Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2,38,Mod(1,2)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 38, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2.1");
S:= CuspForms(chi, 38);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2 \) |
Weight: | \( k \) | \(=\) | \( 38 \) |
Character orbit: | \([\chi]\) | \(=\) | 2.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(17.3428076249\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{2} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 756643680 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{3}\cdot 5 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(27507.7\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −262144. | −0.707107 | ||||||||
\(3\) | −7.39112e8 | −1.10146 | −0.550728 | − | 0.834685i | \(-0.685650\pi\) | ||||
−0.550728 | + | 0.834685i | \(0.685650\pi\) | |||||||
\(4\) | 6.87195e10 | 0.500000 | ||||||||
\(5\) | −3.47974e12 | −0.407945 | −0.203972 | − | 0.978977i | \(-0.565385\pi\) | ||||
−0.203972 | + | 0.978977i | \(0.565385\pi\) | |||||||
\(6\) | 1.93754e14 | 0.778847 | ||||||||
\(7\) | 6.42679e15 | 1.49170 | 0.745848 | − | 0.666116i | \(-0.232045\pi\) | ||||
0.745848 | + | 0.666116i | \(0.232045\pi\) | |||||||
\(8\) | −1.80144e16 | −0.353553 | ||||||||
\(9\) | 9.60023e16 | 0.213204 | ||||||||
\(10\) | 9.12192e17 | 0.288460 | ||||||||
\(11\) | 2.60208e19 | 1.41109 | 0.705547 | − | 0.708663i | \(-0.250701\pi\) | ||||
0.705547 | + | 0.708663i | \(0.250701\pi\) | |||||||
\(12\) | −5.07914e19 | −0.550728 | ||||||||
\(13\) | −1.70663e20 | −0.420908 | −0.210454 | − | 0.977604i | \(-0.567494\pi\) | ||||
−0.210454 | + | 0.977604i | \(0.567494\pi\) | |||||||
\(14\) | −1.68474e21 | −1.05479 | ||||||||
\(15\) | 2.57191e21 | 0.449333 | ||||||||
\(16\) | 4.72237e21 | 0.250000 | ||||||||
\(17\) | −6.89990e22 | −1.18997 | −0.594987 | − | 0.803735i | \(-0.702843\pi\) | ||||
−0.594987 | + | 0.803735i | \(0.702843\pi\) | |||||||
\(18\) | −2.51664e22 | −0.150758 | ||||||||
\(19\) | −6.71981e23 | −1.48052 | −0.740261 | − | 0.672319i | \(-0.765298\pi\) | ||||
−0.740261 | + | 0.672319i | \(0.765298\pi\) | |||||||
\(20\) | −2.39126e23 | −0.203972 | ||||||||
\(21\) | −4.75011e24 | −1.64304 | ||||||||
\(22\) | −6.82120e24 | −0.997794 | ||||||||
\(23\) | 1.55339e25 | 0.998424 | 0.499212 | − | 0.866480i | \(-0.333623\pi\) | ||||
0.499212 | + | 0.866480i | \(0.333623\pi\) | |||||||
\(24\) | 1.33147e25 | 0.389423 | ||||||||
\(25\) | −6.06510e25 | −0.833581 | ||||||||
\(26\) | 4.47383e25 | 0.297627 | ||||||||
\(27\) | 2.61854e26 | 0.866621 | ||||||||
\(28\) | 4.41646e26 | 0.745848 | ||||||||
\(29\) | 1.41680e27 | 1.25010 | 0.625052 | − | 0.780583i | \(-0.285078\pi\) | ||||
0.625052 | + | 0.780583i | \(0.285078\pi\) | |||||||
\(30\) | −6.74212e26 | −0.317726 | ||||||||
\(31\) | −3.59446e27 | −0.923511 | −0.461756 | − | 0.887007i | \(-0.652780\pi\) | ||||
−0.461756 | + | 0.887007i | \(0.652780\pi\) | |||||||
\(32\) | −1.23794e27 | −0.176777 | ||||||||
\(33\) | −1.92323e28 | −1.55426 | ||||||||
\(34\) | 1.80877e28 | 0.841439 | ||||||||
\(35\) | −2.23635e28 | −0.608529 | ||||||||
\(36\) | 6.59722e27 | 0.106602 | ||||||||
\(37\) | −3.04432e28 | −0.296318 | −0.148159 | − | 0.988964i | \(-0.547335\pi\) | ||||
−0.148159 | + | 0.988964i | \(0.547335\pi\) | |||||||
\(38\) | 1.76156e29 | 1.04689 | ||||||||
\(39\) | 1.26139e29 | 0.463612 | ||||||||
\(40\) | 6.26853e28 | 0.144230 | ||||||||
\(41\) | −7.95085e28 | −0.115854 | −0.0579271 | − | 0.998321i | \(-0.518449\pi\) | ||||
−0.0579271 | + | 0.998321i | \(0.518449\pi\) | |||||||
\(42\) | 1.24521e30 | 1.16180 | ||||||||
\(43\) | −2.87613e30 | −1.73637 | −0.868186 | − | 0.496240i | \(-0.834714\pi\) | ||||
−0.868186 | + | 0.496240i | \(0.834714\pi\) | |||||||
\(44\) | 1.78814e30 | 0.705547 | ||||||||
\(45\) | −3.34062e29 | −0.0869754 | ||||||||
\(46\) | −4.07212e30 | −0.705993 | ||||||||
\(47\) | −1.27820e31 | −1.48863 | −0.744315 | − | 0.667829i | \(-0.767224\pi\) | ||||
−0.744315 | + | 0.667829i | \(0.767224\pi\) | |||||||
\(48\) | −3.49036e30 | −0.275364 | ||||||||
\(49\) | 2.27415e31 | 1.22516 | ||||||||
\(50\) | 1.58993e31 | 0.589431 | ||||||||
\(51\) | 5.09980e31 | 1.31070 | ||||||||
\(52\) | −1.17279e31 | −0.210454 | ||||||||
\(53\) | 1.70666e31 | 0.215300 | 0.107650 | − | 0.994189i | \(-0.465667\pi\) | ||||
0.107650 | + | 0.994189i | \(0.465667\pi\) | |||||||
\(54\) | −6.86434e31 | −0.612793 | ||||||||
\(55\) | −9.05455e31 | −0.575648 | ||||||||
\(56\) | −1.15775e32 | −0.527394 | ||||||||
\(57\) | 4.96669e32 | 1.63073 | ||||||||
\(58\) | −3.71406e32 | −0.883957 | ||||||||
\(59\) | −7.46370e32 | −1.29477 | −0.647384 | − | 0.762164i | \(-0.724137\pi\) | ||||
−0.647384 | + | 0.762164i | \(0.724137\pi\) | |||||||
\(60\) | 1.76741e32 | 0.224666 | ||||||||
\(61\) | −2.64957e32 | −0.248070 | −0.124035 | − | 0.992278i | \(-0.539584\pi\) | ||||
−0.124035 | + | 0.992278i | \(0.539584\pi\) | |||||||
\(62\) | 9.42266e32 | 0.653021 | ||||||||
\(63\) | 6.16986e32 | 0.318035 | ||||||||
\(64\) | 3.24519e32 | 0.125000 | ||||||||
\(65\) | 5.93862e32 | 0.171707 | ||||||||
\(66\) | 5.04163e33 | 1.09903 | ||||||||
\(67\) | 1.82198e33 | 0.300718 | 0.150359 | − | 0.988631i | \(-0.451957\pi\) | ||||
0.150359 | + | 0.988631i | \(0.451957\pi\) | |||||||
\(68\) | −4.74157e33 | −0.594987 | ||||||||
\(69\) | −1.14813e34 | −1.09972 | ||||||||
\(70\) | 5.86246e33 | 0.430295 | ||||||||
\(71\) | −7.50959e33 | −0.423972 | −0.211986 | − | 0.977273i | \(-0.567993\pi\) | ||||
−0.211986 | + | 0.977273i | \(0.567993\pi\) | |||||||
\(72\) | −1.72942e33 | −0.0753789 | ||||||||
\(73\) | −4.19120e34 | −1.41536 | −0.707678 | − | 0.706535i | \(-0.750257\pi\) | ||||
−0.707678 | + | 0.706535i | \(0.750257\pi\) | |||||||
\(74\) | 7.98050e33 | 0.209529 | ||||||||
\(75\) | 4.48279e34 | 0.918152 | ||||||||
\(76\) | −4.61782e34 | −0.740261 | ||||||||
\(77\) | 1.67230e35 | 2.10492 | ||||||||
\(78\) | −3.30666e34 | −0.327823 | ||||||||
\(79\) | 1.22253e35 | 0.957543 | 0.478772 | − | 0.877939i | \(-0.341082\pi\) | ||||
0.478772 | + | 0.877939i | \(0.341082\pi\) | |||||||
\(80\) | −1.64326e34 | −0.101986 | ||||||||
\(81\) | −2.36767e35 | −1.16775 | ||||||||
\(82\) | 2.08427e34 | 0.0819214 | ||||||||
\(83\) | −7.58400e34 | −0.238206 | −0.119103 | − | 0.992882i | \(-0.538002\pi\) | ||||
−0.119103 | + | 0.992882i | \(0.538002\pi\) | |||||||
\(84\) | −3.26425e35 | −0.821518 | ||||||||
\(85\) | 2.40098e35 | 0.485444 | ||||||||
\(86\) | 7.53961e35 | 1.22780 | ||||||||
\(87\) | −1.04717e36 | −1.37693 | ||||||||
\(88\) | −4.68749e35 | −0.498897 | ||||||||
\(89\) | 2.32524e35 | 0.200795 | 0.100398 | − | 0.994947i | \(-0.467989\pi\) | ||||
0.100398 | + | 0.994947i | \(0.467989\pi\) | |||||||
\(90\) | 8.75725e34 | 0.0615009 | ||||||||
\(91\) | −1.09682e36 | −0.627867 | ||||||||
\(92\) | 1.06748e36 | 0.499212 | ||||||||
\(93\) | 2.65671e36 | 1.01721 | ||||||||
\(94\) | 3.35071e36 | 1.05262 | ||||||||
\(95\) | 2.33832e36 | 0.603971 | ||||||||
\(96\) | 9.14976e35 | 0.194712 | ||||||||
\(97\) | −8.69459e36 | −1.52747 | −0.763734 | − | 0.645531i | \(-0.776636\pi\) | ||||
−0.763734 | + | 0.645531i | \(0.776636\pi\) | |||||||
\(98\) | −5.96154e36 | −0.866316 | ||||||||
\(99\) | 2.49806e36 | 0.300851 | ||||||||
\(100\) | −4.16791e36 | −0.416791 | ||||||||
\(101\) | 3.03773e36 | 0.252699 | 0.126349 | − | 0.991986i | \(-0.459674\pi\) | ||||
0.126349 | + | 0.991986i | \(0.459674\pi\) | |||||||
\(102\) | −1.33688e37 | −0.926807 | ||||||||
\(103\) | −1.95543e36 | −0.113176 | −0.0565878 | − | 0.998398i | \(-0.518022\pi\) | ||||
−0.0565878 | + | 0.998398i | \(0.518022\pi\) | |||||||
\(104\) | 3.07439e36 | 0.148814 | ||||||||
