Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2,84,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, 84, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2.1");
S:= CuspForms(chi, 84);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2 \) |
Weight: | \( k \) | \(=\) | \( 84 \) |
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: | \(87.2544256533\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 287609867501924274375802127400x - 41230865304567060522794640394926417995512500 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{24}\cdot 3^{7}\cdot 5^{3}\cdot 7\cdot 11\cdot 17 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.56747e14\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.19902e12 | −0.707107 | ||||||||
\(3\) | −7.32556e17 | −0.0115960 | −0.00579801 | − | 0.999983i | \(-0.501846\pi\) | ||||
−0.00579801 | + | 0.999983i | \(0.501846\pi\) | |||||||
\(4\) | 4.83570e24 | 0.500000 | ||||||||
\(5\) | −1.23719e29 | −1.21670 | −0.608348 | − | 0.793670i | \(-0.708168\pi\) | ||||
−0.608348 | + | 0.793670i | \(0.708168\pi\) | |||||||
\(6\) | 1.61091e30 | 0.00819962 | ||||||||
\(7\) | 6.61589e34 | 0.561073 | 0.280537 | − | 0.959843i | \(-0.409488\pi\) | ||||
0.280537 | + | 0.959843i | \(0.409488\pi\) | |||||||
\(8\) | −1.06338e37 | −0.353553 | ||||||||
\(9\) | −3.99030e39 | −0.999866 | ||||||||
\(10\) | 2.72062e41 | 0.860334 | ||||||||
\(11\) | −2.35451e43 | −1.42595 | −0.712974 | − | 0.701191i | \(-0.752652\pi\) | ||||
−0.712974 | + | 0.701191i | \(0.752652\pi\) | |||||||
\(12\) | −3.54242e42 | −0.00579801 | ||||||||
\(13\) | 2.17555e46 | 1.28505 | 0.642525 | − | 0.766265i | \(-0.277887\pi\) | ||||
0.642525 | + | 0.766265i | \(0.277887\pi\) | |||||||
\(14\) | −1.45485e47 | −0.396739 | ||||||||
\(15\) | 9.06313e46 | 0.0141088 | ||||||||
\(16\) | 2.33840e49 | 0.250000 | ||||||||
\(17\) | −2.06003e51 | −1.77928 | −0.889638 | − | 0.456666i | \(-0.849043\pi\) | ||||
−0.889638 | + | 0.456666i | \(0.849043\pi\) | |||||||
\(18\) | 8.77477e51 | 0.707012 | ||||||||
\(19\) | −1.54338e53 | −1.31886 | −0.659429 | − | 0.751767i | \(-0.729202\pi\) | ||||
−0.659429 | + | 0.751767i | \(0.729202\pi\) | |||||||
\(20\) | −5.98270e53 | −0.608348 | ||||||||
\(21\) | −4.84651e52 | −0.00650621 | ||||||||
\(22\) | 5.17762e55 | 1.00830 | ||||||||
\(23\) | 3.09757e56 | 0.953491 | 0.476745 | − | 0.879041i | \(-0.341816\pi\) | ||||
0.476745 | + | 0.879041i | \(0.341816\pi\) | |||||||
\(24\) | 7.78987e54 | 0.00409981 | ||||||||
\(25\) | 4.96671e57 | 0.480350 | ||||||||
\(26\) | −4.78409e58 | −0.908668 | ||||||||
\(27\) | 5.84663e57 | 0.0231905 | ||||||||
\(28\) | 3.19925e59 | 0.280537 | ||||||||
\(29\) | −4.67177e59 | −0.0954914 | −0.0477457 | − | 0.998860i | \(-0.515204\pi\) | ||||
−0.0477457 | + | 0.998860i | \(0.515204\pi\) | |||||||
\(30\) | −1.99300e59 | −0.00997645 | ||||||||
\(31\) | −1.70498e61 | −0.218881 | −0.109441 | − | 0.993993i | \(-0.534906\pi\) | ||||
−0.109441 | + | 0.993993i | \(0.534906\pi\) | |||||||
\(32\) | −5.14220e61 | −0.176777 | ||||||||
\(33\) | 1.72481e61 | 0.0165353 | ||||||||
\(34\) | 4.53006e63 | 1.25814 | ||||||||
\(35\) | −8.18513e63 | −0.682656 | ||||||||
\(36\) | −1.92959e64 | −0.499933 | ||||||||
\(37\) | −9.03184e64 | −0.750593 | −0.375297 | − | 0.926905i | \(-0.622459\pi\) | ||||
−0.375297 | + | 0.926905i | \(0.622459\pi\) | |||||||
\(38\) | 3.39393e65 | 0.932574 | ||||||||
\(39\) | −1.59371e64 | −0.0149015 | ||||||||
\(40\) | 1.31561e66 | 0.430167 | ||||||||
\(41\) | −8.21191e66 | −0.963638 | −0.481819 | − | 0.876271i | \(-0.660024\pi\) | ||||
−0.481819 | + | 0.876271i | \(0.660024\pi\) | |||||||
\(42\) | 1.06576e65 | 0.00460059 | ||||||||
\(43\) | −5.19673e67 | −0.844869 | −0.422435 | − | 0.906393i | \(-0.638824\pi\) | ||||
−0.422435 | + | 0.906393i | \(0.638824\pi\) | |||||||
\(44\) | −1.13857e68 | −0.712974 | ||||||||
\(45\) | 4.93677e68 | 1.21653 | ||||||||
\(46\) | −6.81164e68 | −0.674220 | ||||||||
\(47\) | −3.72927e69 | −1.51204 | −0.756019 | − | 0.654550i | \(-0.772858\pi\) | ||||
−0.756019 | + | 0.654550i | \(0.772858\pi\) | |||||||
\(48\) | −1.71301e67 | −0.00289900 | ||||||||
\(49\) | −9.52692e69 | −0.685197 | ||||||||
\(50\) | −1.09219e70 | −0.339659 | ||||||||
\(51\) | 1.50909e69 | 0.0206325 | ||||||||
\(52\) | 1.05203e71 | 0.642525 | ||||||||
\(53\) | −4.87207e71 | −1.34979 | −0.674893 | − | 0.737916i | \(-0.735810\pi\) | ||||
−0.674893 | + | 0.737916i | \(0.735810\pi\) | |||||||
\(54\) | −1.28569e70 | −0.0163981 | ||||||||
\(55\) | 2.91298e72 | 1.73495 | ||||||||
\(56\) | −7.03522e71 | −0.198369 | ||||||||
\(57\) | 1.13061e71 | 0.0152935 | ||||||||
\(58\) | 1.02733e72 | 0.0675226 | ||||||||
\(59\) | 2.59897e73 | 0.840316 | 0.420158 | − | 0.907451i | \(-0.361975\pi\) | ||||
0.420158 | + | 0.907451i | \(0.361975\pi\) | |||||||
\(60\) | 4.38266e71 | 0.00705441 | ||||||||
\(61\) | −2.95096e73 | −0.239208 | −0.119604 | − | 0.992822i | \(-0.538162\pi\) | ||||
−0.119604 | + | 0.992822i | \(0.538162\pi\) | |||||||
\(62\) | 3.74928e73 | 0.154772 | ||||||||
\(63\) | −2.63994e74 | −0.560998 | ||||||||
\(64\) | 1.13078e74 | 0.125000 | ||||||||
\(65\) | −2.69158e75 | −1.56352 | ||||||||
\(66\) | −3.79289e73 | −0.0116922 | ||||||||
\(67\) | 9.82765e75 | 1.62310 | 0.811550 | − | 0.584283i | \(-0.198624\pi\) | ||||
0.811550 | + | 0.584283i | \(0.198624\pi\) | |||||||
\(68\) | −9.96170e75 | −0.889638 | ||||||||
\(69\) | −2.26915e74 | −0.0110567 | ||||||||
\(70\) | 1.79993e76 | 0.482711 | ||||||||
\(71\) | −2.74633e76 | −0.408819 | −0.204410 | − | 0.978885i | \(-0.565527\pi\) | ||||
−0.204410 | + | 0.978885i | \(0.565527\pi\) | |||||||
\(72\) | 4.24322e76 | 0.353506 | ||||||||
\(73\) | 1.97027e77 | 0.926035 | 0.463017 | − | 0.886349i | \(-0.346767\pi\) | ||||
0.463017 | + | 0.886349i | \(0.346767\pi\) | |||||||
\(74\) | 1.98612e77 | 0.530750 | ||||||||
\(75\) | −3.63839e75 | −0.00557015 | ||||||||
\(76\) | −7.46332e77 | −0.659429 | ||||||||
\(77\) | −1.55772e78 | −0.800061 | ||||||||
\(78\) | 3.50461e76 | 0.0105369 | ||||||||
\(79\) | 2.44890e78 | 0.433957 | 0.216978 | − | 0.976176i | \(-0.430380\pi\) | ||||
0.216978 | + | 0.976176i | \(0.430380\pi\) | |||||||
\(80\) | −2.89306e78 | −0.304174 | ||||||||
\(81\) | 1.59204e79 | 0.999597 | ||||||||
\(82\) | 1.80582e79 | 0.681395 | ||||||||
\(83\) | −4.50780e79 | −1.02855 | −0.514273 | − | 0.857627i | \(-0.671938\pi\) | ||||
−0.514273 | + | 0.857627i | \(0.671938\pi\) | |||||||
\(84\) | −2.34363e77 | −0.00325311 | ||||||||
\(85\) | 2.54866e80 | 2.16484 | ||||||||
\(86\) | 1.14277e80 | 0.597413 | ||||||||
\(87\) | 3.42233e77 | 0.00110732 | ||||||||
\(88\) | 2.50374e80 | 0.504149 | ||||||||
\(89\) | 1.00507e81 | 1.26623 | 0.633115 | − | 0.774058i | \(-0.281776\pi\) | ||||
0.633115 | + | 0.774058i | \(0.281776\pi\) | |||||||
\(90\) | −1.08561e81 | −0.860219 | ||||||||
\(91\) | 1.43932e81 | 0.721007 | ||||||||
\(92\) | 1.49790e81 | 0.476745 | ||||||||
\(93\) | 1.24899e79 | 0.00253815 | ||||||||
\(94\) | 8.20075e81 | 1.06917 | ||||||||
\(95\) | 1.90946e82 | 1.60465 | ||||||||
\(96\) | 3.76695e79 | 0.00204990 | ||||||||
\(97\) | 2.37614e82 | 0.841096 | 0.420548 | − | 0.907270i | \(-0.361838\pi\) | ||||
0.420548 | + | 0.907270i | \(0.361838\pi\) | |||||||
\(98\) | 2.09499e82 | 0.484507 | ||||||||
\(99\) | 9.39519e82 | 1.42576 | ||||||||
\(100\) | 2.40175e82 | 0.240175 | ||||||||
\(101\) | 1.86756e83 | 1.23577 | 0.617884 | − | 0.786269i | \(-0.287990\pi\) | ||||
0.617884 | + | 0.786269i | \(0.287990\pi\) | |||||||
\(102\) | −3.31852e81 | −0.0145894 | ||||||||
\(103\) | −1.33705e83 | −0.392105 | −0.196052 | − | 0.980593i | \(-0.562812\pi\) | ||||
−0.196052 | + | 0.980593i | \(0.562812\pi\) | |||||||
\(104\) | −2.31344e83 | −0.454334 | ||||||||
\(105\) | 5.99607e81 | 0.00791609 | ||||||||
