Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2,42,Mod(1,2)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 42, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2.1");
S:= CuspForms(chi, 42);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2 \) |
Weight: | \( k \) | \(=\) | \( 42 \) |
Character orbit: | \([\chi]\) | \(=\) | 2.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(21.2943340913\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{2} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1139917559892 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{7}\cdot 3^{2}\cdot 5 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.06767e6\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.04858e6 | 0.707107 | ||||||||
\(3\) | −1.71810e9 | −0.284487 | −0.142244 | − | 0.989832i | \(-0.545432\pi\) | ||||
−0.142244 | + | 0.989832i | \(0.545432\pi\) | |||||||
\(4\) | 1.09951e12 | 0.500000 | ||||||||
\(5\) | 3.51885e14 | 1.65012 | 0.825060 | − | 0.565044i | \(-0.191141\pi\) | ||||
0.825060 | + | 0.565044i | \(0.191141\pi\) | |||||||
\(6\) | −1.80156e15 | −0.201163 | ||||||||
\(7\) | −7.89090e16 | −0.373780 | −0.186890 | − | 0.982381i | \(-0.559841\pi\) | ||||
−0.186890 | + | 0.982381i | \(0.559841\pi\) | |||||||
\(8\) | 1.15292e18 | 0.353553 | ||||||||
\(9\) | −3.35211e19 | −0.919067 | ||||||||
\(10\) | 3.68978e20 | 1.16681 | ||||||||
\(11\) | 1.20679e21 | 0.540856 | 0.270428 | − | 0.962740i | \(-0.412835\pi\) | ||||
0.270428 | + | 0.962740i | \(0.412835\pi\) | |||||||
\(12\) | −1.88907e21 | −0.142244 | ||||||||
\(13\) | 9.23598e22 | 1.34786 | 0.673929 | − | 0.738796i | \(-0.264605\pi\) | ||||
0.673929 | + | 0.738796i | \(0.264605\pi\) | |||||||
\(14\) | −8.27420e22 | −0.264303 | ||||||||
\(15\) | −6.04574e23 | −0.469439 | ||||||||
\(16\) | 1.20893e24 | 0.250000 | ||||||||
\(17\) | −4.95668e24 | −0.295793 | −0.147897 | − | 0.989003i | \(-0.547250\pi\) | ||||
−0.147897 | + | 0.989003i | \(0.547250\pi\) | |||||||
\(18\) | −3.51494e25 | −0.649878 | ||||||||
\(19\) | 2.41331e26 | 1.47287 | 0.736435 | − | 0.676508i | \(-0.236508\pi\) | ||||
0.736435 | + | 0.676508i | \(0.236508\pi\) | |||||||
\(20\) | 3.86902e26 | 0.825060 | ||||||||
\(21\) | 1.35574e26 | 0.106336 | ||||||||
\(22\) | 1.26541e27 | 0.382443 | ||||||||
\(23\) | 8.23610e27 | 1.00069 | 0.500347 | − | 0.865825i | \(-0.333206\pi\) | ||||
0.500347 | + | 0.865825i | \(0.333206\pi\) | |||||||
\(24\) | −1.98084e27 | −0.100581 | ||||||||
\(25\) | 7.83484e28 | 1.72290 | ||||||||
\(26\) | 9.68462e28 | 0.953079 | ||||||||
\(27\) | 1.20257e29 | 0.545950 | ||||||||
\(28\) | −8.67613e28 | −0.186890 | ||||||||
\(29\) | 2.60718e29 | 0.273534 | 0.136767 | − | 0.990603i | \(-0.456329\pi\) | ||||
0.136767 | + | 0.990603i | \(0.456329\pi\) | |||||||
\(30\) | −6.33942e29 | −0.331943 | ||||||||
\(31\) | −6.40610e30 | −1.71269 | −0.856346 | − | 0.516402i | \(-0.827271\pi\) | ||||
−0.856346 | + | 0.516402i | \(0.827271\pi\) | |||||||
\(32\) | 1.26765e30 | 0.176777 | ||||||||
\(33\) | −2.07339e30 | −0.153867 | ||||||||
\(34\) | −5.19746e30 | −0.209157 | ||||||||
\(35\) | −2.77669e31 | −0.616783 | ||||||||
\(36\) | −3.68569e31 | −0.459533 | ||||||||
\(37\) | 7.38149e31 | 0.524818 | 0.262409 | − | 0.964957i | \(-0.415483\pi\) | ||||
0.262409 | + | 0.964957i | \(0.415483\pi\) | |||||||
\(38\) | 2.53054e32 | 1.04148 | ||||||||
\(39\) | −1.58683e32 | −0.383448 | ||||||||
\(40\) | 4.05696e32 | 0.583406 | ||||||||
\(41\) | 2.15386e33 | 1.86701 | 0.933507 | − | 0.358558i | \(-0.116732\pi\) | ||||
0.933507 | + | 0.358558i | \(0.116732\pi\) | |||||||
\(42\) | 1.42159e32 | 0.0751908 | ||||||||
\(43\) | −5.67618e33 | −1.85333 | −0.926665 | − | 0.375889i | \(-0.877337\pi\) | ||||
−0.926665 | + | 0.375889i | \(0.877337\pi\) | |||||||
\(44\) | 1.32688e33 | 0.270428 | ||||||||
\(45\) | −1.17956e34 | −1.51657 | ||||||||
\(46\) | 8.63618e33 | 0.707597 | ||||||||
\(47\) | −6.45458e33 | −0.340300 | −0.170150 | − | 0.985418i | \(-0.554425\pi\) | ||||
−0.170150 | + | 0.985418i | \(0.554425\pi\) | |||||||
\(48\) | −2.07706e33 | −0.0711218 | ||||||||
\(49\) | −3.83410e34 | −0.860288 | ||||||||
\(50\) | 8.21542e34 | 1.21827 | ||||||||
\(51\) | 8.51608e33 | 0.0841494 | ||||||||
\(52\) | 1.01551e35 | 0.673929 | ||||||||
\(53\) | −9.99163e34 | −0.448726 | −0.224363 | − | 0.974506i | \(-0.572030\pi\) | ||||
−0.224363 | + | 0.974506i | \(0.572030\pi\) | |||||||
\(54\) | 1.26099e35 | 0.386045 | ||||||||
\(55\) | 4.24652e35 | 0.892479 | ||||||||
\(56\) | −9.09758e34 | −0.132151 | ||||||||
\(57\) | −4.14631e35 | −0.419013 | ||||||||
\(58\) | 2.73383e35 | 0.193418 | ||||||||
\(59\) | −3.33277e36 | −1.66088 | −0.830442 | − | 0.557105i | \(-0.811912\pi\) | ||||
−0.830442 | + | 0.557105i | \(0.811912\pi\) | |||||||
\(60\) | −6.64736e35 | −0.234719 | ||||||||
\(61\) | 2.08511e36 | 0.524648 | 0.262324 | − | 0.964980i | \(-0.415511\pi\) | ||||
0.262324 | + | 0.964980i | \(0.415511\pi\) | |||||||
\(62\) | −6.71729e36 | −1.21106 | ||||||||
\(63\) | 2.64512e36 | 0.343529 | ||||||||
\(64\) | 1.32923e36 | 0.125000 | ||||||||
\(65\) | 3.25000e37 | 2.22413 | ||||||||
\(66\) | −2.17411e36 | −0.108800 | ||||||||
\(67\) | 2.21433e36 | 0.0814159 | 0.0407080 | − | 0.999171i | \(-0.487039\pi\) | ||||
0.0407080 | + | 0.999171i | \(0.487039\pi\) | |||||||
\(68\) | −5.44993e36 | −0.147897 | ||||||||
\(69\) | −1.41505e37 | −0.284685 | ||||||||
\(70\) | −2.91157e37 | −0.436131 | ||||||||
\(71\) | 5.59105e37 | 0.626177 | 0.313089 | − | 0.949724i | \(-0.398636\pi\) | ||||
0.313089 | + | 0.949724i | \(0.398636\pi\) | |||||||
\(72\) | −3.86472e37 | −0.324939 | ||||||||
\(73\) | −2.02164e38 | −1.28110 | −0.640552 | − | 0.767915i | \(-0.721294\pi\) | ||||
−0.640552 | + | 0.767915i | \(0.721294\pi\) | |||||||
\(74\) | 7.74006e37 | 0.371103 | ||||||||
\(75\) | −1.34610e38 | −0.490143 | ||||||||
\(76\) | 2.65346e38 | 0.736435 | ||||||||
\(77\) | −9.52266e37 | −0.202162 | ||||||||
\(78\) | −1.66392e38 | −0.271139 | ||||||||
\(79\) | −2.46315e38 | −0.309126 | −0.154563 | − | 0.987983i | \(-0.549397\pi\) | ||||
−0.154563 | + | 0.987983i | \(0.549397\pi\) | |||||||
\(80\) | 4.25403e38 | 0.412530 | ||||||||
\(81\) | 1.01600e39 | 0.763751 | ||||||||
\(82\) | 2.25848e39 | 1.32018 | ||||||||
\(83\) | −3.59771e37 | −0.0164031 | −0.00820154 | − | 0.999966i | \(-0.502611\pi\) | ||||
−0.00820154 | + | 0.999966i | \(0.502611\pi\) | |||||||
\(84\) | 1.49065e38 | 0.0531679 | ||||||||
\(85\) | −1.74418e39 | −0.488095 | ||||||||
\(86\) | −5.95190e39 | −1.31050 | ||||||||
\(87\) | −4.47940e38 | −0.0778171 | ||||||||
\(88\) | 1.39134e39 | 0.191222 | ||||||||
\(89\) | 5.24223e38 | 0.0571506 | 0.0285753 | − | 0.999592i | \(-0.490903\pi\) | ||||
0.0285753 | + | 0.999592i | \(0.490903\pi\) | |||||||
\(90\) | −1.23686e40 | −1.07238 | ||||||||
\(91\) | −7.28801e39 | −0.503803 | ||||||||
\(92\) | 9.05569e39 | 0.500347 | ||||||||
\(93\) | 1.10063e40 | 0.487239 | ||||||||
\(94\) | −6.76812e39 | −0.240628 | ||||||||
\(95\) | 8.49208e40 | 2.43041 | ||||||||
\(96\) | −2.17795e39 | −0.0502907 | ||||||||
\(97\) | −2.35889e40 | −0.440441 | −0.220221 | − | 0.975450i | \(-0.570678\pi\) | ||||
−0.220221 | + | 0.975450i | \(0.570678\pi\) | |||||||
\(98\) | −4.02035e40 | −0.608316 | ||||||||
\(99\) | −4.04530e40 | −0.497083 | ||||||||
\(100\) | 8.61450e40 | 0.861450 | ||||||||
\(101\) | −1.92595e40 | −0.157057 | −0.0785284 | − | 0.996912i | \(-0.525022\pi\) | ||||
−0.0785284 | + | 0.996912i | \(0.525022\pi\) | |||||||
\(102\) | 8.92976e39 | 0.0595026 | ||||||||
\(103\) | −2.65701e41 | −1.44954 | −0.724770 | − | 0.688991i | \(-0.758054\pi\) | ||||
−0.724770 | + | 0.688991i | \(0.758054\pi\) | |||||||