\(105\) | 1.65291e37 | 0.670268 | ||||||||
\(106\) | −4.47392e36 | −0.152240 | ||||||||
\(107\) | 2.09964e37 | 0.600543 | 0.300271 | − | 0.953854i | \(-0.402923\pi\) | ||||
0.300271 | + | 0.953854i | \(0.402923\pi\) | |||||||
\(108\) | 1.79945e37 | 0.433310 | ||||||||
\(109\) | 9.65773e35 | 0.0196103 | 0.00980516 | − | 0.999952i | \(-0.496879\pi\) | ||||
0.00980516 | + | 0.999952i | \(0.496879\pi\) | |||||||
\(110\) | 2.37360e37 | 0.407045 | ||||||||
\(111\) | 2.25009e37 | 0.326381 | ||||||||
\(112\) | 3.03496e37 | 0.372924 | ||||||||
\(113\) | −8.80397e37 | −0.917756 | −0.458878 | − | 0.888499i | \(-0.651749\pi\) | ||||
−0.458878 | + | 0.888499i | \(0.651749\pi\) | |||||||
\(114\) | −1.30199e38 | −1.15310 | ||||||||
\(115\) | −5.40538e37 | −0.407302 | ||||||||
\(116\) | 9.73619e37 | 0.625052 | ||||||||
\(117\) | −1.63840e37 | −0.0897392 | ||||||||
\(118\) | 1.95657e38 | 0.915540 | ||||||||
\(119\) | −4.43442e38 | −1.77508 | ||||||||
\(120\) | −4.63315e37 | −0.158863 | ||||||||
\(121\) | 3.37043e38 | 0.991187 | ||||||||
\(122\) | 6.94570e37 | 0.175412 | ||||||||
\(123\) | 5.87657e37 | 0.127608 | ||||||||
\(124\) | −2.47009e38 | −0.461756 | ||||||||
\(125\) | 4.64234e38 | 0.748000 | ||||||||
\(126\) | −1.61739e38 | −0.224885 | ||||||||
\(127\) | 1.95704e38 | 0.235088 | 0.117544 | − | 0.993068i | \(-0.462498\pi\) | ||||
0.117544 | + | 0.993068i | \(0.462498\pi\) | |||||||
\(128\) | −8.50706e37 | −0.0883883 | ||||||||
\(129\) | 2.12578e39 | 1.91254 | ||||||||
\(130\) | −1.55677e38 | −0.121415 | ||||||||
\(131\) | −2.24388e38 | −0.151873 | −0.0759367 | − | 0.997113i | \(-0.524195\pi\) | ||||
−0.0759367 | + | 0.997113i | \(0.524195\pi\) | |||||||
\(132\) | −1.32163e39 | −0.777129 | ||||||||
\(133\) | −4.31868e39 | −2.20849 | ||||||||
\(134\) | −4.77621e38 | −0.212640 | ||||||||
\(135\) | −9.11182e38 | −0.353533 | ||||||||
\(136\) | 1.24298e39 | 0.420720 | ||||||||
\(137\) | −4.45772e38 | −0.131760 | −0.0658798 | − | 0.997828i | \(-0.520985\pi\) | ||||
−0.0658798 | + | 0.997828i | \(0.520985\pi\) | |||||||
\(138\) | 3.00975e39 | 0.777619 | ||||||||
\(139\) | 1.52545e39 | 0.344846 | 0.172423 | − | 0.985023i | \(-0.444840\pi\) | ||||
0.172423 | + | 0.985023i | \(0.444840\pi\) | |||||||
\(140\) | −1.53681e39 | −0.304265 | ||||||||
\(141\) | 9.44729e39 | 1.63966 | ||||||||
\(142\) | 1.96859e39 | 0.299793 | ||||||||
\(143\) | −4.44079e39 | −0.593941 | ||||||||
\(144\) | 4.53358e38 | 0.0533010 | ||||||||
\(145\) | −4.93010e39 | −0.509973 | ||||||||
\(146\) | 1.09870e40 | 1.00081 | ||||||||
\(147\) | −1.68085e40 | −1.34945 | ||||||||
\(148\) | −2.09204e39 | −0.148159 | ||||||||
\(149\) | 2.63069e40 | 1.64484 | 0.822421 | − | 0.568879i | \(-0.192623\pi\) | ||||
0.822421 | + | 0.568879i | \(0.192623\pi\) | |||||||
\(150\) | −1.17514e40 | −0.649232 | ||||||||
\(151\) | −2.66162e40 | −1.30039 | −0.650193 | − | 0.759769i | \(-0.725312\pi\) | ||||
−0.650193 | + | 0.759769i | \(0.725312\pi\) | |||||||
\(152\) | 1.21053e40 | 0.523444 | ||||||||
\(153\) | −6.62406e39 | −0.253707 | ||||||||
\(154\) | −4.38384e40 | −1.48841 | ||||||||
\(155\) | 1.25078e40 | 0.376741 | ||||||||
\(156\) | 8.66821e39 | 0.231806 | ||||||||
\(157\) | 6.40937e40 | 1.52290 | 0.761451 | − | 0.648222i | \(-0.224487\pi\) | ||||
0.761451 | + | 0.648222i | \(0.224487\pi\) | |||||||
\(158\) | −3.20479e40 | −0.677085 | ||||||||
\(159\) | −1.26141e40 | −0.237143 | ||||||||
\(160\) | 4.30770e39 | 0.0721151 | ||||||||
\(161\) | 9.98330e40 | 1.48935 | ||||||||
\(162\) | 6.20672e40 | 0.825723 | ||||||||
\(163\) | −1.54833e41 | −1.83820 | −0.919099 | − | 0.394027i | \(-0.871082\pi\) | ||||
−0.919099 | + | 0.394027i | \(0.871082\pi\) | |||||||
\(164\) | −5.46378e39 | −0.0579271 | ||||||||
\(165\) | 6.69233e40 | 0.634051 | ||||||||
\(166\) | 1.98810e40 | 0.168437 | ||||||||
\(167\) | 2.28769e40 | 0.173437 | 0.0867185 | − | 0.996233i | \(-0.472362\pi\) | ||||
0.0867185 | + | 0.996233i | \(0.472362\pi\) | |||||||
\(168\) | 8.55705e40 | 0.580901 | ||||||||
\(169\) | −1.35275e41 | −0.822836 | ||||||||
\(170\) | −6.29403e40 | −0.343261 | ||||||||
\(171\) | −6.45117e40 | −0.315653 | ||||||||
\(172\) | −1.97646e41 | −0.868186 | ||||||||
\(173\) | −2.46815e41 | −0.973909 | −0.486955 | − | 0.873427i | \(-0.661892\pi\) | ||||
−0.486955 | + | 0.873427i | \(0.661892\pi\) | |||||||
\(174\) | 2.74511e41 | 0.973639 | ||||||||
\(175\) | −3.89791e41 | −1.24345 | ||||||||
\(176\) | 1.22880e41 | 0.352774 | ||||||||
\(177\) | 5.51651e41 | 1.42613 | ||||||||
\(178\) | −6.09549e40 | −0.141984 | ||||||||
\(179\) | 2.79681e41 | 0.587330 | 0.293665 | − | 0.955908i | \(-0.405125\pi\) | ||||
0.293665 | + | 0.955908i | \(0.405125\pi\) | |||||||
\(180\) | −2.29566e40 | −0.0434877 | ||||||||
\(181\) | 6.41750e41 | 1.09727 | 0.548633 | − | 0.836063i | \(-0.315148\pi\) | ||||
0.548633 | + | 0.836063i | \(0.315148\pi\) | |||||||
\(182\) | 2.87523e41 | 0.443969 | ||||||||
\(183\) | 1.95833e41 | 0.273238 | ||||||||
\(184\) | −2.79834e41 | −0.352996 | ||||||||
\(185\) | 1.05934e41 | 0.120881 | ||||||||
\(186\) | −6.96440e41 | −0.719274 | ||||||||
\(187\) | −1.79541e42 | −1.67917 | ||||||||
\(188\) | −8.78369e41 | −0.744315 | ||||||||
\(189\) | 1.68288e42 | 1.29273 | ||||||||
\(190\) | −6.12975e41 | −0.427072 | ||||||||
\(191\) | 1.09565e42 | 0.692712 | 0.346356 | − | 0.938103i | \(-0.387419\pi\) | ||||
0.346356 | + | 0.938103i | \(0.387419\pi\) | |||||||
\(192\) | −2.39855e41 | −0.137682 | ||||||||
\(193\) | −2.90412e42 | −1.51427 | −0.757136 | − | 0.653257i | \(-0.773402\pi\) | ||||
−0.757136 | + | 0.653257i | \(0.773402\pi\) | |||||||
\(194\) | 2.27923e42 | 1.08008 | ||||||||
\(195\) | −4.38931e41 | −0.189128 | ||||||||
\(196\) | 1.56278e42 | 0.612578 | ||||||||
\(197\) | 1.05947e42 | 0.377977 | 0.188988 | − | 0.981979i | \(-0.439479\pi\) | ||||
0.188988 | + | 0.981979i | \(0.439479\pi\) | |||||||
\(198\) | −6.54850e41 | −0.212734 | ||||||||
\(199\) | −2.86684e42 | −0.848441 | −0.424220 | − | 0.905559i | \(-0.639452\pi\) | ||||
−0.424220 | + | 0.905559i | \(0.639452\pi\) | |||||||
\(200\) | 1.09259e42 | 0.294715 | ||||||||
\(201\) | −1.34665e42 | −0.331228 | ||||||||
\(202\) | −7.96321e41 | −0.178685 | ||||||||
\(203\) | 9.10548e42 | 1.86477 | ||||||||
\(204\) | 3.50455e42 | 0.655352 | ||||||||
\(205\) | 2.76669e41 | 0.0472621 | ||||||||
\(206\) | 5.12603e41 | 0.0800272 | ||||||||
\(207\) | 1.49129e42 | 0.212868 | ||||||||
\(208\) | −8.05933e41 | −0.105227 | ||||||||
\(209\) | −1.74855e43 | −2.08916 | ||||||||
\(210\) | −4.33302e42 | −0.473951 | ||||||||
\(211\) | −1.88800e42 | −0.189137 | −0.0945686 | − | 0.995518i | \(-0.530147\pi\) | ||||
−0.0945686 | + | 0.995518i | \(0.530147\pi\) | |||||||
\(212\) | 1.17281e42 | 0.107650 | ||||||||
\(213\) | 5.55043e42 | 0.466986 | ||||||||
\(214\) | −5.50407e42 | −0.424648 | ||||||||
\(215\) | 1.00082e43 | 0.708343 | ||||||||
\(216\) | −4.71714e42 | −0.306397 | ||||||||
\(217\) | −2.31008e43 | −1.37760 | ||||||||
\(218\) | −2.53172e41 | −0.0138666 | ||||||||
\(219\) | 3.09777e43 | 1.55895 | ||||||||
\(220\) | −6.22224e42 | −0.287824 | ||||||||
\(221\) | 1.17756e43 | 0.500870 | ||||||||
\(222\) | −5.89848e42 | −0.230786 | ||||||||
\(223\) | 4.29674e43 | 1.54703 | 0.773515 | − | 0.633777i | \(-0.218496\pi\) | ||||
0.773515 | + | 0.633777i | \(0.218496\pi\) | |||||||
\(224\) | −7.95598e42 | −0.263697 | ||||||||
\(225\) | −5.82263e42 | −0.177723 | ||||||||
\(226\) | 2.30791e43 | 0.648952 | ||||||||
\(227\) | −4.38424e43 | −1.13610 | −0.568049 | − | 0.822995i | \(-0.692301\pi\) | ||||
−0.568049 | + | 0.822995i | \(0.692301\pi\) | |||||||
\(228\) | 3.41308e43 | 0.815365 | ||||||||
