Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3,22,Mod(1,3)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3.1");
S:= CuspForms(chi, 22);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 3.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: | \(8.38432032861\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 3.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1728.00 | 1.19324 | 0.596621 | − | 0.802523i | \(-0.296509\pi\) | ||||
0.596621 | + | 0.802523i | \(0.296509\pi\) | |||||||
\(3\) | −59049.0 | −0.577350 | ||||||||
\(4\) | 888832. | 0.423828 | ||||||||
\(5\) | −4.15128e7 | −1.90106 | −0.950532 | − | 0.310627i | \(-0.899461\pi\) | ||||
−0.950532 | + | 0.310627i | \(0.899461\pi\) | |||||||
\(6\) | −1.02037e8 | −0.688919 | ||||||||
\(7\) | 5.38430e8 | 0.720443 | 0.360222 | − | 0.932867i | \(-0.382701\pi\) | ||||
0.360222 | + | 0.932867i | \(0.382701\pi\) | |||||||
\(8\) | −2.08798e9 | −0.687513 | ||||||||
\(9\) | 3.48678e9 | 0.333333 | ||||||||
\(10\) | −7.17341e10 | −2.26843 | ||||||||
\(11\) | −6.41130e10 | −0.745286 | −0.372643 | − | 0.927975i | \(-0.621548\pi\) | ||||
−0.372643 | + | 0.927975i | \(0.621548\pi\) | |||||||
\(12\) | −5.24846e10 | −0.244697 | ||||||||
\(13\) | −1.30980e11 | −0.263512 | −0.131756 | − | 0.991282i | \(-0.542062\pi\) | ||||
−0.131756 | + | 0.991282i | \(0.542062\pi\) | |||||||
\(14\) | 9.30407e11 | 0.859663 | ||||||||
\(15\) | 2.45129e12 | 1.09758 | ||||||||
\(16\) | −5.47204e12 | −1.24420 | ||||||||
\(17\) | 8.24203e12 | 0.991563 | 0.495782 | − | 0.868447i | \(-0.334882\pi\) | ||||
0.495782 | + | 0.868447i | \(0.334882\pi\) | |||||||
\(18\) | 6.02516e12 | 0.397748 | ||||||||
\(19\) | 1.34921e13 | 0.504855 | 0.252428 | − | 0.967616i | \(-0.418771\pi\) | ||||
0.252428 | + | 0.967616i | \(0.418771\pi\) | |||||||
\(20\) | −3.68979e13 | −0.805724 | ||||||||
\(21\) | −3.17937e13 | −0.415948 | ||||||||
\(22\) | −1.10787e14 | −0.889308 | ||||||||
\(23\) | −2.33185e14 | −1.17370 | −0.586851 | − | 0.809695i | \(-0.699633\pi\) | ||||
−0.586851 | + | 0.809695i | \(0.699633\pi\) | |||||||
\(24\) | 1.23293e14 | 0.396936 | ||||||||
\(25\) | 1.24647e15 | 2.61404 | ||||||||
\(26\) | −2.26334e14 | −0.314434 | ||||||||
\(27\) | −2.05891e14 | −0.192450 | ||||||||
\(28\) | 4.78574e14 | 0.305344 | ||||||||
\(29\) | −2.02456e15 | −0.893618 | −0.446809 | − | 0.894629i | \(-0.647440\pi\) | ||||
−0.446809 | + | 0.894629i | \(0.647440\pi\) | |||||||
\(30\) | 4.23582e15 | 1.30968 | ||||||||
\(31\) | −6.86919e15 | −1.50525 | −0.752624 | − | 0.658451i | \(-0.771212\pi\) | ||||
−0.752624 | + | 0.658451i | \(0.771212\pi\) | |||||||
\(32\) | −5.07688e15 | −0.797117 | ||||||||
\(33\) | 3.78581e15 | 0.430291 | ||||||||
\(34\) | 1.42422e16 | 1.18318 | ||||||||
\(35\) | −2.23517e16 | −1.36961 | ||||||||
\(36\) | 3.09917e15 | 0.141276 | ||||||||
\(37\) | 3.44400e15 | 0.117746 | 0.0588728 | − | 0.998265i | \(-0.481249\pi\) | ||||
0.0588728 | + | 0.998265i | \(0.481249\pi\) | |||||||
\(38\) | 2.33144e16 | 0.602415 | ||||||||
\(39\) | 7.73424e15 | 0.152139 | ||||||||
\(40\) | 8.66777e16 | 1.30701 | ||||||||
\(41\) | −2.18424e16 | −0.254138 | −0.127069 | − | 0.991894i | \(-0.540557\pi\) | ||||
−0.127069 | + | 0.991894i | \(0.540557\pi\) | |||||||
\(42\) | −5.49396e16 | −0.496327 | ||||||||
\(43\) | −7.17928e16 | −0.506597 | −0.253298 | − | 0.967388i | \(-0.581515\pi\) | ||||
−0.253298 | + | 0.967388i | \(0.581515\pi\) | |||||||
\(44\) | −5.69857e16 | −0.315873 | ||||||||
\(45\) | −1.44746e17 | −0.633688 | ||||||||
\(46\) | −4.02943e17 | −1.40051 | ||||||||
\(47\) | 2.83545e17 | 0.786310 | 0.393155 | − | 0.919472i | \(-0.371383\pi\) | ||||
0.393155 | + | 0.919472i | \(0.371383\pi\) | |||||||
\(48\) | 3.23118e17 | 0.718338 | ||||||||
\(49\) | −2.68639e17 | −0.480962 | ||||||||
\(50\) | 2.15391e18 | 3.11919 | ||||||||
\(51\) | −4.86684e17 | −0.572479 | ||||||||
\(52\) | −1.16419e17 | −0.111684 | ||||||||
\(53\) | −2.17229e18 | −1.70616 | −0.853081 | − | 0.521779i | \(-0.825269\pi\) | ||||
−0.853081 | + | 0.521779i | \(0.825269\pi\) | |||||||
\(54\) | −3.55780e17 | −0.229640 | ||||||||
\(55\) | 2.66151e18 | 1.41684 | ||||||||
\(56\) | −1.12423e18 | −0.495314 | ||||||||
\(57\) | −7.96695e17 | −0.291478 | ||||||||
\(58\) | −3.49844e18 | −1.06630 | ||||||||
\(59\) | 1.53483e18 | 0.390944 | 0.195472 | − | 0.980709i | \(-0.437376\pi\) | ||||
0.195472 | + | 0.980709i | \(0.437376\pi\) | |||||||
\(60\) | 2.17878e18 | 0.465185 | ||||||||
\(61\) | 4.31159e18 | 0.773881 | 0.386940 | − | 0.922105i | \(-0.373532\pi\) | ||||
0.386940 | + | 0.922105i | \(0.373532\pi\) | |||||||
\(62\) | −1.18700e19 | −1.79613 | ||||||||
\(63\) | 1.87739e18 | 0.240148 | ||||||||
\(64\) | 2.70285e18 | 0.293044 | ||||||||
\(65\) | 5.43735e18 | 0.500953 | ||||||||
\(66\) | 6.54188e18 | 0.513442 | ||||||||
\(67\) | 9.24391e18 | 0.619541 | 0.309771 | − | 0.950811i | \(-0.399748\pi\) | ||||
0.309771 | + | 0.950811i | \(0.399748\pi\) | |||||||
\(68\) | 7.32578e18 | 0.420252 | ||||||||
\(69\) | 1.37693e19 | 0.677637 | ||||||||
\(70\) | −3.86238e19 | −1.63427 | ||||||||
\(71\) | −2.03874e19 | −0.743273 | −0.371636 | − | 0.928378i | \(-0.621203\pi\) | ||||
−0.371636 | + | 0.928378i | \(0.621203\pi\) | |||||||
\(72\) | −7.28033e18 | −0.229171 | ||||||||
\(73\) | 1.66178e19 | 0.452566 | 0.226283 | − | 0.974062i | \(-0.427343\pi\) | ||||
0.226283 | + | 0.974062i | \(0.427343\pi\) | |||||||
\(74\) | 5.95123e18 | 0.140499 | ||||||||
\(75\) | −7.36030e19 | −1.50922 | ||||||||
\(76\) | 1.19922e19 | 0.213972 | ||||||||
\(77\) | −3.45204e19 | −0.536936 | ||||||||
\(78\) | 1.33648e19 | 0.181538 | ||||||||
\(79\) | 6.79403e19 | 0.807315 | 0.403658 | − | 0.914910i | \(-0.367739\pi\) | ||||
0.403658 | + | 0.914910i | \(0.367739\pi\) | |||||||
\(80\) | 2.27160e20 | 2.36530 | ||||||||
\(81\) | 1.21577e19 | 0.111111 | ||||||||
\(82\) | −3.77437e19 | −0.303249 | ||||||||
\(83\) | 3.95037e19 | 0.279459 | 0.139730 | − | 0.990190i | \(-0.455377\pi\) | ||||
0.139730 | + | 0.990190i | \(0.455377\pi\) | |||||||
\(84\) | −2.82593e19 | −0.176290 | ||||||||
\(85\) | −3.42149e20 | −1.88503 | ||||||||
\(86\) | −1.24058e20 | −0.604493 | ||||||||
\(87\) | 1.19548e20 | 0.515931 | ||||||||
\(88\) | 1.33867e20 | 0.512394 | ||||||||
\(89\) | 4.16117e19 | 0.141456 | 0.0707278 | − | 0.997496i | \(-0.477468\pi\) | ||||
0.0707278 | + | 0.997496i | \(0.477468\pi\) | |||||||
\(90\) | −2.50121e20 | −0.756143 | ||||||||
\(91\) | −7.05236e19 | −0.189845 | ||||||||
\(92\) | −2.07262e20 | −0.497448 | ||||||||
\(93\) | 4.05619e20 | 0.869055 | ||||||||
\(94\) | 4.89965e20 | 0.938259 | ||||||||
\(95\) | −5.60095e20 | −0.959762 | ||||||||
\(96\) | 2.99785e20 | 0.460216 | ||||||||
\(97\) | 5.71815e19 | 0.0787322 | 0.0393661 | − | 0.999225i | \(-0.487466\pi\) | ||||
0.0393661 | + | 0.999225i | \(0.487466\pi\) | |||||||
\(98\) | −4.64209e20 | −0.573904 | ||||||||
\(99\) | −2.23548e20 | −0.248429 | ||||||||
\(100\) | 1.10791e21 | 1.10791 | ||||||||
\(101\) | 4.32417e20 | 0.389518 | 0.194759 | − | 0.980851i | \(-0.437607\pi\) | ||||
0.194759 | + | 0.980851i | \(0.437607\pi\) | |||||||
\(102\) | −8.40989e20 | −0.683107 | ||||||||
\(103\) | 1.84123e21 | 1.34995 | 0.674974 | − | 0.737841i | \(-0.264155\pi\) | ||||
0.674974 | + | 0.737841i | \(0.264155\pi\) | |||||||
\(104\) | 2.73483e20 | 0.181168 | ||||||||
\(105\) | 1.31985e21 | 0.790744 | ||||||||
\(106\) | −3.75371e21 | −2.03587 | ||||||||
\(107\) | −2.43805e21 | −1.19815 | −0.599077 | − | 0.800691i | \(-0.704466\pi\) | ||||
−0.599077 | + | 0.800691i | \(0.704466\pi\) | |||||||
\(108\) | −1.83003e20 | −0.0815658 | ||||||||
\(109\) | −4.13676e21 | −1.67372 | −0.836859 | − | 0.547418i | \(-0.815611\pi\) | ||||