\(104\) | 1.06484e41 | 0.476540 | ||||||||
\(105\) | 4.77063e40 | 0.175467 | ||||||||
\(106\) | −1.04770e41 | −0.317297 | ||||||||
\(107\) | −2.47756e41 | −0.618951 | −0.309476 | − | 0.950907i | \(-0.600154\pi\) | ||||
−0.309476 | + | 0.950907i | \(0.600154\pi\) | |||||||
\(108\) | 1.32224e41 | 0.272975 | ||||||||
\(109\) | −5.73631e40 | −0.0980369 | −0.0490184 | − | 0.998798i | \(-0.515609\pi\) | ||||
−0.0490184 | + | 0.998798i | \(0.515609\pi\) | |||||||
\(110\) | 4.45280e41 | 0.631078 | ||||||||
\(111\) | −1.26822e41 | −0.149304 | ||||||||
\(112\) | −9.53951e40 | −0.0934451 | ||||||||
\(113\) | 1.51047e42 | 1.23312 | 0.616558 | − | 0.787310i | \(-0.288527\pi\) | ||||
0.616558 | + | 0.787310i | \(0.288527\pi\) | |||||||
\(114\) | −4.34772e41 | −0.296287 | ||||||||
\(115\) | 2.89816e42 | 1.65127 | ||||||||
\(116\) | 2.86663e41 | 0.136767 | ||||||||
\(117\) | −3.09600e42 | −1.23877 | ||||||||
\(118\) | −3.49466e42 | −1.17442 | ||||||||
\(119\) | 3.91127e41 | 0.110562 | ||||||||
\(120\) | −6.97026e41 | −0.165972 | ||||||||
\(121\) | −3.52217e42 | −0.707474 | ||||||||
\(122\) | 2.18640e42 | 0.370982 | ||||||||
\(123\) | −3.70054e42 | −0.531142 | ||||||||
\(124\) | −7.04359e42 | −0.856346 | ||||||||
\(125\) | 1.15677e43 | 1.19287 | ||||||||
\(126\) | 2.77361e42 | 0.242912 | ||||||||
\(127\) | 7.49737e42 | 0.558384 | 0.279192 | − | 0.960235i | \(-0.409933\pi\) | ||||
0.279192 | + | 0.960235i | \(0.409933\pi\) | |||||||
\(128\) | 1.39380e42 | 0.0883883 | ||||||||
\(129\) | 9.75225e42 | 0.527249 | ||||||||
\(130\) | 3.40787e43 | 1.57270 | ||||||||
\(131\) | −4.11904e43 | −1.62456 | −0.812278 | − | 0.583271i | \(-0.801773\pi\) | ||||
−0.812278 | + | 0.583271i | \(0.801773\pi\) | |||||||
\(132\) | −2.27972e42 | −0.0769334 | ||||||||
\(133\) | −1.90432e43 | −0.550530 | ||||||||
\(134\) | 2.32190e42 | 0.0575698 | ||||||||
\(135\) | 4.23166e43 | 0.900884 | ||||||||
\(136\) | −5.71467e42 | −0.104579 | ||||||||
\(137\) | −3.66801e43 | −0.577643 | −0.288821 | − | 0.957383i | \(-0.593263\pi\) | ||||
−0.288821 | + | 0.957383i | \(0.593263\pi\) | |||||||
\(138\) | −1.48378e43 | −0.201302 | ||||||||
\(139\) | −8.88436e43 | −1.03950 | −0.519748 | − | 0.854320i | \(-0.673974\pi\) | ||||
−0.519748 | + | 0.854320i | \(0.673974\pi\) | |||||||
\(140\) | −3.05300e43 | −0.308391 | ||||||||
\(141\) | 1.10896e43 | 0.0968110 | ||||||||
\(142\) | 5.86264e43 | 0.442774 | ||||||||
\(143\) | 1.11459e44 | 0.728998 | ||||||||
\(144\) | −4.05246e43 | −0.229767 | ||||||||
\(145\) | 9.17428e43 | 0.451365 | ||||||||
\(146\) | −2.11984e44 | −0.905877 | ||||||||
\(147\) | 6.58737e43 | 0.244741 | ||||||||
\(148\) | 8.11604e43 | 0.262409 | ||||||||
\(149\) | 3.54730e44 | 0.999033 | 0.499517 | − | 0.866304i | \(-0.333511\pi\) | ||||
0.499517 | + | 0.866304i | \(0.333511\pi\) | |||||||
\(150\) | −1.41149e44 | −0.346583 | ||||||||
\(151\) | 4.26711e44 | 0.914338 | 0.457169 | − | 0.889380i | \(-0.348863\pi\) | ||||
0.457169 | + | 0.889380i | \(0.348863\pi\) | |||||||
\(152\) | 2.78236e44 | 0.520738 | ||||||||
\(153\) | 1.66154e44 | 0.271854 | ||||||||
\(154\) | −9.98524e43 | −0.142950 | ||||||||
\(155\) | −2.25421e45 | −2.82615 | ||||||||
\(156\) | −1.74474e44 | −0.191724 | ||||||||
\(157\) | −8.24494e43 | −0.0794776 | −0.0397388 | − | 0.999210i | \(-0.512653\pi\) | ||||
−0.0397388 | + | 0.999210i | \(0.512653\pi\) | |||||||
\(158\) | −2.58280e44 | −0.218585 | ||||||||
\(159\) | 1.71666e44 | 0.127657 | ||||||||
\(160\) | 4.46067e44 | 0.291703 | ||||||||
\(161\) | −6.49902e44 | −0.374040 | ||||||||
\(162\) | 1.06536e45 | 0.540054 | ||||||||
\(163\) | 1.78991e44 | 0.0799806 | 0.0399903 | − | 0.999200i | \(-0.487267\pi\) | ||||
0.0399903 | + | 0.999200i | \(0.487267\pi\) | |||||||
\(164\) | 2.36819e45 | 0.933507 | ||||||||
\(165\) | −7.29595e44 | −0.253899 | ||||||||
\(166\) | −3.77248e43 | −0.0115987 | ||||||||
\(167\) | 3.96773e45 | 1.07859 | 0.539293 | − | 0.842118i | \(-0.318692\pi\) | ||||
0.539293 | + | 0.842118i | \(0.318692\pi\) | |||||||
\(168\) | 1.56306e44 | 0.0375954 | ||||||||
\(169\) | 3.83487e45 | 0.816721 | ||||||||
\(170\) | −1.82891e45 | −0.345135 | ||||||||
\(171\) | −8.08969e45 | −1.35367 | ||||||||
\(172\) | −6.24102e45 | −0.926665 | ||||||||
\(173\) | 6.93399e45 | 0.914193 | 0.457097 | − | 0.889417i | \(-0.348889\pi\) | ||||
0.457097 | + | 0.889417i | \(0.348889\pi\) | |||||||
\(174\) | −4.69699e44 | −0.0550250 | ||||||||
\(175\) | −6.18239e45 | −0.643986 | ||||||||
\(176\) | 1.45892e45 | 0.135214 | ||||||||
\(177\) | 5.72604e45 | 0.472500 | ||||||||
\(178\) | 5.49687e44 | 0.0404116 | ||||||||
\(179\) | −1.62403e46 | −1.06441 | −0.532203 | − | 0.846617i | \(-0.678636\pi\) | ||||
−0.532203 | + | 0.846617i | \(0.678636\pi\) | |||||||
\(180\) | −1.29694e46 | −0.758286 | ||||||||
\(181\) | 2.21915e46 | 1.15818 | 0.579090 | − | 0.815264i | \(-0.303408\pi\) | ||||
0.579090 | + | 0.815264i | \(0.303408\pi\) | |||||||
\(182\) | −7.64204e45 | −0.356242 | ||||||||
\(183\) | −3.58243e45 | −0.149256 | ||||||||
\(184\) | 9.49558e45 | 0.353799 | ||||||||
\(185\) | 2.59744e46 | 0.866014 | ||||||||
\(186\) | 1.15410e46 | 0.344530 | ||||||||
\(187\) | −5.98168e45 | −0.159982 | ||||||||
\(188\) | −7.09688e45 | −0.170150 | ||||||||
\(189\) | −9.48935e45 | −0.204066 | ||||||||
\(190\) | 8.90459e46 | 1.71856 | ||||||||
\(191\) | −4.97685e46 | −0.862523 | −0.431262 | − | 0.902227i | \(-0.641931\pi\) | ||||
−0.431262 | + | 0.902227i | \(0.641931\pi\) | |||||||
\(192\) | −2.28375e45 | −0.0355609 | ||||||||
\(193\) | 4.02520e46 | 0.563459 | 0.281730 | − | 0.959494i | \(-0.409092\pi\) | ||||
0.281730 | + | 0.959494i | \(0.409092\pi\) | |||||||
\(194\) | −2.47348e46 | −0.311439 | ||||||||
\(195\) | −5.58383e46 | −0.632736 | ||||||||
\(196\) | −4.21564e46 | −0.430144 | ||||||||
\(197\) | −7.00300e46 | −0.643764 | −0.321882 | − | 0.946780i | \(-0.604315\pi\) | ||||
−0.321882 | + | 0.946780i | \(0.604315\pi\) | |||||||
\(198\) | −4.24180e46 | −0.351491 | ||||||||
\(199\) | −1.17193e47 | −0.875818 | −0.437909 | − | 0.899019i | \(-0.644281\pi\) | ||||
−0.437909 | + | 0.899019i | \(0.644281\pi\) | |||||||
\(200\) | 9.03295e46 | 0.609137 | ||||||||
\(201\) | −3.80445e45 | −0.0231618 | ||||||||
\(202\) | −2.01950e46 | −0.111056 | ||||||||
\(203\) | −2.05730e46 | −0.102242 | ||||||||
\(204\) | 9.36353e45 | 0.0420747 | ||||||||
\(205\) | 7.57910e47 | 3.08080 | ||||||||
\(206\) | −2.78608e47 | −1.02498 | ||||||||
\(207\) | −2.76083e47 | −0.919704 | ||||||||
\(208\) | 1.11656e47 | 0.336964 | ||||||||
\(209\) | 2.91236e47 | 0.796611 | ||||||||
\(210\) | 5.00237e46 | 0.124074 | ||||||||
\(211\) | 5.52367e47 | 1.24290 | 0.621452 | − | 0.783452i | \(-0.286543\pi\) | ||||
0.621452 | + | 0.783452i | \(0.286543\pi\) | |||||||
\(212\) | −1.09859e47 | −0.224363 | ||||||||
\(213\) | −9.60599e46 | −0.178139 | ||||||||
\(214\) | −2.59791e47 | −0.437665 | ||||||||
\(215\) | −1.99736e48 | −3.05822 | ||||||||
\(216\) | 1.38647e47 | 0.193023 | ||||||||
\(217\) | 5.05499e47 | 0.640171 | ||||||||
\(218\) | −6.01496e46 | −0.0693225 | ||||||||
\(219\) | 3.47337e47 | 0.364458 | ||||||||
\(220\) | 4.66910e47 | 0.446239 | ||||||||
\(221\) | −4.57798e47 | −0.398687 | ||||||||
\(222\) | −1.32982e47 | −0.105574 | ||||||||
\(223\) | 1.20926e48 | 0.875531 | 0.437765 | − | 0.899089i | \(-0.355770\pi\) | ||||
0.437765 | + | 0.899089i | \(0.355770\pi\) | |||||||
\(224\) | −1.00029e47 | −0.0660757 | ||||||||
\(225\) | −2.62633e48 | −1.58346 | ||||||||
\(226\) | 1.58384e48 | 0.871944 | ||||||||
\(227\) | −1.02944e48 | −0.517690 | −0.258845 | − | 0.965919i | \(-0.583342\pi\) | ||||
−0.258845 | + | 0.965919i | \(0.583342\pi\) | |||||||
\(228\) | −4.55892e47 | −0.209506 | ||||||||
