Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,104,Mod(1,1)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 104, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 104);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 104 \) |
Character orbit: | \([\chi]\) | \(=\) | 1.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: | \(67.1843880807\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3 x^{7} + \cdots + 10\!\cdots\!50 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | multiple of \( 2^{104}\cdot 3^{40}\cdot 5^{12}\cdot 7^{8}\cdot 11\cdot 13^{3}\cdot 17^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.50366e14\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.46018e15 | −1.71460 | −0.857299 | − | 0.514819i | \(-0.827859\pi\) | ||||
−0.857299 | + | 0.514819i | \(0.827859\pi\) | |||||||
\(3\) | −1.30099e24 | −0.348763 | −0.174382 | − | 0.984678i | \(-0.555793\pi\) | ||||
−0.174382 | + | 0.984678i | \(0.555793\pi\) | |||||||
\(4\) | 1.96724e31 | 1.93984 | ||||||||
\(5\) | −5.30727e35 | −0.534461 | −0.267230 | − | 0.963633i | \(-0.586108\pi\) | ||||
−0.267230 | + | 0.963633i | \(0.586108\pi\) | |||||||
\(6\) | 7.10366e39 | 0.597988 | ||||||||
\(7\) | 2.61912e43 | 0.786334 | 0.393167 | − | 0.919467i | \(-0.371379\pi\) | ||||
0.393167 | + | 0.919467i | \(0.371379\pi\) | |||||||
\(8\) | −5.20418e46 | −1.61145 | ||||||||
\(9\) | −1.22226e49 | −0.878364 | ||||||||
\(10\) | 2.89786e51 | 0.916385 | ||||||||
\(11\) | 4.50261e53 | 1.05133 | 0.525667 | − | 0.850691i | \(-0.323816\pi\) | ||||
0.525667 | + | 0.850691i | \(0.323816\pi\) | |||||||
\(12\) | −2.55936e55 | −0.676546 | ||||||||
\(13\) | 2.00188e57 | 0.857739 | 0.428870 | − | 0.903366i | \(-0.358912\pi\) | ||||
0.428870 | + | 0.903366i | \(0.358912\pi\) | |||||||
\(14\) | −1.43009e59 | −1.34825 | ||||||||
\(15\) | 6.90472e59 | 0.186400 | ||||||||
\(16\) | 8.46561e61 | 0.823150 | ||||||||
\(17\) | 3.55342e63 | 1.52239 | 0.761197 | − | 0.648520i | \(-0.224612\pi\) | ||||
0.761197 | + | 0.648520i | \(0.224612\pi\) | |||||||
\(18\) | 6.67376e64 | 1.50604 | ||||||||
\(19\) | 1.06089e66 | 1.47863 | 0.739315 | − | 0.673360i | \(-0.235149\pi\) | ||||
0.739315 | + | 0.673360i | \(0.235149\pi\) | |||||||
\(20\) | −1.04406e67 | −1.03677 | ||||||||
\(21\) | −3.40746e67 | −0.274244 | ||||||||
\(22\) | −2.45850e69 | −1.80261 | ||||||||
\(23\) | 1.51243e70 | 1.12381 | 0.561905 | − | 0.827202i | \(-0.310069\pi\) | ||||
0.561905 | + | 0.827202i | \(0.310069\pi\) | |||||||
\(24\) | 6.77060e70 | 0.562016 | ||||||||
\(25\) | −7.04405e71 | −0.714352 | ||||||||
\(26\) | −1.09306e73 | −1.47068 | ||||||||
\(27\) | 3.40051e73 | 0.655104 | ||||||||
\(28\) | 5.15243e74 | 1.52536 | ||||||||
\(29\) | −1.95550e75 | −0.950084 | −0.475042 | − | 0.879963i | \(-0.657567\pi\) | ||||
−0.475042 | + | 0.879963i | \(0.657567\pi\) | |||||||
\(30\) | −3.77010e75 | −0.319601 | ||||||||
\(31\) | −6.33189e76 | −0.991759 | −0.495879 | − | 0.868391i | \(-0.665154\pi\) | ||||
−0.495879 | + | 0.868391i | \(0.665154\pi\) | |||||||
\(32\) | 6.55289e76 | 0.200082 | ||||||||
\(33\) | −5.85786e77 | −0.366666 | ||||||||
\(34\) | −1.94023e79 | −2.61029 | ||||||||
\(35\) | −1.39004e79 | −0.420264 | ||||||||
\(36\) | −2.40447e80 | −1.70389 | ||||||||
\(37\) | −3.73954e80 | −0.646293 | −0.323147 | − | 0.946349i | \(-0.604741\pi\) | ||||
−0.323147 | + | 0.946349i | \(0.604741\pi\) | |||||||
\(38\) | −5.79264e81 | −2.53526 | ||||||||
\(39\) | −2.60443e81 | −0.299148 | ||||||||
\(40\) | 2.76200e82 | 0.861258 | ||||||||
\(41\) | 1.79903e83 | 1.57279 | 0.786394 | − | 0.617725i | \(-0.211946\pi\) | ||||
0.786394 | + | 0.617725i | \(0.211946\pi\) | |||||||
\(42\) | 1.86054e83 | 0.470218 | ||||||||
\(43\) | −4.86424e83 | −0.365923 | −0.182961 | − | 0.983120i | \(-0.558568\pi\) | ||||
−0.182961 | + | 0.983120i | \(0.558568\pi\) | |||||||
\(44\) | 8.85768e84 | 2.03942 | ||||||||
\(45\) | 6.48686e84 | 0.469451 | ||||||||
\(46\) | −8.25816e85 | −1.92688 | ||||||||
\(47\) | −1.62041e86 | −1.24907 | −0.624534 | − | 0.780998i | \(-0.714711\pi\) | ||||
−0.624534 | + | 0.780998i | \(0.714711\pi\) | |||||||
\(48\) | −1.10137e86 | −0.287085 | ||||||||
\(49\) | −4.23445e86 | −0.381679 | ||||||||
\(50\) | 3.84618e87 | 1.22483 | ||||||||
\(51\) | −4.62298e87 | −0.530955 | ||||||||
\(52\) | 3.93817e88 | 1.66388 | ||||||||
\(53\) | 7.08477e88 | 1.12232 | 0.561162 | − | 0.827706i | \(-0.310355\pi\) | ||||
0.561162 | + | 0.827706i | \(0.310355\pi\) | |||||||
\(54\) | −1.85674e89 | −1.12324 | ||||||||
\(55\) | −2.38965e89 | −0.561896 | ||||||||
\(56\) | −1.36304e90 | −1.26714 | ||||||||
\(57\) | −1.38021e90 | −0.515692 | ||||||||
\(58\) | 1.06774e91 | 1.62901 | ||||||||
\(59\) | −2.20029e90 | −0.139188 | −0.0695941 | − | 0.997575i | \(-0.522170\pi\) | ||||
−0.0695941 | + | 0.997575i | \(0.522170\pi\) | |||||||
\(60\) | 1.35832e91 | 0.361587 | ||||||||
\(61\) | 4.53670e91 | 0.515529 | 0.257765 | − | 0.966208i | \(-0.417014\pi\) | ||||
0.257765 | + | 0.966208i | \(0.417014\pi\) | |||||||
\(62\) | 3.45732e92 | 1.70047 | ||||||||
\(63\) | −3.20125e92 | −0.690688 | ||||||||
\(64\) | −1.21631e93 | −1.16621 | ||||||||
\(65\) | −1.06245e93 | −0.458428 | ||||||||
\(66\) | 3.19850e93 | 0.628685 | ||||||||
\(67\) | 1.42797e94 | 1.29379 | 0.646897 | − | 0.762577i | \(-0.276066\pi\) | ||||
0.646897 | + | 0.762577i | \(0.276066\pi\) | |||||||
\(68\) | 6.99042e94 | 2.95321 | ||||||||
\(69\) | −1.96767e94 | −0.391944 | ||||||||
\(70\) | 7.58986e94 | 0.720584 | ||||||||
\(71\) | 1.63302e95 | 0.746771 | 0.373386 | − | 0.927676i | \(-0.378197\pi\) | ||||
0.373386 | + | 0.927676i | \(0.378197\pi\) | |||||||
\(72\) | 6.36086e95 | 1.41544 | ||||||||
\(73\) | −1.05405e96 | −1.15275 | −0.576374 | − | 0.817186i | \(-0.695533\pi\) | ||||
−0.576374 | + | 0.817186i | \(0.695533\pi\) | |||||||
\(74\) | 2.04186e96 | 1.10813 | ||||||||
\(75\) | 9.16427e95 | 0.249140 | ||||||||
\(76\) | 2.08702e97 | 2.86831 | ||||||||
\(77\) | 1.17929e97 | 0.826699 | ||||||||
\(78\) | 1.42207e97 | 0.512918 | ||||||||
\(79\) | −7.93552e97 | −1.48518 | −0.742592 | − | 0.669744i | \(-0.766404\pi\) | ||||
−0.742592 | + | 0.669744i | \(0.766404\pi\) | |||||||
\(80\) | −4.49292e97 | −0.439941 | ||||||||
\(81\) | 1.25840e98 | 0.649888 | ||||||||
\(82\) | −9.82303e98 | −2.69670 | ||||||||
\(83\) | 5.44480e98 | 0.800682 | 0.400341 | − | 0.916366i | \(-0.368892\pi\) | ||||
0.400341 | + | 0.916366i | \(0.368892\pi\) | |||||||
\(84\) | −6.70328e98 | −0.531991 | ||||||||
\(85\) | −1.88590e99 | −0.813660 | ||||||||
\(86\) | 2.65596e99 | 0.627410 | ||||||||
\(87\) | 2.54410e99 | 0.331354 | ||||||||
\(88\) | −2.34324e100 | −1.69418 | ||||||||
\(89\) | −3.14467e100 | −1.27054 | −0.635272 | − | 0.772289i | \(-0.719112\pi\) | ||||
−0.635272 | + | 0.772289i | \(0.719112\pi\) | |||||||
\(90\) | −3.54194e100 | −0.804919 | ||||||||
\(91\) | 5.24317e100 | 0.674470 | ||||||||
\(92\) | 2.97532e101 | 2.18002 | ||||||||
\(93\) | 8.23775e100 | 0.345889 | ||||||||
\(94\) | 8.84774e101 | 2.14165 | ||||||||
\(95\) | −5.63042e101 | −0.790269 | ||||||||
\(96\) | −8.52526e100 | −0.0697813 | ||||||||
\(97\) | 6.67281e101 | 0.320305 | 0.160153 | − | 0.987092i | \(-0.448801\pi\) | ||||
0.160153 | + | 0.987092i | \(0.448801\pi\) | |||||||
\(98\) | 2.31208e102 | 0.654426 | ||||||||
\(99\) | −5.50336e102 | −0.923454 | ||||||||
\(100\) | −1.38573e103 | −1.38573 | ||||||||
\(101\) | 9.58727e102 | 0.574307 | 0.287154 | − | 0.957885i | \(-0.407291\pi\) | ||||
0.287154 | + | 0.957885i | \(0.407291\pi\) | |||||||
\(102\) | 2.52423e103 | 0.910374 | ||||||||
\(103\) | −3.71510e102 | −0.0810688 | −0.0405344 | − | 0.999178i | \(-0.512906\pi\) | ||||
−0.0405344 | + | 0.999178i | \(0.512906\pi\) | |||||||
\(104\) | −1.04181e104 | −1.38221 | ||||||||