−0.836859 | + | 0.547418i | \(0.815611\pi\) | |||||||
\(110\) | 4.59909e21 | 1.69063 | ||||||||
\(111\) | −2.03365e20 | −0.0679805 | ||||||||
\(112\) | −2.94631e21 | −0.896374 | ||||||||
\(113\) | 3.47910e21 | 0.964146 | 0.482073 | − | 0.876131i | \(-0.339884\pi\) | ||||
0.482073 | + | 0.876131i | \(0.339884\pi\) | |||||||
\(114\) | −1.37669e21 | −0.347804 | ||||||||
\(115\) | 9.68015e21 | 2.23128 | ||||||||
\(116\) | −1.79950e21 | −0.378741 | ||||||||
\(117\) | −4.56699e20 | −0.0878373 | ||||||||
\(118\) | 2.65219e21 | 0.466491 | ||||||||
\(119\) | 4.43775e21 | 0.714365 | ||||||||
\(120\) | −5.11823e21 | −0.754600 | ||||||||
\(121\) | −3.28977e21 | −0.444548 | ||||||||
\(122\) | 7.45043e21 | 0.923428 | ||||||||
\(123\) | 1.28977e21 | 0.146727 | ||||||||
\(124\) | −6.10556e21 | −0.637966 | ||||||||
\(125\) | −3.19497e22 | −3.06840 | ||||||||
\(126\) | 3.24413e21 | 0.286554 | ||||||||
\(127\) | 1.37141e21 | 0.111488 | 0.0557438 | − | 0.998445i | \(-0.482247\pi\) | ||||
0.0557438 | + | 0.998445i | \(0.482247\pi\) | |||||||
\(128\) | 1.53175e22 | 1.14679 | ||||||||
\(129\) | 4.23929e21 | 0.292484 | ||||||||
\(130\) | 9.39574e21 | 0.597758 | ||||||||
\(131\) | −2.45276e22 | −1.43981 | −0.719907 | − | 0.694071i | \(-0.755815\pi\) | ||||
−0.719907 | + | 0.694071i | \(0.755815\pi\) | |||||||
\(132\) | 3.36495e21 | 0.182370 | ||||||||
\(133\) | 7.26455e21 | 0.363719 | ||||||||
\(134\) | 1.59735e22 | 0.739263 | ||||||||
\(135\) | 8.54711e21 | 0.365860 | ||||||||
\(136\) | −1.72092e22 | −0.681713 | ||||||||
\(137\) | 1.02835e22 | 0.377204 | 0.188602 | − | 0.982054i | \(-0.439604\pi\) | ||||
0.188602 | + | 0.982054i | \(0.439604\pi\) | |||||||
\(138\) | 2.37934e22 | 0.808586 | ||||||||
\(139\) | 8.70692e21 | 0.274289 | 0.137145 | − | 0.990551i | \(-0.456207\pi\) | ||||
0.137145 | + | 0.990551i | \(0.456207\pi\) | |||||||
\(140\) | −1.98669e22 | −0.580478 | ||||||||
\(141\) | −1.67430e22 | −0.453977 | ||||||||
\(142\) | −3.52294e22 | −0.886905 | ||||||||
\(143\) | 8.39753e21 | 0.196392 | ||||||||
\(144\) | −1.90798e22 | −0.414733 | ||||||||
\(145\) | 8.40452e22 | 1.69883 | ||||||||
\(146\) | 2.87155e22 | 0.540022 | ||||||||
\(147\) | 1.58629e22 | 0.277683 | ||||||||
\(148\) | 3.06114e21 | 0.0499039 | ||||||||
\(149\) | −9.03997e22 | −1.37313 | −0.686564 | − | 0.727069i | \(-0.740882\pi\) | ||||
−0.686564 | + | 0.727069i | \(0.740882\pi\) | |||||||
\(150\) | −1.27186e23 | −1.80086 | ||||||||
\(151\) | −4.75206e22 | −0.627514 | −0.313757 | − | 0.949503i | \(-0.601588\pi\) | ||||
−0.313757 | + | 0.949503i | \(0.601588\pi\) | |||||||
\(152\) | −2.81712e22 | −0.347094 | ||||||||
\(153\) | 2.87382e22 | 0.330521 | ||||||||
\(154\) | −5.96512e22 | −0.640695 | ||||||||
\(155\) | 2.85159e23 | 2.86157 | ||||||||
\(156\) | 6.87444e21 | 0.0644806 | ||||||||
\(157\) | −1.50901e23 | −1.32356 | −0.661781 | − | 0.749697i | \(-0.730199\pi\) | ||||
−0.661781 | + | 0.749697i | \(0.730199\pi\) | |||||||
\(158\) | 1.17401e23 | 0.963323 | ||||||||
\(159\) | 1.28271e23 | 0.985053 | ||||||||
\(160\) | 2.10755e23 | 1.51537 | ||||||||
\(161\) | −1.25554e23 | −0.845586 | ||||||||
\(162\) | 2.10084e22 | 0.132583 | ||||||||
\(163\) | −4.83503e22 | −0.286042 | −0.143021 | − | 0.989720i | \(-0.545682\pi\) | ||||
−0.143021 | + | 0.989720i | \(0.545682\pi\) | |||||||
\(164\) | −1.94142e22 | −0.107711 | ||||||||
\(165\) | −1.57159e23 | −0.818011 | ||||||||
\(166\) | 6.82624e22 | 0.333462 | ||||||||
\(167\) | 4.78731e20 | 0.00219568 | 0.00109784 | − | 0.999999i | \(-0.499651\pi\) | ||||
0.00109784 | + | 0.999999i | \(0.499651\pi\) | |||||||
\(168\) | 6.63846e22 | 0.285970 | ||||||||
\(169\) | −2.29909e23 | −0.930562 | ||||||||
\(170\) | −5.91234e23 | −2.24929 | ||||||||
\(171\) | 4.70440e22 | 0.168285 | ||||||||
\(172\) | −6.38118e22 | −0.214710 | ||||||||
\(173\) | −1.61804e23 | −0.512277 | −0.256139 | − | 0.966640i | \(-0.582450\pi\) | ||||
−0.256139 | + | 0.966640i | \(0.582450\pi\) | |||||||
\(174\) | 2.06580e23 | 0.615631 | ||||||||
\(175\) | 6.71138e23 | 1.88327 | ||||||||
\(176\) | 3.50829e23 | 0.927284 | ||||||||
\(177\) | −9.06303e22 | −0.225712 | ||||||||
\(178\) | 7.19050e22 | 0.168791 | ||||||||
\(179\) | −8.76377e22 | −0.193970 | −0.0969849 | − | 0.995286i | \(-0.530920\pi\) | ||||
−0.0969849 | + | 0.995286i | \(0.530920\pi\) | |||||||
\(180\) | −1.28655e23 | −0.268575 | ||||||||
\(181\) | 9.36624e22 | 0.184476 | 0.0922381 | − | 0.995737i | \(-0.470598\pi\) | ||||
0.0922381 | + | 0.995737i | \(0.470598\pi\) | |||||||
\(182\) | −1.21865e23 | −0.226532 | ||||||||
\(183\) | −2.54595e23 | −0.446800 | ||||||||
\(184\) | 4.86885e23 | 0.806936 | ||||||||
\(185\) | −1.42970e23 | −0.223842 | ||||||||
\(186\) | 7.00910e23 | 1.03699 | ||||||||
\(187\) | −5.28422e23 | −0.738999 | ||||||||
\(188\) | 2.52024e23 | 0.333260 | ||||||||
\(189\) | −1.10858e23 | −0.138649 | ||||||||
\(190\) | −9.67843e23 | −1.14523 | ||||||||
\(191\) | 1.20858e24 | 1.35340 | 0.676699 | − | 0.736260i | \(-0.263410\pi\) | ||||
0.676699 | + | 0.736260i | \(0.263410\pi\) | |||||||
\(192\) | −1.59601e23 | −0.169189 | ||||||||
\(193\) | −1.78822e24 | −1.79502 | −0.897509 | − | 0.440997i | \(-0.854625\pi\) | ||||
−0.897509 | + | 0.440997i | \(0.854625\pi\) | |||||||
\(194\) | 9.88096e22 | 0.0939466 | ||||||||
\(195\) | −3.21070e23 | −0.289225 | ||||||||
\(196\) | −2.38775e23 | −0.203845 | ||||||||
\(197\) | 1.90963e24 | 1.54545 | 0.772723 | − | 0.634743i | \(-0.218894\pi\) | ||||
0.772723 | + | 0.634743i | \(0.218894\pi\) | |||||||
\(198\) | −3.86292e23 | −0.296436 | ||||||||
\(199\) | 1.44254e24 | 1.04995 | 0.524977 | − | 0.851116i | \(-0.324074\pi\) | ||||
0.524977 | + | 0.851116i | \(0.324074\pi\) | |||||||
\(200\) | −2.60261e24 | −1.79719 | ||||||||
\(201\) | −5.45844e23 | −0.357692 | ||||||||
\(202\) | 7.47216e23 | 0.464790 | ||||||||
\(203\) | −1.09008e24 | −0.643801 | ||||||||
\(204\) | −4.32580e23 | −0.242633 | ||||||||
\(205\) | 9.06739e23 | 0.483133 | ||||||||
\(206\) | 3.18165e24 | 1.61082 | ||||||||
\(207\) | −8.13065e23 | −0.391234 | ||||||||
\(208\) | 7.16728e23 | 0.327861 | ||||||||
\(209\) | −8.65020e23 | −0.376262 | ||||||||
\(210\) | 2.28069e24 | 0.943549 | ||||||||
\(211\) | 3.98848e24 | 1.56979 | 0.784895 | − | 0.619629i | \(-0.212717\pi\) | ||||
0.784895 | + | 0.619629i | \(0.212717\pi\) | |||||||
\(212\) | −1.93080e24 | −0.723119 | ||||||||
\(213\) | 1.20385e24 | 0.429129 | ||||||||
\(214\) | −4.21295e24 | −1.42969 | ||||||||
\(215\) | 2.98032e24 | 0.963072 | ||||||||
\(216\) | 4.29896e23 | 0.132312 | ||||||||
\(217\) | −3.69858e24 | −1.08445 | ||||||||
\(218\) | −7.14833e24 | −1.99715 | ||||||||
\(219\) | −9.81262e23 | −0.261289 | ||||||||
\(220\) | 2.36564e24 | 0.600495 | ||||||||
\(221\) | −1.07954e24 | −0.261289 | ||||||||
\(222\) | −3.51414e23 | −0.0811172 | ||||||||
\(223\) | −4.62963e24 | −1.01940 | −0.509700 | − | 0.860352i | \(-0.670244\pi\) | ||||
−0.509700 | + | 0.860352i | \(0.670244\pi\) | |||||||
\(224\) | −2.73354e24 | −0.574278 | ||||||||
\(225\) | 4.34618e24 | 0.871348 | ||||||||
\(226\) | 6.01188e24 | 1.15046 | ||||||||
\(227\) | −3.43010e24 | −0.626664 | −0.313332 | − | 0.949644i | \(-0.601445\pi\) | ||||
−0.313332 | + | 0.949644i | \(0.601445\pi\) | |||||||
\(228\) | −7.08128e23 | −0.123537 | ||||||||
\(229\) | 8.11792e23 | 0.135261 | 0.0676304 | − | 0.997710i | \(-0.478456\pi\) | ||||
0.0676304 | + | 0.997710i | \(0.478456\pi\) | |||||||
\(230\) | 1.67273e25 | 2.66246 | ||||||||
\(231\) | 2.03839e24 | 0.310000 | ||||||||
\(232\) | 4.22724e24 | 0.614374 | ||||||||
\(233\) | 8.22188e23 | 0.114218 | 0.0571089 | − | 0.998368i | \(-0.481812\pi\) | ||||
