Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,112,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, 112, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 112);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 112 \) |
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: | \(78.0257547452\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} + \cdots + 83\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | multiple of \( 2^{135}\cdot 3^{56}\cdot 5^{16}\cdot 7^{7}\cdot 11^{3}\cdot 13\cdot 19\cdot 37^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(7.31006e14\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.34436e16 | 1.04889 | 0.524446 | − | 0.851444i | \(-0.324272\pi\) | ||||
0.524446 | + | 0.851444i | \(0.324272\pi\) | |||||||
\(3\) | −3.57964e25 | −0.118470 | −0.0592352 | − | 0.998244i | \(-0.518866\pi\) | ||||
−0.0592352 | + | 0.998244i | \(0.518866\pi\) | |||||||
\(4\) | 2.60068e32 | 0.100174 | ||||||||
\(5\) | −4.56192e38 | −0.735043 | −0.367521 | − | 0.930015i | \(-0.619794\pi\) | ||||
−0.367521 | + | 0.930015i | \(0.619794\pi\) | |||||||
\(6\) | −1.91309e42 | −0.124263 | ||||||||
\(7\) | −2.39634e46 | −0.299645 | −0.149822 | − | 0.988713i | \(-0.547870\pi\) | ||||
−0.149822 | + | 0.988713i | \(0.547870\pi\) | |||||||
\(8\) | −1.24849e50 | −0.943820 | ||||||||
\(9\) | −9.00162e52 | −0.985965 | ||||||||
\(10\) | −2.43805e55 | −0.770980 | ||||||||
\(11\) | −2.36286e57 | −0.376828 | −0.188414 | − | 0.982090i | \(-0.560335\pi\) | ||||
−0.188414 | + | 0.982090i | \(0.560335\pi\) | |||||||
\(12\) | −9.30949e57 | −0.0118677 | ||||||||
\(13\) | −5.27826e60 | −0.0791836 | −0.0395918 | − | 0.999216i | \(-0.512606\pi\) | ||||
−0.0395918 | + | 0.999216i | \(0.512606\pi\) | |||||||
\(14\) | −1.28069e63 | −0.314295 | ||||||||
\(15\) | 1.63300e64 | 0.0870808 | ||||||||
\(16\) | −7.34753e66 | −1.09014 | ||||||||
\(17\) | 3.40054e67 | 0.174435 | 0.0872174 | − | 0.996189i | \(-0.472203\pi\) | ||||
0.0872174 | + | 0.996189i | \(0.472203\pi\) | |||||||
\(18\) | −4.81079e69 | −1.03417 | ||||||||
\(19\) | 1.10518e71 | 1.18197 | 0.590987 | − | 0.806681i | \(-0.298738\pi\) | ||||
0.590987 | + | 0.806681i | \(0.298738\pi\) | |||||||
\(20\) | −1.18641e71 | −0.0736325 | ||||||||
\(21\) | 8.57803e71 | 0.0354990 | ||||||||
\(22\) | −1.26280e74 | −0.395252 | ||||||||
\(23\) | 1.40882e75 | 0.374077 | 0.187038 | − | 0.982353i | \(-0.440111\pi\) | ||||
0.187038 | + | 0.982353i | \(0.440111\pi\) | |||||||
\(24\) | 4.46913e75 | 0.111815 | ||||||||
\(25\) | −1.77075e77 | −0.459712 | ||||||||
\(26\) | −2.82089e77 | −0.0830550 | ||||||||
\(27\) | 6.49039e78 | 0.235278 | ||||||||
\(28\) | −6.23209e78 | −0.0300167 | ||||||||
\(29\) | −7.61762e80 | −0.523276 | −0.261638 | − | 0.965166i | \(-0.584263\pi\) | ||||
−0.261638 | + | 0.965166i | \(0.584263\pi\) | |||||||
\(30\) | 8.72736e80 | 0.0913384 | ||||||||
\(31\) | 2.31300e82 | 0.392285 | 0.196143 | − | 0.980575i | \(-0.437158\pi\) | ||||
0.196143 | + | 0.980575i | \(0.437158\pi\) | |||||||
\(32\) | −6.85528e82 | −0.199619 | ||||||||
\(33\) | 8.45819e82 | 0.0446430 | ||||||||
\(34\) | 1.81737e84 | 0.182963 | ||||||||
\(35\) | 1.09319e85 | 0.220252 | ||||||||
\(36\) | −2.34103e85 | −0.0987684 | ||||||||
\(37\) | 6.32898e85 | 0.0583630 | 0.0291815 | − | 0.999574i | \(-0.490710\pi\) | ||||
0.0291815 | + | 0.999574i | \(0.490710\pi\) | |||||||
\(38\) | 5.90648e87 | 1.23976 | ||||||||
\(39\) | 1.88943e86 | 0.00938092 | ||||||||
\(40\) | 5.69549e88 | 0.693748 | ||||||||
\(41\) | 5.31382e89 | 1.64400 | 0.822002 | − | 0.569485i | \(-0.192857\pi\) | ||||
0.822002 | + | 0.569485i | \(0.192857\pi\) | |||||||
\(42\) | 4.58440e88 | 0.0372346 | ||||||||
\(43\) | 6.52887e90 | 1.43661 | 0.718305 | − | 0.695728i | \(-0.244918\pi\) | ||||
0.718305 | + | 0.695728i | \(0.244918\pi\) | |||||||
\(44\) | −6.14503e89 | −0.0377486 | ||||||||
\(45\) | 4.10647e91 | 0.724726 | ||||||||
\(46\) | 7.52924e91 | 0.392366 | ||||||||
