Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,14,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, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
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: | \(189.798744245\) |
Analytic rank: | \(1\) |
Dimension: | \(31\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −135.114 | −1.49281 | −0.746405 | − | 0.665492i | \(-0.768222\pi\) | ||||
−0.746405 | + | 0.665492i | \(0.768222\pi\) | |||||||
\(3\) | −729.000 | −0.577350 | ||||||||
\(4\) | 10063.7 | 1.22848 | ||||||||
\(5\) | −36751.1 | −1.05188 | −0.525939 | − | 0.850522i | \(-0.676286\pi\) | ||||
−0.525939 | + | 0.850522i | \(0.676286\pi\) | |||||||
\(6\) | 98497.9 | 0.861874 | ||||||||
\(7\) | −177254. | −0.569454 | −0.284727 | − | 0.958609i | \(-0.591903\pi\) | ||||
−0.284727 | + | 0.958609i | \(0.591903\pi\) | |||||||
\(8\) | −252896. | −0.341081 | ||||||||
\(9\) | 531441. | 0.333333 | ||||||||
\(10\) | 4.96558e6 | 1.57025 | ||||||||
\(11\) | −8.38008e6 | −1.42625 | −0.713125 | − | 0.701037i | \(-0.752721\pi\) | ||||
−0.713125 | + | 0.701037i | \(0.752721\pi\) | |||||||
\(12\) | −7.33646e6 | −0.709265 | ||||||||
\(13\) | 4.85093e6 | 0.278736 | 0.139368 | − | 0.990241i | \(-0.455493\pi\) | ||||
0.139368 | + | 0.990241i | \(0.455493\pi\) | |||||||
\(14\) | 2.39495e7 | 0.850087 | ||||||||
\(15\) | 2.67916e7 | 0.607302 | ||||||||
\(16\) | −4.82723e7 | −0.719313 | ||||||||
\(17\) | 1.51868e7 | 0.152598 | 0.0762989 | − | 0.997085i | \(-0.475690\pi\) | ||||
0.0762989 | + | 0.997085i | \(0.475690\pi\) | |||||||
\(18\) | −7.18050e7 | −0.497603 | ||||||||
\(19\) | −1.04615e8 | −0.510146 | −0.255073 | − | 0.966922i | \(-0.582100\pi\) | ||||
−0.255073 | + | 0.966922i | \(0.582100\pi\) | |||||||
\(20\) | −3.69853e8 | −1.29221 | ||||||||
\(21\) | 1.29218e8 | 0.328775 | ||||||||
\(22\) | 1.13226e9 | 2.12912 | ||||||||
\(23\) | 5.03097e8 | 0.708632 | 0.354316 | − | 0.935126i | \(-0.384714\pi\) | ||||
0.354316 | + | 0.935126i | \(0.384714\pi\) | |||||||
\(24\) | 1.84361e8 | 0.196923 | ||||||||
\(25\) | 1.29940e8 | 0.106447 | ||||||||
\(26\) | −6.55428e8 | −0.416100 | ||||||||
\(27\) | −3.87420e8 | −0.192450 | ||||||||
\(28\) | −1.78384e9 | −0.699565 | ||||||||
\(29\) | −4.08283e9 | −1.27460 | −0.637300 | − | 0.770616i | \(-0.719949\pi\) | ||||
−0.637300 | + | 0.770616i | \(0.719949\pi\) | |||||||
\(30\) | −3.61991e9 | −0.906587 | ||||||||
\(31\) | −6.12832e9 | −1.24020 | −0.620098 | − | 0.784524i | \(-0.712907\pi\) | ||||
−0.620098 | + | 0.784524i | \(0.712907\pi\) | |||||||
\(32\) | 8.59398e9 | 1.41488 | ||||||||
\(33\) | 6.10907e9 | 0.823445 | ||||||||
\(34\) | −2.05195e9 | −0.227800 | ||||||||
\(35\) | 6.51428e9 | 0.598996 | ||||||||
\(36\) | 5.34828e9 | 0.409494 | ||||||||
\(37\) | 9.81095e9 | 0.628637 | 0.314318 | − | 0.949318i | \(-0.398224\pi\) | ||||
0.314318 | + | 0.949318i | \(0.398224\pi\) | |||||||
\(38\) | 1.41349e10 | 0.761551 | ||||||||
\(39\) | −3.53633e9 | −0.160928 | ||||||||
\(40\) | 9.29421e9 | 0.358775 | ||||||||
\(41\) | 3.36959e10 | 1.10785 | 0.553927 | − | 0.832565i | \(-0.313129\pi\) | ||||
0.553927 | + | 0.832565i | \(0.313129\pi\) | |||||||
\(42\) | −1.74592e10 | −0.490798 | ||||||||
\(43\) | −3.54505e10 | −0.855219 | −0.427609 | − | 0.903964i | \(-0.640644\pi\) | ||||
−0.427609 | + | 0.903964i | \(0.640644\pi\) | |||||||
\(44\) | −8.43348e10 | −1.75212 | ||||||||
\(45\) | −1.95310e10 | −0.350626 | ||||||||
\(46\) | −6.79753e10 | −1.05785 | ||||||||
\(47\) | 6.44491e10 | 0.872129 | 0.436065 | − | 0.899915i | \(-0.356372\pi\) | ||||
0.436065 | + | 0.899915i | \(0.356372\pi\) | |||||||
\(48\) | 3.51905e10 | 0.415296 | ||||||||
\(49\) | −6.54700e10 | −0.675722 | ||||||||
\(50\) | −1.75567e10 | −0.158905 | ||||||||
\(51\) | −1.10712e10 | −0.0881024 | ||||||||
\(52\) | 4.88185e10 | 0.342423 | ||||||||
\(53\) | −1.40446e11 | −0.870393 | −0.435196 | − | 0.900336i | \(-0.643321\pi\) | ||||
−0.435196 | + | 0.900336i | \(0.643321\pi\) | |||||||
\(54\) | 5.23458e10 | 0.287291 | ||||||||
\(55\) | 3.07977e11 | 1.50024 | ||||||||
\(56\) | 4.48269e10 | 0.194230 | ||||||||
\(57\) | 7.62642e10 | 0.294533 | ||||||||
\(58\) | 5.51646e11 | 1.90274 | ||||||||
\(59\) | −4.21805e10 | −0.130189 | ||||||||
\(60\) | 2.69623e11 | 0.746060 | ||||||||
\(61\) | −7.41838e11 | −1.84359 | −0.921797 | − | 0.387674i | \(-0.873279\pi\) | ||||
−0.921797 | + | 0.387674i | \(0.873279\pi\) | |||||||
\(62\) | 8.28020e11 | 1.85138 | ||||||||
\(63\) | −9.42001e10 | −0.189818 | ||||||||
\(64\) | −7.65718e11 | −1.39283 | ||||||||
\(65\) | −1.78277e11 | −0.293197 | ||||||||
\(66\) | −8.25420e11 | −1.22925 | ||||||||
\(67\) | 9.59565e11 | 1.29595 | 0.647975 | − | 0.761662i | \(-0.275616\pi\) | ||||
0.647975 | + | 0.761662i | \(0.275616\pi\) | |||||||
\(68\) | 1.52836e11 | 0.187464 | ||||||||
\(69\) | −3.66757e11 | −0.409129 | ||||||||
\(70\) | −8.80169e11 | −0.894188 | ||||||||
\(71\) | −7.60819e11 | −0.704859 | −0.352429 | − | 0.935838i | \(-0.614644\pi\) | ||||
−0.352429 | + | 0.935838i | \(0.614644\pi\) | |||||||
\(72\) | −1.34399e11 | −0.113694 | ||||||||
\(73\) | −5.28101e11 | −0.408430 | −0.204215 | − | 0.978926i | \(-0.565464\pi\) | ||||
−0.204215 | + | 0.978926i | \(0.565464\pi\) | |||||||
\(74\) | −1.32559e12 | −0.938435 | ||||||||
\(75\) | −9.47263e10 | −0.0614572 | ||||||||
\(76\) | −1.05281e12 | −0.626706 | ||||||||
\(77\) | 1.48540e12 | 0.812184 | ||||||||
\(78\) | 4.77807e11 | 0.240236 | ||||||||
\(79\) | 1.53934e11 | 0.0712457 | 0.0356229 | − | 0.999365i | \(-0.488658\pi\) | ||||
0.0356229 | + | 0.999365i | \(0.488658\pi\) | |||||||
\(80\) | 1.77406e12 | 0.756630 | ||||||||
\(81\) | 2.82430e11 | 0.111111 | ||||||||
\(82\) | −4.55278e12 | −1.65382 | ||||||||
\(83\) | 4.32516e12 | 1.45210 | 0.726048 | − | 0.687644i | \(-0.241355\pi\) | ||||
0.726048 | + | 0.687644i | \(0.241355\pi\) | |||||||
\(84\) | 1.30042e12 | 0.403894 | ||||||||
\(85\) | −5.58132e11 | −0.160514 | ||||||||
\(86\) | 4.78985e12 | 1.27668 | ||||||||
\(87\) | 2.97638e12 | 0.735891 | ||||||||
\(88\) | 2.11929e12 | 0.486466 | ||||||||
\(89\) | 3.47028e12 | 0.740166 | 0.370083 | − | 0.928999i | \(-0.379329\pi\) | ||||
0.370083 | + | 0.928999i | \(0.379329\pi\) | |||||||
\(90\) | 2.63891e12 | 0.523418 | ||||||||
\(91\) | −8.59848e11 | −0.158728 | ||||||||
\(92\) | 5.06303e12 | 0.870541 | ||||||||
\(93\) | 4.46755e12 | 0.716028 | ||||||||
\(94\) | −8.70796e12 | −1.30192 | ||||||||
\(95\) | 3.84471e12 | 0.536611 | ||||||||
\(96\) | −6.26501e12 | −0.816881 | ||||||||
\(97\) | 5.67818e12 | 0.692138 | 0.346069 | − | 0.938209i | \(-0.387516\pi\) | ||||
0.346069 | + | 0.938209i | \(0.387516\pi\) | |||||||
\(98\) | 8.84590e12 | 1.00872 | ||||||||
\(99\) | −4.45352e12 | −0.475416 | ||||||||
\(100\) | 1.30768e12 | 0.130768 | ||||||||
\(101\) | 2.43651e12 | 0.228391 | 0.114196 | − | 0.993458i | \(-0.463571\pi\) | ||||
0.114196 | + | 0.993458i | \(0.463571\pi\) | |||||||
\(102\) | 1.49587e12 | 0.131520 | ||||||||
\(103\) | 4.75427e12 | 0.392321 | 0.196161 | − | 0.980572i | \(-0.437153\pi\) | ||||
0.196161 | + | 0.980572i | \(0.437153\pi\) | |||||||
\(104\) | −1.22678e12 | −0.0950716 | ||||||||
\(105\) | −4.74891e12 | −0.345831 | ||||||||
\(106\) | 1.89761e13 | 1.29933 | ||||||||
\(107\) | 1.94033e13 | 1.24992 | 0.624958 | − | 0.780658i | \(-0.285116\pi\) | ||||
0.624958 | + | 0.780658i | \(0.285116\pi\) | |||||||
\(108\) | −3.89889e12 | −0.236422 | ||||||||
\(109\) | 3.10438e13 | 1.77297 | 0.886487 | − | 0.462754i | \(-0.153139\pi\) | ||||
0.886487 | + | 0.462754i | \(0.153139\pi\) | |||||||
\(110\) | −4.16119e13 | −2.23957 | ||||||||