0.0571089 | + | 0.998368i | \(0.481812\pi\) | |||||||
\(234\) | −7.89177e23 | −0.104811 | ||||||||
\(235\) | −1.17707e25 | −1.49483 | ||||||||
\(236\) | 1.36421e24 | 0.165693 | ||||||||
\(237\) | −4.01181e24 | −0.466104 | ||||||||
\(238\) | 7.66844e24 | 0.852411 | ||||||||
\(239\) | −8.85525e24 | −0.941940 | −0.470970 | − | 0.882149i | \(-0.656096\pi\) | ||||
−0.470970 | + | 0.882149i | \(0.656096\pi\) | |||||||
\(240\) | −1.34135e25 | −1.36561 | ||||||||
\(241\) | 7.46934e24 | 0.727953 | 0.363977 | − | 0.931408i | \(-0.381419\pi\) | ||||
0.363977 | + | 0.931408i | \(0.381419\pi\) | |||||||
\(242\) | −5.68472e24 | −0.530454 | ||||||||
\(243\) | −7.17898e23 | −0.0641500 | ||||||||
\(244\) | 3.83228e24 | 0.327992 | ||||||||
\(245\) | 1.11520e25 | 0.914339 | ||||||||
\(246\) | 2.22873e24 | 0.175081 | ||||||||
\(247\) | −1.76720e24 | −0.133035 | ||||||||
\(248\) | 1.43427e25 | 1.03488 | ||||||||
\(249\) | −2.33266e24 | −0.161346 | ||||||||
\(250\) | −5.52091e25 | −3.66134 | ||||||||
\(251\) | 9.46474e23 | 0.0601914 | 0.0300957 | − | 0.999547i | \(-0.490419\pi\) | ||||
0.0300957 | + | 0.999547i | \(0.490419\pi\) | |||||||
\(252\) | 1.66868e24 | 0.101781 | ||||||||
\(253\) | 1.49502e25 | 0.874744 | ||||||||
\(254\) | 2.36979e24 | 0.133032 | ||||||||
\(255\) | 2.02036e25 | 1.08832 | ||||||||
\(256\) | 2.08004e25 | 1.07535 | ||||||||
\(257\) | −1.91825e25 | −0.951936 | −0.475968 | − | 0.879463i | \(-0.657902\pi\) | ||||
−0.475968 | + | 0.879463i | \(0.657902\pi\) | |||||||
\(258\) | 7.32550e24 | 0.349004 | ||||||||
\(259\) | 1.85435e24 | 0.0848290 | ||||||||
\(260\) | 4.83289e24 | 0.212318 | ||||||||
\(261\) | −7.05921e24 | −0.297873 | ||||||||
\(262\) | −4.23837e25 | −1.71805 | ||||||||
\(263\) | 8.88429e23 | 0.0346009 | 0.0173004 | − | 0.999850i | \(-0.494493\pi\) | ||||
0.0173004 | + | 0.999850i | \(0.494493\pi\) | |||||||
\(264\) | −7.90469e24 | −0.295831 | ||||||||
\(265\) | 9.01776e25 | 3.24352 | ||||||||
\(266\) | 1.25531e25 | 0.434006 | ||||||||
\(267\) | −2.45713e24 | −0.0816694 | ||||||||
\(268\) | 8.21628e24 | 0.262579 | ||||||||
\(269\) | −2.13847e25 | −0.657211 | −0.328605 | − | 0.944467i | \(-0.606579\pi\) | ||||
−0.328605 | + | 0.944467i | \(0.606579\pi\) | |||||||
\(270\) | 1.47694e25 | 0.436560 | ||||||||
\(271\) | −1.56435e25 | −0.444791 | −0.222395 | − | 0.974957i | \(-0.571388\pi\) | ||||
−0.222395 | + | 0.974957i | \(0.571388\pi\) | |||||||
\(272\) | −4.51007e25 | −1.23370 | ||||||||
\(273\) | 4.16435e24 | 0.109607 | ||||||||
\(274\) | 1.77699e25 | 0.450095 | ||||||||
\(275\) | −7.99152e25 | −1.94821 | ||||||||
\(276\) | 1.22386e25 | 0.287202 | ||||||||
\(277\) | −8.04973e25 | −1.81863 | −0.909313 | − | 0.416112i | \(-0.863392\pi\) | ||||
−0.909313 | + | 0.416112i | \(0.863392\pi\) | |||||||
\(278\) | 1.50456e25 | 0.327294 | ||||||||
\(279\) | −2.39514e25 | −0.501749 | ||||||||
\(280\) | 4.66699e25 | 0.941623 | ||||||||
\(281\) | 8.33171e25 | 1.61926 | 0.809632 | − | 0.586938i | \(-0.199667\pi\) | ||||
0.809632 | + | 0.586938i | \(0.199667\pi\) | |||||||
\(282\) | −2.89320e25 | −0.541704 | ||||||||
\(283\) | −4.46130e24 | −0.0804829 | −0.0402415 | − | 0.999190i | \(-0.512813\pi\) | ||||
−0.0402415 | + | 0.999190i | \(0.512813\pi\) | |||||||
\(284\) | −1.81209e25 | −0.315020 | ||||||||
\(285\) | 3.30730e25 | 0.554119 | ||||||||
\(286\) | 1.45109e25 | 0.234343 | ||||||||
\(287\) | −1.17606e25 | −0.183092 | ||||||||
\(288\) | −1.77020e25 | −0.265706 | ||||||||
\(289\) | −1.16088e24 | −0.0168020 | ||||||||
\(290\) | 1.45230e26 | 2.02711 | ||||||||
\(291\) | −3.37651e24 | −0.0454560 | ||||||||
\(292\) | 1.47704e25 | 0.191810 | ||||||||
\(293\) | 9.67128e25 | 1.21164 | 0.605820 | − | 0.795602i | \(-0.292845\pi\) | ||||
0.605820 | + | 0.795602i | \(0.292845\pi\) | |||||||
\(294\) | 2.74111e25 | 0.331344 | ||||||||
\(295\) | −6.37151e25 | −0.743209 | ||||||||
\(296\) | −7.19099e24 | −0.0809516 | ||||||||
\(297\) | 1.32003e25 | 0.143430 | ||||||||
\(298\) | −1.56211e26 | −1.63848 | ||||||||
\(299\) | 3.05426e25 | 0.309284 | ||||||||
\(300\) | −6.54207e25 | −0.639649 | ||||||||
\(301\) | −3.86554e25 | −0.364974 | ||||||||
\(302\) | −8.21155e25 | −0.748777 | ||||||||
\(303\) | −2.55338e25 | −0.224889 | ||||||||
\(304\) | −7.38293e25 | −0.628140 | ||||||||
\(305\) | −1.78986e26 | −1.47120 | ||||||||
\(306\) | 4.96596e25 | 0.394392 | ||||||||
\(307\) | 1.68163e26 | 1.29056 | 0.645278 | − | 0.763948i | \(-0.276742\pi\) | ||||
0.645278 | + | 0.763948i | \(0.276742\pi\) | |||||||
\(308\) | −3.06828e25 | −0.227569 | ||||||||
\(309\) | −1.08723e26 | −0.779393 | ||||||||
\(310\) | 4.92755e26 | 3.41455 | ||||||||
\(311\) | 2.30370e26 | 1.54327 | 0.771636 | − | 0.636065i | \(-0.219439\pi\) | ||||
0.771636 | + | 0.636065i | \(0.219439\pi\) | |||||||
\(312\) | −1.61489e25 | −0.104597 | ||||||||
\(313\) | −2.79658e26 | −1.75151 | −0.875753 | − | 0.482759i | \(-0.839635\pi\) | ||||
−0.875753 | + | 0.482759i | \(0.839635\pi\) | |||||||
\(314\) | −2.60756e26 | −1.57933 | ||||||||
\(315\) | −7.79356e25 | −0.456536 | ||||||||
\(316\) | 6.03875e25 | 0.342163 | ||||||||
\(317\) | 2.98501e25 | 0.163615 | 0.0818075 | − | 0.996648i | \(-0.473931\pi\) | ||||
0.0818075 | + | 0.996648i | \(0.473931\pi\) | |||||||
\(318\) | 2.21653e26 | 1.17541 | ||||||||
\(319\) | 1.29801e26 | 0.666002 | ||||||||
\(320\) | −1.12203e26 | −0.557095 | ||||||||
\(321\) | 1.43964e26 | 0.691755 | ||||||||
\(322\) | −2.16957e26 | −1.00899 | ||||||||
\(323\) | 1.11202e26 | 0.500596 | ||||||||
\(324\) | 1.08061e25 | 0.0470920 | ||||||||
\(325\) | −1.63263e26 | −0.688831 | ||||||||
\(326\) | −8.35494e25 | −0.341317 | ||||||||
\(327\) | 2.44272e26 | 0.966322 | ||||||||
\(328\) | 4.56064e25 | 0.174723 | ||||||||
\(329\) | 1.52669e26 | 0.566492 | ||||||||
\(330\) | −2.71572e26 | −0.976086 | ||||||||
\(331\) | 2.55594e26 | 0.889933 | 0.444967 | − | 0.895547i | \(-0.353216\pi\) | ||||
0.444967 | + | 0.895547i | \(0.353216\pi\) | |||||||
\(332\) | 3.51122e25 | 0.118443 | ||||||||
\(333\) | 1.20085e25 | 0.0392485 | ||||||||
\(334\) | 8.27248e23 | 0.00261998 | ||||||||
\(335\) | −3.83740e26 | −1.17779 | ||||||||
\(336\) | 1.73977e26 | 0.517522 | ||||||||
\(337\) | −4.91931e25 | −0.141837 | −0.0709187 | − | 0.997482i | \(-0.522593\pi\) | ||||
−0.0709187 | + | 0.997482i | \(0.522593\pi\) | |||||||
\(338\) | −3.97282e26 | −1.11039 | ||||||||
\(339\) | −2.05437e26 | −0.556650 | ||||||||
\(340\) | −3.04113e26 | −0.798927 | ||||||||
\(341\) | 4.40405e26 | 1.12184 | ||||||||
\(342\) | 8.12921e25 | 0.200805 | ||||||||
\(343\) | −4.45381e26 | −1.06695 | ||||||||
\(344\) | 1.49902e26 | 0.348292 | ||||||||
\(345\) | −5.71603e26 | −1.28823 | ||||||||
\(346\) | −2.79597e26 | −0.611271 | ||||||||
\(347\) | 2.98136e26 | 0.632345 | 0.316173 | − | 0.948702i | \(-0.397602\pi\) | ||||
0.316173 | + | 0.948702i | \(0.397602\pi\) | |||||||
\(348\) | 1.06258e26 | 0.218666 | ||||||||
\(349\) | 7.72834e26 | 1.54319 | 0.771595 | − | 0.636115i | \(-0.219459\pi\) | ||||
0.771595 | + | 0.636115i | \(0.219459\pi\) | |||||||
\(350\) | 1.15973e27 | 2.24720 | ||||||||
\(351\) | 2.69676e25 | 0.0507129 | ||||||||
\(352\) | 3.25494e26 | 0.594081 | ||||||||
\(353\) | −7.30755e26 | −1.29461 | −0.647303 | − | 0.762233i | \(-0.724103\pi\) | ||||
−0.647303 | + | 0.762233i | \(0.724103\pi\) | |||||||
\(354\) | −1.56609e26 | −0.269329 | ||||||||
\(355\) | 8.46336e26 | 1.41301 | ||||||||
\(356\) | 3.69858e25 | 0.0599529 | ||||||||
\(357\) | −2.62045e26 | −0.412439 | ||||||||
\(358\) | −1.51438e26 | −0.231453 | ||||||||
\(359\) | −1.58936e25 | −0.0235901 | −0.0117951 | − | 0.999930i | \(-0.503755\pi\) | ||||
−0.0117951 | + | 0.999930i | \(0.503755\pi\) | |||||||