\(47\) | −1.03218e93 | −1.63051 | −0.815255 | − | 0.579102i | \(-0.803403\pi\) | ||||
−0.815255 | + | 0.579102i | \(0.803403\pi\) | |||||||
\(48\) | 2.63015e92 | 0.129149 | ||||||||
\(49\) | −5.82137e93 | −0.910213 | ||||||||
\(50\) | −9.46351e93 | −0.482189 | ||||||||
\(51\) | −1.21727e93 | −0.0206654 | ||||||||
\(52\) | −1.37271e93 | −0.00793217 | ||||||||
\(53\) | 5.63644e95 | 1.13160 | 0.565801 | − | 0.824542i | \(-0.308567\pi\) | ||||
0.565801 | + | 0.824542i | \(0.308567\pi\) | |||||||
\(54\) | 3.46869e95 | 0.246781 | ||||||||
\(55\) | 1.07792e96 | 0.276985 | ||||||||
\(56\) | 2.99179e96 | 0.282810 | ||||||||
\(57\) | −3.95615e96 | −0.140029 | ||||||||
\(58\) | −4.07113e97 | −0.548860 | ||||||||
\(59\) | −1.83167e98 | −0.956226 | −0.478113 | − | 0.878298i | \(-0.658679\pi\) | ||||
−0.478113 | + | 0.878298i | \(0.658679\pi\) | |||||||
\(60\) | 4.24692e96 | 0.00872327 | ||||||||
\(61\) | −2.77182e97 | −0.0227488 | −0.0113744 | − | 0.999935i | \(-0.503621\pi\) | ||||
−0.0113744 | + | 0.999935i | \(0.503621\pi\) | |||||||
\(62\) | 1.23615e99 | 0.411465 | ||||||||
\(63\) | 2.15709e99 | 0.295439 | ||||||||
\(64\) | 1.54116e100 | 0.880761 | ||||||||
\(65\) | 2.40790e99 | 0.0582033 | ||||||||
\(66\) | 4.52036e99 | 0.0468257 | ||||||||
\(67\) | −2.58375e101 | −1.16172 | −0.580858 | − | 0.814005i | \(-0.697283\pi\) | ||||
−0.580858 | + | 0.814005i | \(0.697283\pi\) | |||||||
\(68\) | 8.84371e99 | 0.0174739 | ||||||||
\(69\) | −5.04307e100 | −0.0443170 | ||||||||
\(70\) | 5.84239e101 | 0.231020 | ||||||||
\(71\) | −8.44733e101 | −0.152013 | −0.0760066 | − | 0.997107i | \(-0.524217\pi\) | ||||
−0.0760066 | + | 0.997107i | \(0.524217\pi\) | |||||||
\(72\) | 1.12384e103 | 0.930573 | ||||||||
\(73\) | 2.87008e103 | 1.10529 | 0.552645 | − | 0.833417i | \(-0.313619\pi\) | ||||
0.552645 | + | 0.833417i | \(0.313619\pi\) | |||||||
\(74\) | 3.38243e102 | 0.0612165 | ||||||||
\(75\) | 6.33864e102 | 0.0544623 | ||||||||
\(76\) | 2.87422e103 | 0.118404 | ||||||||
\(77\) | 5.66220e103 | 0.112915 | ||||||||
\(78\) | 1.00978e103 | 0.00983957 | ||||||||
\(79\) | 2.48817e105 | 1.19558 | 0.597788 | − | 0.801654i | \(-0.296046\pi\) | ||||
0.597788 | + | 0.801654i | \(0.296046\pi\) | |||||||
\(80\) | 3.35188e105 | 0.801299 | ||||||||
\(81\) | 7.98593e105 | 0.958091 | ||||||||
\(82\) | 2.83990e106 | 1.72438 | ||||||||
\(83\) | 4.12681e106 | 1.27874 | 0.639368 | − | 0.768901i | \(-0.279196\pi\) | ||||
0.639368 | + | 0.768901i | \(0.279196\pi\) | |||||||
\(84\) | 2.23087e104 | 0.00355609 | ||||||||
\(85\) | −1.55130e106 | −0.128217 | ||||||||
\(86\) | 3.48926e107 | 1.50685 | ||||||||
\(87\) | 2.72684e106 | 0.0619927 | ||||||||
\(88\) | 2.94999e107 | 0.355658 | ||||||||
\(89\) | 1.87807e108 | 1.20939 | 0.604695 | − | 0.796457i | \(-0.293295\pi\) | ||||
0.604695 | + | 0.796457i | \(0.293295\pi\) | |||||||
\(90\) | 2.19464e108 | 0.760159 | ||||||||
\(91\) | 1.26485e107 | 0.0237269 | ||||||||
\(92\) | 3.66389e107 | 0.0374729 | ||||||||
\(93\) | −8.27972e107 | −0.0464742 | ||||||||
\(94\) | −5.51633e109 | −1.71023 | ||||||||
\(95\) | −5.04174e109 | −0.868802 | ||||||||
\(96\) | 2.45395e108 | 0.0236489 | ||||||||
\(97\) | −1.71016e110 | −0.927269 | −0.463634 | − | 0.886027i | \(-0.653455\pi\) | ||||
−0.463634 | + | 0.886027i | \(0.653455\pi\) | |||||||
\(98\) | −3.11115e110 | −0.954715 | ||||||||
\(99\) | 2.12696e110 | 0.371540 | ||||||||
\(100\) | −4.60514e109 | −0.0460514 | ||||||||
\(101\) | −6.38809e110 | −0.367735 | −0.183867 | − | 0.982951i | \(-0.558862\pi\) | ||||
−0.183867 | + | 0.982951i | \(0.558862\pi\) | |||||||
\(102\) | −6.50554e109 | −0.0216757 | ||||||||
\(103\) | −4.63449e111 | −0.898538 | −0.449269 | − | 0.893397i | \(-0.648315\pi\) | ||||
−0.449269 | + | 0.893397i | \(0.648315\pi\) | |||||||
\(104\) | 6.58984e110 | 0.0747350 | ||||||||
\(105\) | −3.91323e110 | −0.0260933 | ||||||||
\(106\) | 3.01231e112 | 1.18693 | ||||||||
\(107\) | 4.78688e112 | 1.12009 | 0.560045 | − | 0.828462i | \(-0.310784\pi\) | ||||
0.560045 | + | 0.828462i | \(0.310784\pi\) | |||||||