\(229\) | 4.31986e43 | 0.951728 | 0.475864 | − | 0.879519i | \(-0.342135\pi\) | ||||
0.475864 | + | 0.879519i | \(0.342135\pi\) | |||||||
\(230\) | 1.41699e43 | 0.288006 | ||||||||
\(231\) | −1.23602e44 | −2.31848 | ||||||||
\(232\) | −2.55228e43 | −0.441978 | ||||||||
\(233\) | −7.61369e43 | −1.21762 | −0.608808 | − | 0.793317i | \(-0.708352\pi\) | ||||
−0.608808 | + | 0.793317i | \(0.708352\pi\) | |||||||
\(234\) | 4.29498e42 | 0.0634552 | ||||||||
\(235\) | 4.44778e43 | 0.607279 | ||||||||
\(236\) | −5.12902e43 | −0.647384 | ||||||||
\(237\) | −9.03587e43 | −1.05469 | ||||||||
\(238\) | 1.16246e44 | 1.25517 | ||||||||
\(239\) | 1.50442e44 | 1.50317 | 0.751586 | − | 0.659635i | \(-0.229289\pi\) | ||||
0.751586 | + | 0.659635i | \(0.229289\pi\) | |||||||
\(240\) | 1.21455e43 | 0.112333 | ||||||||
\(241\) | 6.61898e43 | 0.566860 | 0.283430 | − | 0.958993i | \(-0.408528\pi\) | ||||
0.283430 | + | 0.958993i | \(0.408528\pi\) | |||||||
\(242\) | −8.83537e43 | −0.700875 | ||||||||
\(243\) | 5.70891e43 | 0.419601 | ||||||||
\(244\) | −1.82077e43 | −0.124035 | ||||||||
\(245\) | −7.91344e43 | −0.499796 | ||||||||
\(246\) | −1.54051e43 | −0.0902327 | ||||||||
\(247\) | 1.14682e44 | 0.623164 | ||||||||
\(248\) | 6.47520e43 | 0.326511 | ||||||||
\(249\) | 5.60542e43 | 0.262374 | ||||||||
\(250\) | −1.21696e44 | −0.528916 | ||||||||
\(251\) | −1.83205e44 | −0.739559 | −0.369780 | − | 0.929119i | \(-0.620567\pi\) | ||||
−0.369780 | + | 0.929119i | \(0.620567\pi\) | |||||||
\(252\) | 4.23990e43 | 0.159018 | ||||||||
\(253\) | 4.04204e44 | 1.40887 | ||||||||
\(254\) | −5.13025e43 | −0.166232 | ||||||||
\(255\) | −1.77459e44 | −0.534695 | ||||||||
\(256\) | 2.23007e43 | 0.0625000 | ||||||||
\(257\) | −8.05029e43 | −0.209918 | −0.104959 | − | 0.994477i | \(-0.533471\pi\) | ||||
−0.104959 | + | 0.994477i | \(0.533471\pi\) | |||||||
\(258\) | −5.57261e44 | −1.35237 | ||||||||
\(259\) | −1.95652e44 | −0.442016 | ||||||||
\(260\) | 4.08099e43 | 0.0858536 | ||||||||
\(261\) | 1.36016e44 | 0.266527 | ||||||||
\(262\) | 5.88221e43 | 0.107391 | ||||||||
\(263\) | −7.13601e44 | −1.21416 | −0.607078 | − | 0.794642i | \(-0.707658\pi\) | ||||
−0.607078 | + | 0.794642i | \(0.707658\pi\) | |||||||
\(264\) | 3.46458e44 | 0.549513 | ||||||||
\(265\) | −5.93874e43 | −0.0878305 | ||||||||
\(266\) | 1.13212e45 | 1.56164 | ||||||||
\(267\) | −1.71861e44 | −0.221167 | ||||||||
\(268\) | 1.25206e44 | 0.150359 | ||||||||
\(269\) | 1.26185e45 | 1.41445 | 0.707227 | − | 0.706986i | \(-0.249946\pi\) | ||||
0.707227 | + | 0.706986i | \(0.249946\pi\) | |||||||
\(270\) | 2.38861e44 | 0.249986 | ||||||||
\(271\) | 4.59894e43 | 0.0449496 | 0.0224748 | − | 0.999747i | \(-0.492845\pi\) | ||||
0.0224748 | + | 0.999747i | \(0.492845\pi\) | |||||||
\(272\) | −3.25838e44 | −0.297494 | ||||||||
\(273\) | 8.10669e44 | 0.691567 | ||||||||
\(274\) | 1.16857e44 | 0.0931682 | ||||||||
\(275\) | −1.57819e45 | −1.17626 | ||||||||
\(276\) | −7.88987e44 | −0.549860 | ||||||||
\(277\) | −1.16921e45 | −0.762106 | −0.381053 | − | 0.924553i | \(-0.624438\pi\) | ||||
−0.381053 | + | 0.924553i | \(0.624438\pi\) | |||||||
\(278\) | −3.99889e44 | −0.243843 | ||||||||
\(279\) | −3.45076e44 | −0.196896 | ||||||||
\(280\) | 4.02865e44 | 0.215148 | ||||||||
\(281\) | 2.11366e45 | 1.05674 | 0.528370 | − | 0.849014i | \(-0.322803\pi\) | ||||
0.528370 | + | 0.849014i | \(0.322803\pi\) | |||||||
\(282\) | −2.47655e45 | −1.15941 | ||||||||
\(283\) | 2.78101e44 | 0.121942 | 0.0609710 | − | 0.998140i | \(-0.480580\pi\) | ||||
0.0609710 | + | 0.998140i | \(0.480580\pi\) | |||||||
\(284\) | −5.16055e44 | −0.211986 | ||||||||
\(285\) | −1.72828e45 | −0.665247 | ||||||||
\(286\) | 1.16413e45 | 0.419980 | ||||||||
\(287\) | −5.10984e44 | −0.172819 | ||||||||
\(288\) | −1.18845e44 | −0.0376895 | ||||||||
\(289\) | 1.39876e45 | 0.416039 | ||||||||
\(290\) | 1.29239e45 | 0.360605 | ||||||||
\(291\) | 6.42627e45 | 1.68244 | ||||||||
\(292\) | −2.88017e45 | −0.707678 | ||||||||
\(293\) | −3.24815e45 | −0.749177 | −0.374589 | − | 0.927191i | \(-0.622216\pi\) | ||||
−0.374589 | + | 0.927191i | \(0.622216\pi\) | |||||||
\(294\) | 4.40625e45 | 0.954208 | ||||||||
\(295\) | 2.59717e45 | 0.528194 | ||||||||
\(296\) | 5.48416e44 | 0.104764 | ||||||||
\(297\) | 6.81364e45 | 1.22288 | ||||||||
\(298\) | −6.89620e45 | −1.16308 | ||||||||
\(299\) | −2.65106e45 | −0.420245 | ||||||||
\(300\) | 3.08055e45 | 0.459076 | ||||||||
\(301\) | −1.84843e46 | −2.59014 | ||||||||
\(302\) | 6.97728e45 | 0.919512 | ||||||||
\(303\) | −2.24522e45 | −0.278336 | ||||||||
\(304\) | −3.17334e45 | −0.370131 | ||||||||
\(305\) | 9.21982e44 | 0.101199 | ||||||||
\(306\) | 1.73646e45 | 0.179398 | ||||||||
\(307\) | −9.85048e44 | −0.0958070 | −0.0479035 | − | 0.998852i | \(-0.515254\pi\) | ||||
−0.0479035 | + | 0.998852i | \(0.515254\pi\) | |||||||
\(308\) | 1.14920e46 | 1.05246 | ||||||||
\(309\) | 1.44528e45 | 0.124658 | ||||||||
\(310\) | −3.27884e45 | −0.266396 | ||||||||
\(311\) | −5.05506e45 | −0.386954 | −0.193477 | − | 0.981105i | \(-0.561976\pi\) | ||||
−0.193477 | + | 0.981105i | \(0.561976\pi\) | |||||||
\(312\) | −2.27232e45 | −0.163911 | ||||||||
\(313\) | −6.66761e45 | −0.453315 | −0.226657 | − | 0.973975i | \(-0.572780\pi\) | ||||
−0.226657 | + | 0.973975i | \(0.572780\pi\) | |||||||
\(314\) | −1.68018e46 | −1.07685 | ||||||||
\(315\) | −2.14695e45 | −0.129741 | ||||||||
\(316\) | 8.40116e45 | 0.478772 | ||||||||
\(317\) | 2.02795e46 | 1.09009 | 0.545044 | − | 0.838408i | \(-0.316513\pi\) | ||||
0.545044 | + | 0.838408i | \(0.316513\pi\) | |||||||
\(318\) | 3.30672e45 | 0.167686 | ||||||||
\(319\) | 3.68663e46 | 1.76401 | ||||||||
\(320\) | −1.12924e45 | −0.0509931 | ||||||||
\(321\) | −1.55187e46 | −0.661471 | ||||||||
\(322\) | −2.61706e46 | −1.05313 | ||||||||
\(323\) | 4.63660e46 | 1.76178 | ||||||||
\(324\) | −1.62705e46 | −0.583874 | ||||||||
\(325\) | 1.03509e46 | 0.350861 | ||||||||
\(326\) | 4.05885e46 | 1.29980 | ||||||||
\(327\) | −7.13814e44 | −0.0215999 | ||||||||
\(328\) | 1.43230e45 | 0.0409607 | ||||||||
\(329\) | −8.21469e46 | −2.22058 | ||||||||
\(330\) | −1.75435e46 | −0.448342 | ||||||||
\(331\) | −6.38864e46 | −1.54380 | −0.771899 | − | 0.635745i | \(-0.780693\pi\) | ||||
−0.771899 | + | 0.635745i | \(0.780693\pi\) | |||||||
\(332\) | −5.21168e45 | −0.119103 | ||||||||
\(333\) | −2.92261e45 | −0.0631761 | ||||||||
\(334\) | −5.99703e45 | −0.122638 | ||||||||
\(335\) | −6.34001e45 | −0.122676 | ||||||||
\(336\) | −2.24318e46 | −0.410759 | ||||||||
\(337\) | 7.62763e46 | 1.32202 | 0.661008 | − | 0.750379i | \(-0.270129\pi\) | ||||
0.661008 | + | 0.750379i | \(0.270129\pi\) | |||||||
\(338\) | 3.54615e46 | 0.581833 | ||||||||
\(339\) | 6.50712e46 | 1.01087 | ||||||||
\(340\) | 1.64994e46 | 0.242722 | ||||||||
\(341\) | −9.35307e46 | −1.30316 | ||||||||
\(342\) | 1.69113e46 | 0.223200 | ||||||||
\(343\) | 2.68599e46 | 0.335864 | ||||||||
\(344\) | 5.18118e46 | 0.613900 | ||||||||
\(345\) | 3.99518e46 | 0.448625 | ||||||||
\(346\) | 6.47011e46 | 0.688658 | ||||||||
\(347\) | −9.67434e46 | −0.976171 | −0.488086 | − | 0.872796i | \(-0.662305\pi\) | ||||
−0.488086 | + | 0.872796i | \(0.662305\pi\) | |||||||
\(348\) | −7.19613e46 | −0.688467 | ||||||||
\(349\) | 1.11323e47 | 1.00998 | 0.504992 | − | 0.863124i | \(-0.331495\pi\) | ||||
0.504992 | + | 0.863124i | \(0.331495\pi\) | |||||||
\(350\) | 1.02181e47 | 0.879252 | ||||||||
\(351\) | −4.46887e46 | −0.364768 | ||||||||
\(352\) | −3.22122e46 | −0.249449 | ||||||||
\(353\) | −1.61697e47 | −1.18815 | −0.594074 | − | 0.804410i | \(-0.702481\pi\) | ||||
−0.594074 | + | 0.804410i | \(0.702481\pi\) | |||||||
\(354\) | −1.44612e47 | −1.00843 | ||||||||