\(360\) | 3.02226e26 | 0.435669 | ||||||||
\(361\) | −5.32173e26 | −0.745121 | ||||||||
\(362\) | 1.61849e26 | 0.220125 | ||||||||
\(363\) | 1.94258e26 | 0.256660 | ||||||||
\(364\) | −6.26836e25 | −0.0804618 | ||||||||
\(365\) | −6.89849e26 | −0.860358 | ||||||||
\(366\) | −4.39940e26 | −0.533141 | ||||||||
\(367\) | −1.40734e27 | −1.65732 | −0.828660 | − | 0.559752i | \(-0.810896\pi\) | ||||
−0.828660 | + | 0.559752i | \(0.810896\pi\) | |||||||
\(368\) | 1.27600e27 | 1.46032 | ||||||||
\(369\) | −7.61598e25 | −0.0847127 | ||||||||
\(370\) | −2.47052e26 | −0.267098 | ||||||||
\(371\) | −1.16962e27 | −1.22919 | ||||||||
\(372\) | 3.60527e26 | 0.368330 | ||||||||
\(373\) | −9.30077e26 | −0.923797 | −0.461898 | − | 0.886933i | \(-0.652831\pi\) | ||||
−0.461898 | + | 0.886933i | \(0.652831\pi\) | |||||||
\(374\) | −9.13112e26 | −0.881805 | ||||||||
\(375\) | 1.88660e27 | 1.77154 | ||||||||
\(376\) | −5.92035e26 | −0.540599 | ||||||||
\(377\) | 2.65177e26 | 0.235479 | ||||||||
\(378\) | −1.91562e26 | −0.165442 | ||||||||
\(379\) | 2.18541e27 | 1.83578 | 0.917892 | − | 0.396830i | \(-0.129890\pi\) | ||||
0.917892 | + | 0.396830i | \(0.129890\pi\) | |||||||
\(380\) | −4.97830e26 | −0.406774 | ||||||||
\(381\) | −8.09801e25 | −0.0643674 | ||||||||
\(382\) | 2.08843e27 | 1.61493 | ||||||||
\(383\) | 2.10347e27 | 1.58252 | 0.791258 | − | 0.611482i | \(-0.209426\pi\) | ||||
0.791258 | + | 0.611482i | \(0.209426\pi\) | |||||||
\(384\) | −9.04484e26 | −0.662099 | ||||||||
\(385\) | 1.43304e27 | 1.02075 | ||||||||
\(386\) | −3.09004e27 | −2.14189 | ||||||||
\(387\) | −2.50326e26 | −0.168866 | ||||||||
\(388\) | 5.08247e25 | 0.0333689 | ||||||||
\(389\) | −2.97815e26 | −0.190316 | −0.0951582 | − | 0.995462i | \(-0.530336\pi\) | ||||
−0.0951582 | + | 0.995462i | \(0.530336\pi\) | |||||||
\(390\) | −5.54809e26 | −0.345116 | ||||||||
\(391\) | −1.92192e27 | −1.16380 | ||||||||
\(392\) | 5.60912e26 | 0.330667 | ||||||||
\(393\) | 1.44833e27 | 0.831277 | ||||||||
\(394\) | 3.29984e27 | 1.84409 | ||||||||
\(395\) | −2.82039e27 | −1.53476 | ||||||||
\(396\) | −1.98697e26 | −0.105291 | ||||||||
\(397\) | 6.36504e26 | 0.328474 | 0.164237 | − | 0.986421i | \(-0.447484\pi\) | ||||
0.164237 | + | 0.986421i | \(0.447484\pi\) | |||||||
\(398\) | 2.49271e27 | 1.25285 | ||||||||
\(399\) | −4.28964e26 | −0.209993 | ||||||||
\(400\) | −6.82075e27 | −3.25239 | ||||||||
\(401\) | 2.43888e27 | 1.13286 | 0.566428 | − | 0.824111i | \(-0.308325\pi\) | ||||
0.566428 | + | 0.824111i | \(0.308325\pi\) | |||||||
\(402\) | −9.43218e26 | −0.426814 | ||||||||
\(403\) | 8.99728e26 | 0.396651 | ||||||||
\(404\) | 3.84346e26 | 0.165089 | ||||||||
\(405\) | −5.04698e26 | −0.211229 | ||||||||
\(406\) | −1.88367e27 | −0.768211 | ||||||||
\(407\) | −2.20805e26 | −0.0877542 | ||||||||
\(408\) | 1.01618e27 | 0.393587 | ||||||||
\(409\) | 5.48032e26 | 0.206876 | 0.103438 | − | 0.994636i | \(-0.467016\pi\) | ||||
0.103438 | + | 0.994636i | \(0.467016\pi\) | |||||||
\(410\) | 1.56684e27 | 0.576495 | ||||||||
\(411\) | −6.07232e26 | −0.217779 | ||||||||
\(412\) | 1.63654e27 | 0.572146 | ||||||||
\(413\) | 8.26399e26 | 0.281653 | ||||||||
\(414\) | −1.40498e27 | −0.466837 | ||||||||
\(415\) | −1.63991e27 | −0.531269 | ||||||||
\(416\) | 6.64970e26 | 0.210050 | ||||||||
\(417\) | −5.14135e26 | −0.158361 | ||||||||
\(418\) | −1.49475e27 | −0.448971 | ||||||||
\(419\) | −6.08246e27 | −1.78169 | −0.890844 | − | 0.454309i | \(-0.849886\pi\) | ||||
−0.890844 | + | 0.454309i | \(0.849886\pi\) | |||||||
\(420\) | 1.17312e27 | 0.335139 | ||||||||
\(421\) | −4.05990e27 | −1.13124 | −0.565618 | − | 0.824667i | \(-0.691362\pi\) | ||||
−0.565618 | + | 0.824667i | \(0.691362\pi\) | |||||||
\(422\) | 6.89209e27 | 1.87314 | ||||||||
\(423\) | 9.88659e26 | 0.262103 | ||||||||
\(424\) | 4.53568e27 | 1.17301 | ||||||||
\(425\) | 1.02735e28 | 2.59199 | ||||||||
\(426\) | 2.08026e27 | 0.512055 | ||||||||
\(427\) | 2.32149e27 | 0.557537 | ||||||||
\(428\) | −2.16702e27 | −0.507811 | ||||||||
\(429\) | −4.95866e26 | −0.113387 | ||||||||
\(430\) | 5.14999e27 | 1.14918 | ||||||||
\(431\) | −7.87214e27 | −1.71428 | −0.857140 | − | 0.515084i | \(-0.827761\pi\) | ||||
−0.857140 | + | 0.515084i | \(0.827761\pi\) | |||||||
\(432\) | 1.12664e27 | 0.239446 | ||||||||
\(433\) | −1.73785e27 | −0.360486 | −0.180243 | − | 0.983622i | \(-0.557688\pi\) | ||||
−0.180243 | + | 0.983622i | \(0.557688\pi\) | |||||||
\(434\) | −6.39115e27 | −1.29401 | ||||||||
\(435\) | −4.96278e27 | −0.980817 | ||||||||
\(436\) | −3.67689e27 | −0.709369 | ||||||||
\(437\) | −3.14615e27 | −0.592550 | ||||||||
\(438\) | −1.69562e27 | −0.311782 | ||||||||
\(439\) | 8.37416e27 | 1.50336 | 0.751681 | − | 0.659526i | \(-0.229243\pi\) | ||||
0.751681 | + | 0.659526i | \(0.229243\pi\) | |||||||
\(440\) | −5.55717e27 | −0.974094 | ||||||||
\(441\) | −9.36687e26 | −0.160321 | ||||||||
\(442\) | −1.86545e27 | −0.311781 | ||||||||
\(443\) | −3.30286e25 | −0.00539077 | −0.00269539 | − | 0.999996i | \(-0.500858\pi\) | ||||
−0.00269539 | + | 0.999996i | \(0.500858\pi\) | |||||||
\(444\) | −1.80757e26 | −0.0288120 | ||||||||
\(445\) | −1.72742e27 | −0.268916 | ||||||||
\(446\) | −7.99999e27 | −1.21639 | ||||||||
\(447\) | 5.33801e27 | 0.792776 | ||||||||
\(448\) | 1.45530e27 | 0.211121 | ||||||||
\(449\) | 5.21713e27 | 0.739341 | 0.369670 | − | 0.929163i | \(-0.379471\pi\) | ||||
0.369670 | + | 0.929163i | \(0.379471\pi\) | |||||||
\(450\) | 7.51020e27 | 1.03973 | ||||||||
\(451\) | 1.40038e27 | 0.189406 | ||||||||
\(452\) | 3.09233e27 | 0.408632 | ||||||||
\(453\) | 2.80604e27 | 0.362296 | ||||||||
\(454\) | −5.92721e27 | −0.747763 | ||||||||
\(455\) | 2.92763e27 | 0.360908 | ||||||||
\(456\) | 1.66348e27 | 0.200395 | ||||||||
\(457\) | 2.15211e26 | 0.0253363 | 0.0126682 | − | 0.999920i | \(-0.495967\pi\) | ||||
0.0126682 | + | 0.999920i | \(0.495967\pi\) | |||||||
\(458\) | 1.40278e27 | 0.161399 | ||||||||
\(459\) | −1.69696e27 | −0.190826 | ||||||||
\(460\) | 8.60403e27 | 0.945681 | ||||||||
\(461\) | 1.68699e28 | 1.81239 | 0.906197 | − | 0.422855i | \(-0.138972\pi\) | ||||
0.906197 | + | 0.422855i | \(0.138972\pi\) | |||||||
\(462\) | 3.52234e27 | 0.369906 | ||||||||
\(463\) | −1.90352e28 | −1.95415 | −0.977074 | − | 0.212898i | \(-0.931710\pi\) | ||||
−0.977074 | + | 0.212898i | \(0.931710\pi\) | |||||||
\(464\) | 1.10785e28 | 1.11184 | ||||||||
\(465\) | −1.68384e28 | −1.65213 | ||||||||
\(466\) | 1.42074e27 | 0.136290 | ||||||||
\(467\) | −1.21027e28 | −1.13515 | −0.567576 | − | 0.823321i | \(-0.692119\pi\) | ||||
−0.567576 | + | 0.823321i | \(0.692119\pi\) | |||||||
\(468\) | −4.05929e26 | −0.0372279 | ||||||||
\(469\) | 4.97720e27 | 0.446344 | ||||||||
\(470\) | −2.03398e28 | −1.78369 | ||||||||
\(471\) | 8.91053e27 | 0.764159 | ||||||||
\(472\) | −3.20469e27 | −0.268779 | ||||||||
\(473\) | 4.60286e27 | 0.377559 | ||||||||
\(474\) | −6.93240e27 | −0.556175 | ||||||||
\(475\) | 1.68175e28 | 1.31971 | ||||||||
\(476\) | 3.94442e27 | 0.302768 | ||||||||
\(477\) | −7.57429e27 | −0.568721 | ||||||||
\(478\) | −1.53019e28 | −1.12396 | ||||||||
\(479\) | 6.95253e27 | 0.499597 | 0.249798 | − | 0.968298i | \(-0.419636\pi\) | ||||
0.249798 | + | 0.968298i | \(0.419636\pi\) | |||||||
\(480\) | −1.24449e28 | −0.874900 | ||||||||
\(481\) | −4.51095e26 | −0.0310274 | ||||||||
\(482\) | 1.29070e28 | 0.868625 | ||||||||
\(483\) | 7.41382e27 | 0.488199 | ||||||||
\(484\) | −2.92405e27 | −0.188412 | ||||||||
\(485\) | −2.37376e27 | −0.149675 | ||||||||
\(486\) | −1.24053e27 | −0.0765466 | ||||||||
\(487\) | −1.06412e28 | −0.642596 | −0.321298 | − | 0.946978i | \(-0.604119\pi\) | ||||