\(108\) | 1.68794e111 | 0.0235689 | ||||||||
\(109\) | 1.94080e113 | 1.62484 | 0.812421 | − | 0.583071i | \(-0.198149\pi\) | ||||
0.812421 | + | 0.583071i | \(0.198149\pi\) | |||||||
\(110\) | 5.76078e112 | 0.290527 | ||||||||
\(111\) | −2.26555e111 | −0.00691430 | ||||||||
\(112\) | 1.76071e113 | 0.326654 | ||||||||
\(113\) | −1.37358e114 | −1.55596 | −0.777982 | − | 0.628287i | \(-0.783757\pi\) | ||||
−0.777982 | + | 0.628287i | \(0.783757\pi\) | |||||||
\(114\) | −2.11431e113 | −0.146875 | ||||||||
\(115\) | −6.42693e113 | −0.274962 | ||||||||
\(116\) | −1.98110e113 | −0.0524188 | ||||||||
\(117\) | 4.75129e113 | 0.0780722 | ||||||||
\(118\) | −9.78910e114 | −1.00298 | ||||||||
\(119\) | −8.14884e113 | −0.0522684 | ||||||||
\(120\) | −2.03878e114 | −0.0821886 | ||||||||
\(121\) | −3.37346e115 | −0.858000 | ||||||||
\(122\) | −1.48136e114 | −0.0238611 | ||||||||
\(123\) | −1.90216e115 | −0.194766 | ||||||||
\(124\) | 6.01537e114 | 0.0392970 | ||||||||
\(125\) | 2.56499e116 | 1.07295 | ||||||||
\(126\) | 1.15283e116 | 0.309884 | ||||||||
\(127\) | 7.15774e116 | 1.24071 | 0.620353 | − | 0.784322i | \(-0.286989\pi\) | ||||
0.620353 | + | 0.784322i | \(0.286989\pi\) | |||||||
\(128\) | 1.00162e117 | 1.12344 | ||||||||
\(129\) | −2.33710e116 | −0.170196 | ||||||||
\(130\) | 1.28687e116 | 0.0610490 | ||||||||
\(131\) | −2.34842e117 | −0.728148 | −0.364074 | − | 0.931370i | \(-0.618614\pi\) | ||||
−0.364074 | + | 0.931370i | \(0.618614\pi\) | |||||||
\(132\) | 2.19970e115 | 0.00447209 | ||||||||
\(133\) | −2.64838e117 | −0.354172 | ||||||||
\(134\) | −1.38085e118 | −1.21851 | ||||||||
\(135\) | −2.96086e117 | −0.172939 | ||||||||
\(136\) | −4.24553e117 | −0.164635 | ||||||||
\(137\) | 2.60288e118 | 0.672144 | 0.336072 | − | 0.941836i | \(-0.390901\pi\) | ||||
0.336072 | + | 0.941836i | \(0.390901\pi\) | |||||||
\(138\) | −2.69520e117 | −0.0464838 | ||||||||
\(139\) | −1.02399e119 | −1.18297 | −0.591485 | − | 0.806316i | \(-0.701458\pi\) | ||||
−0.591485 | + | 0.806316i | \(0.701458\pi\) | |||||||
\(140\) | 2.84303e117 | 0.0220636 | ||||||||
\(141\) | 3.69483e118 | 0.193167 | ||||||||
\(142\) | −4.51456e118 | −0.159445 | ||||||||
\(143\) | 1.24718e118 | 0.0298386 | ||||||||
\(144\) | 6.61396e119 | 1.07484 | ||||||||
\(145\) | 3.47510e119 | 0.384630 | ||||||||
\(146\) | 1.53388e120 | 1.15933 | ||||||||
\(147\) | 2.08384e119 | 0.107833 | ||||||||
\(148\) | 1.64596e118 | 0.00584648 | ||||||||
\(149\) | 2.45647e120 | 0.600447 | 0.300223 | − | 0.953869i | \(-0.402939\pi\) | ||||
0.300223 | + | 0.953869i | \(0.402939\pi\) | |||||||
\(150\) | 3.38760e119 | 0.0571251 | ||||||||
\(151\) | −1.49407e121 | −1.74240 | −0.871202 | − | 0.490924i | \(-0.836659\pi\) | ||||
−0.871202 | + | 0.490924i | \(0.836659\pi\) | |||||||
\(152\) | −1.37980e121 | −1.11557 | ||||||||
\(153\) | −3.06104e120 | −0.171987 | ||||||||
\(154\) | 3.02608e120 | 0.118435 | ||||||||
\(155\) | −1.05517e121 | −0.288346 | ||||||||
\(156\) | 4.91380e118 | 0.000939728 0 | ||||||||
\(157\) | −4.18640e121 | −0.561578 | −0.280789 | − | 0.959770i | \(-0.590596\pi\) | ||||
−0.280789 | + | 0.959770i | \(0.590596\pi\) | |||||||
\(158\) | 1.32977e122 | 1.25403 | ||||||||
\(159\) | −2.01764e121 | −0.134062 | ||||||||
\(160\) | 3.12732e121 | 0.146728 | ||||||||
\(161\) | −3.37601e121 | −0.112090 | ||||||||
\(162\) | 4.26797e122 | 1.00493 | ||||||||
\(163\) | −2.89307e122 | −0.484113 | −0.242056 | − | 0.970262i | \(-0.577822\pi\) | ||||
−0.242056 | + | 0.970262i | \(0.577822\pi\) | |||||||
\(164\) | 1.38195e122 | 0.164687 | ||||||||
\(165\) | −3.85856e121 | −0.0328145 | ||||||||
\(166\) | 2.20552e123 | 1.34126 | ||||||||
\(167\) | 6.80177e122 | 0.296386 | 0.148193 | − | 0.988958i | \(-0.452654\pi\) | ||||
0.148193 | + | 0.988958i | \(0.452654\pi\) | |||||||
\(168\) | −1.07095e122 | −0.0335047 | ||||||||
\(169\) | −4.41551e123 | −0.993730 | ||||||||
\(170\) | −8.29071e122 | −0.134486 | ||||||||
\(171\) | −9.94841e123 | −1.16539 | ||||||||