\(106\) | 1.07138e84 | 0.954443 | ||||||||
\(107\) | −1.76716e84 | −1.06623 | −0.533114 | − | 0.846044i | \(-0.678978\pi\) | ||||
−0.533114 | + | 0.846044i | \(0.678978\pi\) | |||||||
\(108\) | 2.82726e82 | 0.0115952 | ||||||||
\(109\) | 1.72699e83 | 0.0483159 | 0.0241579 | − | 0.999708i | \(-0.492310\pi\) | ||||
0.0241579 | + | 0.999708i | \(0.492310\pi\) | |||||||
\(110\) | −6.40571e84 | −1.22679 | ||||||||
\(111\) | 6.61633e82 | 0.00870389 | ||||||||
\(112\) | 1.54706e84 | 0.140268 | ||||||||
\(113\) | −4.40696e84 | −0.276302 | −0.138151 | − | 0.990411i | \(-0.544116\pi\) | ||||
−0.138151 | + | 0.990411i | \(0.544116\pi\) | |||||||
\(114\) | −2.48624e83 | −0.0108141 | ||||||||
\(115\) | −3.83230e85 | −1.16011 | ||||||||
\(116\) | −2.25913e84 | −0.0477457 | ||||||||
\(117\) | −8.68110e85 | −1.28488 | ||||||||
\(118\) | −5.71520e85 | −0.594193 | ||||||||
\(119\) | −1.36289e86 | −0.998305 | ||||||||
\(120\) | −9.63757e83 | −0.00498822 | ||||||||
\(121\) | 2.81728e86 | 1.03333 | ||||||||
\(122\) | 6.48923e85 | 0.169145 | ||||||||
\(123\) | 6.01568e84 | 0.0111744 | ||||||||
\(124\) | −8.24476e85 | −0.109441 | ||||||||
\(125\) | 6.64750e86 | 0.632256 | ||||||||
\(126\) | 5.80529e86 | 0.396685 | ||||||||
\(127\) | 2.59885e87 | 1.27916 | 0.639582 | − | 0.768722i | \(-0.279107\pi\) | ||||
0.639582 | + | 0.768722i | \(0.279107\pi\) | |||||||
\(128\) | −2.48662e86 | −0.0883883 | ||||||||
\(129\) | 3.80690e85 | 0.00979711 | ||||||||
\(130\) | 5.91884e87 | 1.10557 | ||||||||
\(131\) | 7.20837e87 | 0.979667 | 0.489833 | − | 0.871816i | \(-0.337058\pi\) | ||||
0.489833 | + | 0.871816i | \(0.337058\pi\) | |||||||
\(132\) | 8.34066e85 | 0.00826765 | ||||||||
\(133\) | −1.02108e88 | −0.739976 | ||||||||
\(134\) | −2.16112e88 | −1.14770 | ||||||||
\(135\) | −7.23341e86 | −0.0282158 | ||||||||
\(136\) | 2.19060e88 | 0.629069 | ||||||||
\(137\) | 7.82178e88 | 1.65730 | 0.828651 | − | 0.559765i | \(-0.189109\pi\) | ||||
0.828651 | + | 0.559765i | \(0.189109\pi\) | |||||||
\(138\) | 4.98991e86 | 0.00781826 | ||||||||
\(139\) | −1.30461e89 | −1.51484 | −0.757419 | − | 0.652929i | \(-0.773540\pi\) | ||||
−0.757419 | + | 0.652929i | \(0.773540\pi\) | |||||||
\(140\) | −3.95809e88 | −0.341328 | ||||||||
\(141\) | 2.73190e87 | 0.0175336 | ||||||||
\(142\) | 6.03925e88 | 0.289079 | ||||||||
\(143\) | −5.12235e89 | −1.83241 | ||||||||
\(144\) | −9.33093e88 | −0.249966 | ||||||||
\(145\) | 5.77988e88 | 0.116184 | ||||||||
\(146\) | −4.33267e89 | −0.654806 | ||||||||
\(147\) | 6.97900e87 | 0.00794555 | ||||||||
\(148\) | −4.36753e89 | −0.375297 | ||||||||
\(149\) | −3.63174e89 | −0.235985 | −0.117993 | − | 0.993014i | \(-0.537646\pi\) | ||||
−0.117993 | + | 0.993014i | \(0.537646\pi\) | |||||||
\(150\) | 8.00090e87 | 0.00393869 | ||||||||
\(151\) | −1.21094e90 | −0.452458 | −0.226229 | − | 0.974074i | \(-0.572640\pi\) | ||||
−0.226229 | + | 0.974074i | \(0.572640\pi\) | |||||||
\(152\) | 1.64120e90 | 0.466287 | ||||||||
\(153\) | 8.22014e90 | 1.77904 | ||||||||
\(154\) | 3.42545e90 | 0.565729 | ||||||||
\(155\) | 2.10938e90 | 0.266312 | ||||||||
\(156\) | −7.70672e88 | −0.00745073 | ||||||||
\(157\) | 1.43682e91 | 1.06554 | 0.532768 | − | 0.846262i | \(-0.321152\pi\) | ||||
0.532768 | + | 0.846262i | \(0.321152\pi\) | |||||||
\(158\) | −5.38518e90 | −0.306854 | ||||||||
\(159\) | 3.56906e89 | 0.0156521 | ||||||||
\(160\) | 6.36190e90 | 0.215084 | ||||||||
\(161\) | 2.04932e91 | 0.534978 | ||||||||
\(162\) | −3.50093e91 | −0.706822 | ||||||||
\(163\) | −6.52333e90 | −0.102020 | −0.0510098 | − | 0.998698i | \(-0.516244\pi\) | ||||
−0.0510098 | + | 0.998698i | \(0.516244\pi\) | |||||||
\(164\) | −3.97104e91 | −0.481819 | ||||||||
\(165\) | −2.13392e90 | −0.0201184 | ||||||||
\(166\) | 9.91275e91 | 0.727292 | ||||||||
\(167\) | −2.55968e92 | −1.46370 | −0.731849 | − | 0.681467i | \(-0.761342\pi\) | ||||
−0.731849 | + | 0.681467i | \(0.761342\pi\) | |||||||
\(168\) | 5.15369e89 | 0.00230029 | ||||||||
\(169\) | 1.86687e92 | 0.651354 | ||||||||
\(170\) | −5.60455e92 | −1.53077 | ||||||||
\(171\) | 6.15855e92 | 1.31868 | ||||||||
\(172\) | −2.51299e92 | −0.422435 | ||||||||
\(173\) | −1.23154e93 | −1.62755 | −0.813777 | − | 0.581177i | \(-0.802592\pi\) | ||||
−0.813777 | + | 0.581177i | \(0.802592\pi\) | |||||||
\(174\) | −7.52579e89 | −0.000782993 0 | ||||||||
\(175\) | 3.28592e92 | 0.269512 | ||||||||
\(176\) | −5.50579e92 | −0.356487 | ||||||||
\(177\) | −1.90389e91 | −0.00974432 | ||||||||
\(178\) | −2.21018e93 | −0.895360 | ||||||||
\(179\) | 4.00341e93 | 1.28537 | 0.642687 | − | 0.766129i | \(-0.277820\pi\) | ||||
0.642687 | + | 0.766129i | \(0.277820\pi\) | |||||||
\(180\) | 2.38728e93 | 0.608266 | ||||||||
\(181\) | 7.45433e93 | 1.50920 | 0.754602 | − | 0.656183i | \(-0.227830\pi\) | ||||
0.754602 | + | 0.656183i | \(0.227830\pi\) | |||||||
\(182\) | −3.16510e93 | −0.509829 | ||||||||
\(183\) | 2.16174e91 | 0.00277386 | ||||||||
\(184\) | −3.29391e93 | −0.337110 | ||||||||
\(185\) | 1.11741e94 | 0.913244 | ||||||||
\(186\) | −2.74656e91 | −0.00179474 | ||||||||
\(187\) | 4.85036e94 | 2.53716 | ||||||||
\(188\) | −1.80336e94 | −0.756019 | ||||||||
\(189\) | 3.86807e92 | 0.0130116 | ||||||||
\(190\) | −4.19894e94 | −1.13466 | ||||||||
\(191\) | −2.24626e94 | −0.488176 | −0.244088 | − | 0.969753i | \(-0.578488\pi\) | ||||
−0.244088 | + | 0.969753i | \(0.578488\pi\) | |||||||
\(192\) | −8.28361e91 | −0.00144950 | ||||||||
\(193\) | −8.03970e94 | −1.13400 | −0.566998 | − | 0.823719i | \(-0.691895\pi\) | ||||
−0.566998 | + | 0.823719i | \(0.691895\pi\) | |||||||
\(194\) | −5.22519e94 | −0.594744 | ||||||||
\(195\) | 1.97173e93 | 0.0181305 | ||||||||
\(196\) | −4.60694e94 | −0.342598 | ||||||||
\(197\) | 1.17845e95 | 0.709516 | 0.354758 | − | 0.934958i | \(-0.384563\pi\) | ||||
0.354758 | + | 0.934958i | \(0.384563\pi\) | |||||||
\(198\) | −2.06603e95 | −1.00816 | ||||||||
\(199\) | 2.16660e95 | 0.857781 | 0.428891 | − | 0.903356i | \(-0.358905\pi\) | ||||
0.428891 | + | 0.903356i | \(0.358905\pi\) | |||||||
\(200\) | −5.28151e94 | −0.169829 | ||||||||
\(201\) | −7.19930e93 | −0.0188215 | ||||||||
\(202\) | −4.10680e95 | −0.873820 | ||||||||
\(203\) | −3.09079e94 | −0.0535777 | ||||||||
\(204\) | 7.29750e93 | 0.0103163 | ||||||||
\(205\) | 1.01597e96 | 1.17246 | ||||||||
\(206\) | 2.94020e95 | 0.277260 | ||||||||
\(207\) | −1.23603e96 | −0.953363 | ||||||||
\(208\) | 5.08731e95 | 0.321263 | ||||||||
\(209\) | 3.63390e96 | 1.88062 | ||||||||
\(210\) | −1.31855e94 | −0.00559752 | ||||||||
\(211\) | −1.07711e96 | −0.375439 | −0.187719 | − | 0.982223i | \(-0.560110\pi\) | ||||
−0.187719 | + | 0.982223i | \(0.560110\pi\) | |||||||
\(212\) | −2.35599e96 | −0.674893 | ||||||||
\(213\) | 2.01184e94 | 0.00474067 | ||||||||
\(214\) | 3.88603e96 | 0.753936 | ||||||||
\(215\) | 6.42936e96 | 1.02795 | ||||||||
\(216\) | −6.21720e94 | −0.00819907 | ||||||||
\(217\) | −1.12799e96 | −0.122808 | ||||||||
\(218\) | −3.79769e95 | −0.0341645 | ||||||||
\(219\) | −1.44333e95 | −0.0107383 | ||||||||
\(220\) | 1.40863e97 | 0.867473 | ||||||||
\(221\) | −4.48170e97 | −2.28646 | ||||||||
\(222\) | −1.45495e95 | −0.00615458 | ||||||||
\(223\) | −4.04527e97 | −1.42002 | −0.710011 | − | 0.704190i | \(-0.751310\pi\) | ||||
−0.710011 | + | 0.704190i | \(0.751310\pi\) | |||||||
\(224\) | −3.40202e96 | −0.0991847 | ||||||||
\(225\) | −1.98187e97 | −0.480286 | ||||||||
\(226\) | 9.69100e96 | 0.195375 | ||||||||
\(227\) | −8.85082e96 | −0.148563 | −0.0742815 | − | 0.997237i | \(-0.523666\pi\) | ||||
−0.0742815 | + | 0.997237i | \(0.523666\pi\) | |||||||
\(228\) | 5.46730e95 | 0.00764675 | ||||||||
\(229\) | −2.54255e96 | −0.0296549 | −0.0148274 | − | 0.999890i | \(-0.504720\pi\) | ||||
−0.0148274 | + | 0.999890i | \(0.504720\pi\) | |||||||
\(230\) | 8.42731e97 | 0.820321 | ||||||||