−0.321298 | + | 0.946978i | \(0.604119\pi\) | |||||||
\(488\) | −9.00250e27 | −0.532053 | ||||||||
\(489\) | 2.85504e27 | 0.165146 | ||||||||
\(490\) | 1.92706e28 | 1.09103 | ||||||||
\(491\) | 1.68064e28 | 0.931361 | 0.465681 | − | 0.884953i | \(-0.345810\pi\) | ||||
0.465681 | + | 0.884953i | \(0.345810\pi\) | |||||||
\(492\) | 1.14639e27 | 0.0621869 | ||||||||
\(493\) | −1.66865e28 | −0.886079 | ||||||||
\(494\) | −3.05372e27 | −0.158743 | ||||||||
\(495\) | 9.28011e27 | 0.472279 | ||||||||
\(496\) | 3.75885e28 | 1.87283 | ||||||||
\(497\) | −1.09772e28 | −0.535486 | ||||||||
\(498\) | −4.03083e27 | −0.192525 | ||||||||
\(499\) | −5.12285e27 | −0.239583 | −0.119792 | − | 0.992799i | \(-0.538223\pi\) | ||||
−0.119792 | + | 0.992799i | \(0.538223\pi\) | |||||||
\(500\) | −2.83979e28 | −1.30047 | ||||||||
\(501\) | −2.82686e25 | −0.00126768 | ||||||||
\(502\) | 1.63551e27 | 0.0718229 | ||||||||
\(503\) | 1.99606e28 | 0.858442 | 0.429221 | − | 0.903200i | \(-0.358788\pi\) | ||||
0.429221 | + | 0.903200i | \(0.358788\pi\) | |||||||
\(504\) | −3.91994e27 | −0.165105 | ||||||||
\(505\) | −1.79508e28 | −0.740499 | ||||||||
\(506\) | 2.58339e28 | 1.04378 | ||||||||
\(507\) | 1.35759e28 | 0.537260 | ||||||||
\(508\) | 1.21895e27 | 0.0472516 | ||||||||
\(509\) | −2.57966e27 | −0.0979550 | −0.0489775 | − | 0.998800i | \(-0.515596\pi\) | ||||
−0.0489775 | + | 0.998800i | \(0.515596\pi\) | |||||||
\(510\) | 3.49118e28 | 1.29863 | ||||||||
\(511\) | 8.94749e27 | 0.326048 | ||||||||
\(512\) | 3.81989e27 | 0.136369 | ||||||||
\(513\) | −2.77790e27 | −0.0971594 | ||||||||
\(514\) | −3.31474e28 | −1.13589 | ||||||||
\(515\) | −7.64346e28 | −2.56634 | ||||||||
\(516\) | 3.76802e27 | 0.123963 | ||||||||
\(517\) | −1.81789e28 | −0.586026 | ||||||||
\(518\) | 3.20432e27 | 0.101222 | ||||||||
\(519\) | 9.55436e27 | 0.295763 | ||||||||
\(520\) | −1.13531e28 | −0.344412 | ||||||||
\(521\) | −2.61230e28 | −0.776652 | −0.388326 | − | 0.921522i | \(-0.626947\pi\) | ||||
−0.388326 | + | 0.921522i | \(0.626947\pi\) | |||||||
\(522\) | −1.21983e28 | −0.355435 | ||||||||
\(523\) | 6.70750e28 | 1.91555 | 0.957774 | − | 0.287523i | \(-0.0928317\pi\) | ||||
0.957774 | + | 0.287523i | \(0.0928317\pi\) | |||||||
\(524\) | −2.18009e28 | −0.610233 | ||||||||
\(525\) | −3.96300e28 | −1.08731 | ||||||||
\(526\) | 1.53520e27 | 0.0412873 | ||||||||
\(527\) | −5.66161e28 | −1.49255 | ||||||||
\(528\) | −2.07161e28 | −0.535367 | ||||||||
\(529\) | 1.49036e28 | 0.377577 | ||||||||
\(530\) | 1.55827e29 | 3.87031 | ||||||||
\(531\) | 5.35163e27 | 0.130315 | ||||||||
\(532\) | 6.45696e27 | 0.154155 | ||||||||
\(533\) | 2.86092e27 | 0.0669684 | ||||||||
\(534\) | −4.24592e27 | −0.0974514 | ||||||||
\(535\) | 1.01210e29 | 2.27777 | ||||||||
\(536\) | −1.93011e28 | −0.425943 | ||||||||
\(537\) | 5.17492e27 | 0.111988 | ||||||||
\(538\) | −3.69528e28 | −0.784212 | ||||||||
\(539\) | 1.72233e28 | 0.358454 | ||||||||
\(540\) | 7.59695e27 | 0.155062 | ||||||||
\(541\) | −2.15196e28 | −0.430787 | −0.215394 | − | 0.976527i | \(-0.569103\pi\) | ||||
−0.215394 | + | 0.976527i | \(0.569103\pi\) | |||||||
\(542\) | −2.70319e28 | −0.530743 | ||||||||
\(543\) | −5.53067e27 | −0.106507 | ||||||||
\(544\) | −4.18438e28 | −0.790392 | ||||||||
\(545\) | 1.71728e29 | 3.18185 | ||||||||
\(546\) | 7.19599e27 | 0.130788 | ||||||||
\(547\) | −7.46789e28 | −1.33147 | −0.665734 | − | 0.746189i | \(-0.731882\pi\) | ||||
−0.665734 | + | 0.746189i | \(0.731882\pi\) | |||||||
\(548\) | 9.14032e27 | 0.159870 | ||||||||
\(549\) | 1.50336e28 | 0.257960 | ||||||||
\(550\) | −1.38093e29 | −2.32469 | ||||||||
\(551\) | −2.73156e28 | −0.451148 | ||||||||
\(552\) | −2.87500e28 | −0.465884 | ||||||||
\(553\) | 3.65811e28 | 0.581625 | ||||||||
\(554\) | −1.39099e29 | −2.17006 | ||||||||
\(555\) | 8.44223e27 | 0.129235 | ||||||||
\(556\) | 7.73899e27 | 0.116252 | ||||||||
\(557\) | −7.95166e28 | −1.17214 | −0.586068 | − | 0.810262i | \(-0.699325\pi\) | ||||
−0.586068 | + | 0.810262i | \(0.699325\pi\) | |||||||
\(558\) | −4.13880e28 | −0.598709 | ||||||||
\(559\) | 9.40343e27 | 0.133494 | ||||||||
\(560\) | 1.22309e29 | 1.70406 | ||||||||
\(561\) | 3.12028e28 | 0.426661 | ||||||||
\(562\) | 1.43972e29 | 1.93217 | ||||||||
\(563\) | 5.46305e28 | 0.719609 | 0.359805 | − | 0.933028i | \(-0.382843\pi\) | ||||
0.359805 | + | 0.933028i | \(0.382843\pi\) | |||||||
\(564\) | −1.48817e28 | −0.192408 | ||||||||
\(565\) | −1.44427e29 | −1.83290 | ||||||||
\(566\) | −7.70912e27 | −0.0960356 | ||||||||
\(567\) | 6.54605e27 | 0.0800492 | ||||||||
\(568\) | 4.25683e28 | 0.511010 | ||||||||
\(569\) | 9.43478e28 | 1.11187 | 0.555933 | − | 0.831227i | \(-0.312361\pi\) | ||||
0.555933 | + | 0.831227i | \(0.312361\pi\) | |||||||
\(570\) | 5.71502e28 | 0.661198 | ||||||||
\(571\) | 8.05027e28 | 0.914390 | 0.457195 | − | 0.889367i | \(-0.348854\pi\) | ||||
0.457195 | + | 0.889367i | \(0.348854\pi\) | |||||||
\(572\) | 7.46400e27 | 0.0832364 | ||||||||
\(573\) | −7.13655e28 | −0.781384 | ||||||||
\(574\) | −2.03223e28 | −0.218473 | ||||||||
\(575\) | −2.90659e29 | −3.06811 | ||||||||
\(576\) | 9.42426e27 | 0.0976812 | ||||||||
\(577\) | −1.67132e28 | −0.170104 | −0.0850519 | − | 0.996377i | \(-0.527106\pi\) | ||||
−0.0850519 | + | 0.996377i | \(0.527106\pi\) | |||||||
\(578\) | −2.00600e27 | −0.0200488 | ||||||||
\(579\) | 1.05592e29 | 1.03635 | ||||||||
\(580\) | 7.47020e28 | 0.720010 | ||||||||
\(581\) | 2.12700e28 | 0.201334 | ||||||||
\(582\) | −5.83461e27 | −0.0542401 | ||||||||
\(583\) | 1.39272e29 | 1.27158 | ||||||||
\(584\) | −3.46975e28 | −0.311145 | ||||||||
\(585\) | 1.89589e28 | 0.166984 | ||||||||
\(586\) | 1.67120e29 | 1.44578 | ||||||||
\(587\) | 3.15730e28 | 0.268297 | 0.134149 | − | 0.990961i | \(-0.457170\pi\) | ||||
0.134149 | + | 0.990961i | \(0.457170\pi\) | |||||||
\(588\) | 1.40994e28 | 0.117690 | ||||||||
\(589\) | −9.26799e28 | −0.759932 | ||||||||
\(590\) | −1.10100e29 | −0.886829 | ||||||||
\(591\) | −1.12762e29 | −0.892264 | ||||||||
\(592\) | −1.88457e28 | −0.146499 | ||||||||
\(593\) | −5.48493e27 | −0.0418887 | −0.0209443 | − | 0.999781i | \(-0.506667\pi\) | ||||
−0.0209443 | + | 0.999781i | \(0.506667\pi\) | |||||||
\(594\) | 2.28101e28 | 0.171147 | ||||||||
\(595\) | −1.84223e29 | −1.35805 | ||||||||
\(596\) | −8.03502e28 | −0.581971 | ||||||||
\(597\) | −8.51805e28 | −0.606191 | ||||||||
\(598\) | 5.27776e28 | 0.369051 | ||||||||
\(599\) | 1.25621e29 | 0.863136 | 0.431568 | − | 0.902080i | \(-0.357960\pi\) | ||||
0.431568 | + | 0.902080i | \(0.357960\pi\) | |||||||
\(600\) | 1.53681e29 | 1.03761 | ||||||||
\(601\) | 3.99325e28 | 0.264938 | 0.132469 | − | 0.991187i | \(-0.457709\pi\) | ||||
0.132469 | + | 0.991187i | \(0.457709\pi\) | |||||||
\(602\) | −6.67965e28 | −0.435503 | ||||||||
\(603\) | 3.22315e28 | 0.206514 | ||||||||
\(604\) | −4.22378e28 | −0.265958 | ||||||||
\(605\) | 1.36567e29 | 0.845115 | ||||||||
\(606\) | −4.41223e28 | −0.268347 | ||||||||
\(607\) | −2.46990e29 | −1.47638 | −0.738189 | − | 0.674594i | \(-0.764319\pi\) | ||||
−0.738189 | + | 0.674594i | \(0.764319\pi\) | |||||||
\(608\) | −6.84978e28 | −0.402429 | ||||||||
\(609\) | 6.43684e28 | 0.371699 | ||||||||
\(610\) | −3.09288e29 | −1.75549 | ||||||||
\(611\) | −3.71387e28 | −0.207202 | ||||||||
\(612\) | 2.55434e28 | 0.140084 | ||||||||
\(613\) | 2.63911e28 | 0.142273 | 0.0711364 | − | 0.997467i | \(-0.477337\pi\) | ||||
0.0711364 | + | 0.997467i | \(0.477337\pi\) | |||||||
\(614\) | 2.90585e29 | 1.53995 | ||||||||
\(615\) | −5.35420e28 | −0.278937 | ||||||||
\(616\) | 7.20777e28 | 0.369151 | ||||||||
\(617\) | 3.09820e29 | 1.55997 | 0.779984 | − | 0.625800i | \(-0.215227\pi\) | ||||