\(355\) | 2.61314e46 | 0.172957 | ||||||||
\(356\) | 1.59790e46 | 0.100398 | ||||||||
\(357\) | 3.27753e47 | 1.95517 | ||||||||
\(358\) | −7.33168e46 | −0.415305 | ||||||||
\(359\) | −3.46444e47 | −1.86374 | −0.931870 | − | 0.362792i | \(-0.881823\pi\) | ||||
−0.931870 | + | 0.362792i | \(0.881823\pi\) | |||||||
\(360\) | 6.01793e45 | 0.0307504 | ||||||||
\(361\) | 2.45550e47 | 1.19195 | ||||||||
\(362\) | −1.68231e47 | −0.775884 | ||||||||
\(363\) | −2.49112e47 | −1.09175 | ||||||||
\(364\) | −7.53726e46 | −0.313933 | ||||||||
\(365\) | 1.45843e47 | 0.577387 | ||||||||
\(366\) | −5.13365e46 | −0.193208 | ||||||||
\(367\) | 3.11549e47 | 1.11482 | 0.557410 | − | 0.830237i | \(-0.311795\pi\) | ||||
0.557410 | + | 0.830237i | \(0.311795\pi\) | |||||||
\(368\) | 7.33567e46 | 0.249606 | ||||||||
\(369\) | −7.63299e45 | −0.0247006 | ||||||||
\(370\) | −2.77700e46 | −0.0854760 | ||||||||
\(371\) | 1.09684e47 | 0.321162 | ||||||||
\(372\) | 1.82568e47 | 0.508603 | ||||||||
\(373\) | −4.04595e46 | −0.107253 | −0.0536263 | − | 0.998561i | \(-0.517078\pi\) | ||||
−0.0536263 | + | 0.998561i | \(0.517078\pi\) | |||||||
\(374\) | 4.70656e47 | 1.18735 | ||||||||
\(375\) | −3.43121e47 | −0.823888 | ||||||||
\(376\) | 2.30259e47 | 0.526310 | ||||||||
\(377\) | −2.41796e47 | −0.526179 | ||||||||
\(378\) | −4.41156e47 | −0.914101 | ||||||||
\(379\) | 4.45515e47 | 0.879097 | 0.439548 | − | 0.898219i | \(-0.355139\pi\) | ||||
0.439548 | + | 0.898219i | \(0.355139\pi\) | |||||||
\(380\) | 1.60688e47 | 0.301986 | ||||||||
\(381\) | −1.44647e47 | −0.258939 | ||||||||
\(382\) | −2.87217e47 | −0.489822 | ||||||||
\(383\) | 1.15561e47 | 0.187774 | 0.0938868 | − | 0.995583i | \(-0.470071\pi\) | ||||
0.0938868 | + | 0.995583i | \(0.470071\pi\) | |||||||
\(384\) | 6.28767e46 | 0.0973558 | ||||||||
\(385\) | −5.81917e47 | −0.858692 | ||||||||
\(386\) | 7.61297e47 | 1.07075 | ||||||||
\(387\) | −2.76115e47 | −0.370201 | ||||||||
\(388\) | −5.97488e47 | −0.763734 | ||||||||
\(389\) | −5.77044e46 | −0.0703301 | −0.0351650 | − | 0.999382i | \(-0.511196\pi\) | ||||
−0.0351650 | + | 0.999382i | \(0.511196\pi\) | |||||||
\(390\) | 1.15063e47 | 0.133734 | ||||||||
\(391\) | −1.07182e48 | −1.18810 | ||||||||
\(392\) | −4.09674e47 | −0.433158 | ||||||||
\(393\) | 1.65848e47 | 0.167282 | ||||||||
\(394\) | −2.77735e47 | −0.267270 | ||||||||
\(395\) | −4.25408e47 | −0.390625 | ||||||||
\(396\) | 1.71665e47 | 0.150425 | ||||||||
\(397\) | 2.91353e47 | 0.243666 | 0.121833 | − | 0.992551i | \(-0.461123\pi\) | ||||
0.121833 | + | 0.992551i | \(0.461123\pi\) | |||||||
\(398\) | 7.51525e47 | 0.599938 | ||||||||
\(399\) | 3.19198e48 | 2.43255 | ||||||||
\(400\) | −2.86416e47 | −0.208395 | ||||||||
\(401\) | 1.08285e48 | 0.752314 | 0.376157 | − | 0.926556i | \(-0.377245\pi\) | ||||
0.376157 | + | 0.926556i | \(0.377245\pi\) | |||||||
\(402\) | 3.53015e47 | 0.234213 | ||||||||
\(403\) | 6.13441e47 | 0.388714 | ||||||||
\(404\) | 2.08751e47 | 0.126349 | ||||||||
\(405\) | 8.23888e47 | 0.476376 | ||||||||
\(406\) | −2.38695e48 | −1.31859 | ||||||||
\(407\) | −7.92156e47 | −0.418133 | ||||||||
\(408\) | −9.18698e47 | −0.463404 | ||||||||
\(409\) | −5.33536e47 | −0.257207 | −0.128603 | − | 0.991696i | \(-0.541049\pi\) | ||||
−0.128603 | + | 0.991696i | \(0.541049\pi\) | |||||||
\(410\) | −7.25270e46 | −0.0334194 | ||||||||
\(411\) | 3.29476e47 | 0.145127 | ||||||||
\(412\) | −1.34376e47 | −0.0565878 | ||||||||
\(413\) | −4.79676e48 | −1.93140 | ||||||||
\(414\) | −3.90932e47 | −0.150520 | ||||||||
\(415\) | 2.63903e47 | 0.0971750 | ||||||||
\(416\) | 2.11271e47 | 0.0744068 | ||||||||
\(417\) | −1.12748e48 | −0.379833 | ||||||||
\(418\) | 4.58371e48 | 1.47726 | ||||||||
\(419\) | 3.03589e48 | 0.936109 | 0.468055 | − | 0.883700i | \(-0.344955\pi\) | ||||
0.468055 | + | 0.883700i | \(0.344955\pi\) | |||||||
\(420\) | 1.13587e48 | 0.335134 | ||||||||
\(421\) | −5.78685e48 | −1.63389 | −0.816946 | − | 0.576714i | \(-0.804335\pi\) | ||||
−0.816946 | + | 0.576714i | \(0.804335\pi\) | |||||||
\(422\) | 4.94928e47 | 0.133740 | ||||||||
\(423\) | −1.22710e48 | −0.317382 | ||||||||
\(424\) | −3.07445e47 | −0.0761201 | ||||||||
\(425\) | 4.18486e48 | 0.991940 | ||||||||
\(426\) | −1.45501e48 | −0.330209 | ||||||||
\(427\) | −1.70283e48 | −0.370045 | ||||||||
\(428\) | 1.44286e48 | 0.300271 | ||||||||
\(429\) | 3.28224e48 | 0.654200 | ||||||||
\(430\) | −2.62359e48 | −0.500874 | ||||||||
\(431\) | 7.93042e47 | 0.145033 | 0.0725165 | − | 0.997367i | \(-0.476897\pi\) | ||||
0.0725165 | + | 0.997367i | \(0.476897\pi\) | |||||||
\(432\) | 1.23657e48 | 0.216655 | ||||||||
\(433\) | 2.27386e48 | 0.381714 | 0.190857 | − | 0.981618i | \(-0.438873\pi\) | ||||
0.190857 | + | 0.981618i | \(0.438873\pi\) | |||||||
\(434\) | 6.05574e48 | 0.974109 | ||||||||
\(435\) | 3.64389e48 | 0.561713 | ||||||||
\(436\) | 6.63674e46 | 0.00980516 | ||||||||
\(437\) | −1.04385e49 | −1.47819 | ||||||||
\(438\) | −8.12061e48 | −1.10235 | ||||||||
\(439\) | 1.05173e49 | 1.36871 | 0.684354 | − | 0.729150i | \(-0.260084\pi\) | ||||
0.684354 | + | 0.729150i | \(0.260084\pi\) | |||||||
\(440\) | 1.63112e48 | 0.203522 | ||||||||
\(441\) | 2.18323e48 | 0.261208 | ||||||||
\(442\) | −3.08690e48 | −0.354169 | ||||||||
\(443\) | −1.96518e48 | −0.216239 | −0.108119 | − | 0.994138i | \(-0.534483\pi\) | ||||
−0.108119 | + | 0.994138i | \(0.534483\pi\) | |||||||
\(444\) | 1.54625e48 | 0.163191 | ||||||||
\(445\) | −8.09123e47 | −0.0819133 | ||||||||
\(446\) | −1.12636e49 | −1.09392 | ||||||||
\(447\) | −1.94438e49 | −1.81172 | ||||||||
\(448\) | 2.08561e48 | 0.186462 | ||||||||
\(449\) | 2.75656e48 | 0.236488 | 0.118244 | − | 0.992985i | \(-0.462273\pi\) | ||||
0.118244 | + | 0.992985i | \(0.462273\pi\) | |||||||
\(450\) | 1.52637e48 | 0.125669 | ||||||||
\(451\) | −2.06887e48 | −0.163481 | ||||||||
\(452\) | −6.05004e48 | −0.458878 | ||||||||
\(453\) | 1.96723e49 | 1.43232 | ||||||||
\(454\) | 1.14930e49 | 0.803342 | ||||||||
\(455\) | 3.81663e48 | 0.256135 | ||||||||
\(456\) | −8.94719e48 | −0.576550 | ||||||||
\(457\) | 8.54404e48 | 0.528705 | 0.264353 | − | 0.964426i | \(-0.414842\pi\) | ||||
0.264353 | + | 0.964426i | \(0.414842\pi\) | |||||||
\(458\) | −1.13242e49 | −0.672973 | ||||||||
\(459\) | −1.80676e49 | −1.03126 | ||||||||
\(460\) | −3.71455e48 | −0.203651 | ||||||||
\(461\) | 3.55334e49 | 1.87141 | 0.935707 | − | 0.352778i | \(-0.114763\pi\) | ||||
0.935707 | + | 0.352778i | \(0.114763\pi\) | |||||||
\(462\) | 3.24015e49 | 1.63941 | ||||||||
\(463\) | −2.26251e49 | −1.09987 | −0.549937 | − | 0.835206i | \(-0.685348\pi\) | ||||
−0.549937 | + | 0.835206i | \(0.685348\pi\) | |||||||
\(464\) | 6.69066e48 | 0.312526 | ||||||||
\(465\) | −9.24464e48 | −0.414964 | ||||||||
\(466\) | 1.99588e49 | 0.860985 | ||||||||
\(467\) | 1.49204e49 | 0.618612 | 0.309306 | − | 0.950963i | \(-0.399903\pi\) | ||||
0.309306 | + | 0.950963i | \(0.399903\pi\) | |||||||
\(468\) | −1.12590e48 | −0.0448696 | ||||||||
\(469\) | 1.17095e49 | 0.448580 | ||||||||
\(470\) | −1.16596e49 | −0.429411 | ||||||||
\(471\) | −4.73724e49 | −1.67741 | ||||||||
\(472\) | 1.34454e49 | 0.457770 | ||||||||
\(473\) | −7.48393e49 | −2.45018 | ||||||||
\(474\) | 2.36870e49 | 0.745779 | ||||||||
\(475\) | 4.07563e49 | 1.23414 | ||||||||
\(476\) | −3.04731e49 | −0.887540 | ||||||||
\(477\) | 1.63844e48 | 0.0459028 | ||||||||
\(478\) | −3.94375e49 | −1.06290 | ||||||||
\(479\) | 1.98243e49 | 0.514033 | 0.257016 | − | 0.966407i | \(-0.417261\pi\) | ||||
0.257016 | + | 0.966407i | \(0.417261\pi\) | |||||||
\(480\) | −3.18387e48 | −0.0794316 | ||||||||
\(481\) | 5.19553e48 | 0.124723 | ||||||||
