04302e33 | −0.425240 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.68680e31 | −0.0258498 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.53345e33 | 0.928854 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.53588e33 | 0.534178 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.01096e32 | 0.264366 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.97240e33 | −0.617733 | −0.308867 | − | 0.951105i | \(-0.599950\pi\) | ||||
−0.308867 | + | 0.951105i | \(0.599950\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.65764e33 | −0.492806 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −7.26917e32 | −0.205185 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.09927e33 | −0.562725 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.96366e32 | 0.100922 | 0.0504608 | − | 0.998726i | \(-0.483931\pi\) | ||||
0.0504608 | + | 0.998726i | \(0.483931\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9.06968e32 | −0.219397 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.22626e33 | 1.66110 | 0.830548 | − | 0.556947i | \(-0.188027\pi\) | ||||
0.830548 | + | 0.556947i | \(0.188027\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.83515e32 | 0.149335 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.05366e33 | −1.04964 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.51874e33 | −1.48488 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.19830e33 | −1.53981 | −0.769905 | − | 0.638159i | \(-0.779696\pi\) | ||||
−0.769905 | + | 0.638159i | \(0.779696\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.61826e33 | 0.289119 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.72562e33 | −0.803265 | −0.401633 | − | 0.915801i | \(-0.631557\pi\) | ||||
−0.401633 | + | 0.915801i | \(0.631557\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.38264e33 | −0.223649 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.62689e31 | −0.0117422 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.96955e33 | 0.288665 | 0.144332 | − | 0.989529i | \(-0.453897\pi\) | ||||
0.144332 | + | 0.989529i | \(0.453897\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.65720e33 | −0.231267 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.97240e33 | −0.262137 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.60468e33 | 0.456327 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.78267e33 | −0.938635 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.17992e33 | −0.135600 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.39782e33 | 0.810274 | 0.405137 | − | 0.914256i | \(-0.367224\pi\) | ||||
0.405137 | + | 0.914256i | \(0.367224\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.70332e34 | −1.77838 | −0.889191 | − | 0.457535i | \(-0.848732\pi\) | ||||
−0.889191 | + | 0.457535i | \(0.848732\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.93236e33 | −0.192352 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.08146e34 | 1.02654 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.02166e33 | −0.183026 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.05589e34 | 0.911876 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.50029e34 | 1.23619 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.65858e34 | 2.09039 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.71932e33 | −0.354161 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.56792e33 | −0.112322 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.28681e34 | −0.880134 | −0.440067 | − | 0.897965i | \(-0.645045\pi\) | ||||
−0.440067 | + | 0.897965i | \(0.645045\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.60401e33 | −0.104764 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.54519e34 | 2.21148 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.06624e34 | −1.23123 | −0.615616 | − | 0.788046i | \(-0.711093\pi\) | ||||
−0.615616 | + | 0.788046i | \(0.711093\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.29304e33 | −0.415197 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.64974e33 | −0.0897471 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.06175e34 | −0.552022 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.94949e33 | −0.146583 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.28751e33 | −0.156198 | −0.0780992 | − | 0.996946i | \(-0.524885\pi\) | ||||
−0.0780992 | + | 0.996946i | \(0.524885\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.45689e34 | 1.11619 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.15424e33 | 0.180491 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.80804e34 | 0.751371 | 0.375685 | − | 0.926747i | \(-0.377407\pi\) | ||||
0.375685 | + | 0.926747i | \(0.377407\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.53878e34 | 2.20195 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.43048e34 | −0.924493 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.05967e33 | −0.111371 | −0.0556854 | − | 0.998448i | \(-0.517734\pi\) | ||||
−0.0556854 | + | 0.998448i | \(0.517734\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.29884e34 | 0.452486 | 0.226243 | − | 0.974071i | \(-0.427356\pi\) | ||||
0.226243 | + | 0.974071i | \(0.427356\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.07810e33 | −0.0359523 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.39888e34 | 0.765878 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.31490e31 | −0.00223620 | −0.00111810 | − | 0.999999i | \(-0.500356\pi\) | ||||