0.779984 | + | 0.625800i | \(0.215227\pi\) | |||||||
\(618\) | −1.87873e29 | −0.930005 | ||||||||
\(619\) | −2.50758e29 | −1.22040 | −0.610202 | − | 0.792246i | \(-0.708912\pi\) | ||||
−0.610202 | + | 0.792246i | \(0.708912\pi\) | |||||||
\(620\) | 2.53459e29 | 1.21281 | ||||||||
\(621\) | 4.80107e28 | 0.225879 | ||||||||
\(622\) | 3.98080e29 | 1.84150 | ||||||||
\(623\) | 2.24050e28 | 0.101911 | ||||||||
\(624\) | −4.23221e28 | −0.189291 | ||||||||
\(625\) | 7.31956e29 | 3.21918 | ||||||||
\(626\) | −4.83249e29 | −2.08997 | ||||||||
\(627\) | 5.10785e28 | 0.217235 | ||||||||
\(628\) | −1.34125e29 | −0.560963 | ||||||||
\(629\) | 2.83855e28 | 0.116752 | ||||||||
\(630\) | −1.34673e29 | −0.544758 | ||||||||
\(631\) | −4.32770e28 | −0.172167 | −0.0860833 | − | 0.996288i | \(-0.527435\pi\) | ||||
−0.0860833 | + | 0.996288i | \(0.527435\pi\) | |||||||
\(632\) | −1.41858e29 | −0.555039 | ||||||||
\(633\) | −2.35516e29 | −0.906318 | ||||||||
\(634\) | 5.15809e28 | 0.195232 | ||||||||
\(635\) | −5.69309e28 | −0.211945 | ||||||||
\(636\) | 1.14012e29 | 0.417493 | ||||||||
\(637\) | 3.51864e28 | 0.126739 | ||||||||
\(638\) | 2.24296e29 | 0.794702 | ||||||||
\(639\) | −7.10863e28 | −0.247758 | ||||||||
\(640\) | −6.35872e29 | −2.18012 | ||||||||
\(641\) | −8.73381e28 | −0.294574 | −0.147287 | − | 0.989094i | \(-0.547054\pi\) | ||||
−0.147287 | + | 0.989094i | \(0.547054\pi\) | |||||||
\(642\) | 2.48770e29 | 0.825431 | ||||||||
\(643\) | −4.72013e29 | −1.54077 | −0.770386 | − | 0.637578i | \(-0.779937\pi\) | ||||
−0.770386 | + | 0.637578i | \(0.779937\pi\) | |||||||
\(644\) | −1.11596e29 | −0.358383 | ||||||||
\(645\) | −1.75985e29 | −0.556030 | ||||||||
\(646\) | 1.92158e29 | 0.597332 | ||||||||
\(647\) | 1.26799e28 | 0.0387812 | 0.0193906 | − | 0.999812i | \(-0.493827\pi\) | ||||
0.0193906 | + | 0.999812i | \(0.493827\pi\) | |||||||
\(648\) | −2.53849e28 | −0.0763903 | ||||||||
\(649\) | −9.84027e28 | −0.291365 | ||||||||
\(650\) | −2.82119e29 | −0.821943 | ||||||||
\(651\) | 2.18397e29 | 0.626105 | ||||||||
\(652\) | −4.29753e28 | −0.121233 | ||||||||
\(653\) | −2.76226e29 | −0.766790 | −0.383395 | − | 0.923584i | \(-0.625245\pi\) | ||||
−0.383395 | + | 0.923584i | \(0.625245\pi\) | |||||||
\(654\) | 4.22102e29 | 1.15306 | ||||||||
\(655\) | 1.01821e30 | 2.73718 | ||||||||
\(656\) | 1.19523e29 | 0.316198 | ||||||||
\(657\) | 5.79425e28 | 0.150855 | ||||||||
\(658\) | 2.63812e29 | 0.675962 | ||||||||
\(659\) | 6.46511e28 | 0.163034 | 0.0815172 | − | 0.996672i | \(-0.474023\pi\) | ||||
0.0815172 | + | 0.996672i | \(0.474023\pi\) | |||||||
\(660\) | −1.39688e29 | −0.346696 | ||||||||
\(661\) | −2.27730e29 | −0.556295 | −0.278147 | − | 0.960538i | \(-0.589720\pi\) | ||||
−0.278147 | + | 0.960538i | \(0.589720\pi\) | |||||||
\(662\) | 4.41667e29 | 1.06191 | ||||||||
\(663\) | 6.37459e28 | 0.150855 | ||||||||
\(664\) | −8.24829e28 | −0.192132 | ||||||||
\(665\) | −3.01572e29 | −0.691454 | ||||||||
\(666\) | 2.07507e28 | 0.0468330 | ||||||||
\(667\) | 4.72097e29 | 1.04884 | ||||||||
\(668\) | 4.25512e26 | 0.000930591 0 | ||||||||
\(669\) | 2.73375e29 | 0.588551 | ||||||||
\(670\) | −6.63103e29 | −1.40539 | ||||||||
\(671\) | −2.76429e29 | −0.576763 | ||||||||
\(672\) | 1.61413e29 | 0.331559 | ||||||||
\(673\) | −3.79243e29 | −0.766936 | −0.383468 | − | 0.923554i | \(-0.625270\pi\) | ||||
−0.383468 | + | 0.923554i | \(0.625270\pi\) | |||||||
\(674\) | −8.50057e28 | −0.169246 | ||||||||
\(675\) | −2.56638e29 | −0.503073 | ||||||||
\(676\) | −2.04350e29 | −0.394398 | ||||||||
\(677\) | −3.39717e29 | −0.645559 | −0.322780 | − | 0.946474i | \(-0.604617\pi\) | ||||
−0.322780 | + | 0.946474i | \(0.604617\pi\) | |||||||
\(678\) | −3.54995e29 | −0.664218 | ||||||||
\(679\) | 3.07882e28 | 0.0567220 | ||||||||
\(680\) | 7.14400e29 | 1.29598 | ||||||||
\(681\) | 2.02544e29 | 0.361805 | ||||||||
\(682\) | 7.61020e29 | 1.33863 | ||||||||
\(683\) | 4.54742e29 | 0.787677 | 0.393838 | − | 0.919180i | \(-0.371147\pi\) | ||||
0.393838 | + | 0.919180i | \(0.371147\pi\) | |||||||
\(684\) | 4.18143e28 | 0.0713239 | ||||||||
\(685\) | −4.26897e29 | −0.717088 | ||||||||
\(686\) | −7.69619e29 | −1.27313 | ||||||||
\(687\) | −4.79355e28 | −0.0780929 | ||||||||
\(688\) | 3.92853e29 | 0.630306 | ||||||||
\(689\) | 2.84526e29 | 0.449594 | ||||||||
\(690\) | −9.87730e29 | −1.53717 | ||||||||
\(691\) | −3.71838e29 | −0.569947 | −0.284974 | − | 0.958535i | \(-0.591985\pi\) | ||||
−0.284974 | + | 0.958535i | \(0.591985\pi\) | |||||||
\(692\) | −1.43817e29 | −0.217118 | ||||||||
\(693\) | −1.20365e29 | −0.178979 | ||||||||
\(694\) | 5.15178e29 | 0.754542 | ||||||||
\(695\) | −3.61448e29 | −0.521442 | ||||||||
\(696\) | −2.49614e29 | −0.354709 | ||||||||
\(697\) | −1.80026e29 | −0.251994 | ||||||||
\(698\) | 1.33546e30 | 1.84140 | ||||||||
\(699\) | −4.85494e28 | −0.0659437 | ||||||||
\(700\) | 5.96529e29 | 0.798183 | ||||||||
\(701\) | −9.37969e29 | −1.23637 | −0.618186 | − | 0.786032i | \(-0.712132\pi\) | ||||
−0.618186 | + | 0.786032i | \(0.712132\pi\) | |||||||
\(702\) | 4.66001e28 | 0.0605128 | ||||||||
\(703\) | 4.64668e28 | 0.0594445 | ||||||||
\(704\) | −1.73288e29 | −0.218401 | ||||||||
\(705\) | 6.95050e29 | 0.863038 | ||||||||
\(706\) | −1.26275e30 | −1.54478 | ||||||||
\(707\) | 2.32826e29 | 0.280626 | ||||||||
\(708\) | −8.05551e28 | −0.0956629 | ||||||||
\(709\) | −7.54578e29 | −0.882914 | −0.441457 | − | 0.897282i | \(-0.645538\pi\) | ||||
−0.441457 | + | 0.897282i | \(0.645538\pi\) | |||||||
\(710\) | 1.46247e30 | 1.68606 | ||||||||
\(711\) | 2.36893e29 | 0.269105 | ||||||||
\(712\) | −8.68842e28 | −0.0972525 | ||||||||
\(713\) | 1.60179e30 | 1.76671 | ||||||||
\(714\) | −4.52814e29 | −0.492140 | ||||||||
\(715\) | −3.48605e29 | −0.373353 | ||||||||
\(716\) | −7.78952e28 | −0.0822098 | ||||||||
\(717\) | 5.22894e29 | 0.543829 | ||||||||
\(718\) | −2.74641e28 | −0.0281488 | ||||||||
\(719\) | 1.22754e30 | 1.23989 | 0.619944 | − | 0.784646i | \(-0.287155\pi\) | ||||
0.619944 | + | 0.784646i | \(0.287155\pi\) | |||||||
\(720\) | 7.92056e29 | 0.788433 | ||||||||
\(721\) | 9.91374e29 | 0.972561 | ||||||||
\(722\) | −9.19594e29 | −0.889111 | ||||||||
\(723\) | −4.41057e29 | −0.420284 | ||||||||
\(724\) | 8.32502e28 | 0.0781862 | ||||||||
\(725\) | −2.52356e30 | −2.33596 | ||||||||
\(726\) | 3.35677e29 | 0.306258 | ||||||||
\(727\) | 9.04407e29 | 0.813303 | 0.406652 | − | 0.913583i | \(-0.366696\pi\) | ||||
0.406652 | + | 0.913583i | \(0.366696\pi\) | |||||||
\(728\) | 1.47252e29 | 0.130521 | ||||||||
\(729\) | 4.23912e28 | 0.0370370 | ||||||||
\(730\) | −1.19206e30 | −1.02662 | ||||||||
\(731\) | −5.91719e29 | −0.502323 | ||||||||
\(732\) | −2.26292e29 | −0.189367 | ||||||||
\(733\) | −1.38874e30 | −1.14559 | −0.572795 | − | 0.819699i | \(-0.694141\pi\) | ||||
−0.572795 | + | 0.819699i | \(0.694141\pi\) | |||||||
\(734\) | −2.43189e30 | −1.97759 | ||||||||
\(735\) | −6.58512e29 | −0.527894 | ||||||||
\(736\) | 1.18385e30 | 0.935578 | ||||||||
\(737\) | −5.92655e29 | −0.461736 | ||||||||
\(738\) | −1.31604e29 | −0.101083 | ||||||||
\(739\) | 2.11506e30 | 1.60161 | 0.800804 | − | 0.598927i | \(-0.204406\pi\) | ||||
0.800804 | + | 0.598927i | \(0.204406\pi\) | |||||||
\(740\) | −1.27076e29 | −0.0948705 | ||||||||
\(741\) | 1.04351e29 | 0.0768080 | ||||||||
\(742\) | −2.02111e30 | −1.46673 | ||||||||
\(743\) | 2.26805e30 | 1.62282 | 0.811411 | − | 0.584476i | \(-0.198700\pi\) | ||||
0.811411 | + | 0.584476i | \(0.198700\pi\) | |||||||
\(744\) | −8.46923e29 | −0.597487 | ||||||||
\(745\) | 3.75274e30 | 2.61040 | ||||||||
\(746\) | −1.60717e30 | −1.10231 | ||||||||