\(172\) | 1.69795e123 | 0.143912 | ||||||||
\(173\) | −2.53918e124 | −1.56004 | −0.780019 | − | 0.625756i | \(-0.784790\pi\) | ||||
−0.780019 | + | 0.625756i | \(0.784790\pi\) | |||||||
\(174\) | 1.45732e123 | 0.0650237 | ||||||||
\(175\) | 4.24330e123 | 0.137750 | ||||||||
\(176\) | 1.73612e124 | 0.410796 | ||||||||
\(177\) | 6.55672e123 | 0.113285 | ||||||||
\(178\) | 1.00371e125 | 1.26852 | ||||||||
\(179\) | 8.20957e124 | 0.760287 | 0.380143 | − | 0.924928i | \(-0.375875\pi\) | ||||
0.380143 | + | 0.924928i | \(0.375875\pi\) | |||||||
\(180\) | 1.06796e124 | 0.0725990 | ||||||||
\(181\) | 1.48888e123 | 0.00744215 | 0.00372107 | − | 0.999993i | \(-0.498816\pi\) | ||||
0.00372107 | + | 0.999993i | \(0.498816\pi\) | |||||||
\(182\) | 6.75981e123 | 0.0248870 | ||||||||
\(183\) | 9.92213e122 | 0.00269507 | ||||||||
\(184\) | −1.75889e125 | −0.353061 | ||||||||
\(185\) | −2.88723e124 | −0.0428993 | ||||||||
\(186\) | −4.42498e124 | −0.0487465 | ||||||||
\(187\) | −8.03500e124 | −0.0657320 | ||||||||
\(188\) | −2.68436e125 | −0.163335 | ||||||||
\(189\) | −1.55531e125 | −0.0704998 | ||||||||
\(190\) | −2.69449e126 | −0.911279 | ||||||||
\(191\) | 5.46909e125 | 0.138218 | 0.0691088 | − | 0.997609i | \(-0.477984\pi\) | ||||
0.0691088 | + | 0.997609i | \(0.477984\pi\) | |||||||
\(192\) | −5.51679e125 | −0.104344 | ||||||||
\(193\) | 2.13477e125 | 0.0302636 | 0.0151318 | − | 0.999886i | \(-0.495183\pi\) | ||||
0.0151318 | + | 0.999886i | \(0.495183\pi\) | |||||||
\(194\) | −9.13971e126 | −0.972605 | ||||||||
\(195\) | −8.61943e124 | −0.00689537 | ||||||||
\(196\) | −1.51395e126 | −0.0911801 | ||||||||
\(197\) | 3.58980e127 | 1.63002 | 0.815012 | − | 0.579444i | \(-0.196730\pi\) | ||||
0.815012 | + | 0.579444i | \(0.196730\pi\) | |||||||
\(198\) | 1.13672e127 | 0.389705 | ||||||||
\(199\) | 3.11191e127 | 0.806644 | 0.403322 | − | 0.915058i | \(-0.367855\pi\) | ||||
0.403322 | + | 0.915058i | \(0.367855\pi\) | |||||||
\(200\) | 2.21075e127 | 0.433886 | ||||||||
\(201\) | 9.24892e126 | 0.137629 | ||||||||
\(202\) | −3.41402e127 | −0.385714 | ||||||||
\(203\) | 1.82544e127 | 0.156797 | ||||||||
\(204\) | −3.16573e125 | −0.00207014 | ||||||||
\(205\) | −2.42412e128 | −1.20841 | ||||||||
\(206\) | −2.47684e128 | −0.942469 | ||||||||
\(207\) | −1.26817e128 | −0.368826 | ||||||||
\(208\) | 3.87822e127 | 0.0863211 | ||||||||
\(209\) | −2.61138e128 | −0.445402 | ||||||||
\(210\) | −2.09137e127 | −0.0273691 | ||||||||
\(211\) | 9.12305e128 | 0.917199 | 0.458600 | − | 0.888643i | \(-0.348351\pi\) | ||||
0.458600 | + | 0.888643i | \(0.348351\pi\) | |||||||
\(212\) | 1.46586e128 | 0.113358 | ||||||||
\(213\) | 3.02384e127 | 0.0180091 | ||||||||
\(214\) | 2.55828e129 | 1.17485 | ||||||||
\(215\) | −2.97842e129 | −1.05597 | ||||||||
\(216\) | −8.10315e128 | −0.222060 | ||||||||
\(217\) | −5.54273e128 | −0.117546 | ||||||||
\(218\) | 1.03724e130 | 1.70428 | ||||||||
\(219\) | −1.02739e129 | −0.130944 | ||||||||
\(220\) | 2.80331e128 | 0.0277468 | ||||||||
\(221\) | −1.79490e128 | −0.0138124 | ||||||||
\(222\) | −1.21079e128 | −0.00725235 | ||||||||
\(223\) | −4.15061e129 | −0.193728 | −0.0968640 | − | 0.995298i | \(-0.530881\pi\) | ||||
−0.0968640 | + | 0.995298i | \(0.530881\pi\) | |||||||
\(224\) | 1.64275e129 | 0.0598147 | ||||||||
\(225\) | 1.59396e130 | 0.453260 | ||||||||
\(226\) | −7.34089e130 | −1.63204 | ||||||||
\(227\) | −6.19188e130 | −1.07743 | −0.538713 | − | 0.842489i | \(-0.681089\pi\) | ||||
−0.538713 | + | 0.842489i | \(0.681089\pi\) | |||||||
\(228\) | −1.02887e129 | −0.0140273 | ||||||||
\(229\) | 2.44280e129 | 0.0261227 | 0.0130614 | − | 0.999915i | \(-0.495842\pi\) | ||||
0.0130614 | + | 0.999915i | \(0.495842\pi\) | |||||||
\(230\) | −3.43478e130 | −0.288406 | ||||||||
\(231\) | −2.02687e129 | −0.0133770 | ||||||||
\(232\) | 9.51049e130 | 0.493878 | ||||||||
\(233\) | 3.22185e131 | 1.31781 | 0.658904 | − | 0.752227i | \(-0.271020\pi\) | ||||
0.658904 | + | 0.752227i | \(0.271020\pi\) | |||||||