\(482\) | −1.73513e49 | −0.400831 | ||||||||
\(483\) | −7.37877e49 | −1.64045 | ||||||||
\(484\) | 2.31614e49 | 0.495594 | ||||||||
\(485\) | 3.02549e49 | 0.623122 | ||||||||
\(486\) | −1.49656e49 | −0.296703 | ||||||||
\(487\) | 7.79986e49 | 1.48868 | 0.744339 | − | 0.667802i | \(-0.232765\pi\) | ||||
0.744339 | + | 0.667802i | \(0.232765\pi\) | |||||||
\(488\) | 4.77305e48 | 0.0877060 | ||||||||
\(489\) | 1.14439e50 | 2.02469 | ||||||||
\(490\) | 2.07446e49 | 0.353409 | ||||||||
\(491\) | 6.21402e49 | 1.01945 | 0.509724 | − | 0.860338i | \(-0.329747\pi\) | ||||
0.509724 | + | 0.860338i | \(0.329747\pi\) | |||||||
\(492\) | 4.03834e48 | 0.0638042 | ||||||||
\(493\) | −9.77579e49 | −1.48759 | ||||||||
\(494\) | −3.00633e49 | −0.440644 | ||||||||
\(495\) | −8.69257e48 | −0.122730 | ||||||||
\(496\) | −1.69744e49 | −0.230878 | ||||||||
\(497\) | −4.82626e49 | −0.632437 | ||||||||
\(498\) | −1.46943e49 | −0.185526 | ||||||||
\(499\) | −1.01715e48 | −0.0123744 | −0.00618718 | − | 0.999981i | \(-0.501969\pi\) | ||||
−0.00618718 | + | 0.999981i | \(0.501969\pi\) | |||||||
\(500\) | 3.19019e49 | 0.374000 | ||||||||
\(501\) | −1.69086e49 | −0.191033 | ||||||||
\(502\) | 4.80260e49 | 0.522947 | ||||||||
\(503\) | −8.23991e48 | −0.0864798 | −0.0432399 | − | 0.999065i | \(-0.513768\pi\) | ||||
−0.0432399 | + | 0.999065i | \(0.513768\pi\) | |||||||
\(504\) | −1.11146e49 | −0.112442 | ||||||||
\(505\) | −1.05705e49 | −0.103087 | ||||||||
\(506\) | −1.05960e50 | −0.996222 | ||||||||
\(507\) | 9.99833e49 | 0.906317 | ||||||||
\(508\) | 1.34486e49 | 0.117544 | ||||||||
\(509\) | 1.50535e50 | 1.26870 | 0.634350 | − | 0.773046i | \(-0.281268\pi\) | ||||
0.634350 | + | 0.773046i | \(0.281268\pi\) | |||||||
\(510\) | 4.65199e49 | 0.378086 | ||||||||
\(511\) | −2.69360e50 | −2.11128 | ||||||||
\(512\) | −5.84601e48 | −0.0441942 | ||||||||
\(513\) | −1.75961e50 | −1.28305 | ||||||||
\(514\) | 2.11034e49 | 0.148434 | ||||||||
\(515\) | 6.80437e48 | 0.0461694 | ||||||||
\(516\) | 1.46083e50 | 0.956268 | ||||||||
\(517\) | −3.32597e50 | −2.10060 | ||||||||
\(518\) | 5.12890e49 | 0.312553 | ||||||||
\(519\) | 1.82424e50 | 1.07272 | ||||||||
\(520\) | −1.06981e49 | −0.0607077 | ||||||||
\(521\) | 1.38659e49 | 0.0759363 | 0.0379682 | − | 0.999279i | \(-0.487911\pi\) | ||||
0.0379682 | + | 0.999279i | \(0.487911\pi\) | |||||||
\(522\) | −3.56558e49 | −0.188463 | ||||||||
\(523\) | 1.22782e50 | 0.626402 | 0.313201 | − | 0.949687i | \(-0.398599\pi\) | ||||
0.313201 | + | 0.949687i | \(0.398599\pi\) | |||||||
\(524\) | −1.54199e49 | −0.0759367 | ||||||||
\(525\) | 2.88099e50 | 1.36960 | ||||||||
\(526\) | 1.87066e50 | 0.858538 | ||||||||
\(527\) | 2.48014e50 | 1.09895 | ||||||||
\(528\) | −9.08219e49 | −0.388564 | ||||||||
\(529\) | −7.62218e47 | −0.00314883 | ||||||||
\(530\) | 1.55680e49 | 0.0621056 | ||||||||
\(531\) | −7.16532e49 | −0.276050 | ||||||||
\(532\) | −2.96777e50 | −1.10424 | ||||||||
\(533\) | 1.35692e49 | 0.0487640 | ||||||||
\(534\) | 4.50525e49 | 0.156389 | ||||||||
\(535\) | −7.30618e49 | −0.244988 | ||||||||
\(536\) | −3.28219e49 | −0.106320 | ||||||||
\(537\) | −2.06716e50 | −0.646918 | ||||||||
\(538\) | −3.30785e50 | −1.00017 | ||||||||
\(539\) | 5.91752e50 | 1.72881 | ||||||||
\(540\) | −6.26159e49 | −0.176767 | ||||||||
\(541\) | −4.12270e50 | −1.12469 | −0.562344 | − | 0.826904i | \(-0.690100\pi\) | ||||
−0.562344 | + | 0.826904i | \(0.690100\pi\) | |||||||
\(542\) | −1.20558e49 | −0.0317842 | ||||||||
\(543\) | −4.74325e50 | −1.20859 | ||||||||
\(544\) | 8.54166e49 | 0.210360 | ||||||||
\(545\) | −3.36063e48 | −0.00799992 | ||||||||
\(546\) | −2.12512e50 | −0.489012 | ||||||||
\(547\) | 4.73750e50 | 1.05386 | 0.526931 | − | 0.849908i | \(-0.323343\pi\) | ||||
0.526931 | + | 0.849908i | \(0.323343\pi\) | |||||||
\(548\) | −3.06332e49 | −0.0658798 | ||||||||
\(549\) | −2.54365e49 | −0.0528895 | ||||||||
\(550\) | 4.13713e50 | 0.831743 | ||||||||
\(551\) | −9.52063e50 | −1.85081 | ||||||||
\(552\) | 2.06828e50 | 0.388810 | ||||||||
\(553\) | 7.85694e50 | 1.42836 | ||||||||
\(554\) | 3.06500e50 | 0.538890 | ||||||||
\(555\) | −7.82972e49 | −0.133145 | ||||||||
\(556\) | 1.04828e50 | 0.172423 | ||||||||
\(557\) | −1.89090e50 | −0.300848 | −0.150424 | − | 0.988622i | \(-0.548064\pi\) | ||||
−0.150424 | + | 0.988622i | \(0.548064\pi\) | |||||||
\(558\) | 9.04597e49 | 0.139227 | ||||||||
\(559\) | 4.90850e50 | 0.730853 | ||||||||
\(560\) | −1.05609e50 | −0.152132 | ||||||||
\(561\) | 1.32701e51 | 1.84953 | ||||||||
\(562\) | −5.54083e50 | −0.747228 | ||||||||
\(563\) | −6.92011e50 | −0.903041 | −0.451521 | − | 0.892261i | \(-0.649118\pi\) | ||||
−0.451521 | + | 0.892261i | \(0.649118\pi\) | |||||||
\(564\) | 6.49213e50 | 0.819830 | ||||||||
\(565\) | 3.06355e50 | 0.374394 | ||||||||
\(566\) | −7.29024e49 | −0.0862260 | ||||||||
\(567\) | −1.52165e51 | −1.74192 | ||||||||
\(568\) | 1.35281e50 | 0.149897 | ||||||||
\(569\) | 2.37823e50 | 0.255080 | 0.127540 | − | 0.991833i | \(-0.459292\pi\) | ||||
0.127540 | + | 0.991833i | \(0.459292\pi\) | |||||||
\(570\) | 4.53057e50 | 0.470401 | ||||||||
\(571\) | −9.61787e50 | −0.966742 | −0.483371 | − | 0.875416i | \(-0.660588\pi\) | ||||
−0.483371 | + | 0.875416i | \(0.660588\pi\) | |||||||
\(572\) | −3.05169e50 | −0.296971 | ||||||||
\(573\) | −8.09805e50 | −0.762992 | ||||||||
\(574\) | 1.33951e50 | 0.122202 | ||||||||
\(575\) | −9.42146e50 | −0.832268 | ||||||||
\(576\) | 3.11545e49 | 0.0266505 | ||||||||
\(577\) | 3.68489e50 | 0.305262 | 0.152631 | − | 0.988283i | \(-0.451225\pi\) | ||||
0.152631 | + | 0.988283i | \(0.451225\pi\) | |||||||
\(578\) | −3.66678e50 | −0.294184 | ||||||||
\(579\) | 2.14647e51 | 1.66790 | ||||||||
\(580\) | −3.38794e50 | −0.254987 | ||||||||
\(581\) | −4.87407e50 | −0.355331 | ||||||||
\(582\) | −1.68461e51 | −1.18966 | ||||||||
\(583\) | 4.44088e50 | 0.303809 | ||||||||
\(584\) | 7.55020e50 | 0.500404 | ||||||||
\(585\) | 5.70121e49 | 0.0366086 | ||||||||
\(586\) | 8.51482e50 | 0.529748 | ||||||||
\(587\) | 1.48680e51 | 0.896287 | 0.448144 | − | 0.893962i | \(-0.352085\pi\) | ||||
0.448144 | + | 0.893962i | \(0.352085\pi\) | |||||||
\(588\) | −1.15507e51 | −0.674727 | ||||||||
\(589\) | 2.41541e51 | 1.36728 | ||||||||
\(590\) | −6.80833e50 | −0.373490 | ||||||||
\(591\) | −7.83069e50 | −0.416324 | ||||||||
\(592\) | −1.43764e50 | −0.0740795 | ||||||||
\(593\) | −2.32937e51 | −1.16339 | −0.581696 | − | 0.813406i | \(-0.697611\pi\) | ||||
−0.581696 | + | 0.813406i | \(0.697611\pi\) | |||||||
\(594\) | −1.78616e51 | −0.864709 | ||||||||
\(595\) | 1.54306e51 | 0.724134 | ||||||||
\(596\) | 1.80780e51 | 0.822421 | ||||||||
\(597\) | 2.11892e51 | 0.934520 | ||||||||
\(598\) | 6.94959e50 | 0.297158 | ||||||||
\(599\) | −1.32479e51 | −0.549226 | −0.274613 | − | 0.961555i | \(-0.588550\pi\) | ||||
−0.274613 | + | 0.961555i | \(0.588550\pi\) | |||||||
\(600\) | −8.07547e50 | −0.324616 | ||||||||
\(601\) | 1.22549e51 | 0.477675 | 0.238837 | − | 0.971060i | \(-0.423234\pi\) | ||||
0.238837 | + | 0.971060i | \(0.423234\pi\) | |||||||
\(602\) | 4.84555e51 | 1.83150 | ||||||||
\(603\) | 1.74914e50 | 0.0641143 | ||||||||
\(604\) | −1.82905e51 | −0.650193 | ||||||||
\(605\) | −1.17282e51 | −0.404349 | ||||||||
\(606\) | 5.88571e50 | 0.196814 | ||||||||
\(607\) | −2.85022e51 | −0.924460 | −0.462230 | − | 0.886760i | \(-0.652951\pi\) | ||||
−0.462230 | + | 0.886760i | \(0.652951\pi\) | |||||||
\(608\) | 8.31872e50 | 0.261722 | ||||||||
\(609\) | −6.72997e51 | −2.05397 | ||||||||
\(610\) | −2.41692e50 | −0.0715584 | ||||||||
\(611\) | 2.18141e51 | 0.626577 | ||||||||
\(612\) | −4.55202e50 | −0.126854 | ||||||||