\(231\) | 1.14111e96 | 0.00927752 | ||||||||
\(232\) | 4.96788e96 | 0.0337613 | ||||||||
\(233\) | −1.71386e98 | −0.974324 | −0.487162 | − | 0.873312i | \(-0.661968\pi\) | ||||
−0.487162 | + | 0.873312i | \(0.661968\pi\) | |||||||
\(234\) | 1.90899e98 | 0.908545 | ||||||||
\(235\) | 4.61382e98 | 1.83969 | ||||||||
\(236\) | 1.25679e98 | 0.420158 | ||||||||
\(237\) | −1.79395e96 | −0.00503217 | ||||||||
\(238\) | 2.99704e98 | 0.705908 | ||||||||
\(239\) | −6.03124e98 | −1.19370 | −0.596848 | − | 0.802354i | \(-0.703580\pi\) | ||||
−0.596848 | + | 0.802354i | \(0.703580\pi\) | |||||||
\(240\) | 2.11932e96 | 0.00352721 | ||||||||
\(241\) | 5.02162e98 | 0.703293 | 0.351646 | − | 0.936133i | \(-0.385622\pi\) | ||||
0.351646 | + | 0.936133i | \(0.385622\pi\) | |||||||
\(242\) | −6.19527e98 | −0.730673 | ||||||||
\(243\) | −3.49955e97 | −0.0347818 | ||||||||
\(244\) | −1.42700e98 | −0.119604 | ||||||||
\(245\) | 1.17866e99 | 0.833676 | ||||||||
\(246\) | −1.32286e97 | −0.00790147 | ||||||||
\(247\) | −3.35770e99 | −1.69480 | ||||||||
\(248\) | 1.81304e98 | 0.0773861 | ||||||||
\(249\) | 3.30221e97 | 0.0119270 | ||||||||
\(250\) | −1.46180e99 | −0.447072 | ||||||||
\(251\) | 5.27365e99 | 1.36663 | 0.683317 | − | 0.730122i | \(-0.260537\pi\) | ||||
0.683317 | + | 0.730122i | \(0.260537\pi\) | |||||||
\(252\) | −1.27660e99 | −0.280499 | ||||||||
\(253\) | −7.29326e99 | −1.35963 | ||||||||
\(254\) | −5.71493e99 | −0.904506 | ||||||||
\(255\) | −1.86703e98 | −0.0251035 | ||||||||
\(256\) | 5.46813e98 | 0.0625000 | ||||||||
\(257\) | 1.47183e100 | 1.43098 | 0.715488 | − | 0.698625i | \(-0.246204\pi\) | ||||
0.715488 | + | 0.698625i | \(0.246204\pi\) | |||||||
\(258\) | −8.37145e97 | −0.00692760 | ||||||||
\(259\) | −5.97537e99 | −0.421138 | ||||||||
\(260\) | −1.30157e100 | −0.781758 | ||||||||
\(261\) | 1.86418e99 | 0.0954786 | ||||||||
\(262\) | −1.58514e100 | −0.692729 | ||||||||
\(263\) | 3.80826e100 | 1.42090 | 0.710449 | − | 0.703749i | \(-0.248492\pi\) | ||||
0.710449 | + | 0.703749i | \(0.248492\pi\) | |||||||
\(264\) | −1.83413e98 | −0.00584611 | ||||||||
\(265\) | 6.02769e100 | 1.64228 | ||||||||
\(266\) | 2.24538e100 | 0.523242 | ||||||||
\(267\) | −7.36273e98 | −0.0146832 | ||||||||
\(268\) | 4.75236e100 | 0.811550 | ||||||||
\(269\) | −5.22540e100 | −0.764539 | −0.382269 | − | 0.924051i | \(-0.624857\pi\) | ||||
−0.382269 | + | 0.924051i | \(0.624857\pi\) | |||||||
\(270\) | 1.59064e99 | 0.0199516 | ||||||||
\(271\) | 7.94839e100 | 0.855172 | 0.427586 | − | 0.903975i | \(-0.359364\pi\) | ||||
0.427586 | + | 0.903975i | \(0.359364\pi\) | |||||||
\(272\) | −4.81718e100 | −0.444819 | ||||||||
\(273\) | −1.05438e99 | −0.00836081 | ||||||||
\(274\) | −1.72003e101 | −1.17189 | ||||||||
\(275\) | −1.16941e101 | −0.684954 | ||||||||
\(276\) | −1.09729e99 | −0.00552835 | ||||||||
\(277\) | −3.58227e101 | −1.55327 | −0.776637 | − | 0.629948i | \(-0.783076\pi\) | ||||
−0.776637 | + | 0.629948i | \(0.783076\pi\) | |||||||
\(278\) | 2.86887e101 | 1.07115 | ||||||||
\(279\) | 6.80337e100 | 0.218852 | ||||||||
\(280\) | 8.70393e100 | 0.241355 | ||||||||
\(281\) | −5.10359e101 | −1.22057 | −0.610286 | − | 0.792181i | \(-0.708946\pi\) | ||||
−0.610286 | + | 0.792181i | \(0.708946\pi\) | |||||||
\(282\) | −6.00751e99 | −0.0123981 | ||||||||
\(283\) | −4.70816e101 | −0.838907 | −0.419454 | − | 0.907777i | \(-0.637778\pi\) | ||||
−0.419454 | + | 0.907777i | \(0.637778\pi\) | |||||||
\(284\) | −1.32804e101 | −0.204410 | ||||||||
\(285\) | −1.39878e100 | −0.0186075 | ||||||||
\(286\) | 1.12642e102 | 1.29571 | ||||||||
\(287\) | −5.43291e101 | −0.540672 | ||||||||
\(288\) | 2.05189e101 | 0.176753 | ||||||||
\(289\) | 2.90325e102 | 2.16582 | ||||||||
\(290\) | −1.27101e101 | −0.0821546 | ||||||||
\(291\) | −1.74066e100 | −0.00975335 | ||||||||
\(292\) | 9.52765e101 | 0.463017 | ||||||||
\(293\) | −7.77907e101 | −0.328036 | −0.164018 | − | 0.986457i | \(-0.552446\pi\) | ||||
−0.164018 | + | 0.986457i | \(0.552446\pi\) | |||||||
\(294\) | −1.53470e100 | −0.00561835 | ||||||||
\(295\) | −3.21543e102 | −1.02241 | ||||||||
\(296\) | 9.60430e101 | 0.265375 | ||||||||
\(297\) | −1.37659e101 | −0.0330684 | ||||||||
\(298\) | 7.98629e101 | 0.166867 | ||||||||
\(299\) | 6.73893e102 | 1.22528 | ||||||||
\(300\) | −1.75942e100 | −0.00278507 | ||||||||
\(301\) | −3.43810e102 | −0.474034 | ||||||||
\(302\) | 2.66288e102 | 0.319936 | ||||||||
\(303\) | −1.36809e101 | −0.0143300 | ||||||||
\(304\) | −3.60904e102 | −0.329715 | ||||||||
\(305\) | 3.65091e102 | 0.291043 | ||||||||
\(306\) | −1.80763e103 | −1.25797 | ||||||||
\(307\) | −2.89674e102 | −0.176062 | −0.0880312 | − | 0.996118i | \(-0.528058\pi\) | ||||
−0.0880312 | + | 0.996118i | \(0.528058\pi\) | |||||||
\(308\) | −7.53265e102 | −0.400031 | ||||||||
\(309\) | 9.79462e100 | 0.00454685 | ||||||||
\(310\) | −4.63859e102 | −0.188311 | ||||||||
\(311\) | −1.09171e103 | −0.387749 | −0.193875 | − | 0.981026i | \(-0.562105\pi\) | ||||
−0.193875 | + | 0.981026i | \(0.562105\pi\) | |||||||
\(312\) | 1.69473e101 | 0.00526846 | ||||||||
\(313\) | −9.43698e102 | −0.256888 | −0.128444 | − | 0.991717i | \(-0.540998\pi\) | ||||
−0.128444 | + | 0.991717i | \(0.540998\pi\) | |||||||
\(314\) | −3.15961e103 | −0.753447 | ||||||||
\(315\) | 3.26612e103 | 0.682564 | ||||||||
\(316\) | 1.18421e103 | 0.216978 | ||||||||
\(317\) | 2.18142e103 | 0.350574 | 0.175287 | − | 0.984517i | \(-0.443915\pi\) | ||||
0.175287 | + | 0.984517i | \(0.443915\pi\) | |||||||
\(318\) | −7.84845e101 | −0.0110677 | ||||||||
\(319\) | 1.09997e103 | 0.136166 | ||||||||
\(320\) | −1.39900e103 | −0.152087 | ||||||||
\(321\) | 1.29455e102 | 0.0123640 | ||||||||
\(322\) | −4.50651e103 | −0.378287 | ||||||||
\(323\) | 3.17941e104 | 2.34661 | ||||||||
\(324\) | 7.69862e103 | 0.499798 | ||||||||
\(325\) | 1.08053e104 | 0.617274 | ||||||||
\(326\) | 1.43450e103 | 0.0721388 | ||||||||
\(327\) | −1.26512e101 | −0.000560271 0 | ||||||||
\(328\) | 8.73240e103 | 0.340698 | ||||||||
\(329\) | −2.46724e104 | −0.848364 | ||||||||
\(330\) | 4.69254e102 | 0.0142259 | ||||||||
\(331\) | −5.37346e104 | −1.43679 | −0.718394 | − | 0.695637i | \(-0.755122\pi\) | ||||
−0.718394 | + | 0.695637i | \(0.755122\pi\) | |||||||
\(332\) | −2.17984e104 | −0.514273 | ||||||||
\(333\) | 3.60398e104 | 0.750492 | ||||||||
\(334\) | 5.62879e104 | 1.03499 | ||||||||
\(335\) | −1.21587e105 | −1.97482 | ||||||||
\(336\) | −1.13331e102 | −0.00162655 | ||||||||
\(337\) | −6.28692e104 | −0.797622 | −0.398811 | − | 0.917033i | \(-0.630577\pi\) | ||||
−0.398811 | + | 0.917033i | \(0.630577\pi\) | |||||||
\(338\) | −4.10530e104 | −0.460577 | ||||||||
\(339\) | 3.22834e102 | 0.00320400 | ||||||||
\(340\) | 1.23245e105 | 1.08242 | ||||||||
\(341\) | 4.01438e104 | 0.312113 | ||||||||
\(342\) | −1.35428e105 | −0.932448 | ||||||||
\(343\) | −1.55016e105 | −0.945519 | ||||||||
\(344\) | 5.52611e104 | 0.298706 | ||||||||
\(345\) | 2.80737e103 | 0.0134526 | ||||||||
\(346\) | 2.70819e105 | 1.15085 | ||||||||
\(347\) | 3.23846e105 | 1.22086 | 0.610429 | − | 0.792071i | \(-0.290997\pi\) | ||||
0.610429 | + | 0.792071i | \(0.290997\pi\) | |||||||
\(348\) | 1.65494e102 | 0.000553660 0 | ||||||||
\(349\) | −1.45038e105 | −0.430752 | −0.215376 | − | 0.976531i | \(-0.569098\pi\) | ||||
−0.215376 | + | 0.976531i | \(0.569098\pi\) | |||||||
\(350\) | −7.22581e104 | −0.190574 | ||||||||
\(351\) | 1.27196e104 | 0.0298009 | ||||||||
\(352\) | 1.21074e105 | 0.252074 | ||||||||
\(353\) | −1.83016e105 | −0.338718 | −0.169359 | − | 0.985554i | \(-0.554170\pi\) | ||||
−0.169359 | + | 0.985554i | \(0.554170\pi\) | |||||||
\(354\) | 4.18670e103 | 0.00689027 | ||||||||
\(355\) | 3.39774e105 | 0.497409 | ||||||||
\(356\) | 4.86024e105 | 0.633115 | ||||||||