−0.00111810 | + | 0.999999i | \(0.500356\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.08674e33 | 0.119645 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.64018e34 | −1.02075 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.33778e33 | 0.223972 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.90096e34 | −1.26134 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.16226e34 | −1.27310 | −0.636551 | − | 0.771234i | \(-0.719640\pi\) | ||||
−0.636551 | + | 0.771234i | \(0.719640\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.61022e34 | −0.616929 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.17359e34 | −0.265872 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.40705e34 | 0.522758 | 0.261379 | − | 0.965236i | \(-0.415823\pi\) | ||||
0.261379 | + | 0.965236i | \(0.415823\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.30706e34 | −1.52153 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.38684e32 | −0.00875937 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.30672e33 | 0.159072 | 0.0795361 | − | 0.996832i | \(-0.474656\pi\) | ||||
0.0795361 | + | 0.996832i | \(0.474656\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.00405e34 | −0.551792 | −0.275896 | − | 0.961187i | \(-0.588975\pi\) | ||||
−0.275896 | + | 0.961187i | \(0.588975\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.15901e34 | −0.380442 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.77941e34 | 0.469905 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.00963e35 | 1.63796 | 0.818978 | − | 0.573825i | \(-0.194541\pi\) | ||||
0.818978 | + | 0.573825i | \(0.194541\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.07562e33 | 0.0323170 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.54750e34 | −1.12795 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.02453e33 | −0.0146983 | −0.00734915 | − | 0.999973i | \(-0.502339\pi\) | ||||
−0.00734915 | + | 0.999973i | \(0.502339\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.66952e34 | 0.367701 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.53271e34 | 0.599505 | 0.299753 | − | 0.954017i | \(-0.403096\pi\) | ||||
0.299753 | + | 0.954017i | \(0.403096\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.24784e35 | −1.58499 | −0.792496 | − | 0.609878i | \(-0.791219\pi\) | ||||
−0.792496 | + | 0.609878i | \(0.791219\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.08068e34 | −0.375839 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.89239e34 | 0.807736 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.00307e35 | −1.12936 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.00267e34 | −0.108471 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5.11577e34 | −0.531836 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.83338e34 | −0.482930 | −0.241465 | − | 0.970410i | \(-0.577628\pi\) | ||||
−0.241465 | + | 0.970410i | \(0.577628\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.47338e34 | 0.141503 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.49238e35 | 2.30114 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.52054e34 | −0.134976 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.55634e35 | −1.32845 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.30494e34 | 0.681728 | 0.340864 | − | 0.940113i | \(-0.389280\pi\) | ||||
0.340864 | + | 0.940113i | \(0.389280\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.25724e34 | −0.415069 | −0.207535 | − | 0.978228i | \(-0.566544\pi\) | ||||
−0.207535 | + | 0.978228i | \(0.566544\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.37164e34 | 0.332008 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.03021e35 | 1.48333 | 0.741665 | − | 0.670770i | \(-0.234036\pi\) | ||||
0.741665 | + | 0.670770i | \(0.234036\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.09896e35 | 0.772546 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.28404e34 | 0.222150 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.67657e35 | 1.09146 | 0.545728 | − | 0.837962i | \(-0.316253\pi\) | ||||
0.545728 | + | 0.837962i | \(0.316253\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.29826e35 | −0.813479 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.43032e34 | −0.206903 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.92521e35 | 1.69859 | 0.849296 | − | 0.527917i | \(-0.177027\pi\) | ||||
0.849296 | + | 0.527917i | \(0.177027\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.30227e34 | 0.464172 | 0.232086 | − | 0.972695i | \(-0.425445\pi\) | ||||
0.232086 | + | 0.972695i | \(0.425445\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.02872e34 | 0.216894 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.76364e35 | 0.914406 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.57672e34 | −0.128675 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.20103e34 | 0.298289 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.59057e34 | −0.351757 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.23598e35 | −1.44483 | −0.722417 | − | 0.691458i | \(-0.756969\pi\) | ||||
−0.722417 | + | 0.691458i | \(0.756969\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −8.18936e34 | −0.352333 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.76333e34 | 0.321877 | 0.160938 | − | 0.986964i | \(-0.448548\pi\) | ||||
0.160938 | + | 0.986964i | \(0.448548\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.10568e35 | −0.441834 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.54029e34 | −0.290435 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.49909e35 | 0.927945 | 0.463973 | − | 0.885850i | \(-0.346424\pi\) | ||||