\(613\) | −1.66565e51 | −0.450365 | −0.225182 | − | 0.974317i | \(-0.572298\pi\) | ||||
−0.225182 | + | 0.974317i | \(0.572298\pi\) | |||||||
\(614\) | 2.58224e50 | 0.0677458 | ||||||||
\(615\) | −2.04489e50 | −0.0520571 | ||||||||
\(616\) | −3.01255e51 | −0.744203 | ||||||||
\(617\) | −4.81221e51 | −1.15364 | −0.576818 | − | 0.816873i | \(-0.695706\pi\) | ||||
−0.576818 | + | 0.816873i | \(0.695706\pi\) | |||||||
\(618\) | −3.78871e50 | −0.0881464 | ||||||||
\(619\) | 9.79976e50 | 0.221278 | 0.110639 | − | 0.993861i | \(-0.464710\pi\) | ||||
0.110639 | + | 0.993861i | \(0.464710\pi\) | |||||||
\(620\) | 8.59527e50 | 0.188371 | ||||||||
\(621\) | 4.06761e51 | 0.865255 | ||||||||
\(622\) | 1.32515e51 | 0.273618 | ||||||||
\(623\) | 1.49438e51 | 0.299525 | ||||||||
\(624\) | 5.95675e50 | 0.115903 | ||||||||
\(625\) | 2.79753e51 | 0.528439 | ||||||||
\(626\) | 1.74787e51 | 0.320542 | ||||||||
\(627\) | 1.29237e52 | 2.30111 | ||||||||
\(628\) | 4.40449e51 | 0.761451 | ||||||||
\(629\) | 2.10055e51 | 0.352611 | ||||||||
\(630\) | 5.62810e50 | 0.0917406 | ||||||||
\(631\) | −9.71711e51 | −1.53813 | −0.769066 | − | 0.639169i | \(-0.779278\pi\) | ||||
−0.769066 | + | 0.639169i | \(0.779278\pi\) | |||||||
\(632\) | −2.20231e51 | −0.338543 | ||||||||
\(633\) | 1.39544e51 | 0.208326 | ||||||||
\(634\) | −5.31615e51 | −0.770808 | ||||||||
\(635\) | −6.80997e50 | −0.0959028 | ||||||||
\(636\) | −8.66838e50 | −0.118572 | ||||||||
\(637\) | −3.88113e51 | −0.515678 | ||||||||
\(638\) | −9.66428e51 | −1.24735 | ||||||||
\(639\) | −7.20938e50 | −0.0903924 | ||||||||
\(640\) | 2.96023e50 | 0.0360575 | ||||||||
\(641\) | 6.64686e51 | 0.786580 | 0.393290 | − | 0.919415i | \(-0.371337\pi\) | ||||
0.393290 | + | 0.919415i | \(0.371337\pi\) | |||||||
\(642\) | 4.06812e51 | 0.467731 | ||||||||
\(643\) | 1.19542e52 | 1.33542 | 0.667708 | − | 0.744423i | \(-0.267275\pi\) | ||||
0.667708 | + | 0.744423i | \(0.267275\pi\) | |||||||
\(644\) | 6.86047e51 | 0.744673 | ||||||||
\(645\) | −7.39717e51 | −0.780208 | ||||||||
\(646\) | −1.21546e52 | −1.24577 | ||||||||
\(647\) | −1.25086e52 | −1.24589 | −0.622947 | − | 0.782264i | \(-0.714065\pi\) | ||||
−0.622947 | + | 0.782264i | \(0.714065\pi\) | |||||||
\(648\) | 4.26522e51 | 0.412861 | ||||||||
\(649\) | −1.94212e52 | −1.82704 | ||||||||
\(650\) | −2.71342e51 | −0.248096 | ||||||||
\(651\) | 1.70741e52 | 1.51736 | ||||||||
\(652\) | −1.06400e52 | −0.919099 | ||||||||
\(653\) | 1.24143e52 | 1.04239 | 0.521194 | − | 0.853438i | \(-0.325487\pi\) | ||||
0.521194 | + | 0.853438i | \(0.325487\pi\) | |||||||
\(654\) | 1.87122e50 | 0.0152734 | ||||||||
\(655\) | 7.80813e50 | 0.0619559 | ||||||||
\(656\) | −3.75468e50 | −0.0289636 | ||||||||
\(657\) | −4.02365e51 | −0.301759 | ||||||||
\(658\) | 2.15343e52 | 1.57019 | ||||||||
\(659\) | −1.09815e52 | −0.778538 | −0.389269 | − | 0.921124i | \(-0.627272\pi\) | ||||
−0.389269 | + | 0.921124i | \(0.627272\pi\) | |||||||
\(660\) | 4.59893e51 | 0.317025 | ||||||||
\(661\) | −6.97744e51 | −0.467702 | −0.233851 | − | 0.972272i | \(-0.575133\pi\) | ||||
−0.233851 | + | 0.972272i | \(0.575133\pi\) | |||||||
\(662\) | 1.67474e52 | 1.09163 | ||||||||
\(663\) | −8.70347e51 | −0.551686 | ||||||||
\(664\) | 1.36621e51 | 0.0842187 | ||||||||
\(665\) | 1.50279e52 | 0.900941 | ||||||||
\(666\) | 7.66146e50 | 0.0446723 | ||||||||
\(667\) | 2.20084e52 | 1.24813 | ||||||||
\(668\) | 1.57209e51 | 0.0867185 | ||||||||
\(669\) | −3.17577e52 | −1.70399 | ||||||||
\(670\) | 1.66200e51 | 0.0867453 | ||||||||
\(671\) | −6.89441e51 | −0.350050 | ||||||||
\(672\) | 5.88036e51 | 0.290450 | ||||||||
\(673\) | 3.84641e52 | 1.84832 | 0.924160 | − | 0.382006i | \(-0.124767\pi\) | ||||
0.924160 | + | 0.382006i | \(0.124767\pi\) | |||||||
\(674\) | −1.99954e52 | −0.934806 | ||||||||
\(675\) | −1.58817e52 | −0.722399 | ||||||||
\(676\) | −9.29603e51 | −0.411418 | ||||||||
\(677\) | 1.92251e52 | 0.827900 | 0.413950 | − | 0.910300i | \(-0.364149\pi\) | ||||
0.413950 | + | 0.910300i | \(0.364149\pi\) | |||||||
\(678\) | −1.70580e52 | −0.714791 | ||||||||
\(679\) | −5.58783e52 | −2.27852 | ||||||||
\(680\) | −4.32523e51 | −0.171630 | ||||||||
\(681\) | 3.24044e52 | 1.25136 | ||||||||
\(682\) | 2.45185e52 | 0.921474 | ||||||||
\(683\) | 1.99791e52 | 0.730790 | 0.365395 | − | 0.930853i | \(-0.380934\pi\) | ||||
0.365395 | + | 0.930853i | \(0.380934\pi\) | |||||||
\(684\) | −4.43321e51 | −0.157827 | ||||||||
\(685\) | 1.55117e51 | 0.0537507 | ||||||||
\(686\) | −7.04117e51 | −0.237492 | ||||||||
\(687\) | −3.19286e52 | −1.04829 | ||||||||
\(688\) | −1.35822e52 | −0.434093 | ||||||||
\(689\) | −2.91264e51 | −0.0906216 | ||||||||
\(690\) | −1.04731e52 | −0.317226 | ||||||||
\(691\) | −1.88822e52 | −0.556811 | −0.278406 | − | 0.960464i | \(-0.589806\pi\) | ||||
−0.278406 | + | 0.960464i | \(0.589806\pi\) | |||||||
\(692\) | −1.69610e52 | −0.486955 | ||||||||
\(693\) | 1.60545e52 | 0.448778 | ||||||||
\(694\) | 2.53607e52 | 0.690257 | ||||||||
\(695\) | −5.30818e51 | −0.140678 | ||||||||
\(696\) | 1.88642e52 | 0.486820 | ||||||||
\(697\) | 5.48600e51 | 0.137864 | ||||||||
\(698\) | −2.91827e52 | −0.714166 | ||||||||
\(699\) | 5.62737e52 | 1.34115 | ||||||||
\(700\) | −2.67862e52 | −0.621725 | ||||||||
\(701\) | 2.68099e52 | 0.606054 | 0.303027 | − | 0.952982i | \(-0.402003\pi\) | ||||
0.303027 | + | 0.952982i | \(0.402003\pi\) | |||||||
\(702\) | 1.17149e52 | 0.257930 | ||||||||
\(703\) | 2.04572e52 | 0.438706 | ||||||||
\(704\) | 8.44423e51 | 0.176387 | ||||||||
\(705\) | −3.28741e52 | −0.668890 | ||||||||
\(706\) | 4.23880e52 | 0.840148 | ||||||||
\(707\) | 1.95228e52 | 0.376950 | ||||||||
\(708\) | 3.79092e52 | 0.713065 | ||||||||
\(709\) | 5.13576e52 | 0.941129 | 0.470565 | − | 0.882366i | \(-0.344050\pi\) | ||||
0.470565 | + | 0.882366i | \(0.344050\pi\) | |||||||
\(710\) | −6.85019e51 | −0.122299 | ||||||||
\(711\) | 1.17366e52 | 0.204152 | ||||||||
\(712\) | −4.18879e51 | −0.0709918 | ||||||||
\(713\) | −5.58359e52 | −0.922056 | ||||||||
\(714\) | −8.59185e52 | −1.38251 | ||||||||
\(715\) | 1.54528e52 | 0.242295 | ||||||||
\(716\) | 1.92195e52 | 0.293665 | ||||||||
\(717\) | −1.11194e53 | −1.65568 | ||||||||
\(718\) | 9.08181e52 | 1.31786 | ||||||||
\(719\) | −1.27331e53 | −1.80074 | −0.900368 | − | 0.435129i | \(-0.856703\pi\) | ||||
−0.900368 | + | 0.435129i | \(0.856703\pi\) | |||||||
\(720\) | −1.57757e51 | −0.0217438 | ||||||||
\(721\) | −1.25671e52 | −0.168824 | ||||||||
\(722\) | −6.43695e52 | −0.842835 | ||||||||
\(723\) | −4.89217e52 | −0.624371 | ||||||||
\(724\) | 4.41007e52 | 0.548633 | ||||||||
\(725\) | −8.59305e52 | −1.04206 | ||||||||
\(726\) | 6.53033e52 | 0.771983 | ||||||||
\(727\) | 6.59926e51 | 0.0760517 | 0.0380258 | − | 0.999277i | \(-0.487893\pi\) | ||||
0.0380258 | + | 0.999277i | \(0.487893\pi\) | |||||||
\(728\) | 1.97585e52 | 0.221984 | ||||||||
\(729\) | 6.44174e52 | 0.705576 | ||||||||
\(730\) | −3.82318e52 | −0.408274 | ||||||||
\(731\) | 1.98450e53 | 2.06624 | ||||||||
\(732\) | 1.34576e52 | 0.136619 | ||||||||
\(733\) | 1.54131e52 | 0.152569 | 0.0762845 | − | 0.997086i | \(-0.475694\pi\) | ||||
0.0762845 | + | 0.997086i | \(0.475694\pi\) | |||||||
\(734\) | −8.16708e52 | −0.788297 | ||||||||
\(735\) | 5.84891e52 | 0.550503 | ||||||||
\(736\) | −1.92300e52 | −0.176498 | ||||||||
\(737\) | 4.74094e52 | 0.424342 | ||||||||
\(738\) | 2.00094e51 | 0.0174659 | ||||||||
\(739\) | 5.46870e52 | 0.465545 | 0.232773 | − | 0.972531i | \(-0.425220\pi\) | ||||
0.232773 | + | 0.972531i | \(0.425220\pi\) | |||||||
\(740\) | 7.27974e51 | 0.0604407 | ||||||||
\(741\) | −8.47630e52 | −0.686388 | ||||||||
\(742\) | −2.87529e52 | −0.227096 | ||||||||