\(357\) | 9.98396e103 | 0.0115764 | ||||||||
\(358\) | −8.80360e105 | −0.908897 | ||||||||
\(359\) | 1.83689e106 | 1.68913 | 0.844566 | − | 0.535452i | \(-0.179859\pi\) | ||||
0.844566 | + | 0.535452i | \(0.179859\pi\) | |||||||
\(360\) | −5.24968e105 | −0.430109 | ||||||||
\(361\) | 1.01256e106 | 0.739387 | ||||||||
\(362\) | −1.63923e106 | −1.06717 | ||||||||
\(363\) | −2.06382e104 | −0.0119825 | ||||||||
\(364\) | 6.96013e105 | 0.360504 | ||||||||
\(365\) | −2.43761e106 | −1.12670 | ||||||||
\(366\) | −4.75372e103 | −0.00196141 | ||||||||
\(367\) | −2.93248e106 | −1.08042 | −0.540212 | − | 0.841529i | \(-0.681656\pi\) | ||||
−0.540212 | + | 0.841529i | \(0.681656\pi\) | |||||||
\(368\) | 7.24338e105 | 0.238373 | ||||||||
\(369\) | 3.27680e106 | 0.963509 | ||||||||
\(370\) | −2.45722e106 | −0.645761 | ||||||||
\(371\) | −3.22331e106 | −0.757329 | ||||||||
\(372\) | 6.03975e103 | 0.00126907 | ||||||||
\(373\) | 3.30772e106 | 0.621745 | 0.310873 | − | 0.950452i | \(-0.399379\pi\) | ||||
0.310873 | + | 0.950452i | \(0.399379\pi\) | |||||||
\(374\) | −1.06660e107 | −1.79404 | ||||||||
\(375\) | −4.86967e104 | −0.00733165 | ||||||||
\(376\) | 3.96564e106 | 0.534586 | ||||||||
\(377\) | −1.01637e106 | −0.122711 | ||||||||
\(378\) | −8.50597e104 | −0.00920056 | ||||||||
\(379\) | 2.50774e106 | 0.243084 | 0.121542 | − | 0.992586i | \(-0.461216\pi\) | ||||
0.121542 | + | 0.992586i | \(0.461216\pi\) | |||||||
\(380\) | 9.23357e106 | 0.802325 | ||||||||
\(381\) | −1.90380e105 | −0.0148332 | ||||||||
\(382\) | 4.93959e106 | 0.345192 | ||||||||
\(383\) | 1.15247e107 | 0.722571 | 0.361286 | − | 0.932455i | \(-0.382338\pi\) | ||||
0.361286 | + | 0.932455i | \(0.382338\pi\) | |||||||
\(384\) | 1.82159e104 | 0.00102495 | ||||||||
\(385\) | 1.92720e107 | 0.973432 | ||||||||
\(386\) | 1.76795e107 | 0.801856 | ||||||||
\(387\) | 2.07365e107 | 0.844756 | ||||||||
\(388\) | 1.14903e107 | 0.420548 | ||||||||
\(389\) | −3.97495e107 | −1.30744 | −0.653722 | − | 0.756735i | \(-0.726793\pi\) | ||||
−0.653722 | + | 0.756735i | \(0.726793\pi\) | |||||||
\(390\) | −4.33588e105 | −0.0128202 | ||||||||
\(391\) | −6.38110e107 | −1.69652 | ||||||||
\(392\) | 1.01308e107 | 0.242254 | ||||||||
\(393\) | −5.28053e105 | −0.0113602 | ||||||||
\(394\) | −2.59143e107 | −0.501703 | ||||||||
\(395\) | −3.02976e107 | −0.527994 | ||||||||
\(396\) | 4.54324e107 | 0.712878 | ||||||||
\(397\) | 1.94436e107 | 0.274770 | 0.137385 | − | 0.990518i | \(-0.456130\pi\) | ||||
0.137385 | + | 0.990518i | \(0.456130\pi\) | |||||||
\(398\) | −4.76441e107 | −0.606543 | ||||||||
\(399\) | 7.48000e105 | 0.00858077 | ||||||||
\(400\) | 1.16142e107 | 0.120088 | ||||||||
\(401\) | −1.42569e108 | −1.32903 | −0.664513 | − | 0.747277i | \(-0.731361\pi\) | ||||
−0.664513 | + | 0.747277i | \(0.731361\pi\) | |||||||
\(402\) | 1.58314e106 | 0.0133088 | ||||||||
\(403\) | −3.70926e107 | −0.281273 | ||||||||
\(404\) | 9.03095e107 | 0.617884 | ||||||||
\(405\) | −1.96966e108 | −1.21621 | ||||||||
\(406\) | 6.79672e106 | 0.0378852 | ||||||||
\(407\) | 2.12655e108 | 1.07031 | ||||||||
\(408\) | −1.60474e106 | −0.00729469 | ||||||||
\(409\) | 3.38003e108 | 1.38804 | 0.694021 | − | 0.719955i | \(-0.255837\pi\) | ||||
0.694021 | + | 0.719955i | \(0.255837\pi\) | |||||||
\(410\) | −2.23414e108 | −0.829051 | ||||||||
\(411\) | −5.72989e106 | −0.0192181 | ||||||||
\(412\) | −6.46557e107 | −0.196052 | ||||||||
\(413\) | 1.71945e108 | 0.471479 | ||||||||
\(414\) | 2.71805e108 | 0.674129 | ||||||||
\(415\) | 5.57701e108 | 1.25143 | ||||||||
\(416\) | −1.11871e108 | −0.227167 | ||||||||
\(417\) | 9.55699e106 | 0.0175661 | ||||||||
\(418\) | −7.99102e108 | −1.32980 | ||||||||
\(419\) | −1.08958e109 | −1.64202 | −0.821008 | − | 0.570917i | \(-0.806588\pi\) | ||||
−0.821008 | + | 0.570917i | \(0.806588\pi\) | |||||||
\(420\) | 2.89952e106 | 0.00395804 | ||||||||
\(421\) | 1.48564e109 | 1.83741 | 0.918705 | − | 0.394945i | \(-0.129236\pi\) | ||||
0.918705 | + | 0.394945i | \(0.129236\pi\) | |||||||
\(422\) | 2.36859e108 | 0.265475 | ||||||||
\(423\) | 1.48809e109 | 1.51183 | ||||||||
\(424\) | 5.18087e108 | 0.477221 | ||||||||
\(425\) | −1.02316e109 | −0.854676 | ||||||||
\(426\) | −4.42408e106 | −0.00335216 | ||||||||
\(427\) | −1.95232e108 | −0.134213 | ||||||||
\(428\) | −8.54547e108 | −0.533114 | ||||||||
\(429\) | 3.75241e107 | 0.0212487 | ||||||||
\(430\) | −1.41383e109 | −0.726870 | ||||||||
\(431\) | −2.63902e109 | −1.23207 | −0.616035 | − | 0.787719i | \(-0.711262\pi\) | ||||
−0.616035 | + | 0.787719i | \(0.711262\pi\) | |||||||
\(432\) | 1.36718e107 | 0.00579762 | ||||||||
\(433\) | 7.65361e108 | 0.294862 | 0.147431 | − | 0.989072i | \(-0.452900\pi\) | ||||
0.147431 | + | 0.989072i | \(0.452900\pi\) | |||||||
\(434\) | 2.48048e108 | 0.0868386 | ||||||||
\(435\) | −4.23408e106 | −0.00134727 | ||||||||
\(436\) | 8.35120e107 | 0.0241579 | ||||||||
\(437\) | −4.78073e109 | −1.25752 | ||||||||
\(438\) | 3.17392e107 | 0.00759313 | ||||||||
\(439\) | −3.61884e109 | −0.787574 | −0.393787 | − | 0.919202i | \(-0.628835\pi\) | ||||
−0.393787 | + | 0.919202i | \(0.628835\pi\) | |||||||
\(440\) | −3.09761e109 | −0.613396 | ||||||||
\(441\) | 3.80153e109 | 0.685105 | ||||||||
\(442\) | 9.85536e109 | 1.61677 | ||||||||
\(443\) | 5.85530e109 | 0.874570 | 0.437285 | − | 0.899323i | \(-0.355940\pi\) | ||||
0.437285 | + | 0.899323i | \(0.355940\pi\) | |||||||
\(444\) | 3.19946e107 | 0.00435194 | ||||||||
\(445\) | −1.24347e110 | −1.54062 | ||||||||
\(446\) | 8.89564e109 | 1.00411 | ||||||||
\(447\) | 2.66045e107 | 0.00273649 | ||||||||
\(448\) | 7.48113e108 | 0.0701342 | ||||||||
\(449\) | 1.16917e110 | 0.999206 | 0.499603 | − | 0.866255i | \(-0.333479\pi\) | ||||
0.499603 | + | 0.866255i | \(0.333479\pi\) | |||||||
\(450\) | 4.35817e109 | 0.339613 | ||||||||
\(451\) | 1.93350e110 | 1.37410 | ||||||||
\(452\) | −2.13107e109 | −0.138151 | ||||||||
\(453\) | 8.87078e107 | 0.00524670 | ||||||||
\(454\) | 1.94632e109 | 0.105050 | ||||||||
\(455\) | −1.78072e110 | −0.877247 | ||||||||
\(456\) | −1.20227e108 | −0.00540707 | ||||||||
\(457\) | 4.93283e108 | 0.0202570 | 0.0101285 | − | 0.999949i | \(-0.496776\pi\) | ||||
0.0101285 | + | 0.999949i | \(0.496776\pi\) | |||||||
\(458\) | 5.59112e108 | 0.0209692 | ||||||||
\(459\) | −1.20442e109 | −0.0412622 | ||||||||
\(460\) | −1.85319e110 | −0.580055 | ||||||||
\(461\) | −4.52351e110 | −1.29386 | −0.646930 | − | 0.762550i | \(-0.723947\pi\) | ||||
−0.646930 | + | 0.762550i | \(0.723947\pi\) | |||||||
\(462\) | −2.50934e108 | −0.00656020 | ||||||||
\(463\) | −2.00646e110 | −0.479533 | −0.239766 | − | 0.970831i | \(-0.577071\pi\) | ||||
−0.239766 | + | 0.970831i | \(0.577071\pi\) | |||||||
\(464\) | −1.09245e109 | −0.0238729 | ||||||||
\(465\) | −1.54524e108 | −0.00308815 | ||||||||
\(466\) | 3.76881e110 | 0.688951 | ||||||||
\(467\) | −1.74428e110 | −0.291720 | −0.145860 | − | 0.989305i | \(-0.546595\pi\) | ||||
−0.145860 | + | 0.989305i | \(0.546595\pi\) | |||||||
\(468\) | −4.19792e110 | −0.642439 | ||||||||
\(469\) | 6.50186e110 | 0.910678 | ||||||||
\(470\) | −1.01459e111 | −1.30086 | ||||||||
\(471\) | −1.05255e109 | −0.0123560 | ||||||||
\(472\) | −2.76370e110 | −0.297097 | ||||||||
\(473\) | 1.22357e111 | 1.20474 | ||||||||
\(474\) | 3.94495e108 | 0.00355828 | ||||||||
\(475\) | −7.66551e110 | −0.633514 | ||||||||
\(476\) | −6.59055e110 | −0.499152 | ||||||||
\(477\) | 1.94410e111 | 1.34960 | ||||||||
\(478\) | 1.32628e111 | 0.844070 | ||||||||
\(479\) | 1.70754e111 | 0.996431 | 0.498216 | − | 0.867053i | \(-0.333989\pi\) | ||||
0.498216 | + | 0.867053i | \(0.333989\pi\) | |||||||
\(480\) | −4.66044e108 | −0.00249411 | ||||||||
\(481\) | −1.96492e111 | −0.964550 | ||||||||
\(482\) | −1.10426e111 | −0.497303 | ||||||||
