Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [197,12,Mod(1,197)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(197, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("197.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 197 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 197.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: | \(151.363606570\) |
Analytic rank: | \(0\) |
Dimension: | \(92\) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 197.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −59.6321 | −1.31770 | −0.658848 | − | 0.752276i | \(-0.728956\pi\) | ||||
−0.658848 | + | 0.752276i | \(0.728956\pi\) | |||||||
\(3\) | 54.3091 | 0.129035 | 0.0645173 | − | 0.997917i | \(-0.479449\pi\) | ||||
0.0645173 | + | 0.997917i | \(0.479449\pi\) | |||||||
\(4\) | 1507.99 | 0.736322 | ||||||||
\(5\) | −3681.72 | −0.526885 | −0.263443 | − | 0.964675i | \(-0.584858\pi\) | ||||
−0.263443 | + | 0.964675i | \(0.584858\pi\) | |||||||
\(6\) | −3238.57 | −0.170028 | ||||||||
\(7\) | 14583.9 | 0.327970 | 0.163985 | − | 0.986463i | \(-0.447565\pi\) | ||||
0.163985 | + | 0.986463i | \(0.447565\pi\) | |||||||
\(8\) | 32202.1 | 0.347447 | ||||||||
\(9\) | −174198. | −0.983350 | ||||||||
\(10\) | 219549. | 0.694274 | ||||||||
\(11\) | −156448. | −0.292894 | −0.146447 | − | 0.989218i | \(-0.546784\pi\) | ||||
−0.146447 | + | 0.989218i | \(0.546784\pi\) | |||||||
\(12\) | 81897.5 | 0.0950109 | ||||||||
\(13\) | −1.74648e6 | −1.30459 | −0.652296 | − | 0.757964i | \(-0.726194\pi\) | ||||
−0.652296 | + | 0.757964i | \(0.726194\pi\) | |||||||
\(14\) | −869667. | −0.432164 | ||||||||
\(15\) | −199951. | −0.0679864 | ||||||||
\(16\) | −5.00864e6 | −1.19415 | ||||||||
\(17\) | 3.88025e6 | 0.662813 | 0.331406 | − | 0.943488i | \(-0.392477\pi\) | ||||
0.331406 | + | 0.943488i | \(0.392477\pi\) | |||||||
\(18\) | 1.03878e7 | 1.29576 | ||||||||
\(19\) | −1.62315e7 | −1.50388 | −0.751941 | − | 0.659230i | \(-0.770882\pi\) | ||||
−0.751941 | + | 0.659230i | \(0.770882\pi\) | |||||||
\(20\) | −5.55199e6 | −0.387957 | ||||||||
\(21\) | 792037. | 0.0423194 | ||||||||
\(22\) | 9.32934e6 | 0.385946 | ||||||||
\(23\) | −1.86347e6 | −0.0603697 | −0.0301849 | − | 0.999544i | \(-0.509610\pi\) | ||||
−0.0301849 | + | 0.999544i | \(0.509610\pi\) | |||||||
\(24\) | 1.74887e6 | 0.0448327 | ||||||||
\(25\) | −3.52731e7 | −0.722392 | ||||||||
\(26\) | 1.04146e8 | 1.71906 | ||||||||
\(27\) | −1.90812e7 | −0.255921 | ||||||||
\(28\) | 2.19923e7 | 0.241491 | ||||||||
\(29\) | −8.33015e7 | −0.754160 | −0.377080 | − | 0.926181i | \(-0.623072\pi\) | ||||
−0.377080 | + | 0.926181i | \(0.623072\pi\) | |||||||
\(30\) | 1.19235e7 | 0.0895853 | ||||||||
\(31\) | 3.26662e7 | 0.204932 | 0.102466 | − | 0.994737i | \(-0.467327\pi\) | ||||
0.102466 | + | 0.994737i | \(0.467327\pi\) | |||||||
\(32\) | 2.32726e8 | 1.22608 | ||||||||
\(33\) | −8.49657e6 | −0.0377935 | ||||||||
\(34\) | −2.31388e8 | −0.873386 | ||||||||
\(35\) | −5.36938e7 | −0.172802 | ||||||||
\(36\) | −2.62688e8 | −0.724062 | ||||||||
\(37\) | 1.22917e8 | 0.291408 | 0.145704 | − | 0.989328i | \(-0.453455\pi\) | ||||
0.145704 | + | 0.989328i | \(0.453455\pi\) | |||||||
\(38\) | 9.67919e8 | 1.98166 | ||||||||
\(39\) | −9.48497e7 | −0.168337 | ||||||||
\(40\) | −1.18559e8 | −0.183065 | ||||||||
\(41\) | −8.31993e8 | −1.12152 | −0.560762 | − | 0.827977i | \(-0.689492\pi\) | ||||
−0.560762 | + | 0.827977i | \(0.689492\pi\) | |||||||
\(42\) | −4.72309e7 | −0.0557641 | ||||||||
\(43\) | −3.95017e8 | −0.409769 | −0.204885 | − | 0.978786i | \(-0.565682\pi\) | ||||
−0.204885 | + | 0.978786i | \(0.565682\pi\) | |||||||
\(44\) | −2.35922e8 | −0.215665 | ||||||||
\(45\) | 6.41347e8 | 0.518113 | ||||||||
\(46\) | 1.11123e8 | 0.0795489 | ||||||||
\(47\) | −5.91028e7 | −0.0375898 | −0.0187949 | − | 0.999823i | \(-0.505983\pi\) | ||||
−0.0187949 | + | 0.999823i | \(0.505983\pi\) | |||||||
\(48\) | −2.72015e8 | −0.154087 | ||||||||
\(49\) | −1.76464e9 | −0.892436 | ||||||||
\(50\) | 2.10341e9 | 0.951893 | ||||||||
\(51\) | 2.10733e8 | 0.0855257 | ||||||||
\(52\) | −2.63367e9 | −0.960600 | ||||||||
\(53\) | −3.30628e8 | −0.108598 | −0.0542991 | − | 0.998525i | \(-0.517292\pi\) | ||||
−0.0542991 | + | 0.998525i | \(0.517292\pi\) | |||||||
\(54\) | 1.13785e9 | 0.337225 | ||||||||
\(55\) | 5.75999e8 | 0.154322 | ||||||||
\(56\) | 4.69631e8 | 0.113952 | ||||||||
\(57\) | −8.81519e8 | −0.194053 | ||||||||
\(58\) | 4.96744e9 | 0.993754 | ||||||||
\(59\) | 3.02707e9 | 0.551234 | 0.275617 | − | 0.961268i | \(-0.411118\pi\) | ||||
0.275617 | + | 0.961268i | \(0.411118\pi\) | |||||||
\(60\) | −3.01524e8 | −0.0500599 | ||||||||
\(61\) | 4.16365e9 | 0.631190 | 0.315595 | − | 0.948894i | \(-0.397796\pi\) | ||||
0.315595 | + | 0.948894i | \(0.397796\pi\) | |||||||
\(62\) | −1.94795e9 | −0.270037 | ||||||||
\(63\) | −2.54047e9 | −0.322509 | ||||||||
\(64\) | −3.62023e9 | −0.421450 | ||||||||
\(65\) | 6.43005e9 | 0.687370 | ||||||||
\(66\) | 5.06668e8 | 0.0498003 | ||||||||
\(67\) | −1.12005e10 | −1.01351 | −0.506753 | − | 0.862091i | \(-0.669154\pi\) | ||||
−0.506753 | + | 0.862091i | \(0.669154\pi\) | |||||||
\(68\) | 5.85137e9 | 0.488044 | ||||||||
\(69\) | −1.01203e8 | −0.00778978 | ||||||||
\(70\) | 3.20187e9 | 0.227701 | ||||||||
\(71\) | 1.50655e10 | 0.990974 | 0.495487 | − | 0.868615i | \(-0.334990\pi\) | ||||
0.495487 | + | 0.868615i | \(0.334990\pi\) | |||||||
\(72\) | −5.60952e9 | −0.341663 | ||||||||
\(73\) | −1.97083e10 | −1.11269 | −0.556344 | − | 0.830952i | \(-0.687796\pi\) | ||||
−0.556344 | + | 0.830952i | \(0.687796\pi\) | |||||||
\(74\) | −7.32979e9 | −0.383988 | ||||||||
\(75\) | −1.91565e9 | −0.0932135 | ||||||||
\(76\) | −2.44769e10 | −1.10734 | ||||||||
\(77\) | −2.28162e9 | −0.0960605 | ||||||||
\(78\) | 5.65609e9 | 0.221818 | ||||||||
\(79\) | −3.50481e10 | −1.28149 | −0.640745 | − | 0.767753i | \(-0.721375\pi\) | ||||
−0.640745 | + | 0.767753i | \(0.721375\pi\) | |||||||
\(80\) | 1.84404e10 | 0.629181 | ||||||||
\(81\) | 2.98223e10 | 0.950328 | ||||||||
\(82\) | 4.96135e10 | 1.47783 | ||||||||
\(83\) | −4.16870e10 | −1.16164 | −0.580820 | − | 0.814032i | \(-0.697268\pi\) | ||||
−0.580820 | + | 0.814032i | \(0.697268\pi\) | |||||||
\(84\) | 1.19438e9 | 0.0311607 | ||||||||
\(85\) | −1.42860e10 | −0.349226 | ||||||||
\(86\) | 2.35557e10 | 0.539951 | ||||||||
\(87\) | −4.52403e9 | −0.0973127 | ||||||||
\(88\) | −5.03796e9 | −0.101765 | ||||||||
\(89\) | −5.19236e10 | −0.985643 | −0.492821 | − | 0.870130i | \(-0.664034\pi\) | ||||
−0.492821 | + | 0.870130i | \(0.664034\pi\) | |||||||
\(90\) | −3.82449e10 | −0.682715 | ||||||||
\(91\) | −2.54704e10 | −0.427867 | ||||||||
\(92\) | −2.81009e9 | −0.0444515 | ||||||||
\(93\) | 1.77407e9 | 0.0264432 | ||||||||
\(94\) | 3.52442e9 | 0.0495319 | ||||||||
\(95\) | 5.97599e10 | 0.792373 | ||||||||
\(96\) | 1.26391e10 | 0.158207 | ||||||||
\(97\) | −1.13549e10 | −0.134257 | −0.0671286 | − | 0.997744i | \(-0.521384\pi\) | ||||
−0.0671286 | + | 0.997744i | \(0.521384\pi\) | |||||||
\(98\) | 1.05229e11 | 1.17596 | ||||||||
\(99\) | 2.72529e10 | 0.288018 | ||||||||
\(100\) | −5.31913e10 | −0.531913 | ||||||||
\(101\) | −2.49096e10 | −0.235830 | −0.117915 | − | 0.993024i | \(-0.537621\pi\) | ||||
−0.117915 | + | 0.993024i | \(0.537621\pi\) | |||||||
\(102\) | −1.25665e10 | −0.112697 | ||||||||
\(103\) | −1.98283e11 | −1.68531 | −0.842656 | − | 0.538452i | \(-0.819009\pi\) | ||||
−0.842656 | + | 0.538452i | \(0.819009\pi\) | |||||||
\(104\) | −5.62403e10 | −0.453277 | ||||||||
\(105\) | −2.91606e9 | −0.0222975 | ||||||||
\(106\) | 1.97161e10 | 0.143099 | ||||||||
