Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [197,14,Mod(1,197)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(197, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("197.1");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 197 \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
Character orbit: | \([\chi]\) | \(=\) | 197.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(211.244930035\) |
Analytic rank: | \(1\) |
Dimension: | \(104\) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 197.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −147.901 | −1.63409 | −0.817047 | − | 0.576571i | \(-0.804391\pi\) | ||||
−0.817047 | + | 0.576571i | \(0.804391\pi\) | |||||||
\(3\) | 534.557 | 0.423356 | 0.211678 | − | 0.977339i | \(-0.432107\pi\) | ||||
0.211678 | + | 0.977339i | \(0.432107\pi\) | |||||||
\(4\) | 13682.8 | 1.67026 | ||||||||
\(5\) | −7800.19 | −0.223255 | −0.111627 | − | 0.993750i | \(-0.535606\pi\) | ||||
−0.111627 | + | 0.993750i | \(0.535606\pi\) | |||||||
\(6\) | −79061.7 | −0.691804 | ||||||||
\(7\) | 515509. | 1.65615 | 0.828074 | − | 0.560619i | \(-0.189437\pi\) | ||||
0.828074 | + | 0.560619i | \(0.189437\pi\) | |||||||
\(8\) | −812098. | −1.09528 | ||||||||
\(9\) | −1.30857e6 | −0.820770 | ||||||||
\(10\) | 1.15366e6 | 0.364819 | ||||||||
\(11\) | 2.66243e6 | 0.453134 | 0.226567 | − | 0.973996i | \(-0.427250\pi\) | ||||
0.226567 | + | 0.973996i | \(0.427250\pi\) | |||||||
\(12\) | 7.31424e6 | 0.707117 | ||||||||
\(13\) | 1.65269e7 | 0.949639 | 0.474820 | − | 0.880083i | \(-0.342513\pi\) | ||||
0.474820 | + | 0.880083i | \(0.342513\pi\) | |||||||
\(14\) | −7.62445e7 | −2.70630 | ||||||||
\(15\) | −4.16965e6 | −0.0945162 | ||||||||
\(16\) | 8.02079e6 | 0.119519 | ||||||||
\(17\) | −8.87509e7 | −0.891774 | −0.445887 | − | 0.895089i | \(-0.647112\pi\) | ||||
−0.445887 | + | 0.895089i | \(0.647112\pi\) | |||||||
\(18\) | 1.93540e8 | 1.34122 | ||||||||
\(19\) | 3.31694e8 | 1.61748 | 0.808741 | − | 0.588165i | \(-0.200150\pi\) | ||||
0.808741 | + | 0.588165i | \(0.200150\pi\) | |||||||
\(20\) | −1.06729e8 | −0.372894 | ||||||||
\(21\) | 2.75569e8 | 0.701140 | ||||||||
\(22\) | −3.93778e8 | −0.740463 | ||||||||
\(23\) | 1.26386e8 | 0.178020 | 0.0890101 | − | 0.996031i | \(-0.471630\pi\) | ||||
0.0890101 | + | 0.996031i | \(0.471630\pi\) | |||||||
\(24\) | −4.34112e8 | −0.463691 | ||||||||
\(25\) | −1.15986e9 | −0.950157 | ||||||||
\(26\) | −2.44434e9 | −1.55180 | ||||||||
\(27\) | −1.55176e9 | −0.770834 | ||||||||
\(28\) | 7.05361e9 | 2.76621 | ||||||||
\(29\) | 5.69701e9 | 1.77852 | 0.889262 | − | 0.457398i | \(-0.151218\pi\) | ||||
0.889262 | + | 0.457398i | \(0.151218\pi\) | |||||||
\(30\) | 6.16696e8 | 0.154448 | ||||||||
\(31\) | −7.98222e9 | −1.61537 | −0.807686 | − | 0.589613i | \(-0.799280\pi\) | ||||
−0.807686 | + | 0.589613i | \(0.799280\pi\) | |||||||
\(32\) | 5.46642e9 | 0.899970 | ||||||||
\(33\) | 1.42322e9 | 0.191837 | ||||||||
\(34\) | 1.31264e10 | 1.45724 | ||||||||
\(35\) | −4.02107e9 | −0.369743 | ||||||||
\(36\) | −1.79049e10 | −1.37090 | ||||||||
\(37\) | −1.46204e10 | −0.936804 | −0.468402 | − | 0.883516i | \(-0.655170\pi\) | ||||
−0.468402 | + | 0.883516i | \(0.655170\pi\) | |||||||
\(38\) | −4.90580e10 | −2.64312 | ||||||||
\(39\) | 8.83455e9 | 0.402035 | ||||||||
\(40\) | 6.33452e9 | 0.244525 | ||||||||
\(41\) | 1.90194e10 | 0.625321 | 0.312660 | − | 0.949865i | \(-0.398780\pi\) | ||||
0.312660 | + | 0.949865i | \(0.398780\pi\) | |||||||
\(42\) | −4.07570e10 | −1.14573 | ||||||||
\(43\) | 1.26317e10 | 0.304732 | 0.152366 | − | 0.988324i | \(-0.451311\pi\) | ||||
0.152366 | + | 0.988324i | \(0.451311\pi\) | |||||||
\(44\) | 3.64296e10 | 0.756853 | ||||||||
\(45\) | 1.02071e10 | 0.183241 | ||||||||
\(46\) | −1.86927e10 | −0.290902 | ||||||||
\(47\) | −1.26740e10 | −0.171506 | −0.0857529 | − | 0.996316i | \(-0.527330\pi\) | ||||
−0.0857529 | + | 0.996316i | \(0.527330\pi\) | |||||||
\(48\) | 4.28757e9 | 0.0505991 | ||||||||
\(49\) | 1.68861e11 | 1.74283 | ||||||||
\(50\) | 1.71545e11 | 1.55265 | ||||||||
\(51\) | −4.74424e10 | −0.377538 | ||||||||
\(52\) | 2.26134e11 | 1.58615 | ||||||||
\(53\) | −2.90212e11 | −1.79855 | −0.899273 | − | 0.437387i | \(-0.855904\pi\) | ||||
−0.899273 | + | 0.437387i | \(0.855904\pi\) | |||||||
\(54\) | 2.29508e11 | 1.25962 | ||||||||
\(55\) | −2.07675e10 | −0.101164 | ||||||||
\(56\) | −4.18644e11 | −1.81394 | ||||||||
\(57\) | 1.77309e11 | 0.684770 | ||||||||
\(58\) | −8.42595e11 | −2.90628 | ||||||||
\(59\) | −1.35888e11 | −0.419414 | −0.209707 | − | 0.977764i | \(-0.567251\pi\) | ||||
−0.209707 | + | 0.977764i | \(0.567251\pi\) | |||||||
\(60\) | −5.70525e10 | −0.157867 | ||||||||
\(61\) | −7.22733e11 | −1.79612 | −0.898058 | − | 0.439878i | \(-0.855022\pi\) | ||||
−0.898058 | + | 0.439878i | \(0.855022\pi\) | |||||||
\(62\) | 1.18058e12 | 2.63967 | ||||||||
\(63\) | −6.74581e11 | −1.35932 | ||||||||
\(64\) | −8.74197e11 | −1.59016 | ||||||||
\(65\) | −1.28913e11 | −0.212011 | ||||||||
\(66\) | −2.10496e11 | −0.313480 | ||||||||
\(67\) | −1.06472e12 | −1.43797 | −0.718987 | − | 0.695024i | \(-0.755394\pi\) | ||||
−0.718987 | + | 0.695024i | \(0.755394\pi\) | |||||||
\(68\) | −1.21436e12 | −1.48950 | ||||||||
\(69\) | 6.75607e10 | 0.0753659 | ||||||||
\(70\) | 5.94722e11 | 0.604194 | ||||||||
\(71\) | 5.87176e11 | 0.543987 | 0.271994 | − | 0.962299i | \(-0.412317\pi\) | ||||
0.271994 | + | 0.962299i | \(0.412317\pi\) | |||||||
\(72\) | 1.06269e12 | 0.898969 | ||||||||
\(73\) | −2.24613e12 | −1.73715 | −0.868574 | − | 0.495560i | \(-0.834963\pi\) | ||||
−0.868574 | + | 0.495560i | \(0.834963\pi\) | |||||||
\(74\) | 2.16238e12 | 1.53083 | ||||||||
\(75\) | −6.20011e11 | −0.402255 | ||||||||
\(76\) | 4.53851e12 | 2.70162 | ||||||||
\(77\) | 1.37251e12 | 0.750457 | ||||||||
\(78\) | −1.30664e12 | −0.656964 | ||||||||
\(79\) | −2.25245e12 | −1.04251 | −0.521253 | − | 0.853402i | \(-0.674535\pi\) | ||||
−0.521253 | + | 0.853402i | \(0.674535\pi\) | |||||||
\(80\) | −6.25637e10 | −0.0266832 | ||||||||
\(81\) | 1.25678e12 | 0.494433 | ||||||||
\(82\) | −2.81300e12 | −1.02183 | ||||||||
\(83\) | −2.98199e12 | −1.00115 | −0.500575 | − | 0.865693i | \(-0.666878\pi\) | ||||
−0.500575 | + | 0.865693i | \(0.666878\pi\) | |||||||
\(84\) | 3.77056e12 | 1.17109 | ||||||||
\(85\) | 6.92274e11 | 0.199093 | ||||||||
\(86\) | −1.86825e12 | −0.497960 | ||||||||
\(87\) | 3.04537e12 | 0.752949 | ||||||||
\(88\) | −2.16216e12 | −0.496306 | ||||||||
\(89\) | 1.98811e12 | 0.424038 | 0.212019 | − | 0.977266i | \(-0.431996\pi\) | ||||
0.212019 | + | 0.977266i | \(0.431996\pi\) | |||||||
\(90\) | −1.50965e12 | −0.299432 | ||||||||
\(91\) | 8.51975e12 | 1.57274 | ||||||||
\(92\) | 1.72932e12 | 0.297341 | ||||||||
\(93\) | −4.26695e12 | −0.683878 | ||||||||
\(94\) | 1.87451e12 | 0.280257 | ||||||||
\(95\) | −2.58728e12 | −0.361110 | ||||||||
\(96\) | 2.92211e12 | 0.381008 | ||||||||
\(97\) | −5.54163e12 | −0.675494 | −0.337747 | − | 0.941237i | \(-0.609665\pi\) | ||||
−0.337747 | + | 0.941237i | \(0.609665\pi\) | |||||||
\(98\) | −2.49747e13 | −2.84794 | ||||||||
\(99\) | −3.48399e12 | −0.371918 | ||||||||
\(100\) | −1.58701e13 | −1.58701 | ||||||||
\(101\) | 1.55572e13 | 1.45828 | 0.729141 | − | 0.684363i | \(-0.239920\pi\) | ||||
0.729141 | + | 0.684363i | \(0.239920\pi\) | |||||||
\(102\) | 7.01679e12 | 0.616932 | ||||||||
\(103\) | −1.56888e13 | −1.29464 | −0.647318 | − | 0.762220i | \(-0.724109\pi\) | ||||
−0.647318 | + | 0.762220i | \(0.724109\pi\) | |||||||
\(104\) | −1.34214e13 | −1.04012 | ||||||||
\(105\) | −2.14949e12 | −0.156533 | ||||||||