\(483\) | −1.50124e109 | −0.00620362 | ||||||||
\(484\) | 1.36236e111 | 0.516664 | ||||||||
\(485\) | −2.93975e111 | −1.02336 | ||||||||
\(486\) | 7.69559e109 | 0.0245944 | ||||||||
\(487\) | 5.73073e111 | 1.68174 | 0.840869 | − | 0.541239i | \(-0.182045\pi\) | ||||
0.840869 | + | 0.541239i | \(0.182045\pi\) | |||||||
\(488\) | 3.13800e110 | 0.0845727 | ||||||||
\(489\) | 4.77870e108 | 0.00118302 | ||||||||
\(490\) | −2.59191e111 | −0.589498 | ||||||||
\(491\) | 3.97537e111 | 0.830799 | 0.415400 | − | 0.909639i | \(-0.363642\pi\) | ||||
0.415400 | + | 0.909639i | \(0.363642\pi\) | |||||||
\(492\) | 2.90900e109 | 0.00558718 | ||||||||
\(493\) | 9.62399e110 | 0.169906 | ||||||||
\(494\) | 7.38366e111 | 1.19840 | ||||||||
\(495\) | −1.16237e112 | −1.73471 | ||||||||
\(496\) | −3.98692e110 | −0.0547203 | ||||||||
\(497\) | −1.81694e111 | −0.229378 | ||||||||
\(498\) | −7.26164e109 | −0.00843368 | ||||||||
\(499\) | −1.46410e112 | −1.56458 | −0.782288 | − | 0.622916i | \(-0.785948\pi\) | ||||
−0.782288 | + | 0.622916i | \(0.785948\pi\) | |||||||
\(500\) | 3.21453e111 | 0.316128 | ||||||||
\(501\) | 1.87511e110 | 0.0169731 | ||||||||
\(502\) | −1.15969e112 | −0.966356 | ||||||||
\(503\) | 2.83844e111 | 0.217775 | 0.108888 | − | 0.994054i | \(-0.465271\pi\) | ||||
0.108888 | + | 0.994054i | \(0.465271\pi\) | |||||||
\(504\) | 2.80727e111 | 0.198343 | ||||||||
\(505\) | −2.31053e112 | −1.50355 | ||||||||
\(506\) | 1.60381e112 | 0.961402 | ||||||||
\(507\) | −1.36759e110 | −0.00755310 | ||||||||
\(508\) | 1.25673e112 | 0.639582 | ||||||||
\(509\) | −7.25643e111 | −0.340357 | −0.170179 | − | 0.985413i | \(-0.554434\pi\) | ||||
−0.170179 | + | 0.985413i | \(0.554434\pi\) | |||||||
\(510\) | 4.10565e110 | 0.0177509 | ||||||||
\(511\) | 1.30351e112 | 0.519574 | ||||||||
\(512\) | −1.20245e111 | −0.0441942 | ||||||||
\(513\) | −9.02357e110 | −0.0305849 | ||||||||
\(514\) | −3.23658e112 | −1.01185 | ||||||||
\(515\) | 1.65419e112 | 0.477072 | ||||||||
\(516\) | 1.84090e110 | 0.00489856 | ||||||||
\(517\) | 8.78059e112 | 2.15609 | ||||||||
\(518\) | 1.31400e112 | 0.297789 | ||||||||
\(519\) | 9.02172e110 | 0.0188731 | ||||||||
\(520\) | 2.86217e112 | 0.552786 | ||||||||
\(521\) | 5.90803e112 | 1.05360 | 0.526802 | − | 0.849988i | \(-0.323391\pi\) | ||||
0.526802 | + | 0.849988i | \(0.323391\pi\) | |||||||
\(522\) | −4.09937e111 | −0.0675136 | ||||||||
\(523\) | −6.09468e112 | −0.927110 | −0.463555 | − | 0.886068i | \(-0.653426\pi\) | ||||
−0.463555 | + | 0.886068i | \(0.653426\pi\) | |||||||
\(524\) | 3.48575e112 | 0.489833 | ||||||||
\(525\) | −2.40712e110 | −0.00312526 | ||||||||
\(526\) | −8.37445e112 | −1.00473 | ||||||||
\(527\) | 3.51230e112 | 0.389450 | ||||||||
\(528\) | 4.03330e110 | 0.00413383 | ||||||||
\(529\) | −9.58868e111 | −0.0908550 | ||||||||
\(530\) | −1.32550e113 | −1.16127 | ||||||||
\(531\) | −1.03707e113 | −0.840203 | ||||||||
\(532\) | −4.93765e112 | −0.369988 | ||||||||
\(533\) | −1.78654e113 | −1.23832 | ||||||||
\(534\) | 1.61908e111 | 0.0103826 | ||||||||
\(535\) | 2.18632e113 | 1.29727 | ||||||||
\(536\) | −1.04505e113 | −0.573852 | ||||||||
\(537\) | −2.93272e111 | −0.0149052 | ||||||||
\(538\) | 1.14908e113 | 0.540611 | ||||||||
\(539\) | 2.24312e113 | 0.977055 | ||||||||
\(540\) | −3.49786e111 | −0.0141079 | ||||||||
\(541\) | −2.22947e113 | −0.832750 | −0.416375 | − | 0.909193i | \(-0.636700\pi\) | ||||
−0.416375 | + | 0.909193i | \(0.636700\pi\) | |||||||
\(542\) | −1.74787e113 | −0.604698 | ||||||||
\(543\) | −5.46071e111 | −0.0175007 | ||||||||
\(544\) | 1.05931e113 | 0.314535 | ||||||||
\(545\) | −2.13662e112 | −0.0587857 | ||||||||
\(546\) | 2.31861e111 | 0.00591199 | ||||||||
\(547\) | −2.02028e113 | −0.477460 | −0.238730 | − | 0.971086i | \(-0.576731\pi\) | ||||
−0.238730 | + | 0.971086i | \(0.576731\pi\) | |||||||
\(548\) | 3.78238e113 | 0.828651 | ||||||||
\(549\) | 1.17752e113 | 0.239176 | ||||||||
\(550\) | 2.57157e113 | 0.484336 | ||||||||
\(551\) | 7.21031e112 | 0.125940 | ||||||||
\(552\) | 2.41297e111 | 0.00390913 | ||||||||
\(553\) | 1.62016e113 | 0.243482 | ||||||||
\(554\) | 7.87750e113 | 1.09833 | ||||||||
\(555\) | −8.18567e111 | −0.0105900 | ||||||||
\(556\) | −6.30870e113 | −0.757419 | ||||||||
\(557\) | 7.81160e113 | 0.870462 | 0.435231 | − | 0.900319i | \(-0.356667\pi\) | ||||
0.435231 | + | 0.900319i | \(0.356667\pi\) | |||||||
\(558\) | −1.49608e113 | −0.154751 | ||||||||
\(559\) | −1.13058e114 | −1.08570 | ||||||||
\(560\) | −1.91401e113 | −0.170664 | ||||||||
\(561\) | −3.55316e112 | −0.0294209 | ||||||||
\(562\) | 1.12229e114 | 0.863075 | ||||||||
\(563\) | −8.55541e113 | −0.611143 | −0.305571 | − | 0.952169i | \(-0.598847\pi\) | ||||
−0.305571 | + | 0.952169i | \(0.598847\pi\) | |||||||
\(564\) | 1.32106e112 | 0.00876680 | ||||||||
\(565\) | 5.45225e113 | 0.336175 | ||||||||
\(566\) | 1.03534e114 | 0.593197 | ||||||||
\(567\) | 1.05327e114 | 0.560847 | ||||||||
\(568\) | 2.92040e113 | 0.144539 | ||||||||
\(569\) | −3.03861e114 | −1.39803 | −0.699014 | − | 0.715108i | \(-0.746377\pi\) | ||||
−0.699014 | + | 0.715108i | \(0.746377\pi\) | |||||||
\(570\) | 3.07596e112 | 0.0131575 | ||||||||
\(571\) | −2.02235e114 | −0.804372 | −0.402186 | − | 0.915558i | \(-0.631749\pi\) | ||||
−0.402186 | + | 0.915558i | \(0.631749\pi\) | |||||||
\(572\) | −2.47702e114 | −0.916207 | ||||||||
\(573\) | 1.64551e112 | 0.00566089 | ||||||||
\(574\) | 1.19471e114 | 0.382313 | ||||||||
\(575\) | 1.53847e114 | 0.458010 | ||||||||
\(576\) | −4.51216e113 | −0.124983 | ||||||||
\(577\) | −1.99169e114 | −0.513363 | −0.256682 | − | 0.966496i | \(-0.582629\pi\) | ||||
−0.256682 | + | 0.966496i | \(0.582629\pi\) | |||||||
\(578\) | −6.38431e114 | −1.53147 | ||||||||
\(579\) | 5.88953e112 | 0.0131498 | ||||||||
\(580\) | 2.79498e113 | 0.0580920 | ||||||||
\(581\) | −2.98231e114 | −0.577090 | ||||||||
\(582\) | 3.82774e112 | 0.00689666 | ||||||||
\(583\) | 1.14713e115 | 1.92472 | ||||||||
\(584\) | −2.09515e114 | −0.327403 | ||||||||
\(585\) | 1.07402e115 | 1.56331 | ||||||||
\(586\) | 1.71064e114 | 0.231956 | ||||||||
\(587\) | −7.37323e114 | −0.931487 | −0.465743 | − | 0.884920i | \(-0.654213\pi\) | ||||
−0.465743 | + | 0.884920i | \(0.654213\pi\) | |||||||
\(588\) | 3.37484e112 | 0.00397277 | ||||||||
\(589\) | 2.63143e114 | 0.288673 | ||||||||
\(590\) | 7.07080e114 | 0.722953 | ||||||||
\(591\) | −8.63279e112 | −0.00822755 | ||||||||
\(592\) | −2.11201e114 | −0.187648 | ||||||||
\(593\) | 1.20108e115 | 0.994954 | 0.497477 | − | 0.867477i | \(-0.334260\pi\) | ||||
0.497477 | + | 0.867477i | \(0.334260\pi\) | |||||||
\(594\) | 3.02716e113 | 0.0233829 | ||||||||
\(595\) | 1.68616e115 | 1.21463 | ||||||||
\(596\) | −1.75620e114 | −0.117993 | ||||||||
\(597\) | −1.58716e113 | −0.00994684 | ||||||||
\(598\) | −1.48191e115 | −0.866406 | ||||||||
\(599\) | 1.21792e115 | 0.664361 | 0.332181 | − | 0.943216i | \(-0.392216\pi\) | ||||
0.332181 | + | 0.943216i | \(0.392216\pi\) | |||||||
\(600\) | 3.86900e112 | 0.00196934 | ||||||||
\(601\) | −2.21766e115 | −1.05343 | −0.526715 | − | 0.850042i | \(-0.676576\pi\) | ||||
−0.526715 | + | 0.850042i | \(0.676576\pi\) | |||||||
\(602\) | 7.56047e114 | 0.335192 | ||||||||
\(603\) | −3.92153e115 | −1.62288 | ||||||||
\(604\) | −5.85573e114 | −0.226229 | ||||||||
\(605\) | −3.48552e115 | −1.25725 | ||||||||
\(606\) | 3.00846e113 | 0.0101328 | ||||||||
\(607\) | 3.73785e115 | 1.17569 | 0.587844 | − | 0.808975i | \(-0.299977\pi\) | ||||
0.587844 | + | 0.808975i | \(0.299977\pi\) | |||||||
\(608\) | 7.93637e114 | 0.233143 | ||||||||
\(609\) | 2.26418e112 | 0.000621288 0 | ||||||||
\(610\) | −8.02843e114 | −0.205799 | ||||||||
\(611\) | −8.11321e115 | −1.94304 | ||||||||
\(612\) | 3.97502e115 | 0.889519 | ||||||||