\(229\) | 2.04406e48 | 0.858750 | 0.429375 | − | 0.903126i | \(-0.358734\pi\) | ||||
0.429375 | + | 0.903126i | \(0.358734\pi\) | |||||||
\(230\) | 3.03894e48 | 1.16762 | ||||||||
\(231\) | 1.63609e47 | 0.0575124 | ||||||||
\(232\) | 3.00587e47 | 0.0967090 | ||||||||
\(233\) | 4.38442e48 | 1.29156 | 0.645781 | − | 0.763523i | \(-0.276532\pi\) | ||||
0.645781 | + | 0.763523i | \(0.276532\pi\) | |||||||
\(234\) | −3.24639e48 | −0.875944 | ||||||||
\(235\) | −2.27127e48 | −0.561536 | ||||||||
\(236\) | −3.66442e48 | −0.830442 | ||||||||
\(237\) | 4.23194e47 | 0.0879423 | ||||||||
\(238\) | 4.10126e47 | 0.0781789 | ||||||||
\(239\) | 4.33337e48 | 0.757999 | 0.379000 | − | 0.925397i | \(-0.376268\pi\) | ||||
0.379000 | + | 0.925397i | \(0.376268\pi\) | |||||||
\(240\) | −7.30885e47 | −0.117360 | ||||||||
\(241\) | −3.97635e48 | −0.586320 | −0.293160 | − | 0.956063i | \(-0.594707\pi\) | ||||
−0.293160 | + | 0.956063i | \(0.594707\pi\) | |||||||
\(242\) | −3.69327e48 | −0.500260 | ||||||||
\(243\) | −6.13173e48 | −0.763228 | ||||||||
\(244\) | 2.29260e48 | 0.262324 | ||||||||
\(245\) | −1.34916e49 | −1.41958 | ||||||||
\(246\) | −3.88030e48 | −0.375574 | ||||||||
\(247\) | 2.22893e49 | 1.98522 | ||||||||
\(248\) | −7.38574e48 | −0.605528 | ||||||||
\(249\) | 6.18123e46 | 0.00466647 | ||||||||
\(250\) | 1.21297e49 | 0.843487 | ||||||||
\(251\) | 1.35701e49 | 0.869507 | 0.434754 | − | 0.900549i | \(-0.356835\pi\) | ||||
0.434754 | + | 0.900549i | \(0.356835\pi\) | |||||||
\(252\) | 2.90834e48 | 0.171765 | ||||||||
\(253\) | 9.93926e48 | 0.541232 | ||||||||
\(254\) | 7.86156e48 | 0.394837 | ||||||||
\(255\) | 2.99668e48 | 0.138857 | ||||||||
\(256\) | 1.46150e48 | 0.0625000 | ||||||||
\(257\) | −4.30252e49 | −1.69861 | −0.849304 | − | 0.527903i | \(-0.822978\pi\) | ||||
−0.849304 | + | 0.527903i | \(0.822978\pi\) | |||||||
\(258\) | 1.02260e49 | 0.372821 | ||||||||
\(259\) | −5.82466e48 | −0.196167 | ||||||||
\(260\) | 3.57342e49 | 1.11206 | ||||||||
\(261\) | −8.73956e48 | −0.251397 | ||||||||
\(262\) | −4.31913e49 | −1.14873 | ||||||||
\(263\) | −1.54140e49 | −0.379160 | −0.189580 | − | 0.981865i | \(-0.560713\pi\) | ||||
−0.189580 | + | 0.981865i | \(0.560713\pi\) | |||||||
\(264\) | −2.39045e48 | −0.0544001 | ||||||||
\(265\) | −3.51591e49 | −0.740452 | ||||||||
\(266\) | −1.99682e49 | −0.389283 | ||||||||
\(267\) | −9.00667e47 | −0.0162586 | ||||||||
\(268\) | 2.43468e48 | 0.0407080 | ||||||||
\(269\) | 2.17495e49 | 0.336920 | 0.168460 | − | 0.985708i | \(-0.446121\pi\) | ||||
0.168460 | + | 0.985708i | \(0.446121\pi\) | |||||||
\(270\) | 4.43722e49 | 0.637021 | ||||||||
\(271\) | 5.12539e49 | 0.682113 | 0.341056 | − | 0.940043i | \(-0.389215\pi\) | ||||
0.341056 | + | 0.940043i | \(0.389215\pi\) | |||||||
\(272\) | −5.99226e48 | −0.0739483 | ||||||||
\(273\) | 1.25215e49 | 0.143326 | ||||||||
\(274\) | −3.84619e49 | −0.408455 | ||||||||
\(275\) | 9.45501e49 | 0.931841 | ||||||||
\(276\) | −1.55586e49 | −0.142342 | ||||||||
\(277\) | −5.73007e49 | −0.486771 | −0.243385 | − | 0.969930i | \(-0.578258\pi\) | ||||
−0.243385 | + | 0.969930i | \(0.578258\pi\) | |||||||
\(278\) | −9.31592e49 | −0.735034 | ||||||||
\(279\) | 2.14740e50 | 1.57408 | ||||||||
\(280\) | −3.20130e49 | −0.218066 | ||||||||
\(281\) | 1.97230e49 | 0.124880 | 0.0624400 | − | 0.998049i | \(-0.480112\pi\) | ||||
0.0624400 | + | 0.998049i | \(0.480112\pi\) | |||||||
\(282\) | 1.16283e49 | 0.0684557 | ||||||||
\(283\) | −1.39119e49 | −0.0761663 | −0.0380832 | − | 0.999275i | \(-0.512125\pi\) | ||||
−0.0380832 | + | 0.999275i | \(0.512125\pi\) | |||||||
\(284\) | 6.14742e49 | 0.313089 | ||||||||
\(285\) | −1.45902e50 | −0.691422 | ||||||||
\(286\) | 1.16873e50 | 0.515479 | ||||||||
\(287\) | −1.69959e50 | −0.697853 | ||||||||
\(288\) | −4.24931e49 | −0.162470 | ||||||||
\(289\) | −2.56237e50 | −0.912506 | ||||||||
\(290\) | 9.61993e49 | 0.319163 | ||||||||
\(291\) | 4.05282e49 | 0.125300 | ||||||||
\(292\) | −2.22281e50 | −0.640552 | ||||||||
\(293\) | 3.84683e50 | 1.03351 | 0.516757 | − | 0.856132i | \(-0.327139\pi\) | ||||
0.516757 | + | 0.856132i | \(0.327139\pi\) | |||||||
\(294\) | 6.90736e49 | 0.173058 | ||||||||
\(295\) | −1.17275e51 | −2.74066 | ||||||||
\(296\) | 8.51028e49 | 0.185551 | ||||||||
\(297\) | 1.45125e50 | 0.295281 | ||||||||
\(298\) | 3.71962e50 | 0.706423 | ||||||||
\(299\) | 7.60684e50 | 1.34879 | ||||||||
\(300\) | −1.48006e50 | −0.245071 | ||||||||
\(301\) | 4.47901e50 | 0.692738 | ||||||||
\(302\) | 4.47439e50 | 0.646535 | ||||||||
\(303\) | 3.30897e49 | 0.0446807 | ||||||||
\(304\) | 2.91751e50 | 0.368217 | ||||||||
\(305\) | 7.33720e50 | 0.865732 | ||||||||
\(306\) | 1.74225e50 | 0.192230 | ||||||||
\(307\) | −1.33309e51 | −1.37569 | −0.687846 | − | 0.725856i | \(-0.741444\pi\) | ||||
−0.687846 | + | 0.725856i | \(0.741444\pi\) | |||||||
\(308\) | −1.04703e50 | −0.101081 | ||||||||
\(309\) | 4.56501e50 | 0.412376 | ||||||||
\(310\) | −2.36371e51 | −1.99839 | ||||||||
\(311\) | −3.42217e50 | −0.270841 | −0.135420 | − | 0.990788i | \(-0.543239\pi\) | ||||
−0.135420 | + | 0.990788i | \(0.543239\pi\) | |||||||
\(312\) | −1.82949e50 | −0.135570 | ||||||||
\(313\) | 8.29482e50 | 0.575636 | 0.287818 | − | 0.957685i | \(-0.407070\pi\) | ||||
0.287818 | + | 0.957685i | \(0.407070\pi\) | |||||||
\(314\) | −8.64544e49 | −0.0561991 | ||||||||
\(315\) | 9.30777e50 | 0.566865 | ||||||||
\(316\) | −2.70826e50 | −0.154563 | ||||||||
\(317\) | −2.94058e51 | −1.57296 | −0.786481 | − | 0.617615i | \(-0.788099\pi\) | ||||
−0.786481 | + | 0.617615i | \(0.788099\pi\) | |||||||
\(318\) | 1.80005e50 | 0.0902670 | ||||||||
\(319\) | 3.14632e50 | 0.147943 | ||||||||
\(320\) | 4.67736e50 | 0.206265 | ||||||||
\(321\) | 4.25670e50 | 0.176084 | ||||||||
\(322\) | −6.81472e50 | −0.264486 | ||||||||
\(323\) | −1.19620e51 | −0.435665 | ||||||||
\(324\) | 1.11711e51 | 0.381876 | ||||||||
\(325\) | 7.23624e51 | 2.32222 | ||||||||
\(326\) | 1.87685e50 | 0.0565548 | ||||||||
\(327\) | 9.85556e49 | 0.0278902 | ||||||||
\(328\) | 2.48323e51 | 0.660089 | ||||||||
\(329\) | 5.09324e50 | 0.127197 | ||||||||
\(330\) | −7.65035e50 | −0.179534 | ||||||||
\(331\) | −8.47531e51 | −1.86931 | −0.934656 | − | 0.355554i | \(-0.884292\pi\) | ||||
−0.934656 | + | 0.355554i | \(0.884292\pi\) | |||||||
\(332\) | −3.95573e49 | −0.00820154 | ||||||||
\(333\) | −2.47436e51 | −0.482343 | ||||||||
\(334\) | 4.16047e51 | 0.762675 | ||||||||
\(335\) | 7.79191e50 | 0.134346 | ||||||||
\(336\) | 1.63898e50 | 0.0265839 | ||||||||
\(337\) | 2.49054e51 | 0.380085 | 0.190042 | − | 0.981776i | \(-0.439137\pi\) | ||||
0.190042 | + | 0.981776i | \(0.439137\pi\) | |||||||
\(338\) | 4.02116e51 | 0.577509 | ||||||||
\(339\) | −2.59514e51 | −0.350806 | ||||||||
\(340\) | −1.91775e51 | −0.244047 | ||||||||
\(341\) | −7.73083e51 | −0.926321 | ||||||||
\(342\) | −8.48265e51 | −0.957186 | ||||||||
\(343\) | 6.54224e51 | 0.695339 | ||||||||
\(344\) | −6.54419e51 | −0.655251 | ||||||||
\(345\) | −4.97933e51 | −0.469764 | ||||||||
\(346\) | 7.27082e51 | 0.646432 | ||||||||
\(347\) | −1.02424e51 | −0.0858314 | −0.0429157 | − | 0.999079i | \(-0.513665\pi\) | ||||
−0.0429157 | + | 0.999079i | \(0.513665\pi\) | |||||||
\(348\) | −4.92515e50 | −0.0389086 | ||||||||
\(349\) | 7.39758e51 | 0.551022 | 0.275511 | − | 0.961298i | \(-0.411153\pi\) | ||||
0.275511 | + | 0.961298i | \(0.411153\pi\) | |||||||
\(350\) | −6.48271e51 | −0.455367 | ||||||||
\(351\) | 1.11069e52 | 0.735863 | ||||||||
\(352\) | 1.52979e51 | 0.0956108 | ||||||||
\(353\) | −6.47846e51 | −0.382024 | −0.191012 | − | 0.981588i | \(-0.561177\pi\) | ||||
−0.191012 | + | 0.981588i | \(0.561177\pi\) | |||||||