0.463973 | + | 0.885850i | \(0.346424\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.58782e35 | −1.64238 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.11268e35 | −0.384070 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.08584e34 | 0.269144 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.56964e34 | 0.275098 | 0.137549 | − | 0.990495i | \(-0.456078\pi\) | ||||
0.137549 | + | 0.990495i | \(0.456078\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.66176e35 | −0.824146 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.59466e35 | −1.07361 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.63017e35 | 1.33410 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9.70378e34 | 0.269759 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.53464e35 | 1.21637 | 0.608187 | − | 0.793793i | \(-0.291897\pi\) | ||||
0.608187 | + | 0.793793i | \(0.291897\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.23475e35 | 0.319622 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.34295e35 | −0.335504 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.28238e34 | −0.175602 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.93254e35 | −1.14813 | −0.574067 | − | 0.818808i | \(-0.694635\pi\) | ||||
−0.574067 | + | 0.818808i | \(0.694635\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.19776e35 | −0.493868 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.07688e35 | −0.884522 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.10090e35 | −1.06862 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.82004e34 | 0.0570513 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.13499e35 | −0.417142 | −0.208571 | − | 0.978007i | \(-0.566881\pi\) | ||||
−0.208571 | + | 0.978007i | \(0.566881\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.89858e35 | 0.358293 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.25508e34 | −0.114026 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.84968e34 | −0.120627 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.12190e35 | −0.871467 | −0.435734 | − | 0.900076i | \(-0.643511\pi\) | ||||
−0.435734 | + | 0.900076i | \(0.643511\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −4.49296e35 | −0.738649 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.58243e35 | 1.20459 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.77366e35 | 0.272315 | 0.136157 | − | 0.990687i | \(-0.456525\pi\) | ||||
0.136157 | + | 0.990687i | \(0.456525\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.70555e34 | −0.0401481 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.24709e35 | −0.322312 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.13535e36 | 1.57425 | 0.787124 | − | 0.616794i | \(-0.211569\pi\) | ||||
0.787124 | + | 0.616794i | \(0.211569\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −9.72375e34 | −0.130349 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.03749e34 | −0.0523301 | −0.0261651 | − | 0.999658i | \(-0.508330\pi\) | ||||
−0.0261651 | + | 0.999658i | \(0.508330\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.71923e35 | −0.842104 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7.53500e35 | −0.913220 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.40027e36 | 1.64131 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.72405e35 | −0.875681 | −0.437840 | − | 0.899053i | \(-0.644256\pi\) | ||||
−0.437840 | + | 0.899053i | \(0.644256\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.21727e35 | −0.133490 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.62115e35 | 0.914594 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.31585e35 | 0.340327 | 0.170163 | − | 0.985416i | \(-0.445570\pi\) | ||||
0.170163 | + | 0.985416i | \(0.445570\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.56607e35 | −0.155521 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.02230e36 | 1.94329 | 0.971646 | − | 0.236440i | \(-0.0759807\pi\) | ||||
0.971646 | + | 0.236440i | \(0.0759807\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.86725e36 | 1.73639 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.51253e36 | −1.36124 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.06576e36 | 0.928358 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.71193e35 | 0.650255 | 0.325128 | − | 0.945670i | \(-0.394593\pi\) | ||||
0.325128 | + | 0.945670i | \(0.394593\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.49265e35 | −0.366710 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.96060e36 | 1.54934 | 0.774668 | − | 0.632368i | \(-0.217917\pi\) | ||||
0.774668 | + | 0.632368i | \(0.217917\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.08376e36 | −0.829202 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.55350e35 | −0.115093 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.11754e36 | −0.801763 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.61983e36 | −1.12547 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.79649e34 | 0.0591953 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.53393e35 | 0.165167 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.92654e35 | 0.563637 | 0.281818 | − | 0.959468i | \(-0.409062\pi\) | ||||
0.281818 | + | 0.959468i | \(0.409062\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.51418e35 | −0.0926224 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.91727e36 | 1.72890 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.36121e35 | −0.422702 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.43874e35 | 0.0800560 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.35494e36 | −1.26984 | −0.634921 | − | 0.772577i | \(-0.718968\pi\) | ||||