\(743\) | 1.56320e53 | 1.20426 | 0.602132 | − | 0.798397i | \(-0.294318\pi\) | ||||
0.602132 | + | 0.798397i | \(0.294318\pi\) | |||||||
\(744\) | −4.78590e52 | −0.359637 | ||||||||
\(745\) | −9.15412e52 | −0.671005 | ||||||||
\(746\) | 1.06062e52 | 0.0758390 | ||||||||
\(747\) | −7.28081e51 | −0.0507865 | ||||||||
\(748\) | −1.23380e53 | −0.839583 | ||||||||
\(749\) | 1.34939e53 | 0.895827 | ||||||||
\(750\) | 8.99470e52 | 0.582577 | ||||||||
\(751\) | −1.90633e53 | −1.20465 | −0.602324 | − | 0.798252i | \(-0.705758\pi\) | ||||
−0.602324 | + | 0.798252i | \(0.705758\pi\) | |||||||
\(752\) | −6.03611e52 | −0.372158 | ||||||||
\(753\) | 1.35409e53 | 0.814592 | ||||||||
\(754\) | 6.33853e52 | 0.372065 | ||||||||
\(755\) | 9.26173e52 | 0.530486 | ||||||||
\(756\) | 1.15647e53 | 0.646367 | ||||||||
\(757\) | 7.39737e52 | 0.403463 | 0.201731 | − | 0.979441i | \(-0.435343\pi\) | ||||
0.201731 | + | 0.979441i | \(0.435343\pi\) | |||||||
\(758\) | −1.16789e53 | −0.621615 | ||||||||
\(759\) | −2.98752e53 | −1.55181 | ||||||||
\(760\) | −4.21233e52 | −0.213536 | ||||||||
\(761\) | −3.31955e53 | −1.64234 | −0.821169 | − | 0.570685i | \(-0.806678\pi\) | ||||
−0.821169 | + | 0.570685i | \(0.806678\pi\) | |||||||
\(762\) | 3.79183e52 | 0.183097 | ||||||||
\(763\) | 6.20682e51 | 0.0292526 | ||||||||
\(764\) | 7.52922e52 | 0.346356 | ||||||||
\(765\) | 2.30500e52 | 0.103498 | ||||||||
\(766\) | −3.02937e52 | −0.132776 | ||||||||
\(767\) | 1.27378e53 | 0.544979 | ||||||||
\(768\) | −1.64827e52 | −0.0688410 | ||||||||
\(769\) | −3.78094e53 | −1.54157 | −0.770783 | − | 0.637098i | \(-0.780135\pi\) | ||||
−0.770783 | + | 0.637098i | \(0.780135\pi\) | |||||||
\(770\) | 1.52546e53 | 0.607187 | ||||||||
\(771\) | 5.95006e52 | 0.231215 | ||||||||
\(772\) | −1.99569e53 | −0.757136 | ||||||||
\(773\) | 1.75568e53 | 0.650315 | 0.325158 | − | 0.945660i | \(-0.394583\pi\) | ||||
0.325158 | + | 0.945660i | \(0.394583\pi\) | |||||||
\(774\) | 7.23820e52 | 0.261772 | ||||||||
\(775\) | 2.18008e53 | 0.769822 | ||||||||
\(776\) | 1.56628e53 | 0.540041 | ||||||||
\(777\) | 1.44609e53 | 0.486861 | ||||||||
\(778\) | 1.51269e52 | 0.0497309 | ||||||||
\(779\) | 5.34282e52 | 0.171525 | ||||||||
\(780\) | −3.01631e52 | −0.0945639 | ||||||||
\(781\) | −1.95406e53 | −0.598264 | ||||||||
\(782\) | 2.80972e53 | 0.840113 | ||||||||
\(783\) | 3.70995e53 | 1.08337 | ||||||||
\(784\) | 1.07394e53 | 0.306289 | ||||||||
\(785\) | −2.23029e53 | −0.621260 | ||||||||
\(786\) | −4.34761e52 | −0.118286 | ||||||||
\(787\) | −5.64566e53 | −1.50031 | −0.750157 | − | 0.661260i | \(-0.770022\pi\) | ||||
−0.750157 | + | 0.661260i | \(0.770022\pi\) | |||||||
\(788\) | 7.28064e52 | 0.188988 | ||||||||
\(789\) | 5.27431e53 | 1.33734 | ||||||||
\(790\) | 1.11518e53 | 0.276213 | ||||||||
\(791\) | −5.65812e53 | −1.36901 | ||||||||
\(792\) | −4.50010e52 | −0.106367 | ||||||||
\(793\) | 4.52184e52 | 0.104415 | ||||||||
\(794\) | −7.63765e52 | −0.172298 | ||||||||
\(795\) | 4.38939e52 | 0.0967414 | ||||||||
\(796\) | −1.97008e53 | −0.424220 | ||||||||
\(797\) | 5.95809e53 | 1.25351 | 0.626755 | − | 0.779216i | \(-0.284383\pi\) | ||||
0.626755 | + | 0.779216i | \(0.284383\pi\) | |||||||
\(798\) | −8.36760e53 | −1.72007 | ||||||||
\(799\) | 8.81942e53 | 1.77143 | ||||||||
\(800\) | 7.50823e52 | 0.147358 | ||||||||
\(801\) | 2.23229e52 | 0.0428103 | ||||||||
\(802\) | −2.83864e53 | −0.531967 | ||||||||
\(803\) | −1.09058e54 | −1.99720 | ||||||||
\(804\) | −9.25409e52 | −0.165614 | ||||||||
\(805\) | −3.47392e53 | −0.607570 | ||||||||
\(806\) | −1.60810e53 | −0.274862 | ||||||||
\(807\) | −9.32645e53 | −1.55796 | ||||||||
\(808\) | −5.47228e52 | −0.0893425 | ||||||||
\(809\) | 5.07007e53 | 0.809033 | 0.404517 | − | 0.914531i | \(-0.367440\pi\) | ||||
0.404517 | + | 0.914531i | \(0.367440\pi\) | |||||||
\(810\) | −2.15977e53 | −0.336849 | ||||||||
\(811\) | 4.73551e53 | 0.721906 | 0.360953 | − | 0.932584i | \(-0.382451\pi\) | ||||
0.360953 | + | 0.932584i | \(0.382451\pi\) | |||||||
\(812\) | 6.25724e53 | 0.932387 | ||||||||
\(813\) | −3.39913e52 | −0.0495100 | ||||||||
\(814\) | 2.07659e53 | 0.295664 | ||||||||
\(815\) | 5.38777e53 | 0.749883 | ||||||||
\(816\) | 2.40831e53 | 0.327676 | ||||||||
\(817\) | 1.93271e54 | 2.57074 | ||||||||
\(818\) | 1.39863e53 | 0.181873 | ||||||||
\(819\) | −1.05297e53 | −0.133864 | ||||||||
\(820\) | 1.90125e52 | 0.0236311 | ||||||||
\(821\) | −1.06816e54 | −1.29804 | −0.649020 | − | 0.760771i | \(-0.724821\pi\) | ||||
−0.649020 | + | 0.760771i | \(0.724821\pi\) | |||||||
\(822\) | −8.63700e52 | −0.102621 | ||||||||
\(823\) | −6.19938e53 | −0.720197 | −0.360098 | − | 0.932914i | \(-0.617257\pi\) | ||||
−0.360098 | + | 0.932914i | \(0.617257\pi\) | |||||||
\(824\) | 3.52258e52 | 0.0400136 | ||||||||
\(825\) | 1.16646e54 | 1.29560 | ||||||||
\(826\) | 1.25744e54 | 1.36571 | ||||||||
\(827\) | −9.55114e53 | −1.01439 | −0.507193 | − | 0.861832i | \(-0.669317\pi\) | ||||
−0.507193 | + | 0.861832i | \(0.669317\pi\) | |||||||
\(828\) | 1.02481e53 | 0.106434 | ||||||||
\(829\) | −9.44288e53 | −0.959060 | −0.479530 | − | 0.877525i | \(-0.659193\pi\) | ||||
−0.479530 | + | 0.877525i | \(0.659193\pi\) | |||||||
\(830\) | −6.91806e52 | −0.0687131 | ||||||||
\(831\) | 8.64174e53 | 0.839426 | ||||||||
\(832\) | −5.53833e52 | −0.0526135 | ||||||||
\(833\) | −1.56914e54 | −1.45790 | ||||||||
\(834\) | 2.95562e53 | 0.268582 | ||||||||
\(835\) | −7.96054e52 | −0.0707527 | ||||||||
\(836\) | −1.20159e54 | −1.04458 | ||||||||
\(837\) | −9.41223e53 | −0.800334 | ||||||||
\(838\) | −7.95840e53 | −0.661929 | ||||||||
\(839\) | 3.51965e53 | 0.286354 | 0.143177 | − | 0.989697i | \(-0.454268\pi\) | ||||
0.143177 | + | 0.989697i | \(0.454268\pi\) | |||||||
\(840\) | −2.97763e53 | −0.236975 | ||||||||
\(841\) | 7.22851e53 | 0.562760 | ||||||||
\(842\) | 1.51699e54 | 1.15534 | ||||||||
\(843\) | −1.56223e54 | −1.16395 | ||||||||
\(844\) | −1.29742e53 | −0.0945686 | ||||||||
\(845\) | 4.70721e53 | 0.335672 | ||||||||
\(846\) | 3.21676e53 | 0.224423 | ||||||||
\(847\) | 2.16610e54 | 1.47855 | ||||||||
\(848\) | 8.05949e52 | 0.0538250 | ||||||||
\(849\) | −2.05548e53 | −0.134314 | ||||||||
\(850\) | −1.09704e54 | −0.701408 | ||||||||
\(851\) | −4.72901e53 | −0.295851 | ||||||||
\(852\) | 3.81422e53 | 0.233493 | ||||||||
\(853\) | −2.00062e53 | −0.119841 | −0.0599207 | − | 0.998203i | \(-0.519085\pi\) | ||||
−0.0599207 | + | 0.998203i | \(0.519085\pi\) | |||||||
\(854\) | 4.46385e53 | 0.261661 | ||||||||
\(855\) | 2.24484e53 | 0.128769 | ||||||||
\(856\) | −3.78237e53 | −0.212324 | ||||||||
\(857\) | −3.05443e54 | −1.67797 | −0.838987 | − | 0.544152i | \(-0.816851\pi\) | ||||
−0.838987 | + | 0.544152i | \(0.816851\pi\) | |||||||
\(858\) | −8.60419e53 | −0.462589 | ||||||||
\(859\) | 2.43101e54 | 1.27912 | 0.639562 | − | 0.768740i | \(-0.279116\pi\) | ||||
0.639562 | + | 0.768740i | \(0.279116\pi\) | |||||||
\(860\) | 6.87757e53 | 0.354172 | ||||||||
\(861\) | 3.77674e53 | 0.190353 | ||||||||
\(862\) | −2.07891e53 | −0.102554 | ||||||||
\(863\) | 3.92924e54 | 1.89718 | 0.948591 | − | 0.316506i | \(-0.102510\pi\) | ||||
0.948591 | + | 0.316506i | \(0.102510\pi\) | |||||||
\(864\) | −3.24159e53 | −0.153198 | ||||||||
\(865\) | 8.58851e53 | 0.397301 | ||||||||
\(866\) | −5.96080e53 | −0.269913 | ||||||||
\(867\) | −1.03384e54 | −0.458249 | ||||||||
\(868\) | −1.58748e54 | −0.688799 | ||||||||
\(869\) | 3.18112e54 | 1.35118 | ||||||||
\(870\) | −9.55224e53 | −0.397191 | ||||||||
\(871\) | −3.10945e53 | −0.126575 | ||||||||
\(872\) | −1.73978e52 | −0.00693330 | ||||||||
\(873\) | −8.34700e53 | −0.325662 | ||||||||