\(613\) | −3.47576e115 | −0.726842 | −0.363421 | − | 0.931625i | \(-0.618391\pi\) | ||||
−0.363421 | + | 0.931625i | \(0.618391\pi\) | |||||||
\(614\) | 6.37000e114 | 0.124495 | ||||||||
\(615\) | −7.44256e113 | −0.0135958 | ||||||||
\(616\) | 1.65645e115 | 0.282864 | ||||||||
\(617\) | 9.31989e115 | 1.48791 | 0.743955 | − | 0.668230i | \(-0.232948\pi\) | ||||
0.743955 | + | 0.668230i | \(0.232948\pi\) | |||||||
\(618\) | −2.15386e113 | −0.00321511 | ||||||||
\(619\) | −3.57176e115 | −0.498563 | −0.249282 | − | 0.968431i | \(-0.580195\pi\) | ||||
−0.249282 | + | 0.968431i | \(0.580195\pi\) | |||||||
\(620\) | 1.02004e115 | 0.133156 | ||||||||
\(621\) | 1.81104e114 | 0.0221119 | ||||||||
\(622\) | 2.40069e115 | 0.274180 | ||||||||
\(623\) | 6.64946e115 | 0.710448 | ||||||||
\(624\) | −3.72674e113 | −0.00372536 | ||||||||
\(625\) | −1.33597e116 | −1.24961 | ||||||||
\(626\) | 2.07521e115 | 0.181647 | ||||||||
\(627\) | −2.66203e114 | −0.0218077 | ||||||||
\(628\) | 6.94805e115 | 0.532768 | ||||||||
\(629\) | 1.86059e116 | 1.33551 | ||||||||
\(630\) | −7.18226e115 | −0.482646 | ||||||||
\(631\) | 2.74127e116 | 1.72478 | 0.862388 | − | 0.506247i | \(-0.168968\pi\) | ||||
0.862388 | + | 0.506247i | \(0.168968\pi\) | |||||||
\(632\) | −2.60411e115 | −0.153427 | ||||||||
\(633\) | 7.89044e113 | 0.00435359 | ||||||||
\(634\) | −4.79699e115 | −0.247893 | ||||||||
\(635\) | −3.21528e116 | −1.55636 | ||||||||
\(636\) | 1.72589e114 | 0.00782607 | ||||||||
\(637\) | −2.07263e116 | −0.880512 | ||||||||
\(638\) | −2.41886e115 | −0.0962838 | ||||||||
\(639\) | 1.09587e116 | 0.408764 | ||||||||
\(640\) | 3.07642e115 | 0.107542 | ||||||||
\(641\) | 1.15285e114 | 0.00377714 | 0.00188857 | − | 0.999998i | \(-0.499399\pi\) | ||||
0.00188857 | + | 0.999998i | \(0.499399\pi\) | |||||||
\(642\) | −2.84673e114 | −0.00874266 | ||||||||
\(643\) | 5.51605e116 | 1.58808 | 0.794041 | − | 0.607865i | \(-0.207974\pi\) | ||||
0.794041 | + | 0.607865i | \(0.207974\pi\) | |||||||
\(644\) | 9.90991e115 | 0.267489 | ||||||||
\(645\) | −4.70987e114 | −0.0119201 | ||||||||
\(646\) | −6.99159e116 | −1.65931 | ||||||||
\(647\) | 2.69348e116 | 0.599495 | 0.299748 | − | 0.954019i | \(-0.403098\pi\) | ||||
0.299748 | + | 0.954019i | \(0.403098\pi\) | |||||||
\(648\) | −1.69294e116 | −0.353411 | ||||||||
\(649\) | −6.11930e116 | −1.19825 | ||||||||
\(650\) | −2.37611e116 | −0.436479 | ||||||||
\(651\) | 8.26318e113 | 0.00142409 | ||||||||
\(652\) | −3.15449e115 | −0.0510098 | ||||||||
\(653\) | 1.50164e116 | 0.227860 | 0.113930 | − | 0.993489i | \(-0.463656\pi\) | ||||
0.113930 | + | 0.993489i | \(0.463656\pi\) | |||||||
\(654\) | 2.78202e113 | 0.000396172 0 | ||||||||
\(655\) | −8.91815e116 | −1.19196 | ||||||||
\(656\) | −1.92027e116 | −0.240910 | ||||||||
\(657\) | −7.86198e116 | −0.925910 | ||||||||
\(658\) | 5.42553e116 | 0.599884 | ||||||||
\(659\) | 6.97853e116 | 0.724468 | 0.362234 | − | 0.932087i | \(-0.382014\pi\) | ||||
0.362234 | + | 0.932087i | \(0.382014\pi\) | |||||||
\(660\) | −1.03190e115 | −0.0100592 | ||||||||
\(661\) | 1.28721e117 | 1.17839 | 0.589196 | − | 0.807990i | \(-0.299445\pi\) | ||||
0.589196 | + | 0.807990i | \(0.299445\pi\) | |||||||
\(662\) | 1.18164e117 | 1.01596 | ||||||||
\(663\) | 3.28310e115 | 0.0265138 | ||||||||
\(664\) | 4.79351e116 | 0.363646 | ||||||||
\(665\) | 1.26328e117 | 0.900327 | ||||||||
\(666\) | −7.92523e116 | −0.530678 | ||||||||
\(667\) | −1.44712e116 | −0.0910502 | ||||||||
\(668\) | −1.23778e117 | −0.731849 | ||||||||
\(669\) | 2.96338e115 | 0.0164666 | ||||||||
\(670\) | 2.67373e117 | 1.39641 | ||||||||
\(671\) | 6.94806e116 | 0.341098 | ||||||||
\(672\) | 2.49217e114 | 0.00115015 | ||||||||
\(673\) | −1.41274e117 | −0.612966 | −0.306483 | − | 0.951876i | \(-0.599152\pi\) | ||||
−0.306483 | + | 0.951876i | \(0.599152\pi\) | |||||||
\(674\) | 1.38251e117 | 0.564004 | ||||||||
\(675\) | 2.90385e115 | 0.0111395 | ||||||||
\(676\) | 9.02765e116 | 0.325677 | ||||||||
\(677\) | −2.45656e117 | −0.833484 | −0.416742 | − | 0.909025i | \(-0.636828\pi\) | ||||
−0.416742 | + | 0.909025i | \(0.636828\pi\) | |||||||
\(678\) | −7.09920e114 | −0.00226557 | ||||||||
\(679\) | 1.57203e117 | 0.471916 | ||||||||
\(680\) | −2.71020e117 | −0.765386 | ||||||||
\(681\) | 6.48372e114 | 0.00172274 | ||||||||
\(682\) | −8.82771e116 | −0.220697 | ||||||||
\(683\) | −3.59496e117 | −0.845737 | −0.422869 | − | 0.906191i | \(-0.638977\pi\) | ||||
−0.422869 | + | 0.906191i | \(0.638977\pi\) | |||||||
\(684\) | 2.97809e117 | 0.659341 | ||||||||
\(685\) | −9.67705e117 | −2.01643 | ||||||||
\(686\) | 3.40884e117 | 0.668583 | ||||||||
\(687\) | 1.86256e114 | 0.000343878 0 | ||||||||
\(688\) | −1.21521e117 | −0.211217 | ||||||||
\(689\) | −1.05994e118 | −1.73454 | ||||||||
\(690\) | −6.17348e115 | −0.00951245 | ||||||||
\(691\) | 3.64308e117 | 0.528603 | 0.264302 | − | 0.964440i | \(-0.414859\pi\) | ||||
0.264302 | + | 0.964440i | \(0.414859\pi\) | |||||||
\(692\) | −5.95536e117 | −0.813777 | ||||||||
\(693\) | 6.21576e117 | 0.799954 | ||||||||
\(694\) | −7.12144e117 | −0.863276 | ||||||||
\(695\) | 1.61405e118 | 1.84310 | ||||||||
\(696\) | −3.63925e114 | −0.000391497 0 | ||||||||
\(697\) | 1.69168e118 | 1.71458 | ||||||||
\(698\) | 3.18942e117 | 0.304588 | ||||||||
\(699\) | 1.25549e116 | 0.0112983 | ||||||||
\(700\) | 1.58897e117 | 0.134756 | ||||||||
\(701\) | −1.93265e118 | −1.54474 | −0.772371 | − | 0.635172i | \(-0.780929\pi\) | ||||
−0.772371 | + | 0.635172i | \(0.780929\pi\) | |||||||
\(702\) | −2.79708e116 | −0.0210724 | ||||||||
\(703\) | 1.39396e118 | 0.989926 | ||||||||
\(704\) | −2.66243e117 | −0.178243 | ||||||||
\(705\) | −3.37988e116 | −0.0213331 | ||||||||
\(706\) | 4.02456e117 | 0.239510 | ||||||||
\(707\) | 1.23556e118 | 0.693356 | ||||||||
\(708\) | −9.20665e115 | −0.00487216 | ||||||||
\(709\) | 2.50803e117 | 0.125174 | 0.0625870 | − | 0.998040i | \(-0.480065\pi\) | ||||
0.0625870 | + | 0.998040i | \(0.480065\pi\) | |||||||
\(710\) | −7.47171e117 | −0.351721 | ||||||||
\(711\) | −9.77184e117 | −0.433898 | ||||||||
\(712\) | −1.06878e118 | −0.447680 | ||||||||
\(713\) | −5.28129e117 | −0.208701 | ||||||||
\(714\) | −2.19550e116 | −0.00818572 | ||||||||
\(715\) | 6.33733e118 | 2.22949 | ||||||||
\(716\) | 1.93593e118 | 0.642687 | ||||||||
\(717\) | 4.41822e116 | 0.0138421 | ||||||||
\(718\) | −4.03936e118 | −1.19440 | ||||||||
\(719\) | −4.74549e118 | −1.32444 | −0.662220 | − | 0.749309i | \(-0.730386\pi\) | ||||
−0.662220 | + | 0.749309i | \(0.730386\pi\) | |||||||
\(720\) | 1.15442e118 | 0.304133 | ||||||||
\(721\) | −8.84576e117 | −0.220000 | ||||||||
\(722\) | −2.22664e118 | −0.522826 | ||||||||
\(723\) | −3.67861e116 | −0.00815539 | ||||||||
\(724\) | 3.60469e118 | 0.754602 | ||||||||
\(725\) | −2.32033e117 | −0.0458693 | ||||||||
\(726\) | 4.53838e116 | 0.00847289 | ||||||||
\(727\) | −7.22350e118 | −1.27371 | −0.636854 | − | 0.770985i | \(-0.719764\pi\) | ||||
−0.636854 | + | 0.770985i | \(0.719764\pi\) | |||||||
\(728\) | −1.53055e118 | −0.254915 | ||||||||
\(729\) | −6.35100e118 | −0.999193 | ||||||||
\(730\) | 5.36035e118 | 0.796700 | ||||||||
\(731\) | 1.07054e119 | 1.50326 | ||||||||
\(732\) | 1.04536e116 | 0.00138693 | ||||||||
\(733\) | −9.11017e118 | −1.14212 | −0.571060 | − | 0.820908i | \(-0.693468\pi\) | ||||
−0.571060 | + | 0.820908i | \(0.693468\pi\) | |||||||
\(734\) | 6.44860e118 | 0.763975 | ||||||||
\(735\) | −8.63437e116 | −0.00966732 | ||||||||
\(736\) | −1.59284e118 | −0.168555 | ||||||||
\(737\) | −2.31393e119 | −2.31446 | ||||||||
\(738\) | −7.20576e118 | −0.681304 | ||||||||
\(739\) | 1.20282e119 | 1.07512 | 0.537558 | − | 0.843227i | \(-0.319347\pi\) | ||||
0.537558 | + | 0.843227i | \(0.319347\pi\) | |||||||
\(740\) | 5.40348e118 | 0.456622 | ||||||||
\(741\) | 2.45970e117 | 0.0196529 | ||||||||