\(106\) | 4.29227e13 | 2.93900 | ||||||||
\(107\) | 5.76474e12 | 0.371352 | 0.185676 | − | 0.982611i | \(-0.440553\pi\) | ||||
0.185676 | + | 0.982611i | \(0.440553\pi\) | |||||||
\(108\) | −2.12325e13 | −1.28750 | ||||||||
\(109\) | 5.04693e12 | 0.288241 | 0.144120 | − | 0.989560i | \(-0.453965\pi\) | ||||
0.144120 | + | 0.989560i | \(0.453965\pi\) | |||||||
\(110\) | 3.07154e12 | 0.165312 | ||||||||
\(111\) | −7.81544e12 | −0.396601 | ||||||||
\(112\) | 4.13479e12 | 0.197941 | ||||||||
\(113\) | 1.11960e13 | 0.505884 | 0.252942 | − | 0.967481i | \(-0.418602\pi\) | ||||
0.252942 | + | 0.967481i | \(0.418602\pi\) | |||||||
\(114\) | −2.62243e13 | −1.11898 | ||||||||
\(115\) | −9.85838e11 | −0.0397438 | ||||||||
\(116\) | 7.79511e13 | 2.97061 | ||||||||
\(117\) | −2.16266e13 | −0.779435 | ||||||||
\(118\) | 2.00980e13 | 0.685362 | ||||||||
\(119\) | −4.57519e13 | −1.47691 | ||||||||
\(120\) | 3.38616e12 | 0.103521 | ||||||||
\(121\) | −2.74342e13 | −0.794670 | ||||||||
\(122\) | 1.06893e14 | 2.93502 | ||||||||
\(123\) | 1.01670e13 | 0.264733 | ||||||||
\(124\) | −1.09219e14 | −2.69810 | ||||||||
\(125\) | 1.85689e13 | 0.435382 | ||||||||
\(126\) | 9.97714e13 | 2.22125 | ||||||||
\(127\) | 4.98283e13 | 1.05378 | 0.526892 | − | 0.849932i | \(-0.323357\pi\) | ||||
0.526892 | + | 0.849932i | \(0.323357\pi\) | |||||||
\(128\) | 8.45140e13 | 1.69849 | ||||||||
\(129\) | 6.75237e12 | 0.129010 | ||||||||
\(130\) | 1.90664e13 | 0.346446 | ||||||||
\(131\) | 7.78851e12 | 0.134645 | 0.0673226 | − | 0.997731i | \(-0.478554\pi\) | ||||
0.0673226 | + | 0.997731i | \(0.478554\pi\) | |||||||
\(132\) | 1.94737e13 | 0.320418 | ||||||||
\(133\) | 1.70991e14 | 2.67879 | ||||||||
\(134\) | 1.57474e14 | 2.34979 | ||||||||
\(135\) | 1.21040e13 | 0.172092 | ||||||||
\(136\) | 7.20744e13 | 0.976738 | ||||||||
\(137\) | 6.65711e13 | 0.860206 | 0.430103 | − | 0.902780i | \(-0.358477\pi\) | ||||
0.430103 | + | 0.902780i | \(0.358477\pi\) | |||||||
\(138\) | −9.99232e12 | −0.123155 | ||||||||
\(139\) | 1.07241e13 | 0.126115 | 0.0630574 | − | 0.998010i | \(-0.479915\pi\) | ||||
0.0630574 | + | 0.998010i | \(0.479915\pi\) | |||||||
\(140\) | −5.50195e13 | −0.617568 | ||||||||
\(141\) | −6.77499e12 | −0.0726080 | ||||||||
\(142\) | −8.68441e13 | −0.888927 | ||||||||
\(143\) | 4.40017e13 | 0.430314 | ||||||||
\(144\) | −1.04958e13 | −0.0980976 | ||||||||
\(145\) | −4.44378e13 | −0.397064 | ||||||||
\(146\) | 3.32206e14 | 2.83866 | ||||||||
\(147\) | 9.02657e13 | 0.737836 | ||||||||
\(148\) | −2.00048e14 | −1.56471 | ||||||||
\(149\) | −3.82949e13 | −0.286701 | −0.143351 | − | 0.989672i | \(-0.545788\pi\) | ||||
−0.143351 | + | 0.989672i | \(0.545788\pi\) | |||||||
\(150\) | 9.17005e13 | 0.657322 | ||||||||
\(151\) | −3.10744e13 | −0.213330 | −0.106665 | − | 0.994295i | \(-0.534017\pi\) | ||||
−0.106665 | + | 0.994295i | \(0.534017\pi\) | |||||||
\(152\) | −2.69368e14 | −1.77159 | ||||||||
\(153\) | 1.16137e14 | 0.731941 | ||||||||
\(154\) | −2.02996e14 | −1.22632 | ||||||||
\(155\) | 6.22628e13 | 0.360639 | ||||||||
\(156\) | 1.20881e14 | 0.671505 | ||||||||
\(157\) | 1.62776e14 | 0.867446 | 0.433723 | − | 0.901046i | \(-0.357200\pi\) | ||||
0.433723 | + | 0.901046i | \(0.357200\pi\) | |||||||
\(158\) | 3.33140e14 | 1.70355 | ||||||||
\(159\) | −1.55135e14 | −0.761426 | ||||||||
\(160\) | −4.26391e13 | −0.200922 | ||||||||
\(161\) | 6.51533e13 | 0.294828 | ||||||||
\(162\) | −1.85880e14 | −0.807949 | ||||||||
\(163\) | −4.26116e13 | −0.177954 | −0.0889772 | − | 0.996034i | \(-0.528360\pi\) | ||||
−0.0889772 | + | 0.996034i | \(0.528360\pi\) | |||||||
\(164\) | 2.60239e14 | 1.04445 | ||||||||
\(165\) | −1.11014e13 | −0.0428285 | ||||||||
\(166\) | 4.41041e14 | 1.63597 | ||||||||
\(167\) | 5.08677e14 | 1.81462 | 0.907309 | − | 0.420464i | \(-0.138133\pi\) | ||||
0.907309 | + | 0.420464i | \(0.138133\pi\) | |||||||
\(168\) | −2.23789e14 | −0.767942 | ||||||||
\(169\) | −2.97380e13 | −0.0981856 | ||||||||
\(170\) | −1.02388e14 | −0.325336 | ||||||||
\(171\) | −4.34046e14 | −1.32758 | ||||||||
\(172\) | 1.72837e14 | 0.508983 | ||||||||
\(173\) | 3.60888e14 | 1.02347 | 0.511733 | − | 0.859145i | \(-0.329004\pi\) | ||||
0.511733 | + | 0.859145i | \(0.329004\pi\) | |||||||
\(174\) | −4.50415e14 | −1.23039 | ||||||||
\(175\) | −5.97919e14 | −1.57360 | ||||||||
\(176\) | 2.13548e13 | 0.0541581 | ||||||||
\(177\) | −7.26399e13 | −0.177561 | ||||||||
\(178\) | −2.94044e14 | −0.692918 | ||||||||
\(179\) | −1.38990e14 | −0.315818 | −0.157909 | − | 0.987454i | \(-0.550475\pi\) | ||||
−0.157909 | + | 0.987454i | \(0.550475\pi\) | |||||||
\(180\) | 1.39662e14 | 0.306060 | ||||||||
\(181\) | −4.80398e14 | −1.01553 | −0.507763 | − | 0.861497i | \(-0.669527\pi\) | ||||
−0.507763 | + | 0.861497i | \(0.669527\pi\) | |||||||
\(182\) | −1.26008e15 | −2.57001 | ||||||||
\(183\) | −3.86342e14 | −0.760396 | ||||||||
\(184\) | −1.02638e14 | −0.194981 | ||||||||
\(185\) | 1.14042e14 | 0.209146 | ||||||||
\(186\) | 6.31088e14 | 1.11752 | ||||||||
\(187\) | −2.36293e14 | −0.404093 | ||||||||
\(188\) | −1.73416e14 | −0.286460 | ||||||||
\(189\) | −7.99948e14 | −1.27661 | ||||||||
\(190\) | 3.82662e14 | 0.590088 | ||||||||
\(191\) | 1.71838e13 | 0.0256095 | 0.0128048 | − | 0.999918i | \(-0.495924\pi\) | ||||
0.0128048 | + | 0.999918i | \(0.495924\pi\) | |||||||
\(192\) | −4.67308e14 | −0.673202 | ||||||||
\(193\) | −4.23057e14 | −0.589218 | −0.294609 | − | 0.955618i | \(-0.595189\pi\) | ||||
−0.294609 | + | 0.955618i | \(0.595189\pi\) | |||||||
\(194\) | 8.19615e14 | 1.10382 | ||||||||
\(195\) | −6.89112e13 | −0.0897562 | ||||||||
\(196\) | 2.31049e15 | 2.91098 | ||||||||
\(197\) | −5.84517e13 | −0.0712470 | ||||||||
\(198\) | 5.15286e14 | 0.607750 | ||||||||
\(199\) | −5.89406e14 | −0.672775 | −0.336387 | − | 0.941724i | \(-0.609205\pi\) | ||||
−0.336387 | + | 0.941724i | \(0.609205\pi\) | |||||||
\(200\) | 9.41920e14 | 1.04068 | ||||||||
\(201\) | −5.69156e14 | −0.608775 | ||||||||
\(202\) | −2.30093e15 | −2.38297 | ||||||||
\(203\) | 2.93686e15 | 2.94550 | ||||||||
\(204\) | −6.49145e14 | −0.630588 | ||||||||
\(205\) | −1.48355e14 | −0.139606 | ||||||||
\(206\) | 2.32039e15 | 2.11556 | ||||||||
\(207\) | −1.65386e14 | −0.146114 | ||||||||
\(208\) | 1.32558e14 | 0.113500 | ||||||||
\(209\) | 8.83114e14 | 0.732935 | ||||||||
\(210\) | 3.17913e14 | 0.255789 | ||||||||
\(211\) | −1.69305e15 | −1.32079 | −0.660396 | − | 0.750918i | \(-0.729611\pi\) | ||||
−0.660396 | + | 0.750918i | \(0.729611\pi\) | |||||||
\(212\) | −3.97091e15 | −3.00405 | ||||||||
\(213\) | 3.13879e14 | 0.230300 | ||||||||
\(214\) | −8.52613e14 | −0.606823 | ||||||||
\(215\) | −9.85299e13 | −0.0680327 | ||||||||
\(216\) | 1.26018e15 | 0.844275 | ||||||||
\(217\) | −4.11491e15 | −2.67530 | ||||||||
\(218\) | −7.46448e14 | −0.471012 | ||||||||
\(219\) | −1.20069e15 | −0.735432 | ||||||||
\(220\) | −2.84158e14 | −0.168971 | ||||||||
\(221\) | −1.46677e15 | −0.846863 | ||||||||
\(222\) | 1.15591e15 | 0.648084 | ||||||||
\(223\) | −1.03170e15 | −0.561788 | −0.280894 | − | 0.959739i | \(-0.590631\pi\) | ||||
−0.280894 | + | 0.959739i | \(0.590631\pi\) | |||||||
\(224\) | 2.81799e15 | 1.49048 | ||||||||
\(225\) | 1.51776e15 | 0.779860 | ||||||||
\(226\) | −1.65590e15 | −0.826662 | ||||||||
\(227\) | 1.23090e14 | 0.0597109 | 0.0298554 | − | 0.999554i | \(-0.490495\pi\) | ||||
0.0298554 | + | 0.999554i | \(0.490495\pi\) | |||||||
\(228\) | 2.42609e15 | 1.14375 | ||||||||
\(229\) | 3.56608e15 | 1.63403 | 0.817015 | − | 0.576616i | \(-0.195627\pi\) | ||||
0.817015 | + | 0.576616i | \(0.195627\pi\) | |||||||