\(107\) | −2.27153e11 | −1.56570 | −0.782848 | − | 0.622213i | \(-0.786234\pi\) | ||||
−0.782848 | + | 0.622213i | \(0.786234\pi\) | |||||||
\(108\) | −2.87742e10 | −0.188440 | ||||||||
\(109\) | −2.79407e11 | −1.73937 | −0.869684 | − | 0.493609i | \(-0.835677\pi\) | ||||
−0.869684 | + | 0.493609i | \(0.835677\pi\) | |||||||
\(110\) | −3.43480e10 | −0.203349 | ||||||||
\(111\) | 6.67551e9 | 0.0376017 | ||||||||
\(112\) | −7.30453e10 | −0.391646 | ||||||||
\(113\) | −2.19301e11 | −1.11972 | −0.559859 | − | 0.828588i | \(-0.689145\pi\) | ||||
−0.559859 | + | 0.828588i | \(0.689145\pi\) | |||||||
\(114\) | 5.25668e10 | 0.255703 | ||||||||
\(115\) | 6.86078e9 | 0.0318079 | ||||||||
\(116\) | −1.25618e11 | −0.555305 | ||||||||
\(117\) | 3.04232e11 | 1.28287 | ||||||||
\(118\) | −1.80510e11 | −0.726359 | ||||||||
\(119\) | 5.65891e10 | 0.217383 | ||||||||
\(120\) | −6.43884e9 | −0.0236217 | ||||||||
\(121\) | −2.60836e11 | −0.914213 | ||||||||
\(122\) | −2.48287e11 | −0.831716 | ||||||||
\(123\) | −4.51848e10 | −0.144715 | ||||||||
\(124\) | 4.92602e10 | 0.150896 | ||||||||
\(125\) | 3.09637e11 | 0.907503 | ||||||||
\(126\) | 1.51494e11 | 0.424969 | ||||||||
\(127\) | 2.07166e11 | 0.556415 | 0.278207 | − | 0.960521i | \(-0.410260\pi\) | ||||
0.278207 | + | 0.960521i | \(0.410260\pi\) | |||||||
\(128\) | −2.60740e11 | −0.670738 | ||||||||
\(129\) | −2.14530e10 | −0.0528744 | ||||||||
\(130\) | −3.83437e11 | −0.905745 | ||||||||
\(131\) | 1.28725e10 | 0.0291522 | 0.0145761 | − | 0.999894i | \(-0.495360\pi\) | ||||
0.0145761 | + | 0.999894i | \(0.495360\pi\) | |||||||
\(132\) | −1.28127e10 | −0.0278282 | ||||||||
\(133\) | −2.36718e11 | −0.493228 | ||||||||
\(134\) | 6.67910e11 | 1.33549 | ||||||||
\(135\) | 7.02517e10 | 0.134841 | ||||||||
\(136\) | 1.24952e11 | 0.230293 | ||||||||
\(137\) | 2.14830e10 | 0.0380304 | 0.0190152 | − | 0.999819i | \(-0.493947\pi\) | ||||
0.0190152 | + | 0.999819i | \(0.493947\pi\) | |||||||
\(138\) | 6.03497e9 | 0.0102646 | ||||||||
\(139\) | −1.52919e11 | −0.249965 | −0.124983 | − | 0.992159i | \(-0.539887\pi\) | ||||
−0.124983 | + | 0.992159i | \(0.539887\pi\) | |||||||
\(140\) | −8.09695e10 | −0.127238 | ||||||||
\(141\) | −3.20982e9 | −0.00485038 | ||||||||
\(142\) | −8.98387e11 | −1.30580 | ||||||||
\(143\) | 2.73234e11 | 0.382108 | ||||||||
\(144\) | 8.72492e11 | 1.17427 | ||||||||
\(145\) | 3.06693e11 | 0.397356 | ||||||||
\(146\) | 1.17525e12 | 1.46618 | ||||||||
\(147\) | −9.58359e10 | −0.115155 | ||||||||
\(148\) | 1.85357e11 | 0.214570 | ||||||||
\(149\) | 2.26761e11 | 0.252956 | 0.126478 | − | 0.991969i | \(-0.459633\pi\) | ||||
0.126478 | + | 0.991969i | \(0.459633\pi\) | |||||||
\(150\) | 1.14234e11 | 0.122827 | ||||||||
\(151\) | 1.72647e12 | 1.78972 | 0.894862 | − | 0.446344i | \(-0.147274\pi\) | ||||
0.894862 | + | 0.446344i | \(0.147274\pi\) | |||||||
\(152\) | −5.22688e11 | −0.522520 | ||||||||
\(153\) | −6.75930e11 | −0.651777 | ||||||||
\(154\) | 1.36058e11 | 0.126579 | ||||||||
\(155\) | −1.20268e11 | −0.107975 | ||||||||
\(156\) | −1.43032e11 | −0.123951 | ||||||||
\(157\) | 1.64135e12 | 1.37326 | 0.686631 | − | 0.727006i | \(-0.259089\pi\) | ||||
0.686631 | + | 0.727006i | \(0.259089\pi\) | |||||||
\(158\) | 2.08999e12 | 1.68861 | ||||||||
\(159\) | −1.79561e10 | −0.0140129 | ||||||||
\(160\) | −8.56831e11 | −0.646004 | ||||||||
\(161\) | −2.71766e10 | −0.0197994 | ||||||||
\(162\) | −1.77837e12 | −1.25224 | ||||||||
\(163\) | −4.11704e11 | −0.280255 | −0.140127 | − | 0.990133i | \(-0.544751\pi\) | ||||
−0.140127 | + | 0.990133i | \(0.544751\pi\) | |||||||
\(164\) | −1.25464e12 | −0.825803 | ||||||||
\(165\) | 3.12820e10 | 0.0199128 | ||||||||
\(166\) | 2.48589e12 | 1.53069 | ||||||||
\(167\) | −1.19365e12 | −0.711109 | −0.355555 | − | 0.934656i | \(-0.615708\pi\) | ||||
−0.355555 | + | 0.934656i | \(0.615708\pi\) | |||||||
\(168\) | 2.55053e10 | 0.0147038 | ||||||||
\(169\) | 1.25803e12 | 0.701961 | ||||||||
\(170\) | 8.51905e11 | 0.460174 | ||||||||
\(171\) | 2.82749e12 | 1.47884 | ||||||||
\(172\) | −5.95680e11 | −0.301722 | ||||||||
\(173\) | −1.17438e12 | −0.576175 | −0.288087 | − | 0.957604i | \(-0.593019\pi\) | ||||
−0.288087 | + | 0.957604i | \(0.593019\pi\) | |||||||
\(174\) | 2.69777e11 | 0.128229 | ||||||||
\(175\) | −5.14418e11 | −0.236923 | ||||||||
\(176\) | 7.83593e11 | 0.349761 | ||||||||
\(177\) | 1.64397e11 | 0.0711282 | ||||||||
\(178\) | 3.09631e12 | 1.29878 | ||||||||
\(179\) | 2.76587e12 | 1.12497 | 0.562484 | − | 0.826808i | \(-0.309846\pi\) | ||||
0.562484 | + | 0.826808i | \(0.309846\pi\) | |||||||
\(180\) | 9.67143e11 | 0.381498 | ||||||||
\(181\) | 1.68018e12 | 0.642869 | 0.321435 | − | 0.946932i | \(-0.395835\pi\) | ||||
0.321435 | + | 0.946932i | \(0.395835\pi\) | |||||||
\(182\) | 1.51885e12 | 0.563798 | ||||||||
\(183\) | 2.26124e11 | 0.0814453 | ||||||||
\(184\) | −6.00076e10 | −0.0209753 | ||||||||
\(185\) | −4.52546e11 | −0.153539 | ||||||||
\(186\) | −1.05792e11 | −0.0348441 | ||||||||
\(187\) | −6.07059e11 | −0.194134 | ||||||||
\(188\) | −8.91262e10 | −0.0276782 | ||||||||
\(189\) | −2.78278e11 | −0.0839342 | ||||||||
\(190\) | −3.56361e12 | −1.04411 | ||||||||
\(191\) | 7.94093e11 | 0.226041 | 0.113021 | − | 0.993593i | \(-0.463947\pi\) | ||||
0.113021 | + | 0.993593i | \(0.463947\pi\) | |||||||
\(192\) | −1.96611e11 | −0.0543816 | ||||||||
\(193\) | 1.06857e12 | 0.287234 | 0.143617 | − | 0.989633i | \(-0.454127\pi\) | ||||
0.143617 | + | 0.989633i | \(0.454127\pi\) | |||||||
\(194\) | 6.77115e11 | 0.176910 | ||||||||
\(195\) | 3.49210e11 | 0.0886945 | ||||||||
\(196\) | −2.66105e12 | −0.657120 | ||||||||
\(197\) | −2.96709e11 | −0.0712470 | ||||||||
\(198\) | −1.62515e12 | −0.379520 | ||||||||
\(199\) | 1.15668e12 | 0.262736 | 0.131368 | − | 0.991334i | \(-0.458063\pi\) | ||||
0.131368 | + | 0.991334i | \(0.458063\pi\) | |||||||
\(200\) | −1.13587e12 | −0.250993 | ||||||||
\(201\) | −6.08290e11 | −0.130777 | ||||||||
\(202\) | 1.48541e12 | 0.310753 | ||||||||
\(203\) | −1.21486e12 | −0.247342 | ||||||||
\(204\) | 3.17783e11 | 0.0629745 | ||||||||
\(205\) | 3.06317e12 | 0.590914 | ||||||||
\(206\) | 1.18240e13 | 2.22073 | ||||||||
\(207\) | 3.24612e11 | 0.0593646 | ||||||||
\(208\) | 8.74748e12 | 1.55788 | ||||||||
\(209\) | 2.53939e12 | 0.440479 | ||||||||
\(210\) | 1.73891e11 | 0.0293813 | ||||||||
\(211\) | 6.19328e12 | 1.01945 | 0.509727 | − | 0.860336i | \(-0.329746\pi\) | ||||
0.509727 | + | 0.860336i | \(0.329746\pi\) | |||||||
\(212\) | −4.98583e11 | −0.0799633 | ||||||||
\(213\) | 8.18193e11 | 0.127870 | ||||||||
\(214\) | 1.35456e13 | 2.06311 | ||||||||
\(215\) | 1.45434e12 | 0.215901 | ||||||||
\(216\) | −6.14455e11 | −0.0889190 | ||||||||
\(217\) | 4.76399e11 | 0.0672113 | ||||||||
\(218\) | 1.66616e13 | 2.29196 | ||||||||
\(219\) | −1.07034e12 | −0.143575 | ||||||||
\(220\) | 8.68600e11 | 0.113630 | ||||||||
\(221\) | −6.77678e12 | −0.864701 | ||||||||
\(222\) | −3.98075e11 | −0.0495477 | ||||||||
\(223\) | 1.17986e13 | 1.43269 | 0.716346 | − | 0.697745i | \(-0.245813\pi\) | ||||
0.716346 | + | 0.697745i | \(0.245813\pi\) | |||||||
\(224\) | 3.39404e12 | 0.402118 | ||||||||
\(225\) | 6.14448e12 | 0.710364 | ||||||||
\(226\) | 1.30774e13 | 1.47545 | ||||||||
\(227\) | −1.25970e13 | −1.38715 | −0.693577 | − | 0.720382i | \(-0.743966\pi\) | ||||
−0.693577 | + | 0.720382i | \(0.743966\pi\) | |||||||
\(228\) | −1.32932e12 | −0.142885 | ||||||||
\(229\) | −4.02361e12 | −0.422203 | −0.211101 | − | 0.977464i | \(-0.567705\pi\) | ||||
−0.211101 | + | 0.977464i | \(0.567705\pi\) | |||||||
\(230\) | −4.09122e11 | −0.0419131 | ||||||||
\(231\) | −1.23913e11 | −0.0123951 | ||||||||