\(742\) | 7.08813e118 | 0.535512 | ||||||||
\(743\) | 1.32005e119 | 0.943096 | 0.471548 | − | 0.881840i | \(-0.343695\pi\) | ||||
0.471548 | + | 0.881840i | \(0.343695\pi\) | |||||||
\(744\) | −1.32815e116 | −0.000897370 0 | ||||||||
\(745\) | 4.49317e118 | 0.287122 | ||||||||
\(746\) | −7.27376e118 | −0.439640 | ||||||||
\(747\) | 1.79875e119 | 1.02841 | ||||||||
\(748\) | 2.34549e119 | 1.26858 | ||||||||
\(749\) | −1.16914e119 | −0.598232 | ||||||||
\(750\) | 1.07085e117 | 0.00518426 | ||||||||
\(751\) | 1.21121e119 | 0.554833 | 0.277416 | − | 0.960750i | \(-0.410522\pi\) | ||||
0.277416 | + | 0.960750i | \(0.410522\pi\) | |||||||
\(752\) | −8.72053e118 | −0.378009 | ||||||||
\(753\) | −3.86324e117 | −0.0158475 | ||||||||
\(754\) | 2.23501e118 | 0.0867700 | ||||||||
\(755\) | 1.49816e119 | 0.550503 | ||||||||
\(756\) | 1.87048e117 | 0.00650578 | ||||||||
\(757\) | −1.68795e118 | −0.0555750 | −0.0277875 | − | 0.999614i | \(-0.508846\pi\) | ||||
−0.0277875 | + | 0.999614i | \(0.508846\pi\) | |||||||
\(758\) | −5.51459e118 | −0.171886 | ||||||||
\(759\) | 5.34272e117 | 0.0157663 | ||||||||
\(760\) | −2.03048e119 | −0.567330 | ||||||||
\(761\) | −2.63589e118 | −0.0697371 | −0.0348686 | − | 0.999392i | \(-0.511101\pi\) | ||||
−0.0348686 | + | 0.999392i | \(0.511101\pi\) | |||||||
\(762\) | 4.18650e117 | 0.0104887 | ||||||||
\(763\) | 1.14256e118 | 0.0271087 | ||||||||
\(764\) | −1.08623e119 | −0.244088 | ||||||||
\(765\) | −1.01699e120 | −2.16455 | ||||||||
\(766\) | −2.53431e119 | −0.510935 | ||||||||
\(767\) | 5.65419e119 | 1.07985 | ||||||||
\(768\) | −4.00571e116 | −0.000724751 0 | ||||||||
\(769\) | −1.12559e119 | −0.192947 | −0.0964736 | − | 0.995336i | \(-0.530756\pi\) | ||||
−0.0964736 | + | 0.995336i | \(0.530756\pi\) | |||||||
\(770\) | −4.23795e119 | −0.688320 | ||||||||
\(771\) | −1.07820e118 | −0.0165936 | ||||||||
\(772\) | −3.88776e119 | −0.566998 | ||||||||
\(773\) | 1.59287e119 | 0.220157 | 0.110078 | − | 0.993923i | \(-0.464890\pi\) | ||||
0.110078 | + | 0.993923i | \(0.464890\pi\) | |||||||
\(774\) | −4.56001e119 | −0.597332 | ||||||||
\(775\) | −8.46812e118 | −0.105140 | ||||||||
\(776\) | −2.52675e119 | −0.297372 | ||||||||
\(777\) | 4.37729e117 | 0.00488352 | ||||||||
\(778\) | 8.74100e119 | 0.924502 | ||||||||
\(779\) | 1.26741e120 | 1.27090 | ||||||||
\(780\) | 9.53470e117 | 0.00906527 | ||||||||
\(781\) | 6.46626e119 | 0.582955 | ||||||||
\(782\) | 1.40322e120 | 1.19962 | ||||||||
\(783\) | −2.73141e117 | −0.00221449 | ||||||||
\(784\) | −2.22778e119 | −0.171299 | ||||||||
\(785\) | −1.77763e120 | −1.29643 | ||||||||
\(786\) | 1.16120e118 | 0.00803289 | ||||||||
\(787\) | 1.91554e120 | 1.25701 | 0.628506 | − | 0.777805i | \(-0.283667\pi\) | ||||
0.628506 | + | 0.777805i | \(0.283667\pi\) | |||||||
\(788\) | 5.69862e119 | 0.354758 | ||||||||
\(789\) | −2.78976e118 | −0.0164767 | ||||||||
\(790\) | 6.66251e119 | 0.373348 | ||||||||
\(791\) | −2.91559e119 | −0.155025 | ||||||||
\(792\) | −9.99068e119 | −0.504081 | ||||||||
\(793\) | −6.41997e119 | −0.307394 | ||||||||
\(794\) | −4.27569e119 | −0.194292 | ||||||||
\(795\) | −4.41562e118 | −0.0190439 | ||||||||
\(796\) | 1.04770e120 | 0.428891 | ||||||||
\(797\) | −3.07246e120 | −1.19390 | −0.596948 | − | 0.802280i | \(-0.703620\pi\) | ||||
−0.596948 | + | 0.802280i | \(0.703620\pi\) | |||||||
\(798\) | −1.64487e118 | −0.00606752 | ||||||||
\(799\) | 7.68241e120 | 2.69033 | ||||||||
\(800\) | −2.55398e119 | −0.0849147 | ||||||||
\(801\) | −4.01055e120 | −1.26606 | ||||||||
\(802\) | 3.13512e120 | 0.939763 | ||||||||
\(803\) | −4.63902e120 | −1.32048 | ||||||||
\(804\) | −3.48137e118 | −0.00941074 | ||||||||
\(805\) | −2.53541e120 | −0.650906 | ||||||||
\(806\) | 8.15675e119 | 0.198890 | ||||||||
\(807\) | 3.82789e118 | 0.00886560 | ||||||||
\(808\) | −1.98593e120 | −0.436910 | ||||||||
\(809\) | −7.09944e120 | −1.48375 | −0.741874 | − | 0.670539i | \(-0.766063\pi\) | ||||
−0.741874 | + | 0.670539i | \(0.766063\pi\) | |||||||
\(810\) | 4.33132e120 | 0.859987 | ||||||||
\(811\) | 1.43742e120 | 0.271156 | 0.135578 | − | 0.990767i | \(-0.456711\pi\) | ||||
0.135578 | + | 0.990767i | \(0.456711\pi\) | |||||||
\(812\) | −1.49461e119 | −0.0267888 | ||||||||
\(813\) | −5.82264e118 | −0.00991658 | ||||||||
\(814\) | −4.67634e120 | −0.756821 | ||||||||
\(815\) | 8.07062e119 | 0.124127 | ||||||||
\(816\) | 3.52885e118 | 0.00515813 | ||||||||
\(817\) | 8.02053e120 | 1.11426 | ||||||||
\(818\) | −7.43275e120 | −0.981494 | ||||||||
\(819\) | −5.74332e120 | −0.720910 | ||||||||
\(820\) | 4.91294e120 | 0.586228 | ||||||||
\(821\) | −7.78548e119 | −0.0883170 | −0.0441585 | − | 0.999025i | \(-0.514061\pi\) | ||||
−0.0441585 | + | 0.999025i | \(0.514061\pi\) | |||||||
\(822\) | 1.26002e119 | 0.0135892 | ||||||||
\(823\) | 1.65033e121 | 1.69230 | 0.846151 | − | 0.532943i | \(-0.178914\pi\) | ||||
0.846151 | + | 0.532943i | \(0.178914\pi\) | |||||||
\(824\) | 1.42179e120 | 0.138630 | ||||||||
\(825\) | 8.56661e118 | 0.00794274 | ||||||||
\(826\) | −3.78111e120 | −0.333386 | ||||||||
\(827\) | −1.35079e121 | −1.13269 | −0.566343 | − | 0.824170i | \(-0.691642\pi\) | ||||
−0.566343 | + | 0.824170i | \(0.691642\pi\) | |||||||
\(828\) | −5.97705e120 | −0.476681 | ||||||||
\(829\) | 6.10580e120 | 0.463158 | 0.231579 | − | 0.972816i | \(-0.425611\pi\) | ||||
0.231579 | + | 0.972816i | \(0.425611\pi\) | |||||||
\(830\) | −1.22640e121 | −0.884893 | ||||||||
\(831\) | 2.62421e119 | 0.0180118 | ||||||||
\(832\) | 2.46007e120 | 0.160631 | ||||||||
\(833\) | 1.96257e121 | 1.21915 | ||||||||
\(834\) | −2.10160e119 | −0.0124211 | ||||||||
\(835\) | 3.16681e121 | 1.78088 | ||||||||
\(836\) | 1.75724e121 | 0.940312 | ||||||||
\(837\) | −9.96837e118 | −0.00507595 | ||||||||
\(838\) | 2.39601e121 | 1.16108 | ||||||||
\(839\) | 1.35734e121 | 0.625991 | 0.312996 | − | 0.949755i | \(-0.398667\pi\) | ||||
0.312996 | + | 0.949755i | \(0.398667\pi\) | |||||||
\(840\) | −6.37611e118 | −0.00279876 | ||||||||
\(841\) | −2.37168e121 | −0.990881 | ||||||||
\(842\) | −3.26695e121 | −1.29924 | ||||||||
\(843\) | 3.73867e119 | 0.0141538 | ||||||||
\(844\) | −5.20859e120 | −0.187719 | ||||||||
\(845\) | −2.30968e121 | −0.792500 | ||||||||
\(846\) | −3.27235e121 | −1.06903 | ||||||||
\(847\) | 1.86388e121 | 0.579772 | ||||||||
\(848\) | −1.13929e121 | −0.337446 | ||||||||
\(849\) | 3.44899e119 | 0.00972798 | ||||||||
\(850\) | 2.24995e121 | 0.604347 | ||||||||
\(851\) | −2.79768e121 | −0.715684 | ||||||||
\(852\) | 9.72866e118 | 0.00237034 | ||||||||
\(853\) | −1.76135e121 | −0.408752 | −0.204376 | − | 0.978892i | \(-0.565517\pi\) | ||||
−0.204376 | + | 0.978892i | \(0.565517\pi\) | |||||||
\(854\) | 4.29321e120 | 0.0949030 | ||||||||
\(855\) | −7.61931e121 | −1.60443 | ||||||||
\(856\) | 1.87917e121 | 0.376968 | ||||||||
\(857\) | −1.71907e121 | −0.328541 | −0.164270 | − | 0.986415i | \(-0.552527\pi\) | ||||
−0.164270 | + | 0.986415i | \(0.552527\pi\) | |||||||
\(858\) | −8.25163e119 | −0.0150251 | ||||||||
\(859\) | −1.24485e121 | −0.215974 | −0.107987 | − | 0.994152i | \(-0.534440\pi\) | ||||
−0.107987 | + | 0.994152i | \(0.534440\pi\) | |||||||
\(860\) | 3.10905e121 | 0.513975 | ||||||||
\(861\) | 3.97991e119 | 0.00626964 | ||||||||
\(862\) | 5.80326e121 | 0.871205 | ||||||||
\(863\) | −1.09444e122 | −1.56583 | −0.782914 | − | 0.622130i | \(-0.786267\pi\) | ||||
−0.782914 | + | 0.622130i | \(0.786267\pi\) | |||||||
\(864\) | −3.00646e119 | −0.00409953 | ||||||||
\(865\) | 1.52365e122 | 1.98024 | ||||||||
\(866\) | −1.68305e121 | −0.208499 | ||||||||
\(867\) | −2.12679e120 | −0.0251149 | ||||||||
\(868\) | −5.45464e120 | −0.0614042 | ||||||||
\(869\) | −5.76595e121 | −0.618800 | ||||||||
\(870\) | 9.31085e118 | 0.000952665 0 | ||||||||
\(871\) | 2.13805e122 | 2.08576 | ||||||||