\(747\) | 1.37741e29 | 0.0931530 | ||||||||
\(748\) | −4.69678e29 | −0.313208 | ||||||||
\(749\) | −1.31272e30 | −0.863202 | ||||||||
\(750\) | 3.26004e30 | 2.11388 | ||||||||
\(751\) | −6.98349e29 | −0.446533 | −0.223266 | − | 0.974757i | \(-0.571672\pi\) | ||||
−0.223266 | + | 0.974757i | \(0.571672\pi\) | |||||||
\(752\) | −1.55157e30 | −0.978326 | ||||||||
\(753\) | −5.58883e28 | −0.0347515 | ||||||||
\(754\) | 4.58226e29 | 0.280984 | ||||||||
\(755\) | 1.97271e30 | 1.19294 | ||||||||
\(756\) | −9.85341e28 | −0.0587635 | ||||||||
\(757\) | −3.79778e29 | −0.223369 | −0.111685 | − | 0.993744i | \(-0.535625\pi\) | ||||
−0.111685 | + | 0.993744i | \(0.535625\pi\) | |||||||
\(758\) | 3.77639e30 | 2.19054 | ||||||||
\(759\) | −8.82794e29 | −0.505034 | ||||||||
\(760\) | 1.16946e30 | 0.659849 | ||||||||
\(761\) | −7.50371e29 | −0.417577 | −0.208789 | − | 0.977961i | \(-0.566952\pi\) | ||||
−0.208789 | + | 0.977961i | \(0.566952\pi\) | |||||||
\(762\) | −1.39934e29 | −0.0768060 | ||||||||
\(763\) | −2.22736e30 | −1.20582 | ||||||||
\(764\) | 1.07423e30 | 0.573608 | ||||||||
\(765\) | −1.19300e30 | −0.628342 | ||||||||
\(766\) | 3.63479e30 | 1.88833 | ||||||||
\(767\) | −2.01032e29 | −0.103018 | ||||||||
\(768\) | −1.22824e30 | −0.620856 | ||||||||
\(769\) | 2.16884e29 | 0.108144 | 0.0540719 | − | 0.998537i | \(-0.482780\pi\) | ||||
0.0540719 | + | 0.998537i | \(0.482780\pi\) | |||||||
\(770\) | 2.47629e30 | 1.21800 | ||||||||
\(771\) | 1.13271e30 | 0.549600 | ||||||||
\(772\) | −1.58943e30 | −0.760779 | ||||||||
\(773\) | −3.08128e30 | −1.45495 | −0.727473 | − | 0.686136i | \(-0.759305\pi\) | ||||
−0.727473 | + | 0.686136i | \(0.759305\pi\) | |||||||
\(774\) | −4.32563e29 | −0.201498 | ||||||||
\(775\) | −8.56227e30 | −3.93478 | ||||||||
\(776\) | −1.19394e29 | −0.0541294 | ||||||||
\(777\) | −1.09498e29 | −0.0489761 | ||||||||
\(778\) | −5.14625e29 | −0.227094 | ||||||||
\(779\) | −2.94700e29 | −0.128303 | ||||||||
\(780\) | −2.85377e29 | −0.122582 | ||||||||
\(781\) | 1.30710e30 | 0.553951 | ||||||||
\(782\) | −3.32107e30 | −1.38870 | ||||||||
\(783\) | 4.16839e29 | 0.171977 | ||||||||
\(784\) | 1.47000e30 | 0.598412 | ||||||||
\(785\) | 6.26430e30 | 2.51618 | ||||||||
\(786\) | 2.50271e30 | 0.991915 | ||||||||
\(787\) | 1.46460e30 | 0.572775 | 0.286387 | − | 0.958114i | \(-0.407546\pi\) | ||||
0.286387 | + | 0.958114i | \(0.407546\pi\) | |||||||
\(788\) | 1.69734e30 | 0.655004 | ||||||||
\(789\) | −5.24608e28 | −0.0199768 | ||||||||
\(790\) | −4.87363e30 | −1.83134 | ||||||||
\(791\) | 1.87325e30 | 0.694612 | ||||||||
\(792\) | 4.66764e29 | 0.170798 | ||||||||
\(793\) | −5.64732e29 | −0.203927 | ||||||||
\(794\) | 1.09988e30 | 0.391949 | ||||||||
\(795\) | −5.32490e30 | −1.87265 | ||||||||
\(796\) | 1.28217e30 | 0.445000 | ||||||||
\(797\) | 1.27731e30 | 0.437505 | 0.218752 | − | 0.975780i | \(-0.429801\pi\) | ||||
0.218752 | + | 0.975780i | \(0.429801\pi\) | |||||||
\(798\) | −7.41250e29 | −0.250573 | ||||||||
\(799\) | 2.33698e30 | 0.779677 | ||||||||
\(800\) | −6.32819e30 | −2.08370 | ||||||||
\(801\) | 1.45091e29 | 0.0471519 | ||||||||
\(802\) | 4.21439e30 | 1.35177 | ||||||||
\(803\) | −1.06541e30 | −0.337292 | ||||||||
\(804\) | −4.85163e29 | −0.151600 | ||||||||
\(805\) | 5.21208e30 | 1.60751 | ||||||||
\(806\) | 1.55473e30 | 0.473301 | ||||||||
\(807\) | 1.26275e30 | 0.379441 | ||||||||
\(808\) | −9.02876e29 | −0.267799 | ||||||||
\(809\) | −4.24975e30 | −1.24424 | −0.622120 | − | 0.782922i | \(-0.713728\pi\) | ||||
−0.622120 | + | 0.782922i | \(0.713728\pi\) | |||||||
\(810\) | −8.72119e29 | −0.252048 | ||||||||
\(811\) | 2.05863e30 | 0.587298 | 0.293649 | − | 0.955913i | \(-0.405130\pi\) | ||||
0.293649 | + | 0.955913i | \(0.405130\pi\) | |||||||
\(812\) | −9.68902e29 | −0.272861 | ||||||||
\(813\) | 9.23732e29 | 0.256800 | ||||||||
\(814\) | −3.81551e29 | −0.104712 | ||||||||
\(815\) | 2.00716e30 | 0.543784 | ||||||||
\(816\) | 2.66315e30 | 0.712278 | ||||||||
\(817\) | −9.68636e29 | −0.255758 | ||||||||
\(818\) | 9.46999e29 | 0.246854 | ||||||||
\(819\) | −2.45901e29 | −0.0632818 | ||||||||
\(820\) | 8.05938e29 | 0.204765 | ||||||||
\(821\) | −1.80717e29 | −0.0453309 | −0.0226655 | − | 0.999743i | \(-0.507215\pi\) | ||||
−0.0226655 | + | 0.999743i | \(0.507215\pi\) | |||||||
\(822\) | −1.04930e30 | −0.259863 | ||||||||
\(823\) | −6.23532e30 | −1.52462 | −0.762308 | − | 0.647214i | \(-0.775934\pi\) | ||||
−0.762308 | + | 0.647214i | \(0.775934\pi\) | |||||||
\(824\) | −3.84445e30 | −0.928107 | ||||||||
\(825\) | 4.71891e30 | 1.12480 | ||||||||
\(826\) | 1.42802e30 | 0.336080 | ||||||||
\(827\) | 3.37179e30 | 0.783524 | 0.391762 | − | 0.920067i | \(-0.371866\pi\) | ||||
0.391762 | + | 0.920067i | \(0.371866\pi\) | |||||||
\(828\) | −7.22678e29 | −0.165816 | ||||||||
\(829\) | −2.70711e29 | −0.0613315 | −0.0306658 | − | 0.999530i | \(-0.509763\pi\) | ||||
−0.0306658 | + | 0.999530i | \(0.509763\pi\) | |||||||
\(830\) | −2.83376e30 | −0.633933 | ||||||||
\(831\) | 4.75328e30 | 1.04998 | ||||||||
\(832\) | −3.54020e29 | −0.0772205 | ||||||||
\(833\) | −2.21413e30 | −0.476904 | ||||||||
\(834\) | −8.88425e29 | −0.188963 | ||||||||
\(835\) | −1.98735e28 | −0.00417413 | ||||||||
\(836\) | −7.68857e29 | −0.159470 | ||||||||
\(837\) | 1.41431e30 | 0.289685 | ||||||||
\(838\) | −1.05105e31 | −2.12599 | ||||||||
\(839\) | −7.45457e30 | −1.48909 | −0.744547 | − | 0.667570i | \(-0.767334\pi\) | ||||
−0.744547 | + | 0.667570i | \(0.767334\pi\) | |||||||
\(840\) | −2.75581e30 | −0.543646 | ||||||||
\(841\) | −1.03399e30 | −0.201446 | ||||||||
\(842\) | −7.01551e30 | −1.34984 | ||||||||
\(843\) | −4.91979e30 | −0.934882 | ||||||||
\(844\) | 3.54509e30 | 0.665321 | ||||||||
\(845\) | 9.54415e30 | 1.76906 | ||||||||
\(846\) | 1.70840e30 | 0.312753 | ||||||||
\(847\) | −1.77131e30 | −0.320272 | ||||||||
\(848\) | 1.18868e31 | 2.12280 | ||||||||
\(849\) | 2.63435e29 | 0.0464668 | ||||||||
\(850\) | 1.77526e31 | 3.09287 | ||||||||
\(851\) | −8.03088e29 | −0.138198 | ||||||||
\(852\) | 1.07002e30 | 0.181877 | ||||||||
\(853\) | −6.10653e30 | −1.02525 | −0.512625 | − | 0.858613i | \(-0.671327\pi\) | ||||
−0.512625 | + | 0.858613i | \(0.671327\pi\) | |||||||
\(854\) | 4.01153e30 | 0.665277 | ||||||||
\(855\) | −1.95293e30 | −0.319921 | ||||||||
\(856\) | 5.09059e30 | 0.823746 | ||||||||
\(857\) | −4.08307e30 | −0.652662 | −0.326331 | − | 0.945256i | \(-0.605812\pi\) | ||||
−0.326331 | + | 0.945256i | \(0.605812\pi\) | |||||||
\(858\) | −8.56856e29 | −0.135298 | ||||||||
\(859\) | 5.27189e30 | 0.822316 | 0.411158 | − | 0.911564i | \(-0.365125\pi\) | ||||
0.411158 | + | 0.911564i | \(0.365125\pi\) | |||||||
\(860\) | 2.64900e30 | 0.408177 | ||||||||
\(861\) | 6.94452e29 | 0.105708 | ||||||||
\(862\) | −1.36031e31 | −2.04555 | ||||||||
\(863\) | 1.05537e31 | 1.56780 | 0.783902 | − | 0.620884i | \(-0.213226\pi\) | ||||
0.783902 | + | 0.620884i | \(0.213226\pi\) | |||||||
\(864\) | 1.04528e30 | 0.153405 | ||||||||
\(865\) | 6.71693e30 | 0.973872 | ||||||||
\(866\) | −3.00300e30 | −0.430147 | ||||||||
\(867\) | 6.85488e28 | 0.00970062 | ||||||||
\(868\) | −3.28742e30 | −0.459619 | ||||||||
\(869\) | −4.35586e30 | −0.601681 | ||||||||
\(870\) | −8.57569e30 | −1.17035 | ||||||||
\(871\) | −1.21077e30 | −0.163256 | ||||||||
\(872\) | 8.63747e30 | 1.15070 | ||||||||
\(873\) | 1.99379e29 | 0.0262441 | ||||||||
\(874\) | −5.43655e30 | −0.707056 | ||||||||
\(875\) | −1.72027e31 | −2.21061 | ||||||||
\(876\) | −8.72177e29 | −0.110742 | ||||||||
\(877\) | 7.16069e30 | 0.898378 | 0.449189 | − | 0.893437i | \(-0.351713\pi\) | ||||
0.449189 | + | 0.893437i | \(0.351713\pi\) | |||||||