\(232\) | −2.68248e12 | −0.262031 | ||||||||
\(233\) | −1.93281e13 | −1.84388 | −0.921939 | − | 0.387334i | \(-0.873396\pi\) | ||||
−0.921939 | + | 0.387334i | \(0.873396\pi\) | |||||||
\(234\) | −1.81420e13 | −1.69043 | ||||||||
\(235\) | 2.17600e11 | 0.0198055 | ||||||||
\(236\) | 4.56478e12 | 0.405886 | ||||||||
\(237\) | −1.90343e12 | −0.165357 | ||||||||
\(238\) | −3.37453e12 | −0.286444 | ||||||||
\(239\) | −1.17143e13 | −0.971693 | −0.485846 | − | 0.874044i | \(-0.661489\pi\) | ||||
−0.485846 | + | 0.874044i | \(0.661489\pi\) | |||||||
\(240\) | 1.00148e12 | 0.0811861 | ||||||||
\(241\) | 1.19550e13 | 0.947230 | 0.473615 | − | 0.880732i | \(-0.342949\pi\) | ||||
0.473615 | + | 0.880732i | \(0.342949\pi\) | |||||||
\(242\) | 1.55542e13 | 1.20465 | ||||||||
\(243\) | 4.99980e12 | 0.378546 | ||||||||
\(244\) | 6.27873e12 | 0.464759 | ||||||||
\(245\) | 6.49690e12 | 0.470211 | ||||||||
\(246\) | 2.69447e12 | 0.190691 | ||||||||
\(247\) | 2.83480e13 | 1.96195 | ||||||||
\(248\) | 1.05192e12 | 0.0712029 | ||||||||
\(249\) | −2.26399e12 | −0.149892 | ||||||||
\(250\) | −1.84643e13 | −1.19581 | ||||||||
\(251\) | −1.50205e13 | −0.951653 | −0.475826 | − | 0.879539i | \(-0.657851\pi\) | ||||
−0.475826 | + | 0.879539i | \(0.657851\pi\) | |||||||
\(252\) | −3.83100e12 | −0.237470 | ||||||||
\(253\) | 2.91537e11 | 0.0176820 | ||||||||
\(254\) | −1.23538e13 | −0.733186 | ||||||||
\(255\) | −7.75861e11 | −0.0450622 | ||||||||
\(256\) | 2.29627e13 | 1.30528 | ||||||||
\(257\) | 2.14129e13 | 1.19136 | 0.595680 | − | 0.803222i | \(-0.296883\pi\) | ||||
0.595680 | + | 0.803222i | \(0.296883\pi\) | |||||||
\(258\) | 1.27929e12 | 0.0696723 | ||||||||
\(259\) | 1.79260e12 | 0.0955731 | ||||||||
\(260\) | 9.69643e12 | 0.506126 | ||||||||
\(261\) | 1.45109e13 | 0.741604 | ||||||||
\(262\) | −7.67614e11 | −0.0384137 | ||||||||
\(263\) | 2.38120e13 | 1.16691 | 0.583457 | − | 0.812144i | \(-0.301700\pi\) | ||||
0.583457 | + | 0.812144i | \(0.301700\pi\) | |||||||
\(264\) | −2.73607e11 | −0.0131313 | ||||||||
\(265\) | 1.21728e12 | 0.0572188 | ||||||||
\(266\) | 1.41160e13 | 0.649924 | ||||||||
\(267\) | −2.81992e12 | −0.127182 | ||||||||
\(268\) | −1.68902e13 | −0.746267 | ||||||||
\(269\) | 8.47485e12 | 0.366855 | 0.183428 | − | 0.983033i | \(-0.441281\pi\) | ||||
0.183428 | + | 0.983033i | \(0.441281\pi\) | |||||||
\(270\) | −4.18926e12 | −0.177679 | ||||||||
\(271\) | −1.46872e13 | −0.610389 | −0.305194 | − | 0.952290i | \(-0.598721\pi\) | ||||
−0.305194 | + | 0.952290i | \(0.598721\pi\) | |||||||
\(272\) | −1.94348e13 | −0.791499 | ||||||||
\(273\) | −1.38328e12 | −0.0552096 | ||||||||
\(274\) | −1.28107e12 | −0.0501125 | ||||||||
\(275\) | 5.51841e12 | 0.211585 | ||||||||
\(276\) | −1.52613e11 | −0.00573578 | ||||||||
\(277\) | 2.52911e13 | 0.931814 | 0.465907 | − | 0.884834i | \(-0.345728\pi\) | ||||
0.465907 | + | 0.884834i | \(0.345728\pi\) | |||||||
\(278\) | 9.11887e12 | 0.329378 | ||||||||
\(279\) | −5.69036e12 | −0.201519 | ||||||||
\(280\) | −1.72905e12 | −0.0600397 | ||||||||
\(281\) | −1.30811e13 | −0.445410 | −0.222705 | − | 0.974886i | \(-0.571489\pi\) | ||||
−0.222705 | + | 0.974886i | \(0.571489\pi\) | |||||||
\(282\) | 1.91408e11 | 0.00639132 | ||||||||
\(283\) | 2.72947e12 | 0.0893825 | 0.0446912 | − | 0.999001i | \(-0.485770\pi\) | ||||
0.0446912 | + | 0.999001i | \(0.485770\pi\) | |||||||
\(284\) | 2.27186e13 | 0.729676 | ||||||||
\(285\) | 3.24551e12 | 0.102244 | ||||||||
\(286\) | −1.62935e13 | −0.503502 | ||||||||
\(287\) | −1.21337e13 | −0.367826 | ||||||||
\(288\) | −4.05402e13 | −1.20567 | ||||||||
\(289\) | −1.92155e13 | −0.560679 | ||||||||
\(290\) | −1.82887e13 | −0.523594 | ||||||||
\(291\) | −6.16673e11 | −0.0173238 | ||||||||
\(292\) | −2.97198e13 | −0.819296 | ||||||||
\(293\) | 2.53825e13 | 0.686693 | 0.343347 | − | 0.939209i | \(-0.388439\pi\) | ||||
0.343347 | + | 0.939209i | \(0.388439\pi\) | |||||||
\(294\) | 5.71490e12 | 0.151739 | ||||||||
\(295\) | −1.11448e13 | −0.290437 | ||||||||
\(296\) | 3.95818e12 | 0.101249 | ||||||||
\(297\) | 2.98522e12 | 0.0749577 | ||||||||
\(298\) | −1.35223e13 | −0.333319 | ||||||||
\(299\) | 3.25451e12 | 0.0787579 | ||||||||
\(300\) | −2.88877e12 | −0.0686351 | ||||||||
\(301\) | −5.76088e12 | −0.134392 | ||||||||
\(302\) | −1.02953e14 | −2.35831 | ||||||||
\(303\) | −1.35282e12 | −0.0304303 | ||||||||
\(304\) | 8.12977e13 | 1.79586 | ||||||||
\(305\) | −1.53294e13 | −0.332564 | ||||||||
\(306\) | 4.03072e13 | 0.858844 | ||||||||
\(307\) | −7.61067e13 | −1.59280 | −0.796401 | − | 0.604768i | \(-0.793266\pi\) | ||||
−0.796401 | + | 0.604768i | \(0.793266\pi\) | |||||||
\(308\) | −3.44066e12 | −0.0707315 | ||||||||
\(309\) | −1.07686e13 | −0.217464 | ||||||||
\(310\) | 7.17182e12 | 0.142279 | ||||||||
\(311\) | 1.59752e12 | 0.0311361 | 0.0155680 | − | 0.999879i | \(-0.495044\pi\) | ||||
0.0155680 | + | 0.999879i | \(0.495044\pi\) | |||||||
\(312\) | −3.05436e12 | −0.0584884 | ||||||||
\(313\) | 3.92075e13 | 0.737693 | 0.368846 | − | 0.929490i | \(-0.379753\pi\) | ||||
0.368846 | + | 0.929490i | \(0.379753\pi\) | |||||||
\(314\) | −9.78772e13 | −1.80954 | ||||||||
\(315\) | 9.35332e12 | 0.169925 | ||||||||
\(316\) | −5.28521e13 | −0.943590 | ||||||||
\(317\) | 6.08389e13 | 1.06747 | 0.533735 | − | 0.845652i | \(-0.320788\pi\) | ||||
0.533735 | + | 0.845652i | \(0.320788\pi\) | |||||||
\(318\) | 1.07076e12 | 0.0184648 | ||||||||
\(319\) | 1.30324e13 | 0.220889 | ||||||||
\(320\) | 1.33287e13 | 0.222056 | ||||||||
\(321\) | −1.23365e13 | −0.202029 | ||||||||
\(322\) | 1.62060e12 | 0.0260896 | ||||||||
\(323\) | −6.29823e13 | −0.996793 | ||||||||
\(324\) | 4.49716e13 | 0.699747 | ||||||||
\(325\) | 6.16036e13 | 0.942427 | ||||||||
\(326\) | 2.45508e13 | 0.369291 | ||||||||
\(327\) | −1.51743e13 | −0.224439 | ||||||||
\(328\) | −2.67919e13 | −0.389671 | ||||||||
\(329\) | −8.61947e11 | −0.0123283 | ||||||||
\(330\) | −1.86541e12 | −0.0262391 | ||||||||
\(331\) | −1.10951e14 | −1.53489 | −0.767447 | − | 0.641112i | \(-0.778473\pi\) | ||||
−0.767447 | + | 0.641112i | \(0.778473\pi\) | |||||||
\(332\) | −6.28635e13 | −0.855341 | ||||||||
\(333\) | −2.14118e13 | −0.286556 | ||||||||
\(334\) | 7.11798e13 | 0.937026 | ||||||||
\(335\) | 4.12372e13 | 0.534001 | ||||||||
\(336\) | −3.96703e12 | −0.0505358 | ||||||||
\(337\) | 6.79224e13 | 0.851233 | 0.425616 | − | 0.904904i | \(-0.360057\pi\) | ||||
0.425616 | + | 0.904904i | \(0.360057\pi\) | |||||||
\(338\) | −7.50188e13 | −0.924971 | ||||||||
\(339\) | −1.19100e13 | −0.144482 | ||||||||
\(340\) | −2.15431e13 | −0.257143 | ||||||||
\(341\) | −5.11057e12 | −0.0600233 | ||||||||
\(342\) | −1.68609e14 | −1.94867 | ||||||||
\(343\) | −5.45723e13 | −0.620662 | ||||||||
\(344\) | −1.27204e13 | −0.142373 | ||||||||
\(345\) | 3.72603e11 | 0.00410432 | ||||||||
\(346\) | 7.00306e13 | 0.759223 | ||||||||
\(347\) | −6.94224e13 | −0.740777 | −0.370389 | − | 0.928877i | \(-0.620776\pi\) | ||||
−0.370389 | + | 0.928877i | \(0.620776\pi\) | |||||||
\(348\) | −6.82218e12 | −0.0716535 | ||||||||
\(349\) | −5.29484e13 | −0.547411 | −0.273705 | − | 0.961814i | \(-0.588249\pi\) | ||||
−0.273705 | + | 0.961814i | \(0.588249\pi\) | |||||||
\(350\) | 3.06758e13 | 0.312192 | ||||||||
\(351\) | 3.33249e13 | 0.333872 | ||||||||
\(352\) | −3.64095e13 | −0.359112 | ||||||||
\(353\) | 9.49390e13 | 0.921900 | 0.460950 | − | 0.887426i | \(-0.347509\pi\) | ||||
0.460950 | + | 0.887426i | \(0.347509\pi\) | |||||||
\(354\) | −9.80336e12 | −0.0937254 | ||||||||
\(355\) | −5.54669e13 | −0.522129 | ||||||||
\(356\) | −7.83001e13 | −0.725750 | ||||||||