\(872\) | −1.83645e120 | −0.0170822 | ||||||||
\(873\) | −9.48152e121 | −0.840983 | ||||||||
\(874\) | 1.05129e122 | 0.889201 | ||||||||
\(875\) | 4.39791e121 | 0.354742 | ||||||||
\(876\) | −6.97953e119 | −0.00536916 | ||||||||
\(877\) | 8.92250e121 | 0.654642 | 0.327321 | − | 0.944913i | \(-0.393854\pi\) | ||||
0.327321 | + | 0.944913i | \(0.393854\pi\) | |||||||
\(878\) | 7.95791e121 | 0.556899 | ||||||||
\(879\) | 5.69860e119 | 0.00380391 | ||||||||
\(880\) | 6.81172e121 | 0.433736 | ||||||||
\(881\) | 4.39476e121 | 0.266953 | 0.133476 | − | 0.991052i | \(-0.457386\pi\) | ||||
0.133476 | + | 0.991052i | \(0.457386\pi\) | |||||||
\(882\) | −8.35965e121 | −0.484442 | ||||||||
\(883\) | −1.29544e122 | −0.716223 | −0.358112 | − | 0.933679i | \(-0.616579\pi\) | ||||
−0.358112 | + | 0.933679i | \(0.616579\pi\) | |||||||
\(884\) | −2.16722e122 | −1.14323 | ||||||||
\(885\) | 2.35548e120 | 0.0118559 | ||||||||
\(886\) | −1.28759e122 | −0.618414 | ||||||||
\(887\) | −1.63443e122 | −0.749092 | −0.374546 | − | 0.927208i | \(-0.622201\pi\) | ||||
−0.374546 | + | 0.927208i | \(0.622201\pi\) | |||||||
\(888\) | −7.03568e119 | −0.00307729 | ||||||||
\(889\) | 1.71937e122 | 0.717705 | ||||||||
\(890\) | 2.73442e122 | 1.08938 | ||||||||
\(891\) | −3.74846e122 | −1.42537 | ||||||||
\(892\) | −1.95617e122 | −0.710011 | ||||||||
\(893\) | 5.75567e122 | 1.99416 | ||||||||
\(894\) | −5.85040e119 | −0.00193499 | ||||||||
\(895\) | −4.95299e122 | −1.56391 | ||||||||
\(896\) | −1.64512e121 | −0.0495923 | ||||||||
\(897\) | −4.93664e120 | −0.0142084 | ||||||||
\(898\) | −2.57103e122 | −0.706545 | ||||||||
\(899\) | 7.96526e120 | 0.0209013 | ||||||||
\(900\) | −9.58371e121 | −0.240143 | ||||||||
\(901\) | 1.00366e123 | 2.40164 | ||||||||
\(902\) | −4.25181e122 | −0.971634 | ||||||||
\(903\) | 2.51860e120 | 0.00549690 | ||||||||
\(904\) | 4.68628e121 | 0.0976873 | ||||||||
\(905\) | −9.22245e122 | −1.83624 | ||||||||
\(906\) | −1.95071e120 | −0.00370998 | ||||||||
\(907\) | 5.78479e122 | 1.05096 | 0.525479 | − | 0.850807i | \(-0.323886\pi\) | ||||
0.525479 | + | 0.850807i | \(0.323886\pi\) | |||||||
\(908\) | −4.28000e121 | −0.0742815 | ||||||||
\(909\) | −7.45212e122 | −1.23560 | ||||||||
\(910\) | 3.91584e122 | 0.620307 | ||||||||
\(911\) | 4.10656e120 | 0.00621534 | 0.00310767 | − | 0.999995i | \(-0.499011\pi\) | ||||
0.00310767 | + | 0.999995i | \(0.499011\pi\) | |||||||
\(912\) | 2.64382e120 | 0.00382337 | ||||||||
\(913\) | 1.06136e123 | 1.46665 | ||||||||
\(914\) | −1.08474e121 | −0.0143238 | ||||||||
\(915\) | −2.67449e120 | −0.00337494 | ||||||||
\(916\) | −1.22950e121 | −0.0148274 | ||||||||
\(917\) | 4.76898e122 | 0.549665 | ||||||||
\(918\) | 2.64856e121 | 0.0291768 | ||||||||
\(919\) | −8.16430e122 | −0.859657 | −0.429828 | − | 0.902911i | \(-0.641426\pi\) | ||||
−0.429828 | + | 0.902911i | \(0.641426\pi\) | |||||||
\(920\) | 4.07520e122 | 0.410161 | ||||||||
\(921\) | 2.12202e120 | 0.00204162 | ||||||||
\(922\) | 9.94730e122 | 0.914897 | ||||||||
\(923\) | −5.97478e122 | −0.525353 | ||||||||
\(924\) | 5.51809e120 | 0.00463876 | ||||||||
\(925\) | −4.48585e122 | −0.360548 | ||||||||
\(926\) | 4.41224e122 | 0.339081 | ||||||||
\(927\) | 5.33522e122 | 0.392052 | ||||||||
\(928\) | 2.40232e121 | 0.0168807 | ||||||||
\(929\) | 2.25330e123 | 1.51415 | 0.757073 | − | 0.653330i | \(-0.226629\pi\) | ||||
0.757073 | + | 0.653330i | \(0.226629\pi\) | |||||||
\(930\) | 3.39802e120 | 0.00218365 | ||||||||
\(931\) | 1.47037e123 | 0.903677 | ||||||||
\(932\) | −8.28770e122 | −0.487162 | ||||||||
\(933\) | 7.99738e120 | 0.00449634 | ||||||||
\(934\) | 3.83572e122 | 0.206277 | ||||||||
\(935\) | −6.00083e123 | −3.08695 | ||||||||
\(936\) | 9.23133e122 | 0.454273 | ||||||||
\(937\) | 8.41190e122 | 0.396006 | 0.198003 | − | 0.980201i | \(-0.436555\pi\) | ||||
0.198003 | + | 0.980201i | \(0.436555\pi\) | |||||||
\(938\) | −1.42977e123 | −0.643947 | ||||||||
\(939\) | 6.91311e120 | 0.00297887 | ||||||||
\(940\) | 2.23111e123 | 0.919845 | ||||||||
\(941\) | −3.05113e123 | −1.20362 | −0.601812 | − | 0.798638i | \(-0.705554\pi\) | ||||
−0.601812 | + | 0.798638i | \(0.705554\pi\) | |||||||
\(942\) | 2.31459e121 | 0.00873698 | ||||||||
\(943\) | −2.54370e123 | −0.918820 | ||||||||
\(944\) | 6.07744e122 | 0.210079 | ||||||||
\(945\) | −4.78554e121 | −0.0158311 | ||||||||
\(946\) | −2.69067e123 | −0.851879 | ||||||||
\(947\) | −5.94796e123 | −1.80237 | −0.901185 | − | 0.433436i | \(-0.857301\pi\) | ||||
−0.901185 | + | 0.433436i | \(0.857301\pi\) | |||||||
\(948\) | −8.67503e120 | −0.00251608 | ||||||||
\(949\) | 4.28643e123 | 1.19000 | ||||||||
\(950\) | 1.68566e123 | 0.447962 | ||||||||
\(951\) | −1.59801e121 | −0.00406526 | ||||||||
\(952\) | 1.44928e123 | 0.352954 | ||||||||
\(953\) | 6.37411e123 | 1.48615 | 0.743077 | − | 0.669206i | \(-0.233365\pi\) | ||||
0.743077 | + | 0.669206i | \(0.233365\pi\) | |||||||
\(954\) | −4.27513e123 | −0.954314 | ||||||||
\(955\) | 2.77906e123 | 0.593961 | ||||||||
\(956\) | −2.91653e123 | −0.596848 | ||||||||
\(957\) | −8.05790e120 | −0.00157898 | ||||||||
\(958\) | −3.75492e123 | −0.704583 | ||||||||
\(959\) | 5.17480e123 | 0.929868 | ||||||||
\(960\) | 1.02484e121 | 0.00176360 | ||||||||
\(961\) | −5.77696e123 | −0.952091 | ||||||||
\(962\) | 4.32091e123 | 0.682040 | ||||||||
\(963\) | 7.05151e123 | 1.06608 | ||||||||
\(964\) | 2.42830e123 | 0.351646 | ||||||||
\(965\) | 9.94666e123 | 1.37973 | ||||||||
\(966\) | 3.30127e121 | 0.00438662 | ||||||||
\(967\) | 3.24393e123 | 0.412927 | 0.206463 | − | 0.978454i | \(-0.433805\pi\) | ||||
0.206463 | + | 0.978454i | \(0.433805\pi\) | |||||||
\(968\) | −2.99585e123 | −0.365336 | ||||||||
\(969\) | −2.32909e122 | −0.0272114 | ||||||||
\(970\) | 6.46457e123 | 0.723623 | ||||||||
\(971\) | 8.24664e123 | 0.884462 | 0.442231 | − | 0.896901i | \(-0.354187\pi\) | ||||
0.442231 | + | 0.896901i | \(0.354187\pi\) | |||||||
\(972\) | −1.69228e122 | −0.0173909 | ||||||||
\(973\) | −8.63115e123 | −0.849936 | ||||||||
\(974\) | −1.26020e124 | −1.18917 | ||||||||
\(975\) | −7.91550e121 | −0.00715792 | ||||||||
\(976\) | −6.90054e122 | −0.0598020 | ||||||||
\(977\) | 4.25843e123 | 0.353692 | 0.176846 | − | 0.984239i | \(-0.443411\pi\) | ||||
0.176846 | + | 0.984239i | \(0.443411\pi\) | |||||||
\(978\) | −1.05085e121 | −0.000836522 0 | ||||||||
\(979\) | −2.36645e124 | −1.80558 | ||||||||
\(980\) | 5.69967e123 | 0.416838 | ||||||||
\(981\) | −6.89120e122 | −0.0483094 | ||||||||
\(982\) | −8.74194e123 | −0.587464 | ||||||||
\(983\) | 4.08523e123 | 0.263175 | 0.131588 | − | 0.991305i | \(-0.457993\pi\) | ||||
0.131588 | + | 0.991305i | \(0.457993\pi\) | |||||||
\(984\) | −6.39697e121 | −0.00395073 | ||||||||
\(985\) | −1.45797e124 | −0.863265 | ||||||||
\(986\) | −2.11634e123 | −0.120141 | ||||||||
\(987\) | 1.80739e122 | 0.00983764 | ||||||||
\(988\) | −1.62368e124 | −0.847400 | ||||||||
\(989\) | −1.60973e124 | −0.805575 | ||||||||
\(990\) | 2.55607e124 | 1.22663 | ||||||||
\(991\) | 3.01427e124 | 1.38716 | 0.693578 | − | 0.720382i | \(-0.256033\pi\) | ||||
0.693578 | + | 0.720382i | \(0.256033\pi\) | |||||||
\(992\) | 8.76733e122 | 0.0386931 | ||||||||
\(993\) | 3.93636e122 | 0.0166610 | ||||||||
\(994\) | 3.99550e123 | 0.162194 | ||||||||
\(995\) | −2.68050e124 | −1.04366 | ||||||||
\(996\) | 1.59685e122 | 0.00596351 | ||||||||
\(997\) | 4.45172e123 | 0.159470 | 0.0797350 | − | 0.996816i | \(-0.474593\pi\) | ||||
0.0797350 | + | 0.996816i | \(0.474593\pi\) | |||||||
\(998\) | 3.21958e124 | 1.10632 | ||||||||
\(999\) | −5.28058e122 | −0.0174066 |
(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 | 2.84.a.a.1.2 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2.84.a.a.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial |