Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,10,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(91.1613430010\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −12.8477 | −0.567794 | −0.283897 | − | 0.958855i | \(-0.591627\pi\) | ||||
−0.283897 | + | 0.958855i | \(0.591627\pi\) | |||||||
\(3\) | 81.0000 | 0.577350 | ||||||||
\(4\) | −346.936 | −0.677610 | ||||||||
\(5\) | −288.160 | −0.206190 | −0.103095 | − | 0.994671i | \(-0.532875\pi\) | ||||
−0.103095 | + | 0.994671i | \(0.532875\pi\) | |||||||
\(6\) | −1040.66 | −0.327816 | ||||||||
\(7\) | −11158.8 | −1.75661 | −0.878307 | − | 0.478098i | \(-0.841327\pi\) | ||||
−0.878307 | + | 0.478098i | \(0.841327\pi\) | |||||||
\(8\) | 11035.4 | 0.952537 | ||||||||
\(9\) | 6561.00 | 0.333333 | ||||||||
\(10\) | 3702.19 | 0.117074 | ||||||||
\(11\) | −5354.27 | −0.110264 | −0.0551320 | − | 0.998479i | \(-0.517558\pi\) | ||||
−0.0551320 | + | 0.998479i | \(0.517558\pi\) | |||||||
\(12\) | −28101.8 | −0.391218 | ||||||||
\(13\) | −11968.9 | −0.116228 | −0.0581139 | − | 0.998310i | \(-0.518509\pi\) | ||||
−0.0581139 | + | 0.998310i | \(0.518509\pi\) | |||||||
\(14\) | 143365. | 0.997394 | ||||||||
\(15\) | −23340.9 | −0.119044 | ||||||||
\(16\) | 35852.3 | 0.136766 | ||||||||
\(17\) | −253224. | −0.735334 | −0.367667 | − | 0.929957i | \(-0.619843\pi\) | ||||
−0.367667 | + | 0.929957i | \(0.619843\pi\) | |||||||
\(18\) | −84293.8 | −0.189265 | ||||||||
\(19\) | −368392. | −0.648514 | −0.324257 | − | 0.945969i | \(-0.605114\pi\) | ||||
−0.324257 | + | 0.945969i | \(0.605114\pi\) | |||||||
\(20\) | 99973.1 | 0.139717 | ||||||||
\(21\) | −903863. | −1.01418 | ||||||||
\(22\) | 68790.1 | 0.0626072 | ||||||||
\(23\) | −1.43580e6 | −1.06984 | −0.534920 | − | 0.844902i | \(-0.679658\pi\) | ||||
−0.534920 | + | 0.844902i | \(0.679658\pi\) | |||||||
\(24\) | 893865. | 0.549947 | ||||||||
\(25\) | −1.87009e6 | −0.957486 | ||||||||
\(26\) | 153773. | 0.0659934 | ||||||||
\(27\) | 531441. | 0.192450 | ||||||||
\(28\) | 3.87139e6 | 1.19030 | ||||||||
\(29\) | −4.56562e6 | −1.19869 | −0.599347 | − | 0.800489i | \(-0.704573\pi\) | ||||
−0.599347 | + | 0.800489i | \(0.704573\pi\) | |||||||
\(30\) | 299878. | 0.0675925 | ||||||||
\(31\) | −552087. | −0.107369 | −0.0536847 | − | 0.998558i | \(-0.517097\pi\) | ||||
−0.0536847 | + | 0.998558i | \(0.517097\pi\) | |||||||
\(32\) | −6.11073e6 | −1.03019 | ||||||||
\(33\) | −433696. | −0.0636609 | ||||||||
\(34\) | 3.25335e6 | 0.417518 | ||||||||
\(35\) | 3.21552e6 | 0.362197 | ||||||||
\(36\) | −2.27625e6 | −0.225870 | ||||||||
\(37\) | 5.14812e6 | 0.451586 | 0.225793 | − | 0.974175i | \(-0.427503\pi\) | ||||
0.225793 | + | 0.974175i | \(0.427503\pi\) | |||||||
\(38\) | 4.73300e6 | 0.368222 | ||||||||
\(39\) | −969482. | −0.0671041 | ||||||||
\(40\) | −3.17995e6 | −0.196404 | ||||||||
\(41\) | −1.80732e7 | −0.998865 | −0.499432 | − | 0.866353i | \(-0.666458\pi\) | ||||
−0.499432 | + | 0.866353i | \(0.666458\pi\) | |||||||
\(42\) | 1.16126e7 | 0.575846 | ||||||||
\(43\) | −1.18322e7 | −0.527787 | −0.263893 | − | 0.964552i | \(-0.585007\pi\) | ||||
−0.263893 | + | 0.964552i | \(0.585007\pi\) | |||||||
\(44\) | 1.85759e6 | 0.0747159 | ||||||||
\(45\) | −1.89062e6 | −0.0687301 | ||||||||
\(46\) | 1.84468e7 | 0.607449 | ||||||||
\(47\) | 3.30018e7 | 0.986500 | 0.493250 | − | 0.869888i | \(-0.335809\pi\) | ||||
0.493250 | + | 0.869888i | \(0.335809\pi\) | |||||||
\(48\) | 2.90403e6 | 0.0789617 | ||||||||
\(49\) | 8.41652e7 | 2.08569 | ||||||||
\(50\) | 2.40264e7 | 0.543654 | ||||||||
\(51\) | −2.05111e7 | −0.424545 | ||||||||
\(52\) | 4.15245e6 | 0.0787571 | ||||||||
\(53\) | −4.28341e7 | −0.745673 | −0.372836 | − | 0.927897i | \(-0.621615\pi\) | ||||
−0.372836 | + | 0.927897i | \(0.621615\pi\) | |||||||
\(54\) | −6.82780e6 | −0.109272 | ||||||||
\(55\) | 1.54289e6 | 0.0227354 | ||||||||
\(56\) | −1.23141e8 | −1.67324 | ||||||||
\(57\) | −2.98398e7 | −0.374420 | ||||||||
\(58\) | 5.86577e7 | 0.680612 | ||||||||
\(59\) | −1.21174e7 | −0.130189 | ||||||||
\(60\) | 8.09782e6 | 0.0806655 | ||||||||
\(61\) | 9.99497e7 | 0.924266 | 0.462133 | − | 0.886811i | \(-0.347084\pi\) | ||||
0.462133 | + | 0.886811i | \(0.347084\pi\) | |||||||
\(62\) | 7.09306e6 | 0.0609636 | ||||||||
\(63\) | −7.32129e7 | −0.585538 | ||||||||
\(64\) | 6.01525e7 | 0.448171 | ||||||||
\(65\) | 3.44896e6 | 0.0239650 | ||||||||
\(66\) | 5.57200e6 | 0.0361463 | ||||||||
\(67\) | −1.80984e8 | −1.09724 | −0.548622 | − | 0.836070i | \(-0.684848\pi\) | ||||
−0.548622 | + | 0.836070i | \(0.684848\pi\) | |||||||
\(68\) | 8.78526e7 | 0.498270 | ||||||||
\(69\) | −1.16300e8 | −0.617673 | ||||||||
\(70\) | −4.13120e7 | −0.205653 | ||||||||
\(71\) | −2.83834e8 | −1.32557 | −0.662784 | − | 0.748811i | \(-0.730625\pi\) | ||||
−0.662784 | + | 0.748811i | \(0.730625\pi\) | |||||||
\(72\) | 7.24030e7 | 0.317512 | ||||||||
\(73\) | −1.11541e8 | −0.459706 | −0.229853 | − | 0.973225i | \(-0.573825\pi\) | ||||
−0.229853 | + | 0.973225i | \(0.573825\pi\) | |||||||
\(74\) | −6.61415e7 | −0.256408 | ||||||||
\(75\) | −1.51477e8 | −0.552805 | ||||||||
\(76\) | 1.27809e8 | 0.439440 | ||||||||
\(77\) | 5.97473e7 | 0.193691 | ||||||||
\(78\) | 1.24556e7 | 0.0381013 | ||||||||
\(79\) | 4.87439e8 | 1.40799 | 0.703993 | − | 0.710206i | \(-0.251398\pi\) | ||||
0.703993 | + | 0.710206i | \(0.251398\pi\) | |||||||
\(80\) | −1.03312e7 | −0.0281997 | ||||||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | 2.32199e8 | 0.567149 | ||||||||
\(83\) | 7.30631e7 | 0.168984 | 0.0844922 | − | 0.996424i | \(-0.473073\pi\) | ||||
0.0844922 | + | 0.996424i | \(0.473073\pi\) | |||||||
\(84\) | 3.13583e8 | 0.687220 | ||||||||
\(85\) | 7.29690e7 | 0.151619 | ||||||||
\(86\) | 1.52017e8 | 0.299674 | ||||||||
\(87\) | −3.69815e8 | −0.692067 | ||||||||
\(88\) | −5.90864e7 | −0.105030 | ||||||||
\(89\) | 6.25788e8 | 1.05724 | 0.528619 | − | 0.848859i | \(-0.322710\pi\) | ||||
0.528619 | + | 0.848859i | \(0.322710\pi\) | |||||||
\(90\) | 2.42901e7 | 0.0390245 | ||||||||
\(91\) | 1.33559e8 | 0.204167 | ||||||||
\(92\) | 4.98132e8 | 0.724935 | ||||||||
\(93\) | −4.47191e7 | −0.0619897 | ||||||||
\(94\) | −4.23997e8 | −0.560129 | ||||||||
\(95\) | 1.06156e8 | 0.133717 | ||||||||
\(96\) | −4.94969e8 | −0.594781 | ||||||||
\(97\) | 1.65134e8 | 0.189393 | 0.0946965 | − | 0.995506i | \(-0.469812\pi\) | ||||
0.0946965 | + | 0.995506i | \(0.469812\pi\) | |||||||
\(98\) | −1.08133e9 | −1.18424 | ||||||||
\(99\) | −3.51294e7 | −0.0367546 | ||||||||
\(100\) | 6.48802e8 | 0.648802 | ||||||||
\(101\) | 8.61651e7 | 0.0823920 | 0.0411960 | − | 0.999151i | \(-0.486883\pi\) | ||||
0.0411960 | + | 0.999151i | \(0.486883\pi\) | |||||||
\(102\) | 2.63521e8 | 0.241054 | ||||||||
\(103\) | −4.41594e8 | −0.386595 | −0.193297 | − | 0.981140i | \(-0.561918\pi\) | ||||
−0.193297 | + | 0.981140i | \(0.561918\pi\) | |||||||
\(104\) | −1.32081e8 | −0.110711 | ||||||||
\(105\) | 2.60457e8 | 0.209114 | ||||||||
\(106\) | 5.50320e8 | 0.423388 | ||||||||
\(107\) | −1.38847e9 | −1.02402 | −0.512012 | − | 0.858978i | \(-0.671100\pi\) | ||||
−0.512012 | + | 0.858978i | \(0.671100\pi\) | |||||||
\(108\) | −1.84376e8 | −0.130406 | ||||||||
\(109\) | −2.18603e9 | −1.48333 | −0.741664 | − | 0.670771i | \(-0.765963\pi\) | ||||
−0.741664 | + | 0.670771i | \(0.765963\pi\) | |||||||
\(110\) | −1.98226e7 | −0.0129090 | ||||||||
\(111\) | 4.16998e8 | 0.260724 | ||||||||
\(112\) | −4.00068e8 | −0.240244 | ||||||||
\(113\) | 2.86843e9 | 1.65498 | 0.827488 | − | 0.561483i | \(-0.189769\pi\) | ||||
0.827488 | + | 0.561483i | \(0.189769\pi\) | |||||||
\(114\) | 3.83373e8 | 0.212593 | ||||||||
\(115\) | 4.13740e8 | 0.220591 | ||||||||
\(116\) | 1.58398e9 | 0.812248 | ||||||||
\(117\) | −7.85281e7 | −0.0387426 | ||||||||
\(118\) | 1.55680e8 | 0.0739205 | ||||||||
\(119\) | 2.82568e9 | 1.29170 | ||||||||
\(120\) | −2.57576e8 | −0.113394 | ||||||||
\(121\) | −2.32928e9 | −0.987842 | ||||||||
\(122\) | −1.28412e9 | −0.524793 | ||||||||
\(123\) | −1.46393e9 | −0.576695 | ||||||||
\(124\) | 1.91539e8 | 0.0727545 | ||||||||
\(125\) | 1.10170e9 | 0.403615 | ||||||||
\(126\) | 9.40618e8 | 0.332465 | ||||||||
\(127\) | 4.81144e9 | 1.64119 | 0.820595 | − | 0.571510i | \(-0.193642\pi\) | ||||
0.820595 | + | 0.571510i | \(0.193642\pi\) | |||||||
\(128\) | 2.35587e9 | 0.775723 | ||||||||
\(129\) | −9.58410e8 | −0.304718 | ||||||||
\(130\) | −4.43112e7 | −0.0136072 | ||||||||
\(131\) | 3.84589e9 | 1.14098 | 0.570488 | − | 0.821306i | \(-0.306754\pi\) | ||||
0.570488 | + | 0.821306i | \(0.306754\pi\) | |||||||
\(132\) | 1.50465e8 | 0.0431373 | ||||||||
\(133\) | 4.11082e9 | 1.13919 | ||||||||
\(134\) | 2.32523e9 | 0.623009 | ||||||||
\(135\) | −1.53140e8 | −0.0396814 | ||||||||
\(136\) | −2.79442e9 | −0.700433 | ||||||||
\(137\) | 4.88795e9 | 1.18545 | 0.592727 | − | 0.805404i | \(-0.298051\pi\) | ||||
0.592727 | + | 0.805404i | \(0.298051\pi\) | |||||||
\(138\) | 1.49419e9 | 0.350711 | ||||||||
\(139\) | 4.04703e9 | 0.919539 | 0.459769 | − | 0.888038i | \(-0.347932\pi\) | ||||
0.459769 | + | 0.888038i | \(0.347932\pi\) | |||||||
\(140\) | −1.11558e9 | −0.245428 | ||||||||
\(141\) | 2.67314e9 | 0.569556 | ||||||||
\(142\) | 3.64662e9 | 0.752649 | ||||||||
\(143\) | 6.40848e7 | 0.0128157 | ||||||||
\(144\) | 2.35227e8 | 0.0455885 | ||||||||
\(145\) | 1.31563e9 | 0.247159 | ||||||||
\(146\) | 1.43304e9 | 0.261018 | ||||||||
\(147\) | 6.81738e9 | 1.20417 | ||||||||
\(148\) | −1.78607e9 | −0.305999 | ||||||||
\(149\) | 4.92185e9 | 0.818070 | 0.409035 | − | 0.912519i | \(-0.365865\pi\) | ||||
0.409035 | + | 0.912519i | \(0.365865\pi\) | |||||||
\(150\) | 1.94613e9 | 0.313879 | ||||||||
\(151\) | 7.11467e9 | 1.11367 | 0.556837 | − | 0.830621i | \(-0.312015\pi\) | ||||
0.556837 | + | 0.830621i | \(0.312015\pi\) | |||||||
\(152\) | −4.06534e9 | −0.617733 | ||||||||
\(153\) | −1.66140e9 | −0.245111 | ||||||||
\(154\) | −7.67615e8 | −0.109977 | ||||||||
\(155\) | 1.59089e8 | 0.0221385 | ||||||||
\(156\) | 3.36349e8 | 0.0454704 | ||||||||
\(157\) | 7.84897e9 | 1.03101 | 0.515507 | − | 0.856886i | \(-0.327604\pi\) | ||||
0.515507 | + | 0.856886i | \(0.327604\pi\) | |||||||
\(158\) | −6.26248e9 | −0.799446 | ||||||||
\(159\) | −3.46956e9 | −0.430514 | ||||||||
\(160\) | 1.76087e9 | 0.212416 | ||||||||
\(161\) | 1.60218e10 | 1.87930 | ||||||||
\(162\) | −5.53052e8 | −0.0630882 | ||||||||
\(163\) | 1.00224e10 | 1.11206 | 0.556029 | − | 0.831163i | \(-0.312324\pi\) | ||||
0.556029 | + | 0.831163i | \(0.312324\pi\) | |||||||
\(164\) | 6.27023e9 | 0.676841 | ||||||||
\(165\) | 1.24974e8 | 0.0131263 | ||||||||
\(166\) | −9.38693e8 | −0.0959483 | ||||||||
\(167\) | −5.55108e9 | −0.552273 | −0.276136 | − | 0.961118i | \(-0.589054\pi\) | ||||
−0.276136 | + | 0.961118i | \(0.589054\pi\) | |||||||
\(168\) | −9.97445e9 | −0.966045 | ||||||||
\(169\) | −1.04612e10 | −0.986491 | ||||||||
\(170\) | −9.37484e8 | −0.0860882 | ||||||||
\(171\) | −2.41702e9 | −0.216171 | ||||||||
\(172\) | 4.10503e9 | 0.357634 | ||||||||
\(173\) | −5.37563e9 | −0.456270 | −0.228135 | − | 0.973629i | \(-0.573263\pi\) | ||||
−0.228135 | + | 0.973629i | \(0.573263\pi\) | |||||||
\(174\) | 4.75128e9 | 0.392951 | ||||||||
\(175\) | 2.08679e10 | 1.68193 | ||||||||
\(176\) | −1.91963e8 | −0.0150803 | ||||||||
\(177\) | −9.81506e8 | −0.0751646 | ||||||||
\(178\) | −8.03995e9 | −0.600293 | ||||||||
\(179\) | −1.07723e10 | −0.784275 | −0.392137 | − | 0.919907i | \(-0.628264\pi\) | ||||
−0.392137 | + | 0.919907i | \(0.628264\pi\) | |||||||
\(180\) | 6.55924e8 | 0.0465722 | ||||||||
\(181\) | −2.27451e10 | −1.57520 | −0.787598 | − | 0.616189i | \(-0.788676\pi\) | ||||
−0.787598 | + | 0.616189i | \(0.788676\pi\) | |||||||
\(182\) | −1.71592e9 | −0.115925 | ||||||||
\(183\) | 8.09592e9 | 0.533625 | ||||||||
\(184\) | −1.58446e10 | −1.01906 | ||||||||
\(185\) | −1.48348e9 | −0.0931128 | ||||||||
\(186\) | 5.74538e8 | 0.0351974 | ||||||||
\(187\) | 1.35583e9 | 0.0810808 | ||||||||
\(188\) | −1.14495e10 | −0.668462 | ||||||||
\(189\) | −5.93024e9 | −0.338060 | ||||||||
\(190\) | −1.36386e9 | −0.0759239 | ||||||||
\(191\) | −4.63754e9 | −0.252138 | −0.126069 | − | 0.992021i | \(-0.540236\pi\) | ||||
−0.126069 | + | 0.992021i | \(0.540236\pi\) | |||||||
\(192\) | 4.87235e9 | 0.258752 | ||||||||
\(193\) | 1.78697e10 | 0.927066 | 0.463533 | − | 0.886080i | \(-0.346582\pi\) | ||||
0.463533 | + | 0.886080i | \(0.346582\pi\) | |||||||
\(194\) | −2.12159e9 | −0.107536 | ||||||||
\(195\) | 2.79366e8 | 0.0138362 | ||||||||
\(196\) | −2.92000e10 | −1.41329 | ||||||||
\(197\) | 5.80897e9 | 0.274790 | 0.137395 | − | 0.990516i | \(-0.456127\pi\) | ||||
0.137395 | + | 0.990516i | \(0.456127\pi\) | |||||||
\(198\) | 4.51332e8 | 0.0208691 | ||||||||
\(199\) | 2.52274e9 | 0.114034 | 0.0570168 | − | 0.998373i | \(-0.481841\pi\) | ||||
0.0570168 | + | 0.998373i | \(0.481841\pi\) | |||||||
\(200\) | −2.06371e10 | −0.912040 | ||||||||
\(201\) | −1.46597e10 | −0.633495 | ||||||||
\(202\) | −1.10702e9 | −0.0467817 | ||||||||
\(203\) | 5.09468e10 | 2.10564 | ||||||||
\(204\) | 7.11606e9 | 0.287676 | ||||||||
\(205\) | 5.20796e9 | 0.205956 | ||||||||
\(206\) | 5.67347e9 | 0.219506 | ||||||||
\(207\) | −9.42029e9 | −0.356614 | ||||||||
\(208\) | −4.29113e8 | −0.0158960 | ||||||||
\(209\) | 1.97247e9 | 0.0715077 | ||||||||
\(210\) | −3.34627e9 | −0.118734 | ||||||||
\(211\) | −2.26437e10 | −0.786459 | −0.393230 | − | 0.919440i | \(-0.628642\pi\) | ||||
−0.393230 | + | 0.919440i | \(0.628642\pi\) | |||||||
\(212\) | 1.48607e10 | 0.505275 | ||||||||
\(213\) | −2.29906e10 | −0.765317 | ||||||||
\(214\) | 1.78387e10 | 0.581435 | ||||||||
\(215\) | 3.40957e9 | 0.108825 | ||||||||
\(216\) | 5.86465e9 | 0.183316 | ||||||||
\(217\) | 6.16063e9 | 0.188606 | ||||||||
\(218\) | 2.80855e10 | 0.842225 | ||||||||
\(219\) | −9.03479e9 | −0.265412 | ||||||||
\(220\) | −5.35283e8 | −0.0154057 | ||||||||
\(221\) | 3.03082e9 | 0.0854662 | ||||||||
\(222\) | −5.35746e9 | −0.148037 | ||||||||
\(223\) | −5.70112e10 | −1.54379 | −0.771895 | − | 0.635750i | \(-0.780691\pi\) | ||||
−0.771895 | + | 0.635750i | \(0.780691\pi\) | |||||||
\(224\) | 6.81884e10 | 1.80965 | ||||||||
\(225\) | −1.22697e10 | −0.319162 | ||||||||
\(226\) | −3.68528e10 | −0.939685 | ||||||||
\(227\) | 4.70965e9 | 0.117726 | 0.0588629 | − | 0.998266i | \(-0.481253\pi\) | ||||
0.0588629 | + | 0.998266i | \(0.481253\pi\) | |||||||
\(228\) | 1.03525e10 | 0.253711 | ||||||||
\(229\) | −9.30975e9 | −0.223706 | −0.111853 | − | 0.993725i | \(-0.535679\pi\) | ||||
−0.111853 | + | 0.993725i | \(0.535679\pi\) | |||||||
\(230\) | −5.31561e9 | −0.125250 | ||||||||
\(231\) | 4.83953e9 | 0.111828 | ||||||||
\(232\) | −5.03833e10 | −1.14180 | ||||||||
\(233\) | −2.22868e10 | −0.495388 | −0.247694 | − | 0.968838i | \(-0.579673\pi\) | ||||
−0.247694 | + | 0.968838i | \(0.579673\pi\) | |||||||
\(234\) | 1.00891e9 | 0.0219978 | ||||||||
\(235\) | −9.50979e9 | −0.203407 | ||||||||
\(236\) | 4.20395e9 | 0.0882173 | ||||||||
\(237\) | 3.94826e10 | 0.812902 | ||||||||
\(238\) | −3.63035e10 | −0.733418 | ||||||||
\(239\) | 6.22197e10 | 1.23349 | 0.616747 | − | 0.787161i | \(-0.288450\pi\) | ||||
0.616747 | + | 0.787161i | \(0.288450\pi\) | |||||||
\(240\) | −8.36826e8 | −0.0162811 | ||||||||
\(241\) | −7.82772e10 | −1.49471 | −0.747357 | − | 0.664422i | \(-0.768678\pi\) | ||||
−0.747357 | + | 0.664422i | \(0.768678\pi\) | |||||||
\(242\) | 2.99259e10 | 0.560891 | ||||||||
\(243\) | 3.48678e9 | 0.0641500 | ||||||||
\(244\) | −3.46762e10 | −0.626292 | ||||||||
\(245\) | −2.42530e10 | −0.430049 | ||||||||
\(246\) | 1.88081e10 | 0.327444 | ||||||||
\(247\) | 4.40926e9 | 0.0753753 | ||||||||
\(248\) | −6.09248e9 | −0.102273 | ||||||||
\(249\) | 5.91811e9 | 0.0975632 | ||||||||
\(250\) | −1.41543e10 | −0.229170 | ||||||||
\(251\) | −4.20358e10 | −0.668479 | −0.334239 | − | 0.942488i | \(-0.608479\pi\) | ||||
−0.334239 | + | 0.942488i | \(0.608479\pi\) | |||||||
\(252\) | 2.54002e10 | 0.396766 | ||||||||
\(253\) | 7.68767e9 | 0.117965 | ||||||||
\(254\) | −6.18160e10 | −0.931857 | ||||||||
\(255\) | 5.91049e9 | 0.0875372 | ||||||||
\(256\) | −6.10656e10 | −0.888621 | ||||||||
\(257\) | 3.72649e10 | 0.532845 | 0.266423 | − | 0.963856i | \(-0.414158\pi\) | ||||
0.266423 | + | 0.963856i | \(0.414158\pi\) | |||||||
\(258\) | 1.23134e10 | 0.173017 | ||||||||
\(259\) | −5.74468e10 | −0.793263 | ||||||||
\(260\) | −1.19657e9 | −0.0162390 | ||||||||
\(261\) | −2.99550e10 | −0.399565 | ||||||||
\(262\) | −4.94109e10 | −0.647839 | ||||||||
\(263\) | −3.73389e9 | −0.0481239 | −0.0240619 | − | 0.999710i | \(-0.507660\pi\) | ||||
−0.0240619 | + | 0.999710i | \(0.507660\pi\) | |||||||
\(264\) | −4.78599e9 | −0.0606394 | ||||||||
\(265\) | 1.23431e10 | 0.153751 | ||||||||
\(266\) | −5.28146e10 | −0.646824 | ||||||||
\(267\) | 5.06889e10 | 0.610396 | ||||||||
\(268\) | 6.27899e10 | 0.743504 | ||||||||
\(269\) | −9.73102e10 | −1.13311 | −0.566556 | − | 0.824023i | \(-0.691725\pi\) | ||||
−0.566556 | + | 0.824023i | \(0.691725\pi\) | |||||||
\(270\) | 1.96750e9 | 0.0225308 | ||||||||
\(271\) | 1.33771e11 | 1.50661 | 0.753305 | − | 0.657671i | \(-0.228458\pi\) | ||||
0.753305 | + | 0.657671i | \(0.228458\pi\) | |||||||
\(272\) | −9.07866e9 | −0.100568 | ||||||||
\(273\) | 1.08183e10 | 0.117876 | ||||||||
\(274\) | −6.27990e10 | −0.673093 | ||||||||
\(275\) | 1.00130e10 | 0.105576 | ||||||||
\(276\) | 4.03487e10 | 0.418541 | ||||||||
\(277\) | 2.30470e10 | 0.235210 | 0.117605 | − | 0.993060i | \(-0.462478\pi\) | ||||
0.117605 | + | 0.993060i | \(0.462478\pi\) | |||||||
\(278\) | −5.19951e10 | −0.522109 | ||||||||
\(279\) | −3.62225e9 | −0.0357898 | ||||||||
\(280\) | 3.54844e10 | 0.345006 | ||||||||
\(281\) | 6.46954e10 | 0.619006 | 0.309503 | − | 0.950899i | \(-0.399837\pi\) | ||||
0.309503 | + | 0.950899i | \(0.399837\pi\) | |||||||
\(282\) | −3.43438e10 | −0.323390 | ||||||||
\(283\) | −2.08643e10 | −0.193359 | −0.0966796 | − | 0.995316i | \(-0.530822\pi\) | ||||
−0.0966796 | + | 0.995316i | \(0.530822\pi\) | |||||||
\(284\) | 9.84723e10 | 0.898218 | ||||||||
\(285\) | 8.59862e9 | 0.0772017 | ||||||||
\(286\) | −8.23343e8 | −0.00727669 | ||||||||
\(287\) | 2.01675e11 | 1.75462 | ||||||||
\(288\) | −4.00925e10 | −0.343397 | ||||||||
\(289\) | −5.44655e10 | −0.459284 | ||||||||
\(290\) | −1.69028e10 | −0.140336 | ||||||||
\(291\) | 1.33759e10 | 0.109346 | ||||||||
\(292\) | 3.86975e10 | 0.311502 | ||||||||
\(293\) | −1.83552e11 | −1.45497 | −0.727486 | − | 0.686123i | \(-0.759311\pi\) | ||||
−0.727486 | + | 0.686123i | \(0.759311\pi\) | |||||||
\(294\) | −8.75877e10 | −0.683723 | ||||||||
\(295\) | 3.49174e9 | 0.0268437 | ||||||||
\(296\) | 5.68114e10 | 0.430153 | ||||||||
\(297\) | −2.84548e9 | −0.0212203 | ||||||||
\(298\) | −6.32345e10 | −0.464495 | ||||||||
\(299\) | 1.71850e10 | 0.124345 | ||||||||
\(300\) | 5.25530e10 | 0.374586 | ||||||||
\(301\) | 1.32033e11 | 0.927117 | ||||||||
\(302\) | −9.14072e10 | −0.632338 | ||||||||
\(303\) | 6.97937e9 | 0.0475690 | ||||||||
\(304\) | −1.32077e10 | −0.0886944 | ||||||||
\(305\) | −2.88015e10 | −0.190575 | ||||||||
\(306\) | 2.13452e10 | 0.139173 | ||||||||
\(307\) | 1.37976e10 | 0.0886503 | 0.0443251 | − | 0.999017i | \(-0.485886\pi\) | ||||
0.0443251 | + | 0.999017i | \(0.485886\pi\) | |||||||
\(308\) | −2.07285e10 | −0.131247 | ||||||||
\(309\) | −3.57691e10 | −0.223201 | ||||||||
\(310\) | −2.04393e9 | −0.0125701 | ||||||||
\(311\) | −1.38946e10 | −0.0842217 | −0.0421109 | − | 0.999113i | \(-0.513408\pi\) | ||||
−0.0421109 | + | 0.999113i | \(0.513408\pi\) | |||||||
\(312\) | −1.06986e10 | −0.0639191 | ||||||||
\(313\) | −2.49015e11 | −1.46648 | −0.733238 | − | 0.679972i | \(-0.761992\pi\) | ||||
−0.733238 | + | 0.679972i | \(0.761992\pi\) | |||||||
\(314\) | −1.00841e11 | −0.585403 | ||||||||
\(315\) | 2.10970e10 | 0.120732 | ||||||||
\(316\) | −1.69110e11 | −0.954066 | ||||||||
\(317\) | 2.53996e11 | 1.41273 | 0.706365 | − | 0.707847i | \(-0.250334\pi\) | ||||
0.706365 | + | 0.707847i | \(0.250334\pi\) | |||||||
\(318\) | 4.45759e10 | 0.244443 | ||||||||
\(319\) | 2.44456e10 | 0.132173 | ||||||||
\(320\) | −1.73335e10 | −0.0924085 | ||||||||
\(321\) | −1.12466e11 | −0.591221 | ||||||||
\(322\) | −2.05844e11 | −1.06705 | ||||||||
\(323\) | 9.32858e10 | 0.476874 | ||||||||
\(324\) | −1.49345e10 | −0.0752900 | ||||||||
\(325\) | 2.23829e10 | 0.111286 | ||||||||
\(326\) | −1.28765e11 | −0.631419 | ||||||||
\(327\) | −1.77069e11 | −0.856400 | ||||||||
\(328\) | −1.99444e11 | −0.951455 | ||||||||
\(329\) | −3.68260e11 | −1.73290 | ||||||||
\(330\) | −1.60563e9 | −0.00745301 | ||||||||
\(331\) | 1.69491e11 | 0.776106 | 0.388053 | − | 0.921637i | \(-0.373148\pi\) | ||||
0.388053 | + | 0.921637i | \(0.373148\pi\) | |||||||
\(332\) | −2.53482e10 | −0.114506 | ||||||||
\(333\) | 3.37768e10 | 0.150529 | ||||||||
\(334\) | 7.13187e10 | 0.313577 | ||||||||
\(335\) | 5.21523e10 | 0.226241 | ||||||||
\(336\) | −3.24055e10 | −0.138705 | ||||||||
\(337\) | 2.08297e11 | 0.879728 | 0.439864 | − | 0.898064i | \(-0.355027\pi\) | ||||
0.439864 | + | 0.898064i | \(0.355027\pi\) | |||||||
\(338\) | 1.34403e11 | 0.560124 | ||||||||
\(339\) | 2.32343e11 | 0.955501 | ||||||||
\(340\) | −2.53156e10 | −0.102738 | ||||||||
\(341\) | 2.95603e9 | 0.0118390 | ||||||||
\(342\) | 3.10532e10 | 0.122741 | ||||||||
\(343\) | −4.88884e11 | −1.90714 | ||||||||
\(344\) | −1.30573e11 | −0.502736 | ||||||||
\(345\) | 3.35130e10 | 0.127358 | ||||||||
\(346\) | 6.90645e10 | 0.259067 | ||||||||
\(347\) | 3.01426e11 | 1.11609 | 0.558043 | − | 0.829812i | \(-0.311552\pi\) | ||||
0.558043 | + | 0.829812i | \(0.311552\pi\) | |||||||
\(348\) | 1.28302e11 | 0.468951 | ||||||||
\(349\) | 2.59548e10 | 0.0936489 | 0.0468244 | − | 0.998903i | \(-0.485090\pi\) | ||||
0.0468244 | + | 0.998903i | \(0.485090\pi\) | |||||||
\(350\) | −2.68105e11 | −0.954991 | ||||||||
\(351\) | −6.36077e9 | −0.0223680 | ||||||||
\(352\) | 3.27185e10 | 0.113593 | ||||||||
\(353\) | −1.72509e11 | −0.591325 | −0.295662 | − | 0.955293i | \(-0.595540\pi\) | ||||
−0.295662 | + | 0.955293i | \(0.595540\pi\) | |||||||
\(354\) | 1.26101e10 | 0.0426780 | ||||||||
\(355\) | 8.17895e10 | 0.273319 | ||||||||
\(356\) | −2.17109e11 | −0.716395 | ||||||||
\(357\) | 2.28880e11 | 0.745762 | ||||||||
\(358\) | 1.38399e11 | 0.445306 | ||||||||
\(359\) | −2.87460e11 | −0.913383 | −0.456692 | − | 0.889625i | \(-0.650966\pi\) | ||||
−0.456692 | + | 0.889625i | \(0.650966\pi\) | |||||||
\(360\) | −2.08636e10 | −0.0654680 | ||||||||
\(361\) | −1.86975e11 | −0.579430 | ||||||||
\(362\) | 2.92223e11 | 0.894387 | ||||||||
\(363\) | −1.88672e11 | −0.570331 | ||||||||