\(357\) | 3.07331e12 | 0.0280499 | ||||||||
\(358\) | −1.64935e14 | −1.48236 | ||||||||
\(359\) | 3.28215e13 | 0.290496 | 0.145248 | − | 0.989395i | \(-0.453602\pi\) | ||||
0.145248 | + | 0.989395i | \(0.453602\pi\) | |||||||
\(360\) | 2.06527e13 | 0.180017 | ||||||||
\(361\) | 1.46972e14 | 1.26166 | ||||||||
\(362\) | −1.00192e14 | −0.847106 | ||||||||
\(363\) | −1.41658e13 | −0.117965 | ||||||||
\(364\) | −3.84091e13 | −0.315048 | ||||||||
\(365\) | 7.25604e13 | 0.586258 | ||||||||
\(366\) | −1.34843e13 | −0.107320 | ||||||||
\(367\) | −9.38110e12 | −0.0735513 | −0.0367757 | − | 0.999324i | \(-0.511709\pi\) | ||||
−0.0367757 | + | 0.999324i | \(0.511709\pi\) | |||||||
\(368\) | 9.33344e12 | 0.0720906 | ||||||||
\(369\) | 1.44931e14 | 1.10285 | ||||||||
\(370\) | 2.69863e13 | 0.202317 | ||||||||
\(371\) | −4.82184e12 | −0.0356169 | ||||||||
\(372\) | 2.67528e12 | 0.0194707 | ||||||||
\(373\) | −7.34751e13 | −0.526917 | −0.263458 | − | 0.964671i | \(-0.584863\pi\) | ||||
−0.263458 | + | 0.964671i | \(0.584863\pi\) | |||||||
\(374\) | 3.62002e13 | 0.255810 | ||||||||
\(375\) | 1.68161e13 | 0.117099 | ||||||||
\(376\) | −1.90323e12 | −0.0130605 | ||||||||
\(377\) | 1.45484e14 | 0.983872 | ||||||||
\(378\) | 1.65943e13 | 0.110600 | ||||||||
\(379\) | 2.22745e14 | 1.46316 | 0.731580 | − | 0.681756i | \(-0.238783\pi\) | ||||
0.731580 | + | 0.681756i | \(0.238783\pi\) | |||||||
\(380\) | 9.01171e13 | 0.583442 | ||||||||
\(381\) | 1.12510e13 | 0.0717967 | ||||||||
\(382\) | −4.73534e13 | −0.297854 | ||||||||
\(383\) | −1.03751e13 | −0.0643280 | −0.0321640 | − | 0.999483i | \(-0.510240\pi\) | ||||
−0.0321640 | + | 0.999483i | \(0.510240\pi\) | |||||||
\(384\) | −1.41606e13 | −0.0865484 | ||||||||
\(385\) | 8.40030e12 | 0.0506129 | ||||||||
\(386\) | −6.37208e13 | −0.378487 | ||||||||
\(387\) | 6.88110e13 | 0.402946 | ||||||||
\(388\) | −1.71230e13 | −0.0988566 | ||||||||
\(389\) | 2.32767e14 | 1.32495 | 0.662474 | − | 0.749085i | \(-0.269506\pi\) | ||||
0.662474 | + | 0.749085i | \(0.269506\pi\) | |||||||
\(390\) | −2.08241e13 | −0.116872 | ||||||||
\(391\) | −7.23073e12 | −0.0400138 | ||||||||
\(392\) | −5.68250e13 | −0.310075 | ||||||||
\(393\) | 6.99094e11 | 0.00376163 | ||||||||
\(394\) | 1.76934e13 | 0.0938819 | ||||||||
\(395\) | 1.29037e14 | 0.675198 | ||||||||
\(396\) | 4.10970e13 | 0.212074 | ||||||||
\(397\) | 2.47962e14 | 1.26193 | 0.630967 | − | 0.775810i | \(-0.282658\pi\) | ||||
0.630967 | + | 0.775810i | \(0.282658\pi\) | |||||||
\(398\) | −6.89751e13 | −0.346207 | ||||||||
\(399\) | −1.28560e13 | −0.0636434 | ||||||||
\(400\) | 1.76670e14 | 0.862646 | ||||||||
\(401\) | 1.70142e14 | 0.819438 | 0.409719 | − | 0.912212i | \(-0.365627\pi\) | ||||
0.409719 | + | 0.912212i | \(0.365627\pi\) | |||||||
\(402\) | 3.62736e13 | 0.172325 | ||||||||
\(403\) | −5.70507e13 | −0.267352 | ||||||||
\(404\) | −3.75634e13 | −0.173647 | ||||||||
\(405\) | −1.09797e14 | −0.500713 | ||||||||
\(406\) | 7.24446e13 | 0.325921 | ||||||||
\(407\) | −1.92301e13 | −0.0853519 | ||||||||
\(408\) | 6.78605e12 | 0.0297157 | ||||||||
\(409\) | −1.08911e14 | −0.470535 | −0.235267 | − | 0.971931i | \(-0.575597\pi\) | ||||
−0.235267 | + | 0.971931i | \(0.575597\pi\) | |||||||
\(410\) | −1.82663e14 | −0.778645 | ||||||||
\(411\) | 1.16672e12 | 0.00490724 | ||||||||
\(412\) | −2.99008e14 | −1.24093 | ||||||||
\(413\) | 4.41464e13 | 0.180788 | ||||||||
\(414\) | −1.93573e13 | −0.0782244 | ||||||||
\(415\) | 1.53480e14 | 0.612051 | ||||||||
\(416\) | −4.06450e14 | −1.59954 | ||||||||
\(417\) | −8.30488e12 | −0.0322541 | ||||||||
\(418\) | −1.51429e14 | −0.580417 | ||||||||
\(419\) | 1.61974e14 | 0.612728 | 0.306364 | − | 0.951914i | \(-0.400888\pi\) | ||||
0.306364 | + | 0.951914i | \(0.400888\pi\) | |||||||
\(420\) | −4.39738e12 | −0.0164181 | ||||||||
\(421\) | 3.20398e14 | 1.18070 | 0.590349 | − | 0.807148i | \(-0.298990\pi\) | ||||
0.590349 | + | 0.807148i | \(0.298990\pi\) | |||||||
\(422\) | −3.69319e14 | −1.34333 | ||||||||
\(423\) | 1.02956e13 | 0.0369639 | ||||||||
\(424\) | −1.06469e13 | −0.0377322 | ||||||||
\(425\) | −1.36868e14 | −0.478811 | ||||||||
\(426\) | −4.87906e13 | −0.168494 | ||||||||
\(427\) | 6.07221e13 | 0.207011 | ||||||||
\(428\) | −3.42544e14 | −1.15286 | ||||||||
\(429\) | 1.48391e13 | 0.0493051 | ||||||||
\(430\) | −8.67255e13 | −0.284492 | ||||||||
\(431\) | −1.16939e14 | −0.378735 | −0.189368 | − | 0.981906i | \(-0.560644\pi\) | ||||
−0.189368 | + | 0.981906i | \(0.560644\pi\) | |||||||
\(432\) | 9.55709e13 | 0.305608 | ||||||||
\(433\) | −5.72084e14 | −1.80624 | −0.903122 | − | 0.429385i | \(-0.858730\pi\) | ||||
−0.903122 | + | 0.429385i | \(0.858730\pi\) | |||||||
\(434\) | −2.84087e13 | −0.0885641 | ||||||||
\(435\) | 1.66562e13 | 0.0512726 | ||||||||
\(436\) | −4.21342e14 | −1.28073 | ||||||||
\(437\) | 3.02469e13 | 0.0907890 | ||||||||
\(438\) | 6.38266e13 | 0.189188 | ||||||||
\(439\) | −3.90439e13 | −0.114287 | −0.0571437 | − | 0.998366i | \(-0.518199\pi\) | ||||
−0.0571437 | + | 0.998366i | \(0.518199\pi\) | |||||||
\(440\) | 1.85484e13 | 0.0536187 | ||||||||
\(441\) | 3.07395e14 | 0.877577 | ||||||||
\(442\) | 4.04114e14 | 1.13941 | ||||||||
\(443\) | −1.17408e14 | −0.326946 | −0.163473 | − | 0.986548i | \(-0.552270\pi\) | ||||
−0.163473 | + | 0.986548i | \(0.552270\pi\) | |||||||
\(444\) | 1.00666e13 | 0.0276870 | ||||||||
\(445\) | 1.91168e14 | 0.519321 | ||||||||
\(446\) | −7.03574e14 | −1.88785 | ||||||||
\(447\) | 1.23152e13 | 0.0326400 | ||||||||
\(448\) | −5.27970e13 | −0.138223 | ||||||||
\(449\) | −1.70371e14 | −0.440597 | −0.220298 | − | 0.975433i | \(-0.570703\pi\) | ||||
−0.220298 | + | 0.975433i | \(0.570703\pi\) | |||||||
\(450\) | −3.66408e14 | −0.936044 | ||||||||
\(451\) | 1.30164e14 | 0.328488 | ||||||||
\(452\) | −3.30703e14 | −0.824473 | ||||||||
\(453\) | 9.37631e13 | 0.230936 | ||||||||
\(454\) | 7.51185e14 | 1.82785 | ||||||||
\(455\) | 9.37750e13 | 0.225437 | ||||||||
\(456\) | −2.83868e13 | −0.0674232 | ||||||||
\(457\) | −7.02155e14 | −1.64776 | −0.823880 | − | 0.566764i | \(-0.808195\pi\) | ||||
−0.823880 | + | 0.566764i | \(0.808195\pi\) | |||||||
\(458\) | 2.39936e14 | 0.556334 | ||||||||
\(459\) | −7.40399e13 | −0.169627 | ||||||||
\(460\) | 1.03460e13 | 0.0234209 | ||||||||
\(461\) | −2.37670e14 | −0.531642 | −0.265821 | − | 0.964022i | \(-0.585643\pi\) | ||||
−0.265821 | + | 0.964022i | \(0.585643\pi\) | |||||||
\(462\) | 7.38919e12 | 0.0163330 | ||||||||
\(463\) | 2.98063e14 | 0.651048 | 0.325524 | − | 0.945534i | \(-0.394459\pi\) | ||||
0.325524 | + | 0.945534i | \(0.394459\pi\) | |||||||
\(464\) | 4.17227e14 | 0.900582 | ||||||||
\(465\) | −6.53163e12 | −0.0139326 | ||||||||
\(466\) | 1.15258e15 | 2.42967 | ||||||||
\(467\) | −7.66413e14 | −1.59669 | −0.798344 | − | 0.602202i | \(-0.794290\pi\) | ||||
−0.798344 | + | 0.602202i | \(0.794290\pi\) | |||||||
\(468\) | 4.58778e14 | 0.944606 | ||||||||
\(469\) | −1.63347e14 | −0.332399 | ||||||||
\(470\) | −1.29759e13 | −0.0260976 | ||||||||
\(471\) | 8.91403e13 | 0.177198 | ||||||||
\(472\) | 9.74779e13 | 0.191525 | ||||||||
\(473\) | 6.17997e13 | 0.120019 | ||||||||
\(474\) | 1.13506e14 | 0.217890 | ||||||||
\(475\) | 5.72535e14 | 1.08639 | ||||||||
\(476\) | 8.53357e13 | 0.160064 | ||||||||
\(477\) | 5.75946e13 | 0.106790 | ||||||||
\(478\) | 6.98550e14 | 1.28040 | ||||||||
\(479\) | −1.94492e14 | −0.352417 | −0.176209 | − | 0.984353i | \(-0.556383\pi\) | ||||
−0.176209 | + | 0.984353i | \(0.556383\pi\) | |||||||
\(480\) | −4.65337e13 | −0.0833568 | ||||||||
\(481\) | −2.14672e14 | −0.380169 | ||||||||
\(482\) | −7.12901e14 | −1.24816 | ||||||||