\(105\) | 1.80843e103 | 0.146573 | ||||||||
\(106\) | −3.86841e104 | −1.92433 | ||||||||
\(107\) | −3.82474e104 | −1.17311 | −0.586553 | − | 0.809911i | \(-0.699516\pi\) | ||||
−0.586553 | + | 0.809911i | \(0.699516\pi\) | |||||||
\(108\) | 6.68961e104 | 1.27080 | ||||||||
\(109\) | 8.09300e104 | 0.956411 | 0.478206 | − | 0.878248i | \(-0.341287\pi\) | ||||
0.478206 | + | 0.878248i | \(0.341287\pi\) | |||||||
\(110\) | 1.30479e105 | 0.963426 | ||||||||
\(111\) | 4.86512e104 | 0.225403 | ||||||||
\(112\) | 2.21725e105 | 0.647271 | ||||||||
\(113\) | 4.33478e105 | 0.800621 | 0.400311 | − | 0.916379i | \(-0.368902\pi\) | ||||
0.400311 | + | 0.916379i | \(0.368902\pi\) | |||||||
\(114\) | 7.53619e105 | 0.884204 | ||||||||
\(115\) | −8.02689e105 | −0.600632 | ||||||||
\(116\) | −3.84694e106 | −1.84301 | ||||||||
\(117\) | −2.44682e106 | −0.753408 | ||||||||
\(118\) | 1.20140e106 | 0.238652 | ||||||||
\(119\) | 9.30685e106 | 1.19711 | ||||||||
\(120\) | −3.59334e106 | −0.300375 | ||||||||
\(121\) | 1.93146e106 | 0.105302 | ||||||||
\(122\) | −2.47712e107 | −0.883925 | ||||||||
\(123\) | −2.34053e107 | −0.548530 | ||||||||
\(124\) | −1.24563e108 | −1.92386 | ||||||||
\(125\) | 8.97184e107 | 0.916253 | ||||||||
\(126\) | 1.74794e108 | 1.18425 | ||||||||
\(127\) | −8.30922e107 | −0.374687 | −0.187344 | − | 0.982294i | \(-0.559988\pi\) | ||||
−0.187344 | + | 0.982294i | \(0.559988\pi\) | |||||||
\(128\) | 5.97675e108 | 1.79950 | ||||||||
\(129\) | 6.32834e107 | 0.127620 | ||||||||
\(130\) | 5.80117e108 | 0.786019 | ||||||||
\(131\) | 3.82011e108 | 0.348823 | 0.174411 | − | 0.984673i | \(-0.444198\pi\) | ||||
0.174411 | + | 0.984673i | \(0.444198\pi\) | |||||||
\(132\) | −1.15238e109 | −0.711276 | ||||||||
\(133\) | 2.77860e109 | 1.16270 | ||||||||
\(134\) | −7.79695e109 | −2.21834 | ||||||||
\(135\) | −1.80474e109 | −0.350127 | ||||||||
\(136\) | −1.84926e110 | −2.45327 | ||||||||
\(137\) | 1.58709e110 | 1.44375 | 0.721874 | − | 0.692024i | \(-0.243281\pi\) | ||||
0.721874 | + | 0.692024i | \(0.243281\pi\) | |||||||
\(138\) | 1.07438e110 | 0.672026 | ||||||||
\(139\) | 1.90197e110 | 0.820242 | 0.410121 | − | 0.912031i | \(-0.365487\pi\) | ||||
0.410121 | + | 0.912031i | \(0.365487\pi\) | |||||||
\(140\) | −2.73453e110 | −0.815247 | ||||||||
\(141\) | 2.10815e110 | 0.435629 | ||||||||
\(142\) | −8.91660e110 | −1.28041 | ||||||||
\(143\) | 9.01367e110 | 0.901770 | ||||||||
\(144\) | −1.03472e111 | −0.723026 | ||||||||
\(145\) | 1.03784e111 | 0.507782 | ||||||||
\(146\) | 5.75531e111 | 1.97650 | ||||||||
\(147\) | 5.50899e110 | 0.133116 | ||||||||
\(148\) | −7.35656e111 | −1.25371 | ||||||||
\(149\) | 1.31408e112 | 1.58317 | 0.791585 | − | 0.611059i | \(-0.209256\pi\) | ||||
0.791585 | + | 0.611059i | \(0.209256\pi\) | |||||||
\(150\) | −5.00386e111 | −0.427174 | ||||||||
\(151\) | 2.22106e112 | 1.34663 | 0.673314 | − | 0.739357i | \(-0.264870\pi\) | ||||
0.673314 | + | 0.739357i | \(0.264870\pi\) | |||||||
\(152\) | −5.52106e112 | −2.38274 | ||||||||
\(153\) | −4.34321e112 | −1.33722 | ||||||||
\(154\) | −6.43912e112 | −1.41746 | ||||||||
\(155\) | 3.36050e112 | 0.530056 | ||||||||
\(156\) | −5.12353e112 | −0.580300 | ||||||||
\(157\) | 1.03035e113 | 0.839755 | 0.419878 | − | 0.907581i | \(-0.362073\pi\) | ||||
0.419878 | + | 0.907581i | \(0.362073\pi\) | |||||||
\(158\) | 4.33294e113 | 2.54649 | ||||||||
\(159\) | −9.21723e112 | −0.391425 | ||||||||
\(160\) | −3.47779e112 | −0.106936 | ||||||||
\(161\) | 3.96125e113 | 0.883690 | ||||||||
\(162\) | −6.87106e113 | −1.11430 | ||||||||
\(163\) | −1.34400e114 | −1.58759 | −0.793796 | − | 0.608184i | \(-0.791898\pi\) | ||||
−0.793796 | + | 0.608184i | \(0.791898\pi\) | |||||||
\(164\) | 3.53912e114 | 3.05096 | ||||||||
\(165\) | 3.10892e113 | 0.195969 | ||||||||
\(166\) | −2.97296e114 | −1.37285 | ||||||||
\(167\) | −2.30653e114 | −0.781737 | −0.390868 | − | 0.920447i | \(-0.627825\pi\) | ||||
−0.390868 | + | 0.920447i | \(0.627825\pi\) | |||||||
\(168\) | 1.77330e114 | 0.441932 | ||||||||
\(169\) | −1.43958e114 | −0.264283 | ||||||||
\(170\) | 1.02973e115 | 1.39510 | ||||||||
\(171\) | −1.29668e115 | −1.29878 | ||||||||
\(172\) | −9.56910e114 | −0.709833 | ||||||||
\(173\) | −6.66123e114 | −0.366589 | −0.183295 | − | 0.983058i | \(-0.558676\pi\) | ||||
−0.183295 | + | 0.983058i | \(0.558676\pi\) | |||||||
\(174\) | −1.38912e115 | −0.568139 | ||||||||
\(175\) | −1.84492e115 | −0.561719 | ||||||||
\(176\) | 3.81173e115 | 0.865406 | ||||||||
\(177\) | 2.86257e114 | 0.0485437 | ||||||||
\(178\) | 1.71705e116 | 2.17847 | ||||||||
\(179\) | 9.46546e115 | 0.899934 | 0.449967 | − | 0.893045i | \(-0.351436\pi\) | ||||
0.449967 | + | 0.893045i | \(0.351436\pi\) | |||||||
\(180\) | 1.27612e116 | 0.910662 | ||||||||
\(181\) | −6.71300e115 | −0.360139 | −0.180069 | − | 0.983654i | \(-0.557632\pi\) | ||||
−0.180069 | + | 0.983654i | \(0.557632\pi\) | |||||||
\(182\) | −2.86287e116 | −1.15644 | ||||||||
\(183\) | −5.90221e115 | −0.179798 | ||||||||
\(184\) | −7.87098e116 | −1.81097 | ||||||||
\(185\) | 1.98467e116 | 0.345418 | ||||||||
\(186\) | −4.49796e116 | −0.593060 | ||||||||
\(187\) | 1.59997e117 | 1.60054 | ||||||||
\(188\) | −3.18773e117 | −2.42300 | ||||||||
\(189\) | 8.90636e116 | 0.515131 | ||||||||
\(190\) | 3.07431e117 | 1.35499 | ||||||||
\(191\) | −1.50316e117 | −0.505577 | −0.252789 | − | 0.967522i | \(-0.581348\pi\) | ||||
−0.252789 | + | 0.967522i | \(0.581348\pi\) | |||||||
\(192\) | 1.58242e117 | 0.406731 | ||||||||
\(193\) | 3.67640e117 | 0.723138 | 0.361569 | − | 0.932345i | \(-0.382241\pi\) | ||||
0.361569 | + | 0.932345i | \(0.382241\pi\) | |||||||
\(194\) | −3.64347e117 | −0.549195 | ||||||||
\(195\) | 1.38224e117 | 0.159883 | ||||||||
\(196\) | −8.33015e117 | −0.740398 | ||||||||
\(197\) | −1.11233e118 | −0.760716 | −0.380358 | − | 0.924839i | \(-0.624199\pi\) | ||||
−0.380358 | + | 0.924839i | \(0.624199\pi\) | |||||||
\(198\) | 3.00493e118 | 1.58335 | ||||||||
\(199\) | 2.74913e118 | 1.11754 | 0.558768 | − | 0.829324i | \(-0.311274\pi\) | ||||
0.558768 | + | 0.829324i | \(0.311274\pi\) | |||||||
\(200\) | 3.66585e118 | 1.15115 | ||||||||
\(201\) | −1.85777e118 | −0.451228 | ||||||||
\(202\) | −5.23482e118 | −0.984706 | ||||||||
\(203\) | −5.12171e118 | −0.747083 | ||||||||
\(204\) | −9.09449e118 | −1.02997 | ||||||||
\(205\) | −9.54794e118 | −0.840593 | ||||||||
\(206\) | 2.02851e118 | 0.139000 | ||||||||
\(207\) | −1.84859e119 | −0.987115 | ||||||||
\(208\) | 1.69471e119 | 0.706049 | ||||||||
\(209\) | 4.77676e119 | 1.55453 | ||||||||
\(210\) | −9.87436e118 | −0.251313 | ||||||||
\(211\) | −5.77832e119 | −1.15148 | −0.575738 | − | 0.817634i | \(-0.695285\pi\) | ||||
−0.575738 | + | 0.817634i | \(0.695285\pi\) | |||||||
\(212\) | 1.39374e120 | 2.17713 | ||||||||
\(213\) | −2.12455e119 | −0.260446 | ||||||||
\(214\) | 2.08838e120 | 2.01141 | ||||||||
\(215\) | 2.58158e119 | 0.195571 | ||||||||
\(216\) | −1.76969e120 | −1.05567 | ||||||||
\(217\) | −1.65840e120 | −0.779853 | ||||||||
\(218\) | −4.41892e120 | −1.63986 | ||||||||
\(219\) | 1.37131e120 | 0.402036 | ||||||||
\(220\) | −4.70101e120 | −1.08999 | ||||||||
\(221\) | 7.11352e120 | 1.30582 | ||||||||
\(222\) | −2.65644e120 | −0.386476 | ||||||||
\(223\) | 6.96461e120 | 0.803889 | 0.401944 | − | 0.915664i | \(-0.368334\pi\) | ||||
0.401944 | + | 0.915664i | \(0.368334\pi\) | |||||||
\(224\) | 1.71628e120 | 0.157331 | ||||||||
\(225\) | 8.60967e120 | 0.627461 | ||||||||
\(226\) | −2.36687e121 | −1.37274 | ||||||||
\(227\) | −2.51778e121 | −1.16329 | −0.581643 | − | 0.813444i | \(-0.697590\pi\) | ||||
−0.581643 | + | 0.813444i | \(0.697590\pi\) | |||||||
\(228\) | −2.71520e121 | −1.00036 | ||||||||
\(229\) | 5.94832e121 | 1.74931 | 0.874656 | − | 0.484745i | \(-0.161088\pi\) | ||||
0.874656 | + | 0.484745i | \(0.161088\pi\) | |||||||
\(230\) | 4.38283e121 | 1.02984 | ||||||||
\(231\) | −1.53425e121 | −0.288322 | ||||||||
\(232\) | 1.01768e122 | 1.53102 | ||||||||
\(233\) | −1.21145e122 | −1.46041 | −0.730207 | − | 0.683226i | \(-0.760576\pi\) | ||||
−0.730207 | + | 0.683226i | \(0.760576\pi\) | |||||||
\(234\) | 1.33601e122 | 1.29179 | ||||||||
\(235\) | 8.59996e121 | 0.667577 | ||||||||
\(236\) | −4.32850e121 | −0.270003 | ||||||||
\(237\) | 1.03241e122 | 0.517977 | ||||||||
\(238\) | −5.08171e122 | −2.05256 | ||||||||
\(239\) | −2.55458e122 | −0.831434 | −0.415717 | − | 0.909494i | \(-0.636469\pi\) | ||||
−0.415717 | + | 0.909494i | \(0.636469\pi\) | |||||||
\(240\) | 5.84527e121 | 0.153435 | ||||||||
\(241\) | −4.59650e122 | −0.973980 | −0.486990 | − | 0.873408i | \(-0.661905\pi\) | ||||
−0.486990 | + | 0.873408i | \(0.661905\pi\) | |||||||
\(242\) | −1.05461e122 | −0.180551 | ||||||||
\(243\) | −6.36904e122 | −0.881761 | ||||||||
\(244\) | 8.92475e122 | 1.00005 | ||||||||
\(245\) | 2.24733e122 | 0.203992 | ||||||||
\(246\) | 1.27797e123 | 0.940509 | ||||||||
\(247\) | 2.12377e123 | 1.26828 | ||||||||
\(248\) | 3.29523e123 | 1.59817 | ||||||||
\(249\) | −7.08365e122 | −0.279248 | ||||||||
\(250\) | −4.89878e123 | −1.57101 | ||||||||
\(251\) | −8.18914e122 | −0.213817 | −0.106908 | − | 0.994269i | \(-0.534095\pi\) | ||||
−0.106908 | + | 0.994269i | \(0.534095\pi\) | |||||||
\(252\) | −6.29762e123 | −1.33983 | ||||||||
\(253\) | 6.80990e123 | 1.18150 | ||||||||
\(254\) | 4.53698e123 | 0.642437 | ||||||||
\(255\) | 2.45354e123 | 0.283775 | ||||||||
\(256\) | −2.02992e124 | −1.91921 | ||||||||
\(257\) | 1.57942e124 | 1.22163 | 0.610817 | − | 0.791772i | \(-0.290841\pi\) | ||||
0.610817 | + | 0.791772i | \(0.290841\pi\) | |||||||
\(258\) | −3.45539e123 | −0.218817 | ||||||||
\(259\) | −9.79432e123 | −0.508202 | ||||||||
\(260\) | −2.09009e124 | −0.889278 | ||||||||
\(261\) | 2.39014e124 | 0.834520 | ||||||||
\(262\) | −2.08585e124 | −0.598090 | ||||||||
\(263\) | 2.58576e124 | 0.609351 | 0.304675 | − | 0.952456i | \(-0.401452\pi\) | ||||
0.304675 | + | 0.952456i | \(0.401452\pi\) | |||||||
\(264\) | 3.04854e124 | 0.590866 | ||||||||
\(265\) | −3.76007e124 | −0.599838 | ||||||||
\(266\) | −1.51717e125 | −1.99356 | ||||||||
\(267\) | 4.09120e124 | 0.443119 | ||||||||
\(268\) | 2.80914e125 | 2.50976 | ||||||||
\(269\) | −9.10642e124 | −0.671592 | −0.335796 | − | 0.941935i | \(-0.609005\pi\) | ||||
−0.335796 | + | 0.941935i | \(0.609005\pi\) | |||||||
\(270\) | 9.85421e124 | 0.600327 | ||||||||
\(271\) | 3.36714e125 | 1.69567 | 0.847837 | − | 0.530256i | \(-0.177904\pi\) | ||||
0.847837 | + | 0.530256i | \(0.177904\pi\) | |||||||
\(272\) | 3.00819e125 | 1.25316 | ||||||||
\(273\) | −6.82133e124 | −0.235230 | ||||||||
\(274\) | −8.66578e125 | −2.47545 | ||||||||
\(275\) | −3.17166e125 | −0.751022 | ||||||||
\(276\) | −3.87087e125 | −0.760310 | ||||||||
\(277\) | −4.58923e125 | −0.748224 | −0.374112 | − | 0.927384i | \(-0.622052\pi\) | ||||
−0.374112 | + | 0.927384i | \(0.622052\pi\) | |||||||
\(278\) | −1.03851e126 | −1.40638 | ||||||||
\(279\) | 7.73922e125 | 0.871125 | ||||||||
\(280\) | 7.23401e125 | 0.677237 | ||||||||
\(281\) | 1.57573e126 | 1.22774 | 0.613871 | − | 0.789406i | \(-0.289611\pi\) | ||||
0.613871 | + | 0.789406i | \(0.289611\pi\) | |||||||
\(282\) | −1.15109e126 | −0.746928 | ||||||||
\(283\) | 3.29385e125 | 0.178116 | 0.0890579 | − | 0.996026i | \(-0.471614\pi\) | ||||
0.0890579 | + | 0.996026i | \(0.471614\pi\) | |||||||
\(284\) | 3.21254e126 | 1.44862 | ||||||||
\(285\) | 7.32514e125 | 0.275617 | ||||||||
\(286\) | −4.92163e126 | −1.54617 | ||||||||
\(287\) | 4.71189e126 | 1.23674 | ||||||||
\(288\) | −8.00934e125 | −0.175745 | ||||||||
\(289\) | 7.17878e126 | 1.31769 | ||||||||
\(290\) | −5.66678e126 | −0.870642 | ||||||||
\(291\) | −8.68128e125 | −0.111711 | ||||||||
\(292\) | −2.07357e127 | −2.23615 | ||||||||
\(293\) | 1.39826e127 | 1.26446 | 0.632229 | − | 0.774781i | \(-0.282140\pi\) | ||||
0.632229 | + | 0.774781i | \(0.282140\pi\) | |||||||
\(294\) | −3.00801e126 | −0.228240 | ||||||||
\(295\) | 1.16775e126 | 0.0743906 | ||||||||
\(296\) | 1.94612e127 | 1.04147 | ||||||||
\(297\) | 1.53112e127 | 0.688733 | ||||||||
\(298\) | −7.17509e127 | −2.71450 | ||||||||
\(299\) | 3.02771e127 | 0.963937 | ||||||||
\(300\) | 1.80283e127 | 0.483292 | ||||||||
\(301\) | −1.27400e127 | −0.287737 | ||||||||
\(302\) | −1.21274e128 | −2.30892 | ||||||||
\(303\) | −1.24730e127 | −0.200297 | ||||||||
\(304\) | 8.98107e127 | 1.21713 | ||||||||
\(305\) | −2.40774e127 | −0.275530 | ||||||||
\(306\) | 2.37147e128 | 2.29279 | ||||||||
\(307\) | −2.54064e127 | −0.207643 | −0.103822 | − | 0.994596i | \(-0.533107\pi\) | ||||
−0.103822 | + | 0.994596i | \(0.533107\pi\) | |||||||
\(308\) | 2.31994e128 | 1.60367 | ||||||||
\(309\) | 4.83333e126 | 0.0282738 | ||||||||
\(310\) | −1.83489e128 | −0.908832 | ||||||||
\(311\) | −1.19727e127 | −0.0502379 | −0.0251190 | − | 0.999684i | \(-0.507996\pi\) | ||||
−0.0251190 | + | 0.999684i | \(0.507996\pi\) | |||||||
\(312\) | 1.35539e128 | 0.482063 | ||||||||
\(313\) | 2.34857e127 | 0.0708387 | 0.0354193 | − | 0.999373i | \(-0.488723\pi\) | ||||
0.0354193 | + | 0.999373i | \(0.488723\pi\) | |||||||
\(314\) | −5.62590e128 | −1.43984 | ||||||||
\(315\) | 1.69899e128 | 0.369145 | ||||||||
\(316\) | −1.56110e129 | −2.88102 | ||||||||
\(317\) | 4.05413e128 | 0.635837 | 0.317919 | − | 0.948118i | \(-0.397016\pi\) | ||||
0.317919 | + | 0.948118i | \(0.397016\pi\) | |||||||
\(318\) | 5.03278e128 | 0.671137 | ||||||||
\(319\) | −8.80486e128 | −0.998855 | ||||||||
\(320\) | 6.45530e128 | 0.623294 | ||||||||
\(321\) | 4.97597e128 | 0.409136 | ||||||||
\(322\) | −2.16292e129 | −1.51517 | ||||||||
\(323\) | 3.76979e129 | 2.25106 | ||||||||
\(324\) | 2.47556e129 | 1.26068 | ||||||||
\(325\) | −1.41014e129 | −0.612728 | ||||||||
\(326\) | 7.33850e129 | 2.72208 | ||||||||
\(327\) | −1.05289e129 | −0.333561 | ||||||||
\(328\) | −9.36248e129 | −2.53447 | ||||||||
\(329\) | −4.24406e129 | −0.982184 | ||||||||
\(330\) | −1.69753e129 | −0.336007 | ||||||||
\(331\) | −3.80412e129 | −0.644336 | −0.322168 | − | 0.946682i | \(-0.604412\pi\) | ||||
−0.322168 | + | 0.946682i | \(0.604412\pi\) | |||||||
\(332\) | 1.07112e130 | 1.55320 | ||||||||
\(333\) | 4.57070e129 | 0.567681 | ||||||||
\(334\) | 1.25941e130 | 1.34036 | ||||||||
\(335\) | −7.57859e129 | −0.691482 | ||||||||
\(336\) | −2.88463e129 | −0.225744 | ||||||||
\(337\) | −1.67977e130 | −1.12800 | −0.564001 | − | 0.825774i | \(-0.690739\pi\) | ||||
−0.564001 | + | 0.825774i | \(0.690739\pi\) | |||||||
\(338\) | 7.86034e129 | 0.453139 | ||||||||
\(339\) | −5.63952e129 | −0.279227 | ||||||||
\(340\) | −3.71000e130 | −1.57837 | ||||||||
\(341\) | −2.85100e130 | −1.04267 | ||||||||
\(342\) | 7.08012e130 | 2.22688 | ||||||||
\(343\) | −4.01478e130 | −1.08646 | ||||||||
\(344\) | 2.53144e130 | 0.589667 | ||||||||
\(345\) | 1.04429e130 | 0.209478 | ||||||||
\(346\) | 3.63715e130 | 0.628553 | ||||||||
\(347\) | 2.25423e130 | 0.335760 | 0.167880 | − | 0.985807i | \(-0.446308\pi\) | ||||
0.167880 | + | 0.985807i | \(0.446308\pi\) | |||||||
\(348\) | 5.00484e130 | 0.642775 | ||||||||
\(349\) | −5.83015e130 | −0.645908 | −0.322954 | − | 0.946415i | \(-0.604676\pi\) | ||||
−0.322954 | + | 0.946415i | \(0.604676\pi\) | |||||||
\(350\) | 1.00736e131 | 0.963122 | ||||||||
\(351\) | 6.80742e130 | 0.561909 | ||||||||
\(352\) | 2.95051e130 | 0.210353 | ||||||||
\(353\) | 1.98835e130 | 0.122489 | 0.0612444 | − | 0.998123i | \(-0.480493\pi\) | ||||
0.0612444 | + | 0.998123i | \(0.480493\pi\) | |||||||
\(354\) | −1.56301e130 | −0.0832329 | ||||||||
\(355\) | −8.66689e130 | −0.399120 | ||||||||
\(356\) | −6.18631e131 | −2.46466 | ||||||||
\(357\) | −1.21082e131 | −0.417508 | ||||||||
\(358\) | −5.16831e131 | −1.54302 | ||||||||
\(359\) | 3.69274e131 | 0.954960 | 0.477480 | − | 0.878643i | \(-0.341550\pi\) | ||||
0.477480 | + | 0.878643i | \(0.341550\pi\) | |||||||
\(360\) | −3.37588e131 | −0.756499 | ||||||||
\(361\) | 6.10707e131 | 1.18635 | ||||||||
\(362\) | 3.66542e131 | 0.617493 | ||||||||
\(363\) | −2.51281e130 | −0.0367256 | ||||||||
\(364\) | 1.03146e132 | 1.30837 | ||||||||
\(365\) | 5.59413e131 | 0.616099 | ||||||||
\(366\) | 3.22271e131 | 0.308280 | ||||||||
\(367\) | −1.08880e132 | −0.904998 | −0.452499 | − | 0.891765i | \(-0.649467\pi\) | ||||
−0.452499 | + | 0.891765i | \(0.649467\pi\) | |||||||
\(368\) | 1.28037e132 | 0.925065 | ||||||||
\(369\) | −2.19889e132 | −1.38148 | ||||||||
\(370\) | −1.08367e132 | −0.592253 | ||||||||
\(371\) | 1.85559e132 | 0.882521 | ||||||||
\(372\) | 1.62056e132 | 0.670970 | ||||||||
\(373\) | 3.00190e132 | 1.08241 | 0.541205 | − | 0.840891i | \(-0.317968\pi\) | ||||
0.541205 | + | 0.840891i | \(0.317968\pi\) | |||||||
\(374\) | −8.73610e132 | −2.74429 | ||||||||
\(375\) | −1.16723e132 | −0.319555 | ||||||||
\(376\) | 8.43292e132 | 2.01281 | ||||||||
\(377\) | −3.91468e132 | −0.814924 | ||||||||
\(378\) | −4.86303e132 | −0.883242 | ||||||||
\(379\) | 9.93644e132 | 1.57511 | 0.787556 | − | 0.616243i | \(-0.211346\pi\) | ||||
0.787556 | + | 0.616243i | \(0.211346\pi\) | |||||||
\(380\) | −1.10764e133 | −1.53300 | ||||||||
\(381\) | 1.08102e132 | 0.130677 | ||||||||
\(382\) | 8.20753e132 | 0.866861 | ||||||||
\(383\) | −3.74392e132 | −0.345613 | −0.172806 | − | 0.984956i | \(-0.555283\pi\) | ||||
−0.172806 | + | 0.984956i | \(0.555283\pi\) | |||||||
\(384\) | −7.77572e132 | −0.627599 | ||||||||
\(385\) | −6.25879e132 | −0.441838 | ||||||||
\(386\) | −2.00738e133 | −1.23989 | ||||||||
\(387\) | 5.94537e132 | 0.321413 | ||||||||
\(388\) | 1.31270e133 | 0.621342 | ||||||||
\(389\) | 2.61673e133 | 1.08481 | 0.542406 | − | 0.840116i | \(-0.317513\pi\) | ||||
0.542406 | + | 0.840116i | \(0.317513\pi\) | |||||||
\(390\) | −7.54729e132 | −0.274135 | ||||||||
\(391\) | 5.37432e133 | 1.71088 | ||||||||
\(392\) | 2.20368e133 | 0.615058 | ||||||||
\(393\) | −4.96995e132 | −0.121656 | ||||||||
\(394\) | 6.07352e133 | 1.30432 | ||||||||
\(395\) | 4.21159e133 | 0.793772 | ||||||||
\(396\) | −1.08264e134 | −1.79136 | ||||||||
\(397\) | −7.05323e133 | −1.02489 | −0.512444 | − | 0.858720i | \(-0.671260\pi\) | ||||
−0.512444 | + | 0.858720i | \(0.671260\pi\) | |||||||
\(398\) | −1.50107e134 | −1.91612 | ||||||||
\(399\) | −3.61494e133 | −0.405506 | ||||||||
\(400\) | −5.96322e133 | −0.588019 | ||||||||
\(401\) | 9.04492e132 | 0.0784277 | 0.0392138 | − | 0.999231i | \(-0.487515\pi\) | ||||
0.0392138 | + | 0.999231i | \(0.487515\pi\) | |||||||
\(402\) | 1.01438e134 | 0.773674 | ||||||||
\(403\) | −1.26757e134 | −0.850671 | ||||||||
\(404\) | 1.88604e134 | 1.11407 | ||||||||
\(405\) | −6.67864e133 | −0.347340 | ||||||||
\(406\) | 2.79654e134 | 1.28095 | ||||||||
\(407\) | −1.68377e134 | −0.679470 | ||||||||
\(408\) | 2.40588e134 | 0.855610 | ||||||||
\(409\) | −1.98753e134 | −0.623107 | −0.311554 | − | 0.950229i | \(-0.600849\pi\) | ||||
−0.311554 | + | 0.950229i | \(0.600849\pi\) | |||||||
\(410\) | 5.21335e134 | 1.44128 | ||||||||
\(411\) | −2.06479e134 | −0.503526 | ||||||||
\(412\) | −7.30849e133 | −0.157261 | ||||||||
\(413\) | −5.76284e133 | −0.109448 | ||||||||
\(414\) | 1.00936e135 | 1.69250 | ||||||||
\(415\) | −2.88970e134 | −0.427933 | ||||||||
\(416\) | 1.31181e134 | 0.171618 | ||||||||
\(417\) | −2.47445e134 | −0.286070 | ||||||||
\(418\) | −2.60820e135 | −2.66540 | ||||||||
\(419\) | −1.34542e135 | −1.21573 | −0.607865 | − | 0.794040i | \(-0.707974\pi\) | ||||
−0.607865 | + | 0.794040i | \(0.707974\pi\) | |||||||
\(420\) | 3.55761e134 | 0.284328 | ||||||||
\(421\) | 2.13498e135 | 1.50961 | 0.754807 | − | 0.655947i | \(-0.227730\pi\) | ||||
0.754807 | + | 0.655947i | \(0.227730\pi\) | |||||||
\(422\) | 3.15507e135 | 1.97432 | ||||||||
\(423\) | 1.98057e135 | 1.09714 | ||||||||
\(424\) | −3.68704e135 | −1.80857 | ||||||||
\(425\) | −2.50305e135 | −1.08753 | ||||||||
\(426\) | 1.16004e135 | 0.446560 | ||||||||
\(427\) | 1.18822e135 | 0.405378 | ||||||||
\(428\) | −7.52417e135 | −2.27564 | ||||||||
\(429\) | −1.17267e135 | −0.314504 | ||||||||
\(430\) | −1.40959e135 | −0.335326 | ||||||||
\(431\) | 9.22168e135 | 1.94639 | 0.973196 | − | 0.229976i | \(-0.0738648\pi\) | ||||
0.973196 | + | 0.229976i | \(0.0738648\pi\) | |||||||
\(432\) | 2.87874e135 | 0.539249 | ||||||||
\(433\) | −8.87148e135 | −1.47526 | −0.737632 | − | 0.675203i | \(-0.764056\pi\) | ||||
−0.737632 | + | 0.675203i | \(0.764056\pi\) | |||||||
\(434\) | 9.05516e135 | 1.33713 | ||||||||
\(435\) | −1.35022e135 | −0.177096 | ||||||||
\(436\) | 1.59208e136 | 1.85529 | ||||||||
\(437\) | 1.60453e136 | 1.66170 | ||||||||
\(438\) | −7.48762e135 | −0.689330 | ||||||||
\(439\) | −1.83247e136 | −1.50008 | −0.750041 | − | 0.661391i | \(-0.769966\pi\) | ||||
−0.750041 | + | 0.661391i | \(0.769966\pi\) | |||||||
\(440\) | 1.24362e136 | 0.905470 | ||||||||
\(441\) | 5.17560e135 | 0.335253 | ||||||||
\(442\) | −3.88411e136 | −2.23895 | ||||||||
\(443\) | −1.12684e136 | −0.578188 | −0.289094 | − | 0.957301i | \(-0.593354\pi\) | ||||
−0.289094 | + | 0.957301i | \(0.593354\pi\) | |||||||
\(444\) | 9.57084e135 | 0.437247 | ||||||||
\(445\) | 1.66896e136 | 0.679056 | ||||||||
\(446\) | −3.80280e136 | −1.37835 | ||||||||
\(447\) | −1.70960e136 | −0.552151 | ||||||||
\(448\) | −3.18568e136 | −0.917031 | ||||||||
\(449\) | 1.86589e135 | 0.0478849 | 0.0239425 | − | 0.999713i | \(-0.492378\pi\) | ||||
0.0239425 | + | 0.999713i | \(0.492378\pi\) | |||||||
\(450\) | −4.70104e136 | −1.07584 | ||||||||
\(451\) | 8.10033e136 | 1.65352 | ||||||||
\(452\) | 8.52753e136 | 1.55308 | ||||||||
\(453\) | −2.88959e136 | −0.469654 | ||||||||
\(454\) | 1.37475e137 | 1.99457 | ||||||||
\(455\) | −2.78269e136 | −0.360477 | ||||||||
\(456\) | 7.18286e136 | 0.831013 | ||||||||
\(457\) | 1.50996e137 | 1.56056 | 0.780281 | − | 0.625429i | \(-0.215076\pi\) | ||||
0.780281 | + | 0.625429i | \(0.215076\pi\) | |||||||
\(458\) | −3.24789e137 | −2.99936 | ||||||||
\(459\) | 1.20835e137 | 0.997327 | ||||||||
\(460\) | −1.57908e137 | −1.16513 | ||||||||
\(461\) | −5.70758e136 | −0.376577 | −0.188289 | − | 0.982114i | \(-0.560294\pi\) | ||||
−0.188289 | + | 0.982114i | \(0.560294\pi\) | |||||||
\(462\) | 8.37726e136 | 0.494356 | ||||||||
\(463\) | −1.56763e137 | −0.827602 | −0.413801 | − | 0.910367i | \(-0.635799\pi\) | ||||
−0.413801 | + | 0.910367i | \(0.635799\pi\) | |||||||
\(464\) | −1.65545e137 | −0.782062 | ||||||||
\(465\) | −4.37199e136 | −0.184864 | ||||||||
\(466\) | 6.61474e137 | 2.50402 | ||||||||
\(467\) | 1.07059e137 | 0.362913 | 0.181456 | − | 0.983399i | \(-0.441919\pi\) | ||||
0.181456 | + | 0.983399i | \(0.441919\pi\) | |||||||
\(468\) | −4.81347e137 | −1.46149 | ||||||||
\(469\) | 3.74002e137 | 1.01735 | ||||||||
\(470\) | −4.69573e137 | −1.14463 | ||||||||
\(471\) | −1.34048e137 | −0.292876 | ||||||||
\(472\) | 1.14507e137 | 0.224295 | ||||||||
\(473\) | −2.19017e137 | −0.384707 | ||||||||
\(474\) | −5.63712e137 | −0.888123 | ||||||||
\(475\) | −7.47296e137 | −1.05626 | ||||||||
\(476\) | 1.83088e138 | 2.32221 | ||||||||
\(477\) | −8.65943e137 | −0.985809 | ||||||||
\(478\) | 1.39485e138 | 1.42557 | ||||||||
\(479\) | −3.24976e137 | −0.298244 | −0.149122 | − | 0.988819i | \(-0.547645\pi\) | ||||
−0.149122 | + | 0.988819i | \(0.547645\pi\) | |||||||
\(480\) | 4.52458e136 | 0.0372954 | ||||||||
\(481\) | −7.48611e137 | −0.554351 | ||||||||
\(482\) | 2.50977e138 | 1.66998 | ||||||||
\(483\) | −5.15357e137 | −0.308199 | ||||||||
\(484\) | 3.79963e137 | 0.204270 | ||||||||
\(485\) | −3.54144e137 | −0.171191 | ||||||||
\(486\) | 3.47761e138 | 1.51187 | ||||||||
\(487\) | −1.50996e138 | −0.590504 | −0.295252 | − | 0.955419i | \(-0.595404\pi\) | ||||
−0.295252 | + | 0.955419i | \(0.595404\pi\) | |||||||
\(488\) | −2.36098e138 | −0.830751 | ||||||||
\(489\) | 1.74854e138 | 0.553694 | ||||||||
\(490\) | −1.22708e138 | −0.349765 | ||||||||
\(491\) | 1.86965e138 | 0.479804 | 0.239902 | − | 0.970797i | \(-0.422885\pi\) | ||||
0.239902 | + | 0.970797i | \(0.422885\pi\) | |||||||
\(492\) | −4.60437e138 | −1.06406 | ||||||||
\(493\) | −6.94873e138 | −1.44640 | ||||||||
\(494\) | −1.15962e139 | −2.17459 | ||||||||
\(495\) | 2.92078e138 | 0.493550 | ||||||||
\(496\) | −5.36033e138 | −0.816367 | ||||||||
\(497\) | 4.27709e138 | 0.587211 | ||||||||
\(498\) | 3.86780e138 | 0.478799 | ||||||||
\(499\) | 1.11104e139 | 1.24037 | 0.620184 | − | 0.784456i | \(-0.287058\pi\) | ||||
0.620184 | + | 0.784456i | \(0.287058\pi\) | |||||||
\(500\) | 1.76497e139 | 1.77739 | ||||||||
\(501\) | 3.00078e138 | 0.272641 | ||||||||
\(502\) | 4.47142e138 | 0.366610 | ||||||||
\(503\) | 5.25435e138 | 0.388837 | 0.194419 | − | 0.980919i | \(-0.437718\pi\) | ||||
0.194419 | + | 0.980919i | \(0.437718\pi\) | |||||||
\(504\) | 1.66599e139 | 1.11301 | ||||||||
\(505\) | −5.08822e138 | −0.306945 | ||||||||
\(506\) | −3.71833e139 | −2.02580 | ||||||||
\(507\) | 1.87288e138 | 0.0921722 | ||||||||
\(508\) | −1.63462e139 | −0.726834 | ||||||||
\(509\) | 1.69031e139 | 0.679204 | 0.339602 | − | 0.940569i | \(-0.389708\pi\) | ||||
0.339602 | + | 0.940569i | \(0.389708\pi\) | |||||||
\(510\) | −1.33968e139 | −0.486559 | ||||||||
\(511\) | −2.76069e139 | −0.906445 | ||||||||
\(512\) | 5.02261e139 | 1.49117 | ||||||||
\(513\) | 3.60757e139 | 0.968657 | ||||||||
\(514\) | −8.62390e139 | −2.09461 | ||||||||
\(515\) | 1.97170e138 | 0.0433281 | ||||||||
\(516\) | 1.24493e139 | 0.247564 | ||||||||
\(517\) | −7.29608e139 | −1.31319 | ||||||||
\(518\) | 5.34788e139 | 0.871362 | ||||||||
\(519\) | 8.66621e138 | 0.127853 | ||||||||
\(520\) | 5.52918e139 | 0.738735 | ||||||||
\(521\) | −1.49839e139 | −0.181335 | −0.0906677 | − | 0.995881i | \(-0.528900\pi\) | ||||
−0.0906677 | + | 0.995881i | \(0.528900\pi\) | |||||||
\(522\) | −1.30506e140 | −1.43087 | ||||||||
\(523\) | 1.48013e140 | 1.47049 | 0.735244 | − | 0.677802i | \(-0.237067\pi\) | ||||
0.735244 | + | 0.677802i | \(0.237067\pi\) | |||||||
\(524\) | 7.51507e139 | 0.676661 | ||||||||
\(525\) | 2.40024e139 | 0.195907 | ||||||||
\(526\) | −1.41187e140 | −1.04479 | ||||||||
\(527\) | −2.24999e140 | −1.50985 | ||||||||
\(528\) | −4.95904e139 | −0.301822 | ||||||||
\(529\) | 4.76256e139 | 0.262950 | ||||||||
\(530\) | 2.05307e140 | 1.02848 | ||||||||
\(531\) | 2.68933e139 | 0.122258 | ||||||||
\(532\) | 5.46616e140 | 2.25545 | ||||||||
\(533\) | 3.60144e140 | 1.34904 | ||||||||
\(534\) | −2.23387e140 | −0.759770 | ||||||||
\(535\) | 2.02989e140 | 0.626979 | ||||||||
\(536\) | −7.43138e140 | −2.08489 | ||||||||
\(537\) | −1.23145e140 | −0.313864 | ||||||||
\(538\) | 4.97227e140 | 1.15151 | ||||||||
\(539\) | −1.90660e140 | −0.401272 | ||||||||
\(540\) | −3.55035e140 | −0.679192 | ||||||||
\(541\) | −2.50038e140 | −0.434858 | −0.217429 | − | 0.976076i | \(-0.569767\pi\) | ||||
−0.217429 | + | 0.976076i | \(0.569767\pi\) | |||||||
\(542\) | −1.83852e141 | −2.90740 | ||||||||
\(543\) | 8.73357e139 | 0.125603 | ||||||||
\(544\) | 2.32852e140 | 0.304604 | ||||||||
\(545\) | −4.29517e140 | −0.511164 | ||||||||
\(546\) | 3.72457e140 | 0.403325 | ||||||||
\(547\) | 1.55005e140 | 0.152756 | 0.0763781 | − | 0.997079i | \(-0.475664\pi\) | ||||
0.0763781 | + | 0.997079i | \(0.475664\pi\) | |||||||
\(548\) | 3.12217e141 | 2.80065 | ||||||||
\(549\) | −5.54503e140 | −0.452822 | ||||||||
\(550\) | 1.73178e141 | 1.28770 | ||||||||
\(551\) | −2.07457e141 | −1.40482 | ||||||||
\(552\) | 1.02401e141 | 0.631599 | ||||||||
\(553\) | −2.07841e141 | −1.16785 | ||||||||
\(554\) | 2.50580e141 | 1.28290 | ||||||||
\(555\) | −2.58205e140 | −0.120469 | ||||||||
\(556\) | 3.74163e141 | 1.59114 | ||||||||
\(557\) | 2.89920e141 | 1.12392 | 0.561959 | − | 0.827165i | \(-0.310048\pi\) | ||||
0.561959 | + | 0.827165i | \(0.310048\pi\) | |||||||
\(558\) | −4.22575e141 | −1.49363 | ||||||||
\(559\) | −9.73762e140 | −0.313866 | ||||||||
\(560\) | −1.17675e141 | −0.345941 | ||||||||
\(561\) | −2.08154e141 | −0.558211 | ||||||||
\(562\) | −8.60378e141 | −2.10508 | ||||||||
\(563\) | 6.09221e139 | 0.0136017 | 0.00680084 | − | 0.999977i | \(-0.497835\pi\) | ||||
0.00680084 | + | 0.999977i | \(0.497835\pi\) | |||||||
\(564\) | 4.14722e141 | 0.845052 | ||||||||
\(565\) | −2.30058e141 | −0.427901 | ||||||||
\(566\) | −1.79850e141 | −0.305397 | ||||||||
\(567\) | 3.29589e141 | 0.511029 | ||||||||
\(568\) | −8.49855e141 | −1.20339 | ||||||||
\(569\) | 1.48496e142 | 1.92058 | 0.960289 | − | 0.279006i | \(-0.0900048\pi\) | ||||
0.960289 | + | 0.279006i | \(0.0900048\pi\) | |||||||
\(570\) | −3.99966e141 | −0.472572 | ||||||||
\(571\) | 5.27044e141 | 0.568968 | 0.284484 | − | 0.958681i | \(-0.408178\pi\) | ||||
0.284484 | + | 0.958681i | \(0.408178\pi\) | |||||||
\(572\) | 1.77320e142 | 1.74929 | ||||||||
\(573\) | 1.95560e141 | 0.176327 | ||||||||
\(574\) | −2.57277e142 | −2.12050 | ||||||||
\(575\) | −1.06537e142 | −0.802796 | ||||||||
\(576\) | 1.48665e142 | 1.02436 | ||||||||
\(577\) | 8.50107e141 | 0.535697 | 0.267849 | − | 0.963461i | \(-0.413687\pi\) | ||||
0.267849 | + | 0.963461i | \(0.413687\pi\) | |||||||
\(578\) | −3.91974e142 | −2.25930 | ||||||||
\(579\) | −4.78297e141 | −0.252204 | ||||||||
\(580\) | 2.04167e142 | 0.985018 | ||||||||
\(581\) | 1.42606e142 | 0.629604 | ||||||||
\(582\) | 4.74013e141 | 0.191539 | ||||||||
\(583\) | 3.18999e142 | 1.17994 | ||||||||
\(584\) | 5.48547e142 | 1.85760 | ||||||||
\(585\) | 1.29859e142 | 0.402667 | ||||||||
\(586\) | −7.63474e142 | −2.16804 | ||||||||
\(587\) | 2.15480e142 | 0.560460 | 0.280230 | − | 0.959933i | \(-0.409589\pi\) | ||||
0.280230 | + | 0.959933i | \(0.409589\pi\) | |||||||
\(588\) | 1.08375e142 | 0.258224 | ||||||||
\(589\) | −6.71743e142 | −1.46644 | ||||||||
\(590\) | −6.37615e141 | −0.127550 | ||||||||
\(591\) | 1.44713e142 | 0.265310 | ||||||||
\(592\) | −3.16575e142 | −0.531996 | ||||||||
\(593\) | −9.57113e142 | −1.47451 | −0.737253 | − | 0.675617i | \(-0.763877\pi\) | ||||
−0.737253 | + | 0.675617i | \(0.763877\pi\) | |||||||
\(594\) | −8.36017e142 | −1.18090 | ||||||||
\(595\) | −4.93939e142 | −0.639808 | ||||||||
\(596\) | 2.58510e143 | 3.07110 | ||||||||
\(597\) | −3.57660e142 | −0.389755 | ||||||||
\(598\) | −1.65319e143 | −1.65276 | ||||||||
\(599\) | 9.42752e142 | 0.864801 | 0.432401 | − | 0.901682i | \(-0.357667\pi\) | ||||
0.432401 | + | 0.901682i | \(0.357667\pi\) | |||||||
\(600\) | −4.76925e142 | −0.401477 | ||||||||
\(601\) | 1.35464e143 | 1.04662 | 0.523310 | − | 0.852142i | \(-0.324697\pi\) | ||||
0.523310 | + | 0.852142i | \(0.324697\pi\) | |||||||
\(602\) | 6.95629e142 | 0.493354 | ||||||||
\(603\) | −1.74535e143 | −1.13642 | ||||||||
\(604\) | 4.36935e143 | 2.61225 | ||||||||
\(605\) | −1.02508e142 | −0.0562800 | ||||||||
\(606\) | 6.81047e142 | 0.343429 | ||||||||
\(607\) | 1.82567e143 | 0.845679 | 0.422839 | − | 0.906205i | \(-0.361033\pi\) | ||||
0.422839 | + | 0.906205i | \(0.361033\pi\) | |||||||
\(608\) | 6.95188e142 | 0.295848 | ||||||||
\(609\) | 6.66331e142 | 0.260555 | ||||||||
\(610\) | 1.31467e143 | 0.472423 | ||||||||
\(611\) | −3.24387e143 | −1.07137 | ||||||||
\(612\) | −8.54411e143 | −2.59399 | ||||||||
\(613\) | −4.77180e143 | −1.33189 | −0.665945 | − | 0.746001i | \(-0.731971\pi\) | ||||
−0.665945 | + | 0.746001i | \(0.731971\pi\) | |||||||
\(614\) | 1.38724e143 | 0.356024 | ||||||||
\(615\) | 1.24218e143 | 0.293168 | ||||||||
\(616\) | −6.13723e143 | −1.33219 | ||||||||
\(617\) | 2.49860e143 | 0.498896 | 0.249448 | − | 0.968388i | \(-0.419751\pi\) | ||||
0.249448 | + | 0.968388i | \(0.419751\pi\) | |||||||
\(618\) | −2.63908e142 | −0.0484782 | ||||||||
\(619\) | 4.34805e143 | 0.734896 | 0.367448 | − | 0.930044i | \(-0.380232\pi\) | ||||
0.367448 | + | 0.930044i | \(0.380232\pi\) | |||||||
\(620\) | 6.61090e143 | 1.02823 | ||||||||
\(621\) | 5.14305e143 | 0.736213 | ||||||||
\(622\) | 6.53730e142 | 0.0861378 | ||||||||
\(623\) | −8.23628e143 | −0.999072 | ||||||||
\(624\) | −2.20481e143 | −0.246244 | ||||||||
\(625\) | 2.18438e143 | 0.224651 | ||||||||
\(626\) | −1.28236e143 | −0.121460 | ||||||||
\(627\) | −6.21454e143 | −0.542164 | ||||||||
\(628\) | 2.02694e144 | 1.62899 | ||||||||
\(629\) | −1.32882e144 | −0.983913 | ||||||||
\(630\) | −9.27679e143 | −0.632935 | ||||||||
\(631\) | −2.31627e143 | −0.145639 | −0.0728196 | − | 0.997345i | \(-0.523200\pi\) | ||||
−0.0728196 | + | 0.997345i | \(0.523200\pi\) | |||||||
\(632\) | 4.12979e144 | 2.39331 | ||||||||
\(633\) | 7.51756e143 | 0.401593 | ||||||||
\(634\) | −2.21363e144 | −1.09021 | ||||||||
\(635\) | 4.40992e143 | 0.200255 | ||||||||
\(636\) | −1.81325e144 | −0.759304 | ||||||||
\(637\) | −8.47685e143 | −0.327381 | ||||||||
\(638\) | 4.80761e144 | 1.71263 | ||||||||
\(639\) | −1.99598e144 | −0.655937 | ||||||||
\(640\) | −3.17202e144 | −0.961762 | ||||||||
\(641\) | 1.76803e144 | 0.494655 | 0.247327 | − | 0.968932i | \(-0.420448\pi\) | ||||
0.247327 | + | 0.968932i | \(0.420448\pi\) | |||||||
\(642\) | −2.71697e144 | −0.701504 | ||||||||
\(643\) | 5.06126e144 | 1.20613 | 0.603064 | − | 0.797692i | \(-0.293946\pi\) | ||||
0.603064 | + | 0.797692i | \(0.293946\pi\) | |||||||
\(644\) | 7.79272e144 | 1.71422 | ||||||||
\(645\) | −3.35862e143 | −0.0682080 | ||||||||
\(646\) | −2.05837e145 | −3.85966 | ||||||||
\(647\) | 3.35045e144 | 0.580140 | 0.290070 | − | 0.957005i | \(-0.406321\pi\) | ||||
0.290070 | + | 0.957005i | \(0.406321\pi\) | |||||||
\(648\) | −6.54891e144 | −1.04726 | ||||||||
\(649\) | −9.90706e143 | −0.146333 | ||||||||
\(650\) | 7.69959e144 | 1.05058 | ||||||||
\(651\) | 2.15757e144 | 0.271984 | ||||||||
\(652\) | −2.64397e145 | −3.07968 | ||||||||
\(653\) | 1.16215e145 | 1.25093 | 0.625465 | − | 0.780252i | \(-0.284909\pi\) | ||||
0.625465 | + | 0.780252i | \(0.284909\pi\) | |||||||
\(654\) | 5.74899e144 | 0.571923 | ||||||||
\(655\) | −2.02744e144 | −0.186432 | ||||||||
\(656\) | 1.52299e145 | 1.29464 | ||||||||
\(657\) | 1.28833e145 | 1.01253 | ||||||||
\(658\) | 2.31733e145 | 1.68405 | ||||||||
\(659\) | 6.04023e144 | 0.405933 | 0.202967 | − | 0.979186i | \(-0.434942\pi\) | ||||
0.202967 | + | 0.979186i | \(0.434942\pi\) | |||||||
\(660\) | 6.11598e144 | 0.380149 | ||||||||
\(661\) | −1.76758e144 | −0.101626 | −0.0508129 | − | 0.998708i | \(-0.516181\pi\) | ||||
−0.0508129 | + | 0.998708i | \(0.516181\pi\) | |||||||
\(662\) | 2.07712e145 | 1.10478 | ||||||||
\(663\) | −9.25465e144 | −0.455421 | ||||||||
\(664\) | −2.83357e145 | −1.29026 | ||||||||
\(665\) | −1.47468e145 | −0.621416 | ||||||||
\(666\) | −2.49568e145 | −0.973344 | ||||||||
\(667\) | −2.95757e145 | −1.06771 | ||||||||
\(668\) | −4.53748e145 | −1.51645 | ||||||||
\(669\) | −9.06091e144 | −0.280367 | ||||||||
\(670\) | 4.13805e145 | 1.18561 | ||||||||
\(671\) | 2.04269e145 | 0.541993 | ||||||||
\(672\) | −2.23287e144 | −0.0548714 | ||||||||
\(673\) | −3.31245e145 | −0.754004 | −0.377002 | − | 0.926212i | \(-0.623045\pi\) | ||||
−0.377002 | + | 0.926212i | \(0.623045\pi\) | |||||||
\(674\) | 9.17185e145 | 1.93407 | ||||||||
\(675\) | −2.39534e145 | −0.467975 | ||||||||
\(676\) | −2.83198e145 | −0.512668 | ||||||||
\(677\) | −8.09936e145 | −1.35873 | −0.679367 | − | 0.733799i | \(-0.737746\pi\) | ||||
−0.679367 | + | 0.733799i | \(0.737746\pi\) | |||||||
\(678\) | 3.07928e145 | 0.478762 | ||||||||
\(679\) | 1.74769e145 | 0.251867 | ||||||||
\(680\) | 9.81454e145 | 1.31118 | ||||||||
\(681\) | 3.27562e145 | 0.405711 | ||||||||
\(682\) | 1.55670e146 | 1.78776 | ||||||||
\(683\) | 7.49413e144 | 0.0798096 | 0.0399048 | − | 0.999203i | \(-0.487295\pi\) | ||||
0.0399048 | + | 0.999203i | \(0.487295\pi\) | |||||||
\(684\) | −2.55088e146 | −2.51942 | ||||||||
\(685\) | −8.42309e145 | −0.771627 | ||||||||
\(686\) | 2.19214e146 | 1.86284 | ||||||||
\(687\) | −7.73873e145 | −0.610095 | ||||||||
\(688\) | −4.11787e145 | −0.301209 | ||||||||
\(689\) | 1.41828e146 | 0.962661 | ||||||||
\(690\) | −5.70203e145 | −0.359171 | ||||||||
\(691\) | 1.42862e146 | 0.835215 | 0.417608 | − | 0.908628i | \(-0.362869\pi\) | ||||
0.417608 | + | 0.908628i | \(0.362869\pi\) | |||||||
\(692\) | −1.31042e146 | −0.711126 | ||||||||
\(693\) | −1.44140e146 | −0.726143 | ||||||||
\(694\) | −1.23085e146 | −0.575694 | ||||||||
\(695\) | −1.00943e146 | −0.438387 | ||||||||
\(696\) | −1.32399e146 | −0.533962 | ||||||||
\(697\) | 6.39272e146 | 2.39440 | ||||||||
\(698\) | 3.18337e146 | 1.10747 | ||||||||
\(699\) | 1.57609e146 | 0.509339 | ||||||||
\(700\) | −3.62940e146 | −1.08965 | ||||||||
\(701\) | −1.30604e146 | −0.364317 | −0.182158 | − | 0.983269i | \(-0.558308\pi\) | ||||
−0.182158 | + | 0.983269i | \(0.558308\pi\) | |||||||
\(702\) | −3.71697e146 | −0.963447 | ||||||||
\(703\) | −3.96724e146 | −0.955629 | ||||||||
\(704\) | −5.47658e146 | −1.22608 | ||||||||
\(705\) | −1.11885e146 | −0.232826 | ||||||||
\(706\) | −1.08568e146 | −0.210019 | ||||||||
\(707\) | 2.51103e146 | 0.451597 | ||||||||
\(708\) | 5.63135e145 | 0.0941672 | ||||||||
\(709\) | −1.50306e146 | −0.233719 | −0.116860 | − | 0.993148i | \(-0.537283\pi\) | ||||
−0.116860 | + | 0.993148i | \(0.537283\pi\) | |||||||
\(710\) | 4.73228e146 | 0.684330 | ||||||||
\(711\) | 9.69928e146 | 1.30453 | ||||||||
\(712\) | 1.63654e147 | 2.04742 | ||||||||
\(713\) | −9.57657e146 | −1.11455 | ||||||||
\(714\) | 6.61127e146 | 0.715858 | ||||||||
\(715\) | −4.78380e146 | −0.481961 | ||||||||
\(716\) | 1.86208e147 | 1.74573 | ||||||||
\(717\) | 3.32349e146 | 0.289974 | ||||||||
\(718\) | −2.01630e147 | −1.63737 | ||||||||
\(719\) | 4.52946e146 | 0.342380 | 0.171190 | − | 0.985238i | \(-0.445239\pi\) | ||||
0.171190 | + | 0.985238i | \(0.445239\pi\) | |||||||
\(720\) | 5.49153e146 | 0.386429 | ||||||||
\(721\) | −9.73032e145 | −0.0637472 | ||||||||
\(722\) | −3.33457e147 | −2.03411 | ||||||||
\(723\) | 5.98002e146 | 0.339688 | ||||||||
\(724\) | −1.32060e147 | −0.698613 | ||||||||
\(725\) | 1.37747e147 | 0.678694 | ||||||||
\(726\) | 1.37204e146 | 0.0629697 | ||||||||
\(727\) | −7.96559e146 | −0.340562 | −0.170281 | − | 0.985396i | \(-0.554468\pi\) | ||||
−0.170281 | + | 0.985396i | \(0.554468\pi\) | |||||||
\(728\) | −2.72864e147 | −1.08688 | ||||||||
\(729\) | −9.22473e146 | −0.342362 | ||||||||
\(730\) | −3.05450e147 | −1.05636 | ||||||||
\(731\) | −1.72847e147 | −0.557079 | ||||||||
\(732\) | −1.16110e147 | −0.348779 | ||||||||
\(733\) | 3.53939e147 | 0.990999 | 0.495500 | − | 0.868608i | \(-0.334985\pi\) | ||||
0.495500 | + | 0.868608i | \(0.334985\pi\) | |||||||
\(734\) | 5.94507e147 | 1.55171 | ||||||||
\(735\) | −2.92377e146 | −0.0711450 | ||||||||
\(736\) | 9.91081e146 | 0.224855 | ||||||||
\(737\) | 6.42956e147 | 1.36021 | ||||||||
\(738\) | 1.20063e148 | 2.36868 | ||||||||
\(739\) | −4.95197e147 | −0.911150 | −0.455575 | − | 0.890198i | \(-0.650566\pi\) | ||||
−0.455575 | + | 0.890198i | \(0.650566\pi\) | |||||||
\(740\) | 3.90432e147 | 0.670057 | ||||||||
\(741\) | −2.76301e147 | −0.442329 | ||||||||
\(742\) | −1.01318e148 | −1.51317 | ||||||||
\(743\) | 5.33251e147 | 0.743033 | 0.371516 | − | 0.928426i | \(-0.378838\pi\) | ||||
0.371516 | + | 0.928426i | \(0.378838\pi\) | |||||||
\(744\) | −4.28707e147 | −0.557384 | ||||||||
\(745\) | −6.97415e147 | −0.846142 | ||||||||
\(746\) | −1.63909e148 | −1.85590 | ||||||||
\(747\) | −6.65497e147 | −0.703291 | ||||||||
\(748\) | 3.14751e148 | 3.10481 | ||||||||
\(749\) | −1.00175e148 | −0.922454 | ||||||||
\(750\) | 6.37329e147 | 0.547909 | ||||||||
\(751\) | 5.96070e147 | 0.478454 | 0.239227 | − | 0.970964i | \(-0.423106\pi\) | ||||
0.239227 | + | 0.970964i | \(0.423106\pi\) | |||||||
\(752\) | −1.37178e148 | −1.02817 | ||||||||
\(753\) | 1.06540e147 | 0.0745714 | ||||||||
\(754\) | 2.13749e148 | 1.39727 | ||||||||
\(755\) | −1.17878e148 | −0.719719 | ||||||||
\(756\) | 1.75209e148 | 0.999273 | ||||||||
\(757\) | 8.31494e147 | 0.443018 | 0.221509 | − | 0.975158i | \(-0.428902\pi\) | ||||
0.221509 | + | 0.975158i | \(0.428902\pi\) | |||||||
\(758\) | −5.42547e148 | −2.70068 | ||||||||
\(759\) | −8.85963e147 | −0.412064 | ||||||||
\(760\) | 2.93017e148 | 1.27348 | ||||||||
\(761\) | −4.38910e148 | −1.78265 | −0.891325 | − | 0.453365i | \(-0.850223\pi\) | ||||
−0.891325 | + | 0.453365i | \(0.850223\pi\) | |||||||
\(762\) | −5.90259e147 | −0.224058 | ||||||||
\(763\) | 2.11966e148 | 0.752059 | ||||||||
\(764\) | −2.95707e148 | −0.980741 | ||||||||
\(765\) | 2.30506e148 | 0.714690 | ||||||||
\(766\) | 2.04425e148 | 0.592586 | ||||||||
\(767\) | −4.40473e147 | −0.119387 | ||||||||
\(768\) | 2.64092e148 | 0.669349 | ||||||||
\(769\) | −9.80404e147 | −0.232380 | −0.116190 | − | 0.993227i | \(-0.537068\pi\) | ||||
−0.116190 | + | 0.993227i | \(0.537068\pi\) | |||||||
\(770\) | 3.41741e148 | 0.757574 | ||||||||
\(771\) | −2.05481e148 | −0.426061 | ||||||||
\(772\) | 7.23234e148 | 1.40277 | ||||||||
\(773\) | 3.27776e148 | 0.594748 | 0.297374 | − | 0.954761i | \(-0.403889\pi\) | ||||
0.297374 | + | 0.954761i | \(0.403889\pi\) | |||||||
\(774\) | −3.24628e148 | −0.551095 | ||||||||
\(775\) | 4.46022e148 | 0.708465 | ||||||||
\(776\) | −3.47265e148 | −0.516157 | ||||||||
\(777\) | 1.27424e148 | 0.177242 | ||||||||
\(778\) | −1.42878e149 | −1.86002 | ||||||||
\(779\) | 1.90857e149 | 2.32557 | ||||||||
\(780\) | 2.71920e148 | 0.310148 | ||||||||
\(781\) | 7.35286e148 | 0.785106 | ||||||||
\(782\) | −2.93447e149 | −2.93348 | ||||||||
\(783\) | −6.64972e148 | −0.622404 | ||||||||
\(784\) | −3.58472e148 | −0.314179 | ||||||||
\(785\) | −5.46834e148 | −0.448816 | ||||||||
\(786\) | 2.71368e148 | 0.208592 | ||||||||
\(787\) | −2.62026e148 | −0.188645 | −0.0943225 | − | 0.995542i | \(-0.530068\pi\) | ||||
−0.0943225 | + | 0.995542i | \(0.530068\pi\) | |||||||
\(788\) | −2.18821e149 | −1.47567 | ||||||||
\(789\) | −3.36406e148 | −0.212519 | ||||||||
\(790\) | −2.29960e149 | −1.36100 | ||||||||
\(791\) | 1.13533e149 | 0.629556 | ||||||||
\(792\) | 2.86405e149 | 1.48810 | ||||||||
\(793\) | 9.08192e148 | 0.442190 | ||||||||
\(794\) | 3.85119e149 | 1.75727 | ||||||||
\(795\) | 4.89183e148 | 0.209201 | ||||||||
\(796\) | 5.40818e149 | 2.16784 | ||||||||
\(797\) | −8.15941e148 | −0.306588 | −0.153294 | − | 0.988181i | \(-0.548988\pi\) | ||||
−0.153294 | + | 0.988181i | \(0.548988\pi\) | |||||||
\(798\) | 1.97382e149 | 0.695279 | ||||||||
\(799\) | −5.75801e149 | −1.90157 | ||||||||
\(800\) | −4.61589e148 | −0.142929 | ||||||||
\(801\) | 3.84361e149 | 1.11600 | ||||||||
\(802\) | −4.93869e148 | −0.134472 | ||||||||
\(803\) | −4.74598e149 | −1.21192 | ||||||||
\(804\) | −3.65468e149 | −0.875311 | ||||||||
\(805\) | −2.10234e149 | −0.472297 | ||||||||
\(806\) | 6.92115e149 | 1.45856 | ||||||||
\(807\) | 1.18474e149 | 0.234226 | ||||||||
\(808\) | −4.98939e149 | −0.925470 | ||||||||
\(809\) | −3.06884e149 | −0.534104 | −0.267052 | − | 0.963682i | \(-0.586050\pi\) | ||||
−0.267052 | + | 0.963682i | \(0.586050\pi\) | |||||||
\(810\) | 3.64666e149 | 0.595547 | ||||||||
\(811\) | 1.75625e149 | 0.269161 | 0.134580 | − | 0.990903i | \(-0.457031\pi\) | ||||
0.134580 | + | 0.990903i | \(0.457031\pi\) | |||||||
\(812\) | −1.00756e150 | −1.44922 | ||||||||
\(813\) | −4.38063e149 | −0.591389 | ||||||||
\(814\) | 9.19367e149 | 1.16502 | ||||||||
\(815\) | 7.13299e149 | 0.848505 | ||||||||
\(816\) | −3.91363e149 | −0.437056 | ||||||||
\(817\) | −5.16042e149 | −0.541064 | ||||||||
\(818\) | 1.08523e150 | 1.06838 | ||||||||
\(819\) | −6.40852e149 | −0.592430 | ||||||||
\(820\) | −1.87830e150 | −1.63062 | ||||||||
\(821\) | 8.24093e149 | 0.671898 | 0.335949 | − | 0.941880i | \(-0.390943\pi\) | ||||
0.335949 | + | 0.941880i | \(0.390943\pi\) | |||||||
\(822\) | 1.12741e150 | 0.863345 | ||||||||
\(823\) | −1.47424e149 | −0.106042 | −0.0530210 | − | 0.998593i | \(-0.516885\pi\) | ||||
−0.0530210 | + | 0.998593i | \(0.516885\pi\) | |||||||
\(824\) | 1.93341e149 | 0.130639 | ||||||||
\(825\) | 4.12631e149 | 0.261929 | ||||||||
\(826\) | 3.14662e149 | 0.187660 | ||||||||
\(827\) | 4.73345e149 | 0.265243 | 0.132622 | − | 0.991167i | \(-0.457661\pi\) | ||||
0.132622 | + | 0.991167i | \(0.457661\pi\) | |||||||
\(828\) | −3.63661e150 | −1.91485 | ||||||||
\(829\) | 1.42057e150 | 0.702918 | 0.351459 | − | 0.936203i | \(-0.385686\pi\) | ||||
0.351459 | + | 0.936203i | \(0.385686\pi\) | |||||||
\(830\) | 1.57783e150 | 0.733733 | ||||||||
\(831\) | 5.97056e149 | 0.260953 | ||||||||
\(832\) | −2.43492e150 | −1.00031 | ||||||||
\(833\) | −1.50468e150 | −0.581066 | ||||||||
\(834\) | 1.35110e150 | 0.490495 | ||||||||
\(835\) | 1.22414e150 | 0.417807 | ||||||||
\(836\) | 9.39702e150 | 3.01555 | ||||||||
\(837\) | −2.15317e150 | −0.649705 | ||||||||
\(838\) | 7.34626e150 | 2.08449 | ||||||||
\(839\) | −1.36874e150 | −0.365242 | −0.182621 | − | 0.983183i | \(-0.558458\pi\) | ||||
−0.182621 | + | 0.983183i | \(0.558458\pi\) | |||||||
\(840\) | −9.41140e149 | −0.236195 | ||||||||
\(841\) | −4.12372e149 | −0.0973409 | ||||||||
\(842\) | −1.16574e151 | −2.58838 | ||||||||
\(843\) | −2.05002e150 | −0.428191 | ||||||||
\(844\) | −1.13673e151 | −2.23369 | ||||||||
\(845\) | 7.64021e149 | 0.141249 | ||||||||
\(846\) | −1.08143e151 | −1.88115 | ||||||||
\(847\) | 5.05873e149 | 0.0828029 | ||||||||
\(848\) | 5.99769e150 | 0.923841 | ||||||||
\(849\) | −4.28528e149 | −0.0621202 | ||||||||
\(850\) | 1.36671e151 | 1.86467 | ||||||||
\(851\) | −5.65581e150 | −0.726311 | ||||||||
\(852\) | −4.17950e150 | −0.505225 | ||||||||
\(853\) | 7.71668e150 | 0.878123 | 0.439062 | − | 0.898457i | \(-0.355311\pi\) | ||||
0.439062 | + | 0.898457i | \(0.355311\pi\) | |||||||
\(854\) | −6.48788e150 | −0.695060 | ||||||||
\(855\) | 6.88184e150 | 0.694144 | ||||||||
\(856\) | 1.99046e151 | 1.89041 | ||||||||
\(857\) | 1.36517e151 | 1.22088 | 0.610440 | − | 0.792063i | \(-0.290993\pi\) | ||||
0.610440 | + | 0.792063i | \(0.290993\pi\) | |||||||
\(858\) | 6.40301e150 | 0.539248 | ||||||||
\(859\) | −4.88128e150 | −0.387156 | −0.193578 | − | 0.981085i | \(-0.562009\pi\) | ||||
−0.193578 | + | 0.981085i | \(0.562009\pi\) | |||||||
\(860\) | 5.07858e150 | 0.379378 | ||||||||
\(861\) | −6.13013e150 | −0.431328 | ||||||||
\(862\) | −5.03520e151 | −3.33728 | ||||||||
\(863\) | 2.58884e151 | 1.61640 | 0.808201 | − | 0.588906i | \(-0.200441\pi\) | ||||
0.808201 | + | 0.588906i | \(0.200441\pi\) | |||||||
\(864\) | 2.22832e150 | 0.131075 | ||||||||
\(865\) | 3.53529e150 | 0.195928 | ||||||||
\(866\) | 4.84399e151 | 2.52948 | ||||||||
\(867\) | −9.33955e150 | −0.459560 | ||||||||
\(868\) | −3.26246e151 | −1.51279 | ||||||||
\(869\) | −3.57305e151 | −1.56142 | ||||||||
\(870\) | 7.37245e150 | 0.303648 | ||||||||
\(871\) | 2.85861e151 | 1.10974 | ||||||||