\(111\) | −7.15218e12 | −0.362944 | ||||||||
\(112\) | 8.55646e12 | 0.409616 | ||||||||
\(113\) | 2.47488e13 | 1.11826 | 0.559132 | − | 0.829078i | \(-0.311134\pi\) | ||||
0.559132 | + | 0.829078i | \(0.311134\pi\) | |||||||
\(114\) | −1.03043e13 | −0.439682 | ||||||||
\(115\) | −1.84894e13 | −0.745394 | ||||||||
\(116\) | −4.10885e13 | −1.56582 | ||||||||
\(117\) | 2.57798e12 | 0.0929121 | ||||||||
\(118\) | 5.69917e12 | 0.194347 | ||||||||
\(119\) | −2.69192e12 | −0.0868975 | ||||||||
\(120\) | −6.77548e12 | −0.207139 | ||||||||
\(121\) | 3.57029e13 | 1.03419 | ||||||||
\(122\) | 1.00233e14 | 2.75213 | ||||||||
\(123\) | −2.45643e13 | −0.639620 | ||||||||
\(124\) | −6.16737e13 | −1.52356 | ||||||||
\(125\) | 4.00867e13 | 0.939909 | ||||||||
\(126\) | 1.27277e13 | 0.283362 | ||||||||
\(127\) | 9.17463e13 | 1.94028 | 0.970140 | − | 0.242545i | \(-0.0779822\pi\) | ||||
0.970140 | + | 0.242545i | \(0.0779822\pi\) | |||||||
\(128\) | 3.30572e13 | 0.664356 | ||||||||
\(129\) | 2.58434e13 | 0.493761 | ||||||||
\(130\) | 2.40877e13 | 0.437687 | ||||||||
\(131\) | 2.51976e12 | 0.0435607 | 0.0217804 | − | 0.999763i | \(-0.493067\pi\) | ||||
0.0217804 | + | 0.999763i | \(0.493067\pi\) | |||||||
\(132\) | 6.14801e13 | 1.01159 | ||||||||
\(133\) | 1.85434e13 | 0.290505 | ||||||||
\(134\) | −1.29650e14 | −1.93461 | ||||||||
\(135\) | 1.42381e13 | 0.202434 | ||||||||
\(136\) | −3.84068e12 | −0.0520482 | ||||||||
\(137\) | 1.51614e12 | 0.0195909 | 0.00979545 | − | 0.999952i | \(-0.496882\pi\) | ||||
0.00979545 | + | 0.999952i | \(0.496882\pi\) | |||||||
\(138\) | 4.95540e13 | 0.610751 | ||||||||
\(139\) | 8.90817e13 | 1.04759 | 0.523796 | − | 0.851844i | \(-0.324515\pi\) | ||||
0.523796 | + | 0.851844i | \(0.324515\pi\) | |||||||
\(140\) | 6.55580e13 | 0.735857 | ||||||||
\(141\) | −4.69834e13 | −0.503524 | ||||||||
\(142\) | 1.02797e14 | 1.05222 | ||||||||
\(143\) | −4.06512e13 | −0.397547 | ||||||||
\(144\) | −2.56539e13 | −0.239771 | ||||||||
\(145\) | 1.50048e14 | 1.34072 | ||||||||
\(146\) | 7.13537e13 | 0.609709 | ||||||||
\(147\) | 4.77276e13 | 0.390128 | ||||||||
\(148\) | 9.87347e13 | 0.772269 | ||||||||
\(149\) | 1.99945e14 | 1.49692 | 0.748462 | − | 0.663177i | \(-0.230792\pi\) | ||||
0.748462 | + | 0.663177i | \(0.230792\pi\) | |||||||
\(150\) | 1.27988e13 | 0.0917439 | ||||||||
\(151\) | −1.57341e14 | −1.08017 | −0.540086 | − | 0.841610i | \(-0.681608\pi\) | ||||
−0.540086 | + | 0.841610i | \(0.681608\pi\) | |||||||
\(152\) | 2.64567e13 | 0.174001 | ||||||||
\(153\) | 8.07089e12 | 0.0508660 | ||||||||
\(154\) | −2.00698e14 | −1.21244 | ||||||||
\(155\) | 2.25222e14 | 1.30453 | ||||||||
\(156\) | −3.55887e13 | −0.197698 | ||||||||
\(157\) | 1.30345e13 | 0.0694618 | 0.0347309 | − | 0.999397i | \(-0.488943\pi\) | ||||
0.0347309 | + | 0.999397i | \(0.488943\pi\) | |||||||
\(158\) | −2.07986e13 | −0.106356 | ||||||||
\(159\) | 1.02385e14 | 0.502521 | ||||||||
\(160\) | −3.15838e14 | −1.48828 | ||||||||
\(161\) | −8.91759e13 | −0.403533 | ||||||||
\(162\) | −3.81601e13 | −0.165868 | ||||||||
\(163\) | −3.61627e14 | −1.51023 | −0.755113 | − | 0.655595i | \(-0.772418\pi\) | ||||
−0.755113 | + | 0.655595i | \(0.772418\pi\) | |||||||
\(164\) | 3.39107e14 | 1.36098 | ||||||||
\(165\) | −2.24515e14 | −0.866164 | ||||||||
\(166\) | −5.84389e14 | −2.16770 | ||||||||
\(167\) | −5.37036e14 | −1.91578 | −0.957892 | − | 0.287130i | \(-0.907299\pi\) | ||||
−0.957892 | + | 0.287130i | \(0.907299\pi\) | |||||||
\(168\) | −3.26788e13 | −0.112139 | ||||||||
\(169\) | −2.79344e14 | −0.922306 | ||||||||
\(170\) | 7.54113e13 | 0.239617 | ||||||||
\(171\) | −5.55966e13 | −0.170049 | ||||||||
\(172\) | −3.56764e14 | −1.05062 | ||||||||
\(173\) | −5.14188e14 | −1.45822 | −0.729108 | − | 0.684398i | \(-0.760065\pi\) | ||||
−0.729108 | + | 0.684398i | \(0.760065\pi\) | |||||||
\(174\) | −4.02150e14 | −1.09855 | ||||||||
\(175\) | −2.30324e13 | −0.0606167 | ||||||||
\(176\) | 4.04526e14 | 1.02592 | ||||||||
\(177\) | 3.07496e13 | 0.0751646 | ||||||||
\(178\) | −4.68882e14 | −1.10493 | ||||||||
\(179\) | 4.60252e14 | 1.04581 | 0.522903 | − | 0.852392i | \(-0.324849\pi\) | ||||
0.522903 | + | 0.852392i | \(0.324849\pi\) | |||||||
\(180\) | −1.96555e14 | −0.430738 | ||||||||
\(181\) | 2.21457e14 | 0.468143 | 0.234072 | − | 0.972219i | \(-0.424795\pi\) | ||||
0.234072 | + | 0.972219i | \(0.424795\pi\) | |||||||
\(182\) | 1.16177e14 | 0.236950 | ||||||||
\(183\) | 5.40800e14 | 1.06440 | ||||||||
\(184\) | −1.27231e14 | −0.241701 | ||||||||
\(185\) | −3.60563e14 | −0.661249 | ||||||||
\(186\) | −6.03627e14 | −1.06889 | ||||||||
\(187\) | −1.27267e14 | −0.217643 | ||||||||
\(188\) | 6.48598e14 | 1.07140 | ||||||||
\(189\) | 6.86719e13 | 0.109592 | ||||||||
\(190\) | −5.19473e14 | −0.801059 | ||||||||
\(191\) | 7.56917e14 | 1.12806 | 0.564029 | − | 0.825755i | \(-0.309251\pi\) | ||||
0.564029 | + | 0.825755i | \(0.309251\pi\) | |||||||
\(192\) | 5.58208e14 | 0.804152 | ||||||||
\(193\) | −1.80083e14 | −0.250813 | −0.125407 | − | 0.992105i | \(-0.540024\pi\) | ||||
−0.125407 | + | 0.992105i | \(0.540024\pi\) | |||||||
\(194\) | −7.67200e14 | −1.03323 | ||||||||
\(195\) | 1.29964e14 | 0.169277 | ||||||||
\(196\) | −6.58872e14 | −0.830112 | ||||||||
\(197\) | 9.49115e14 | 1.15688 | 0.578440 | − | 0.815725i | \(-0.303662\pi\) | ||||
0.578440 | + | 0.815725i | \(0.303662\pi\) | |||||||
\(198\) | 6.01731e14 | 0.709707 | ||||||||
\(199\) | 3.59484e14 | 0.410331 | 0.205166 | − | 0.978727i | \(-0.434227\pi\) | ||||
0.205166 | + | 0.978727i | \(0.434227\pi\) | |||||||
\(200\) | −3.28614e13 | −0.0363070 | ||||||||
\(201\) | −6.99523e14 | −0.748217 | ||||||||
\(202\) | −3.29206e14 | −0.340945 | ||||||||
\(203\) | 7.23698e14 | 0.725827 | ||||||||
\(204\) | −1.11417e14 | −0.108232 | ||||||||
\(205\) | −1.23836e15 | −1.16533 | ||||||||
\(206\) | −6.42367e14 | −0.585661 | ||||||||
\(207\) | 2.67366e14 | 0.236211 | ||||||||
\(208\) | −2.34166e14 | −0.200499 | ||||||||
\(209\) | 8.76680e14 | 0.727596 | ||||||||
\(210\) | 6.41643e14 | 0.516260 | ||||||||
\(211\) | −1.32993e15 | −1.03751 | −0.518755 | − | 0.854923i | \(-0.673604\pi\) | ||||
−0.518755 | + | 0.854923i | \(0.673604\pi\) | |||||||
\(212\) | −1.41341e15 | −1.06926 | ||||||||
\(213\) | 5.54637e14 | 0.406950 | ||||||||
\(214\) | −2.62165e15 | −1.86589 | ||||||||
\(215\) | 1.30284e15 | 0.899586 | ||||||||
\(216\) | 9.79772e13 | 0.0656410 | ||||||||
\(217\) | 1.08627e15 | 0.706235 | ||||||||
\(218\) | −4.19444e15 | −2.64671 | ||||||||
\(219\) | 3.84985e14 | 0.235807 | ||||||||
\(220\) | 3.09940e15 | 1.84302 | ||||||||
\(221\) | 7.36702e13 | 0.0425346 | ||||||||
\(222\) | 9.66358e14 | 0.541806 | ||||||||
\(223\) | −1.66917e15 | −0.908907 | −0.454454 | − | 0.890770i | \(-0.650165\pi\) | ||||
−0.454454 | + | 0.890770i | \(0.650165\pi\) | |||||||
\(224\) | −1.52332e15 | −0.805709 | ||||||||
\(225\) | 6.90555e13 | 0.0354823 | ||||||||
\(226\) | −3.34391e15 | −1.66936 | ||||||||
\(227\) | 2.67853e15 | 1.29935 | 0.649677 | − | 0.760210i | \(-0.274904\pi\) | ||||
0.649677 | + | 0.760210i | \(0.274904\pi\) | |||||||
\(228\) | 7.67502e14 | 0.361829 | ||||||||
\(229\) | 2.33451e15 | 1.06971 | 0.534853 | − | 0.844945i | \(-0.320367\pi\) | ||||
0.534853 | + | 0.844945i | \(0.320367\pi\) | |||||||
\(230\) | 2.49817e15 | 1.11273 | ||||||||
\(231\) | −1.08286e15 | −0.468915 | ||||||||
\(232\) | 1.03253e15 | 0.434742 | ||||||||
\(233\) | 5.83561e14 | 0.238931 | 0.119466 | − | 0.992838i | \(-0.461882\pi\) | ||||
0.119466 | + | 0.992838i | \(0.461882\pi\) | |||||||
\(234\) | −3.48321e14 | −0.138700 | ||||||||
\(235\) | −2.36857e15 | −0.917373 | ||||||||
\(236\) | −4.24493e14 | −0.159935 | ||||||||
\(237\) | −1.12218e14 | −0.0411337 | ||||||||
\(238\) | 3.63716e14 | 0.129722 | ||||||||
\(239\) | −2.79102e15 | −0.968670 | −0.484335 | − | 0.874883i | \(-0.660938\pi\) | ||||
−0.484335 | + | 0.874883i | \(0.660938\pi\) | |||||||
\(240\) | −1.29329e15 | −0.436840 | ||||||||
\(241\) | 8.64348e14 | 0.284170 | 0.142085 | − | 0.989854i | \(-0.454619\pi\) | ||||
0.142085 | + | 0.989854i | \(0.454619\pi\) | |||||||
\(242\) | −4.82396e15 | −1.54385 | ||||||||
\(243\) | −2.05891e14 | −0.0641500 | ||||||||
\(244\) | −7.46566e15 | −2.26482 | ||||||||
\(245\) | 2.40609e15 | 0.710777 | ||||||||
\(246\) | 3.31898e15 | 0.954831 | ||||||||
\(247\) | −5.07479e14 | −0.142196 | ||||||||
\(248\) | 1.54983e15 | 0.423007 | ||||||||
\(249\) | −3.15305e15 | −0.838367 | ||||||||
\(250\) | −5.41627e15 | −1.40311 | ||||||||
\(251\) | 1.93339e15 | 0.488023 | 0.244011 | − | 0.969772i | \(-0.421537\pi\) | ||||
0.244011 | + | 0.969772i | \(0.421537\pi\) | |||||||
\(252\) | −9.48004e14 | −0.233188 | ||||||||
\(253\) | −4.21599e15 | −1.01069 | ||||||||
\(254\) | −1.23962e16 | −2.89647 | ||||||||
\(255\) | 4.06878e14 | 0.0926730 | ||||||||
\(256\) | 1.80628e15 | 0.401076 | ||||||||
\(257\) | 5.14069e15 | 1.11290 | 0.556450 | − | 0.830881i | \(-0.312163\pi\) | ||||
0.556450 | + | 0.830881i | \(0.312163\pi\) | |||||||
\(258\) | −3.49180e15 | −0.737091 | ||||||||
\(259\) | −1.73903e15 | −0.357980 | ||||||||
\(260\) | −1.79413e15 | −0.360187 | ||||||||
\(261\) | −2.16978e15 | −0.424867 | ||||||||
\(262\) | −3.40454e14 | −0.0650279 | ||||||||
\(263\) | −5.52213e15 | −1.02895 | −0.514475 | − | 0.857505i | \(-0.672013\pi\) | ||||
−0.514475 | + | 0.857505i | \(0.672013\pi\) | |||||||
\(264\) | −1.54496e15 | −0.280861 | ||||||||
\(265\) | 5.16153e15 | 0.915547 | ||||||||
\(266\) | −2.50547e15 | −0.433669 | ||||||||
\(267\) | −2.52983e15 | −0.427335 | ||||||||
\(268\) | 9.65680e15 | 1.59205 | ||||||||
\(269\) | −5.12039e15 | −0.823974 | −0.411987 | − | 0.911190i | \(-0.635165\pi\) | ||||
−0.411987 | + | 0.911190i | \(0.635165\pi\) | |||||||
\(270\) | −1.92377e15 | −0.302196 | ||||||||
\(271\) | −1.04149e16 | −1.59718 | −0.798589 | − | 0.601876i | \(-0.794420\pi\) | ||||
−0.798589 | + | 0.601876i | \(0.794420\pi\) | |||||||
\(272\) | −7.33102e14 | −0.109766 | ||||||||
\(273\) | 6.26829e14 | 0.0916414 | ||||||||
\(274\) | −2.04851e14 | −0.0292455 | ||||||||
\(275\) | −1.08891e15 | −0.151820 | ||||||||
\(276\) | −3.69095e15 | −0.502607 | ||||||||
\(277\) | −6.95643e15 | −0.925268 | −0.462634 | − | 0.886549i | \(-0.653096\pi\) | ||||
−0.462634 | + | 0.886549i | \(0.653096\pi\) | |||||||
\(278\) | −1.20362e16 | −1.56386 | ||||||||
\(279\) | −3.25684e15 | −0.413399 | ||||||||
\(280\) | −1.64744e15 | −0.204306 | ||||||||
\(281\) | −3.47038e15 | −0.420520 | −0.210260 | − | 0.977646i | \(-0.567431\pi\) | ||||
−0.210260 | + | 0.977646i | \(0.567431\pi\) | |||||||
\(282\) | 6.34810e15 | 0.751666 | ||||||||
\(283\) | 6.56657e15 | 0.759848 | 0.379924 | − | 0.925018i | \(-0.375950\pi\) | ||||
0.379924 | + | 0.925018i | \(0.375950\pi\) | |||||||
\(284\) | −7.65668e15 | −0.865907 | ||||||||
\(285\) | −2.80279e15 | −0.309813 | ||||||||
\(286\) | 5.49253e15 | 0.593463 | ||||||||
\(287\) | −5.97274e15 | −0.630872 | ||||||||
\(288\) | 4.56719e15 | 0.471626 | ||||||||
\(289\) | −9.67394e15 | −0.976714 | ||||||||
\(290\) | −2.02736e16 | −2.00145 | ||||||||
\(291\) | −4.13939e15 | −0.399606 | ||||||||
\(292\) | −5.31466e15 | −0.501750 | ||||||||
\(293\) | 1.71602e16 | 1.58446 | 0.792232 | − | 0.610221i | \(-0.208919\pi\) | ||||
0.792232 | + | 0.610221i | \(0.208919\pi\) | |||||||
\(294\) | −6.44866e15 | −0.582387 | ||||||||
\(295\) | 1.55018e15 | 0.136943 | ||||||||
\(296\) | −2.48115e15 | −0.214416 | ||||||||
\(297\) | 3.24661e15 | 0.274482 | ||||||||
\(298\) | −2.70153e16 | −2.23462 | ||||||||
\(299\) | 2.44049e15 | 0.197521 | ||||||||
\(300\) | −9.53300e14 | −0.0754990 | ||||||||
\(301\) | 6.28374e15 | 0.487008 | ||||||||
\(302\) | 2.12590e16 | 1.61249 | ||||||||
\(303\) | −1.77622e15 | −0.131862 | ||||||||
\(304\) | 5.05000e15 | 0.366955 | ||||||||
\(305\) | 2.72634e16 | 1.93923 | ||||||||
\(306\) | −1.09049e15 | −0.0759332 | ||||||||
\(307\) | 1.11248e15 | 0.0758390 | 0.0379195 | − | 0.999281i | \(-0.487927\pi\) | ||||
0.0379195 | + | 0.999281i | \(0.487927\pi\) | |||||||
\(308\) | 1.49487e16 | 0.997754 | ||||||||
\(309\) | −3.46586e15 | −0.226507 | ||||||||
\(310\) | −3.04307e16 | −1.94742 | ||||||||
\(311\) | −1.98978e16 | −1.24699 | −0.623493 | − | 0.781829i | \(-0.714287\pi\) | ||||
−0.623493 | + | 0.781829i | \(0.714287\pi\) | |||||||
\(312\) | 8.94324e14 | 0.0548896 | ||||||||
\(313\) | −1.75088e15 | −0.105249 | −0.0526246 | − | 0.998614i | \(-0.516759\pi\) | ||||
−0.0526246 | + | 0.998614i | \(0.516759\pi\) | |||||||
\(314\) | −1.76114e15 | −0.103693 | ||||||||
\(315\) | 3.46196e15 | 0.199665 | ||||||||
\(316\) | 1.54915e15 | 0.0875241 | ||||||||
\(317\) | 4.90894e15 | 0.271708 | 0.135854 | − | 0.990729i | \(-0.456622\pi\) | ||||
0.135854 | + | 0.990729i | \(0.456622\pi\) | |||||||
\(318\) | −1.38336e16 | −0.750169 | ||||||||
\(319\) | 3.42144e16 | 1.81790 | ||||||||
\(320\) | 2.81410e16 | 1.46509 | ||||||||
\(321\) | −1.41450e16 | −0.721640 | ||||||||
\(322\) | 1.20489e16 | 0.602399 | ||||||||
\(323\) | −1.58876e15 | −0.0778472 | ||||||||
\(324\) | 2.84229e15 | 0.136498 | ||||||||
\(325\) | 6.30331e14 | 0.0296706 | ||||||||
\(326\) | 4.88608e16 | 2.25448 | ||||||||
\(327\) | −2.26309e16 | −1.02363 | ||||||||
\(328\) | −8.52157e15 | −0.377868 | ||||||||
\(329\) | −1.14239e16 | −0.496638 | ||||||||
\(330\) | 3.03351e16 | 1.29302 | ||||||||
\(331\) | 1.20282e16 | 0.502710 | 0.251355 | − | 0.967895i | \(-0.419124\pi\) | ||||
0.251355 | + | 0.967895i | \(0.419124\pi\) | |||||||
\(332\) | 4.35273e16 | 1.78387 | ||||||||
\(333\) | 5.21394e15 | 0.209546 | ||||||||
\(334\) | 7.25610e16 | 2.85990 | ||||||||
\(335\) | −3.52651e16 | −1.36318 | ||||||||
\(336\) | −6.23766e15 | −0.236492 | ||||||||
\(337\) | −2.09057e16 | −0.777447 | −0.388723 | − | 0.921355i | \(-0.627084\pi\) | ||||
−0.388723 | + | 0.921355i | \(0.627084\pi\) | |||||||
\(338\) | 3.77432e16 | 1.37683 | ||||||||
\(339\) | −1.80419e16 | −0.645630 | ||||||||
\(340\) | −5.61689e15 | −0.197189 | ||||||||
\(341\) | 5.13558e16 | 1.76883 | ||||||||
\(342\) | 7.51186e15 | 0.253850 | ||||||||
\(343\) | 2.87788e16 | 0.954247 | ||||||||
\(344\) | 8.96529e15 | 0.291699 | ||||||||
\(345\) | 1.34787e16 | 0.430353 | ||||||||
\(346\) | 6.94738e16 | 2.17684 | ||||||||
\(347\) | 2.79978e16 | 0.860959 | 0.430479 | − | 0.902600i | \(-0.358345\pi\) | ||||
0.430479 | + | 0.902600i | \(0.358345\pi\) | |||||||
\(348\) | 2.99535e16 | 0.904029 | ||||||||
\(349\) | −9.68362e15 | −0.286862 | −0.143431 | − | 0.989660i | \(-0.545813\pi\) | ||||
−0.143431 | + | 0.989660i | \(0.545813\pi\) | |||||||
\(350\) | 3.11200e15 | 0.0904892 | ||||||||
\(351\) | −1.87935e15 | −0.0536428 | ||||||||
\(352\) | −7.20182e16 | −2.01797 | ||||||||
\(353\) | −4.80443e16 | −1.32162 | −0.660809 | − | 0.750554i | \(-0.729787\pi\) | ||||
−0.660809 | + | 0.750554i | \(0.729787\pi\) | |||||||
\(354\) | −4.15470e15 | −0.112206 | ||||||||
\(355\) | 2.79609e16 | 0.741425 | ||||||||
\(356\) | 3.49239e16 | 0.909280 | ||||||||
\(357\) | 1.96241e15 | 0.0501703 | ||||||||
\(358\) | −6.21864e16 | −1.56119 | ||||||||
\(359\) | −4.48117e16 | −1.10478 | −0.552392 | − | 0.833584i | \(-0.686285\pi\) | ||||
−0.552392 | + | 0.833584i | \(0.686285\pi\) | |||||||
\(360\) | 4.93933e15 | 0.119592 | ||||||||
\(361\) | −3.11087e16 | −0.739751 | ||||||||
\(362\) | −2.99219e16 | −0.698849 | ||||||||
\(363\) | −2.60274e16 | −0.597088 | ||||||||
\(364\) | −8.65327e15 | −0.194994 | ||||||||
\(365\) | 1.94083e16 | 0.429619 | ||||||||
\(366\) | −7.30695e16 | −1.58895 | ||||||||
\(367\) | 1.97937e16 | 0.422861 | 0.211430 | − | 0.977393i | \(-0.432188\pi\) | ||||
0.211430 | + | 0.977393i | \(0.432188\pi\) | |||||||
\(368\) | −2.42856e16 | −0.509728 | ||||||||
\(369\) | 1.79074e16 | 0.369285 | ||||||||
\(370\) | 4.87170e16 | 0.987119 | ||||||||
\(371\) | 2.48946e16 | 0.495649 | ||||||||
\(372\) | 4.49602e16 | 0.879627 | ||||||||
\(373\) | 6.21356e16 | 1.19463 | 0.597315 | − | 0.802007i | \(-0.296234\pi\) | ||||
0.597315 | + | 0.802007i | \(0.296234\pi\) | |||||||
\(374\) | 1.71955e16 | 0.324899 | ||||||||
\(375\) | −2.92232e16 | −0.542657 | ||||||||
\(376\) | −1.62989e16 | −0.297466 | ||||||||
\(377\) | −1.98055e16 | −0.355277 | ||||||||
\(378\) | −9.27851e15 | −0.163599 | ||||||||
\(379\) | −2.69500e16 | −0.467094 | −0.233547 | − | 0.972345i | \(-0.575033\pi\) | ||||
−0.233547 | + | 0.972345i | \(0.575033\pi\) | |||||||
\(380\) | 3.86921e16 | 0.659218 | ||||||||
\(381\) | −6.68831e16 | −1.12022 | ||||||||
\(382\) | −1.02270e17 | −1.68398 | ||||||||
\(383\) | −2.91675e16 | −0.472179 | −0.236089 | − | 0.971731i | \(-0.575866\pi\) | ||||
−0.236089 | + | 0.971731i | \(0.575866\pi\) | |||||||
\(384\) | −2.40987e16 | −0.383566 | ||||||||
\(385\) | −5.45902e16 | −0.854318 | ||||||||
\(386\) | 2.43317e16 | 0.374417 | ||||||||
\(387\) | −1.88398e16 | −0.285073 | ||||||||
\(388\) | 5.71436e16 | 0.850279 | ||||||||
\(389\) | 9.35821e16 | 1.36937 | 0.684684 | − | 0.728840i | \(-0.259940\pi\) | ||||
0.684684 | + | 0.728840i | \(0.259940\pi\) | |||||||
\(390\) | −1.75599e16 | −0.252699 | ||||||||
\(391\) | 7.64043e15 | 0.108136 | ||||||||
\(392\) | 1.65571e16 | 0.230476 | ||||||||
\(393\) | −1.83690e15 | −0.0251498 | ||||||||
\(394\) | −1.28238e17 | −1.72700 | ||||||||
\(395\) | −5.65725e15 | −0.0749418 | ||||||||
\(396\) | −4.48190e16 | −0.584041 | ||||||||
\(397\) | −2.26960e16 | −0.290945 | −0.145473 | − | 0.989362i | \(-0.546470\pi\) | ||||
−0.145473 | + | 0.989362i | \(0.546470\pi\) | |||||||
\(398\) | −4.85712e16 | −0.612546 | ||||||||
\(399\) | −1.35181e16 | −0.167723 | ||||||||
\(400\) | −6.27251e15 | −0.0765687 | ||||||||
\(401\) | 6.63148e16 | 0.796475 | 0.398238 | − | 0.917282i | \(-0.369622\pi\) | ||||
0.398238 | + | 0.917282i | \(0.369622\pi\) | |||||||
\(402\) | 9.45151e16 | 1.11695 | ||||||||
\(403\) | −2.97281e16 | −0.345688 | ||||||||
\(404\) | 2.45204e16 | 0.280574 | ||||||||
\(405\) | −1.03796e16 | −0.116875 | ||||||||
\(406\) | −9.77815e16 | −1.08352 | ||||||||
\(407\) | −8.22165e16 | −0.896593 | ||||||||
\(408\) | 2.79986e15 | 0.0300500 | ||||||||
\(409\) | 3.74208e16 | 0.395286 | 0.197643 | − | 0.980274i | \(-0.436671\pi\) | ||||
0.197643 | + | 0.980274i | \(0.436671\pi\) | |||||||
\(410\) | 1.67320e17 | 1.73961 | ||||||||
\(411\) | −1.10526e15 | −0.0113108 | ||||||||
\(412\) | 4.78457e16 | 0.481960 | ||||||||
\(413\) | 7.47667e15 | 0.0741366 | ||||||||
\(414\) | −3.61249e16 | −0.352617 | ||||||||
\(415\) | −1.58955e17 | −1.52743 | ||||||||
\(416\) | 4.16888e16 | 0.394378 | ||||||||
\(417\) | −6.49406e16 | −0.604828 | ||||||||
\(418\) | −1.18451e17 | −1.08616 | ||||||||
\(419\) | −2.41263e16 | −0.217821 | −0.108910 | − | 0.994052i | \(-0.534736\pi\) | ||||
−0.108910 | + | 0.994052i | \(0.534736\pi\) | |||||||
\(420\) | −4.77917e16 | −0.424847 | ||||||||
\(421\) | 2.19706e16 | 0.192313 | 0.0961563 | − | 0.995366i | \(-0.469345\pi\) | ||||
0.0961563 | + | 0.995366i | \(0.469345\pi\) | |||||||
\(422\) | 1.79692e17 | 1.54881 | ||||||||
\(423\) | 3.42509e16 | 0.290710 | ||||||||
\(424\) | 3.55182e16 | 0.296874 | ||||||||
\(425\) | 1.97337e15 | 0.0162436 | ||||||||
\(426\) | −7.49391e16 | −0.607500 | ||||||||
\(427\) | 1.31494e17 | 1.04984 | ||||||||
\(428\) | 1.95270e17 | 1.53550 | ||||||||
\(429\) | 2.96347e16 | 0.229524 | ||||||||
\(430\) | −1.76032e17 | −1.34291 | ||||||||
\(431\) | 7.37220e16 | 0.553981 | 0.276991 | − | 0.960873i | \(-0.410663\pi\) | ||||
0.276991 | + | 0.960873i | \(0.410663\pi\) | |||||||
\(432\) | 1.87017e16 | 0.138432 | ||||||||
\(433\) | 9.16974e16 | 0.668630 | 0.334315 | − | 0.942461i | \(-0.391495\pi\) | ||||
0.334315 | + | 0.942461i | \(0.391495\pi\) | |||||||
\(434\) | −1.46770e17 | −1.05428 | ||||||||
\(435\) | −1.09385e17 | −0.774067 | ||||||||
\(436\) | 3.12416e17 | 2.17807 | ||||||||
\(437\) | −5.26313e16 | −0.361506 | ||||||||
\(438\) | −5.20168e16 | −0.352016 | ||||||||
\(439\) | 1.77992e17 | 1.18681 | 0.593404 | − | 0.804905i | \(-0.297784\pi\) | ||||
0.593404 | + | 0.804905i | \(0.297784\pi\) | |||||||
\(440\) | −7.78862e16 | −0.511703 | ||||||||
\(441\) | −3.47934e16 | −0.225241 | ||||||||
\(442\) | −9.95385e15 | −0.0634960 | ||||||||
\(443\) | 1.71435e17 | 1.07765 | 0.538823 | − | 0.842419i | \(-0.318869\pi\) | ||||
0.538823 | + | 0.842419i | \(0.318869\pi\) | |||||||
\(444\) | −7.19776e16 | −0.445870 | ||||||||
\(445\) | −1.27536e17 | −0.778564 | ||||||||
\(446\) | 2.25528e17 | 1.35683 | ||||||||
\(447\) | −1.45760e17 | −0.864250 | ||||||||
\(448\) | 1.35727e17 | 0.793155 | ||||||||
\(449\) | 1.55418e17 | 0.895158 | 0.447579 | − | 0.894244i | \(-0.352286\pi\) | ||||
0.447579 | + | 0.894244i | \(0.352286\pi\) | |||||||
\(450\) | −9.33035e15 | −0.0529684 | ||||||||
\(451\) | −2.82374e17 | −1.58008 | ||||||||
\(452\) | 2.49065e17 | 1.37377 | ||||||||
\(453\) | 1.14702e17 | 0.623637 | ||||||||
\(454\) | −3.61906e17 | −1.93969 | ||||||||
\(455\) | 3.16003e16 | 0.166962 | ||||||||
\(456\) | −1.92869e16 | −0.100460 | ||||||||
\(457\) | −1.55484e17 | −0.798417 | −0.399208 | − | 0.916860i | \(-0.630715\pi\) | ||||
−0.399208 | + | 0.916860i | \(0.630715\pi\) | |||||||
\(458\) | −3.15424e17 | −1.59687 | ||||||||
\(459\) | −5.88368e15 | −0.0293675 | ||||||||
\(460\) | −1.86072e17 | −0.915703 | ||||||||
\(461\) | 1.69476e17 | 0.822342 | 0.411171 | − | 0.911558i | \(-0.365120\pi\) | ||||
0.411171 | + | 0.911558i | \(0.365120\pi\) | |||||||
\(462\) | 1.46309e17 | 0.700001 | ||||||||
\(463\) | −5.34879e16 | −0.252336 | −0.126168 | − | 0.992009i | \(-0.540268\pi\) | ||||
−0.126168 | + | 0.992009i | \(0.540268\pi\) | |||||||
\(464\) | 1.97087e17 | 0.916837 | ||||||||
\(465\) | −1.64187e17 | −0.753174 | ||||||||
\(466\) | −7.88471e16 | −0.356679 | ||||||||
\(467\) | −7.43957e16 | −0.331885 | −0.165943 | − | 0.986135i | \(-0.553067\pi\) | ||||
−0.165943 | + | 0.986135i | \(0.553067\pi\) | |||||||
\(468\) | 2.59441e16 | 0.114141 | ||||||||
\(469\) | −1.70087e17 | −0.737984 | ||||||||
\(470\) | 3.20027e17 | 1.36946 | ||||||||
\(471\) | −9.50214e15 | −0.0401038 | ||||||||
\(472\) | 1.06673e16 | 0.0444049 | ||||||||
\(473\) | 2.97078e17 | 1.21976 | ||||||||
\(474\) | 1.51622e16 | 0.0614049 | ||||||||
\(475\) | −1.35937e16 | −0.0543035 | ||||||||
\(476\) | −2.70908e16 | −0.106752 | ||||||||
\(477\) | −7.46386e16 | −0.290131 | ||||||||
\(478\) | 3.77105e17 | 1.44604 | ||||||||
\(479\) | −3.24024e17 | −1.22573 | −0.612867 | − | 0.790186i | \(-0.709984\pi\) | ||||
−0.612867 | + | 0.790186i | \(0.709984\pi\) | |||||||
\(480\) | 2.30246e17 | 0.859259 | ||||||||
\(481\) | 4.75922e16 | 0.175224 | ||||||||
\(482\) | −1.16785e17 | −0.424212 | ||||||||
\(483\) | 6.50093e16 | 0.232980 | ||||||||
\(484\) | 3.59305e17 | 1.27048 | ||||||||
\(485\) | −2.08679e17 | −0.728045 | ||||||||
\(486\) | 2.78187e16 | 0.0957638 | ||||||||
\(487\) | −4.34696e17 | −1.47655 | −0.738274 | − | 0.674501i | \(-0.764359\pi\) | ||||
−0.738274 | + | 0.674501i | \(0.764359\pi\) | |||||||
\(488\) | 1.87608e17 | 0.628814 | ||||||||
\(489\) | 2.63626e17 | 0.871929 | ||||||||
\(490\) | −3.25096e17 | −1.06105 | ||||||||
\(491\) | −1.57154e17 | −0.506170 | −0.253085 | − | 0.967444i | \(-0.581445\pi\) | ||||
−0.253085 | + | 0.967444i | \(0.581445\pi\) | |||||||
\(492\) | −2.47209e17 | −0.785761 | ||||||||
\(493\) | −6.20051e16 | −0.194501 | ||||||||
\(494\) | 6.85674e16 | 0.212272 | ||||||||
\(495\) | 1.63672e17 | 0.500080 | ||||||||
\(496\) | 2.95828e17 | 0.892090 | ||||||||
\(497\) | 1.34858e17 | 0.401385 | ||||||||
\(498\) | 4.26020e17 | 1.25152 | ||||||||
\(499\) | 1.37480e17 | 0.398643 | 0.199322 | − | 0.979934i | \(-0.436126\pi\) | ||||
0.199322 | + | 0.979934i | \(0.436126\pi\) | |||||||
\(500\) | 4.03422e17 | 1.15466 | ||||||||
\(501\) | 3.91499e17 | 1.10608 | ||||||||
\(502\) | −2.61227e17 | −0.728525 | ||||||||
\(503\) | −2.33300e17 | −0.642278 | −0.321139 | − | 0.947032i | \(-0.604066\pi\) | ||||
−0.321139 | + | 0.947032i | \(0.604066\pi\) | |||||||
\(504\) | 2.38228e16 | 0.0647433 | ||||||||
\(505\) | −8.95444e16 | −0.240240 | ||||||||
\(506\) | 5.69638e17 | 1.50876 | ||||||||
\(507\) | 2.03641e17 | 0.532494 | ||||||||
\(508\) | 9.23310e17 | 2.38360 | ||||||||
\(509\) | 3.95297e16 | 0.100753 | 0.0503765 | − | 0.998730i | \(-0.483958\pi\) | ||||
0.0503765 | + | 0.998730i | \(0.483958\pi\) | |||||||
\(510\) | −5.49748e16 | −0.138343 | ||||||||
\(511\) | 9.36080e16 | 0.232583 | ||||||||
\(512\) | −5.14858e17 | −1.26309 | ||||||||
\(513\) | 4.05299e16 | 0.0981777 | ||||||||
\(514\) | −6.94578e17 | −1.66135 | ||||||||
\(515\) | −1.74725e17 | −0.412674 | ||||||||
\(516\) | 2.60081e17 | 0.606577 | ||||||||
\(517\) | −5.40088e17 | −1.24387 | ||||||||
\(518\) | 2.34967e17 | 0.534396 | ||||||||
\(519\) | 3.74843e17 | 0.841902 | ||||||||
\(520\) | 4.50856e16 | 0.100004 | ||||||||
\(521\) | 7.26203e17 | 1.59079 | 0.795395 | − | 0.606092i | \(-0.207263\pi\) | ||||
0.795395 | + | 0.606092i | \(0.207263\pi\) | |||||||
\(522\) | 2.93167e17 | 0.634245 | ||||||||
\(523\) | −3.14235e17 | −0.671419 | −0.335709 | − | 0.941966i | \(-0.608976\pi\) | ||||
−0.335709 | + | 0.941966i | \(0.608976\pi\) | |||||||
\(524\) | 2.53581e16 | 0.0535136 | ||||||||
\(525\) | 1.67906e16 | 0.0349970 | ||||||||
\(526\) | 7.46116e17 | 1.53603 | ||||||||
\(527\) | −9.30696e16 | −0.189251 | ||||||||
\(528\) | −2.94899e17 | −0.592315 | ||||||||
\(529\) | −2.50930e17 | −0.497841 | ||||||||
\(530\) | −6.97394e17 | −1.36674 | ||||||||
\(531\) | −2.24165e16 | −0.0433963 | ||||||||
\(532\) | 1.86616e17 | 0.356880 | ||||||||
\(533\) | 1.63457e17 | 0.308799 | ||||||||
\(534\) | 3.41815e17 | 0.637930 | ||||||||
\(535\) | −7.13093e17 | −1.31476 | ||||||||
\(536\) | −2.42670e17 | −0.442023 | ||||||||
\(537\) | −3.35524e17 | −0.603796 | ||||||||
\(538\) | 6.91836e17 | 1.23004 | ||||||||
\(539\) | 5.48644e17 | 0.963748 | ||||||||
\(540\) | 1.43289e17 | 0.248687 | ||||||||
\(541\) | 1.07834e17 | 0.184915 | 0.0924574 | − | 0.995717i | \(-0.470528\pi\) | ||||
0.0924574 | + | 0.995717i | \(0.470528\pi\) | |||||||
\(542\) | 1.40719e18 | 2.38429 | ||||||||
\(543\) | −1.61442e17 | −0.270283 | ||||||||
\(544\) | 1.30515e17 | 0.215908 | ||||||||
\(545\) | −1.14089e18 | −1.86495 | ||||||||
\(546\) | −8.46932e16 | −0.136803 | ||||||||
\(547\) | −1.07320e18 | −1.71302 | −0.856509 | − | 0.516132i | \(-0.827371\pi\) | ||||
−0.856509 | + | 0.516132i | \(0.827371\pi\) | |||||||
\(548\) | 1.52580e16 | 0.0240671 | ||||||||
\(549\) | −3.94243e17 | −0.614531 | ||||||||
\(550\) | 1.47126e17 | 0.226638 | ||||||||
\(551\) | 4.27124e17 | 0.650232 | ||||||||
\(552\) | 9.27516e16 | 0.139546 | ||||||||
\(553\) | −2.72855e16 | −0.0405712 | ||||||||
\(554\) | 9.39909e17 | 1.38125 | ||||||||
\(555\) | 2.62850e17 | 0.381772 | ||||||||
\(556\) | 8.96494e17 | 1.28695 | ||||||||
\(557\) | 2.97270e17 | 0.421787 | 0.210893 | − | 0.977509i | \(-0.432363\pi\) | ||||
0.210893 | + | 0.977509i | \(0.432363\pi\) | |||||||
\(558\) | 4.40044e17 | 0.617126 | ||||||||
\(559\) | −1.71968e17 | −0.238381 | ||||||||
\(560\) | −3.14459e17 | −0.430866 | ||||||||
\(561\) | 9.27773e16 | 0.125656 | ||||||||
\(562\) | 4.68897e17 | 0.627756 | ||||||||
\(563\) | −9.38201e17 | −1.24163 | −0.620814 | − | 0.783958i | \(-0.713198\pi\) | ||||
−0.620814 | + | 0.783958i | \(0.713198\pi\) | |||||||
\(564\) | −4.72828e17 | −0.618570 | ||||||||
\(565\) | −9.09546e17 | −1.17628 | ||||||||
\(566\) | −8.87234e17 | −1.13431 | ||||||||
\(567\) | −5.00618e16 | −0.0632727 | ||||||||
\(568\) | 1.92408e17 | 0.240414 | ||||||||
\(569\) | −2.02313e17 | −0.249916 | −0.124958 | − | 0.992162i | \(-0.539880\pi\) | ||||
−0.124958 | + | 0.992162i | \(0.539880\pi\) | |||||||
\(570\) | 3.78696e17 | 0.462492 | ||||||||
\(571\) | 8.75809e17 | 1.05749 | 0.528743 | − | 0.848782i | \(-0.322664\pi\) | ||||
0.528743 | + | 0.848782i | \(0.322664\pi\) | |||||||
\(572\) | −4.09102e17 | −0.488380 | ||||||||
\(573\) | −5.51792e17 | −0.651284 | ||||||||
\(574\) | 8.06999e17 | 0.941772 | ||||||||
\(575\) | 6.53724e16 | 0.0754317 | ||||||||
\(576\) | −4.06934e17 | −0.464278 | ||||||||
\(577\) | 1.28222e17 | 0.144651 | 0.0723254 | − | 0.997381i | \(-0.476958\pi\) | ||||
0.0723254 | + | 0.997381i | \(0.476958\pi\) | |||||||
\(578\) | 1.30708e18 | 1.45805 | ||||||||
\(579\) | 1.31281e17 | 0.144807 | ||||||||
\(580\) | 1.51005e18 | 1.64706 | ||||||||
\(581\) | −7.66653e17 | −0.826902 | ||||||||
\(582\) | 5.59289e17 | 0.596536 | ||||||||
\(583\) | 1.17695e18 | 1.24140 | ||||||||
\(584\) | 1.33555e17 | 0.139308 | ||||||||
\(585\) | −9.47438e16 | −0.0977322 | ||||||||
\(586\) | −2.31858e18 | −2.36530 | ||||||||
\(587\) | 1.30462e18 | 1.31624 | 0.658122 | − | 0.752911i | \(-0.271351\pi\) | ||||
0.658122 | + | 0.752911i | \(0.271351\pi\) | |||||||
\(588\) | 4.80318e17 | 0.479266 | ||||||||
\(589\) | 6.41113e17 | 0.632681 | ||||||||
\(590\) | −2.09451e17 | −0.204430 | ||||||||
\(591\) | −6.91905e17 | −0.667925 | ||||||||
\(592\) | −4.73597e17 | −0.452187 | ||||||||
\(593\) | 6.13712e17 | 0.579575 | 0.289787 | − | 0.957091i | \(-0.406415\pi\) | ||||
0.289787 | + | 0.957091i | \(0.406415\pi\) | |||||||
\(594\) | −4.38662e17 | −0.409749 | ||||||||
\(595\) | 9.89311e16 | 0.0914056 | ||||||||
\(596\) | 2.01219e18 | 1.83895 | ||||||||
\(597\) | −2.62064e17 | −0.236905 | ||||||||
\(598\) | −3.29744e17 | −0.294862 | ||||||||
\(599\) | −1.94525e18 | −1.72068 | −0.860340 | − | 0.509721i | \(-0.829749\pi\) | ||||
−0.860340 | + | 0.509721i | \(0.829749\pi\) | |||||||
\(600\) | 2.39559e16 | 0.0209619 | ||||||||
\(601\) | 1.80265e18 | 1.56036 | 0.780182 | − | 0.625552i | \(-0.215126\pi\) | ||||
0.780182 | + | 0.625552i | \(0.215126\pi\) | |||||||
\(602\) | −8.49020e17 | −0.727011 | ||||||||
\(603\) | 5.09952e17 | 0.431983 | ||||||||
\(604\) | −1.58344e18 | −1.32697 | ||||||||
\(605\) | −1.31212e18 | −1.08784 | ||||||||
\(606\) | 2.39991e17 | 0.196844 | ||||||||
\(607\) | −4.92005e17 | −0.399248 | −0.199624 | − | 0.979873i | \(-0.563972\pi\) | ||||
−0.199624 | + | 0.979873i | \(0.563972\pi\) | |||||||
\(608\) | −8.99057e17 | −0.721795 | ||||||||
\(609\) | −5.27576e17 | −0.419056 | ||||||||
\(610\) | −3.68366e18 | −2.89491 | ||||||||
\(611\) | 3.12638e17 | 0.243094 | ||||||||
\(612\) | 8.12233e16 | 0.0624879 | ||||||||
\(613\) | 6.31596e17 | 0.480780 | 0.240390 | − | 0.970676i | \(-0.422725\pi\) | ||||
0.240390 | + | 0.970676i | \(0.422725\pi\) | |||||||
\(614\) | −1.50311e17 | −0.113213 | ||||||||
\(615\) | 9.02766e17 | 0.672802 | ||||||||
\(616\) | −3.75653e17 | −0.277020 | ||||||||
\(617\) | 6.34814e17 | 0.463226 | 0.231613 | − | 0.972808i | \(-0.425600\pi\) | ||||
0.231613 | + | 0.972808i | \(0.425600\pi\) | |||||||
\(618\) | 4.68286e17 | 0.338131 | ||||||||
\(619\) | −1.99491e18 | −1.42539 | −0.712694 | − | 0.701475i | \(-0.752525\pi\) | ||||
−0.712694 | + | 0.701475i | \(0.752525\pi\) | |||||||
\(620\) | 2.26658e18 | 1.60260 | ||||||||
\(621\) | −1.94910e17 | −0.136376 | ||||||||
\(622\) | 2.68846e18 | 1.86151 | ||||||||
\(623\) | −6.15120e17 | −0.421491 | ||||||||
\(624\) | 1.70707e17 | 0.115758 | ||||||||
\(625\) | −1.63185e18 | −1.09512 | ||||||||
\(626\) | 2.36568e17 | 0.157117 | ||||||||
\(627\) | −6.39100e17 | −0.420078 | ||||||||
\(628\) | 1.31176e17 | 0.0853326 | ||||||||
\(629\) | 1.48997e17 | 0.0959286 | ||||||||
\(630\) | −4.67758e17 | −0.298063 | ||||||||
\(631\) | 3.26786e16 | 0.0206098 | 0.0103049 | − | 0.999947i | \(-0.496720\pi\) | ||||
0.0103049 | + | 0.999947i | \(0.496720\pi\) | |||||||
\(632\) | −3.89294e16 | −0.0243006 | ||||||||
\(633\) | 9.69518e17 | 0.599007 | ||||||||
\(634\) | −6.63266e17 | −0.405609 | ||||||||
\(635\) | −3.37178e18 | −2.04094 | ||||||||
\(636\) | 1.03037e18 | 0.617339 | ||||||||
\(637\) | −3.17591e17 | −0.188348 | ||||||||
\(638\) | −4.62284e18 | −2.71378 | ||||||||
\(639\) | −4.04330e17 | −0.234953 | ||||||||
\(640\) | −1.21489e18 | −0.698821 | ||||||||
\(641\) | 5.86346e17 | 0.333869 | 0.166935 | − | 0.985968i | \(-0.446613\pi\) | ||||
0.166935 | + | 0.985968i | \(0.446613\pi\) | |||||||
\(642\) | 1.91119e18 | 1.07727 | ||||||||
\(643\) | 1.70659e18 | 0.952267 | 0.476133 | − | 0.879373i | \(-0.342038\pi\) | ||||
0.476133 | + | 0.879373i | \(0.342038\pi\) | |||||||
\(644\) | −8.97442e17 | −0.495734 | ||||||||
\(645\) | −9.49774e17 | −0.519376 | ||||||||
\(646\) | 2.14664e17 | 0.116211 | ||||||||
\(647\) | −2.16639e18 | −1.16107 | −0.580537 | − | 0.814234i | \(-0.697157\pi\) | ||||
−0.580537 | + | 0.814234i | \(0.697157\pi\) | |||||||
\(648\) | −7.14253e16 | −0.0378979 | ||||||||
\(649\) | 3.53476e17 | 0.185682 | ||||||||
\(650\) | −8.51663e16 | −0.0442926 | ||||||||
\(651\) | −7.91891e17 | −0.407745 | ||||||||
\(652\) | −3.63932e18 | −1.85529 | ||||||||
\(653\) | 1.60954e16 | 0.00812394 | 0.00406197 | − | 0.999992i | \(-0.498707\pi\) | ||||
0.00406197 | + | 0.999992i | \(0.498707\pi\) | |||||||
\(654\) | 3.05775e18 | 1.52808 | ||||||||
\(655\) | −9.26038e16 | −0.0458206 | ||||||||
\(656\) | −1.62658e18 | −0.796894 | ||||||||
\(657\) | −2.80654e17 | −0.136143 | ||||||||
\(658\) | 1.54352e18 | 0.741386 | ||||||||
\(659\) | 2.79209e18 | 1.32793 | 0.663965 | − | 0.747764i | \(-0.268873\pi\) | ||||
0.663965 | + | 0.747764i | \(0.268873\pi\) | |||||||
\(660\) | −2.25946e18 | −1.06407 | ||||||||
\(661\) | −3.90908e18 | −1.82291 | −0.911455 | − | 0.411401i | \(-0.865040\pi\) | ||||
−0.911455 | + | 0.411401i | \(0.865040\pi\) | |||||||
\(662\) | −1.62517e18 | −0.750451 | ||||||||
\(663\) | −5.37056e16 | −0.0245573 | ||||||||
\(664\) | −1.09382e18 | −0.495282 | ||||||||
\(665\) | −6.81490e17 | −0.305576 | ||||||||
\(666\) | −7.04475e17 | −0.312812 | ||||||||
\(667\) | −2.05406e18 | −0.903222 | ||||||||
\(668\) | −5.40459e18 | −2.35351 | ||||||||
\(669\) | 1.21683e18 | 0.524758 | ||||||||
\(670\) | 4.76479e18 | 2.03497 | ||||||||
\(671\) | 6.21666e18 | 2.62942 | ||||||||
\(672\) | 1.11050e18 | 0.465176 | ||||||||
\(673\) | −4.15377e18 | −1.72323 | −0.861617 | − | 0.507559i | \(-0.830548\pi\) | ||||
−0.861617 | + | 0.507559i | \(0.830548\pi\) | |||||||
\(674\) | 2.82465e18 | 1.16058 | ||||||||
\(675\) | −5.03415e16 | −0.0204857 | ||||||||
\(676\) | −2.81124e18 | −1.13304 | ||||||||
\(677\) | −2.72367e18 | −1.08725 | −0.543624 | − | 0.839329i | \(-0.682948\pi\) | ||||
−0.543624 | + | 0.839329i | \(0.682948\pi\) | |||||||
\(678\) | 2.43771e18 | 0.963804 | ||||||||
\(679\) | −1.00648e18 | −0.394141 | ||||||||
\(680\) | 1.41149e17 | 0.0547484 | ||||||||
\(681\) | −1.95265e18 | −0.750183 | ||||||||
\(682\) | −6.93887e18 | −2.64053 | ||||||||
\(683\) | 2.96098e18 | 1.11609 | 0.558046 | − | 0.829810i | \(-0.311551\pi\) | ||||
0.558046 | + | 0.829810i | \(0.311551\pi\) | |||||||
\(684\) | −5.59509e17 | −0.208902 | ||||||||
\(685\) | −5.57196e16 | −0.0206072 | ||||||||
\(686\) | −3.88841e18 | −1.42451 | ||||||||
\(687\) | −1.70186e18 | −0.617595 | ||||||||
\(688\) | 1.71128e18 | 0.615170 | ||||||||
\(689\) | −6.81293e17 | −0.242610 | ||||||||
\(690\) | −1.82116e18 | −0.642436 | ||||||||
\(691\) | 3.39708e18 | 1.18713 | 0.593566 | − | 0.804785i | \(-0.297720\pi\) | ||||
0.593566 | + | 0.804785i | \(0.297720\pi\) | |||||||
\(692\) | −5.17464e18 | −1.79139 | ||||||||
\(693\) | 7.89404e17 | 0.270728 | ||||||||
\(694\) | −3.78289e18 | −1.28525 | ||||||||
\(695\) | −3.27385e18 | −1.10194 | ||||||||
\(696\) | −7.52715e17 | −0.250998 | ||||||||
\(697\) | 5.11734e17 | 0.169056 | ||||||||
\(698\) | 1.30839e18 | 0.428230 | ||||||||
\(699\) | −4.25416e17 | −0.137947 | ||||||||
\(700\) | −2.31792e17 | −0.0744665 | ||||||||
\(701\) | −3.98665e18 | −1.26894 | −0.634470 | − | 0.772947i | \(-0.718782\pi\) | ||||
−0.634470 | + | 0.772947i | \(0.718782\pi\) | |||||||
\(702\) | 2.53926e17 | 0.0800786 | ||||||||
\(703\) | −1.02637e18 | −0.320697 | ||||||||
\(704\) | 6.41677e18 | 1.98653 | ||||||||
\(705\) | 1.72669e18 | 0.529646 | ||||||||
\(706\) | 6.49144e18 | 1.97293 | ||||||||
\(707\) | −4.31881e17 | −0.130058 | ||||||||
\(708\) | 3.09456e17 | 0.0923384 | ||||||||
\(709\) | −2.82310e18 | −0.834692 | −0.417346 | − | 0.908748i | \(-0.637040\pi\) | ||||
−0.417346 | + | 0.908748i | \(0.637040\pi\) | |||||||
\(710\) | −3.77791e18 | −1.10681 | ||||||||
\(711\) | 8.18069e16 | 0.0237486 | ||||||||
\(712\) | −8.77619e17 | −0.252456 | ||||||||
\(713\) | −3.08314e18 | −0.878842 | ||||||||
\(714\) | −2.65149e17 | −0.0748947 | ||||||||
\(715\) | 1.49398e18 | 0.418171 | ||||||||
\(716\) | 4.63185e18 | 1.28475 | ||||||||
\(717\) | 2.03465e18 | 0.559262 | ||||||||
\(718\) | 6.05468e18 | 1.64923 | ||||||||
\(719\) | 1.65057e17 | 0.0445551 | 0.0222775 | − | 0.999752i | \(-0.492908\pi\) | ||||
0.0222775 | + | 0.999752i | \(0.492908\pi\) | |||||||
\(720\) | 9.42808e17 | 0.252210 | ||||||||
\(721\) | −8.42713e17 | −0.223409 | ||||||||
\(722\) | 4.20322e18 | 1.10431 | ||||||||
\(723\) | −6.30110e17 | −0.164066 | ||||||||
\(724\) | 2.22868e18 | 0.575106 | ||||||||
\(725\) | −5.30523e17 | −0.135677 | ||||||||
\(726\) | 3.51667e18 | 0.891339 | ||||||||
\(727\) | 4.92778e18 | 1.23788 | 0.618938 | − | 0.785440i | \(-0.287563\pi\) | ||||
0.618938 | + | 0.785440i | \(0.287563\pi\) | |||||||
\(728\) | 2.17452e17 | 0.0541389 | ||||||||
\(729\) | 1.50095e17 | 0.0370370 | ||||||||
\(730\) | −2.62233e18 | −0.641340 | ||||||||
\(731\) | −5.38380e17 | −0.130505 | ||||||||
\(732\) | 5.44246e18 | 1.30760 | ||||||||
\(733\) | −2.75180e18 | −0.655301 | −0.327651 | − | 0.944799i | \(-0.606257\pi\) | ||||
−0.327651 | + | 0.944799i | \(0.606257\pi\) | |||||||
\(734\) | −2.67440e18 | −0.631251 | ||||||||
\(735\) | −1.75404e18 | −0.410367 | ||||||||
\(736\) | 4.32360e18 | 1.00263 | ||||||||
\(737\) | −8.04122e18 | −1.84835 | ||||||||
\(738\) | −2.41954e18 | −0.551272 | ||||||||
\(739\) | 3.04067e18 | 0.686722 | 0.343361 | − | 0.939204i | \(-0.388435\pi\) | ||||
0.343361 | + | 0.939204i | \(0.388435\pi\) | |||||||
\(740\) | −3.62861e18 | −0.812333 | ||||||||
\(741\) | 3.69952e17 | 0.0820970 | ||||||||
\(742\) | −3.36360e18 | −0.739910 | ||||||||