\(483\) | −1.47594e12 | −0.00255481 | ||||||||
\(484\) | −3.93337e14 | −0.673155 | ||||||||
\(485\) | 4.18055e13 | 0.0707382 | ||||||||
\(486\) | −2.98149e14 | −0.498808 | ||||||||
\(487\) | −8.15070e14 | −1.34830 | −0.674148 | − | 0.738596i | \(-0.735489\pi\) | ||||
−0.674148 | + | 0.738596i | \(0.735489\pi\) | |||||||
\(488\) | 1.34078e14 | 0.219305 | ||||||||
\(489\) | −2.23593e13 | −0.0361626 | ||||||||
\(490\) | −3.87424e14 | −0.619595 | ||||||||
\(491\) | −5.34800e14 | −0.845752 | −0.422876 | − | 0.906188i | \(-0.638979\pi\) | ||||
−0.422876 | + | 0.906188i | \(0.638979\pi\) | |||||||
\(492\) | −6.81381e13 | −0.106557 | ||||||||
\(493\) | −3.23231e14 | −0.499867 | ||||||||
\(494\) | −1.69045e15 | −2.58526 | ||||||||
\(495\) | −1.00338e14 | −0.151752 | ||||||||
\(496\) | −1.63613e14 | −0.244719 | ||||||||
\(497\) | 2.19713e14 | 0.325009 | ||||||||
\(498\) | 1.35006e14 | 0.197512 | ||||||||
\(499\) | 2.42900e14 | 0.351459 | 0.175729 | − | 0.984439i | \(-0.443772\pi\) | ||||
0.175729 | + | 0.984439i | \(0.443772\pi\) | |||||||
\(500\) | 4.66929e14 | 0.668214 | ||||||||
\(501\) | −6.48261e13 | −0.0917576 | ||||||||
\(502\) | 8.95703e14 | 1.25399 | ||||||||
\(503\) | −4.30988e14 | −0.596816 | −0.298408 | − | 0.954438i | \(-0.596456\pi\) | ||||
−0.298408 | + | 0.954438i | \(0.596456\pi\) | |||||||
\(504\) | −8.18086e13 | −0.112055 | ||||||||
\(505\) | 9.17104e13 | 0.124256 | ||||||||
\(506\) | −1.73849e13 | −0.0232994 | ||||||||
\(507\) | 6.83223e13 | 0.0905772 | ||||||||
\(508\) | 3.12404e14 | 0.409701 | ||||||||
\(509\) | 4.42162e14 | 0.573633 | 0.286816 | − | 0.957986i | \(-0.407403\pi\) | ||||
0.286816 | + | 0.957986i | \(0.407403\pi\) | |||||||
\(510\) | 4.62662e13 | 0.0593783 | ||||||||
\(511\) | −2.87423e14 | −0.364928 | ||||||||
\(512\) | −8.35319e14 | −1.04922 | ||||||||
\(513\) | 3.09717e14 | 0.384875 | ||||||||
\(514\) | −1.27690e15 | −1.56985 | ||||||||
\(515\) | 7.30022e14 | 0.887966 | ||||||||
\(516\) | −3.23509e13 | −0.0389325 | ||||||||
\(517\) | 9.24653e12 | 0.0110098 | ||||||||
\(518\) | −1.06897e14 | −0.125936 | ||||||||
\(519\) | −6.37794e13 | −0.0743464 | ||||||||
\(520\) | 2.07061e14 | 0.238825 | ||||||||
\(521\) | 1.50039e14 | 0.171237 | 0.0856186 | − | 0.996328i | \(-0.472713\pi\) | ||||
0.0856186 | + | 0.996328i | \(0.472713\pi\) | |||||||
\(522\) | −8.65316e14 | −0.977208 | ||||||||
\(523\) | 5.71183e14 | 0.638287 | 0.319143 | − | 0.947706i | \(-0.396605\pi\) | ||||
0.319143 | + | 0.947706i | \(0.396605\pi\) | |||||||
\(524\) | 1.94116e13 | 0.0214654 | ||||||||
\(525\) | −2.79376e13 | −0.0305712 | ||||||||
\(526\) | −1.41996e15 | −1.53764 | ||||||||
\(527\) | 1.26753e14 | 0.135831 | ||||||||
\(528\) | 4.25562e13 | 0.0451312 | ||||||||
\(529\) | −9.49337e14 | −0.996355 | ||||||||
\(530\) | −7.25891e13 | −0.0753970 | ||||||||
\(531\) | −5.27308e14 | −0.542056 | ||||||||
\(532\) | −3.56968e14 | −0.363175 | ||||||||
\(533\) | 1.45306e15 | 1.46313 | ||||||||
\(534\) | 1.68158e14 | 0.167587 | ||||||||
\(535\) | 8.36314e14 | 0.824942 | ||||||||
\(536\) | −3.60680e14 | −0.352140 | ||||||||
\(537\) | 1.50212e14 | 0.145160 | ||||||||
\(538\) | −5.05373e14 | −0.483404 | ||||||||
\(539\) | 2.76075e14 | 0.261390 | ||||||||
\(540\) | 1.05939e14 | 0.0992862 | ||||||||
\(541\) | 7.30107e14 | 0.677332 | 0.338666 | − | 0.940907i | \(-0.390024\pi\) | ||||
0.338666 | + | 0.940907i | \(0.390024\pi\) | |||||||
\(542\) | 8.75826e14 | 0.804307 | ||||||||
\(543\) | 9.12489e13 | 0.0829523 | ||||||||
\(544\) | 9.03034e14 | 0.812663 | ||||||||
\(545\) | 1.02870e15 | 0.916447 | ||||||||
\(546\) | 8.24877e13 | 0.0727494 | ||||||||
\(547\) | 1.13981e15 | 0.995181 | 0.497590 | − | 0.867412i | \(-0.334218\pi\) | ||||
0.497590 | + | 0.867412i | \(0.334218\pi\) | |||||||
\(548\) | 3.23960e13 | 0.0280026 | ||||||||
\(549\) | −7.25297e14 | −0.620680 | ||||||||
\(550\) | −3.29074e14 | −0.278804 | ||||||||
\(551\) | 1.35211e15 | 1.13417 | ||||||||
\(552\) | −3.25896e12 | −0.00270654 | ||||||||
\(553\) | −5.11137e14 | −0.420290 | ||||||||
\(554\) | −1.50816e15 | −1.22785 | ||||||||
\(555\) | −2.45774e13 | −0.0198118 | ||||||||
\(556\) | −2.30600e14 | −0.184055 | ||||||||
\(557\) | 4.30559e14 | 0.340274 | 0.170137 | − | 0.985420i | \(-0.445579\pi\) | ||||
0.170137 | + | 0.985420i | \(0.445579\pi\) | |||||||
\(558\) | 3.39328e14 | 0.265541 | ||||||||
\(559\) | 6.89889e14 | 0.534582 | ||||||||
\(560\) | 2.68933e14 | 0.206352 | ||||||||
\(561\) | −3.29688e13 | −0.0250500 | ||||||||
\(562\) | 7.80055e14 | 0.586915 | ||||||||
\(563\) | 1.38321e15 | 1.03060 | 0.515301 | − | 0.857009i | \(-0.327680\pi\) | ||||
0.515301 | + | 0.857009i | \(0.327680\pi\) | |||||||
\(564\) | −4.84037e12 | −0.00357144 | ||||||||
\(565\) | 8.07404e14 | 0.589963 | ||||||||
\(566\) | −1.62764e14 | −0.117779 | ||||||||
\(567\) | 4.34924e14 | 0.311679 | ||||||||
\(568\) | 4.85140e14 | 0.344311 | ||||||||
\(569\) | −2.76214e15 | −1.94146 | −0.970730 | − | 0.240172i | \(-0.922796\pi\) | ||||
−0.970730 | + | 0.240172i | \(0.922796\pi\) | |||||||
\(570\) | −1.93536e14 | −0.134726 | ||||||||
\(571\) | 7.65857e14 | 0.528018 | 0.264009 | − | 0.964520i | \(-0.414955\pi\) | ||||
0.264009 | + | 0.964520i | \(0.414955\pi\) | |||||||
\(572\) | 4.12033e14 | 0.281354 | ||||||||
\(573\) | 4.31265e13 | 0.0291671 | ||||||||
\(574\) | 7.23557e14 | 0.484683 | ||||||||
\(575\) | 6.57302e13 | 0.0436106 | ||||||||
\(576\) | 6.30635e14 | 0.414433 | ||||||||
\(577\) | 1.78338e15 | 1.16085 | 0.580425 | − | 0.814313i | \(-0.302886\pi\) | ||||
0.580425 | + | 0.814313i | \(0.302886\pi\) | |||||||
\(578\) | 1.14586e15 | 0.738804 | ||||||||
\(579\) | 5.80329e13 | 0.0370631 | ||||||||
\(580\) | 4.62489e14 | 0.292582 | ||||||||
\(581\) | −6.07959e14 | −0.380983 | ||||||||
\(582\) | 3.67735e13 | 0.0228275 | ||||||||
\(583\) | 5.17263e13 | 0.0318078 | ||||||||
\(584\) | −6.34648e14 | −0.386600 | ||||||||
\(585\) | −1.12010e15 | −0.675926 | ||||||||
\(586\) | −1.51361e15 | −0.904853 | ||||||||
\(587\) | −1.76590e14 | −0.104582 | −0.0522909 | − | 0.998632i | \(-0.516652\pi\) | ||||
−0.0522909 | + | 0.998632i | \(0.516652\pi\) | |||||||
\(588\) | −1.44519e14 | −0.0847912 | ||||||||
\(589\) | −5.30221e14 | −0.308193 | ||||||||
\(590\) | 6.64589e14 | 0.382708 | ||||||||
\(591\) | −1.61140e13 | −0.00919333 | ||||||||
\(592\) | −6.15646e14 | −0.347986 | ||||||||
\(593\) | 2.06251e15 | 1.15503 | 0.577517 | − | 0.816379i | \(-0.304022\pi\) | ||||
0.577517 | + | 0.816379i | \(0.304022\pi\) | |||||||
\(594\) | −1.78015e14 | −0.0987715 | ||||||||
\(595\) | −2.08345e14 | −0.114536 | ||||||||
\(596\) | 3.41953e14 | 0.186257 | ||||||||
\(597\) | 6.28181e13 | 0.0339021 | ||||||||
\(598\) | −1.94073e14 | −0.103779 | ||||||||
\(599\) | 2.68938e14 | 0.142497 | 0.0712483 | − | 0.997459i | \(-0.477302\pi\) | ||||
0.0712483 | + | 0.997459i | \(0.477302\pi\) | |||||||
\(600\) | −6.16879e13 | −0.0323868 | ||||||||
\(601\) | 3.19450e15 | 1.66186 | 0.830928 | − | 0.556380i | \(-0.187810\pi\) | ||||
0.830928 | + | 0.556380i | \(0.187810\pi\) | |||||||
\(602\) | 3.43533e14 | 0.177088 | ||||||||
\(603\) | 1.95110e15 | 0.996631 | ||||||||
\(604\) | 2.60350e15 | 1.31781 | ||||||||
\(605\) | 9.60324e14 | 0.481685 | ||||||||
\(606\) | 8.06715e13 | 0.0400978 | ||||||||
\(607\) | −9.76362e14 | −0.480920 | −0.240460 | − | 0.970659i | \(-0.577298\pi\) | ||||
−0.240460 | + | 0.970659i | \(0.577298\pi\) | |||||||
\(608\) | −3.77749e15 | −1.84388 | ||||||||
\(609\) | −6.59779e13 | −0.0319156 | ||||||||
\(610\) | 9.14124e14 | 0.438219 | ||||||||
\(611\) | 1.03222e14 | 0.0490393 | ||||||||
\(612\) | −1.01929e15 | −0.479918 | ||||||||