\(364\) | −4.63364e10 | −0.138346 | ||||||||
\(365\) | 3.21415e10 | 0.0947870 | ||||||||
\(366\) | −1.04014e11 | −0.302989 | ||||||||
\(367\) | 6.06272e11 | 1.74450 | 0.872249 | − | 0.489062i | \(-0.162661\pi\) | ||||
0.872249 | + | 0.489062i | \(0.162661\pi\) | |||||||
\(368\) | −5.14768e10 | −0.146317 | ||||||||
\(369\) | −1.18578e11 | −0.332955 | ||||||||
\(370\) | 1.90593e10 | 0.0528688 | ||||||||
\(371\) | 4.77977e11 | 1.30986 | ||||||||
\(372\) | 1.55147e10 | 0.0420048 | ||||||||
\(373\) | −1.10006e11 | −0.294256 | −0.147128 | − | 0.989117i | \(-0.547003\pi\) | ||||
−0.147128 | + | 0.989117i | \(0.547003\pi\) | |||||||
\(374\) | −1.74193e10 | −0.0460372 | ||||||||
\(375\) | 8.92374e10 | 0.233027 | ||||||||
\(376\) | 3.64187e11 | 0.939677 | ||||||||
\(377\) | 5.46455e10 | 0.139322 | ||||||||
\(378\) | 7.61900e10 | 0.191949 | ||||||||
\(379\) | −1.53320e11 | −0.381701 | −0.190850 | − | 0.981619i | \(-0.561125\pi\) | ||||
−0.190850 | + | 0.981619i | \(0.561125\pi\) | |||||||
\(380\) | −3.68293e10 | −0.0906082 | ||||||||
\(381\) | 3.89727e11 | 0.947541 | ||||||||
\(382\) | 5.95818e10 | 0.143162 | ||||||||
\(383\) | −8.02971e8 | −0.00190680 | −0.000953400 | − | 1.00000i | \(-0.500303\pi\) | ||||
−0.000953400 | 1.00000i | \(0.500303\pi\) | ||||||||
\(384\) | 1.90826e11 | 0.447864 | ||||||||
\(385\) | −1.72168e10 | −0.0399372 | ||||||||
\(386\) | −2.29585e11 | −0.526382 | ||||||||
\(387\) | −7.76312e10 | −0.175929 | ||||||||
\(388\) | −5.72910e10 | −0.128335 | ||||||||
\(389\) | 7.71042e11 | 1.70728 | 0.853640 | − | 0.520864i | \(-0.174390\pi\) | ||||
0.853640 | + | 0.520864i | \(0.174390\pi\) | |||||||
\(390\) | −3.58921e9 | −0.00785612 | ||||||||
\(391\) | 3.63579e11 | 0.786691 | ||||||||
\(392\) | 9.28793e11 | 1.98670 | ||||||||
\(393\) | 3.11517e11 | 0.658743 | ||||||||
\(394\) | −7.46319e10 | −0.156024 | ||||||||
\(395\) | −1.40460e11 | −0.290313 | ||||||||
\(396\) | 1.21877e10 | 0.0249053 | ||||||||
\(397\) | −8.59617e11 | −1.73679 | −0.868396 | − | 0.495872i | \(-0.834849\pi\) | ||||
−0.868396 | + | 0.495872i | \(0.834849\pi\) | |||||||
\(398\) | −3.24114e10 | −0.0647476 | ||||||||
\(399\) | 3.32976e11 | 0.657711 | ||||||||
\(400\) | −6.70470e10 | −0.130951 | ||||||||
\(401\) | 5.09559e11 | 0.984113 | 0.492056 | − | 0.870563i | \(-0.336245\pi\) | ||||
0.492056 | + | 0.870563i | \(0.336245\pi\) | |||||||
\(402\) | 1.88344e11 | 0.359694 | ||||||||
\(403\) | 6.60789e9 | 0.0124793 | ||||||||
\(404\) | −2.98938e10 | −0.0558297 | ||||||||
\(405\) | −1.24043e10 | −0.0229100 | ||||||||
\(406\) | −6.54550e11 | −1.19557 | ||||||||
\(407\) | −2.75644e10 | −0.0497937 | ||||||||
\(408\) | −2.26348e11 | −0.404395 | ||||||||
\(409\) | −2.01097e11 | −0.355346 | −0.177673 | − | 0.984090i | \(-0.556857\pi\) | ||||
−0.177673 | + | 0.984090i | \(0.556857\pi\) | |||||||
\(410\) | −6.69103e10 | −0.116941 | ||||||||
\(411\) | 3.95924e11 | 0.684422 | ||||||||
\(412\) | 1.53205e11 | 0.261961 | ||||||||
\(413\) | 1.35215e11 | 0.228692 | ||||||||
\(414\) | 1.21029e11 | 0.202483 | ||||||||
\(415\) | −2.10538e10 | −0.0348430 | ||||||||
\(416\) | 7.31388e10 | 0.119737 | ||||||||
\(417\) | 3.27810e11 | 0.530896 | ||||||||
\(418\) | −2.53418e10 | −0.0406016 | ||||||||
\(419\) | 5.57874e11 | 0.884247 | 0.442123 | − | 0.896954i | \(-0.354225\pi\) | ||||
0.442123 | + | 0.896954i | \(0.354225\pi\) | |||||||
\(420\) | −9.03620e10 | −0.141698 | ||||||||
\(421\) | −1.23812e12 | −1.92085 | −0.960424 | − | 0.278542i | \(-0.910149\pi\) | ||||
−0.960424 | + | 0.278542i | \(0.910149\pi\) | |||||||
\(422\) | 2.90920e11 | 0.446547 | ||||||||
\(423\) | 2.16525e11 | 0.328833 | ||||||||
\(424\) | −4.72690e11 | −0.710281 | ||||||||
\(425\) | 4.73551e11 | 0.704072 | ||||||||
\(426\) | 2.95376e11 | 0.434542 | ||||||||
\(427\) | −1.11532e12 | −1.62358 | ||||||||
\(428\) | 4.81712e11 | 0.693889 | ||||||||
\(429\) | 5.19087e9 | 0.00739916 | ||||||||
\(430\) | −4.38052e10 | −0.0617899 | ||||||||
\(431\) | −6.13759e11 | −0.856743 | −0.428371 | − | 0.903603i | \(-0.640913\pi\) | ||||
−0.428371 | + | 0.903603i | \(0.640913\pi\) | |||||||
\(432\) | 1.90534e10 | 0.0263206 | ||||||||
\(433\) | −3.09324e11 | −0.422881 | −0.211440 | − | 0.977391i | \(-0.567815\pi\) | ||||
−0.211440 | + | 0.977391i | \(0.567815\pi\) | |||||||
\(434\) | −7.91500e10 | −0.107090 | ||||||||
\(435\) | 1.06566e11 | 0.142698 | ||||||||
\(436\) | 7.58414e11 | 1.00512 | ||||||||
\(437\) | 5.28938e11 | 0.693807 | ||||||||
\(438\) | 1.16076e11 | 0.150699 | ||||||||
\(439\) | 2.58853e11 | 0.332632 | 0.166316 | − | 0.986073i | \(-0.446813\pi\) | ||||
0.166316 | + | 0.986073i | \(0.446813\pi\) | |||||||
\(440\) | 1.70263e10 | 0.0216563 | ||||||||
\(441\) | 5.52208e11 | 0.695230 | ||||||||
\(442\) | −3.89391e10 | −0.0485272 | ||||||||
\(443\) | −6.08274e11 | −0.750382 | −0.375191 | − | 0.926948i | \(-0.622423\pi\) | ||||
−0.375191 | + | 0.926948i | \(0.622423\pi\) | |||||||
\(444\) | −1.44672e11 | −0.176669 | ||||||||
\(445\) | −1.80327e11 | −0.217992 | ||||||||
\(446\) | 7.32463e11 | 0.876554 | ||||||||
\(447\) | 3.98670e11 | 0.472313 | ||||||||
\(448\) | −6.71229e11 | −0.787263 | ||||||||
\(449\) | −9.88861e11 | −1.14822 | −0.574112 | − | 0.818777i | \(-0.694653\pi\) | ||||
−0.574112 | + | 0.818777i | \(0.694653\pi\) | |||||||
\(450\) | 1.57637e11 | 0.181218 | ||||||||
\(451\) | 9.67686e10 | 0.110139 | ||||||||
\(452\) | −9.95164e11 | −1.12143 | ||||||||
\(453\) | 5.76288e11 | 0.642981 | ||||||||
\(454\) | −6.05082e10 | −0.0668440 | ||||||||
\(455\) | −3.84863e10 | −0.0420973 | ||||||||
\(456\) | −3.29293e11 | −0.356649 | ||||||||
\(457\) | 3.06396e11 | 0.328595 | 0.164297 | − | 0.986411i | \(-0.447464\pi\) | ||||
0.164297 | + | 0.986411i | \(0.447464\pi\) | |||||||
\(458\) | 1.19609e11 | 0.127019 | ||||||||
\(459\) | −1.34574e11 | −0.141515 | ||||||||
\(460\) | −1.43542e11 | −0.149475 | ||||||||
\(461\) | 4.36858e11 | 0.450491 | 0.225245 | − | 0.974302i | \(-0.427682\pi\) | ||||
0.225245 | + | 0.974302i | \(0.427682\pi\) | |||||||
\(462\) | −6.21768e10 | −0.0634950 | ||||||||
\(463\) | −1.25176e12 | −1.26592 | −0.632960 | − | 0.774185i | \(-0.718160\pi\) | ||||
−0.632960 | + | 0.774185i | \(0.718160\pi\) | |||||||
\(464\) | −1.63688e11 | −0.163940 | ||||||||
\(465\) | 1.28862e10 | 0.0127817 | ||||||||
\(466\) | 2.86334e11 | 0.281278 | ||||||||
\(467\) | −7.55685e11 | −0.735216 | −0.367608 | − | 0.929981i | \(-0.619823\pi\) | ||||
−0.367608 | + | 0.929981i | \(0.619823\pi\) | |||||||
\(468\) | 2.72442e10 | 0.0262524 | ||||||||
\(469\) | 2.01956e12 | 1.92744 | ||||||||
\(470\) | 1.22179e11 | 0.115493 | ||||||||
\(471\) | 6.35767e11 | 0.595256 | ||||||||
\(472\) | −1.33719e11 | −0.124010 | ||||||||
\(473\) | 6.33530e10 | 0.0581958 | ||||||||
\(474\) | −5.07261e11 | −0.461561 | ||||||||
\(475\) | 6.88926e11 | 0.620943 | ||||||||
\(476\) | −9.80330e11 | −0.875268 | ||||||||
\(477\) | −2.81035e11 | −0.248558 | ||||||||
\(478\) | −7.99380e11 | −0.700371 | ||||||||
\(479\) | 1.35024e12 | 1.17193 | 0.585963 | − | 0.810338i | \(-0.300716\pi\) | ||||
0.585963 | + | 0.810338i | \(0.300716\pi\) | |||||||
\(480\) | 1.42630e11 | 0.122638 | ||||||||
\(481\) | −6.16174e10 | −0.0524869 | ||||||||
\(482\) | 1.00568e12 | 0.848690 | ||||||||
\(483\) | 1.29777e12 | 1.08501 | ||||||||
\(484\) | 8.08112e11 | 0.669372 | ||||||||
\(485\) | −4.75850e10 | −0.0390510 | ||||||||
\(486\) | −4.47972e10 | −0.0364240 | ||||||||
\(487\) | 1.13263e12 | 0.912447 | 0.456224 | − | 0.889865i | \(-0.349202\pi\) | ||||
0.456224 | + | 0.889865i | \(0.349202\pi\) | |||||||
\(488\) | 1.10298e12 | 0.880398 | ||||||||
\(489\) | 8.11814e11 | 0.642047 | ||||||||
\(490\) | 3.11596e11 | 0.244179 | ||||||||
\(491\) | 9.25546e11 | 0.718673 | 0.359337 | − | 0.933208i | \(-0.383003\pi\) | ||||
0.359337 | + | 0.933208i | \(0.383003\pi\) | |||||||
\(492\) | 5.07889e11 | 0.390774 | ||||||||
\(493\) | 1.15612e12 | 0.881441 | ||||||||
\(494\) | −5.66488e10 | −0.0427976 | ||||||||
\(495\) | 1.01229e10 | 0.00757845 | ||||||||
\(496\) | −1.97936e10 | −0.0146844 | ||||||||
\(497\) | 3.16725e12 | 2.32851 | ||||||||
\(498\) | −7.60342e10 | −0.0553958 | ||||||||
\(499\) | −2.72332e12 | −1.96628 | −0.983141 | − | 0.182847i | \(-0.941469\pi\) | ||||
−0.983141 | + | 0.182847i | \(0.941469\pi\) | |||||||
\(500\) | −3.82219e11 | −0.273493 | ||||||||
\(501\) | −4.49638e11 | −0.318855 | ||||||||
\(502\) | 5.40064e11 | 0.379558 | ||||||||
\(503\) | −2.02205e12 | −1.40843 | −0.704216 | − | 0.709985i | \(-0.748701\pi\) | ||||
−0.704216 | + | 0.709985i | \(0.748701\pi\) | |||||||
\(504\) | −8.07931e11 | −0.557746 | ||||||||
\(505\) | −2.48293e10 | −0.0169884 | ||||||||
\(506\) | −9.87690e10 | −0.0669797 | ||||||||
\(507\) | −8.47361e11 | −0.569551 | ||||||||
\(508\) | −1.66927e12 | −1.11209 | ||||||||
\(509\) | 3.50255e10 | 0.0231289 | 0.0115644 | − | 0.999933i | \(-0.496319\pi\) | ||||
0.0115644 | + | 0.999933i | \(0.496319\pi\) | |||||||
\(510\) | −7.59362e10 | −0.0497031 | ||||||||
\(511\) | 1.24466e12 | 0.807526 | ||||||||
\(512\) | −4.21653e11 | −0.271169 | ||||||||
\(513\) | −1.95779e11 | −0.124807 | ||||||||
\(514\) | −4.78769e11 | −0.302546 | ||||||||
\(515\) | 1.27250e11 | 0.0797121 | ||||||||
\(516\) | 3.32507e11 | 0.206480 | ||||||||
\(517\) | −1.76701e11 | −0.108775 | ||||||||
\(518\) | 7.38060e11 | 0.450410 | ||||||||
\(519\) | −4.35426e11 | −0.263428 | ||||||||
\(520\) | 3.80605e10 | 0.0228276 | ||||||||
\(521\) | 6.72889e9 | 0.00400105 | 0.00200052 | − | 0.999998i | \(-0.499363\pi\) | ||||
0.00200052 | + | 0.999998i | \(0.499363\pi\) | |||||||
\(522\) | 3.84853e11 | 0.226871 | ||||||||
\(523\) | −1.94157e12 | −1.13474 | −0.567370 | − | 0.823463i | \(-0.692039\pi\) | ||||
−0.567370 | + | 0.823463i | \(0.692039\pi\) | |||||||
\(524\) | −1.33428e12 | −0.773137 | ||||||||
\(525\) | 1.69030e12 | 0.971064 | ||||||||
\(526\) | 4.79719e10 | 0.0273244 | ||||||||
\(527\) | 1.39802e11 | 0.0789523 | ||||||||
\(528\) | −1.55490e10 | −0.00870662 | ||||||||
\(529\) | 2.60374e11 | 0.144560 | ||||||||
\(530\) | −1.58580e11 | −0.0872986 | ||||||||
\(531\) | −7.95020e10 | −0.0433963 | ||||||||
\(532\) | −1.42619e12 | −0.771926 | ||||||||
\(533\) | 2.16316e11 | 0.116096 | ||||||||
\(534\) | −6.51236e11 | −0.346579 | ||||||||
\(535\) | 4.00102e11 | 0.211144 | ||||||||
\(536\) | −1.99722e12 | −1.04517 | ||||||||
\(537\) | −8.72553e11 | −0.452801 | ||||||||
\(538\) | 1.25021e12 | 0.643374 | ||||||||
\(539\) | −4.50643e11 | −0.229976 | ||||||||
\(540\) | 5.31298e10 | 0.0268885 | ||||||||
\(541\) | −4.30477e11 | −0.216054 | −0.108027 | − | 0.994148i | \(-0.534453\pi\) | ||||
−0.108027 | + | 0.994148i | \(0.534453\pi\) | |||||||
\(542\) | −1.71865e12 | −0.855444 | ||||||||
\(543\) | −1.84236e12 | −0.909440 | ||||||||
\(544\) | 1.54738e12 | 0.757535 | ||||||||
\(545\) | 6.29927e11 | 0.305848 | ||||||||
\(546\) | −1.38990e11 | −0.0669293 | ||||||||
\(547\) | 3.69233e12 | 1.76343 | 0.881714 | − | 0.471784i | \(-0.156390\pi\) | ||||
0.881714 | + | 0.471784i | \(0.156390\pi\) | |||||||
\(548\) | −1.69581e12 | −0.803275 | ||||||||
\(549\) | 6.55770e11 | 0.308089 | ||||||||
\(550\) | −1.28644e11 | −0.0599455 | ||||||||
\(551\) | 1.68194e12 | 0.777370 | ||||||||
\(552\) | −1.28341e12 | −0.588356 | ||||||||
\(553\) | −5.43924e12 | −2.47329 | ||||||||
\(554\) | −2.96101e11 | −0.133551 | ||||||||
\(555\) | −1.20162e11 | −0.0537587 | ||||||||
\(556\) | −1.40406e12 | −0.623089 | ||||||||
\(557\) | 1.24067e12 | 0.546147 | 0.273073 | − | 0.961993i | \(-0.411960\pi\) | ||||
0.273073 | + | 0.961993i | \(0.411960\pi\) | |||||||
\(558\) | 4.65375e10 | 0.0203212 | ||||||||
\(559\) | 1.41619e11 | 0.0613434 | ||||||||
\(560\) | 1.15284e11 | 0.0495361 | ||||||||
\(561\) | 1.09822e11 | 0.0468120 | ||||||||
\(562\) | −8.31187e11 | −0.351468 | ||||||||
\(563\) | 1.17319e12 | 0.492132 | 0.246066 | − | 0.969253i | \(-0.420862\pi\) | ||||
0.246066 | + | 0.969253i | \(0.420862\pi\) | |||||||
\(564\) | −9.27411e11 | −0.385937 | ||||||||
\(565\) | −8.26567e11 | −0.341240 | ||||||||
\(566\) | 2.68059e11 | 0.109788 | ||||||||
\(567\) | −4.80350e11 | −0.195179 | ||||||||
\(568\) | −3.13221e12 | −1.26265 | ||||||||
\(569\) | −2.91701e12 | −1.16663 | −0.583314 | − | 0.812247i | \(-0.698244\pi\) | ||||
−0.583314 | + | 0.812247i | \(0.698244\pi\) | |||||||
\(570\) | −1.10473e11 | −0.0438347 | ||||||||
\(571\) | 2.19394e11 | 0.0863699 | 0.0431850 | − | 0.999067i | \(-0.486250\pi\) | ||||
0.0431850 | + | 0.999067i | \(0.486250\pi\) | |||||||
\(572\) | −2.22334e10 | −0.00868406 | ||||||||
\(573\) | −3.75641e11 | −0.145572 | ||||||||
\(574\) | −2.59106e12 | −0.996262 | ||||||||
\(575\) | 2.68508e12 | 1.02436 | ||||||||
\(576\) | 3.94660e11 | 0.149390 | ||||||||
\(577\) | 3.01436e12 | 1.13215 | 0.566075 | − | 0.824353i | \(-0.308461\pi\) | ||||
0.566075 | + | 0.824353i | \(0.308461\pi\) | |||||||
\(578\) | 6.99757e11 | 0.260778 | ||||||||
\(579\) | 1.44745e12 | 0.535242 | ||||||||
\(580\) | −4.56439e11 | −0.167478 | ||||||||
\(581\) | −8.15296e11 | −0.296840 | ||||||||
\(582\) | −1.71849e11 | −0.0620860 | ||||||||
\(583\) | 2.29346e11 | 0.0822208 | ||||||||
\(584\) | −1.23089e12 | −0.437887 | ||||||||
\(585\) | 2.26286e10 | 0.00798835 | ||||||||
\(586\) | 2.35822e12 | 0.826124 | ||||||||
\(587\) | −3.73815e12 | −1.29953 | −0.649764 | − | 0.760136i | \(-0.725132\pi\) | ||||
−0.649764 | + | 0.760136i | \(0.725132\pi\) | |||||||
\(588\) | −2.36520e12 | −0.815961 | ||||||||
\(589\) | 2.03385e11 | 0.0696305 | ||||||||
\(590\) | −4.48608e10 | −0.0152417 | ||||||||
\(591\) | 4.70526e11 | 0.158650 | ||||||||
\(592\) | 1.84572e11 | 0.0617615 | ||||||||
\(593\) | 5.21655e12 | 1.73236 | 0.866179 | − | 0.499734i | \(-0.166569\pi\) | ||||
0.866179 | + | 0.499734i | \(0.166569\pi\) | |||||||
\(594\) | 3.65579e10 | 0.0120488 | ||||||||
\(595\) | −8.14246e11 | −0.266336 | ||||||||
\(596\) | −1.70757e12 | −0.554332 | ||||||||
\(597\) | 2.04342e11 | 0.0658373 | ||||||||
\(598\) | −2.20788e11 | −0.0706024 | ||||||||
\(599\) | −3.22617e11 | −0.102392 | −0.0511960 | − | 0.998689i | \(-0.516303\pi\) | ||||
−0.0511960 | + | 0.998689i | \(0.516303\pi\) | |||||||
\(600\) | −1.67161e12 | −0.526567 | ||||||||
\(601\) | 5.74234e11 | 0.179537 | 0.0897685 | − | 0.995963i | \(-0.471387\pi\) | ||||
0.0897685 | + | 0.995963i | \(0.471387\pi\) | |||||||
\(602\) | −1.69633e12 | −0.526411 | ||||||||
\(603\) | −1.18744e12 | −0.365748 | ||||||||
\(604\) | −2.46834e12 | −0.754637 | ||||||||
\(605\) | 6.71205e11 | 0.203683 | ||||||||
\(606\) | −8.96689e10 | −0.0270094 | ||||||||
\(607\) | −4.53684e11 | −0.135645 | −0.0678226 | − | 0.997697i | \(-0.521605\pi\) | ||||
−0.0678226 | + | 0.997697i | \(0.521605\pi\) | |||||||
\(608\) | 2.25114e12 | 0.668094 | ||||||||
\(609\) | 4.12669e12 | 1.21569 | ||||||||
\(610\) | 3.70033e11 | 0.108207 | ||||||||
\(611\) | −3.94996e11 | −0.114659 | ||||||||
\(612\) | 5.76401e11 | 0.166090 | ||||||||
\(613\) | −3.50305e12 | −1.00201 | −0.501007 | − | 0.865443i | \(-0.667037\pi\) | ||||
−0.501007 | + | 0.865443i | \(0.667037\pi\) | |||||||
\(614\) | −1.77267e11 | −0.0503351 | ||||||||
\(615\) | 4.21844e11 | 0.118909 | ||||||||
\(616\) | 6.59333e11 | 0.184498 | ||||||||