\(743\) | −7.85000e17 | −0.171176 | −0.0855879 | − | 0.996331i | \(-0.527277\pi\) | ||||
−0.0855879 | + | 0.996331i | \(0.527277\pi\) | |||||||
\(744\) | −1.12982e18 | −0.244223 | ||||||||
\(745\) | −7.34820e18 | −1.57458 | ||||||||
\(746\) | −8.39538e18 | −1.78336 | ||||||||
\(747\) | 2.29857e18 | 0.484032 | ||||||||
\(748\) | −1.28078e18 | −0.267370 | ||||||||
\(749\) | −3.43931e18 | −0.711771 | ||||||||
\(750\) | 3.94846e18 | 0.810083 | ||||||||
\(751\) | −6.27619e18 | −1.27655 | −0.638273 | − | 0.769810i | \(-0.720351\pi\) | ||||
−0.638273 | + | 0.769810i | \(0.720351\pi\) | |||||||
\(752\) | −3.11111e18 | −0.627334 | ||||||||
\(753\) | −1.40944e18 | −0.281760 | ||||||||
\(754\) | 2.67600e18 | 0.530362 | ||||||||
\(755\) | 5.78246e18 | 1.13621 | ||||||||
\(756\) | 6.91095e17 | 0.134631 | ||||||||
\(757\) | 5.40715e18 | 1.04435 | 0.522174 | − | 0.852839i | \(-0.325121\pi\) | ||||
0.522174 | + | 0.852839i | \(0.325121\pi\) | |||||||
\(758\) | 3.64132e18 | 0.697283 | ||||||||
\(759\) | 3.07346e18 | 0.583519 | ||||||||
\(760\) | −9.72312e17 | −0.183028 | ||||||||
\(761\) | −4.05663e18 | −0.757121 | −0.378561 | − | 0.925577i | \(-0.623581\pi\) | ||||
−0.378561 | + | 0.925577i | \(0.623581\pi\) | |||||||
\(762\) | 9.03682e18 | 1.67228 | ||||||||
\(763\) | −5.50263e18 | −1.00963 | ||||||||
\(764\) | 7.61740e18 | 1.38580 | ||||||||
\(765\) | −2.96614e17 | −0.0535048 | ||||||||
\(766\) | 3.94092e18 | 0.704873 | ||||||||
\(767\) | −2.04615e17 | −0.0362884 | ||||||||
\(768\) | −1.31678e18 | −0.231561 | ||||||||
\(769\) | −4.92529e18 | −0.858837 | −0.429419 | − | 0.903106i | \(-0.641281\pi\) | ||||
−0.429419 | + | 0.903106i | \(0.641281\pi\) | |||||||
\(770\) | 7.37588e18 | 1.27534 | ||||||||
\(771\) | −3.74757e18 | −0.642533 | ||||||||
\(772\) | −1.81231e18 | −0.308120 | ||||||||
\(773\) | 1.58560e18 | 0.267318 | 0.133659 | − | 0.991027i | \(-0.457327\pi\) | ||||
0.133659 | + | 0.991027i | \(0.457327\pi\) | |||||||
\(774\) | 2.54552e18 | 0.425560 | ||||||||
\(775\) | −7.96314e17 | −0.132015 | ||||||||
\(776\) | −1.43599e18 | −0.236075 | ||||||||
\(777\) | 1.26775e18 | 0.206680 | ||||||||
\(778\) | −1.26442e19 | −2.04421 | ||||||||
\(779\) | −3.52509e18 | −0.565167 | ||||||||
\(780\) | 1.30792e18 | 0.207954 | ||||||||
\(781\) | 6.37572e18 | 1.00530 | ||||||||
\(782\) | −1.03233e18 | −0.161426 | ||||||||
\(783\) | 1.58177e18 | 0.245297 | ||||||||
\(784\) | 3.16039e18 | 0.486056 | ||||||||
\(785\) | −4.79032e17 | −0.0730653 | ||||||||
\(786\) | 2.48191e17 | 0.0375439 | ||||||||
\(787\) | 3.72631e17 | 0.0559041 | 0.0279521 | − | 0.999609i | \(-0.491101\pi\) | ||||
0.0279521 | + | 0.999609i | \(0.491101\pi\) | |||||||
\(788\) | 9.55163e18 | 1.42121 | ||||||||
\(789\) | 4.02563e18 | 0.594065 | ||||||||
\(790\) | 7.64372e17 | 0.111874 | ||||||||
\(791\) | −4.38683e18 | −0.636801 | ||||||||
\(792\) | 1.12628e18 | 0.162155 | ||||||||
\(793\) | −3.59861e18 | −0.513876 | ||||||||
\(794\) | 3.06654e18 | 0.434326 | ||||||||
\(795\) | −3.76276e18 | −0.528591 | ||||||||
\(796\) | 3.61775e18 | 0.504084 | ||||||||
\(797\) | 1.14973e19 | 1.58897 | 0.794484 | − | 0.607285i | \(-0.207741\pi\) | ||||
0.794484 | + | 0.607285i | \(0.207741\pi\) | |||||||
\(798\) | 1.82649e18 | 0.250379 | ||||||||
\(799\) | 9.78776e17 | 0.133085 | ||||||||
\(800\) | 1.11670e18 | 0.150610 | ||||||||
\(801\) | 1.84425e18 | 0.246722 | ||||||||
\(802\) | −8.96005e18 | −1.18899 | ||||||||
\(803\) | 4.42552e18 | 0.582524 | ||||||||
\(804\) | −7.03980e18 | −0.919171 | ||||||||
\(805\) | 3.27731e18 | 0.424468 | ||||||||
\(806\) | 4.01667e18 | 0.516046 | ||||||||
\(807\) | 3.73277e18 | 0.475722 | ||||||||
\(808\) | −6.16184e17 | −0.0778998 | ||||||||
\(809\) | −1.08696e19 | −1.36317 | −0.681585 | − | 0.731739i | \(-0.738709\pi\) | ||||
−0.681585 | + | 0.731739i | \(0.738709\pi\) | |||||||
\(810\) | 1.40243e18 | 0.174473 | ||||||||
\(811\) | −9.14789e17 | −0.112898 | −0.0564489 | − | 0.998405i | \(-0.517978\pi\) | ||||
−0.0564489 | + | 0.998405i | \(0.517978\pi\) | |||||||
\(812\) | 7.28310e18 | 0.891665 | ||||||||
\(813\) | 7.59244e18 | 0.922132 | ||||||||
\(814\) | 1.11086e19 | 1.33844 | ||||||||
\(815\) | 1.32902e19 | 1.58857 | ||||||||
\(816\) | 5.34431e17 | 0.0633733 | ||||||||
\(817\) | 3.70865e18 | 0.436287 | ||||||||
\(818\) | −5.05606e18 | −0.590087 | ||||||||
\(819\) | −4.56958e17 | −0.0529092 | ||||||||
\(820\) | −1.24625e19 | −1.43158 | ||||||||
\(821\) | 1.18804e19 | 1.35394 | 0.676972 | − | 0.736009i | \(-0.263292\pi\) | ||||
0.676972 | + | 0.736009i | \(0.263292\pi\) | |||||||
\(822\) | 1.49336e17 | 0.0168849 | ||||||||
\(823\) | 1.10207e18 | 0.123627 | 0.0618133 | − | 0.998088i | \(-0.480312\pi\) | ||||
0.0618133 | + | 0.998088i | \(0.480312\pi\) | |||||||
\(824\) | −1.20234e18 | −0.133813 | ||||||||
\(825\) | 7.93814e17 | 0.0876532 | ||||||||
\(826\) | −1.01020e18 | −0.110672 | ||||||||
\(827\) | 5.65393e18 | 0.614561 | 0.307280 | − | 0.951619i | \(-0.400581\pi\) | ||||
0.307280 | + | 0.951619i | \(0.400581\pi\) | |||||||
\(828\) | 2.69070e18 | 0.290180 | ||||||||
\(829\) | 6.06514e18 | 0.648987 | 0.324494 | − | 0.945888i | \(-0.394806\pi\) | ||||
0.324494 | + | 0.945888i | \(0.394806\pi\) | |||||||
\(830\) | 2.14769e19 | 2.28016 | ||||||||
\(831\) | 5.07124e18 | 0.534204 | ||||||||
\(832\) | −3.71445e18 | −0.388233 | ||||||||
\(833\) | −9.94280e17 | −0.103114 | ||||||||
\(834\) | 8.77436e18 | 0.902893 | ||||||||
\(835\) | 1.97367e19 | 2.01517 | ||||||||
\(836\) | 8.82267e18 | 0.893838 | ||||||||
\(837\) | 2.37424e18 | 0.238676 | ||||||||
\(838\) | 3.25980e18 | 0.325165 | ||||||||
\(839\) | 1.37363e19 | 1.35962 | 0.679812 | − | 0.733387i | \(-0.262062\pi\) | ||||
0.679812 | + | 0.733387i | \(0.262062\pi\) | |||||||
\(840\) | 1.20098e18 | 0.117956 | ||||||||
\(841\) | 6.40885e18 | 0.624606 | ||||||||
\(842\) | −2.96853e18 | −0.287086 | ||||||||
\(843\) | 2.52991e18 | 0.242787 | ||||||||
\(844\) | −1.33840e19 | −1.27456 | ||||||||
\(845\) | 1.02662e19 | 0.970153 | ||||||||
\(846\) | −4.62777e18 | −0.433974 | ||||||||
\(847\) | −6.32849e18 | −0.588922 | ||||||||
\(848\) | 6.77964e18 | 0.626085 | ||||||||
\(849\) | −4.78703e18 | −0.438698 | ||||||||
\(850\) | −2.66630e17 | −0.0242486 | ||||||||
\(851\) | 4.93585e18 | 0.445472 | ||||||||
\(852\) | 5.58172e18 | 0.499931 | ||||||||
\(853\) | −3.26824e18 | −0.290499 | −0.145250 | − | 0.989395i | \(-0.546399\pi\) | ||||
−0.145250 | + | 0.989395i | \(0.546399\pi\) | |||||||
\(854\) | −1.77666e19 | −1.56722 | ||||||||
\(855\) | 2.04324e18 | 0.178870 | ||||||||
\(856\) | −4.90702e18 | −0.426323 | ||||||||
\(857\) | 4.29308e18 | 0.370164 | 0.185082 | − | 0.982723i | \(-0.440745\pi\) | ||||
0.185082 | + | 0.982723i | \(0.440745\pi\) | |||||||
\(858\) | −4.00406e18 | −0.342636 | ||||||||
\(859\) | −8.04363e18 | −0.683119 | −0.341560 | − | 0.939860i | \(-0.610955\pi\) | ||||
−0.341560 | + | 0.939860i | \(0.610955\pi\) | |||||||
\(860\) | 1.31115e19 | 1.10513 | ||||||||
\(861\) | 4.35413e18 | 0.364234 | ||||||||
\(862\) | −9.96086e18 | −0.826989 | ||||||||
\(863\) | 2.89038e18 | 0.238169 | 0.119084 | − | 0.992884i | \(-0.462004\pi\) | ||||
0.119084 | + | 0.992884i | \(0.462004\pi\) | |||||||
\(864\) | −3.32948e18 | −0.272294 | ||||||||
\(865\) | 1.88970e19 | 1.53387 | ||||||||
\(866\) | −1.23896e19 | −0.998138 | ||||||||
\(867\) | 7.05230e18 | 0.563906 | ||||||||
\(868\) | 1.09319e19 | 0.867597 | ||||||||
\(869\) | −1.28998e18 | −0.101614 | ||||||||
\(870\) | 1.47795e19 | 1.15554 | ||||||||
\(871\) | 4.65478e18 | 0.361228 | ||||||||
\(872\) | −7.85085e18 | −0.604727 | ||||||||
\(873\) | 3.01762e18 | 0.230713 | ||||||||
\(874\) | 7.11122e18 | 0.539659 | ||||||||
\(875\) | −7.10554e18 | −0.535235 | ||||||||
\(876\) | 3.87439e18 | 0.289685 | ||||||||
\(877\) | 1.94577e19 | 1.44409 | 0.722043 | − | 0.691848i | \(-0.243203\pi\) | ||||
0.722043 | + | 0.691848i | \(0.243203\pi\) | |||||||
\(878\) | −2.40491e19 | −1.77168 | ||||||||
\(879\) | −1.25098e19 | −0.914790 | ||||||||
\(880\) | −1.48668e19 | −1.07914 | ||||||||
\(881\) | −7.85383e18 | −0.565898 | −0.282949 | − | 0.959135i | \(-0.591313\pi\) | ||||
−0.282949 | + | 0.959135i | \(0.591313\pi\) | |||||||
\(882\) | 4.70107e18 | 0.336241 | ||||||||
\(883\) | −2.26828e19 | −1.61047 | −0.805234 | − | 0.592957i | \(-0.797960\pi\) | ||||
−0.805234 | + | 0.592957i | \(0.797960\pi\) | |||||||
\(884\) | 7.41397e17 | 0.0522530 | ||||||||
\(885\) | −1.13008e18 | −0.0790640 | ||||||||
\(886\) | −2.31633e19 | −1.60872 | ||||||||
\(887\) | 8.05272e18 | 0.555187 | 0.277593 | − | 0.960699i | \(-0.410463\pi\) | ||||
0.277593 | + | 0.960699i | \(0.410463\pi\) | |||||||
\(888\) | 1.80876e18 | 0.123793 | ||||||||
\(889\) | −1.62624e19 | −1.10490 | ||||||||
\(890\) | 1.72319e19 | 1.16225 | ||||||||
\(891\) | −2.36678e18 | −0.158472 | ||||||||
\(892\) | −1.67981e19 | −1.11658 | ||||||||
\(893\) | −6.74233e18 | −0.444913 | ||||||||
\(894\) | 1.96942e19 | 1.29016 | ||||||||
\(895\) | −1.69148e19 | −1.10006 | ||||||||
\(896\) | −5.85952e18 | −0.378320 | ||||||||
\(897\) | −1.77912e18 | −0.114039 | ||||||||
\(898\) | −2.09991e19 | −1.33630 | ||||||||
\(899\) | 2.50209e19 | 1.58075 | ||||||||
\(900\) | 6.94956e17 | 0.0435894 | ||||||||
\(901\) | −2.13292e18 | −0.132820 | ||||||||
\(902\) | 3.81527e19 | 2.35875 | ||||||||
\(903\) | −4.58085e18 | −0.281174 | ||||||||
\(904\) | −6.25888e18 | −0.381419 | ||||||||
\(905\) | −8.13879e18 | −0.492430 | ||||||||
\(906\) | −1.54978e19 | −0.930972 | ||||||||
\(907\) | −1.59480e18 | −0.0951170 | −0.0475585 | − | 0.998868i | \(-0.515144\pi\) | ||||
−0.0475585 | + | 0.998868i | \(0.515144\pi\) | |||||||
\(908\) | 2.69560e19 | 1.59623 | ||||||||
\(909\) | 1.29486e18 | 0.0761304 | ||||||||
\(910\) | −4.26964e18 | −0.249243 | ||||||||
\(911\) | −8.38863e18 | −0.486208 | −0.243104 | − | 0.970000i | \(-0.578166\pi\) | ||||
−0.243104 | + | 0.970000i | \(0.578166\pi\) | |||||||
\(912\) | −3.68145e18 | −0.211862 | ||||||||
\(913\) | −3.62452e19 | −2.07105 | ||||||||
\(914\) | 2.10080e19 | 1.19188 | ||||||||
\(915\) | −1.98750e19 | −1.11962 | ||||||||
\(916\) | 2.34938e19 | 1.31412 | ||||||||
\(917\) | −4.46637e17 | −0.0248059 | ||||||||
\(918\) | 7.94966e17 | 0.0438401 | ||||||||
\(919\) | 3.45407e19 | 1.89139 | 0.945693 | − | 0.325062i | \(-0.105385\pi\) | ||||
0.945693 | + | 0.325062i | \(0.105385\pi\) | |||||||
\(920\) | 4.67589e18 | 0.254240 | ||||||||
\(921\) | −8.10998e17 | −0.0437857 | ||||||||
\(922\) | −2.28986e19 | −1.22760 | ||||||||
\(923\) | −3.69068e18 | −0.196470 | ||||||||
\(924\) | −1.08976e19 | −0.576053 | ||||||||
\(925\) | 1.27484e18 | 0.0669164 | ||||||||
\(926\) | 7.22695e18 | 0.376690 | ||||||||
\(927\) | 2.52661e18 | 0.130774 | ||||||||
\(928\) | −3.50877e19 | −1.80341 | ||||||||
\(929\) | −1.60387e19 | −0.818593 | −0.409297 | − | 0.912401i | \(-0.634226\pi\) | ||||
−0.409297 | + | 0.912401i | \(0.634226\pi\) | |||||||
\(930\) | 2.21839e19 | 1.12435 | ||||||||
\(931\) | 6.84913e18 | 0.344717 | ||||||||
\(932\) | 5.87280e18 | 0.293523 | ||||||||
\(933\) | 1.45055e19 | 0.719948 | ||||||||
\(934\) | 1.00519e19 | 0.495442 | ||||||||
\(935\) | 4.67719e18 | 0.228933 | ||||||||
\(936\) | −6.51962e17 | −0.0316905 | ||||||||
\(937\) | 1.46031e19 | 0.704917 | 0.352458 | − | 0.935827i | \(-0.385346\pi\) | ||||
0.352458 | + | 0.935827i | \(0.385346\pi\) | |||||||
\(938\) | 2.29811e19 | 1.10167 | ||||||||
\(939\) | 1.27639e18 | 0.0607656 | ||||||||
\(940\) | −2.38367e19 | −1.12698 | ||||||||
\(941\) | 1.53211e19 | 0.719377 | 0.359689 | − | 0.933072i | \(-0.382883\pi\) | ||||
0.359689 | + | 0.933072i | \(0.382883\pi\) | |||||||
\(942\) | 1.28387e18 | 0.0598674 | ||||||||
\(943\) | 1.69523e19 | 0.785060 | ||||||||
\(944\) | 2.03615e18 | 0.0936466 | ||||||||
\(945\) | −2.52377e18 | −0.115277 | ||||||||
\(946\) | −4.01393e19 | −1.82086 | ||||||||
\(947\) | −2.81915e19 | −1.27012 | −0.635058 | − | 0.772465i | \(-0.719024\pi\) | ||||
−0.635058 | + | 0.772465i | \(0.719024\pi\) | |||||||
\(948\) | −1.12933e18 | −0.0505321 | ||||||||
\(949\) | −2.56178e18 | −0.113844 | ||||||||
\(950\) | 1.83669e18 | 0.0810648 | ||||||||
\(951\) | −3.57862e18 | −0.156871 | ||||||||
\(952\) | 6.80777e17 | 0.0296391 | ||||||||
\(953\) | −6.50868e18 | −0.281442 | −0.140721 | − | 0.990049i | \(-0.544942\pi\) | ||||
−0.140721 | + | 0.990049i | \(0.544942\pi\) | |||||||
\(954\) | 1.00847e19 | 0.433110 | ||||||||
\(955\) | −2.78175e19 | −1.18658 | ||||||||
\(956\) | −2.80880e19 | −1.18999 | ||||||||
\(957\) | −2.49423e19 | −1.04956 | ||||||||
\(958\) | 4.37801e19 | 1.82979 | ||||||||
\(959\) | −2.68741e17 | −0.0111561 | ||||||||
\(960\) | −2.05148e19 | −0.845870 | ||||||||
\(961\) | 1.31388e19 | 0.538087 | ||||||||
\(962\) | −6.43037e18 | −0.261576 | ||||||||
\(963\) | 1.03117e19 | 0.416639 | ||||||||
\(964\) | 8.69856e18 | 0.349098 | ||||||||
\(965\) | 6.61825e18 | 0.263825 | ||||||||
\(966\) | −8.78364e18 | −0.347795 | ||||||||
\(967\) | −1.04592e19 | −0.411365 | −0.205683 | − | 0.978619i | \(-0.565941\pi\) | ||||
−0.205683 | + | 0.978619i | \(0.565941\pi\) | |||||||
\(968\) | −9.02914e18 | −0.352741 | ||||||||
\(969\) | 1.15821e18 | 0.0449451 | ||||||||
\(970\) | 2.81954e19 | 1.08683 | ||||||||
\(971\) | −1.64057e19 | −0.628158 | −0.314079 | − | 0.949397i | \(-0.601696\pi\) | ||||
−0.314079 | + | 0.949397i | \(0.601696\pi\) | |||||||
\(972\) | −2.07203e18 | −0.0788072 | ||||||||
\(973\) | −1.57901e19 | −0.596556 | ||||||||
\(974\) | 5.87334e19 | 2.20421 | ||||||||
\(975\) | −4.59511e17 | −0.0171303 | ||||||||
\(976\) | 3.58102e19 | 1.32612 | ||||||||
\(977\) | 3.21003e19 | 1.18085 | 0.590424 | − | 0.807093i | \(-0.298960\pi\) | ||||
0.590424 | + | 0.807093i | \(0.298960\pi\) | |||||||
\(978\) | −3.56196e19 | −1.30163 | ||||||||
\(979\) | −2.90812e19 | −1.05566 | ||||||||
\(980\) | 2.42143e19 | 0.873177 | ||||||||
\(981\) | 1.64979e19 | 0.590991 | ||||||||
\(982\) | 2.12337e19 | 0.755615 | ||||||||
\(983\) | −2.01546e19 | −0.712486 | −0.356243 | − | 0.934393i | \(-0.615942\pi\) | ||||
−0.356243 | + | 0.934393i | \(0.615942\pi\) | |||||||
\(984\) | 6.21223e18 | 0.218162 | ||||||||
\(985\) | −3.48810e19 | −1.21690 | ||||||||
\(986\) | 8.37774e18 | 0.290353 | ||||||||
\(987\) | 8.32800e18 | 0.286734 | ||||||||
\(988\) | −5.10713e18 | −0.174686 | ||||||||
\(989\) | −1.78350e19 | −0.606035 | ||||||||
\(990\) | −2.21143e19 | −0.746525 | ||||||||
\(991\) | 4.63111e19 | 1.55313 | 0.776563 | − | 0.630040i | \(-0.216961\pi\) | ||||
0.776563 | + | 0.630040i | \(0.216961\pi\) | |||||||
\(992\) | −5.26666e19 | −1.75473 | ||||||||
\(993\) | −8.76854e18 | −0.290240 | ||||||||
\(994\) | −1.82212e19 | −0.599191 | ||||||||
\(995\) | −1.32114e19 | −0.431618 | ||||||||
\(996\) | −3.17314e19 | −1.02992 | ||||||||
\(997\) | 1.23578e19 | 0.398494 | 0.199247 | − | 0.979949i | \(-0.436150\pi\) | ||||
0.199247 | + | 0.979949i | \(0.436150\pi\) | |||||||
\(998\) | −1.85754e19 | −0.595099 | ||||||||
\(999\) | −3.80096e18 | −0.120981 |
(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 | 177.14.a.b.1.6 | ✓ | 31 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.14.a.b.1.6 | ✓ | 31 | 1.1 | even | 1 | trivial |