\(613\) | 1.06345e15 | 0.496233 | 0.248116 | − | 0.968730i | \(-0.420188\pi\) | ||||
0.248116 | + | 0.968730i | \(0.420188\pi\) | |||||||
\(614\) | 4.53840e15 | 2.09883 | ||||||||
\(615\) | 1.66358e14 | 0.0762483 | ||||||||
\(616\) | −7.34730e13 | −0.0333760 | ||||||||
\(617\) | −8.68888e14 | −0.391197 | −0.195598 | − | 0.980684i | \(-0.562665\pi\) | ||||
−0.195598 | + | 0.980684i | \(0.562665\pi\) | |||||||
\(618\) | 6.42152e14 | 0.286551 | ||||||||
\(619\) | 5.77597e14 | 0.255462 | 0.127731 | − | 0.991809i | \(-0.459231\pi\) | ||||
0.127731 | + | 0.991809i | \(0.459231\pi\) | |||||||
\(620\) | −1.81362e14 | −0.0795046 | ||||||||
\(621\) | 3.55573e13 | 0.0154499 | ||||||||
\(622\) | −9.52635e13 | −0.0410279 | ||||||||
\(623\) | −7.57247e14 | −0.323261 | ||||||||
\(624\) | 4.75068e14 | 0.201020 | ||||||||
\(625\) | 5.82319e14 | 0.244242 | ||||||||
\(626\) | −2.33803e15 | −0.972054 | ||||||||
\(627\) | 1.37912e14 | 0.0568370 | ||||||||
\(628\) | 2.47514e15 | 1.01116 | ||||||||
\(629\) | 4.76949e14 | 0.193149 | ||||||||
\(630\) | −5.57758e14 | −0.223910 | ||||||||
\(631\) | −1.25642e15 | −0.500004 | −0.250002 | − | 0.968245i | \(-0.580431\pi\) | ||||
−0.250002 | + | 0.968245i | \(0.580431\pi\) | |||||||
\(632\) | −1.12862e15 | −0.445251 | ||||||||
\(633\) | 3.36352e14 | 0.131545 | ||||||||
\(634\) | −3.62795e15 | −1.40660 | ||||||||
\(635\) | −7.62729e14 | −0.293167 | ||||||||
\(636\) | −2.70776e13 | −0.0103180 | ||||||||
\(637\) | 3.08190e15 | 1.16426 | ||||||||
\(638\) | −7.77148e14 | −0.291065 | ||||||||
\(639\) | −2.62437e15 | −0.974474 | ||||||||
\(640\) | 9.59973e14 | 0.353402 | ||||||||
\(641\) | −1.84677e15 | −0.674051 | −0.337026 | − | 0.941496i | \(-0.609421\pi\) | ||||
−0.337026 | + | 0.941496i | \(0.609421\pi\) | |||||||
\(642\) | 7.35650e14 | 0.266213 | ||||||||
\(643\) | −4.17247e15 | −1.49704 | −0.748518 | − | 0.663114i | \(-0.769234\pi\) | ||||
−0.748518 | + | 0.663114i | \(0.769234\pi\) | |||||||
\(644\) | −4.09820e13 | −0.0145788 | ||||||||
\(645\) | 7.89841e13 | 0.0278587 | ||||||||
\(646\) | 3.75577e15 | 1.31347 | ||||||||
\(647\) | −2.50532e15 | −0.868740 | −0.434370 | − | 0.900735i | \(-0.643029\pi\) | ||||
−0.434370 | + | 0.900735i | \(0.643029\pi\) | |||||||
\(648\) | 9.60340e14 | 0.330189 | ||||||||
\(649\) | −4.73580e14 | −0.161453 | ||||||||
\(650\) | −3.67355e15 | −1.24183 | ||||||||
\(651\) | 2.58728e13 | 0.00867258 | ||||||||
\(652\) | −6.20844e14 | −0.206358 | ||||||||
\(653\) | −1.09329e15 | −0.360341 | −0.180170 | − | 0.983635i | \(-0.557665\pi\) | ||||
−0.180170 | + | 0.983635i | \(0.557665\pi\) | |||||||
\(654\) | 9.04878e14 | 0.295742 | ||||||||
\(655\) | −4.73930e13 | −0.0153598 | ||||||||
\(656\) | 4.16715e15 | 1.33927 | ||||||||
\(657\) | 3.43313e15 | 1.09416 | ||||||||
\(658\) | 5.13997e13 | 0.0162449 | ||||||||
\(659\) | 2.81792e15 | 0.883201 | 0.441600 | − | 0.897212i | \(-0.354411\pi\) | ||||
0.441600 | + | 0.897212i | \(0.354411\pi\) | |||||||
\(660\) | 4.71729e13 | 0.0146623 | ||||||||
\(661\) | 3.94426e15 | 1.21579 | 0.607894 | − | 0.794018i | \(-0.292014\pi\) | ||||
0.607894 | + | 0.794018i | \(0.292014\pi\) | |||||||
\(662\) | 6.61626e15 | 2.02252 | ||||||||
\(663\) | −3.68041e14 | −0.111576 | ||||||||
\(664\) | −1.34241e15 | −0.403609 | ||||||||
\(665\) | 8.71531e14 | 0.259874 | ||||||||
\(666\) | 1.27683e15 | 0.377594 | ||||||||
\(667\) | 1.55230e14 | 0.0455285 | ||||||||
\(668\) | −1.80001e15 | −0.523605 | ||||||||
\(669\) | 6.40770e14 | 0.184867 | ||||||||
\(670\) | −2.45906e15 | −0.703651 | ||||||||
\(671\) | −6.51396e14 | −0.184872 | ||||||||
\(672\) | 1.84327e14 | 0.0518870 | ||||||||
\(673\) | 4.49130e15 | 1.25398 | 0.626988 | − | 0.779029i | \(-0.284288\pi\) | ||||
0.626988 | + | 0.779029i | \(0.284288\pi\) | |||||||
\(674\) | −4.05035e15 | −1.12167 | ||||||||
\(675\) | 6.73053e14 | 0.184875 | ||||||||
\(676\) | 1.89709e15 | 0.516869 | ||||||||
\(677\) | 6.65605e15 | 1.79878 | 0.899392 | − | 0.437142i | \(-0.144009\pi\) | ||||
0.899392 | + | 0.437142i | \(0.144009\pi\) | |||||||
\(678\) | 7.10220e14 | 0.190384 | ||||||||
\(679\) | −1.65598e14 | −0.0440323 | ||||||||
\(680\) | −4.60039e14 | −0.121338 | ||||||||
\(681\) | −6.84132e14 | −0.178991 | ||||||||
\(682\) | 3.04754e14 | 0.0790925 | ||||||||
\(683\) | −3.87670e15 | −0.998041 | −0.499020 | − | 0.866590i | \(-0.666307\pi\) | ||||
−0.499020 | + | 0.866590i | \(0.666307\pi\) | |||||||
\(684\) | 4.26382e15 | 1.08890 | ||||||||
\(685\) | −7.90943e13 | −0.0200377 | ||||||||
\(686\) | 3.25426e15 | 0.817843 | ||||||||
\(687\) | −2.18519e14 | −0.0544787 | ||||||||
\(688\) | 1.97850e15 | 0.489327 | ||||||||
\(689\) | 5.77435e14 | 0.141676 | ||||||||
\(690\) | −2.22191e13 | −0.00540824 | ||||||||
\(691\) | 7.31622e15 | 1.76668 | 0.883339 | − | 0.468735i | \(-0.155290\pi\) | ||||
0.883339 | + | 0.468735i | \(0.155290\pi\) | |||||||
\(692\) | −1.77095e15 | −0.424250 | ||||||||
\(693\) | 3.97453e14 | 0.0944611 | ||||||||
\(694\) | 4.13981e15 | 0.976119 | ||||||||
\(695\) | 5.63004e14 | 0.131703 | ||||||||
\(696\) | −1.45683e14 | −0.0338111 | ||||||||
\(697\) | −3.22834e15 | −0.743361 | ||||||||
\(698\) | 3.15743e15 | 0.721321 | ||||||||
\(699\) | −1.04969e15 | −0.237924 | ||||||||
\(700\) | −7.75735e14 | −0.174451 | ||||||||
\(701\) | −7.67409e15 | −1.71229 | −0.856146 | − | 0.516734i | \(-0.827147\pi\) | ||||
−0.856146 | + | 0.516734i | \(0.827147\pi\) | |||||||
\(702\) | −1.98724e15 | −0.439942 | ||||||||
\(703\) | −1.99513e15 | −0.438244 | ||||||||
\(704\) | 5.66379e14 | 0.123440 | ||||||||
\(705\) | 1.18177e13 | 0.00255559 | ||||||||
\(706\) | −5.66141e15 | −1.21478 | ||||||||
\(707\) | −3.63279e14 | −0.0773452 | ||||||||
\(708\) | 2.47909e14 | 0.0523733 | ||||||||
\(709\) | 7.60848e15 | 1.59494 | 0.797469 | − | 0.603360i | \(-0.206172\pi\) | ||||
0.797469 | + | 0.603360i | \(0.206172\pi\) | |||||||
\(710\) | 3.30761e15 | 0.688008 | ||||||||
\(711\) | 6.10529e15 | 1.26015 | ||||||||
\(712\) | −1.67205e15 | −0.342459 | ||||||||
\(713\) | −6.08724e13 | −0.0123717 | ||||||||
\(714\) | −1.83268e14 | −0.0369612 | ||||||||
\(715\) | −1.00597e15 | −0.201327 | ||||||||
\(716\) | 4.17089e15 | 0.828338 | ||||||||
\(717\) | −6.36195e14 | −0.125382 | ||||||||
\(718\) | −1.95722e15 | −0.382785 | ||||||||
\(719\) | 1.29989e15 | 0.252289 | 0.126144 | − | 0.992012i | \(-0.459740\pi\) | ||||
0.126144 | + | 0.992012i | \(0.459740\pi\) | |||||||
\(720\) | −3.21227e15 | −0.618705 | ||||||||
\(721\) | −2.89173e15 | −0.552732 | ||||||||
\(722\) | −8.76422e15 | −1.66249 | ||||||||
\(723\) | 6.49265e14 | 0.122225 | ||||||||
\(724\) | 2.53368e15 | 0.473359 | ||||||||
\(725\) | 2.93830e15 | 0.544800 | ||||||||
\(726\) | 8.44734e14 | 0.155442 | ||||||||
\(727\) | −5.30782e15 | −0.969342 | −0.484671 | − | 0.874696i | \(-0.661061\pi\) | ||||
−0.484671 | + | 0.874696i | \(0.661061\pi\) | |||||||
\(728\) | −8.20201e14 | −0.148661 | ||||||||
\(729\) | −5.01139e15 | −0.901482 | ||||||||
\(730\) | −4.32693e15 | −0.772510 | ||||||||
\(731\) | −1.53277e15 | −0.271600 | ||||||||
\(732\) | 3.40992e14 | 0.0599699 | ||||||||
\(733\) | −9.22269e14 | −0.160985 | −0.0804926 | − | 0.996755i | \(-0.525649\pi\) | ||||
−0.0804926 | + | 0.996755i | \(0.525649\pi\) | |||||||
\(734\) | 5.59415e14 | 0.0969183 | ||||||||
\(735\) | 3.52841e14 | 0.0606735 | ||||||||
\(736\) | −4.33677e14 | −0.0740182 | ||||||||
\(737\) | 1.75230e15 | 0.296850 | ||||||||
\(738\) | −8.64255e15 | −1.45322 | ||||||||
\(739\) | 2.80660e15 | 0.468420 | 0.234210 | − | 0.972186i | \(-0.424750\pi\) | ||||
0.234210 | + | 0.972186i | \(0.424750\pi\) | |||||||
\(740\) | −6.82433e14 | −0.113054 | ||||||||
\(741\) | 1.53955e15 | 0.253160 | ||||||||