\(617\) | 3.03553e12 | 0.843239 | 0.421620 | − | 0.906773i | \(-0.361462\pi\) | ||||
0.421620 | + | 0.906773i | \(0.361462\pi\) | |||||||
\(618\) | 4.59551e11 | 0.126732 | ||||||||
\(619\) | −3.99709e12 | −1.09430 | −0.547149 | − | 0.837035i | \(-0.684287\pi\) | ||||
−0.547149 | + | 0.837035i | \(0.684287\pi\) | |||||||
\(620\) | −5.51939e10 | −0.0150013 | ||||||||
\(621\) | −7.63044e11 | −0.205891 | ||||||||
\(622\) | 1.78514e11 | 0.0478206 | ||||||||
\(623\) | −6.98305e12 | −1.85716 | ||||||||
\(624\) | −3.47581e10 | −0.00917753 | ||||||||
\(625\) | 3.33505e12 | 0.874264 | ||||||||
\(626\) | 3.19927e12 | 0.832657 | ||||||||
\(627\) | 1.59770e11 | 0.0412850 | ||||||||
\(628\) | −2.72309e12 | −0.698625 | ||||||||
\(629\) | −1.30363e12 | −0.332067 | ||||||||
\(630\) | −2.71048e11 | −0.0685510 | ||||||||
\(631\) | −3.92587e12 | −0.985834 | −0.492917 | − | 0.870076i | \(-0.664069\pi\) | ||||
−0.492917 | + | 0.870076i | \(0.664069\pi\) | |||||||
\(632\) | 5.37907e12 | 1.34116 | ||||||||
\(633\) | −1.83414e12 | −0.454063 | ||||||||
\(634\) | −3.26326e12 | −0.802140 | ||||||||
\(635\) | −1.38646e12 | −0.338397 | ||||||||
\(636\) | 1.20372e12 | 0.291721 | ||||||||
\(637\) | −1.00737e12 | −0.242415 | ||||||||
\(638\) | −3.14070e11 | −0.0750469 | ||||||||
\(639\) | −1.86223e12 | −0.441856 | ||||||||
\(640\) | −6.78867e11 | −0.159947 | ||||||||
\(641\) | 1.53691e12 | 0.359573 | 0.179787 | − | 0.983706i | \(-0.442459\pi\) | ||||
0.179787 | + | 0.983706i | \(0.442459\pi\) | |||||||
\(642\) | 1.44493e12 | 0.335691 | ||||||||
\(643\) | 9.66855e11 | 0.223055 | 0.111528 | − | 0.993761i | \(-0.464426\pi\) | ||||
0.111528 | + | 0.993761i | \(0.464426\pi\) | |||||||
\(644\) | −5.55855e12 | −1.27343 | ||||||||
\(645\) | 2.76175e11 | 0.0628299 | ||||||||
\(646\) | −1.19851e12 | −0.270766 | ||||||||
\(647\) | −5.92400e12 | −1.32906 | −0.664532 | − | 0.747260i | \(-0.731369\pi\) | ||||
−0.664532 | + | 0.747260i | \(0.731369\pi\) | |||||||
\(648\) | 4.75036e11 | 0.105837 | ||||||||
\(649\) | 6.48797e10 | 0.0143551 | ||||||||
\(650\) | −2.87569e11 | −0.0631877 | ||||||||
\(651\) | 4.99011e11 | 0.108892 | ||||||||
\(652\) | −3.47713e12 | −0.753541 | ||||||||
\(653\) | 1.50571e12 | 0.324065 | 0.162033 | − | 0.986785i | \(-0.448195\pi\) | ||||
0.162033 | + | 0.986785i | \(0.448195\pi\) | |||||||
\(654\) | 2.27493e12 | 0.486259 | ||||||||
\(655\) | −1.10823e12 | −0.235258 | ||||||||
\(656\) | −6.47964e11 | −0.136610 | ||||||||
\(657\) | −7.31818e11 | −0.153235 | ||||||||
\(658\) | 4.73130e12 | 0.983929 | ||||||||
\(659\) | 1.30444e12 | 0.269426 | 0.134713 | − | 0.990885i | \(-0.456989\pi\) | ||||
0.134713 | + | 0.990885i | \(0.456989\pi\) | |||||||
\(660\) | −4.33580e10 | −0.00889449 | ||||||||
\(661\) | 1.94983e12 | 0.397273 | 0.198637 | − | 0.980073i | \(-0.436349\pi\) | ||||
0.198637 | + | 0.980073i | \(0.436349\pi\) | |||||||
\(662\) | −2.17757e12 | −0.440668 | ||||||||
\(663\) | 2.45496e11 | 0.0493439 | ||||||||
\(664\) | 8.06278e11 | 0.160964 | ||||||||
\(665\) | −1.18457e12 | −0.234890 | ||||||||
\(666\) | −4.33955e11 | −0.0854693 | ||||||||
\(667\) | 6.55532e12 | 1.28241 | ||||||||
\(668\) | 1.92587e12 | 0.374225 | ||||||||
\(669\) | −4.61790e12 | −0.891307 | ||||||||
\(670\) | −6.70038e11 | −0.128458 | ||||||||
\(671\) | −5.35158e11 | −0.101913 | ||||||||
\(672\) | 5.52326e12 | 1.04480 | ||||||||
\(673\) | 1.57403e12 | 0.295765 | 0.147882 | − | 0.989005i | \(-0.452754\pi\) | ||||
0.147882 | + | 0.989005i | \(0.452754\pi\) | |||||||
\(674\) | −2.67614e12 | −0.499504 | ||||||||
\(675\) | −9.93842e11 | −0.184268 | ||||||||
\(676\) | 3.62939e12 | 0.668456 | ||||||||
\(677\) | −9.48856e11 | −0.173601 | −0.0868003 | − | 0.996226i | \(-0.527664\pi\) | ||||
−0.0868003 | + | 0.996226i | \(0.527664\pi\) | |||||||
\(678\) | −2.98508e12 | −0.542527 | ||||||||
\(679\) | −1.84270e12 | −0.332690 | ||||||||
\(680\) | 8.05239e11 | 0.144422 | ||||||||
\(681\) | 3.81481e11 | 0.0679691 | ||||||||
\(682\) | −3.79782e10 | −0.00672209 | ||||||||
\(683\) | −6.32726e12 | −1.11256 | −0.556279 | − | 0.830996i | \(-0.687771\pi\) | ||||
−0.556279 | + | 0.830996i | \(0.687771\pi\) | |||||||
\(684\) | 8.38553e11 | 0.146480 | ||||||||
\(685\) | −1.40851e12 | −0.244429 | ||||||||
\(686\) | 6.28104e12 | 1.08286 | ||||||||
\(687\) | −7.54090e11 | −0.129157 | ||||||||
\(688\) | −4.24212e11 | −0.0721830 | ||||||||
\(689\) | 5.12678e11 | 0.0866679 | ||||||||
\(690\) | −4.30565e11 | −0.0723132 | ||||||||
\(691\) | 1.32805e12 | 0.221597 | 0.110798 | − | 0.993843i | \(-0.464659\pi\) | ||||
0.110798 | + | 0.993843i | \(0.464659\pi\) | |||||||
\(692\) | 1.86500e12 | 0.309173 | ||||||||
\(693\) | 3.92002e11 | 0.0645637 | ||||||||
\(694\) | −3.87263e12 | −0.633707 | ||||||||
\(695\) | −1.16619e12 | −0.189600 | ||||||||
\(696\) | −4.08104e12 | −0.659219 | ||||||||
\(697\) | 4.57656e12 | 0.734499 | ||||||||
\(698\) | −3.33459e11 | −0.0531732 | ||||||||
\(699\) | −1.80523e12 | −0.286012 | ||||||||
\(700\) | −7.23985e12 | −1.13969 | ||||||||
\(701\) | 2.84917e12 | 0.445643 | 0.222822 | − | 0.974859i | \(-0.428473\pi\) | ||||
0.222822 | + | 0.974859i | \(0.428473\pi\) | |||||||
\(702\) | 8.17214e10 | 0.0127004 | ||||||||
\(703\) | −1.89653e12 | −0.292860 | ||||||||
\(704\) | −3.22073e11 | −0.0494171 | ||||||||
\(705\) | −7.70293e11 | −0.117437 | ||||||||
\(706\) | 2.21635e12 | 0.335750 | ||||||||
\(707\) | −9.61499e11 | −0.144731 | ||||||||
\(708\) | 3.40520e11 | 0.0509323 | ||||||||
\(709\) | 1.69917e12 | 0.252540 | 0.126270 | − | 0.991996i | \(-0.459700\pi\) | ||||
0.126270 | + | 0.991996i | \(0.459700\pi\) | |||||||
\(710\) | −1.05081e12 | −0.155189 | ||||||||
\(711\) | 3.19809e12 | 0.469329 | ||||||||
\(712\) | 6.90580e12 | 1.00706 | ||||||||
\(713\) | 7.92688e11 | 0.114868 | ||||||||
\(714\) | −2.94058e12 | −0.423439 | ||||||||
\(715\) | −1.84667e10 | −0.00264248 | ||||||||
\(716\) | 3.73729e12 | 0.531432 | ||||||||
\(717\) | 5.03979e12 | 0.712158 | ||||||||
\(718\) | 3.69321e12 | 0.518613 | ||||||||
\(719\) | 8.44614e12 | 1.17863 | 0.589316 | − | 0.807902i | \(-0.299397\pi\) | ||||
0.589316 | + | 0.807902i | \(0.299397\pi\) | |||||||
\(720\) | −6.77829e10 | −0.00939992 | ||||||||
\(721\) | 4.92766e12 | 0.679098 | ||||||||
\(722\) | 2.40220e12 | 0.328997 | ||||||||
\(723\) | −6.34045e12 | −0.862974 | ||||||||
\(724\) | 7.89111e12 | 1.06737 | ||||||||
\(725\) | 8.53811e12 | 1.14773 | ||||||||
\(726\) | 2.42400e12 | 0.323830 | ||||||||
\(727\) | −4.74564e12 | −0.630071 | −0.315036 | − | 0.949080i | \(-0.602016\pi\) | ||||
−0.315036 | + | 0.949080i | \(0.602016\pi\) | |||||||
\(728\) | 1.47387e12 | 0.194477 | ||||||||
\(729\) | 2.82430e11 | 0.0370370 | ||||||||
\(730\) | −4.12945e11 | −0.0538195 | ||||||||
\(731\) | 2.99620e12 | 0.388100 | ||||||||
\(732\) | −2.80877e12 | −0.361590 | ||||||||
\(733\) | 1.07965e13 | 1.38138 | 0.690692 | − | 0.723149i | \(-0.257306\pi\) | ||||
0.690692 | + | 0.723149i | \(0.257306\pi\) | |||||||
\(734\) | −7.78921e12 | −0.990515 | ||||||||
\(735\) | −1.96449e12 | −0.248289 | ||||||||
\(736\) | 8.77379e12 | 1.10214 | ||||||||
\(737\) | 9.69038e11 | 0.120987 | ||||||||
\(738\) | 1.52346e12 | 0.189050 | ||||||||
\(739\) | −2.90351e12 | −0.358116 | −0.179058 | − | 0.983839i | \(-0.557305\pi\) | ||||
−0.179058 | + | 0.983839i | \(0.557305\pi\) | |||||||
\(740\) | 5.14673e11 | 0.0630941 | ||||||||
\(741\) | 3.57150e11 | 0.0435180 | ||||||||
\(742\) | −6.14091e12 | −0.743730 | ||||||||
\(743\) | 1.37305e13 | 1.65286 | 0.826429 | − | 0.563041i | \(-0.190369\pi\) | ||||