\(230\) | 1.45807e14 | 0.0649451 | ||||||||
\(231\) | 7.33684e14 | 0.317710 | ||||||||
\(232\) | −4.62653e15 | −1.94797 | ||||||||
\(233\) | −3.74981e15 | −1.53531 | −0.767655 | − | 0.640864i | \(-0.778576\pi\) | ||||
−0.767655 | + | 0.640864i | \(0.778576\pi\) | |||||||
\(234\) | 3.19860e15 | 1.27367 | ||||||||
\(235\) | 9.88600e13 | 0.0382895 | ||||||||
\(236\) | −1.85933e15 | −0.700533 | ||||||||
\(237\) | −1.20406e15 | −0.441352 | ||||||||
\(238\) | 6.76677e15 | 2.41341 | ||||||||
\(239\) | −1.14364e15 | −0.396920 | −0.198460 | − | 0.980109i | \(-0.563594\pi\) | ||||
−0.198460 | + | 0.980109i | \(0.563594\pi\) | |||||||
\(240\) | −3.34438e13 | −0.0112965 | ||||||||
\(241\) | 8.81238e14 | 0.289723 | 0.144861 | − | 0.989452i | \(-0.453726\pi\) | ||||
0.144861 | + | 0.989452i | \(0.453726\pi\) | |||||||
\(242\) | 4.05755e15 | 1.29857 | ||||||||
\(243\) | 3.14583e15 | 0.980155 | ||||||||
\(244\) | −9.88902e15 | −2.99999 | ||||||||
\(245\) | −1.31715e15 | −0.389094 | ||||||||
\(246\) | −1.50371e15 | −0.432599 | ||||||||
\(247\) | 5.48186e15 | 1.53602 | ||||||||
\(248\) | 6.48234e15 | 1.76928 | ||||||||
\(249\) | −1.59404e15 | −0.423843 | ||||||||
\(250\) | −2.74636e15 | −0.711455 | ||||||||
\(251\) | −4.55421e15 | −1.14957 | −0.574783 | − | 0.818306i | \(-0.694914\pi\) | ||||
−0.574783 | + | 0.818306i | \(0.694914\pi\) | |||||||
\(252\) | −9.23016e15 | −2.27042 | ||||||||
\(253\) | 3.36495e14 | 0.0806670 | ||||||||
\(254\) | −7.36967e15 | −1.72198 | ||||||||
\(255\) | 3.70060e14 | 0.0842870 | ||||||||
\(256\) | −5.33831e15 | −1.18534 | ||||||||
\(257\) | −5.44780e15 | −1.17939 | −0.589693 | − | 0.807627i | \(-0.700751\pi\) | ||||
−0.589693 | + | 0.807627i | \(0.700751\pi\) | |||||||
\(258\) | −9.98685e14 | −0.210815 | ||||||||
\(259\) | −7.53696e15 | −1.55149 | ||||||||
\(260\) | −1.76389e15 | −0.354115 | ||||||||
\(261\) | −7.45495e15 | −1.45976 | ||||||||
\(262\) | −1.15193e15 | −0.220023 | ||||||||
\(263\) | 2.92179e14 | 0.0544423 | 0.0272211 | − | 0.999629i | \(-0.491334\pi\) | ||||
0.0272211 | + | 0.999629i | \(0.491334\pi\) | |||||||
\(264\) | −1.15580e15 | −0.210114 | ||||||||
\(265\) | 2.26371e15 | 0.401534 | ||||||||
\(266\) | −2.52898e16 | −4.37739 | ||||||||
\(267\) | 1.06276e15 | 0.179519 | ||||||||
\(268\) | −1.45684e16 | −2.40180 | ||||||||
\(269\) | −6.76225e15 | −1.08818 | −0.544091 | − | 0.839026i | \(-0.683125\pi\) | ||||
−0.544091 | + | 0.839026i | \(0.683125\pi\) | |||||||
\(270\) | −1.79020e15 | −0.281215 | ||||||||
\(271\) | 8.99311e15 | 1.37914 | 0.689572 | − | 0.724217i | \(-0.257799\pi\) | ||||
0.689572 | + | 0.724217i | \(0.257799\pi\) | |||||||
\(272\) | −7.11852e14 | −0.106584 | ||||||||
\(273\) | 4.55429e15 | 0.665830 | ||||||||
\(274\) | −9.84596e15 | −1.40566 | ||||||||
\(275\) | −3.08805e15 | −0.430548 | ||||||||
\(276\) | 9.24420e14 | 0.125881 | ||||||||
\(277\) | −8.32255e14 | −0.110697 | −0.0553487 | − | 0.998467i | \(-0.517627\pi\) | ||||
−0.0553487 | + | 0.998467i | \(0.517627\pi\) | |||||||
\(278\) | −1.58611e15 | −0.206083 | ||||||||
\(279\) | 1.04453e16 | 1.32585 | ||||||||
\(280\) | 3.26550e15 | 0.404970 | ||||||||
\(281\) | 1.32987e16 | 1.61146 | 0.805729 | − | 0.592284i | \(-0.201774\pi\) | ||||
0.805729 | + | 0.592284i | \(0.201774\pi\) | |||||||
\(282\) | 1.00203e15 | 0.118648 | ||||||||
\(283\) | 4.75010e15 | 0.549656 | 0.274828 | − | 0.961493i | \(-0.411379\pi\) | ||||
0.274828 | + | 0.961493i | \(0.411379\pi\) | |||||||
\(284\) | 8.03421e15 | 0.908603 | ||||||||
\(285\) | −1.38305e15 | −0.152878 | ||||||||
\(286\) | −6.50791e15 | −0.703173 | ||||||||
\(287\) | 9.80470e15 | 1.03562 | ||||||||
\(288\) | −7.15320e15 | −0.738668 | ||||||||
\(289\) | −2.02786e15 | −0.204740 | ||||||||
\(290\) | 6.57241e15 | 0.648840 | ||||||||
\(291\) | −2.96232e15 | −0.285974 | ||||||||
\(292\) | −3.07334e16 | −2.90150 | ||||||||
\(293\) | −1.49169e16 | −1.37733 | −0.688665 | − | 0.725080i | \(-0.741803\pi\) | ||||
−0.688665 | + | 0.725080i | \(0.741803\pi\) | |||||||
\(294\) | −1.33504e16 | −1.20569 | ||||||||
\(295\) | 1.05995e15 | 0.0936361 | ||||||||
\(296\) | 1.18732e16 | 1.02606 | ||||||||
\(297\) | −4.13147e15 | −0.349291 | ||||||||
\(298\) | 5.66386e15 | 0.468497 | ||||||||
\(299\) | 2.08877e15 | 0.169055 | ||||||||
\(300\) | −8.48349e15 | −0.671872 | ||||||||
\(301\) | 6.51177e15 | 0.504681 | ||||||||
\(302\) | 4.59594e15 | 0.348601 | ||||||||
\(303\) | 8.31619e15 | 0.617373 | ||||||||
\(304\) | 2.66045e15 | 0.193320 | ||||||||
\(305\) | 5.63746e15 | 0.400991 | ||||||||
\(306\) | −1.71768e16 | −1.19606 | ||||||||
\(307\) | 1.89012e16 | 1.28852 | 0.644258 | − | 0.764808i | \(-0.277166\pi\) | ||||
0.644258 | + | 0.764808i | \(0.277166\pi\) | |||||||
\(308\) | 1.87798e16 | 1.25346 | ||||||||
\(309\) | −8.38656e15 | −0.548092 | ||||||||
\(310\) | −9.20876e15 | −0.589318 | ||||||||
\(311\) | 4.91406e13 | 0.00307962 | 0.00153981 | − | 0.999999i | \(-0.499510\pi\) | ||||
0.00153981 | + | 0.999999i | \(0.499510\pi\) | |||||||
\(312\) | −7.17452e15 | −0.440340 | ||||||||
\(313\) | 1.31483e16 | 0.790374 | 0.395187 | − | 0.918601i | \(-0.370680\pi\) | ||||
0.395187 | + | 0.918601i | \(0.370680\pi\) | |||||||
\(314\) | −2.40748e16 | −1.41749 | ||||||||
\(315\) | 5.26186e15 | 0.303474 | ||||||||
\(316\) | −3.08198e16 | −1.74126 | ||||||||
\(317\) | 1.54783e16 | 0.856719 | 0.428360 | − | 0.903608i | \(-0.359092\pi\) | ||||
0.428360 | + | 0.903608i | \(0.359092\pi\) | |||||||
\(318\) | 2.29446e16 | 1.24424 | ||||||||
\(319\) | 1.51679e16 | 0.805910 | ||||||||
\(320\) | 6.81891e15 | 0.355009 | ||||||||
\(321\) | 3.08158e15 | 0.157214 | ||||||||
\(322\) | −9.63626e15 | −0.481776 | ||||||||
\(323\) | −2.94381e16 | −1.44243 | ||||||||
\(324\) | 1.71963e16 | 0.825833 | ||||||||
\(325\) | −1.91688e16 | −0.902307 | ||||||||
\(326\) | 6.30232e15 | 0.290794 | ||||||||
\(327\) | 2.69787e15 | 0.122028 | ||||||||
\(328\) | −1.54456e16 | −0.684898 | ||||||||
\(329\) | −6.53358e15 | −0.284039 | ||||||||
\(330\) | 1.64191e15 | 0.0699858 | ||||||||
\(331\) | 1.39764e16 | 0.584134 | 0.292067 | − | 0.956398i | \(-0.405657\pi\) | ||||
0.292067 | + | 0.956398i | \(0.405657\pi\) | |||||||
\(332\) | −4.08020e16 | −1.67218 | ||||||||
\(333\) | 1.91319e16 | 0.768900 | ||||||||
\(334\) | −7.52341e16 | −2.96526 | ||||||||
\(335\) | 8.30506e15 | 0.321034 | ||||||||
\(336\) | 2.21028e15 | 0.0837996 | ||||||||
\(337\) | −4.61405e16 | −1.71588 | −0.857942 | − | 0.513747i | \(-0.828257\pi\) | ||||
−0.857942 | + | 0.513747i | \(0.828257\pi\) | |||||||
\(338\) | 4.39829e15 | 0.160445 | ||||||||
\(339\) | 5.98487e15 | 0.214169 | ||||||||
\(340\) | 9.47225e15 | 0.332537 | ||||||||
\(341\) | −2.12521e16 | −0.731980 | ||||||||
\(342\) | 6.41959e16 | 2.16939 | ||||||||
\(343\) | 3.71021e16 | 1.23023 | ||||||||
\(344\) | −1.02582e16 | −0.333765 | ||||||||
\(345\) | −5.26986e14 | −0.0168258 | ||||||||
\(346\) | −5.33759e16 | −1.67244 | ||||||||
\(347\) | −4.69919e16 | −1.44505 | −0.722523 | − | 0.691347i | \(-0.757018\pi\) | ||||
−0.722523 | + | 0.691347i | \(0.757018\pi\) | |||||||
\(348\) | 4.16693e16 | 1.25762 | ||||||||
\(349\) | −5.80573e16 | −1.71985 | −0.859927 | − | 0.510418i | \(-0.829491\pi\) | ||||
−0.859927 | + | 0.510418i | \(0.829491\pi\) | |||||||
\(350\) | 8.84330e16 | 2.57141 | ||||||||
\(351\) | −2.56458e16 | −0.732014 | ||||||||
\(352\) | 1.45540e16 | 0.407807 | ||||||||
\(353\) | −3.84932e16 | −1.05888 | −0.529442 | − | 0.848346i | \(-0.677599\pi\) | ||||
−0.529442 | + | 0.848346i | \(0.677599\pi\) | |||||||
\(354\) | 1.07435e16 | 0.290152 | ||||||||
\(355\) | −4.58008e15 | −0.121448 | ||||||||