\(234\) | 2.53926e130 | 0.0818893 | ||||||||
\(235\) | 4.70872e131 | 1.19850 | ||||||||
\(236\) | −4.76358e130 | −0.0957893 | ||||||||
\(237\) | −8.90677e130 | −0.141640 | ||||||||
\(238\) | −4.35503e130 | −0.0548239 | ||||||||
\(239\) | 3.84696e131 | 0.383737 | 0.191869 | − | 0.981421i | \(-0.438545\pi\) | ||||
0.191869 | + | 0.981421i | \(0.438545\pi\) | |||||||
\(240\) | −1.19985e131 | −0.0949303 | ||||||||
\(241\) | −1.48848e132 | −0.934969 | −0.467485 | − | 0.884001i | \(-0.654840\pi\) | ||||
−0.467485 | + | 0.884001i | \(0.654840\pi\) | |||||||
\(242\) | −1.80290e132 | −0.899950 | ||||||||
\(243\) | −8.78424e131 | −0.348784 | ||||||||
\(244\) | −7.20861e129 | −0.00227885 | ||||||||
\(245\) | 2.65567e132 | 0.669045 | ||||||||
\(246\) | −1.01658e132 | −0.204288 | ||||||||
\(247\) | −5.83343e131 | −0.0935930 | ||||||||
\(248\) | −2.88775e132 | −0.370247 | ||||||||
\(249\) | −1.47725e132 | −0.151492 | ||||||||
\(250\) | 1.37082e133 | 1.12541 | ||||||||
\(251\) | −1.59684e133 | −1.05043 | −0.525217 | − | 0.850968i | \(-0.676016\pi\) | ||||
−0.525217 | + | 0.850968i | \(0.676016\pi\) | |||||||
\(252\) | 5.60989e131 | 0.0295954 | ||||||||
\(253\) | −3.32884e132 | −0.140963 | ||||||||
\(254\) | 3.82535e133 | 1.30137 | ||||||||
\(255\) | 5.55310e131 | 0.0151899 | ||||||||
\(256\) | 1.35196e133 | 0.297608 | ||||||||
\(257\) | 4.64499e133 | 0.823562 | 0.411781 | − | 0.911283i | \(-0.364907\pi\) | ||||
0.411781 | + | 0.911283i | \(0.364907\pi\) | |||||||
\(258\) | −1.24903e133 | −0.178517 | ||||||||
\(259\) | −1.51664e132 | −0.0174882 | ||||||||
\(260\) | 6.26218e131 | 0.00583048 | ||||||||
\(261\) | 6.85709e133 | 0.515931 | ||||||||
\(262\) | −1.25508e134 | −0.763749 | ||||||||
\(263\) | −3.24421e134 | −1.59795 | −0.798977 | − | 0.601361i | \(-0.794625\pi\) | ||||
−0.798977 | + | 0.601361i | \(0.794625\pi\) | |||||||
\(264\) | −1.05599e133 | −0.0421350 | ||||||||
\(265\) | −2.57130e134 | −0.831776 | ||||||||
\(266\) | −1.41539e134 | −0.371488 | ||||||||
\(267\) | −6.72282e133 | −0.143277 | ||||||||
\(268\) | −6.71951e133 | −0.116374 | ||||||||
\(269\) | 1.30498e135 | 1.83803 | 0.919016 | − | 0.394220i | \(-0.128985\pi\) | ||||
0.919016 | + | 0.394220i | \(0.128985\pi\) | |||||||
\(270\) | −1.58239e134 | −0.181395 | ||||||||
\(271\) | 9.74078e134 | 0.909491 | 0.454745 | − | 0.890621i | \(-0.349730\pi\) | ||||
0.454745 | + | 0.890621i | \(0.349730\pi\) | |||||||
\(272\) | −2.49856e134 | −0.190158 | ||||||||
\(273\) | −4.52771e132 | −0.00281094 | ||||||||
\(274\) | 1.39107e135 | 0.705007 | ||||||||
\(275\) | 4.18403e134 | 0.173233 | ||||||||
\(276\) | −1.31154e133 | −0.00443943 | ||||||||
\(277\) | 1.98298e135 | 0.549150 | 0.274575 | − | 0.961566i | \(-0.411463\pi\) | ||||
0.274575 | + | 0.961566i | \(0.411463\pi\) | |||||||
\(278\) | −5.47256e135 | −1.24081 | ||||||||
\(279\) | −2.08208e135 | −0.386780 | ||||||||
\(280\) | −1.36483e135 | −0.207878 | ||||||||
\(281\) | 1.92173e135 | 0.240155 | 0.120077 | − | 0.992765i | \(-0.461686\pi\) | ||||
0.120077 | + | 0.992765i | \(0.461686\pi\) | |||||||
\(282\) | 1.97465e135 | 0.202612 | ||||||||
\(283\) | −7.90343e135 | −0.666298 | −0.333149 | − | 0.942874i | \(-0.608111\pi\) | ||||
−0.333149 | + | 0.942874i | \(0.608111\pi\) | |||||||
\(284\) | −2.19688e134 | −0.0152278 | ||||||||
\(285\) | 1.80476e135 | 0.102927 | ||||||||
\(286\) | 6.66537e134 | 0.0312975 | ||||||||
\(287\) | −1.27337e136 | −0.492617 | ||||||||
\(288\) | 6.17086e135 | 0.196817 | ||||||||
\(289\) | −3.68477e136 | −0.969573 | ||||||||
\(290\) | 1.85722e136 | 0.403435 | ||||||||
\(291\) | 6.12176e135 | 0.109854 | ||||||||
\(292\) | 7.46416e135 | 0.110722 | ||||||||
\(293\) | 1.03292e137 | 1.26740 | 0.633700 | − | 0.773579i | \(-0.281536\pi\) | ||||
0.633700 | + | 0.773579i | \(0.281536\pi\) | |||||||
\(294\) | 1.11368e136 | 0.113106 | ||||||||
\(295\) | 8.35593e136 | 0.702867 | ||||||||
\(296\) | −7.90164e135 | −0.0550842 | ||||||||
\(297\) | −1.53359e136 | −0.0886595 | ||||||||