0.826429 | + | 0.563041i | \(0.190369\pi\) | |||||||
\(744\) | −4.93491e11 | −0.0590475 | ||||||||
\(745\) | −1.41828e12 | −0.168678 | ||||||||
\(746\) | 1.41332e12 | 0.167077 | ||||||||
\(747\) | 4.79367e11 | 0.0563281 | ||||||||
\(748\) | −4.70387e11 | −0.0549412 | ||||||||
\(749\) | 1.54937e13 | 1.79881 | ||||||||
\(750\) | −1.14650e12 | −0.132311 | ||||||||
\(751\) | 1.33843e13 | 1.53538 | 0.767691 | − | 0.640821i | \(-0.221406\pi\) | ||||
0.767691 | + | 0.640821i | \(0.221406\pi\) | |||||||
\(752\) | 1.18319e12 | 0.134919 | ||||||||
\(753\) | −3.40490e12 | −0.385946 | ||||||||
\(754\) | −7.02070e11 | −0.0791059 | ||||||||
\(755\) | −2.05016e12 | −0.229629 | ||||||||
\(756\) | 2.05742e12 | 0.229073 | ||||||||
\(757\) | 6.94181e12 | 0.768319 | 0.384159 | − | 0.923267i | \(-0.374491\pi\) | ||||
0.384159 | + | 0.923267i | \(0.374491\pi\) | |||||||
\(758\) | 1.96981e12 | 0.216727 | ||||||||
\(759\) | 6.22702e11 | 0.0681070 | ||||||||
\(760\) | 1.17147e12 | 0.127371 | ||||||||
\(761\) | −1.81658e13 | −1.96346 | −0.981732 | − | 0.190269i | \(-0.939064\pi\) | ||||
−0.981732 | + | 0.190269i | \(0.939064\pi\) | |||||||
\(762\) | −5.00710e12 | −0.538008 | ||||||||
\(763\) | 2.43935e13 | 2.60563 | ||||||||
\(764\) | 1.60893e12 | 0.170851 | ||||||||
\(765\) | 4.78749e11 | 0.0505396 | ||||||||
\(766\) | 1.03163e10 | 0.00108267 | ||||||||
\(767\) | 1.45032e11 | 0.0151316 | ||||||||
\(768\) | −4.94631e12 | −0.513046 | ||||||||
\(769\) | 6.48177e12 | 0.668382 | 0.334191 | − | 0.942505i | \(-0.391537\pi\) | ||||
0.334191 | + | 0.942505i | \(0.391537\pi\) | |||||||
\(770\) | 2.21196e11 | 0.0226761 | ||||||||
\(771\) | 3.01846e12 | 0.307638 | ||||||||
\(772\) | −6.19966e12 | −0.628189 | ||||||||
\(773\) | −3.31272e12 | −0.333716 | −0.166858 | − | 0.985981i | \(-0.553362\pi\) | ||||
−0.166858 | + | 0.985981i | \(0.553362\pi\) | |||||||
\(774\) | 9.97383e11 | 0.0998913 | ||||||||
\(775\) | 1.03245e12 | 0.102805 | ||||||||
\(776\) | 1.82231e12 | 0.180404 | ||||||||
\(777\) | −4.65319e12 | −0.457990 | ||||||||
\(778\) | −9.90612e12 | −0.969383 | ||||||||
\(779\) | 6.65801e12 | 0.647778 | ||||||||
\(780\) | −9.69222e10 | −0.00937556 | ||||||||
\(781\) | 1.51972e12 | 0.146162 | ||||||||
\(782\) | −4.67116e12 | −0.446678 | ||||||||
\(783\) | −2.42636e12 | −0.230689 | ||||||||
\(784\) | 3.01751e12 | 0.285251 | ||||||||
\(785\) | −2.26176e12 | −0.212585 | ||||||||
\(786\) | −4.00229e12 | −0.374030 | ||||||||
\(787\) | 1.37042e13 | 1.27341 | 0.636704 | − | 0.771108i | \(-0.280297\pi\) | ||||
0.636704 | + | 0.771108i | \(0.280297\pi\) | |||||||
\(788\) | −2.01534e12 | −0.186200 | ||||||||
\(789\) | −3.02445e11 | −0.0277843 | ||||||||
\(790\) | 1.80459e12 | 0.164838 | ||||||||
\(791\) | −3.20083e13 | −2.90715 | ||||||||
\(792\) | −3.87666e11 | −0.0350101 | ||||||||
\(793\) | −1.19629e12 | −0.107425 | ||||||||
\(794\) | 1.10441e13 | 0.986140 | ||||||||
\(795\) | 9.99789e11 | 0.0887679 | ||||||||
\(796\) | −8.75229e11 | −0.0772703 | ||||||||
\(797\) | −1.12390e13 | −0.986659 | −0.493329 | − | 0.869843i | \(-0.664220\pi\) | ||||
−0.493329 | + | 0.869843i | \(0.664220\pi\) | |||||||
\(798\) | −4.27798e12 | −0.373444 | ||||||||
\(799\) | −8.35684e12 | −0.725407 | ||||||||
\(800\) | 1.14276e13 | 0.986393 | ||||||||
\(801\) | 4.10580e12 | 0.352412 | ||||||||
\(802\) | −6.54667e12 | −0.558773 | ||||||||
\(803\) | 5.97219e11 | 0.0506890 | ||||||||
\(804\) | 5.08598e12 | 0.429262 | ||||||||
\(805\) | −4.61684e12 | −0.387493 | ||||||||
\(806\) | −8.48962e10 | −0.00708566 | ||||||||
\(807\) | −7.88212e12 | −0.654203 | ||||||||
\(808\) | 9.50863e11 | 0.0784814 | ||||||||
\(809\) | 6.71071e12 | 0.550808 | 0.275404 | − | 0.961329i | \(-0.411188\pi\) | ||||
0.275404 | + | 0.961329i | \(0.411188\pi\) | |||||||
\(810\) | 1.59367e11 | 0.0130082 | ||||||||
\(811\) | 3.22992e12 | 0.262179 | 0.131090 | − | 0.991371i | \(-0.458152\pi\) | ||||
0.131090 | + | 0.991371i | \(0.458152\pi\) | |||||||
\(812\) | −1.76753e13 | −1.42681 | ||||||||
\(813\) | 1.08355e13 | 0.869842 | ||||||||
\(814\) | 3.54140e11 | 0.0282725 | ||||||||
\(815\) | −2.88805e12 | −0.229295 | ||||||||
\(816\) | −7.35371e11 | −0.0580632 | ||||||||
\(817\) | 4.35890e12 | 0.342277 | ||||||||
\(818\) | 2.58364e12 | 0.201763 | ||||||||
\(819\) | 8.76279e11 | 0.0680557 | ||||||||
\(820\) | −1.80683e12 | −0.139558 | ||||||||
\(821\) | −5.85236e12 | −0.449559 | −0.224780 | − | 0.974410i | \(-0.572166\pi\) | ||||
−0.224780 | + | 0.974410i | \(0.572166\pi\) | |||||||
\(822\) | −5.08672e12 | −0.388611 | ||||||||
\(823\) | 1.73378e13 | 1.31733 | 0.658665 | − | 0.752437i | \(-0.271122\pi\) | ||||
0.658665 | + | 0.752437i | \(0.271122\pi\) | |||||||
\(824\) | −4.87315e12 | −0.368246 | ||||||||
\(825\) | 8.11050e11 | 0.0609544 | ||||||||
\(826\) | −1.73721e12 | −0.129850 | ||||||||
\(827\) | −1.21426e12 | −0.0902683 | −0.0451341 | − | 0.998981i | \(-0.514372\pi\) | ||||
−0.0451341 | + | 0.998981i | \(0.514372\pi\) | |||||||
\(828\) | 3.26824e12 | 0.241645 | ||||||||
\(829\) | 1.64938e13 | 1.21290 | 0.606449 | − | 0.795122i | \(-0.292593\pi\) | ||||
0.606449 | + | 0.795122i | \(0.292593\pi\) | |||||||
\(830\) | 2.70494e11 | 0.0197836 | ||||||||
\(831\) | 1.86681e12 | 0.135799 | ||||||||
\(832\) | −7.19960e11 | −0.0520899 | ||||||||
\(833\) | −2.13126e13 | −1.53368 | ||||||||
\(834\) | −4.21160e12 | −0.301440 | ||||||||
\(835\) | 1.59960e12 | 0.113873 | ||||||||
\(836\) | −6.84323e11 | −0.0484543 | ||||||||
\(837\) | −2.93402e11 | −0.0206632 | ||||||||
\(838\) | −7.16741e12 | −0.502070 | ||||||||
\(839\) | 2.54317e13 | 1.77193 | 0.885964 | − | 0.463754i | \(-0.153498\pi\) | ||||
0.885964 | + | 0.463754i | \(0.153498\pi\) | |||||||
\(840\) | 2.87424e12 | 0.199189 | ||||||||
\(841\) | 6.33773e12 | 0.436869 | ||||||||
\(842\) | 1.59070e13 | 1.09065 | ||||||||
\(843\) | 5.24032e12 | 0.357383 | ||||||||
\(844\) | 7.85592e12 | 0.532913 | ||||||||
\(845\) | 3.01451e12 | 0.203405 | ||||||||
\(846\) | −2.78185e12 | −0.186710 | ||||||||
\(847\) | 2.59920e13 | 1.73526 | ||||||||
\(848\) | −1.53570e12 | −0.101982 | ||||||||
\(849\) | −1.69001e12 | −0.111636 | ||||||||
\(850\) | −6.08405e12 | −0.399768 | ||||||||
\(851\) | −7.39168e12 | −0.483126 | ||||||||
\(852\) | 7.97626e12 | 0.518586 | ||||||||
\(853\) | −2.00195e12 | −0.129474 | −0.0647370 | − | 0.997902i | \(-0.520621\pi\) | ||||
−0.0647370 | + | 0.997902i | \(0.520621\pi\) | |||||||
\(854\) | 1.43293e13 | 0.921858 | ||||||||
\(855\) | 6.96488e11 | 0.0445724 | ||||||||
\(856\) | −1.53223e13 | −0.975421 | ||||||||
\(857\) | 1.17946e13 | 0.746913 | 0.373457 | − | 0.927648i | \(-0.378172\pi\) | ||||
0.373457 | + | 0.927648i | \(0.378172\pi\) | |||||||
\(858\) | −6.66908e10 | −0.00420120 | ||||||||
\(859\) | −2.87741e12 | −0.180315 | −0.0901577 | − | 0.995927i | \(-0.528737\pi\) | ||||
−0.0901577 | + | 0.995927i | \(0.528737\pi\) | |||||||
\(860\) | −1.18290e12 | −0.0737406 | ||||||||
\(861\) | 1.63356e13 | 1.01303 | ||||||||
\(862\) | 7.88540e12 | 0.486453 | ||||||||
\(863\) | 9.28264e12 | 0.569669 | 0.284835 | − | 0.958577i | \(-0.408061\pi\) | ||||
0.284835 | + | 0.958577i | \(0.408061\pi\) | |||||||
\(864\) | −3.24749e12 | −0.198260 | ||||||||
\(865\) | 1.54904e12 | 0.0940785 | ||||||||
\(866\) | 3.97410e12 | 0.240109 | ||||||||
\(867\) | −4.41170e12 | −0.265168 | ||||||||
\(868\) | −2.13735e12 | −0.127802 | ||||||||
\(869\) | −2.60988e12 | −0.155250 | ||||||||
\(870\) | −1.36913e12 | −0.0810228 | ||||||||
\(871\) | 2.16618e12 | 0.127530 | ||||||||
\(872\) | −2.41237e13 | −1.41292 | ||||||||
\(873\) | 1.08344e12 | 0.0631310 | ||||||||