\(874\) | 2.73638e54 | 1.04524 | ||||||||
\(875\) | 2.98353e54 | 1.11579 | ||||||||
\(876\) | 2.12877e54 | 0.779476 | ||||||||
\(877\) | −5.07395e54 | −1.81909 | −0.909544 | − | 0.415607i | \(-0.863569\pi\) | ||||
−0.909544 | + | 0.415607i | \(0.863569\pi\) | |||||||
\(878\) | −2.75705e54 | −0.967823 | ||||||||
\(879\) | 2.40074e54 | 0.825185 | ||||||||
\(880\) | −4.27589e53 | −0.143912 | ||||||||
\(881\) | −2.84352e54 | −0.937133 | −0.468567 | − | 0.883428i | \(-0.655229\pi\) | ||||
−0.468567 | + | 0.883428i | \(0.655229\pi\) | |||||||
\(882\) | −5.72322e53 | −0.184702 | ||||||||
\(883\) | −5.21769e54 | −1.64894 | −0.824471 | − | 0.565904i | \(-0.808527\pi\) | ||||
−0.824471 | + | 0.565904i | \(0.808527\pi\) | |||||||
\(884\) | 8.09211e53 | 0.250435 | ||||||||
\(885\) | −1.91960e54 | −0.581782 | ||||||||
\(886\) | 5.15160e53 | 0.152904 | ||||||||
\(887\) | −3.57280e54 | −1.03854 | −0.519269 | − | 0.854611i | \(-0.673796\pi\) | ||||
−0.519269 | + | 0.854611i | \(0.673796\pi\) | |||||||
\(888\) | −4.05340e53 | −0.115393 | ||||||||
\(889\) | 1.25775e54 | 0.350679 | ||||||||
\(890\) | 2.12107e53 | 0.0579215 | ||||||||
\(891\) | −6.16088e54 | −1.64780 | ||||||||
\(892\) | 2.95270e54 | 0.773515 | ||||||||
\(893\) | 8.58922e54 | 2.20395 | ||||||||
\(894\) | 5.09707e54 | 1.28108 | ||||||||
\(895\) | −9.73217e53 | −0.239598 | ||||||||
\(896\) | −5.46731e53 | −0.131849 | ||||||||
\(897\) | 1.95943e54 | 0.462881 | ||||||||
\(898\) | −7.22614e53 | −0.167222 | ||||||||
\(899\) | −5.09264e54 | −1.15449 | ||||||||
\(900\) | −4.00128e53 | −0.0888614 | ||||||||
\(901\) | −1.17758e54 | −0.256202 | ||||||||
\(902\) | 5.42343e53 | 0.115599 | ||||||||
\(903\) | 1.36620e55 | 2.85292 | ||||||||
\(904\) | 1.58598e54 | 0.324476 | ||||||||
\(905\) | −2.23312e54 | −0.447624 | ||||||||
\(906\) | −5.15699e54 | −1.01280 | ||||||||
\(907\) | 3.79043e54 | 0.729380 | 0.364690 | − | 0.931129i | \(-0.381175\pi\) | ||||
0.364690 | + | 0.931129i | \(0.381175\pi\) | |||||||
\(908\) | −3.01282e54 | −0.568049 | ||||||||
\(909\) | 2.91628e53 | 0.0538763 | ||||||||
\(910\) | −1.00051e54 | −0.181115 | ||||||||
\(911\) | 5.53419e54 | 0.981667 | 0.490833 | − | 0.871253i | \(-0.336692\pi\) | ||||
0.490833 | + | 0.871253i | \(0.336692\pi\) | |||||||
\(912\) | 2.34545e54 | 0.407682 | ||||||||
\(913\) | −1.97342e54 | −0.336132 | ||||||||
\(914\) | −2.23977e54 | −0.373851 | ||||||||
\(915\) | −6.81448e53 | −0.111466 | ||||||||
\(916\) | 2.96858e54 | 0.475864 | ||||||||
\(917\) | −1.44210e54 | −0.226549 | ||||||||
\(918\) | 4.73632e54 | 0.729209 | ||||||||
\(919\) | −9.55457e54 | −1.44170 | −0.720849 | − | 0.693092i | \(-0.756248\pi\) | ||||
−0.720849 | + | 0.693092i | \(0.756248\pi\) | |||||||
\(920\) | 9.73747e53 | 0.144003 | ||||||||
\(921\) | 7.28060e53 | 0.105527 | ||||||||
\(922\) | −9.31487e54 | −1.32329 | ||||||||
\(923\) | 1.28161e54 | 0.178453 | ||||||||
\(924\) | −8.49385e54 | −1.15924 | ||||||||
\(925\) | 1.84641e54 | 0.247005 | ||||||||
\(926\) | 5.93104e54 | 0.777728 | ||||||||
\(927\) | −1.87725e53 | −0.0241295 | ||||||||
\(928\) | −1.75392e54 | −0.220989 | ||||||||
\(929\) | −2.71937e54 | −0.335875 | −0.167937 | − | 0.985798i | \(-0.553711\pi\) | ||||
−0.167937 | + | 0.985798i | \(0.553711\pi\) | |||||||
\(930\) | 2.42343e54 | 0.293424 | ||||||||
\(931\) | −1.52818e55 | −1.81387 | ||||||||
\(932\) | −5.23209e54 | −0.608808 | ||||||||
\(933\) | 3.73626e54 | 0.426213 | ||||||||
\(934\) | −3.91130e54 | −0.437425 | ||||||||
\(935\) | 6.24755e54 | 0.685007 | ||||||||
\(936\) | 2.95149e53 | 0.0317276 | ||||||||
\(937\) | 9.91981e54 | 1.04549 | 0.522746 | − | 0.852488i | \(-0.324907\pi\) | ||||
0.522746 | + | 0.852488i | \(0.324907\pi\) | |||||||
\(938\) | −3.06957e54 | −0.317194 | ||||||||
\(939\) | 4.92811e54 | 0.499306 | ||||||||
\(940\) | 3.05649e54 | 0.303639 | ||||||||
\(941\) | 1.26474e55 | 1.23195 | 0.615976 | − | 0.787765i | \(-0.288762\pi\) | ||||
0.615976 | + | 0.787765i | \(0.288762\pi\) | |||||||
\(942\) | 1.24184e55 | 1.18611 | ||||||||
\(943\) | −1.23508e54 | −0.115672 | ||||||||
\(944\) | −3.52463e54 | −0.323692 | ||||||||
\(945\) | −5.85597e54 | −0.527364 | ||||||||
\(946\) | 1.96187e55 | 1.73254 | ||||||||
\(947\) | −1.03728e55 | −0.898297 | −0.449148 | − | 0.893457i | \(-0.648273\pi\) | ||||
−0.449148 | + | 0.893457i | \(0.648273\pi\) | |||||||
\(948\) | −6.20940e54 | −0.527346 | ||||||||
\(949\) | 7.15283e54 | 0.595735 | ||||||||
\(950\) | −1.06840e55 | −0.872666 | ||||||||
\(951\) | −1.49888e55 | −1.20068 | ||||||||
\(952\) | 7.98834e54 | 0.627585 | ||||||||
\(953\) | 1.87492e55 | 1.44466 | 0.722329 | − | 0.691550i | \(-0.243072\pi\) | ||||
0.722329 | + | 0.691550i | \(0.243072\pi\) | |||||||
\(954\) | −4.29506e53 | −0.0324582 | ||||||||
\(955\) | −3.81256e54 | −0.282588 | ||||||||
\(956\) | 1.03383e55 | 0.751586 | ||||||||
\(957\) | −2.72483e55 | −1.94298 | ||||||||
\(958\) | −5.19682e54 | −0.363476 | ||||||||
\(959\) | −2.86488e54 | −0.196545 | ||||||||
\(960\) | 8.34634e53 | 0.0561666 | ||||||||
\(961\) | −2.22882e54 | −0.147127 | ||||||||
\(962\) | −1.36198e54 | −0.0881923 | ||||||||
\(963\) | 2.01570e54 | 0.128038 | ||||||||
\(964\) | 4.54853e54 | 0.283430 | ||||||||
\(965\) | 1.01056e55 | 0.617739 | ||||||||
\(966\) | 1.93430e55 | 1.15997 | ||||||||
\(967\) | 2.38613e55 | 1.40380 | 0.701900 | − | 0.712276i | \(-0.252335\pi\) | ||||
0.701900 | + | 0.712276i | \(0.252335\pi\) | |||||||
\(968\) | −6.07162e54 | −0.350438 | ||||||||
\(969\) | −3.42696e55 | −1.94053 | ||||||||
\(970\) | −7.93113e54 | −0.440614 | ||||||||
\(971\) | −1.05062e55 | −0.572650 | −0.286325 | − | 0.958133i | \(-0.592434\pi\) | ||||
−0.286325 | + | 0.958133i | \(0.592434\pi\) | |||||||
\(972\) | 3.92313e54 | 0.209801 | ||||||||
\(973\) | 9.80377e54 | 0.514406 | ||||||||
\(974\) | −2.04469e55 | −1.05265 | ||||||||
\(975\) | −7.65046e54 | −0.386458 | ||||||||
\(976\) | −1.25123e54 | −0.0620175 | ||||||||
\(977\) | 2.06489e55 | 1.00426 | 0.502131 | − | 0.864792i | \(-0.332549\pi\) | ||||
0.502131 | + | 0.864792i | \(0.332549\pi\) | |||||||
\(978\) | −2.99994e55 | −1.43167 | ||||||||
\(979\) | 6.05047e54 | 0.283341 | ||||||||
\(980\) | −5.43807e54 | −0.249898 | ||||||||
\(981\) | 9.27164e52 | 0.00418100 | ||||||||
\(982\) | −1.62897e55 | −0.720859 | ||||||||
\(983\) | −1.98554e55 | −0.862259 | −0.431130 | − | 0.902290i | \(-0.641885\pi\) | ||||
−0.431130 | + | 0.902290i | \(0.641885\pi\) | |||||||
\(984\) | −1.05863e54 | −0.0451164 | ||||||||
\(985\) | −3.68669e54 | −0.154193 | ||||||||
\(986\) | 2.56266e55 | 1.05189 | ||||||||
\(987\) | 6.07157e55 | 2.44587 | ||||||||
\(988\) | 7.88090e54 | 0.311582 | ||||||||
\(989\) | −4.46775e55 | −1.73364 | ||||||||
\(990\) | 2.27871e54 | 0.0867835 | ||||||||
\(991\) | 3.30495e55 | 1.23539 | 0.617693 | − | 0.786419i | \(-0.288067\pi\) | ||||
0.617693 | + | 0.786419i | \(0.288067\pi\) | |||||||
\(992\) | 4.44973e54 | 0.163255 | ||||||||
\(993\) | 4.72192e55 | 1.70042 | ||||||||
\(994\) | 1.26517e55 | 0.447200 | ||||||||
\(995\) | 9.97585e54 | 0.346117 | ||||||||
\(996\) | 3.85202e54 | 0.131187 | ||||||||
\(997\) | −2.73187e55 | −0.913269 | −0.456635 | − | 0.889654i | \(-0.650945\pi\) | ||||
−0.456635 | + | 0.889654i | \(0.650945\pi\) | |||||||
\(998\) | 2.66639e53 | 0.00875000 | ||||||||
\(999\) | −7.97166e54 | −0.256795 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2.38.a.a.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 18.38.a.f.1.1 | 2 | |||
4.3 | odd | 2 | 16.38.a.a.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2.38.a.a.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
16.38.a.a.1.2 | 2 | 4.3 | odd | 2 | |||
18.38.a.f.1.1 | 2 | 3.2 | odd | 2 |