\(354\) | 6.00418e51 | 0.334108 | ||||||||
\(355\) | 1.96741e52 | 1.03327 | ||||||||
\(356\) | 5.76389e50 | 0.0285753 | ||||||||
\(357\) | −6.71995e50 | −0.0314534 | ||||||||
\(358\) | −1.70292e52 | −0.752648 | ||||||||
\(359\) | 2.46025e52 | 1.02693 | 0.513467 | − | 0.858109i | \(-0.328361\pi\) | ||||
0.513467 | + | 0.858109i | \(0.328361\pi\) | |||||||
\(360\) | −1.35994e52 | −0.536189 | ||||||||
\(361\) | 3.13936e52 | 1.16935 | ||||||||
\(362\) | 2.32695e52 | 0.818957 | ||||||||
\(363\) | 6.05145e51 | 0.201267 | ||||||||
\(364\) | −8.01325e51 | −0.251901 | ||||||||
\(365\) | −7.11383e52 | −2.11398 | ||||||||
\(366\) | −3.75645e51 | −0.105540 | ||||||||
\(367\) | −4.93112e52 | −1.31006 | −0.655030 | − | 0.755603i | \(-0.727344\pi\) | ||||
−0.655030 | + | 0.755603i | \(0.727344\pi\) | |||||||
\(368\) | 9.95684e51 | 0.250173 | ||||||||
\(369\) | −7.21997e52 | −1.71591 | ||||||||
\(370\) | 2.72361e52 | 0.612364 | ||||||||
\(371\) | 7.88429e51 | 0.167725 | ||||||||
\(372\) | 1.21016e52 | 0.243620 | ||||||||
\(373\) | 3.70443e52 | 0.705815 | 0.352907 | − | 0.935658i | \(-0.385193\pi\) | ||||
0.352907 | + | 0.935658i | \(0.385193\pi\) | |||||||
\(374\) | −6.27225e51 | −0.113124 | ||||||||
\(375\) | −1.98746e52 | −0.339357 | ||||||||
\(376\) | −7.44162e51 | −0.120314 | ||||||||
\(377\) | 2.40799e52 | 0.368686 | ||||||||
\(378\) | −9.95031e51 | −0.144296 | ||||||||
\(379\) | 1.03809e53 | 1.42604 | 0.713021 | − | 0.701143i | \(-0.247327\pi\) | ||||
0.713021 | + | 0.701143i | \(0.247327\pi\) | |||||||
\(380\) | 9.33714e52 | 1.21521 | ||||||||
\(381\) | −1.28812e52 | −0.158853 | ||||||||
\(382\) | −5.21861e52 | −0.609896 | ||||||||
\(383\) | −1.27369e52 | −0.141088 | −0.0705440 | − | 0.997509i | \(-0.522474\pi\) | ||||
−0.0705440 | + | 0.997509i | \(0.522474\pi\) | |||||||
\(384\) | −2.39468e51 | −0.0251454 | ||||||||
\(385\) | −3.35088e52 | −0.333591 | ||||||||
\(386\) | 4.22073e52 | 0.398426 | ||||||||
\(387\) | 1.90272e53 | 1.70333 | ||||||||
\(388\) | −2.59363e52 | −0.220221 | ||||||||
\(389\) | −1.61862e53 | −1.30371 | −0.651853 | − | 0.758346i | \(-0.726008\pi\) | ||||
−0.651853 | + | 0.758346i | \(0.726008\pi\) | |||||||
\(390\) | −5.85507e52 | −0.447412 | ||||||||
\(391\) | −4.08237e52 | −0.295998 | ||||||||
\(392\) | −4.42042e52 | −0.304158 | ||||||||
\(393\) | 7.07693e52 | 0.462166 | ||||||||
\(394\) | −7.34318e52 | −0.455210 | ||||||||
\(395\) | −8.66745e52 | −0.510095 | ||||||||
\(396\) | −4.44785e52 | −0.248542 | ||||||||
\(397\) | 2.20821e53 | 1.17175 | 0.585876 | − | 0.810401i | \(-0.300751\pi\) | ||||
0.585876 | + | 0.810401i | \(0.300751\pi\) | |||||||
\(398\) | −1.22886e53 | −0.619297 | ||||||||
\(399\) | 3.27181e52 | 0.156619 | ||||||||
\(400\) | 9.47174e52 | 0.430725 | ||||||||
\(401\) | −1.18852e52 | −0.0513509 | −0.0256755 | − | 0.999670i | \(-0.508174\pi\) | ||||
−0.0256755 | + | 0.999670i | \(0.508174\pi\) | |||||||
\(402\) | −3.98925e51 | −0.0163779 | ||||||||
\(403\) | −5.91666e53 | −2.30847 | ||||||||
\(404\) | −2.11760e52 | −0.0785284 | ||||||||
\(405\) | 3.57516e53 | 1.26028 | ||||||||
\(406\) | −2.15723e52 | −0.0722959 | ||||||||
\(407\) | 8.90792e52 | 0.283851 | ||||||||
\(408\) | 9.81837e51 | 0.0297513 | ||||||||
\(409\) | −9.36392e52 | −0.269855 | −0.134927 | − | 0.990856i | \(-0.543080\pi\) | ||||
−0.134927 | + | 0.990856i | \(0.543080\pi\) | |||||||
\(410\) | 7.94726e53 | 2.17845 | ||||||||
\(411\) | 6.30202e52 | 0.164332 | ||||||||
\(412\) | −2.92141e53 | −0.724770 | ||||||||
\(413\) | 2.62985e53 | 0.620806 | ||||||||
\(414\) | −2.89494e53 | −0.650329 | ||||||||
\(415\) | −1.26598e52 | −0.0270671 | ||||||||
\(416\) | 1.17080e53 | 0.238270 | ||||||||
\(417\) | 1.52642e53 | 0.295723 | ||||||||
\(418\) | 3.05383e53 | 0.563289 | ||||||||
\(419\) | −4.45575e53 | −0.782588 | −0.391294 | − | 0.920266i | \(-0.627972\pi\) | ||||
−0.391294 | + | 0.920266i | \(0.627972\pi\) | |||||||
\(420\) | 5.24536e52 | 0.0877335 | ||||||||
\(421\) | −5.72623e53 | −0.912191 | −0.456096 | − | 0.889931i | \(-0.650752\pi\) | ||||
−0.456096 | + | 0.889931i | \(0.650752\pi\) | |||||||
\(422\) | 5.79199e53 | 0.878866 | ||||||||
\(423\) | 2.16365e53 | 0.312758 | ||||||||
\(424\) | −1.15196e53 | −0.158649 | ||||||||
\(425\) | −3.88348e53 | −0.509622 | ||||||||
\(426\) | −1.00726e53 | −0.125964 | ||||||||
\(427\) | −1.64534e53 | −0.196103 | ||||||||
\(428\) | −2.72410e53 | −0.309476 | ||||||||
\(429\) | −1.91498e53 | −0.207391 | ||||||||
\(430\) | −2.09439e54 | −2.16249 | ||||||||
\(431\) | −7.99569e53 | −0.787176 | −0.393588 | − | 0.919287i | \(-0.628766\pi\) | ||||
−0.393588 | + | 0.919287i | \(0.628766\pi\) | |||||||
\(432\) | 1.45382e53 | 0.136488 | ||||||||
\(433\) | 1.41016e54 | 1.26261 | 0.631303 | − | 0.775536i | \(-0.282520\pi\) | ||||
0.631303 | + | 0.775536i | \(0.282520\pi\) | |||||||
\(434\) | 5.30054e53 | 0.452669 | ||||||||
\(435\) | −1.57623e53 | −0.128408 | ||||||||
\(436\) | −6.30714e52 | −0.0490184 | ||||||||
\(437\) | 1.98763e54 | 1.47389 | ||||||||
\(438\) | 3.64210e53 | 0.257711 | ||||||||
\(439\) | 9.48293e53 | 0.640353 | 0.320177 | − | 0.947358i | \(-0.396258\pi\) | ||||
0.320177 | + | 0.947358i | \(0.396258\pi\) | |||||||
\(440\) | 4.89590e53 | 0.315539 | ||||||||
\(441\) | 1.28523e54 | 0.790662 | ||||||||
\(442\) | −4.80036e53 | −0.281914 | ||||||||
\(443\) | −1.15125e54 | −0.645494 | −0.322747 | − | 0.946485i | \(-0.604606\pi\) | ||||
−0.322747 | + | 0.946485i | \(0.604606\pi\) | |||||||
\(444\) | −1.39442e53 | −0.0746521 | ||||||||
\(445\) | 1.84466e53 | 0.0943054 | ||||||||
\(446\) | 1.26801e54 | 0.619094 | ||||||||
\(447\) | −6.09463e53 | −0.284212 | ||||||||
\(448\) | −1.04888e53 | −0.0467225 | ||||||||
\(449\) | −1.29162e54 | −0.549649 | −0.274824 | − | 0.961494i | \(-0.588620\pi\) | ||||
−0.274824 | + | 0.961494i | \(0.588620\pi\) | |||||||
\(450\) | −2.75390e54 | −1.11968 | ||||||||
\(451\) | 2.59925e54 | 1.00979 | ||||||||
\(452\) | 1.66078e54 | 0.616558 | ||||||||
\(453\) | −7.33133e53 | −0.260118 | ||||||||
\(454\) | −1.07944e54 | −0.366062 | ||||||||
\(455\) | −2.56454e54 | −0.831336 | ||||||||
\(456\) | −4.78037e53 | −0.148143 | ||||||||
\(457\) | −5.70144e54 | −1.68928 | −0.844641 | − | 0.535332i | \(-0.820186\pi\) | ||||
−0.844641 | + | 0.535332i | \(0.820186\pi\) | |||||||
\(458\) | 2.14335e54 | 0.607228 | ||||||||
\(459\) | −5.96076e53 | −0.161488 | ||||||||
\(460\) | 3.18656e54 | 0.825633 | ||||||||
\(461\) | −5.36766e54 | −1.33020 | −0.665098 | − | 0.746756i | \(-0.731610\pi\) | ||||
−0.665098 | + | 0.746756i | \(0.731610\pi\) | |||||||
\(462\) | 1.71556e53 | 0.0406674 | ||||||||
\(463\) | 6.24453e54 | 1.41609 | 0.708043 | − | 0.706170i | \(-0.249578\pi\) | ||||
0.708043 | + | 0.706170i | \(0.249578\pi\) | |||||||
\(464\) | 3.15189e53 | 0.0683836 | ||||||||
\(465\) | 3.87296e54 | 0.804004 | ||||||||
\(466\) | 4.59739e54 | 0.913272 | ||||||||
\(467\) | −8.52716e53 | −0.162109 | −0.0810547 | − | 0.996710i | \(-0.525829\pi\) | ||||
−0.0810547 | + | 0.996710i | \(0.525829\pi\) | |||||||
\(468\) | −3.40409e54 | −0.619386 | ||||||||
\(469\) | −1.74731e53 | −0.0304317 | ||||||||
\(470\) | −2.38160e54 | −0.397066 | ||||||||
\(471\) | 1.41656e53 | 0.0226104 | ||||||||
\(472\) | −3.84242e54 | −0.587211 | ||||||||
\(473\) | −6.84996e54 | −1.00239 | ||||||||
\(474\) | 4.43751e53 | 0.0621846 | ||||||||
\(475\) | 1.89079e55 | 2.53761 | ||||||||
\(476\) | 4.30048e53 | 0.0552809 | ||||||||
\(477\) | 3.34931e54 | 0.412409 | ||||||||
\(478\) | 4.54387e54 | 0.535986 | ||||||||
\(479\) | −6.54754e54 | −0.739947 | −0.369973 | − | 0.929042i | \(-0.620633\pi\) | ||||
−0.369973 | + | 0.929042i | \(0.620633\pi\) | |||||||
\(480\) | −7.66389e53 | −0.0829858 | ||||||||
\(481\) | 6.81753e54 | 0.707380 | ||||||||
\(482\) | −4.16950e54 | −0.414591 | ||||||||
\(483\) | 1.11660e54 | 0.106410 | ||||||||
\(484\) | −3.87267e54 | −0.353737 | ||||||||
\(485\) | −8.30060e54 | −0.726781 | ||||||||
\(486\) | −6.42958e54 | −0.539684 | ||||||||
\(487\) | −4.90744e54 | −0.394922 | −0.197461 | − | 0.980311i | \(-0.563270\pi\) | ||||
−0.197461 | + | 0.980311i | \(0.563270\pi\) | |||||||
\(488\) | 2.40397e54 | 0.185491 | ||||||||
\(489\) | −3.07524e53 | −0.0227535 | ||||||||
\(490\) | −1.41470e55 | −1.00379 | ||||||||
\(491\) | 2.65373e54 | 0.180587 | 0.0902935 | − | 0.995915i | \(-0.471219\pi\) | ||||
0.0902935 | + | 0.995915i | \(0.471219\pi\) | |||||||
\(492\) | −4.06879e54 | −0.265571 | ||||||||
\(493\) | −1.29230e54 | −0.0809097 | ||||||||
\(494\) | 2.33720e55 | 1.40376 | ||||||||
\(495\) | −1.42348e55 | −0.820248 | ||||||||
\(496\) | −7.74451e54 | −0.428173 | ||||||||
\(497\) | −4.41184e54 | −0.234053 | ||||||||
\(498\) | 6.48149e52 | 0.00329969 | ||||||||
\(499\) | 6.02973e53 | 0.0294603 | 0.0147301 | − | 0.999892i | \(-0.495311\pi\) | ||||
0.0147301 | + | 0.999892i | \(0.495311\pi\) | |||||||
\(500\) | 1.27189e55 | 0.596435 | ||||||||
\(501\) | −6.81696e54 | −0.306844 | ||||||||
\(502\) | 1.42293e55 | 0.614834 | ||||||||
\(503\) | 4.08674e55 | 1.69525 | 0.847625 | − | 0.530596i | \(-0.178032\pi\) | ||||
0.847625 | + | 0.530596i | \(0.178032\pi\) | |||||||
\(504\) | 3.04961e54 | 0.121456 | ||||||||
\(505\) | −6.77713e54 | −0.259163 | ||||||||
\(506\) | 1.04221e55 | 0.382709 | ||||||||
\(507\) | −6.58870e54 | −0.232347 | ||||||||
\(508\) | 8.24344e54 | 0.279192 | ||||||||
\(509\) | 4.17871e54 | 0.135934 | 0.0679670 | − | 0.997688i | \(-0.478349\pi\) | ||||
0.0679670 | + | 0.997688i | \(0.478349\pi\) | |||||||
\(510\) | 3.14225e54 | 0.0981865 | ||||||||
\(511\) | 1.59525e55 | 0.478851 | ||||||||
\(512\) | 1.53250e54 | 0.0441942 | ||||||||
\(513\) | 2.90217e55 | 0.804114 | ||||||||
\(514\) | −4.51151e55 | −1.20110 | ||||||||
\(515\) | −9.34962e55 | −2.39192 | ||||||||
\(516\) | 1.07227e55 | 0.263624 | ||||||||
\(517\) | −7.78933e54 | −0.184053 | ||||||||
\(518\) | −6.10760e54 | −0.138711 | ||||||||
\(519\) | −1.19133e55 | −0.260076 | ||||||||
\(520\) | 3.74700e55 | 0.786348 | ||||||||
\(521\) | 2.55519e55 | 0.515525 | 0.257763 | − | 0.966208i | \(-0.417015\pi\) | ||||
0.257763 | + | 0.966208i | \(0.417015\pi\) | |||||||
\(522\) | −9.16409e54 | −0.177764 | ||||||||
\(523\) | −6.45058e55 | −1.20314 | −0.601568 | − | 0.798822i | \(-0.705457\pi\) | ||||
−0.601568 | + | 0.798822i | \(0.705457\pi\) | |||||||
\(524\) | −4.52893e55 | −0.812278 | ||||||||
\(525\) | 1.06220e55 | 0.183206 | ||||||||
\(526\) | −1.61627e55 | −0.268107 | ||||||||
\(527\) | 3.17530e55 | 0.506603 | ||||||||
\(528\) | −2.50657e54 | −0.0384667 | ||||||||
\(529\) | 9.40022e52 | 0.00138770 | ||||||||
\(530\) | −3.68670e55 | −0.523579 | ||||||||
\(531\) | 1.11718e56 | 1.52646 | ||||||||
\(532\) | −2.09382e55 | −0.275265 | ||||||||
\(533\) | 1.98930e56 | 2.51647 | ||||||||
\(534\) | −9.44418e53 | −0.0114966 | ||||||||
\(535\) | −8.71816e55 | −1.02134 | ||||||||
\(536\) | 2.55295e54 | 0.0287849 | ||||||||
\(537\) | 2.79025e55 | 0.302810 | ||||||||
\(538\) | 2.28060e55 | 0.238238 | ||||||||
\(539\) | −4.62696e55 | −0.465292 | ||||||||
\(540\) | 4.65276e55 | 0.450442 | ||||||||
\(541\) | −1.14581e56 | −1.06799 | −0.533995 | − | 0.845488i | \(-0.679310\pi\) | ||||
−0.533995 | + | 0.845488i | \(0.679310\pi\) | |||||||
\(542\) | 5.37436e55 | 0.482327 | ||||||||
\(543\) | −3.81273e55 | −0.329488 | ||||||||
\(544\) | −6.28334e54 | −0.0522894 | ||||||||
\(545\) | −2.01852e55 | −0.161773 | ||||||||
\(546\) | 1.31298e55 | 0.101346 | ||||||||
\(547\) | 6.76717e55 | 0.503114 | 0.251557 | − | 0.967842i | \(-0.419057\pi\) | ||||
0.251557 | + | 0.967842i | \(0.419057\pi\) | |||||||
\(548\) | −4.03302e55 | −0.288821 | ||||||||
\(549\) | −6.98953e55 | −0.482186 | ||||||||
\(550\) | 9.91430e55 | 0.658911 | ||||||||
\(551\) | 6.29194e55 | 0.402881 | ||||||||
\(552\) | −1.63144e55 | −0.100651 | ||||||||
\(553\) | 1.94364e55 | 0.115545 | ||||||||
\(554\) | −6.00841e55 | −0.344199 | ||||||||
\(555\) | −4.46266e55 | −0.246370 | ||||||||
\(556\) | −9.76845e55 | −0.519748 | ||||||||
\(557\) | −1.91017e56 | −0.979584 | −0.489792 | − | 0.871839i | \(-0.662927\pi\) | ||||
−0.489792 | + | 0.871839i | \(0.662927\pi\) | |||||||
\(558\) | 2.25171e56 | 1.11304 | ||||||||
\(559\) | −5.24250e56 | −2.49802 | ||||||||
\(560\) | −3.35681e55 | −0.154196 | ||||||||
\(561\) | 1.02771e55 | 0.0455128 | ||||||||
\(562\) | 2.06810e55 | 0.0883035 | ||||||||
\(563\) | 2.46904e56 | 1.01650 | 0.508249 | − | 0.861210i | \(-0.330293\pi\) | ||||
0.508249 | + | 0.861210i | \(0.330293\pi\) | |||||||
\(564\) | 1.21932e55 | 0.0484055 | ||||||||
\(565\) | 5.31511e56 | 2.03479 | ||||||||
\(566\) | −1.45876e55 | −0.0538577 | ||||||||
\(567\) | −8.01717e55 | −0.285475 | ||||||||
\(568\) | 6.44604e55 | 0.221387 | ||||||||
\(569\) | −4.36145e56 | −1.44487 | −0.722437 | − | 0.691437i | \(-0.756978\pi\) | ||||
−0.722437 | + | 0.691437i | \(0.756978\pi\) | |||||||
\(570\) | −1.52990e56 | −0.488909 | ||||||||
\(571\) | 3.87246e56 | 1.19384 | 0.596920 | − | 0.802300i | \(-0.296391\pi\) | ||||
0.596920 | + | 0.802300i | \(0.296391\pi\) | |||||||
\(572\) | 1.22550e56 | 0.364499 | ||||||||
\(573\) | 8.55074e55 | 0.245377 | ||||||||
\(574\) | −1.78214e56 | −0.493457 | ||||||||
\(575\) | 6.45285e56 | 1.72409 | ||||||||
\(576\) | −4.45572e55 | −0.114883 | ||||||||
\(577\) | 3.88180e56 | 0.965893 | 0.482947 | − | 0.875650i | \(-0.339567\pi\) | ||||
0.482947 | + | 0.875650i | \(0.339567\pi\) | |||||||
\(578\) | −2.68684e56 | −0.645239 | ||||||||
\(579\) | −6.91570e55 | −0.160297 | ||||||||
\(580\) | 1.00872e56 | 0.225682 | ||||||||
\(581\) | 2.83892e54 | 0.00613115 | ||||||||
\(582\) | 4.24969e55 | 0.0886004 | ||||||||
\(583\) | −1.20578e56 | −0.242696 | ||||||||
\(584\) | −2.33079e56 | −0.452938 | ||||||||
\(585\) | −1.08944e57 | −2.04412 | ||||||||
\(586\) | 4.03369e56 | 0.730805 | ||||||||
\(587\) | 5.00890e56 | 0.876317 | 0.438158 | − | 0.898898i | \(-0.355631\pi\) | ||||
0.438158 | + | 0.898898i | \(0.355631\pi\) | |||||||
\(588\) | 7.24289e55 | 0.122371 | ||||||||
\(589\) | −1.54599e57 | −2.52257 | ||||||||
\(590\) | −1.22972e57 | −1.93794 | ||||||||
\(591\) | 1.20319e56 | 0.183143 | ||||||||
\(592\) | 8.92368e55 | 0.131205 | ||||||||
\(593\) | 9.63914e56 | 1.36904 | 0.684521 | − | 0.728993i | \(-0.260011\pi\) | ||||
0.684521 | + | 0.728993i | \(0.260011\pi\) | |||||||
\(594\) | 1.52175e56 | 0.208795 | ||||||||
\(595\) | 1.37632e56 | 0.182440 | ||||||||
\(596\) | 3.90030e56 | 0.499517 | ||||||||
\(597\) | 2.01350e56 | 0.249159 | ||||||||
\(598\) | 7.97635e56 | 0.953740 | ||||||||
\(599\) | −1.39170e56 | −0.160803 | −0.0804016 | − | 0.996763i | \(-0.525620\pi\) | ||||
−0.0804016 | + | 0.996763i | \(0.525620\pi\) | |||||||
\(600\) | −1.55195e56 | −0.173292 | ||||||||
\(601\) | −1.72237e56 | −0.185866 | −0.0929330 | − | 0.995672i | \(-0.529624\pi\) | ||||
−0.0929330 | + | 0.995672i | \(0.529624\pi\) | |||||||
\(602\) | 4.69659e56 | 0.489840 | ||||||||
\(603\) | −7.42269e55 | −0.0748267 | ||||||||
\(604\) | 4.69174e56 | 0.457169 | ||||||||
\(605\) | −1.23940e57 | −1.16742 | ||||||||
\(606\) | 3.46971e55 | 0.0315940 | ||||||||
\(607\) | 1.22974e57 | 1.08254 | 0.541270 | − | 0.840849i | \(-0.317944\pi\) | ||||
0.541270 | + | 0.840849i | \(0.317944\pi\) | |||||||
\(608\) | 3.05923e56 | 0.260369 | ||||||||
\(609\) | 3.53465e55 | 0.0290865 | ||||||||
\(610\) | 7.69361e56 | 0.612165 | ||||||||
\(611\) | −5.96143e56 | −0.458676 | ||||||||
\(612\) | 1.82688e56 | 0.135927 | ||||||||
\(613\) | 2.53270e57 | 1.82240 | 0.911199 | − | 0.411966i | \(-0.135158\pi\) | ||||
0.911199 | + | 0.411966i | \(0.135158\pi\) | |||||||
\(614\) | −1.39784e57 | −0.972762 | ||||||||
\(615\) | −1.30217e57 | −0.876449 | ||||||||
\(616\) | −1.09789e56 | −0.0714749 | ||||||||
\(617\) | −2.74089e56 | −0.172602 | −0.0863011 | − | 0.996269i | \(-0.527505\pi\) | ||||
−0.0863011 | + | 0.996269i | \(0.527505\pi\) | |||||||
\(618\) | 4.78676e56 | 0.291594 | ||||||||
\(619\) | −1.90431e57 | −1.12222 | −0.561112 | − | 0.827740i | \(-0.689626\pi\) | ||||
−0.561112 | + | 0.827740i | \(0.689626\pi\) | |||||||
\(620\) | −2.47853e57 | −1.41307 | ||||||||
\(621\) | 9.90449e56 | 0.546329 | ||||||||
\(622\) | −3.58841e56 | −0.191513 | ||||||||
\(623\) | −4.13659e55 | −0.0213618 | ||||||||
\(624\) | −1.91836e56 | −0.0958621 | ||||||||
\(625\) | 5.07645e56 | 0.245482 | ||||||||
\(626\) | 8.69774e56 | 0.407036 | ||||||||
\(627\) | −5.00373e56 | −0.226626 | ||||||||
\(628\) | −9.06541e55 | −0.0397388 | ||||||||
\(629\) | −3.65877e56 | −0.155238 | ||||||||
\(630\) | 9.75991e56 | 0.400834 | ||||||||
\(631\) | 1.91059e57 | 0.759565 | 0.379782 | − | 0.925076i | \(-0.375999\pi\) | ||||
0.379782 | + | 0.925076i | \(0.375999\pi\) | |||||||
\(632\) | −2.83982e56 | −0.109292 | ||||||||
\(633\) | −9.49023e56 | −0.353590 | ||||||||
\(634\) | −3.08342e57 | −1.11225 | ||||||||
\(635\) | 2.63821e57 | 0.921400 | ||||||||
\(636\) | 1.88749e56 | 0.0638284 | ||||||||
\(637\) | −3.54117e57 | −1.15955 | ||||||||
\(638\) | 3.29916e56 | 0.104611 | ||||||||
\(639\) | −1.87418e57 | −0.575499 | ||||||||
\(640\) | 4.90456e56 | 0.145851 | ||||||||
\(641\) | 6.02067e57 | 1.73403 | 0.867013 | − | 0.498286i | \(-0.166037\pi\) | ||||
0.867013 | + | 0.498286i | \(0.166037\pi\) | |||||||
\(642\) | 4.46347e56 | 0.124510 | ||||||||
\(643\) | 5.41099e57 | 1.46201 | 0.731007 | − | 0.682370i | \(-0.239051\pi\) | ||||
0.731007 | + | 0.682370i | \(0.239051\pi\) | |||||||
\(644\) | −7.14575e56 | −0.187020 | ||||||||
\(645\) | 3.43167e57 | 0.870024 | ||||||||
\(646\) | −1.25431e57 | −0.308062 | ||||||||
\(647\) | −6.44976e57 | −1.53464 | −0.767319 | − | 0.641266i | \(-0.778410\pi\) | ||||
−0.767319 | + | 0.641266i | \(0.778410\pi\) | |||||||
\(648\) | 1.17137e57 | 0.270027 | ||||||||
\(649\) | −4.02196e57 | −0.898300 | ||||||||
\(650\) | 7.58774e57 | 1.64206 | ||||||||
\(651\) | −8.68498e56 | −0.182120 | ||||||||
\(652\) | 1.96802e56 | 0.0399903 | ||||||||
\(653\) | 5.84519e57 | 1.15101 | 0.575504 | − | 0.817799i | \(-0.304806\pi\) | ||||
0.575504 | + | 0.817799i | \(0.304806\pi\) | |||||||
\(654\) | 1.03343e56 | 0.0197214 | ||||||||
\(655\) | −1.44943e58 | −2.68071 | ||||||||
\(656\) | 2.60385e57 | 0.466754 | ||||||||
\(657\) | 6.77675e57 | 1.17742 | ||||||||
\(658\) | 5.34065e56 | 0.0899422 | ||||||||
\(659\) | −3.68490e57 | −0.601554 | −0.300777 | − | 0.953694i | \(-0.597246\pi\) | ||||
−0.300777 | + | 0.953694i | \(0.597246\pi\) | |||||||
\(660\) | −8.02198e56 | −0.126949 | ||||||||
\(661\) | −6.04679e57 | −0.927672 | −0.463836 | − | 0.885921i | \(-0.653527\pi\) | ||||
−0.463836 | + | 0.885921i | \(0.653527\pi\) | |||||||
\(662\) | −8.88701e57 | −1.32180 | ||||||||
\(663\) | 7.86543e56 | 0.113421 | ||||||||
\(664\) | −4.14788e55 | −0.00579937 | ||||||||
\(665\) | −6.70101e57 | −0.908441 | ||||||||
\(666\) | −2.59455e57 | −0.341068 | ||||||||
\(667\) | 2.14730e57 | 0.273724 | ||||||||
\(668\) | 4.36257e57 | 0.539293 | ||||||||
\(669\) | −2.07764e57 | −0.249077 | ||||||||
\(670\) | 8.17041e56 | 0.0949971 | ||||||||
\(671\) | 2.51629e57 | 0.283759 | ||||||||
\(672\) | 1.71860e56 | 0.0187977 | ||||||||
\(673\) | 6.56510e57 | 0.696518 | 0.348259 | − | 0.937398i | \(-0.386773\pi\) | ||||
0.348259 | + | 0.937398i | \(0.386773\pi\) | |||||||
\(674\) | 2.61152e57 | 0.268761 | ||||||||
\(675\) | 9.42194e57 | 0.940617 | ||||||||
\(676\) | 4.21649e57 | 0.408360 | ||||||||
\(677\) | 1.10721e58 | 1.04031 | 0.520155 | − | 0.854072i | \(-0.325874\pi\) | ||||
0.520155 | + | 0.854072i | \(0.325874\pi\) | |||||||
\(678\) | −2.72120e57 | −0.248057 | ||||||||
\(679\) | 1.86138e57 | 0.164628 | ||||||||
\(680\) | −2.01091e57 | −0.172568 | ||||||||
\(681\) | 1.76868e57 | 0.147276 | ||||||||
\(682\) | −8.10636e57 | −0.655008 | ||||||||
\(683\) | 1.97103e58 | 1.54550 | 0.772749 | − | 0.634711i | \(-0.218881\pi\) | ||||
0.772749 | + | 0.634711i | \(0.218881\pi\) | |||||||
\(684\) | −8.89471e57 | −0.676833 | ||||||||
\(685\) | −1.29072e58 | −0.953180 | ||||||||
\(686\) | 6.86003e57 | 0.491679 | ||||||||
\(687\) | −3.51190e57 | −0.244303 | ||||||||
\(688\) | −6.86208e57 | −0.463332 | ||||||||
\(689\) | −9.22825e57 | −0.604819 | ||||||||
\(690\) | −5.22121e57 | −0.332173 | ||||||||
\(691\) | 1.78821e58 | 1.10438 | 0.552191 | − | 0.833718i | \(-0.313792\pi\) | ||||
0.552191 | + | 0.833718i | \(0.313792\pi\) | |||||||
\(692\) | 7.62400e57 | 0.457097 | ||||||||
\(693\) | 3.19210e57 | 0.185800 | ||||||||
\(694\) | −1.07399e57 | −0.0606920 | ||||||||
\(695\) | −3.12627e58 | −1.71529 | ||||||||
\(696\) | −5.16440e56 | −0.0275125 | ||||||||
\(697\) | −1.06760e58 | −0.552250 | ||||||||
\(698\) | 7.75693e57 | 0.389631 | ||||||||
\(699\) | −7.53287e57 | −0.367433 | ||||||||
\(700\) | −6.79761e57 | −0.321993 | ||||||||
\(701\) | −2.83192e58 | −1.30275 | −0.651375 | − | 0.758756i | \(-0.725807\pi\) | ||||
−0.651375 | + | 0.758756i | \(0.725807\pi\) | |||||||
\(702\) | 1.16464e58 | 0.520334 | ||||||||
\(703\) | 1.78138e58 | 0.772989 | ||||||||
\(704\) | 1.60410e57 | 0.0676071 | ||||||||
\(705\) | 3.90227e57 | 0.159750 | ||||||||
\(706\) | −6.79315e57 | −0.270131 | ||||||||
\(707\) | 1.51975e57 | 0.0587047 | ||||||||
\(708\) | 6.29584e57 | 0.236250 | ||||||||
\(709\) | 3.01107e58 | 1.09767 | 0.548836 | − | 0.835930i | \(-0.315071\pi\) | ||||
0.548836 | + | 0.835930i | \(0.315071\pi\) | |||||||
\(710\) | 2.06298e58 | 0.730631 | ||||||||
\(711\) | 8.25675e57 | 0.284107 | ||||||||
\(712\) | 6.04388e56 | 0.0202058 | ||||||||
\(713\) | −5.27613e58 | −1.71388 | ||||||||
\(714\) | −7.04638e56 | −0.0222409 | ||||||||
\(715\) | 3.92207e58 | 1.20293 | ||||||||
\(716\) | −1.78564e58 | −0.532203 | ||||||||
\(717\) | −7.44516e57 | −0.215641 | ||||||||
\(718\) | 2.57976e58 | 0.726153 | ||||||||
\(719\) | −3.81485e58 | −1.04360 | −0.521802 | − | 0.853067i | \(-0.674740\pi\) | ||||
−0.521802 | + | 0.853067i | \(0.674740\pi\) | |||||||
\(720\) | −1.42600e58 | −0.379143 | ||||||||
\(721\) | 2.09662e58 | 0.541809 | ||||||||
\(722\) | 3.29185e58 | 0.826852 | ||||||||
\(723\) | 6.83176e57 | 0.166801 | ||||||||
\(724\) | 2.43998e58 | 0.579090 | ||||||||
\(725\) | 2.04268e58 | 0.471272 | ||||||||
\(726\) | 6.34540e57 | 0.142318 | ||||||||
\(727\) | 3.32784e58 | 0.725617 | 0.362808 | − | 0.931864i | \(-0.381818\pi\) | ||||
0.362808 | + | 0.931864i | \(0.381818\pi\) | |||||||
\(728\) | −8.40251e57 | −0.178121 | ||||||||
\(729\) | −2.65217e58 | −0.546622 | ||||||||
\(730\) | −7.45939e58 | −1.49481 | ||||||||
\(731\) | 2.81350e58 | 0.548202 | ||||||||
\(732\) | −3.93893e57 | −0.0746278 | ||||||||
\(733\) | −2.73207e58 | −0.503338 | −0.251669 | − | 0.967813i | \(-0.580979\pi\) | ||||
−0.251669 | + | 0.967813i | \(0.580979\pi\) | |||||||
\(734\) | −5.17065e58 | −0.926352 | ||||||||
\(735\) | 2.31800e58 | 0.403852 | ||||||||
\(736\) | 1.04405e58 | 0.176899 | ||||||||
\(737\) | 2.67224e57 | 0.0440343 | ||||||||
\(738\) | −7.57069e58 | −1.21333 | ||||||||
\(739\) | −2.78923e58 | −0.434784 | −0.217392 | − | 0.976084i | \(-0.569755\pi\) | ||||
−0.217392 | + | 0.976084i | \(0.569755\pi\) | |||||||
\(740\) | 2.85591e58 | 0.433007 | ||||||||
\(741\) | −3.82952e58 | −0.564770 | ||||||||
\(742\) | 8.26728e57 | 0.118599 | ||||||||
\(743\) | −5.29149e58 | −0.738427 | −0.369214 | − | 0.929345i | \(-0.620373\pi\) | ||||
−0.369214 | + | 0.929345i | \(0.620373\pi\) | |||||||
\(744\) | 1.26894e58 | 0.172265 | ||||||||
\(745\) | 1.24824e59 | 1.64853 | ||||||||
\(746\) | 3.88438e58 | 0.499086 | ||||||||
\(747\) | 1.20599e57 | 0.0150755 | ||||||||
\(748\) | −6.57693e57 | −0.0799908 | ||||||||
\(749\) | 1.95502e58 | 0.231352 | ||||||||
\(750\) | −2.08400e58 | −0.239961 | ||||||||
\(751\) | −1.65688e59 | −1.85641 | −0.928203 | − | 0.372075i | \(-0.878647\pi\) | ||||
−0.928203 | + | 0.372075i | \(0.878647\pi\) | |||||||
\(752\) | −7.80311e57 | −0.0850750 | ||||||||
\(753\) | −2.33149e58 | −0.247364 | ||||||||
\(754\) | 2.52496e58 | 0.260700 | ||||||||
\(755\) | 1.50153e59 | 1.50877 | ||||||||
\(756\) | −1.04337e58 | −0.102033 | ||||||||
\(757\) | 1.30792e59 | 1.24485 | 0.622424 | − | 0.782680i | \(-0.286148\pi\) | ||||
0.622424 | + | 0.782680i | \(0.286148\pi\) | |||||||
\(758\) | 1.08852e59 | 1.00836 | ||||||||
\(759\) | −1.70766e58 | −0.153974 | ||||||||
\(760\) | 9.79070e58 | 0.859281 | ||||||||
\(761\) | 8.10267e58 | 0.692218 | 0.346109 | − | 0.938194i | \(-0.387503\pi\) | ||||
0.346109 | + | 0.938194i | \(0.387503\pi\) | |||||||
\(762\) | −1.35070e58 | −0.112326 | ||||||||
\(763\) | 4.52646e57 | 0.0366443 | ||||||||
\(764\) | −5.47211e58 | −0.431262 | ||||||||
\(765\) | 5.84670e58 | 0.448592 | ||||||||
\(766\) | −1.33556e58 | −0.0997643 | ||||||||
\(767\) | −3.07814e59 | −2.23863 | ||||||||
\(768\) | −2.51101e57 | −0.0177805 | ||||||||
\(769\) | −5.87182e58 | −0.404839 | −0.202420 | − | 0.979299i | \(-0.564881\pi\) | ||||
−0.202420 | + | 0.979299i | \(0.564881\pi\) | |||||||
\(770\) | −3.51366e58 | −0.235884 | ||||||||
\(771\) | 7.39216e58 | 0.483233 | ||||||||
\(772\) | 4.42575e58 | 0.281730 | ||||||||
\(773\) | −2.32645e59 | −1.44216 | −0.721081 | − | 0.692850i | \(-0.756355\pi\) | ||||
−0.721081 | + | 0.692850i | \(0.756355\pi\) | |||||||
\(774\) | 1.99515e59 | 1.20444 | ||||||||
\(775\) | −5.01908e59 | −2.95080 | ||||||||
\(776\) | −2.71962e58 | −0.155719 | ||||||||
\(777\) | 1.00074e58 | 0.0558070 | ||||||||
\(778\) | −1.69725e59 | −0.921859 | ||||||||
\(779\) | 5.19792e59 | 2.74987 | ||||||||
\(780\) | −6.13949e58 | −0.316368 | ||||||||
\(781\) | 6.74723e58 | 0.338672 | ||||||||
\(782\) | −4.28068e58 | −0.209302 | ||||||||
\(783\) | 3.13532e58 | 0.149336 | ||||||||
\(784\) | −4.63514e58 | −0.215072 | ||||||||
\(785\) | −2.90127e58 | −0.131148 | ||||||||
\(786\) | 7.42070e58 | 0.326800 | ||||||||
\(787\) | 2.24048e59 | 0.961299 | 0.480649 | − | 0.876913i | \(-0.340401\pi\) | ||||
0.480649 | + | 0.876913i | \(0.340401\pi\) | |||||||
\(788\) | −7.69988e58 | −0.321882 | ||||||||
\(789\) | 2.64828e58 | 0.107866 | ||||||||
\(790\) | −9.08848e58 | −0.360691 | ||||||||
\(791\) | −1.19190e59 | −0.460914 | ||||||||
\(792\) | −4.66391e58 | −0.175745 | ||||||||
\(793\) | 1.92580e59 | 0.707150 | ||||||||
\(794\) | 2.31548e59 | 0.828553 | ||||||||
\(795\) | 6.04068e58 | 0.210649 | ||||||||
\(796\) | −1.28855e59 | −0.437909 | ||||||||
\(797\) | 3.32067e59 | 1.09984 | 0.549921 | − | 0.835217i | \(-0.314658\pi\) | ||||
0.549921 | + | 0.835217i | \(0.314658\pi\) | |||||||
\(798\) | 3.43074e58 | 0.110746 | ||||||||
\(799\) | 3.19933e58 | 0.100658 | ||||||||
\(800\) | 9.93184e58 | 0.304568 | ||||||||
\(801\) | −1.75725e58 | −0.0525252 | ||||||||
\(802\) | −1.24626e58 | −0.0363106 | ||||||||
\(803\) | −2.43969e59 | −0.692893 | ||||||||
\(804\) | −4.18303e57 | −0.0115809 | ||||||||
\(805\) | −2.28691e59 | −0.617211 | ||||||||
\(806\) | −6.20407e59 | −1.63233 | ||||||||
\(807\) | −3.73678e58 | −0.0958495 | ||||||||
\(808\) | −2.22047e58 | −0.0555279 | ||||||||
\(809\) | 7.35141e59 | 1.79236 | 0.896182 | − | 0.443687i | \(-0.146330\pi\) | ||||
0.896182 | + | 0.443687i | \(0.146330\pi\) | |||||||
\(810\) | 3.74883e59 | 0.891154 | ||||||||
\(811\) | −7.34195e58 | −0.170170 | −0.0850852 | − | 0.996374i | \(-0.527116\pi\) | ||||
−0.0850852 | + | 0.996374i | \(0.527116\pi\) | |||||||
\(812\) | −2.26202e58 | −0.0511209 | ||||||||
\(813\) | −8.80593e58 | −0.194053 | ||||||||
\(814\) | 9.34063e58 | 0.200713 | ||||||||
\(815\) | 6.29842e58 | 0.131978 | ||||||||
\(816\) | 1.02953e58 | 0.0210374 | ||||||||
\(817\) | −1.36984e60 | −2.72971 | ||||||||
\(818\) | −9.81878e58 | −0.190816 | ||||||||
\(819\) | 2.44302e59 | 0.463029 | ||||||||
\(820\) | 8.33331e59 | 1.54040 | ||||||||
\(821\) | −7.00875e59 | −1.26359 | −0.631794 | − | 0.775136i | \(-0.717681\pi\) | ||||
−0.631794 | + | 0.775136i | \(0.717681\pi\) | |||||||
\(822\) | 6.60814e58 | 0.116200 | ||||||||
\(823\) | −4.10799e59 | −0.704584 | −0.352292 | − | 0.935890i | \(-0.614598\pi\) | ||||
−0.352292 | + | 0.935890i | \(0.614598\pi\) | |||||||
\(824\) | −3.06332e59 | −0.512490 | ||||||||
\(825\) | −1.62447e59 | −0.265097 | ||||||||
\(826\) | 2.75760e59 | 0.438976 | ||||||||
\(827\) | 2.98123e59 | 0.462949 | 0.231474 | − | 0.972841i | \(-0.425645\pi\) | ||||
0.231474 | + | 0.972841i | \(0.425645\pi\) | |||||||
\(828\) | −3.03557e59 | −0.459852 | ||||||||
\(829\) | 3.83752e59 | 0.567130 | 0.283565 | − | 0.958953i | \(-0.408483\pi\) | ||||
0.283565 | + | 0.958953i | \(0.408483\pi\) | |||||||
\(830\) | −1.32748e58 | −0.0191393 | ||||||||
\(831\) | 9.84484e58 | 0.138480 | ||||||||
\(832\) | 1.22767e59 | 0.168482 | ||||||||
\(833\) | 1.90044e59 | 0.254467 | ||||||||
\(834\) | 1.60057e59 | 0.209108 | ||||||||
\(835\) | 1.39618e60 | 1.77980 | ||||||||
\(836\) | 3.20218e59 | 0.398306 | ||||||||
\(837\) | −7.70379e59 | −0.935045 | ||||||||
\(838\) | −4.67219e59 | −0.553373 | ||||||||
\(839\) | 9.98054e59 | 1.15354 | 0.576772 | − | 0.816905i | \(-0.304312\pi\) | ||||
0.576772 | + | 0.816905i | \(0.304312\pi\) | |||||||
\(840\) | 5.50016e58 | 0.0620369 | ||||||||
\(841\) | −8.40511e59 | −0.925179 | ||||||||
\(842\) | −6.00439e59 | −0.645017 | ||||||||
\(843\) | −3.38861e58 | −0.0355268 | ||||||||
\(844\) | 6.07334e59 | 0.621452 | ||||||||
\(845\) | 1.34943e60 | 1.34769 | ||||||||
\(846\) | 2.26875e59 | 0.221154 | ||||||||
\(847\) | 2.77931e59 | 0.264440 | ||||||||
\(848\) | −1.20791e59 | −0.112181 | ||||||||
\(849\) | 2.39020e58 | 0.0216684 | ||||||||
\(850\) | −4.07212e59 | −0.360357 | ||||||||
\(851\) | 6.07948e59 | 0.525182 | ||||||||
\(852\) | −1.05619e59 | −0.0890697 | ||||||||
\(853\) | −1.04133e60 | −0.857302 | −0.428651 | − | 0.903470i | \(-0.641011\pi\) | ||||
−0.428651 | + | 0.903470i | \(0.641011\pi\) | |||||||
\(854\) | −1.72526e59 | −0.138666 | ||||||||
\(855\) | −2.84664e60 | −2.23371 | ||||||||
\(856\) | −2.85643e59 | −0.218832 | ||||||||
\(857\) | −2.22118e59 | −0.166141 | −0.0830705 | − | 0.996544i | \(-0.526473\pi\) | ||||
−0.0830705 | + | 0.996544i | \(0.526473\pi\) | |||||||
\(858\) | −2.00800e59 | −0.146647 | ||||||||
\(859\) | 1.83508e60 | 1.30856 | 0.654282 | − | 0.756250i | \(-0.272971\pi\) | ||||
0.654282 | + | 0.756250i | \(0.272971\pi\) | |||||||
\(860\) | −2.19612e60 | −1.52911 | ||||||||
\(861\) | 2.92006e59 | 0.198530 | ||||||||
\(862\) | −8.38409e59 | −0.556618 | ||||||||
\(863\) | −2.51134e60 | −1.62811 | −0.814055 | − | 0.580788i | \(-0.802744\pi\) | ||||
−0.814055 | + | 0.580788i | \(0.802744\pi\) | |||||||
\(864\) | 1.52444e59 | 0.0965113 | ||||||||
\(865\) | 2.43997e60 | 1.50853 | ||||||||
\(866\) | 1.47866e60 | 0.892797 | ||||||||
\(867\) | 4.40241e59 | 0.259597 | ||||||||
\(868\) | 5.55802e59 | 0.320085 | ||||||||
\(869\) | −2.97250e59 | −0.167193 | ||||||||
\(870\) | −1.65280e59 | −0.0907979 | ||||||||
\(871\) | 2.04515e59 | 0.109737 | ||||||||
\(872\) | −6.61351e58 | −0.0346613 | ||||||||
\(873\) | 7.90728e59 | 0.404795 | ||||||||