\(298\) | 1.31283e137 | 0.629804 | ||||||||
\(299\) | −7.43613e135 | −0.0296207 | ||||||||
\(300\) | 1.64848e135 | 0.00545573 | ||||||||
\(301\) | −1.56454e137 | −0.430472 | ||||||||
\(302\) | −7.98482e137 | −1.82759 | ||||||||
\(303\) | 2.28671e136 | 0.0435657 | ||||||||
\(304\) | −8.12034e137 | −1.28852 | ||||||||
\(305\) | 1.26448e136 | 0.0167214 | ||||||||
\(306\) | −1.63593e137 | −0.180395 | ||||||||
\(307\) | 1.30314e138 | 1.19897 | 0.599487 | − | 0.800384i | \(-0.295371\pi\) | ||||
0.599487 | + | 0.800384i | \(0.295371\pi\) | |||||||
\(308\) | 1.47256e136 | 0.0113112 | ||||||||
\(309\) | 1.65898e137 | 0.106450 | ||||||||
\(310\) | −5.63923e137 | −0.302444 | ||||||||
\(311\) | 3.28214e138 | 1.47216 | 0.736082 | − | 0.676892i | \(-0.236674\pi\) | ||||
0.736082 | + | 0.676892i | \(0.236674\pi\) | |||||||
\(312\) | −2.35893e136 | −0.00885389 | ||||||||
\(313\) | 2.85491e138 | 0.897185 | 0.448593 | − | 0.893736i | \(-0.351925\pi\) | ||||
0.448593 | + | 0.893736i | \(0.351925\pi\) | |||||||
\(314\) | −2.23736e138 | −0.589035 | ||||||||
\(315\) | −9.84047e137 | −0.217160 | ||||||||
\(316\) | 6.47093e137 | 0.119766 | ||||||||
\(317\) | 5.52179e137 | 0.0857613 | 0.0428806 | − | 0.999080i | \(-0.486346\pi\) | ||||
0.0428806 | + | 0.999080i | \(0.486346\pi\) | |||||||
\(318\) | −1.07830e138 | −0.140616 | ||||||||
\(319\) | 1.79994e138 | 0.197185 | ||||||||
\(320\) | −7.03063e138 | −0.647397 | ||||||||
\(321\) | −1.71353e138 | −0.132698 | ||||||||
\(322\) | −1.80426e138 | −0.117570 | ||||||||
\(323\) | 3.75821e138 | 0.206177 | ||||||||
\(324\) | 2.07688e138 | 0.0959762 | ||||||||
\(325\) | 9.34647e137 | 0.0364017 | ||||||||
\(326\) | −1.54616e139 | −0.507782 | ||||||||
\(327\) | −6.94739e138 | −0.192496 | ||||||||
\(328\) | −6.63423e139 | −1.55164 | ||||||||
\(329\) | 2.47345e139 | 0.488574 | ||||||||
\(330\) | −2.06215e138 | −0.0344189 | ||||||||
\(331\) | 6.93834e139 | 0.979043 | 0.489521 | − | 0.871991i | \(-0.337172\pi\) | ||||
0.489521 | + | 0.871991i | \(0.337172\pi\) | |||||||
\(332\) | 1.07325e139 | 0.128097 | ||||||||
\(333\) | −5.69711e138 | −0.0575439 | ||||||||
\(334\) | 3.63511e139 | 0.310877 | ||||||||
\(335\) | 1.17869e140 | 0.853910 | ||||||||
\(336\) | −6.30273e138 | −0.0386989 | ||||||||
\(337\) | 3.33481e140 | 1.73625 | 0.868123 | − | 0.496349i | \(-0.165326\pi\) | ||||
0.868123 | + | 0.496349i | \(0.165326\pi\) | |||||||
\(338\) | −2.35980e140 | −1.04232 | ||||||||
\(339\) | 4.91692e139 | 0.184336 | ||||||||
\(340\) | −4.03443e138 | −0.0128441 | ||||||||
\(341\) | −5.46530e139 | −0.147824 | ||||||||
\(342\) | −5.31679e140 | −1.22236 | ||||||||
\(343\) | 2.92760e140 | 0.572385 | ||||||||
\(344\) | −8.15120e140 | −1.35590 | ||||||||
\(345\) | 2.30061e139 | 0.0325749 | ||||||||
\(346\) | −1.35703e141 | −1.63631 | ||||||||
\(347\) | −6.95029e139 | −0.0714031 | −0.0357016 | − | 0.999362i | \(-0.511367\pi\) | ||||
−0.0357016 | + | 0.999362i | \(0.511367\pi\) | |||||||
\(348\) | 7.09162e138 | 0.00621008 | ||||||||
\(349\) | 2.64284e141 | 1.97360 | 0.986801 | − | 0.161940i | \(-0.0517751\pi\) | ||||
0.986801 | + | 0.161940i | \(0.0517751\pi\) | |||||||
\(350\) | 2.26777e140 | 0.144485 | ||||||||
\(351\) | −3.42580e139 | −0.0186302 | ||||||||
\(352\) | 1.61981e140 | 0.0752220 | ||||||||
\(353\) | 1.11293e141 | 0.441543 | 0.220771 | − | 0.975326i | \(-0.429143\pi\) | ||||
0.220771 | + | 0.975326i | \(0.429143\pi\) | |||||||
\(354\) | 3.50415e140 | 0.118823 | ||||||||
\(355\) | 3.85360e140 | 0.111736 | ||||||||
\(356\) | 4.88425e140 | 0.121150 | ||||||||
\(357\) | 2.91699e139 | 0.00619227 | ||||||||
\(358\) | 4.38749e141 | 0.797458 | ||||||||
\(359\) | −4.88931e141 | −0.761212 | −0.380606 | − | 0.924737i | \(-0.624285\pi\) | ||||
−0.380606 | + | 0.924737i | \(0.624285\pi\) | |||||||
\(360\) | −5.12686e141 | −0.684011 | ||||||||
\(361\) | 3.47144e141 | 0.397064 | ||||||||
\(362\) | 7.95710e139 | 0.00780601 | ||||||||
\(363\) | 1.20758e141 | 0.101648 | ||||||||
\(364\) | 3.28946e139 | 0.00237683 | ||||||||
\(365\) | −1.30931e142 | −0.812435 | ||||||||
\(366\) | 5.30274e139 | 0.00282683 | ||||||||
\(367\) | 2.44261e142 | 1.11915 | 0.559575 | − | 0.828780i | \(-0.310965\pi\) | ||||
0.559575 | + | 0.828780i | \(0.310965\pi\) | |||||||
\(368\) | −1.03513e142 | −0.407796 | ||||||||
\(369\) | −4.78330e142 | −1.62093 | ||||||||
\(370\) | −1.54304e141 | −0.0449968 | ||||||||
\(371\) | −1.35068e142 | −0.339079 | ||||||||
\(372\) | −2.15329e140 | −0.00465553 | ||||||||
\(373\) | 3.20357e142 | 0.596752 | 0.298376 | − | 0.954448i | \(-0.403555\pi\) | ||||
0.298376 | + | 0.954448i | \(0.403555\pi\) | |||||||
\(374\) | −4.29419e141 | −0.0689458 | ||||||||
\(375\) | −9.18175e141 | −0.127113 | ||||||||
\(376\) | 1.28866e143 | 1.53891 | ||||||||
\(377\) | 4.02078e141 | 0.0414348 | ||||||||
\(378\) | −8.31216e141 | −0.0739467 | ||||||||
\(379\) | 2.06241e143 | 1.58452 | 0.792262 | − | 0.610181i | \(-0.208903\pi\) | ||||
0.792262 | + | 0.610181i | \(0.208903\pi\) | |||||||
\(380\) | −1.31119e142 | −0.0870317 | ||||||||
\(381\) | −2.56221e142 | −0.146987 | ||||||||
\(382\) | 2.92288e142 | 0.144975 | ||||||||
\(383\) | −2.12876e143 | −0.913263 | −0.456631 | − | 0.889656i | \(-0.650944\pi\) | ||||
−0.456631 | + | 0.889656i | \(0.650944\pi\) | |||||||
\(384\) | −3.58545e142 | −0.133095 | ||||||||
\(385\) | −2.58305e142 | −0.0829970 | ||||||||
\(386\) | 1.14090e142 | 0.0317432 | ||||||||
\(387\) | −5.87704e143 | −1.41645 | ||||||||
\(388\) | −4.44757e142 | −0.0928886 | ||||||||
\(389\) | −6.73075e143 | −1.21860 | −0.609299 | − | 0.792941i | \(-0.708549\pi\) | ||||
−0.609299 | + | 0.792941i | \(0.708549\pi\) | |||||||
\(390\) | −4.60653e141 | −0.00723250 | ||||||||
\(391\) | 4.79075e142 | 0.0652520 | ||||||||
\(392\) | 7.26790e143 | 0.859077 | ||||||||
\(393\) | 8.40652e142 | 0.0862640 | ||||||||
\(394\) | 1.91851e144 | 1.70972 | ||||||||
\(395\) | −1.13509e144 | −0.878799 | ||||||||
\(396\) | 5.53152e142 | 0.0372188 | ||||||||
\(397\) | −1.28955e143 | −0.0754338 | −0.0377169 | − | 0.999288i | \(-0.512009\pi\) | ||||
−0.0377169 | + | 0.999288i | \(0.512009\pi\) | |||||||
\(398\) | 1.66312e144 | 0.846083 | ||||||||
\(399\) | 9.48026e142 | 0.0419589 | ||||||||
\(400\) | 1.30106e144 | 0.501151 | ||||||||
\(401\) | −1.49726e144 | −0.502094 | −0.251047 | − | 0.967975i | \(-0.580775\pi\) | ||||
−0.251047 | + | 0.967975i | \(0.580775\pi\) | |||||||
\(402\) | 4.94295e143 | 0.144358 | ||||||||
\(403\) | −1.22086e143 | −0.0310626 | ||||||||
\(404\) | −1.66133e143 | −0.0368376 | ||||||||
\(405\) | −3.64312e144 | −0.704238 | ||||||||
\(406\) | 9.75579e143 | 0.164463 | ||||||||
\(407\) | −1.49545e143 | −0.0219929 | ||||||||
\(408\) | 1.51975e143 | 0.0195044 | ||||||||
\(409\) | 7.55497e144 | 0.846426 | 0.423213 | − | 0.906030i | \(-0.360902\pi\) | ||||
0.423213 | + | 0.906030i | \(0.360902\pi\) | |||||||
\(410\) | −1.29554e145 | −1.26749 | ||||||||
\(411\) | −9.31738e143 | −0.0796293 | ||||||||
\(412\) | −1.20528e144 | −0.0900105 | ||||||||
\(413\) | 4.38929e144 | 0.286528 | ||||||||
\(414\) | −6.77753e144 | −0.386859 | ||||||||
\(415\) | −1.88262e145 | −0.939925 | ||||||||
\(416\) | 3.61840e143 | 0.0158065 | ||||||||
\(417\) | 3.66551e144 | 0.140147 | ||||||||
\(418\) | −1.39562e145 | −0.467178 | ||||||||
\(419\) | 2.30213e145 | 0.674919 | 0.337460 | − | 0.941340i | \(-0.390432\pi\) | ||||
0.337460 | + | 0.941340i | \(0.390432\pi\) | |||||||
\(420\) | −1.01770e143 | −0.00261388 | ||||||||
\(421\) | 4.33827e145 | 0.976472 | 0.488236 | − | 0.872712i | \(-0.337640\pi\) | ||||
0.488236 | + | 0.872712i | \(0.337640\pi\) | |||||||
\(422\) | 4.87568e145 | 0.962043 | ||||||||
\(423\) | 9.29128e145 | 1.60763 | ||||||||
\(424\) | −7.03701e145 | −1.06803 | ||||||||
\(425\) | −6.02150e144 | −0.0801898 | ||||||||
\(426\) | 1.61605e144 | 0.0188896 | ||||||||
\(427\) | 6.64221e143 | 0.00681657 | ||||||||
\(428\) | 1.24491e145 | 0.112204 | ||||||||
\(429\) | −4.46446e143 | −0.00353500 | ||||||||