\(878\) | 1.44706e31 | 1.79388 | ||||||||
\(879\) | −5.71079e30 | −0.699541 | ||||||||
\(880\) | −1.45639e31 | −1.76283 | ||||||||
\(881\) | −1.05943e31 | −1.26714 | −0.633568 | − | 0.773687i | \(-0.718410\pi\) | ||||
−0.633568 | + | 0.773687i | \(0.718410\pi\) | |||||||
\(882\) | −1.61860e30 | −0.191301 | ||||||||
\(883\) | 6.60744e30 | 0.771695 | 0.385848 | − | 0.922562i | \(-0.373909\pi\) | ||||
0.385848 | + | 0.922562i | \(0.373909\pi\) | |||||||
\(884\) | −9.59531e29 | −0.110742 | ||||||||
\(885\) | 3.76231e30 | 0.429092 | ||||||||
\(886\) | −5.70734e28 | −0.00643250 | ||||||||
\(887\) | −2.74467e30 | −0.305698 | −0.152849 | − | 0.988250i | \(-0.548845\pi\) | ||||
−0.152849 | + | 0.988250i | \(0.548845\pi\) | |||||||
\(888\) | 4.24621e29 | 0.0467374 | ||||||||
\(889\) | 7.38406e29 | 0.0803205 | ||||||||
\(890\) | −2.98497e30 | −0.320882 | ||||||||
\(891\) | −7.79465e29 | −0.0828096 | ||||||||
\(892\) | −4.11496e30 | −0.432051 | ||||||||
\(893\) | 3.82561e30 | 0.396973 | ||||||||
\(894\) | 9.22409e30 | 0.945974 | ||||||||
\(895\) | 3.63808e30 | 0.368749 | ||||||||
\(896\) | 8.24741e30 | 0.826196 | ||||||||
\(897\) | −1.80351e30 | −0.178565 | ||||||||
\(898\) | 9.01519e30 | 0.882213 | ||||||||
\(899\) | 1.39071e31 | 1.34512 | ||||||||
\(900\) | 3.86303e30 | 0.369302 | ||||||||
\(901\) | −1.79040e31 | −1.69177 | ||||||||
\(902\) | 2.41986e30 | 0.226007 | ||||||||
\(903\) | 2.28256e30 | 0.210718 | ||||||||
\(904\) | −7.26427e30 | −0.662863 | ||||||||
\(905\) | −3.88819e30 | −0.350701 | ||||||||
\(906\) | 4.84884e30 | 0.432307 | ||||||||
\(907\) | 5.45568e30 | 0.480809 | 0.240404 | − | 0.970673i | \(-0.422720\pi\) | ||||
0.240404 | + | 0.970673i | \(0.422720\pi\) | |||||||
\(908\) | −3.04878e30 | −0.265598 | ||||||||
\(909\) | 1.50774e30 | 0.129839 | ||||||||
\(910\) | 5.05894e30 | 0.430651 | ||||||||
\(911\) | −8.75739e30 | −0.736940 | −0.368470 | − | 0.929640i | \(-0.620118\pi\) | ||||
−0.368470 | + | 0.929640i | \(0.620118\pi\) | |||||||
\(912\) | 4.35955e30 | 0.362657 | ||||||||
\(913\) | −2.53270e30 | −0.208277 | ||||||||
\(914\) | 3.71884e29 | 0.0302324 | ||||||||
\(915\) | 1.05689e31 | 0.849396 | ||||||||
\(916\) | 7.21547e29 | 0.0573274 | ||||||||
\(917\) | −1.32064e31 | −1.03730 | ||||||||
\(918\) | −2.93235e30 | −0.227702 | ||||||||
\(919\) | 1.24295e31 | 0.954206 | 0.477103 | − | 0.878847i | \(-0.341687\pi\) | ||||
0.477103 | + | 0.878847i | \(0.341687\pi\) | |||||||
\(920\) | −2.02119e31 | −1.53404 | ||||||||
\(921\) | −9.92984e30 | −0.745102 | ||||||||
\(922\) | 2.91512e31 | 2.16263 | ||||||||
\(923\) | 2.67034e30 | 0.195861 | ||||||||
\(924\) | 1.81179e30 | 0.131387 | ||||||||
\(925\) | 4.29285e30 | 0.307792 | ||||||||
\(926\) | −3.28929e31 | −2.33177 | ||||||||
\(927\) | 6.41997e30 | 0.449983 | ||||||||
\(928\) | 1.02785e31 | 0.712319 | ||||||||
\(929\) | 2.24310e31 | 1.53703 | 0.768517 | − | 0.639829i | \(-0.220995\pi\) | ||||
0.768517 | + | 0.639829i | \(0.220995\pi\) | |||||||
\(930\) | −2.90967e31 | −1.97139 | ||||||||
\(931\) | −3.62451e30 | −0.242816 | ||||||||
\(932\) | 7.30787e29 | 0.0484087 | ||||||||
\(933\) | −1.36031e31 | −0.891008 | ||||||||
\(934\) | −2.09134e31 | −1.35451 | ||||||||
\(935\) | 2.19362e31 | 1.40488 | ||||||||
\(936\) | 9.53578e29 | 0.0603893 | ||||||||
\(937\) | −1.10052e31 | −0.689176 | −0.344588 | − | 0.938754i | \(-0.611981\pi\) | ||||
−0.344588 | + | 0.938754i | \(0.611981\pi\) | |||||||
\(938\) | 8.60060e30 | 0.532597 | ||||||||
\(939\) | 1.65135e31 | 1.01123 | ||||||||
\(940\) | −1.04622e31 | −0.633549 | ||||||||
\(941\) | −2.38036e31 | −1.42545 | −0.712725 | − | 0.701444i | \(-0.752539\pi\) | ||||
−0.712725 | + | 0.701444i | \(0.752539\pi\) | |||||||
\(942\) | 1.53974e31 | 0.911828 | ||||||||
\(943\) | 5.09332e30 | 0.298283 | ||||||||
\(944\) | −8.39866e30 | −0.486412 | ||||||||
\(945\) | 4.60202e30 | 0.263581 | ||||||||
\(946\) | 7.95373e30 | 0.450520 | ||||||||
\(947\) | 8.09762e30 | 0.453610 | 0.226805 | − | 0.973940i | \(-0.427172\pi\) | ||||
0.226805 | + | 0.973940i | \(0.427172\pi\) | |||||||
\(948\) | −3.56582e30 | −0.197548 | ||||||||
\(949\) | −2.17660e30 | −0.119257 | ||||||||
\(950\) | 2.90607e31 | 1.57474 | ||||||||
\(951\) | −1.76262e30 | −0.0944631 | ||||||||
\(952\) | −9.26593e30 | −0.491135 | ||||||||
\(953\) | −3.42232e30 | −0.179410 | −0.0897048 | − | 0.995968i | \(-0.528592\pi\) | ||||
−0.0897048 | + | 0.995968i | \(0.528592\pi\) | |||||||
\(954\) | −1.30884e31 | −0.678622 | ||||||||
\(955\) | −5.01715e31 | −2.57290 | ||||||||
\(956\) | −7.87083e30 | −0.399220 | ||||||||
\(957\) | −7.66461e30 | −0.384516 | ||||||||
\(958\) | 1.20140e31 | 0.596140 | ||||||||
\(959\) | 5.53695e30 | 0.271754 | ||||||||
\(960\) | 6.62546e30 | 0.321639 | ||||||||
\(961\) | 2.63603e31 | 1.26577 | ||||||||
\(962\) | −7.79493e29 | −0.0370232 | ||||||||
\(963\) | −8.50095e30 | −0.399385 | ||||||||
\(964\) | 6.63899e30 | 0.308527 | ||||||||
\(965\) | 7.42339e31 | 3.41244 | ||||||||
\(966\) | 1.28111e31 | 0.582540 | ||||||||
\(967\) | 1.33121e31 | 0.598780 | 0.299390 | − | 0.954131i | \(-0.403217\pi\) | ||||
0.299390 | + | 0.954131i | \(0.403217\pi\) | |||||||
\(968\) | 6.86896e30 | 0.305633 | ||||||||
\(969\) | −6.56638e30 | −0.289019 | ||||||||
\(970\) | −4.10186e30 | −0.178598 | ||||||||
\(971\) | 9.71774e30 | 0.418565 | 0.209283 | − | 0.977855i | \(-0.432887\pi\) | ||||
0.209283 | + | 0.977855i | \(0.432887\pi\) | |||||||
\(972\) | −6.38091e29 | −0.0271886 | ||||||||
\(973\) | 4.68806e30 | 0.197610 | ||||||||
\(974\) | −1.83881e31 | −0.766773 | ||||||||
\(975\) | 9.64053e30 | 0.397697 | ||||||||
\(976\) | −2.35932e31 | −0.962861 | ||||||||
\(977\) | −1.40637e31 | −0.567816 | −0.283908 | − | 0.958851i | \(-0.591631\pi\) | ||||
−0.283908 | + | 0.958851i | \(0.591631\pi\) | |||||||
\(978\) | 4.93351e30 | 0.197060 | ||||||||
\(979\) | −2.66785e30 | −0.105425 | ||||||||
\(980\) | 9.91222e30 | 0.387523 | ||||||||
\(981\) | −1.44240e31 | −0.557906 | ||||||||
\(982\) | 2.90414e31 | 1.11134 | ||||||||
\(983\) | −4.87291e31 | −1.84492 | −0.922458 | − | 0.386098i | \(-0.873823\pi\) | ||||
−0.922458 | + | 0.386098i | \(0.873823\pi\) | |||||||
\(984\) | −2.69301e30 | −0.100877 | ||||||||
\(985\) | −7.92741e31 | −2.93799 | ||||||||
\(986\) | −2.88343e31 | −1.05731 | ||||||||
\(987\) | −9.01495e30 | −0.327064 | ||||||||
\(988\) | −1.57074e30 | −0.0563841 | ||||||||
\(989\) | 1.67410e31 | 0.594594 | ||||||||
\(990\) | 1.60360e31 | 0.563543 | ||||||||
\(991\) | 1.17847e30 | 0.0409773 | 0.0204887 | − | 0.999790i | \(-0.493478\pi\) | ||||
0.0204887 | + | 0.999790i | \(0.493478\pi\) | |||||||
\(992\) | 3.48741e31 | 1.19986 | ||||||||
\(993\) | −1.50926e31 | −0.513803 | ||||||||
\(994\) | −1.89685e31 | −0.638965 | ||||||||
\(995\) | −5.98838e31 | −1.99603 | ||||||||
\(996\) | −2.07334e30 | −0.0683829 | ||||||||
\(997\) | 5.05438e31 | 1.64956 | 0.824781 | − | 0.565453i | \(-0.191299\pi\) | ||||
0.824781 | + | 0.565453i | \(0.191299\pi\) | |||||||
\(998\) | −8.85229e30 | −0.285881 | ||||||||
\(999\) | −7.09089e29 | −0.0226602 |
(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 | 3.22.a.b.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 9.22.a.a.1.1 | 1 | |||
4.3 | odd | 2 | 48.22.a.d.1.1 | 1 | |||
5.2 | odd | 4 | 75.22.b.b.49.2 | 2 | |||
5.3 | odd | 4 | 75.22.b.b.49.1 | 2 | |||
5.4 | even | 2 | 75.22.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.22.a.b.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
9.22.a.a.1.1 | 1 | 3.2 | odd | 2 | |||
48.22.a.d.1.1 | 1 | 4.3 | odd | 2 | |||
75.22.a.a.1.1 | 1 | 5.4 | even | 2 | |||
75.22.b.b.49.1 | 2 | 5.3 | odd | 4 | |||
75.22.b.b.49.2 | 2 | 5.2 | odd | 4 |