\(356\) | 2.72029e16 | 0.708256 | ||||||||
\(357\) | −2.44570e16 | −0.625258 | ||||||||
\(358\) | 2.05567e16 | 0.516077 | ||||||||
\(359\) | −3.36564e16 | −0.829762 | −0.414881 | − | 0.909876i | \(-0.636177\pi\) | ||||
−0.414881 | + | 0.909876i | \(0.636177\pi\) | |||||||
\(360\) | −8.28917e15 | −0.200699 | ||||||||
\(361\) | 6.79680e16 | 1.61625 | ||||||||
\(362\) | 7.10515e16 | 1.65946 | ||||||||
\(363\) | −1.46651e16 | −0.336428 | ||||||||
\(364\) | 1.16574e17 | 2.62690 | ||||||||
\(365\) | 1.75203e16 | 0.387826 | ||||||||
\(366\) | 5.71405e16 | 1.24256 | ||||||||
\(367\) | −3.11244e16 | −0.664924 | −0.332462 | − | 0.943117i | \(-0.607879\pi\) | ||||
−0.332462 | + | 0.943117i | \(0.607879\pi\) | |||||||
\(368\) | 1.01372e15 | 0.0212768 | ||||||||
\(369\) | −2.48883e16 | −0.513244 | ||||||||
\(370\) | −1.68670e16 | −0.341764 | ||||||||
\(371\) | −1.49607e17 | −2.97866 | ||||||||
\(372\) | −5.83838e16 | −1.14226 | ||||||||
\(373\) | 9.20915e16 | 1.77057 | 0.885283 | − | 0.465052i | \(-0.153964\pi\) | ||||
0.885283 | + | 0.465052i | \(0.153964\pi\) | |||||||
\(374\) | 3.49481e16 | 0.660326 | ||||||||
\(375\) | 9.92611e15 | 0.184321 | ||||||||
\(376\) | 1.02926e16 | 0.187846 | ||||||||
\(377\) | 9.41537e16 | 1.68896 | ||||||||
\(378\) | 1.18313e17 | 2.08611 | ||||||||
\(379\) | 7.13898e16 | 1.23732 | 0.618659 | − | 0.785660i | \(-0.287676\pi\) | ||||
0.618659 | + | 0.785660i | \(0.287676\pi\) | |||||||
\(380\) | −3.54012e16 | −0.603149 | ||||||||
\(381\) | 2.66361e16 | 0.446126 | ||||||||
\(382\) | −2.54150e15 | −0.0418484 | ||||||||
\(383\) | 1.61608e16 | 0.261620 | 0.130810 | − | 0.991407i | \(-0.458242\pi\) | ||||
0.130810 | + | 0.991407i | \(0.458242\pi\) | |||||||
\(384\) | 4.51775e16 | 0.719067 | ||||||||
\(385\) | −1.07058e16 | −0.167543 | ||||||||
\(386\) | 6.25707e16 | 0.962838 | ||||||||
\(387\) | −1.65295e16 | −0.250115 | ||||||||
\(388\) | −7.58251e16 | −1.12825 | ||||||||
\(389\) | 8.20627e16 | 1.20081 | 0.600404 | − | 0.799697i | \(-0.295007\pi\) | ||||
0.600404 | + | 0.799697i | \(0.295007\pi\) | |||||||
\(390\) | 1.01921e16 | 0.146670 | ||||||||
\(391\) | −1.12169e16 | −0.158754 | ||||||||
\(392\) | −1.37131e17 | −1.90887 | ||||||||
\(393\) | 4.16340e15 | 0.0570029 | ||||||||
\(394\) | 8.64509e15 | 0.116424 | ||||||||
\(395\) | 1.75695e16 | 0.232744 | ||||||||
\(396\) | −4.76707e16 | −0.621202 | ||||||||
\(397\) | 1.04725e17 | 1.34249 | 0.671247 | − | 0.741234i | \(-0.265759\pi\) | ||||
0.671247 | + | 0.741234i | \(0.265759\pi\) | |||||||
\(398\) | 8.71740e16 | 1.09938 | ||||||||
\(399\) | 9.14046e16 | 1.13408 | ||||||||
\(400\) | −9.30299e15 | −0.113562 | ||||||||
\(401\) | −9.89387e16 | −1.18830 | −0.594152 | − | 0.804353i | \(-0.702512\pi\) | ||||
−0.594152 | + | 0.804353i | \(0.702512\pi\) | |||||||
\(402\) | 8.41789e16 | 0.994796 | ||||||||
\(403\) | −1.31921e17 | −1.53402 | ||||||||
\(404\) | 2.12866e17 | 2.43572 | ||||||||
\(405\) | −9.80314e15 | −0.110384 | ||||||||
\(406\) | −4.34366e17 | −4.81323 | ||||||||
\(407\) | −3.89259e16 | −0.424497 | ||||||||
\(408\) | 3.85279e16 | 0.413508 | ||||||||
\(409\) | −5.43168e16 | −0.573764 | −0.286882 | − | 0.957966i | \(-0.592619\pi\) | ||||
−0.286882 | + | 0.957966i | \(0.592619\pi\) | |||||||
\(410\) | 2.19420e16 | 0.228129 | ||||||||
\(411\) | 3.55861e16 | 0.364173 | ||||||||
\(412\) | −2.14667e17 | −2.16239 | ||||||||
\(413\) | −7.00515e16 | −0.694612 | ||||||||
\(414\) | 2.44608e16 | 0.238763 | ||||||||
\(415\) | 2.32601e16 | 0.223511 | ||||||||
\(416\) | 9.03428e16 | 0.854647 | ||||||||
\(417\) | 5.73266e15 | 0.0533914 | ||||||||
\(418\) | −1.30614e17 | −1.19769 | ||||||||
\(419\) | 6.51208e16 | 0.587934 | 0.293967 | − | 0.955816i | \(-0.405024\pi\) | ||||
0.293967 | + | 0.955816i | \(0.405024\pi\) | |||||||
\(420\) | −2.94111e16 | −0.261451 | ||||||||
\(421\) | −6.75894e16 | −0.591623 | −0.295811 | − | 0.955246i | \(-0.595590\pi\) | ||||
−0.295811 | + | 0.955246i | \(0.595590\pi\) | |||||||
\(422\) | 2.50405e17 | 2.15830 | ||||||||
\(423\) | 1.65849e16 | 0.140767 | ||||||||
\(424\) | 2.35680e17 | 1.96990 | ||||||||
\(425\) | 1.02939e17 | 0.847325 | ||||||||
\(426\) | −4.64231e16 | −0.376332 | ||||||||
\(427\) | −3.72576e17 | −2.97463 | ||||||||
\(428\) | 7.88778e16 | 0.620255 | ||||||||
\(429\) | 2.35214e16 | 0.182176 | ||||||||
\(430\) | 1.45727e16 | 0.111172 | ||||||||
\(431\) | 1.42668e17 | 1.07207 | 0.536035 | − | 0.844196i | \(-0.319922\pi\) | ||||
0.536035 | + | 0.844196i | \(0.319922\pi\) | |||||||
\(432\) | −1.24464e16 | −0.0921293 | ||||||||
\(433\) | −4.77089e16 | −0.347879 | −0.173939 | − | 0.984756i | \(-0.555650\pi\) | ||||
−0.173939 | + | 0.984756i | \(0.555650\pi\) | |||||||
\(434\) | 6.08600e17 | 4.37169 | ||||||||
\(435\) | −2.37545e16 | −0.168099 | ||||||||
\(436\) | 6.90562e16 | 0.481438 | ||||||||
\(437\) | 4.19216e16 | 0.287944 | ||||||||
\(438\) | 1.77583e17 | 1.20176 | ||||||||
\(439\) | 1.78581e16 | 0.119074 | 0.0595369 | − | 0.998226i | \(-0.481038\pi\) | ||||
0.0595369 | + | 0.998226i | \(0.481038\pi\) | |||||||
\(440\) | 1.68652e16 | 0.110803 | ||||||||
\(441\) | −2.20966e17 | −1.43046 | ||||||||
\(442\) | 2.16938e17 | 1.38385 | ||||||||
\(443\) | −2.16454e17 | −1.36063 | −0.680317 | − | 0.732918i | \(-0.738158\pi\) | ||||
−0.680317 | + | 0.732918i | \(0.738158\pi\) | |||||||
\(444\) | −1.06937e17 | −0.662429 | ||||||||
\(445\) | −1.55076e16 | −0.0946684 | ||||||||
\(446\) | 1.52590e17 | 0.918014 | ||||||||
\(447\) | −2.04708e16 | −0.121377 | ||||||||
\(448\) | −4.50657e17 | −2.63353 | ||||||||
\(449\) | 3.77058e15 | 0.0217173 | 0.0108587 | − | 0.999941i | \(-0.496544\pi\) | ||||
0.0108587 | + | 0.999941i | \(0.496544\pi\) | |||||||
\(450\) | −2.24479e17 | −1.27437 | ||||||||
\(451\) | 5.06380e16 | 0.283354 | ||||||||
\(452\) | 1.53192e17 | 0.844960 | ||||||||
\(453\) | −1.66110e16 | −0.0903145 | ||||||||
\(454\) | −1.82051e16 | −0.0975732 | ||||||||
\(455\) | −6.64557e16 | −0.351122 | ||||||||
\(456\) | −1.43992e17 | −0.750012 | ||||||||
\(457\) | −3.18715e17 | −1.63662 | −0.818308 | − | 0.574780i | \(-0.805087\pi\) | ||||
−0.818308 | + | 0.574780i | \(0.805087\pi\) | |||||||
\(458\) | −5.27428e17 | −2.67016 | ||||||||
\(459\) | 1.37720e17 | 0.687409 | ||||||||
\(460\) | −1.34890e16 | −0.0663827 | ||||||||
\(461\) | −2.23376e17 | −1.08388 | −0.541938 | − | 0.840418i | \(-0.682309\pi\) | ||||
−0.541938 | + | 0.840418i | \(0.682309\pi\) | |||||||
\(462\) | −1.08513e17 | −0.519169 | ||||||||
\(463\) | 1.33005e17 | 0.627468 | 0.313734 | − | 0.949511i | \(-0.398420\pi\) | ||||
0.313734 | + | 0.949511i | \(0.398420\pi\) | |||||||
\(464\) | 4.56945e16 | 0.212568 | ||||||||
\(465\) | 3.32830e16 | 0.152679 | ||||||||
\(466\) | 5.54602e17 | 2.50884 | ||||||||
\(467\) | −2.46819e17 | −1.10108 | −0.550540 | − | 0.834809i | \(-0.685578\pi\) | ||||
−0.550540 | + | 0.834809i | \(0.685578\pi\) | |||||||
\(468\) | −2.95912e17 | −1.30186 | ||||||||
\(469\) | −5.48875e17 | −2.38150 | ||||||||
\(470\) | −1.46215e16 | −0.0625686 | ||||||||
\(471\) | 8.70129e16 | 0.367238 | ||||||||
\(472\) | 1.10354e17 | 0.459374 | ||||||||
\(473\) | 3.36311e16 | 0.138084 | ||||||||
\(474\) | 1.78082e17 | 0.721210 | ||||||||
\(475\) | −3.84719e17 | −1.53686 | ||||||||
\(476\) | −6.26014e17 | −2.46683 | ||||||||
\(477\) | 3.79763e17 | 1.47619 | ||||||||
\(478\) | 1.69146e17 | 0.648605 | ||||||||
\(479\) | −3.33942e17 | −1.26325 | −0.631627 | − | 0.775273i | \(-0.717612\pi\) | ||||
−0.631627 | + | 0.775273i | \(0.717612\pi\) | |||||||
\(480\) | −2.27930e16 | −0.0850617 | ||||||||
\(481\) | −2.41630e17 | −0.889625 | ||||||||