\(874\) | 2.08418e60 | 1.04220 | ||||||||
\(875\) | −9.12799e59 | −0.445872 | ||||||||
\(876\) | 3.81901e59 | 0.182229 | ||||||||
\(877\) | 1.15614e60 | 0.538913 | 0.269457 | − | 0.963013i | \(-0.413156\pi\) | ||||
0.269457 | + | 0.963013i | \(0.413156\pi\) | |||||||
\(878\) | 9.94357e59 | 0.452798 | ||||||||
\(879\) | −6.60924e59 | −0.294022 | ||||||||
\(880\) | 5.13372e59 | 0.223120 | ||||||||
\(881\) | −2.91398e60 | −1.23732 | −0.618658 | − | 0.785661i | \(-0.712323\pi\) | ||||
−0.618658 | + | 0.785661i | \(0.712323\pi\) | |||||||
\(882\) | 1.34767e60 | 0.559083 | ||||||||
\(883\) | 1.84407e60 | 0.747452 | 0.373726 | − | 0.927539i | \(-0.378080\pi\) | ||||
0.373726 | + | 0.927539i | \(0.378080\pi\) | |||||||
\(884\) | −5.03354e59 | −0.199344 | ||||||||
\(885\) | 2.01491e60 | 0.779683 | ||||||||
\(886\) | −1.20717e60 | −0.456433 | ||||||||
\(887\) | −4.08939e59 | −0.151086 | −0.0755431 | − | 0.997143i | \(-0.524069\pi\) | ||||
−0.0755431 | + | 0.997143i | \(0.524069\pi\) | |||||||
\(888\) | −1.46215e59 | −0.0527870 | ||||||||
\(889\) | −5.91610e59 | −0.208713 | ||||||||
\(890\) | 1.93427e59 | 0.0666840 | ||||||||
\(891\) | 1.22610e60 | 0.413080 | ||||||||
\(892\) | 1.32960e60 | 0.437765 | ||||||||
\(893\) | −1.55769e60 | −0.501217 | ||||||||
\(894\) | −6.39068e59 | −0.200968 | ||||||||
\(895\) | −5.71472e60 | −1.75640 | ||||||||
\(896\) | −1.09983e59 | −0.0330378 | ||||||||
\(897\) | −1.30693e60 | −0.383714 | ||||||||
\(898\) | −1.35436e60 | −0.388660 | ||||||||
\(899\) | −1.67019e60 | −0.468480 | ||||||||
\(900\) | −2.88768e60 | −0.791730 | ||||||||
\(901\) | 4.95254e59 | 0.132730 | ||||||||
\(902\) | 2.72552e60 | 0.714027 | ||||||||
\(903\) | −7.69540e59 | −0.197075 | ||||||||
\(904\) | 1.74145e60 | 0.435972 | ||||||||
\(905\) | 7.80886e60 | 1.91114 | ||||||||
\(906\) | −7.68746e59 | −0.183931 | ||||||||
\(907\) | 1.20769e60 | 0.282492 | 0.141246 | − | 0.989975i | \(-0.454889\pi\) | ||||
0.141246 | + | 0.989975i | \(0.454889\pi\) | |||||||
\(908\) | −1.13188e60 | −0.258845 | ||||||||
\(909\) | 6.45600e59 | 0.144346 | ||||||||
\(910\) | −2.68912e60 | −0.587843 | ||||||||
\(911\) | 5.09758e59 | 0.108953 | 0.0544763 | − | 0.998515i | \(-0.482651\pi\) | ||||
0.0544763 | + | 0.998515i | \(0.482651\pi\) | |||||||
\(912\) | −5.01258e59 | −0.104753 | ||||||||
\(913\) | −4.34169e58 | −0.00887172 | ||||||||
\(914\) | −5.97839e60 | −1.19450 | ||||||||
\(915\) | −1.26060e60 | −0.246290 | ||||||||
\(916\) | 2.24747e60 | 0.429375 | ||||||||
\(917\) | 3.25029e60 | 0.607227 | ||||||||
\(918\) | −6.25031e59 | −0.114190 | ||||||||
\(919\) | −5.01795e60 | −0.896517 | −0.448259 | − | 0.893904i | \(-0.647956\pi\) | ||||
−0.448259 | + | 0.893904i | \(0.647956\pi\) | |||||||
\(920\) | 3.34135e60 | 0.583811 | ||||||||
\(921\) | 2.29038e60 | 0.391367 | ||||||||
\(922\) | −5.62840e60 | −0.940591 | ||||||||
\(923\) | 5.16388e60 | 0.843998 | ||||||||
\(924\) | 1.79890e59 | 0.0287562 | ||||||||
\(925\) | 5.78328e60 | 0.904209 | ||||||||
\(926\) | 6.54787e60 | 1.00132 | ||||||||
\(927\) | 8.90660e60 | 1.33222 | ||||||||
\(928\) | 3.30499e59 | 0.0483545 | ||||||||
\(929\) | −3.15656e60 | −0.451744 | −0.225872 | − | 0.974157i | \(-0.572523\pi\) | ||||
−0.225872 | + | 0.974157i | \(0.572523\pi\) | |||||||
\(930\) | 4.06110e60 | 0.568516 | ||||||||
\(931\) | −9.25288e60 | −1.26709 | ||||||||
\(932\) | 4.82072e60 | 0.645781 | ||||||||
\(933\) | 5.87964e59 | 0.0770508 | ||||||||
\(934\) | −8.94138e59 | −0.114629 | ||||||||
\(935\) | −2.10486e60 | −0.263989 | ||||||||
\(936\) | −3.56945e60 | −0.437972 | ||||||||
\(937\) | −5.64418e60 | −0.677547 | −0.338773 | − | 0.940868i | \(-0.610012\pi\) | ||||
−0.338773 | + | 0.940868i | \(0.610012\pi\) | |||||||
\(938\) | −1.83218e59 | −0.0215185 | ||||||||
\(939\) | −1.42513e60 | −0.163761 | ||||||||
\(940\) | −2.49729e60 | −0.280768 | ||||||||
\(941\) | −1.57154e61 | −1.72877 | −0.864385 | − | 0.502831i | \(-0.832292\pi\) | ||||
−0.864385 | + | 0.502831i | \(0.832292\pi\) | |||||||
\(942\) | 1.48537e59 | 0.0159879 | ||||||||
\(943\) | 1.77394e61 | 1.86831 | ||||||||
\(944\) | −4.02907e60 | −0.415221 | ||||||||
\(945\) | −3.33916e60 | −0.336733 | ||||||||
\(946\) | −7.18270e60 | −0.708793 | ||||||||
\(947\) | −3.54084e60 | −0.341926 | −0.170963 | − | 0.985277i | \(-0.554688\pi\) | ||||
−0.170963 | + | 0.985277i | \(0.554688\pi\) | |||||||
\(948\) | 4.65306e59 | 0.0439712 | ||||||||
\(949\) | −1.86718e61 | −1.72675 | ||||||||
\(950\) | 1.98264e61 | 1.79436 | ||||||||
\(951\) | 5.05221e60 | 0.447488 | ||||||||
\(952\) | 4.50938e59 | 0.0390895 | ||||||||
\(953\) | −3.82394e60 | −0.324420 | −0.162210 | − | 0.986756i | \(-0.551862\pi\) | ||||
−0.162210 | + | 0.986756i | \(0.551862\pi\) | |||||||
\(954\) | 3.51200e60 | 0.291617 | ||||||||
\(955\) | −1.75128e61 | −1.42327 | ||||||||
\(956\) | 4.76459e60 | 0.379000 | ||||||||
\(957\) | −5.40570e59 | −0.0420879 | ||||||||
\(958\) | −6.86560e60 | −0.523221 | ||||||||
\(959\) | 2.89439e60 | 0.215912 | ||||||||
\(960\) | −8.03617e59 | −0.0586798 | ||||||||
\(961\) | 2.70478e61 | 1.93331 | ||||||||
\(962\) | 7.14870e60 | 0.500193 | ||||||||
\(963\) | 8.30505e60 | 0.568858 | ||||||||
\(964\) | −4.37204e60 | −0.293160 | ||||||||
\(965\) | 1.41641e61 | 0.929776 | ||||||||
\(966\) | 1.17084e60 | 0.0752429 | ||||||||
\(967\) | 1.08706e61 | 0.683930 | 0.341965 | − | 0.939713i | \(-0.388908\pi\) | ||||
0.341965 | + | 0.939713i | \(0.388908\pi\) | |||||||
\(968\) | −4.06079e60 | −0.250130 | ||||||||
\(969\) | 2.05519e60 | 0.123941 | ||||||||
\(970\) | −8.70381e60 | −0.513912 | ||||||||
\(971\) | 1.86961e61 | 1.08083 | 0.540416 | − | 0.841398i | \(-0.318267\pi\) | ||||
0.540416 | + | 0.841398i | \(0.318267\pi\) | |||||||
\(972\) | −6.74190e60 | −0.381614 | ||||||||
\(973\) | 7.01055e60 | 0.388543 | ||||||||
\(974\) | −5.14582e60 | −0.279252 | ||||||||
\(975\) | −1.24326e61 | −0.660643 | ||||||||
\(976\) | 2.52075e60 | 0.131162 | ||||||||
\(977\) | −2.93813e61 | −1.49704 | −0.748518 | − | 0.663115i | \(-0.769234\pi\) | ||||
−0.748518 | + | 0.663115i | \(0.769234\pi\) | |||||||
\(978\) | −3.22462e59 | −0.0160891 | ||||||||
\(979\) | 6.32627e59 | 0.0309103 | ||||||||
\(980\) | −1.48342e61 | −0.709790 | ||||||||
\(981\) | 1.92288e60 | 0.0901024 | ||||||||
\(982\) | 2.78264e60 | 0.127694 | ||||||||
\(983\) | 2.55719e61 | 1.14925 | 0.574626 | − | 0.818416i | \(-0.305148\pi\) | ||||
0.574626 | + | 0.818416i | \(0.305148\pi\) | |||||||
\(984\) | −4.26644e60 | −0.187787 | ||||||||
\(985\) | −2.46425e61 | −1.06229 | ||||||||
\(986\) | −1.35507e60 | −0.0572118 | ||||||||
\(987\) | −8.75070e59 | −0.0361861 | ||||||||
\(988\) | 2.45073e61 | 0.992610 | ||||||||
\(989\) | −4.67496e61 | −1.85461 | ||||||||
\(990\) | −1.49263e61 | −0.580003 | ||||||||
\(991\) | 1.53747e61 | 0.585188 | 0.292594 | − | 0.956237i | \(-0.405482\pi\) | ||||
0.292594 | + | 0.956237i | \(0.405482\pi\) | |||||||
\(992\) | −8.12070e60 | −0.302764 | ||||||||
\(993\) | 1.45614e61 | 0.531796 | ||||||||
\(994\) | −4.62615e60 | −0.165500 | ||||||||
\(995\) | −4.12385e61 | −1.44521 | ||||||||
\(996\) | 6.79634e58 | 0.00233324 | ||||||||
\(997\) | 4.42141e61 | 1.48700 | 0.743499 | − | 0.668737i | \(-0.233165\pi\) | ||||
0.743499 | + | 0.668737i | \(0.233165\pi\) | |||||||
\(998\) | 6.32263e59 | 0.0208316 | ||||||||
\(999\) | 8.87676e60 | 0.286525 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2.42.a.b.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 18.42.a.c.1.1 | 2 | |||
4.3 | odd | 2 | 16.42.a.b.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2.42.a.b.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
16.42.a.b.1.2 | 2 | 4.3 | odd | 2 | |||
18.42.a.c.1.1 | 2 | 3.2 | odd | 2 |