\(742\) | 2.87537e14 | 0.0469323 | ||||||||
\(743\) | −6.63578e15 | −1.07511 | −0.537556 | − | 0.843228i | \(-0.680652\pi\) | ||||
−0.537556 | + | 0.843228i | \(0.680652\pi\) | |||||||
\(744\) | 5.71288e13 | 0.00918764 | ||||||||
\(745\) | −8.34873e14 | −0.133279 | ||||||||
\(746\) | 4.38148e15 | 0.694316 | ||||||||
\(747\) | 7.26178e15 | 1.14230 | ||||||||
\(748\) | −9.15437e14 | −0.142945 | ||||||||
\(749\) | −3.31277e15 | −0.513501 | ||||||||
\(750\) | −1.00278e15 | −0.154301 | ||||||||
\(751\) | 5.83015e15 | 0.890554 | 0.445277 | − | 0.895393i | \(-0.353105\pi\) | ||||
0.445277 | + | 0.895393i | \(0.353105\pi\) | |||||||
\(752\) | 2.96024e14 | 0.0448879 | ||||||||
\(753\) | −8.15749e14 | −0.122796 | ||||||||
\(754\) | −8.67553e15 | −1.29644 | ||||||||
\(755\) | −6.35638e15 | −0.942979 | ||||||||
\(756\) | −4.19640e14 | −0.0618026 | ||||||||
\(757\) | −7.70624e15 | −1.12672 | −0.563359 | − | 0.826212i | \(-0.690491\pi\) | ||||
−0.563359 | + | 0.826212i | \(0.690491\pi\) | |||||||
\(758\) | −1.32827e16 | −1.92800 | ||||||||
\(759\) | 1.58331e13 | 0.00228158 | ||||||||
\(760\) | 1.92439e15 | 0.275308 | ||||||||
\(761\) | −1.82857e15 | −0.259714 | −0.129857 | − | 0.991533i | \(-0.541452\pi\) | ||||
−0.129857 | + | 0.991533i | \(0.541452\pi\) | |||||||
\(762\) | −6.70922e14 | −0.0946063 | ||||||||
\(763\) | −4.07484e15 | −0.570460 | ||||||||
\(764\) | 1.19748e15 | 0.166439 | ||||||||
\(765\) | 2.48859e15 | 0.343412 | ||||||||
\(766\) | 6.18690e14 | 0.0847647 | ||||||||
\(767\) | −5.28671e15 | −0.719136 | ||||||||
\(768\) | 1.24708e15 | 0.168426 | ||||||||
\(769\) | −6.76987e15 | −0.907790 | −0.453895 | − | 0.891055i | \(-0.649966\pi\) | ||||
−0.453895 | + | 0.891055i | \(0.649966\pi\) | |||||||
\(770\) | −5.00928e14 | −0.0666923 | ||||||||
\(771\) | 1.16292e15 | 0.153727 | ||||||||
\(772\) | 1.61138e15 | 0.211497 | ||||||||
\(773\) | −5.41600e15 | −0.705816 | −0.352908 | − | 0.935658i | \(-0.614807\pi\) | ||||
−0.352908 | + | 0.935658i | \(0.614807\pi\) | |||||||
\(774\) | −4.10334e15 | −0.530961 | ||||||||
\(775\) | −1.15224e15 | −0.148041 | ||||||||
\(776\) | −3.65651e14 | −0.0466473 | ||||||||
\(777\) | 9.73548e13 | 0.0123322 | ||||||||
\(778\) | −1.38804e16 | −1.74588 | ||||||||
\(779\) | 1.35045e16 | 1.68664 | ||||||||
\(780\) | 5.26605e14 | 0.0653077 | ||||||||
\(781\) | −2.35697e15 | −0.290251 | ||||||||
\(782\) | 4.31184e14 | 0.0527261 | ||||||||
\(783\) | 1.58949e15 | 0.193005 | ||||||||
\(784\) | 8.83843e15 | 1.06570 | ||||||||
\(785\) | −6.04299e15 | −0.723551 | ||||||||
\(786\) | −4.16885e13 | −0.00495669 | ||||||||
\(787\) | −1.32704e16 | −1.56683 | −0.783416 | − | 0.621498i | \(-0.786524\pi\) | ||||
−0.783416 | + | 0.621498i | \(0.786524\pi\) | |||||||
\(788\) | −4.47434e14 | −0.0524608 | ||||||||
\(789\) | 1.29321e15 | 0.150572 | ||||||||
\(790\) | −7.69477e15 | −0.889706 | ||||||||
\(791\) | −3.19825e15 | −0.367233 | ||||||||
\(792\) | 8.77601e14 | 0.100071 | ||||||||
\(793\) | −7.27172e15 | −0.823445 | ||||||||
\(794\) | −1.47865e16 | −1.66285 | ||||||||
\(795\) | 6.61095e13 | 0.00738320 | ||||||||
\(796\) | 1.74425e15 | 0.193459 | ||||||||
\(797\) | 1.10962e16 | 1.22223 | 0.611117 | − | 0.791540i | \(-0.290721\pi\) | ||||
0.611117 | + | 0.791540i | \(0.290721\pi\) | |||||||
\(798\) | 7.66628e14 | 0.0838627 | ||||||||
\(799\) | −2.29334e14 | −0.0249150 | ||||||||
\(800\) | −8.20894e15 | −0.885711 | ||||||||
\(801\) | 9.04496e15 | 0.969232 | ||||||||
\(802\) | −1.01459e16 | −1.07977 | ||||||||
\(803\) | 3.08333e15 | 0.325900 | ||||||||
\(804\) | −9.17293e14 | −0.0962942 | ||||||||
\(805\) | 1.00057e14 | 0.0104320 | ||||||||
\(806\) | 3.40206e15 | 0.352289 | ||||||||
\(807\) | 4.60262e14 | 0.0473370 | ||||||||
\(808\) | −8.02143e14 | −0.0819387 | ||||||||
\(809\) | 1.30343e16 | 1.32242 | 0.661211 | − | 0.750200i | \(-0.270043\pi\) | ||||
0.661211 | + | 0.750200i | \(0.270043\pi\) | |||||||
\(810\) | 6.54745e15 | 0.659788 | ||||||||
\(811\) | −1.50810e16 | −1.50943 | −0.754717 | − | 0.656051i | \(-0.772226\pi\) | ||||
−0.754717 | + | 0.656051i | \(0.772226\pi\) | |||||||
\(812\) | −1.83199e15 | −0.182123 | ||||||||
\(813\) | −7.97646e14 | −0.0787612 | ||||||||
\(814\) | 1.14673e15 | 0.112468 | ||||||||
\(815\) | 1.51578e15 | 0.147662 | ||||||||
\(816\) | −1.05549e15 | −0.102131 | ||||||||
\(817\) | 6.41172e15 | 0.616245 | ||||||||
\(818\) | 6.49456e15 | 0.620022 | ||||||||
\(819\) | 4.43688e15 | 0.420743 | ||||||||
\(820\) | 4.61922e15 | 0.435103 | ||||||||
\(821\) | 9.41101e14 | 0.0880540 | 0.0440270 | − | 0.999030i | \(-0.485981\pi\) | ||||
0.0440270 | + | 0.999030i | \(0.485981\pi\) | |||||||
\(822\) | −6.95740e13 | −0.00646624 | ||||||||
\(823\) | 3.69420e15 | 0.341053 | 0.170526 | − | 0.985353i | \(-0.445453\pi\) | ||||
0.170526 | + | 0.985353i | \(0.445453\pi\) | |||||||
\(824\) | −6.38512e15 | −0.585558 | ||||||||
\(825\) | 2.99700e14 | 0.0273017 | ||||||||
\(826\) | −2.63254e15 | −0.238224 | ||||||||
\(827\) | −1.75606e16 | −1.57855 | −0.789276 | − | 0.614038i | \(-0.789544\pi\) | ||||
−0.789276 | + | 0.614038i | \(0.789544\pi\) | |||||||
\(828\) | 4.89510e14 | 0.0437114 | ||||||||
\(829\) | −7.62266e15 | −0.676171 | −0.338085 | − | 0.941115i | \(-0.609779\pi\) | ||||
−0.338085 | + | 0.941115i | \(0.609779\pi\) | |||||||
\(830\) | −9.15234e15 | −0.806497 | ||||||||
\(831\) | 1.37354e15 | 0.120236 | ||||||||
\(832\) | 6.32265e15 | 0.549821 | ||||||||
\(833\) | −6.84724e15 | −0.591518 | ||||||||
\(834\) | 4.95238e14 | 0.0425011 | ||||||||
\(835\) | 4.39469e15 | 0.374673 | ||||||||
\(836\) | 3.82937e15 | 0.324334 | ||||||||
\(837\) | −6.23310e14 | −0.0524462 | ||||||||
\(838\) | −9.65884e15 | −0.807389 | ||||||||
\(839\) | −1.55469e16 | −1.29108 | −0.645539 | − | 0.763728i | \(-0.723367\pi\) | ||||
−0.645539 | + | 0.763728i | \(0.723367\pi\) | |||||||
\(840\) | −9.39033e13 | −0.00774720 | ||||||||
\(841\) | −5.26137e15 | −0.431242 | ||||||||
\(842\) | −1.91060e16 | −1.55580 | ||||||||
\(843\) | −7.10424e14 | −0.0574733 | ||||||||
\(844\) | 9.33939e15 | 0.750646 | ||||||||
\(845\) | −4.63170e15 | −0.369853 | ||||||||
\(846\) | −6.13945e14 | −0.0487072 | ||||||||
\(847\) | −3.80399e15 | −0.299834 | ||||||||
\(848\) | 1.65600e15 | 0.129683 | ||||||||
\(849\) | 1.48235e14 | 0.0115334 | ||||||||
\(850\) | 8.16175e15 | 0.630927 | ||||||||
\(851\) | −2.29052e14 | −0.0175922 | ||||||||
\(852\) | 1.23383e15 | 0.0941534 | ||||||||
\(853\) | 4.18469e15 | 0.317280 | 0.158640 | − | 0.987336i | \(-0.449289\pi\) | ||||
0.158640 | + | 0.987336i | \(0.449289\pi\) | |||||||
\(854\) | −3.62099e15 | −0.272778 | ||||||||
\(855\) | −1.04100e16 | −0.779181 | ||||||||
\(856\) | −7.31480e15 | −0.543997 | ||||||||
\(857\) | −3.28964e15 | −0.243083 | −0.121541 | − | 0.992586i | \(-0.538784\pi\) | ||||
−0.121541 | + | 0.992586i | \(0.538784\pi\) | |||||||
\(858\) | −8.84886e14 | −0.0649691 | ||||||||
\(859\) | −1.11698e16 | −0.814859 | −0.407430 | − | 0.913237i | \(-0.633575\pi\) | ||||
−0.407430 | + | 0.913237i | \(0.633575\pi\) | |||||||
\(860\) | 2.19313e15 | 0.158973 | ||||||||
\(861\) | −6.58970e14 | −0.0474622 | ||||||||
\(862\) | 6.97334e15 | 0.499058 | ||||||||
\(863\) | −2.90899e15 | −0.206863 | −0.103432 | − | 0.994637i | \(-0.532982\pi\) | ||||
−0.103432 | + | 0.994637i | \(0.532982\pi\) | |||||||
\(864\) | −4.44069e15 | −0.313780 | ||||||||
\(865\) | 4.32373e15 | 0.303578 | ||||||||
\(866\) | 3.41146e16 | 2.38008 | ||||||||
\(867\) | −1.04358e15 | −0.0723469 | ||||||||
\(868\) | 7.18404e14 | 0.0494892 | ||||||||
\(869\) | 5.48322e15 | 0.375342 | ||||||||
\(870\) | −9.93246e14 | −0.0675617 | ||||||||