\(482\) | −1.30336e17 | −0.473434 | ||||||||
\(483\) | 3.48282e16 | 0.124817 | ||||||||
\(484\) | −3.75376e17 | −1.32731 | ||||||||
\(485\) | 4.32258e16 | 0.150807 | ||||||||
\(486\) | −4.65273e17 | −1.60167 | ||||||||
\(487\) | 1.04619e17 | 0.355363 | 0.177682 | − | 0.984088i | \(-0.443140\pi\) | ||||
0.177682 | + | 0.984088i | \(0.443140\pi\) | |||||||
\(488\) | 5.86930e17 | 1.96724 | ||||||||
\(489\) | −2.27783e16 | −0.0753381 | ||||||||
\(490\) | 1.94808e17 | 0.635816 | ||||||||
\(491\) | 5.50979e17 | 1.77462 | 0.887310 | − | 0.461174i | \(-0.152572\pi\) | ||||
0.887310 | + | 0.461174i | \(0.152572\pi\) | |||||||
\(492\) | 1.39113e17 | 0.442175 | ||||||||
\(493\) | −5.05614e17 | −1.58604 | ||||||||
\(494\) | −8.10775e17 | −2.51001 | ||||||||
\(495\) | 2.71758e16 | 0.0830325 | ||||||||
\(496\) | −6.40237e16 | −0.193068 | ||||||||
\(497\) | 3.02694e17 | 0.900923 | ||||||||
\(498\) | 2.35761e17 | 0.692599 | ||||||||
\(499\) | 3.56426e17 | 1.03351 | 0.516757 | − | 0.856132i | \(-0.327139\pi\) | ||||
0.516757 | + | 0.856132i | \(0.327139\pi\) | |||||||
\(500\) | 2.54074e17 | 0.727202 | ||||||||
\(501\) | 2.71917e17 | 0.768230 | ||||||||
\(502\) | 6.73574e17 | 1.87850 | ||||||||
\(503\) | −3.83898e17 | −1.05688 | −0.528438 | − | 0.848972i | \(-0.677222\pi\) | ||||
−0.528438 | + | 0.848972i | \(0.677222\pi\) | |||||||
\(504\) | 5.47826e17 | 1.48883 | ||||||||
\(505\) | −1.21349e17 | −0.325568 | ||||||||
\(506\) | −4.97681e16 | −0.131817 | ||||||||
\(507\) | −1.58966e16 | −0.0415675 | ||||||||
\(508\) | 6.81791e17 | 1.76010 | ||||||||
\(509\) | −4.18856e17 | −1.06758 | −0.533789 | − | 0.845618i | \(-0.679232\pi\) | ||||
−0.533789 | + | 0.845618i | \(0.679232\pi\) | |||||||
\(510\) | −5.47323e16 | −0.137733 | ||||||||
\(511\) | −1.15790e18 | −2.87697 | ||||||||
\(512\) | 9.72049e16 | 0.238470 | ||||||||
\(513\) | −5.14710e17 | −1.24681 | ||||||||
\(514\) | 8.05737e17 | 1.92723 | ||||||||
\(515\) | 1.22376e17 | 0.289033 | ||||||||
\(516\) | 9.23914e16 | 0.215481 | ||||||||
\(517\) | −3.37438e16 | −0.0777151 | ||||||||
\(518\) | 1.11473e18 | 2.53527 | ||||||||
\(519\) | 1.92915e17 | 0.433290 | ||||||||
\(520\) | 1.04690e17 | 0.232211 | ||||||||
\(521\) | −5.11992e17 | −1.12155 | −0.560774 | − | 0.827969i | \(-0.689496\pi\) | ||||
−0.560774 | + | 0.827969i | \(0.689496\pi\) | |||||||
\(522\) | 1.10260e18 | 2.38538 | ||||||||
\(523\) | 5.42076e17 | 1.15824 | 0.579121 | − | 0.815242i | \(-0.303396\pi\) | ||||
0.579121 | + | 0.815242i | \(0.303396\pi\) | |||||||
\(524\) | 1.06569e17 | 0.224893 | ||||||||
\(525\) | −3.19621e17 | −0.666194 | ||||||||
\(526\) | −4.32136e16 | −0.0889639 | ||||||||
\(527\) | 7.08429e17 | 1.44055 | ||||||||
\(528\) | 1.14154e16 | 0.0229282 | ||||||||
\(529\) | −4.88063e17 | −0.968309 | ||||||||
\(530\) | −3.34805e17 | −0.656144 | ||||||||
\(531\) | 1.77819e17 | 0.344242 | ||||||||
\(532\) | 2.33964e18 | 4.47429 | ||||||||
\(533\) | 3.14332e17 | 0.593829 | ||||||||
\(534\) | −1.57183e17 | −0.293351 | ||||||||
\(535\) | −4.49661e16 | −0.0829059 | ||||||||
\(536\) | 8.64660e17 | 1.57498 | ||||||||
\(537\) | −7.42978e16 | −0.133704 | ||||||||
\(538\) | 1.00015e18 | 1.77819 | ||||||||
\(539\) | 4.49581e17 | 0.789733 | ||||||||
\(540\) | 1.65617e17 | 0.287439 | ||||||||
\(541\) | −6.73638e17 | −1.15517 | −0.577583 | − | 0.816332i | \(-0.696004\pi\) | ||||
−0.577583 | + | 0.816332i | \(0.696004\pi\) | |||||||
\(542\) | −1.33009e18 | −2.25365 | ||||||||
\(543\) | −2.56800e17 | −0.429929 | ||||||||
\(544\) | −4.85149e17 | −0.802570 | ||||||||
\(545\) | −3.93670e16 | −0.0643510 | ||||||||
\(546\) | −6.73586e17 | −1.08803 | ||||||||
\(547\) | 8.73991e17 | 1.39505 | 0.697524 | − | 0.716561i | \(-0.254285\pi\) | ||||
0.697524 | + | 0.716561i | \(0.254285\pi\) | |||||||
\(548\) | 9.10880e17 | 1.43677 | ||||||||
\(549\) | 9.45749e17 | 1.47420 | ||||||||
\(550\) | 4.56727e17 | 0.703557 | ||||||||
\(551\) | 1.88966e18 | 2.87673 | ||||||||
\(552\) | −5.48659e16 | −0.0825464 | ||||||||
\(553\) | −1.16116e18 | −1.72655 | ||||||||
\(554\) | 1.23092e17 | 0.180890 | ||||||||
\(555\) | 6.09620e16 | 0.0885431 | ||||||||
\(556\) | 1.46736e17 | 0.210645 | ||||||||
\(557\) | 7.55036e17 | 1.07129 | 0.535647 | − | 0.844442i | \(-0.320068\pi\) | ||||
0.535647 | + | 0.844442i | \(0.320068\pi\) | |||||||
\(558\) | −1.54487e18 | −2.16656 | ||||||||
\(559\) | 2.08763e17 | 0.289385 | ||||||||
\(560\) | −3.22522e16 | −0.0441913 | ||||||||
\(561\) | −1.26312e17 | −0.171075 | ||||||||
\(562\) | −1.96690e18 | −2.63328 | ||||||||
\(563\) | −1.09722e17 | −0.145208 | −0.0726038 | − | 0.997361i | \(-0.523131\pi\) | ||||
−0.0726038 | + | 0.997361i | \(0.523131\pi\) | |||||||
\(564\) | −9.27009e16 | −0.121275 | ||||||||
\(565\) | −8.73306e16 | −0.112941 | ||||||||
\(566\) | −7.02547e17 | −0.898190 | ||||||||
\(567\) | 6.47882e17 | 0.818854 | ||||||||
\(568\) | −4.76844e17 | −0.595816 | ||||||||
\(569\) | −4.45545e17 | −0.550378 | −0.275189 | − | 0.961390i | \(-0.588741\pi\) | ||||
−0.275189 | + | 0.961390i | \(0.588741\pi\) | |||||||
\(570\) | 2.04555e17 | 0.249817 | ||||||||
\(571\) | 1.49536e18 | 1.80556 | 0.902781 | − | 0.430100i | \(-0.141522\pi\) | ||||
0.902781 | + | 0.430100i | \(0.141522\pi\) | |||||||
\(572\) | 6.02066e17 | 0.718737 | ||||||||
\(573\) | 9.18569e15 | 0.0108419 | ||||||||
\(574\) | −1.45013e18 | −1.69231 | ||||||||
\(575\) | −1.46590e17 | −0.169147 | ||||||||
\(576\) | 1.14395e18 | 1.30515 | ||||||||
\(577\) | 9.27665e17 | 1.04652 | 0.523261 | − | 0.852172i | \(-0.324715\pi\) | ||||
0.523261 | + | 0.852172i | \(0.324715\pi\) | |||||||
\(578\) | 2.99923e17 | 0.334564 | ||||||||
\(579\) | −2.26148e17 | −0.249449 | ||||||||
\(580\) | −6.08033e17 | −0.663201 | ||||||||
\(581\) | −1.53724e18 | −1.65805 | ||||||||
\(582\) | 4.38131e17 | 0.467309 | ||||||||
\(583\) | −7.72670e17 | −0.814982 | ||||||||
\(584\) | 1.82408e18 | 1.90265 | ||||||||
\(585\) | 1.68692e17 | 0.174012 | ||||||||
\(586\) | 2.20622e18 | 2.25069 | ||||||||
\(587\) | 4.46667e17 | 0.450647 | 0.225323 | − | 0.974284i | \(-0.427656\pi\) | ||||
0.225323 | + | 0.974284i | \(0.427656\pi\) | |||||||
\(588\) | 1.23509e18 | 1.23238 | ||||||||
\(589\) | −2.64765e18 | −2.61283 | ||||||||
\(590\) | −1.56768e17 | −0.153010 | ||||||||
\(591\) | −3.12458e16 | −0.0301629 | ||||||||
\(592\) | −1.17267e17 | −0.111966 | ||||||||
\(593\) | −7.48723e17 | −0.707075 | −0.353537 | − | 0.935420i | \(-0.615021\pi\) | ||||
−0.353537 | + | 0.935420i | \(0.615021\pi\) | |||||||
\(594\) | 6.11049e17 | 0.570774 | ||||||||
\(595\) | 3.56874e17 | 0.329727 | ||||||||
\(596\) | −5.23981e17 | −0.478867 | ||||||||
\(597\) | −3.15071e17 | −0.284823 | ||||||||
\(598\) | −3.08932e17 | −0.276252 | ||||||||
\(599\) | −1.54595e18 | −1.36748 | −0.683740 | − | 0.729726i | \(-0.739648\pi\) | ||||
−0.683740 | + | 0.729726i | \(0.739648\pi\) | |||||||
\(600\) | 5.03510e17 | 0.440580 | ||||||||
\(601\) | −6.29555e17 | −0.544941 | −0.272470 | − | 0.962164i | \(-0.587841\pi\) | ||||
−0.272470 | + | 0.962164i | \(0.587841\pi\) | |||||||
\(602\) | −9.63099e17 | −0.824696 | ||||||||
\(603\) | 1.39327e18 | 1.18025 | ||||||||
\(604\) | −4.25184e17 | −0.356318 | ||||||||
\(605\) | 2.13992e17 | 0.177414 | ||||||||
\(606\) | −1.22998e18 | −1.00885 | ||||||||
\(607\) | −2.08261e18 | −1.68998 | −0.844991 | − | 0.534780i | \(-0.820394\pi\) | ||||
−0.844991 | + | 0.534780i | \(0.820394\pi\) | |||||||
\(608\) | 1.81318e18 | 1.45568 | ||||||||
\(609\) | 1.56992e18 | 1.24700 | ||||||||
\(610\) | −8.33788e17 | −0.655257 | ||||||||
\(611\) | −2.09462e17 | −0.162869 | ||||||||
\(612\) | 1.58908e18 | 1.22253 | ||||||||
\(613\) | −9.58740e17 | −0.729806 | −0.364903 | − | 0.931045i | \(-0.618898\pi\) | ||||
−0.364903 | + | 0.931045i | \(0.618898\pi\) | |||||||
\(614\) | −2.79551e18 | −2.10556 | ||||||||
\(615\) | −7.93044e16 | −0.0591029 | ||||||||
\(616\) | −1.11461e18 | −0.821957 | ||||||||
\(617\) | 1.22241e18 | 0.891994 | 0.445997 | − | 0.895034i | \(-0.352849\pi\) | ||||
0.445997 | + | 0.895034i | \(0.352849\pi\) | |||||||
\(618\) | 1.24038e18 | 0.895634 | ||||||||
\(619\) | 1.55068e18 | 1.10798 | 0.553992 | − | 0.832522i | \(-0.313104\pi\) | ||||
0.553992 | + | 0.832522i | \(0.313104\pi\) | |||||||
\(620\) | 8.51930e17 | 0.602363 | ||||||||
\(621\) | −1.96122e17 | −0.137224 | ||||||||
\(622\) | −7.26796e15 | −0.00503240 | ||||||||
\(623\) | 1.02489e18 | 0.702270 | ||||||||
\(624\) | 7.08600e16 | 0.0480509 | ||||||||
\(625\) | 1.27100e18 | 0.852956 | ||||||||
\(626\) | −1.94466e18 | −1.29155 | ||||||||
\(627\) | 4.72074e17 | 0.310293 | ||||||||
\(628\) | 2.22723e18 | 1.44886 | ||||||||
\(629\) | 1.29757e18 | 0.835417 | ||||||||
\(630\) | −7.78236e17 | −0.495904 | ||||||||
\(631\) | −1.46698e18 | −0.925194 | −0.462597 | − | 0.886569i | \(-0.653082\pi\) | ||||
−0.462597 | + | 0.886569i | \(0.653082\pi\) | |||||||
\(632\) | 1.82921e18 | 1.14183 | ||||||||
\(633\) | −9.05032e17 | −0.559165 | ||||||||
\(634\) | −2.28926e18 | −1.39996 | ||||||||
\(635\) | −3.88670e17 | −0.235262 | ||||||||
\(636\) | −2.12268e18 | −1.27178 | ||||||||
\(637\) | 2.79074e18 | 1.65506 | ||||||||
\(638\) | −2.24335e18 | −1.31693 | ||||||||
\(639\) | −7.68362e17 | −0.446488 | ||||||||
\(640\) | −6.59226e17 | −0.379196 | ||||||||
\(641\) | −3.15148e18 | −1.79448 | −0.897238 | − | 0.441546i | \(-0.854430\pi\) | ||||
−0.897238 | + | 0.441546i | \(0.854430\pi\) | |||||||
\(642\) | −4.55770e17 | −0.256902 | ||||||||
\(643\) | 4.59086e16 | 0.0256167 | 0.0128083 | − | 0.999918i | \(-0.495923\pi\) | ||||
0.0128083 | + | 0.999918i | \(0.495923\pi\) | |||||||
\(644\) | 8.91480e17 | 0.492440 | ||||||||
\(645\) | −5.26698e16 | −0.0288021 | ||||||||
\(646\) | 4.35394e18 | 2.35706 | ||||||||
\(647\) | −2.24460e18 | −1.20299 | −0.601493 | − | 0.798878i | \(-0.705427\pi\) | ||||
−0.601493 | + | 0.798878i | \(0.705427\pi\) | |||||||
\(648\) | −1.02063e18 | −0.541540 | ||||||||
\(649\) | −3.61793e17 | −0.190051 | ||||||||
\(650\) | 2.83510e18 | 1.47445 | ||||||||
\(651\) | −2.19965e18 | −1.13260 | ||||||||
\(652\) | −5.83047e17 | −0.297231 | ||||||||
\(653\) | −7.53849e17 | −0.380495 | −0.190247 | − | 0.981736i | \(-0.560929\pi\) | ||||
−0.190247 | + | 0.981736i | \(0.560929\pi\) | |||||||
\(654\) | −3.99019e17 | −0.199406 | ||||||||
\(655\) | −6.07519e16 | −0.0300602 | ||||||||
\(656\) | 1.52551e17 | 0.0747377 | ||||||||
\(657\) | 2.93923e18 | 1.42580 | ||||||||
\(658\) | 9.66326e17 | 0.464147 | ||||||||
\(659\) | 3.06841e18 | 1.45935 | 0.729673 | − | 0.683796i | \(-0.239672\pi\) | ||||
0.729673 | + | 0.683796i | \(0.239672\pi\) | |||||||
\(660\) | −1.51898e17 | −0.0715349 | ||||||||
\(661\) | 1.33227e18 | 0.621273 | 0.310636 | − | 0.950529i | \(-0.399458\pi\) | ||||
0.310636 | + | 0.950529i | \(0.399458\pi\) | |||||||
\(662\) | −2.06713e18 | −0.954531 | ||||||||
\(663\) | −7.84074e17 | −0.358525 | ||||||||
\(664\) | 2.42167e18 | 1.09653 | ||||||||
\(665\) | −1.33377e18 | −0.598052 | ||||||||
\(666\) | −2.82963e18 | −1.25646 | ||||||||
\(667\) | 7.20024e17 | 0.316613 | ||||||||
\(668\) | 6.96013e18 | 3.03089 | ||||||||
\(669\) | −5.51503e17 | −0.237836 | ||||||||
\(670\) | −1.22833e18 | −0.524600 | ||||||||
\(671\) | −1.92423e18 | −0.813880 | ||||||||
\(672\) | 1.50638e18 | 0.631005 | ||||||||
\(673\) | −1.45836e18 | −0.605016 | −0.302508 | − | 0.953147i | \(-0.597824\pi\) | ||||
−0.302508 | + | 0.953147i | \(0.597824\pi\) | |||||||
\(674\) | 6.82424e18 | 2.80392 | ||||||||
\(675\) | 1.79983e18 | 0.732413 | ||||||||
\(676\) | −4.06899e17 | −0.163996 | ||||||||
\(677\) | −3.65197e18 | −1.45781 | −0.728905 | − | 0.684615i | \(-0.759970\pi\) | ||||
−0.728905 | + | 0.684615i | \(0.759970\pi\) | |||||||
\(678\) | −8.85171e17 | −0.349973 | ||||||||
\(679\) | −2.85676e18 | −1.11872 | ||||||||
\(680\) | −5.62194e17 | −0.218061 | ||||||||
\(681\) | 6.57984e16 | 0.0252790 | ||||||||
\(682\) | 3.14322e18 | 1.19612 | ||||||||
\(683\) | 1.94656e18 | 0.733724 | 0.366862 | − | 0.930275i | \(-0.380432\pi\) | ||||
0.366862 | + | 0.930275i | \(0.380432\pi\) | |||||||
\(684\) | −5.93896e18 | −2.21741 | ||||||||
\(685\) | −5.19268e17 | −0.192045 | ||||||||
\(686\) | −5.48745e18 | −2.01031 | ||||||||
\(687\) | 1.90627e18 | 0.691777 | ||||||||
\(688\) | 1.01316e17 | 0.0364212 | ||||||||
\(689\) | −4.79629e18 | −1.70797 | ||||||||
\(690\) | 7.79420e16 | 0.0274949 | ||||||||
\(691\) | 1.92534e18 | 0.672822 | 0.336411 | − | 0.941715i | \(-0.390787\pi\) | ||||
0.336411 | + | 0.941715i | \(0.390787\pi\) | |||||||
\(692\) | 4.93797e18 | 1.70946 | ||||||||
\(693\) | −1.79603e18 | −0.615952 | ||||||||
\(694\) | 6.95017e18 | 2.36134 | ||||||||
\(695\) | −8.36503e16 | −0.0281557 | ||||||||
\(696\) | −2.47314e18 | −0.824687 | ||||||||
\(697\) | −1.68799e18 | −0.557644 | ||||||||
\(698\) | 8.58675e18 | 2.81040 | ||||||||
\(699\) | −2.00449e18 | −0.649982 | ||||||||
\(700\) | −8.18120e18 | −2.62833 | ||||||||
\(701\) | −2.24425e18 | −0.714339 | −0.357169 | − | 0.934040i | \(-0.616258\pi\) | ||||
−0.357169 | + | 0.934040i | \(0.616258\pi\) | |||||||
\(702\) | 3.79304e18 | 1.19618 | ||||||||
\(703\) | −4.84951e18 | −1.51526 | ||||||||
\(704\) | −2.32749e18 | −0.720553 | ||||||||
\(705\) | 5.28463e16 | 0.0162101 | ||||||||
\(706\) | 5.69320e18 | 1.73032 | ||||||||
\(707\) | 8.01986e18 | 2.41513 | ||||||||
\(708\) | −9.93917e17 | −0.296575 | ||||||||
\(709\) | 1.91148e18 | 0.565156 | 0.282578 | − | 0.959244i | \(-0.408810\pi\) | ||||
0.282578 | + | 0.959244i | \(0.408810\pi\) | |||||||
\(710\) | 6.77400e17 | 0.198457 | ||||||||
\(711\) | 2.94749e18 | 0.855658 | ||||||||
\(712\) | −1.61454e18 | −0.464438 | ||||||||
\(713\) | −1.00884e18 | −0.287569 | ||||||||
\(714\) | 3.61722e18 | 1.02173 | ||||||||
\(715\) | −3.43222e17 | −0.0960695 | ||||||||
\(716\) | −1.90177e18 | −0.527500 | ||||||||
\(717\) | −6.11340e17 | −0.168038 | ||||||||
\(718\) | 4.97783e18 | 1.35591 | ||||||||
\(719\) | −3.58784e18 | −0.968491 | −0.484246 | − | 0.874932i | \(-0.660906\pi\) | ||||
−0.484246 | + | 0.874932i | \(0.660906\pi\) | |||||||
\(720\) | 8.18691e16 | 0.0219007 | ||||||||
\(721\) | −8.08772e18 | −2.14411 | ||||||||
\(722\) | −1.00526e19 | −2.64110 | ||||||||
\(723\) | 4.71072e17 | 0.122656 | ||||||||
\(724\) | −6.57320e18 | −1.69620 | ||||||||
\(725\) | −6.60773e18 | −1.68988 | ||||||||
\(726\) | 2.16899e18 | 0.549756 | ||||||||
\(727\) | −1.76161e18 | −0.442524 | −0.221262 | − | 0.975214i | \(-0.571018\pi\) | ||||
−0.221262 | + | 0.975214i | \(0.571018\pi\) | |||||||
\(728\) | −6.91887e18 | −1.72259 | ||||||||
\(729\) | −3.22089e17 | −0.0794781 | ||||||||
\(730\) | −2.59127e18 | −0.633744 | ||||||||
\(731\) | −1.12108e18 | −0.271752 | ||||||||
\(732\) | −5.28624e18 | −1.27006 | ||||||||
\(733\) | −4.58156e18 | −1.09103 | −0.545516 | − | 0.838101i | \(-0.683666\pi\) | ||||
−0.545516 | + | 0.838101i | \(0.683666\pi\) | |||||||
\(734\) | 4.60334e18 | 1.08655 | ||||||||
\(735\) | −7.04090e17 | −0.164725 | ||||||||
\(736\) | 6.90881e17 | 0.160213 | ||||||||
\(737\) | −2.83476e18 | −0.651595 | ||||||||
\(738\) | 3.68101e18 | 0.838689 | ||||||||
\(739\) | 2.02965e18 | 0.458387 | 0.229193 | − | 0.973381i | \(-0.426391\pi\) | ||||
0.229193 | + | 0.973381i | \(0.426391\pi\) | |||||||
\(740\) | 1.56042e18 | 0.349329 | ||||||||