\(874\) | −6.79564e12 | −0.393939 | ||||||||
\(875\) | −1.22936e13 | −0.708995 | ||||||||
\(876\) | 3.13450e12 | 0.179846 | ||||||||
\(877\) | 4.93768e12 | 0.281854 | 0.140927 | − | 0.990020i | \(-0.454992\pi\) | ||||
0.140927 | + | 0.990020i | \(0.454992\pi\) | |||||||
\(878\) | −3.32567e12 | −0.188866 | ||||||||
\(879\) | −1.48677e13 | −0.840028 | ||||||||
\(880\) | 5.53160e10 | 0.00310941 | ||||||||
\(881\) | −6.10283e11 | −0.0341303 | −0.0170651 | − | 0.999854i | \(-0.505432\pi\) | ||||
−0.0170651 | + | 0.999854i | \(0.505432\pi\) | |||||||
\(882\) | −7.09460e12 | −0.394748 | ||||||||
\(883\) | −7.15626e11 | −0.0396153 | −0.0198076 | − | 0.999804i | \(-0.506305\pi\) | ||||
−0.0198076 | + | 0.999804i | \(0.506305\pi\) | |||||||
\(884\) | −1.05150e12 | −0.0579128 | ||||||||
\(885\) | 2.82831e11 | 0.0154982 | ||||||||
\(886\) | 7.81493e12 | 0.426062 | ||||||||
\(887\) | −2.10952e13 | −1.14427 | −0.572134 | − | 0.820160i | \(-0.693884\pi\) | ||||
−0.572134 | + | 0.820160i | \(0.693884\pi\) | |||||||
\(888\) | 4.60172e12 | 0.248349 | ||||||||
\(889\) | −5.36899e13 | −2.88294 | ||||||||
\(890\) | 2.31679e12 | 0.123775 | ||||||||
\(891\) | −2.30484e11 | −0.0122515 | ||||||||
\(892\) | 1.97792e13 | 1.04609 | ||||||||
\(893\) | −1.21576e13 | −0.639759 | ||||||||
\(894\) | −5.12199e12 | −0.268176 | ||||||||
\(895\) | 3.10413e12 | 0.161710 | ||||||||
\(896\) | −2.62887e13 | −1.36265 | ||||||||
\(897\) | 1.39198e12 | 0.0717907 | ||||||||
\(898\) | 1.27046e13 | 0.651955 | ||||||||
\(899\) | 2.52062e12 | 0.128703 | ||||||||
\(900\) | 4.25679e12 | 0.216267 | ||||||||
\(901\) | 1.08466e13 | 0.548319 | ||||||||
\(902\) | −1.24325e12 | −0.0625361 | ||||||||
\(903\) | 1.06947e13 | 0.535271 | ||||||||
\(904\) | 3.16542e13 | 1.57643 | ||||||||
\(905\) | 6.55423e12 | 0.324790 | ||||||||
\(906\) | −7.40398e12 | −0.365080 | ||||||||
\(907\) | −7.69464e12 | −0.377533 | −0.188767 | − | 0.982022i | \(-0.560449\pi\) | ||||
−0.188767 | + | 0.982022i | \(0.560449\pi\) | |||||||
\(908\) | −1.63395e12 | −0.0797723 | ||||||||
\(909\) | 5.65329e11 | 0.0274640 | ||||||||
\(910\) | 4.94460e11 | 0.0239026 | ||||||||
\(911\) | −1.62851e13 | −0.783353 | −0.391676 | − | 0.920103i | \(-0.628105\pi\) | ||||
−0.391676 | + | 0.920103i | \(0.628105\pi\) | |||||||
\(912\) | −1.06982e12 | −0.0512077 | ||||||||
\(913\) | −3.91200e11 | −0.0186329 | ||||||||
\(914\) | −3.93649e12 | −0.186574 | ||||||||
\(915\) | −2.33292e12 | −0.110028 | ||||||||
\(916\) | 3.22989e12 | 0.151586 | ||||||||
\(917\) | −4.29156e13 | −2.00425 | ||||||||
\(918\) | 1.72896e12 | 0.0803514 | ||||||||
\(919\) | 6.17320e12 | 0.285490 | 0.142745 | − | 0.989759i | \(-0.454407\pi\) | ||||
0.142745 | + | 0.989759i | \(0.454407\pi\) | |||||||
\(920\) | 4.56577e12 | 0.210121 | ||||||||
\(921\) | 1.11760e12 | 0.0511823 | ||||||||
\(922\) | −5.61262e12 | −0.255786 | ||||||||
\(923\) | 3.39719e12 | 0.154068 | ||||||||
\(924\) | −1.67901e12 | −0.0757755 | ||||||||
\(925\) | −9.62744e12 | −0.432387 | ||||||||
\(926\) | 1.60822e13 | 0.718781 | ||||||||
\(927\) | −2.89730e12 | −0.128865 | ||||||||
\(928\) | 2.78992e13 | 1.23489 | ||||||||
\(929\) | −2.36498e13 | −1.04173 | −0.520867 | − | 0.853638i | \(-0.674391\pi\) | ||||
−0.520867 | + | 0.853638i | \(0.674391\pi\) | |||||||
\(930\) | −1.65559e11 | −0.00725736 | ||||||||
\(931\) | −3.10058e13 | −1.35260 | ||||||||
\(932\) | 7.73209e12 | 0.335680 | ||||||||
\(933\) | −1.12546e12 | −0.0486254 | ||||||||
\(934\) | 9.70882e12 | 0.417451 | ||||||||
\(935\) | −3.90696e11 | −0.0167181 | ||||||||
\(936\) | −8.66586e11 | −0.0369037 | ||||||||
\(937\) | −4.58998e13 | −1.94528 | −0.972642 | − | 0.232309i | \(-0.925372\pi\) | ||||
−0.972642 | + | 0.232309i | \(0.925372\pi\) | |||||||
\(938\) | −2.59468e13 | −1.09439 | ||||||||
\(939\) | −2.01702e13 | −0.846671 | ||||||||
\(940\) | 3.29929e12 | 0.137830 | ||||||||
\(941\) | 3.09088e13 | 1.28507 | 0.642537 | − | 0.766254i | \(-0.277882\pi\) | ||||
0.642537 | + | 0.766254i | \(0.277882\pi\) | |||||||
\(942\) | −8.16814e12 | −0.337983 | ||||||||
\(943\) | 2.59495e13 | 1.06863 | ||||||||
\(944\) | −4.34435e11 | −0.0178054 | ||||||||
\(945\) | 1.70886e12 | 0.0697048 | ||||||||
\(946\) | −8.13940e11 | −0.0330432 | ||||||||
\(947\) | −3.03772e12 | −0.122736 | −0.0613682 | − | 0.998115i | \(-0.519546\pi\) | ||||
−0.0613682 | + | 0.998115i | \(0.519546\pi\) | |||||||
\(948\) | −1.36979e13 | −0.550830 | ||||||||
\(949\) | 1.33502e12 | 0.0534306 | ||||||||
\(950\) | −8.85113e12 | −0.352567 | ||||||||
\(951\) | 2.05736e13 | 0.815641 | ||||||||
\(952\) | 3.11824e13 | 1.23039 | ||||||||
\(953\) | 2.25232e13 | 0.884528 | 0.442264 | − | 0.896885i | \(-0.354175\pi\) | ||||
0.442264 | + | 0.896885i | \(0.354175\pi\) | |||||||
\(954\) | 3.61065e12 | 0.141129 | ||||||||
\(955\) | 1.33635e12 | 0.0519884 | ||||||||
\(956\) | −2.15863e13 | −0.835828 | ||||||||
\(957\) | 1.98009e12 | 0.0763100 | ||||||||
\(958\) | −1.73474e13 | −0.665412 | ||||||||
\(959\) | −5.45437e13 | −2.08238 | ||||||||
\(960\) | −1.40402e12 | −0.0533521 | ||||||||
\(961\) | −2.61348e13 | −0.988472 | ||||||||
\(962\) | 7.91642e11 | 0.0298017 | ||||||||
\(963\) | −9.10977e12 | −0.341341 | ||||||||
\(964\) | 2.71572e13 | 1.01283 | ||||||||
\(965\) | −5.14934e12 | −0.191152 | ||||||||
\(966\) | −1.66733e13 | −0.616064 | ||||||||
\(967\) | −2.80300e13 | −1.03087 | −0.515434 | − | 0.856929i | \(-0.672369\pi\) | ||||
−0.515434 | + | 0.856929i | \(0.672369\pi\) | |||||||
\(968\) | −2.57044e13 | −0.940956 | ||||||||
\(969\) | 7.55615e12 | 0.275324 | ||||||||
\(970\) | 6.11358e11 | 0.0221729 | ||||||||
\(971\) | −1.48038e13 | −0.534424 | −0.267212 | − | 0.963638i | \(-0.586102\pi\) | ||||
−0.267212 | + | 0.963638i | \(0.586102\pi\) | |||||||
\(972\) | −1.20969e12 | −0.0434687 | ||||||||
\(973\) | −4.51600e13 | −1.61527 | ||||||||
\(974\) | −1.45517e13 | −0.518082 | ||||||||
\(975\) | 1.81302e12 | 0.0642512 | ||||||||
\(976\) | 3.58342e12 | 0.126408 | ||||||||
\(977\) | −4.58267e13 | −1.60914 | −0.804569 | − | 0.593859i | \(-0.797604\pi\) | ||||
−0.804569 | + | 0.593859i | \(0.797604\pi\) | |||||||
\(978\) | −1.04299e13 | −0.364550 | ||||||||
\(979\) | −3.35064e12 | −0.116575 | ||||||||
\(980\) | 8.41425e12 | 0.291406 | ||||||||
\(981\) | −1.43426e13 | −0.494443 | ||||||||
\(982\) | −1.18911e13 | −0.408058 | ||||||||
\(983\) | 4.73679e13 | 1.61806 | 0.809028 | − | 0.587770i | \(-0.199994\pi\) | ||||
0.809028 | + | 0.587770i | \(0.199994\pi\) | |||||||
\(984\) | −1.61550e13 | −0.549323 | ||||||||
\(985\) | −1.67391e12 | −0.0566590 | ||||||||
\(986\) | −1.48535e13 | −0.500477 | ||||||||
\(987\) | −2.98291e13 | −1.00049 | ||||||||
\(988\) | −1.52973e12 | −0.0510751 | ||||||||
\(989\) | 1.69887e13 | 0.564648 | ||||||||
\(990\) | −1.30056e11 | −0.00430300 | ||||||||
\(991\) | 3.56521e13 | 1.17423 | 0.587116 | − | 0.809503i | \(-0.300263\pi\) | ||||
0.587116 | + | 0.809503i | \(0.300263\pi\) | |||||||
\(992\) | 3.37365e12 | 0.110611 | ||||||||
\(993\) | 1.37288e13 | 0.448085 | ||||||||
\(994\) | −4.06919e13 | −1.32211 | ||||||||
\(995\) | −7.26951e11 | −0.0235126 | ||||||||
\(996\) | −2.05321e12 | −0.0661098 | ||||||||
\(997\) | 8.44601e11 | 0.0270722 | 0.0135361 | − | 0.999908i | \(-0.495691\pi\) | ||||
0.0135361 | + | 0.999908i | \(0.495691\pi\) | |||||||
\(998\) | 3.49884e13 | 1.11644 | ||||||||
\(999\) | 2.73592e12 | 0.0869078 |
(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 | 177.10.a.d.1.8 | ✓ | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.10.a.d.1.8 | ✓ | 22 | 1.1 | even | 1 | trivial |