−0.634921 | + | 0.772577i | \(0.718968\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.32930e36 | −1.21728 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.42669e36 | 0.722643 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.57026e35 | −0.175289 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.75462e36 | 1.31103 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.09317e35 | 0.327281 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.29617e36 | −0.579834 | −0.289917 | − | 0.957052i | \(-0.593628\pi\) | ||||
−0.289917 | + | 0.957052i | \(0.593628\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.63606e36 | −1.14339 | −0.571695 | − | 0.820467i | \(-0.693714\pi\) | ||||
−0.571695 | + | 0.820467i | \(0.693714\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7.10313e35 | 0.298757 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.43691e36 | 1.40184 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.83010e36 | −0.723935 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.58133e36 | −0.990366 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.92271e35 | −0.220410 | −0.110205 | − | 0.993909i | \(-0.535151\pi\) | ||||
−0.110205 | + | 0.993909i | \(0.535151\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.76928e35 | −0.172169 | −0.0860845 | − | 0.996288i | \(-0.527436\pi\) | ||||
−0.0860845 | + | 0.996288i | \(0.527436\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.16308e35 | −0.145794 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.17794e36 | −1.41953 | −0.709763 | − | 0.704440i | \(-0.751198\pi\) | ||||
−0.709763 | + | 0.704440i | \(0.751198\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.18023e36 | −1.04840 | −0.524199 | − | 0.851596i | \(-0.675635\pi\) | ||||
−0.524199 | + | 0.851596i | \(0.675635\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.98924e35 | −0.159596 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.69267e35 | −0.145666 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.13232e36 | −1.84733 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.39178e36 | 0.406913 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.57270e36 | 1.01384 | 0.506922 | − | 0.861992i | \(-0.330783\pi\) | ||||
0.506922 | + | 0.861992i | \(0.330783\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.55679e36 | −0.979733 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 7.04537e35 | 0.188390 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.89018e35 | 0.0750266 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.46391e36 | 0.368954 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.48489e35 | −0.183164 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.92855e36 | 0.458258 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.75466e36 | −0.404884 | −0.202442 | − | 0.979294i | \(-0.564888\pi\) | ||||
−0.202442 | + | 0.979294i | \(0.564888\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.65065e36 | 0.818075 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.10324e36 | 1.54595 | 0.772976 | − | 0.634435i | \(-0.218767\pi\) | ||||
0.772976 | + | 0.634435i | \(0.218767\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.56695e36 | 1.59958 | 0.799791 | − | 0.600279i | \(-0.204944\pi\) | ||||
0.799791 | + | 0.600279i | \(0.204944\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.40604e36 | 0.288707 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5.72195e36 | −1.14132 | −0.570662 | − | 0.821185i | \(-0.693313\pi\) | ||||
−0.570662 | + | 0.821185i | \(0.693313\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.47125e36 | 0.866418 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.13423e35 | 0.0213532 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.28742e36 | −0.418407 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.17919e36 | −0.387318 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.28871e36 | −0.395288 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.31931e36 | −0.221435 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.21926e36 | 0.525123 | 0.262561 | − | 0.964915i | \(-0.415433\pi\) | ||||
0.262561 | + | 0.964915i | \(0.415433\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.54558e34 | 0.00403576 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.04633e37 | −1.61238 | −0.806191 | − | 0.591655i | \(-0.798475\pi\) | ||||
−0.806191 | + | 0.591655i | \(0.798475\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.11745e36 | −0.616765 | −0.308382 | − | 0.951263i | \(-0.599788\pi\) | ||||
−0.308382 | + | 0.951263i | \(0.599788\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.89634e36 | 0.276137 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.52904e36 | 0.358022 | 0.179011 | − | 0.983847i | \(-0.442710\pi\) | ||||
0.179011 | + | 0.983847i | \(0.442710\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.31273e37 | 1.80678 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.23622e36 | −0.700723 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.62202e36 | 0.731558 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.78836e37 | 2.26291 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.51875e36 | −0.186887 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.16410e36 | 0.139314 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.49544e36 | 0.290460 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.30254e36 | 0.260682 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.07833e36 | 0.669387 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.93129e36 | 0.528286 | 0.264143 | − | 0.964484i | \(-0.414911\pi\) | ||||
0.264143 | + | 0.964484i | \(0.414911\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.50742e36 | −0.157103 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.10548e36 | 0.720466 | 0.360233 | − | 0.932862i | \(-0.382697\pi\) | ||||
0.360233 | + | 0.932862i | \(0.382697\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.84240e36 | −0.773685 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.30981e36 | −0.125731 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.83795e36 | −0.638718 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.64155e36 | −0.240112 | −0.120056 | − | 0.992767i | \(-0.538307\pi\) | ||||
−0.120056 | + | 0.992767i | \(0.538307\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.81179e36 | −0.248735 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.57089e37 | −1.35246 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.12665e36 | 0.429597 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.92997e36 | 0.320548 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.01934e36 | 0.398520 | 0.199260 | − | 0.979947i | \(-0.436146\pi\) | ||||
0.199260 | + | 0.979947i | \(0.436146\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.13263e36 | 0.0875419 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.39835e36 | 0.330955 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.57423e37 | −1.15325 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.70189e37 | −1.21391 | −0.606956 | − | 0.794735i | \(-0.707610\pi\) | ||||
−0.606956 | + | 0.794735i | \(0.707610\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.70123e35 | −0.0187604 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.51254e37 | −1.02291 | −0.511455 | − | 0.859310i | \(-0.670893\pi\) | ||||
−0.511455 | + | 0.859310i | \(0.670893\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.74548e37 | −1.14953 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −9.40380e36 | −0.603123 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.65329e36 | −0.103270 | −0.0516351 | − | 0.998666i | \(-0.516443\pi\) | ||||
−0.0516351 | + | 0.998666i | \(0.516443\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.46238e36 | −0.210643 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.01260e36 | −0.119262 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.77784e37 | 1.60341 | 0.801706 | − | 0.597718i | \(-0.203926\pi\) | ||||
0.801706 | + | 0.597718i | \(0.203926\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.08541e36 | 0.229717 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.47171e35 | 0.0244948 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.41640e37 | −1.28955 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.14395e35 | −0.0423441 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.89850e37 | 1.46840 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.54865e37 | −0.764473 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.82441e36 | −0.183965 | −0.0919823 | − | 0.995761i | \(-0.529320\pi\) | ||||
−0.0919823 | + | 0.995761i | \(0.529320\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.00093e36 | −0.140672 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.67087e37 | 0.763311 | 0.381655 | − | 0.924305i | \(-0.375354\pi\) | ||||
0.381655 | + | 0.924305i | \(0.375354\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.89331e37 | −0.842967 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.03728e36 | −0.175199 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.54376e37 | −1.49893 | −0.749466 | − | 0.662043i | \(-0.769690\pi\) | ||||
−0.749466 | + | 0.662043i | \(0.769690\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.48490e37 | 0.612227 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.86512e37 | 1.55346 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.26759e37 | −0.888476 | −0.444238 | − | 0.895909i | \(-0.646525\pi\) | ||||
−0.444238 | + | 0.895909i | \(0.646525\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.44726e37 | 1.69879 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −7.07334e36 | −0.263427 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.85843e37 | −1.03794 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.82706e36 | 0.0646891 | 0.0323445 | − | 0.999477i | \(-0.489703\pi\) | ||||
0.0323445 | + | 0.999477i | \(0.489703\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.12657e36 | 0.0388949 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.66237e36 | 0.0559680 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.34599e37 | 0.770260 | 0.385130 | − | 0.922862i | \(-0.374157\pi\) | ||||
0.385130 | + | 0.922862i | \(0.374157\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.58373e36 | −0.210816 |
(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 | 16.26.a.b.1.1 | 1 | ||
4.3 | odd | 2 | 1.26.a.a.1.1 | ✓ | 1 | ||
12.11 | even | 2 | 9.26.a.a.1.1 | 1 | |||
20.3 | even | 4 | 25.26.b.a.24.2 | 2 | |||
20.7 | even | 4 | 25.26.b.a.24.1 | 2 | |||
20.19 | odd | 2 | 25.26.a.a.1.1 | 1 | |||
28.27 | even | 2 | 49.26.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.26.a.a.1.1 | ✓ | 1 | 4.3 | odd | 2 | ||
9.26.a.a.1.1 | 1 | 12.11 | even | 2 | |||
16.26.a.b.1.1 | 1 | 1.1 | even | 1 | trivial | ||
25.26.a.a.1.1 | 1 | 20.19 | odd | 2 | |||
25.26.b.a.24.1 | 2 | 20.7 | even | 4 | |||
25.26.b.a.24.2 | 2 | 20.3 | even | 4 | |||
49.26.a.a.1.1 | 1 | 28.27 | even | 2 |