\(871\) | 1.95614e16 | 1.32221 | ||||||||
\(872\) | −8.99749e15 | −0.604339 | ||||||||
\(873\) | 1.97799e15 | 0.132022 | ||||||||
\(874\) | −1.80369e15 | −0.119632 | ||||||||
\(875\) | 4.51571e15 | 0.297633 | ||||||||
\(876\) | −1.61406e15 | −0.105717 | ||||||||
\(877\) | 4.54147e14 | 0.0295596 | 0.0147798 | − | 0.999891i | \(-0.495295\pi\) | ||||
0.0147798 | + | 0.999891i | \(0.495295\pi\) | |||||||
\(878\) | 2.32827e15 | 0.150596 | ||||||||
\(879\) | 1.37850e15 | 0.0886071 | ||||||||
\(880\) | −2.88497e15 | −0.184284 | ||||||||
\(881\) | −2.13080e16 | −1.35262 | −0.676308 | − | 0.736619i | \(-0.736421\pi\) | ||||
−0.676308 | + | 0.736619i | \(0.736421\pi\) | |||||||
\(882\) | −1.83306e16 | −1.15638 | ||||||||
\(883\) | 2.43871e16 | 1.52889 | 0.764446 | − | 0.644688i | \(-0.223013\pi\) | ||||
0.764446 | + | 0.644688i | \(0.223013\pi\) | |||||||
\(884\) | −1.02193e16 | −0.636698 | ||||||||
\(885\) | −6.05266e14 | −0.0374764 | ||||||||
\(886\) | 7.00128e15 | 0.430816 | ||||||||
\(887\) | −2.95854e15 | −0.180925 | −0.0904624 | − | 0.995900i | \(-0.528834\pi\) | ||||
−0.0904624 | + | 0.995900i | \(0.528834\pi\) | |||||||
\(888\) | 2.14965e14 | 0.0130646 | ||||||||
\(889\) | 3.02129e15 | 0.182487 | ||||||||
\(890\) | −1.13998e16 | −0.684307 | ||||||||
\(891\) | −4.66565e15 | −0.278346 | ||||||||
\(892\) | 1.77921e16 | 1.05492 | ||||||||
\(893\) | 9.59327e14 | 0.0565306 | ||||||||
\(894\) | −7.34382e14 | −0.0430096 | ||||||||
\(895\) | −1.01832e16 | −0.592729 | ||||||||
\(896\) | −3.80260e15 | −0.219982 | ||||||||
\(897\) | 1.76750e14 | 0.0101625 | ||||||||
\(898\) | 1.01596e16 | 0.580572 | ||||||||
\(899\) | −2.72114e15 | −0.154551 | ||||||||
\(900\) | 9.26579e15 | 0.523057 | ||||||||
\(901\) | −1.28292e15 | −0.0719803 | ||||||||
\(902\) | −7.76195e15 | −0.432847 | ||||||||
\(903\) | −3.12868e14 | −0.0173412 | ||||||||
\(904\) | −7.06194e15 | −0.389043 | ||||||||
\(905\) | −6.18594e15 | −0.338718 | ||||||||
\(906\) | −5.59129e15 | −0.304303 | ||||||||
\(907\) | 2.55989e16 | 1.38478 | 0.692392 | − | 0.721522i | \(-0.256557\pi\) | ||||
0.692392 | + | 0.721522i | \(0.256557\pi\) | |||||||
\(908\) | −1.89961e16 | −1.02139 | ||||||||
\(909\) | 4.33920e15 | 0.231904 | ||||||||
\(910\) | −5.59200e15 | −0.297057 | ||||||||
\(911\) | 1.66008e16 | 0.876554 | 0.438277 | − | 0.898840i | \(-0.355589\pi\) | ||||
0.438277 | + | 0.898840i | \(0.355589\pi\) | |||||||
\(912\) | 4.41521e15 | 0.231729 | ||||||||
\(913\) | 6.52187e15 | 0.340238 | ||||||||
\(914\) | 4.18710e16 | 2.17125 | ||||||||
\(915\) | −8.32526e14 | −0.0429123 | ||||||||
\(916\) | −6.06755e15 | −0.310877 | ||||||||
\(917\) | 1.87731e14 | 0.00956102 | ||||||||
\(918\) | 4.41516e15 | 0.223517 | ||||||||
\(919\) | 3.18784e16 | 1.60421 | 0.802105 | − | 0.597184i | \(-0.203714\pi\) | ||||
0.802105 | + | 0.597184i | \(0.203714\pi\) | |||||||
\(920\) | 2.20931e14 | 0.0110516 | ||||||||
\(921\) | −4.13329e15 | −0.205527 | ||||||||
\(922\) | 1.41727e16 | 0.700542 | ||||||||
\(923\) | −2.63115e16 | −1.29282 | ||||||||
\(924\) | −1.86859e14 | −0.00912680 | ||||||||
\(925\) | −4.33565e15 | −0.210511 | ||||||||
\(926\) | −1.77741e16 | −0.857883 | ||||||||
\(927\) | 3.45404e16 | 1.65725 | ||||||||
\(928\) | −1.93864e16 | −0.924662 | ||||||||
\(929\) | −2.37259e16 | −1.12496 | −0.562479 | − | 0.826811i | \(-0.690152\pi\) | ||||
−0.562479 | + | 0.826811i | \(0.690152\pi\) | |||||||
\(930\) | 3.89495e14 | 0.0183589 | ||||||||
\(931\) | 2.86427e16 | 1.34212 | ||||||||
\(932\) | −2.91466e16 | −1.35769 | ||||||||
\(933\) | 8.67599e13 | 0.00401763 | ||||||||
\(934\) | 4.57028e16 | 2.10395 | ||||||||
\(935\) | 2.23502e15 | 0.102286 | ||||||||
\(936\) | 9.79691e15 | 0.445730 | ||||||||
\(937\) | 2.63273e15 | 0.119080 | 0.0595400 | − | 0.998226i | \(-0.481037\pi\) | ||||
0.0595400 | + | 0.998226i | \(0.481037\pi\) | |||||||
\(938\) | 9.74071e15 | 0.438001 | ||||||||
\(939\) | 2.12933e15 | 0.0951878 | ||||||||
\(940\) | 3.28138e14 | 0.0145832 | ||||||||
\(941\) | 1.32794e16 | 0.586726 | 0.293363 | − | 0.956001i | \(-0.405226\pi\) | ||||
0.293363 | + | 0.956001i | \(0.405226\pi\) | |||||||
\(942\) | −5.31562e15 | −0.233493 | ||||||||
\(943\) | 1.55039e15 | 0.0677061 | ||||||||
\(944\) | −1.51615e16 | −0.658257 | ||||||||
\(945\) | 1.02454e15 | 0.0442237 | ||||||||
\(946\) | −3.68525e15 | −0.158149 | ||||||||
\(947\) | 3.47962e16 | 1.48459 | 0.742296 | − | 0.670072i | \(-0.233737\pi\) | ||||
0.742296 | + | 0.670072i | \(0.233737\pi\) | |||||||
\(948\) | −2.87035e15 | −0.121756 | ||||||||
\(949\) | 3.44201e16 | 1.45160 | ||||||||
\(950\) | −3.41414e16 | −1.43154 | ||||||||
\(951\) | 3.30411e15 | 0.137740 | ||||||||
\(952\) | 1.82229e15 | 0.0755290 | ||||||||
\(953\) | 1.20181e16 | 0.495249 | 0.247625 | − | 0.968856i | \(-0.420350\pi\) | ||||
0.247625 | + | 0.968856i | \(0.420350\pi\) | |||||||
\(954\) | −3.43449e15 | −0.140717 | ||||||||
\(955\) | −2.92363e15 | −0.119098 | ||||||||
\(956\) | −1.76651e16 | −0.715479 | ||||||||
\(957\) | 7.07777e14 | 0.0285024 | ||||||||
\(958\) | 1.15980e16 | 0.464379 | ||||||||
\(959\) | 3.13305e14 | 0.0124728 | ||||||||
\(960\) | 7.23869e14 | 0.0286529 | ||||||||
\(961\) | −2.43414e16 | −0.958003 | ||||||||
\(962\) | 1.28013e16 | 0.500947 | ||||||||
\(963\) | 3.95695e16 | 1.53963 | ||||||||
\(964\) | 1.80280e16 | 0.697466 | ||||||||
\(965\) | −3.93416e15 | −0.151339 | ||||||||
\(966\) | 8.80133e13 | 0.00336646 | ||||||||
\(967\) | −3.16167e15 | −0.120246 | −0.0601231 | − | 0.998191i | \(-0.519149\pi\) | ||||
−0.0601231 | + | 0.998191i | \(0.519149\pi\) | |||||||
\(968\) | −8.39945e15 | −0.317641 | ||||||||
\(969\) | −3.42052e15 | −0.128621 | ||||||||
\(970\) | −2.49295e15 | −0.0932114 | ||||||||
\(971\) | −1.09754e16 | −0.408051 | −0.204025 | − | 0.978966i | \(-0.565403\pi\) | ||||
−0.204025 | + | 0.978966i | \(0.565403\pi\) | |||||||
\(972\) | 7.53964e15 | 0.278731 | ||||||||
\(973\) | −2.23015e15 | −0.0819810 | ||||||||
\(974\) | 4.86043e16 | 1.77664 | ||||||||
\(975\) | 3.34564e15 | 0.121606 | ||||||||
\(976\) | −2.08542e16 | −0.753736 | ||||||||
\(977\) | −4.62054e15 | −0.166063 | −0.0830315 | − | 0.996547i | \(-0.526460\pi\) | ||||
−0.0830315 | + | 0.996547i | \(0.526460\pi\) | |||||||
\(978\) | 1.33333e15 | 0.0476512 | ||||||||
\(979\) | 8.12336e15 | 0.288689 | ||||||||
\(980\) | 9.79725e15 | 0.346227 | ||||||||
\(981\) | 4.86720e16 | 1.71041 | ||||||||
\(982\) | 3.18912e16 | 1.11444 | ||||||||
\(983\) | −6.60643e15 | −0.229574 | −0.114787 | − | 0.993390i | \(-0.536619\pi\) | ||||
−0.114787 | + | 0.993390i | \(0.536619\pi\) | |||||||
\(984\) | −1.45505e15 | −0.0502810 | ||||||||
\(985\) | 1.09240e15 | 0.0375390 | ||||||||
\(986\) | 1.92749e16 | 0.658673 | ||||||||
\(987\) | −4.68116e13 | −0.00159078 | ||||||||
\(988\) | 4.27484e16 | 1.44463 | ||||||||
\(989\) | 7.36102e14 | 0.0247376 | ||||||||
\(990\) | 5.98334e15 | 0.199963 | ||||||||
\(991\) | −4.54195e16 | −1.50951 | −0.754757 | − | 0.656004i | \(-0.772245\pi\) | ||||
−0.754757 | + | 0.656004i | \(0.772245\pi\) | |||||||
\(992\) | 7.60225e15 | 0.251263 | ||||||||
\(993\) | −6.02567e15 | −0.198054 | ||||||||
\(994\) | −1.31020e16 | −0.428264 | ||||||||
\(995\) | −4.25856e15 | −0.138432 | ||||||||
\(996\) | −3.41406e15 | −0.110368 | ||||||||
\(997\) | 3.73274e16 | 1.20006 | 0.600032 | − | 0.799976i | \(-0.295154\pi\) | ||||
0.600032 | + | 0.799976i | \(0.295154\pi\) | |||||||
\(998\) | −1.44846e16 | −0.463116 | ||||||||
\(999\) | −2.34540e15 | −0.0745774 |
(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 | 197.12.a.b.1.18 | ✓ | 92 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
197.12.a.b.1.18 | ✓ | 92 | 1.1 | even | 1 | trivial |