\(741\) | 2.93037e18 | 0.650285 | ||||||||
\(742\) | 2.21270e19 | 4.86741 | ||||||||
\(743\) | 4.10138e18 | 0.894340 | 0.447170 | − | 0.894449i | \(-0.352432\pi\) | ||||
0.447170 | + | 0.894449i | \(0.352432\pi\) | |||||||
\(744\) | 3.46518e18 | 0.749034 | ||||||||
\(745\) | 2.98707e17 | 0.0640074 | ||||||||
\(746\) | −1.36205e19 | −2.89327 | ||||||||
\(747\) | 3.90215e18 | 0.821713 | ||||||||
\(748\) | −3.23316e18 | −0.674942 | ||||||||
\(749\) | 2.97178e18 | 0.615013 | ||||||||
\(750\) | −1.46808e18 | −0.301199 | ||||||||
\(751\) | −2.47765e18 | −0.503943 | −0.251971 | − | 0.967735i | \(-0.581079\pi\) | ||||
−0.251971 | + | 0.967735i | \(0.581079\pi\) | |||||||
\(752\) | −1.01656e17 | −0.0204982 | ||||||||
\(753\) | −2.43449e18 | −0.486676 | ||||||||
\(754\) | −1.39255e19 | −2.75991 | ||||||||
\(755\) | 2.42386e17 | 0.0476269 | ||||||||
\(756\) | −1.09455e19 | −2.13228 | ||||||||
\(757\) | −4.82152e18 | −0.931239 | −0.465619 | − | 0.884985i | \(-0.654168\pi\) | ||||
−0.465619 | + | 0.884985i | \(0.654168\pi\) | |||||||
\(758\) | −1.05586e19 | −2.02189 | ||||||||
\(759\) | 1.79876e17 | 0.0341508 | ||||||||
\(760\) | 2.10112e18 | 0.395515 | ||||||||
\(761\) | 1.03824e19 | 1.93775 | 0.968873 | − | 0.247559i | \(-0.0796283\pi\) | ||||
0.968873 | + | 0.247559i | \(0.0796283\pi\) | |||||||
\(762\) | −3.93951e18 | −0.729012 | ||||||||
\(763\) | 2.60174e18 | 0.477369 | ||||||||
\(764\) | 2.35122e17 | 0.0427746 | ||||||||
\(765\) | −9.05890e17 | −0.163409 | ||||||||
\(766\) | −2.39020e18 | −0.427512 | ||||||||
\(767\) | −2.24580e18 | −0.398292 | ||||||||
\(768\) | −2.85363e18 | −0.501822 | ||||||||
\(769\) | −8.18910e18 | −1.42796 | −0.713978 | − | 0.700168i | \(-0.753109\pi\) | ||||
−0.713978 | + | 0.700168i | \(0.753109\pi\) | |||||||
\(770\) | 1.58341e18 | 0.273781 | ||||||||
\(771\) | −2.91216e18 | −0.499300 | ||||||||
\(772\) | −5.78860e18 | −0.984150 | ||||||||
\(773\) | 4.20651e18 | 0.709178 | 0.354589 | − | 0.935022i | \(-0.384621\pi\) | ||||
0.354589 | + | 0.935022i | \(0.384621\pi\) | |||||||
\(774\) | 2.44474e18 | 0.408711 | ||||||||
\(775\) | 9.25826e18 | 1.53486 | ||||||||
\(776\) | 4.50035e18 | 0.739852 | ||||||||
\(777\) | −4.02893e18 | −0.656831 | ||||||||
\(778\) | −1.21372e19 | −1.96223 | ||||||||
\(779\) | 6.30864e18 | 1.01144 | ||||||||
\(780\) | −9.42898e17 | −0.149917 | ||||||||
\(781\) | 1.56332e18 | 0.246499 | ||||||||
\(782\) | 1.65899e18 | 0.259419 | ||||||||
\(783\) | −8.84040e18 | −1.37095 | ||||||||
\(784\) | 1.35440e18 | 0.208301 | ||||||||
\(785\) | −1.26968e18 | −0.193661 | ||||||||
\(786\) | −6.15773e17 | −0.0931480 | ||||||||
\(787\) | −1.12250e19 | −1.68404 | −0.842020 | − | 0.539447i | \(-0.818633\pi\) | ||||
−0.842020 | + | 0.539447i | \(0.818633\pi\) | |||||||
\(788\) | −7.99784e17 | −0.119001 | ||||||||
\(789\) | 1.56186e17 | 0.0230485 | ||||||||
\(790\) | −2.59856e18 | −0.380326 | ||||||||
\(791\) | 5.77162e18 | 0.837819 | ||||||||
\(792\) | 2.82934e18 | 0.407353 | ||||||||
\(793\) | −1.19445e19 | −1.70566 | ||||||||
\(794\) | −1.54890e19 | −2.19376 | ||||||||
\(795\) | 1.21008e18 | 0.169992 | ||||||||
\(796\) | −8.06473e18 | −1.12371 | ||||||||
\(797\) | 4.39876e18 | 0.607927 | 0.303964 | − | 0.952684i | \(-0.401690\pi\) | ||||
0.303964 | + | 0.952684i | \(0.401690\pi\) | |||||||
\(798\) | −1.35189e19 | −1.85320 | ||||||||
\(799\) | 1.12483e18 | 0.152944 | ||||||||
\(800\) | −6.34028e18 | −0.855113 | ||||||||
\(801\) | −2.60158e18 | −0.348038 | ||||||||
\(802\) | 1.46332e19 | 1.94180 | ||||||||
\(803\) | −5.98018e18 | −0.787160 | ||||||||
\(804\) | −7.78765e18 | −1.01682 | ||||||||
\(805\) | −5.08209e17 | −0.0658216 | ||||||||
\(806\) | 1.95113e19 | 2.50673 | ||||||||
\(807\) | −3.61481e18 | −0.460688 | ||||||||
\(808\) | −1.26339e19 | −1.59722 | ||||||||
\(809\) | 2.90564e18 | 0.364399 | 0.182199 | − | 0.983262i | \(-0.441678\pi\) | ||||
0.182199 | + | 0.983262i | \(0.441678\pi\) | |||||||
\(810\) | 1.44990e18 | 0.180378 | ||||||||
\(811\) | 5.29580e18 | 0.653575 | 0.326788 | − | 0.945098i | \(-0.394034\pi\) | ||||
0.326788 | + | 0.945098i | \(0.394034\pi\) | |||||||
\(812\) | 4.01845e19 | 4.91976 | ||||||||
\(813\) | 4.80733e18 | 0.583869 | ||||||||
\(814\) | 5.75719e18 | 0.693669 | ||||||||
\(815\) | 3.32379e17 | 0.0397291 | ||||||||
\(816\) | −3.80525e17 | −0.0451229 | ||||||||
\(817\) | 4.18987e18 | 0.492898 | ||||||||
\(818\) | 8.03353e18 | 0.937584 | ||||||||
\(819\) | −1.11487e19 | −1.29086 | ||||||||
\(820\) | −2.02992e18 | −0.233178 | ||||||||
\(821\) | 6.82729e18 | 0.778068 | 0.389034 | − | 0.921223i | \(-0.372809\pi\) | ||||
0.389034 | + | 0.921223i | \(0.372809\pi\) | |||||||
\(822\) | −5.26323e18 | −0.595093 | ||||||||
\(823\) | −6.91413e18 | −0.775602 | −0.387801 | − | 0.921743i | \(-0.626765\pi\) | ||||
−0.387801 | + | 0.921743i | \(0.626765\pi\) | |||||||
\(824\) | 1.27408e19 | 1.41798 | ||||||||
\(825\) | −1.65074e18 | −0.182275 | ||||||||
\(826\) | 1.03607e19 | 1.13506 | ||||||||
\(827\) | 5.09534e18 | 0.553843 | 0.276922 | − | 0.960892i | \(-0.410686\pi\) | ||||
0.276922 | + | 0.960892i | \(0.410686\pi\) | |||||||
\(828\) | −2.26294e18 | −0.244048 | ||||||||
\(829\) | −8.76965e18 | −0.938378 | −0.469189 | − | 0.883098i | \(-0.655454\pi\) | ||||
−0.469189 | + | 0.883098i | \(0.655454\pi\) | |||||||
\(830\) | −3.44020e18 | −0.365238 | ||||||||
\(831\) | −4.44887e17 | −0.0468644 | ||||||||
\(832\) | −1.44477e19 | −1.51007 | ||||||||
\(833\) | −1.49865e19 | −1.55421 | ||||||||
\(834\) | −8.47867e17 | −0.0872466 | ||||||||
\(835\) | −3.96778e18 | −0.405122 | ||||||||
\(836\) | 1.20835e19 | 1.22420 | ||||||||
\(837\) | 1.23865e19 | 1.24518 | ||||||||
\(838\) | −9.63146e18 | −0.960740 | ||||||||
\(839\) | 1.11763e18 | 0.110623 | 0.0553113 | − | 0.998469i | \(-0.482385\pi\) | ||||
0.0553113 | + | 0.998469i | \(0.482385\pi\) | |||||||
\(840\) | 1.74560e18 | 0.171446 | ||||||||
\(841\) | 2.21953e19 | 2.16315 | ||||||||
\(842\) | 9.99656e18 | 0.966767 | ||||||||
\(843\) | 7.10893e18 | 0.682221 | ||||||||
\(844\) | −2.31657e19 | −2.20607 | ||||||||
\(845\) | 2.31962e17 | 0.0219204 | ||||||||
\(846\) | −2.45293e18 | −0.230026 | ||||||||
\(847\) | −1.41426e19 | −1.31609 | ||||||||
\(848\) | −2.32773e18 | −0.214961 | ||||||||
\(849\) | 2.53920e18 | 0.232700 | ||||||||
\(850\) | −1.52248e19 | −1.38461 | ||||||||
\(851\) | −1.84782e18 | −0.166770 | ||||||||
\(852\) | 4.29474e18 | 0.384662 | ||||||||
\(853\) | −4.03242e17 | −0.0358424 | −0.0179212 | − | 0.999839i | \(-0.505705\pi\) | ||||
−0.0179212 | + | 0.999839i | \(0.505705\pi\) | |||||||
\(854\) | 5.51044e19 | 4.86083 | ||||||||
\(855\) | 3.38564e18 | 0.296388 | ||||||||
\(856\) | −4.68153e18 | −0.406732 | ||||||||
\(857\) | 1.64069e18 | 0.141466 | 0.0707330 | − | 0.997495i | \(-0.477466\pi\) | ||||
0.0707330 | + | 0.997495i | \(0.477466\pi\) | |||||||
\(858\) | −3.47885e18 | −0.297692 | ||||||||
\(859\) | 1.86876e19 | 1.58708 | 0.793538 | − | 0.608521i | \(-0.208237\pi\) | ||||
0.793538 | + | 0.608521i | \(0.208237\pi\) | |||||||
\(860\) | −1.34817e18 | −0.113633 | ||||||||
\(861\) | 5.24117e18 | 0.438437 | ||||||||
\(862\) | −2.11007e19 | −1.75186 | ||||||||
\(863\) | 1.18272e19 | 0.974563 | 0.487282 | − | 0.873245i | \(-0.337989\pi\) | ||||
0.487282 | + | 0.873245i | \(0.337989\pi\) | |||||||
\(864\) | −8.48258e18 | −0.693727 | ||||||||
\(865\) | −2.81500e18 | −0.228493 | ||||||||
\(866\) | 7.05621e18 | 0.568467 | ||||||||
\(867\) | −1.08401e18 | −0.0866778 | ||||||||
\(868\) | −5.63035e19 | −4.46845 | ||||||||
\(869\) | −5.99700e18 | −0.472395 | ||||||||
\(870\) | 3.51332e18 | 0.274690 | ||||||||
\(871\) | −1.75966e19 | −1.36556 | ||||||||
\(872\) | −4.09860e18 | −0.315703 | ||||||||
\(873\) | 7.25162e18 | 0.554425 | ||||||||
\(874\) | −6.20026e18 | −0.470528 | ||||||||
\(875\) | 9.57241e18 | 0.721056 | ||||||||
\(876\) | −1.64287e19 | −1.22837 | ||||||||
\(877\) | 5.36616e18 | 0.398260 | 0.199130 | − | 0.979973i | \(-0.436188\pi\) | ||||
0.199130 | + | 0.979973i | \(0.436188\pi\) | |||||||
\(878\) | −2.64124e18 | −0.194578 | ||||||||
\(879\) | −7.97391e18 | −0.583101 | ||||||||
\(880\) | −1.66572e17 | −0.0120910 | ||||||||
\(881\) | −2.33175e19 | −1.68011 | −0.840057 | − | 0.542498i | \(-0.817479\pi\) | ||||
−0.840057 | + | 0.542498i | \(0.817479\pi\) | |||||||
\(882\) | 3.26812e19 | 2.33751 | ||||||||
\(883\) | −8.04431e17 | −0.0571142 | −0.0285571 | − | 0.999592i | \(-0.509091\pi\) | ||||
−0.0285571 | + | 0.999592i | \(0.509091\pi\) | |||||||
\(884\) | −2.00696e19 | −1.41449 | ||||||||
\(885\) | 5.66605e17 | 0.0396414 | ||||||||
\(886\) | 3.20138e19 | 2.22340 | ||||||||
\(887\) | 6.74205e18 | 0.464824 | 0.232412 | − | 0.972617i | \(-0.425338\pi\) | ||||
0.232412 | + | 0.972617i | \(0.425338\pi\) | |||||||
\(888\) | 6.34690e18 | 0.434388 | ||||||||
\(889\) | 2.56869e19 | 1.74522 | ||||||||
\(890\) | 2.29360e18 | 0.154697 | ||||||||
\(891\) | 3.34610e18 | 0.224044 | ||||||||
\(892\) | −1.41166e19 | −0.938334 | ||||||||
\(893\) | −4.20390e18 | −0.277408 | ||||||||
\(894\) | 3.02766e18 | 0.198341 | ||||||||
\(895\) | 1.08415e18 | 0.0705079 | ||||||||
\(896\) | 4.35677e19 | 2.81296 | ||||||||
\(897\) | 1.11657e18 | 0.0715704 | ||||||||
\(898\) | −5.57674e17 | −0.0354882 | ||||||||
\(899\) | −4.54748e19 | −2.87298 | ||||||||
\(900\) | 2.07672e19 | 1.30257 | ||||||||
\(901\) | 2.57565e19 | 1.60390 | ||||||||
\(902\) | −7.48943e18 | −0.463027 | ||||||||
\(903\) | 3.48091e18 | 0.213660 | ||||||||
\(904\) | −9.09221e18 | −0.554083 | ||||||||
\(905\) | 3.74720e18 | 0.226721 | ||||||||
\(906\) | 2.45679e18 | 0.147582 | ||||||||
\(907\) | −5.92732e17 | −0.0353517 | −0.0176759 | − | 0.999844i | \(-0.505627\pi\) | ||||
−0.0176759 | + | 0.999844i | \(0.505627\pi\) | |||||||
\(908\) | 1.68421e18 | 0.0997330 | ||||||||
\(909\) | −2.03577e19 | −1.19691 | ||||||||
\(910\) | 9.82889e18 | 0.573767 | ||||||||
\(911\) | −3.49053e18 | −0.202312 | −0.101156 | − | 0.994871i | \(-0.532254\pi\) | ||||
−0.101156 | + | 0.994871i | \(0.532254\pi\) | |||||||
\(912\) | 1.42216e18 | 0.0818431 | ||||||||
\(913\) | −7.93936e18 | −0.453655 | ||||||||
\(914\) | 4.71383e19 | 2.67438 | ||||||||
\(915\) | 3.01354e18 | 0.169762 | ||||||||
\(916\) | 4.87939e19 | 2.72926 | ||||||||
\(917\) | 4.01505e18 | 0.222992 | ||||||||
\(918\) | −2.03690e19 | −1.12329 | ||||||||
\(919\) | −2.99518e19 | −1.64011 | −0.820054 | − | 0.572286i | \(-0.806057\pi\) | ||||
−0.820054 | + | 0.572286i | \(0.806057\pi\) | |||||||
\(920\) | 8.00597e17 | 0.0435304 | ||||||||
\(921\) | 1.01038e19 | 0.545501 | ||||||||
\(922\) | 3.30376e19 | 1.77116 | ||||||||
\(923\) | 9.70417e18 | 0.516592 | ||||||||
\(924\) | 1.00389e19 | 0.530660 | ||||||||
\(925\) | 1.69576e19 | 0.890111 | ||||||||
\(926\) | −1.96716e19 | −1.02534 | ||||||||
\(927\) | 2.05299e19 | 1.06260 | ||||||||
\(928\) | 3.11422e19 | 1.60062 | ||||||||
\(929\) | −4.24088e17 | −0.0216448 | −0.0108224 | − | 0.999941i | \(-0.503445\pi\) | ||||
−0.0108224 | + | 0.999941i | \(0.503445\pi\) | |||||||
\(930\) | −4.92260e18 | −0.249492 | ||||||||
\(931\) | 5.60101e19 | 2.81899 | ||||||||
\(932\) | −5.13079e19 | −2.56437 | ||||||||
\(933\) | 2.62684e16 | 0.00130378 | ||||||||
\(934\) | 3.65049e19 | 1.79927 | ||||||||
\(935\) | 1.84313e18 | 0.0902155 | ||||||||
\(936\) | 1.75629e19 | 0.853696 | ||||||||
\(937\) | −1.16943e19 | −0.564502 | −0.282251 | − | 0.959341i | \(-0.591081\pi\) | ||||
−0.282251 | + | 0.959341i | \(0.591081\pi\) | |||||||
\(938\) | 8.11794e19 | 3.89159 | ||||||||
\(939\) | 7.02854e18 | 0.334610 | ||||||||
\(940\) | 1.35268e18 | 0.0639535 | ||||||||
\(941\) | 3.34650e19 | 1.57130 | 0.785648 | − | 0.618674i | \(-0.212330\pi\) | ||||
0.785648 | + | 0.618674i | \(0.212330\pi\) | |||||||
\(942\) | −1.28693e19 | −0.600102 | ||||||||
\(943\) | 2.40380e18 | 0.111320 | ||||||||
\(944\) | −1.08993e18 | −0.0501280 | ||||||||
\(945\) | 6.23975e18 | 0.285010 | ||||||||
\(946\) | −4.97409e18 | −0.225643 | ||||||||
\(947\) | −2.95774e19 | −1.33255 | −0.666276 | − | 0.745705i | \(-0.732113\pi\) | ||||
−0.666276 | + | 0.745705i | \(0.732113\pi\) | |||||||
\(948\) | −1.64750e19 | −0.737174 | ||||||||
\(949\) | −3.71215e19 | −1.64966 | ||||||||
\(950\) | 5.69004e19 | 2.51138 | ||||||||
\(951\) | 8.27404e18 | 0.362697 | ||||||||
\(952\) | 3.71550e19 | 1.61762 | ||||||||
\(953\) | −1.82956e19 | −0.791120 | −0.395560 | − | 0.918440i | \(-0.629450\pi\) | ||||
−0.395560 | + | 0.918440i | \(0.629450\pi\) | |||||||
\(954\) | −5.61674e19 | −2.41224 | ||||||||
\(955\) | −1.34037e17 | −0.00571744 | ||||||||
\(956\) | −1.56482e19 | −0.662961 | ||||||||
\(957\) | 8.10811e18 | 0.341187 | ||||||||
\(958\) | 4.93905e19 | 2.06428 | ||||||||
\(959\) | 3.43180e19 | 1.42463 | ||||||||
\(960\) | 3.64509e18 | 0.150295 | ||||||||
\(961\) | 3.92983e19 | 1.60943 | ||||||||
\(962\) | 3.57373e19 | 1.45373 | ||||||||
\(963\) | −7.54358e18 | −0.304794 | ||||||||
\(964\) | 1.20578e19 | 0.483913 | ||||||||
\(965\) | 3.29992e18 | 0.131546 | ||||||||
\(966\) | −5.15113e18 | −0.203963 | ||||||||
\(967\) | 1.97967e19 | 0.778610 | 0.389305 | − | 0.921109i | \(-0.372715\pi\) | ||||
0.389305 | + | 0.921109i | \(0.372715\pi\) | |||||||
\(968\) | 2.22792e19 | 0.870382 | ||||||||
\(969\) | −1.57364e19 | −0.610660 | ||||||||
\(970\) | −6.39315e18 | −0.246433 | ||||||||
\(971\) | −2.43674e19 | −0.933005 | −0.466503 | − | 0.884520i | \(-0.654486\pi\) | ||||
−0.466503 | + | 0.884520i | \(0.654486\pi\) | |||||||
\(972\) | 4.30438e19 | 1.63712 | ||||||||
\(973\) | 5.52839e18 | 0.208865 | ||||||||
\(974\) | −1.54733e19 | −0.580698 | ||||||||
\(975\) | −1.02468e19 | −0.381997 | ||||||||
\(976\) | −5.79689e18 | −0.214670 | ||||||||
\(977\) | 3.07695e19 | 1.13189 | 0.565947 | − | 0.824442i | \(-0.308511\pi\) | ||||
0.565947 | + | 0.824442i | \(0.308511\pi\) | |||||||
\(978\) | 3.36895e18 | 0.123110 | ||||||||
\(979\) | 5.29321e18 | 0.192146 | ||||||||
\(980\) | −1.80223e19 | −0.649890 | ||||||||
\(981\) | −6.60427e18 | −0.236579 | ||||||||
\(982\) | −8.14905e19 | −2.89990 | ||||||||
\(983\) | −3.07549e19 | −1.08722 | −0.543609 | − | 0.839339i | \(-0.682943\pi\) | ||||
−0.543609 | + | 0.839339i | \(0.682943\pi\) | |||||||
\(984\) | −8.25658e18 | −0.289956 | ||||||||
\(985\) | 4.55935e17 | 0.0159062 | ||||||||
\(986\) | 7.47811e19 | 2.59174 | ||||||||
\(987\) | −3.49257e18 | −0.120250 | ||||||||
\(988\) | 7.50073e19 | 2.56557 | ||||||||
\(989\) | 1.59648e18 | 0.0542484 | ||||||||
\(990\) | −4.01933e18 | −0.135683 | ||||||||
\(991\) | −2.75978e19 | −0.925541 | −0.462770 | − | 0.886478i | \(-0.653145\pi\) | ||||
−0.462770 | + | 0.886478i | \(0.653145\pi\) | |||||||
\(992\) | −4.36342e19 | −1.45379 | ||||||||
\(993\) | 7.47117e18 | 0.247297 | ||||||||
\(994\) | −4.47689e19 | −1.47219 | ||||||||
\(995\) | 4.59748e18 | 0.150200 | ||||||||
\(996\) | −2.18110e19 | −0.707930 | ||||||||
\(997\) | −1.21160e19 | −0.390697 | −0.195348 | − | 0.980734i | \(-0.562584\pi\) | ||||
−0.195348 | + | 0.980734i | \(0.562584\pi\) | |||||||
\(998\) | −5.27159e19 | −1.68886 | ||||||||
\(999\) | 2.26874e19 | 0.722120 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 197.14.a.a.1.12 | ✓ | 104 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
197.14.a.a.1.12 | ✓ | 104 | 1.1 | even | 1 | trivial |