\(872\) | −4.21174e151 | −1.54121 | ||||||||
\(873\) | −8.15591e150 | −0.281345 | ||||||||
\(874\) | −8.76100e151 | −2.84915 | ||||||||
\(875\) | 2.34983e151 | 0.720481 | ||||||||
\(876\) | 2.69770e151 | 0.779888 | ||||||||
\(877\) | 5.48140e150 | 0.149421 | 0.0747107 | − | 0.997205i | \(-0.476197\pi\) | ||||
0.0747107 | + | 0.997205i | \(0.476197\pi\) | |||||||
\(878\) | 1.00056e152 | 2.57204 | ||||||||
\(879\) | −1.81912e151 | −0.440997 | ||||||||
\(880\) | −2.02299e151 | −0.462525 | ||||||||
\(881\) | 3.41155e151 | 0.735685 | 0.367843 | − | 0.929888i | \(-0.380097\pi\) | ||||
0.367843 | + | 0.929888i | \(0.380097\pi\) | |||||||
\(882\) | −2.82597e151 | −0.574824 | ||||||||
\(883\) | −8.15917e151 | −1.56556 | −0.782780 | − | 0.622299i | \(-0.786199\pi\) | ||||
−0.782780 | + | 0.622299i | \(0.786199\pi\) | |||||||
\(884\) | 1.39940e152 | 2.53308 | ||||||||
\(885\) | −1.51924e150 | −0.0259447 | ||||||||
\(886\) | 6.15273e151 | 0.991359 | ||||||||
\(887\) | −9.60570e151 | −1.46037 | −0.730184 | − | 0.683250i | \(-0.760566\pi\) | ||||
−0.730184 | + | 0.683250i | \(0.760566\pi\) | |||||||
\(888\) | −2.53190e151 | −0.363227 | ||||||||
\(889\) | −2.17629e151 | −0.294629 | ||||||||
\(890\) | −9.11282e151 | −1.16431 | ||||||||
\(891\) | 5.66606e151 | 0.683249 | ||||||||
\(892\) | 1.37010e152 | 1.55942 | ||||||||
\(893\) | −1.71908e152 | −1.84691 | ||||||||
\(894\) | 9.33474e151 | 0.946717 | ||||||||
\(895\) | −5.02357e151 | −0.480979 | ||||||||
\(896\) | 1.56539e152 | 1.41501 | ||||||||
\(897\) | −3.93904e151 | −0.336186 | ||||||||
\(898\) | −1.01881e151 | −0.0821034 | ||||||||
\(899\) | 1.23820e152 | 0.942254 | ||||||||
\(900\) | 1.69373e152 | 1.21718 | ||||||||
\(901\) | 2.51752e152 | 1.70862 | ||||||||
\(902\) | −4.42292e152 | −2.83513 | ||||||||
\(903\) | 1.65747e151 | 0.100352 | ||||||||
\(904\) | −2.25590e152 | −1.29016 | ||||||||
\(905\) | 3.56277e151 | 0.192480 | ||||||||
\(906\) | 1.57777e152 | 0.805268 | ||||||||
\(907\) | −2.92428e152 | −1.41008 | −0.705039 | − | 0.709168i | \(-0.749071\pi\) | ||||
−0.705039 | + | 0.709168i | \(0.749071\pi\) | |||||||
\(908\) | −4.95307e152 | −2.25659 | ||||||||
\(909\) | −1.17181e152 | −0.504451 | ||||||||
\(910\) | 1.51940e152 | 0.618073 | ||||||||
\(911\) | 3.06739e152 | 1.17916 | 0.589580 | − | 0.807710i | \(-0.299293\pi\) | ||||
0.589580 | + | 0.807710i | \(0.299293\pi\) | |||||||
\(912\) | −1.16843e152 | −0.424492 | ||||||||
\(913\) | 2.45158e152 | 0.841784 | ||||||||
\(914\) | −8.24465e152 | −2.67573 | ||||||||
\(915\) | 3.13246e151 | 0.0960947 | ||||||||
\(916\) | 1.17017e153 | 3.39339 | ||||||||
\(917\) | 1.00054e152 | 0.274291 | ||||||||
\(918\) | −6.59778e152 | −1.71001 | ||||||||
\(919\) | 2.60238e152 | 0.637709 | 0.318854 | − | 0.947804i | \(-0.396702\pi\) | ||||
0.318854 | + | 0.947804i | \(0.396702\pi\) | |||||||
\(920\) | 4.17734e152 | 0.967891 | ||||||||
\(921\) | 3.30536e151 | 0.0724182 | ||||||||
\(922\) | 3.11644e152 | 0.645678 | ||||||||
\(923\) | 3.26912e152 | 0.640535 | ||||||||
\(924\) | −3.01822e152 | −0.559300 | ||||||||
\(925\) | 2.63415e152 | 0.461681 | ||||||||
\(926\) | 8.55952e152 | 1.41900 | ||||||||
\(927\) | 4.54083e151 | 0.0712080 | ||||||||
\(928\) | −1.28142e152 | −0.190095 | ||||||||
\(929\) | −1.69956e152 | −0.238521 | −0.119260 | − | 0.992863i | \(-0.538052\pi\) | ||||
−0.119260 | + | 0.992863i | \(0.538052\pi\) | |||||||
\(930\) | 2.38719e152 | 0.316967 | ||||||||
\(931\) | −4.49228e152 | −0.564362 | ||||||||
\(932\) | −2.38321e153 | −2.83298 | ||||||||
\(933\) | 1.55764e151 | 0.0175211 | ||||||||
\(934\) | −5.84560e152 | −0.622250 | ||||||||
\(935\) | −8.49144e152 | −0.855428 | ||||||||
\(936\) | 1.27337e153 | 1.21408 | ||||||||
\(937\) | −1.54910e153 | −1.39794 | −0.698971 | − | 0.715150i | \(-0.746359\pi\) | ||||
−0.698971 | + | 0.715150i | \(0.746359\pi\) | |||||||
\(938\) | −2.04212e153 | −1.74435 | ||||||||
\(939\) | −3.05548e151 | −0.0247059 | ||||||||
\(940\) | 1.69181e153 | 1.29500 | ||||||||
\(941\) | 1.95873e153 | 1.41941 | 0.709707 | − | 0.704497i | \(-0.248827\pi\) | ||||
0.709707 | + | 0.704497i | \(0.248827\pi\) | |||||||
\(942\) | 7.31926e152 | 0.502164 | ||||||||
\(943\) | 2.72092e153 | 1.76752 | ||||||||
\(944\) | −1.86268e152 | −0.114573 | ||||||||
\(945\) | −4.72684e152 | −0.275317 | ||||||||
\(946\) | 1.19587e153 | 0.659617 | ||||||||
\(947\) | −3.18920e153 | −1.66594 | −0.832968 | − | 0.553321i | \(-0.813360\pi\) | ||||
−0.832968 | + | 0.553321i | \(0.813360\pi\) | |||||||
\(948\) | 2.03099e153 | 1.00480 | ||||||||
\(949\) | −2.11008e153 | −0.988758 | ||||||||
\(950\) | 4.08037e153 | 1.81106 | ||||||||
\(951\) | −5.27440e152 | −0.221757 | ||||||||
\(952\) | −4.84345e153 | −1.92909 | ||||||||
\(953\) | −1.81979e153 | −0.686654 | −0.343327 | − | 0.939216i | \(-0.611554\pi\) | ||||
−0.343327 | + | 0.939216i | \(0.611554\pi\) | |||||||
\(954\) | 4.72820e153 | 1.69027 | ||||||||
\(955\) | 7.97768e152 | 0.270211 | ||||||||
\(956\) | −5.02546e153 | −1.61285 | ||||||||
\(957\) | 1.14551e153 | 0.348364 | ||||||||
\(958\) | 1.77442e153 | 0.511368 | ||||||||
\(959\) | 4.15678e153 | 1.13527 | ||||||||
\(960\) | −8.39831e152 | −0.217382 | ||||||||
\(961\) | −6.69097e151 | −0.0164148 | ||||||||
\(962\) | 4.08755e153 | 0.950489 | ||||||||
\(963\) | 4.67483e153 | 1.03042 | ||||||||
\(964\) | −9.04240e153 | −1.88937 | ||||||||
\(965\) | −1.95116e153 | −0.386489 | ||||||||
\(966\) | 2.81394e153 | 0.528436 | ||||||||
\(967\) | −4.30897e153 | −0.767202 | −0.383601 | − | 0.923499i | \(-0.625316\pi\) | ||||
−0.383601 | + | 0.923499i | \(0.625316\pi\) | |||||||
\(968\) | −1.00517e153 | −0.169690 | ||||||||
\(969\) | −4.90447e153 | −0.785086 | ||||||||
\(970\) | 1.93369e153 | 0.293523 | ||||||||
\(971\) | 7.26145e152 | 0.104528 | 0.0522641 | − | 0.998633i | \(-0.483356\pi\) | ||||
0.0522641 | + | 0.998633i | \(0.483356\pi\) | |||||||
\(972\) | −1.25294e154 | −1.71048 | ||||||||
\(973\) | 4.98150e153 | 0.644984 | ||||||||
\(974\) | 8.24463e153 | 1.01248 | ||||||||
\(975\) | 1.83458e153 | 0.213697 | ||||||||
\(976\) | 3.84059e153 | 0.424358 | ||||||||
\(977\) | 4.14163e153 | 0.434112 | 0.217056 | − | 0.976159i | \(-0.430355\pi\) | ||||
0.217056 | + | 0.976159i | \(0.430355\pi\) | |||||||
\(978\) | −9.54735e153 | −0.949362 | ||||||||
\(979\) | −1.41592e154 | −1.33577 | ||||||||
\(980\) | 4.42103e153 | 0.395713 | ||||||||
\(981\) | −9.89175e153 | −0.840078 | ||||||||
\(982\) | −1.02086e154 | −0.822671 | ||||||||
\(983\) | −4.71221e153 | −0.360345 | −0.180172 | − | 0.983635i | \(-0.557666\pi\) | ||||
−0.180172 | + | 0.983635i | \(0.557666\pi\) | |||||||
\(984\) | 1.21805e154 | 0.883931 | ||||||||
\(985\) | 5.90343e153 | 0.406573 | ||||||||
\(986\) | 3.79413e154 | 2.48000 | ||||||||
\(987\) | 5.52150e153 | 0.342550 | ||||||||
\(988\) | 4.17796e154 | 2.46026 | ||||||||
\(989\) | −7.35684e153 | −0.411228 | ||||||||
\(990\) | −1.59480e154 | −0.846239 | ||||||||
\(991\) | 2.54041e154 | 1.27971 | 0.639854 | − | 0.768497i | \(-0.278995\pi\) | ||||
0.639854 | + | 0.768497i | \(0.278995\pi\) | |||||||
\(992\) | −4.14921e153 | −0.198433 | ||||||||
\(993\) | 4.94914e153 | 0.224721 | ||||||||
\(994\) | −2.33537e154 | −1.00683 | ||||||||
\(995\) | −1.45903e154 | −0.597279 | ||||||||
\(996\) | −1.39352e154 | −0.541698 | ||||||||
\(997\) | 1.47094e154 | 0.542991 | 0.271496 | − | 0.962440i | \(-0.412482\pi\) | ||||
0.271496 | + | 0.962440i | \(0.412482\pi\) | |||||||
\(998\) | −6.06646e154 | −2.12673 | ||||||||
\(999\) | −1.27164e154 | −0.423389 |
(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 | 1.104.a.a.1.1 | ✓ | 8 | |
3.2 | odd | 2 | 9.104.a.a.1.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.104.a.a.1.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
9.104.a.a.1.8 | 8 | 3.2 | odd | 2 |