\(430\) | −1.59177e146 | −1.10760 | ||||||||
\(431\) | −4.36552e145 | −0.267022 | −0.133511 | − | 0.991047i | \(-0.542625\pi\) | ||||
−0.133511 | + | 0.991047i | \(0.542625\pi\) | |||||||
\(432\) | −4.76883e145 | −0.256486 | ||||||||
\(433\) | −2.99169e146 | −1.41527 | −0.707633 | − | 0.706580i | \(-0.750237\pi\) | ||||
−0.707633 | + | 0.706580i | \(0.750237\pi\) | |||||||
\(434\) | −2.96223e145 | −0.123293 | ||||||||
\(435\) | −1.24396e145 | −0.0455673 | ||||||||
\(436\) | 5.04740e145 | 0.162768 | ||||||||
\(437\) | 1.55700e146 | 0.442149 | ||||||||
\(438\) | −5.49073e145 | −0.137346 | ||||||||
\(439\) | 3.63494e146 | 0.801154 | 0.400577 | − | 0.916263i | \(-0.368810\pi\) | ||||
0.400577 | + | 0.916263i | \(0.368810\pi\) | |||||||
\(440\) | −1.34576e146 | −0.261424 | ||||||||
\(441\) | 5.24018e146 | 0.897438 | ||||||||
\(442\) | −9.59257e144 | −0.0144877 | ||||||||
\(443\) | 9.45240e146 | 1.25932 | 0.629659 | − | 0.776872i | \(-0.283195\pi\) | ||||
0.629659 | + | 0.776872i | \(0.283195\pi\) | |||||||
\(444\) | −5.89196e143 | −0.000692636 0 | ||||||||
\(445\) | −8.56761e146 | −0.888953 | ||||||||
\(446\) | −2.21824e146 | −0.203200 | ||||||||
\(447\) | −8.79330e145 | −0.0711352 | ||||||||
\(448\) | −3.69313e146 | −0.263915 | ||||||||
\(449\) | 1.39885e147 | 0.883283 | 0.441641 | − | 0.897192i | \(-0.354396\pi\) | ||||
0.441641 | + | 0.897192i | \(0.354396\pi\) | |||||||
\(450\) | 8.51869e146 | 0.475421 | ||||||||
\(451\) | −1.25558e147 | −0.619507 | ||||||||
\(452\) | −3.57223e146 | −0.155868 | ||||||||
\(453\) | 5.34822e146 | 0.206423 | ||||||||
\(454\) | −3.30916e147 | −1.13010 | ||||||||
\(455\) | −5.77014e145 | −0.0174403 | ||||||||
\(456\) | 4.93919e146 | 0.132162 | ||||||||
\(457\) | 4.78656e146 | 0.113416 | 0.0567080 | − | 0.998391i | \(-0.481940\pi\) | ||||
0.0567080 | + | 0.998391i | \(0.481940\pi\) | |||||||
\(458\) | 1.30552e146 | 0.0273999 | ||||||||
\(459\) | 2.20708e146 | 0.0410407 | ||||||||
\(460\) | −1.67144e146 | −0.0275442 | ||||||||
\(461\) | −7.78882e147 | −1.13781 | −0.568906 | − | 0.822403i | \(-0.692633\pi\) | ||||
−0.568906 | + | 0.822403i | \(0.692633\pi\) | |||||||
\(462\) | −1.08323e146 | −0.0140311 | ||||||||
\(463\) | −5.98097e147 | −0.687111 | −0.343555 | − | 0.939132i | \(-0.611631\pi\) | ||||
−0.343555 | + | 0.939132i | \(0.611631\pi\) | |||||||
\(464\) | 5.59707e147 | 0.570444 | ||||||||
\(465\) | 3.77714e146 | 0.0341605 | ||||||||
\(466\) | 1.72187e148 | 1.38224 | ||||||||
\(467\) | −3.42519e147 | −0.244117 | −0.122058 | − | 0.992523i | \(-0.538950\pi\) | ||||
−0.122058 | + | 0.992523i | \(0.538950\pi\) | |||||||
\(468\) | 1.23566e146 | 0.00782084 | ||||||||
\(469\) | 6.19154e147 | 0.348102 | ||||||||
\(470\) | 2.51651e148 | 1.25709 | ||||||||
\(471\) | 1.49858e147 | 0.0665304 | ||||||||
\(472\) | 2.28681e148 | 0.902505 | ||||||||
\(473\) | −1.54268e148 | −0.541356 | ||||||||
\(474\) | −4.76010e147 | −0.148566 | ||||||||
\(475\) | −1.95699e148 | −0.543368 | ||||||||
\(476\) | −2.11925e146 | −0.00523596 | ||||||||
\(477\) | −5.07371e148 | −1.11572 | ||||||||
\(478\) | 2.05595e148 | 0.402499 | ||||||||
\(479\) | −7.68061e148 | −1.33898 | −0.669491 | − | 0.742820i | \(-0.733488\pi\) | ||||
−0.669491 | + | 0.742820i | \(0.733488\pi\) | |||||||
\(480\) | −1.11947e147 | −0.0173830 | ||||||||
\(481\) | −3.34060e146 | −0.00462139 | ||||||||
\(482\) | −7.95497e148 | −0.980682 | ||||||||
\(483\) | 1.20849e147 | 0.0132794 | ||||||||
\(484\) | −8.77328e147 | −0.0859497 | ||||||||
\(485\) | 7.80162e148 | 0.681582 | ||||||||
\(486\) | −4.69461e148 | −0.365836 | ||||||||
\(487\) | 2.59840e149 | 1.80655 | 0.903273 | − | 0.429066i | \(-0.141157\pi\) | ||||
0.903273 | + | 0.429066i | \(0.141157\pi\) | |||||||
\(488\) | 3.46058e147 | 0.0214708 | ||||||||
\(489\) | 1.03561e148 | 0.0573531 | ||||||||
\(490\) | 1.41928e149 | 0.701756 | ||||||||
\(491\) | 3.04588e148 | 0.134490 | 0.0672449 | − | 0.997736i | \(-0.478579\pi\) | ||||
0.0672449 | + | 0.997736i | \(0.478579\pi\) | |||||||
\(492\) | −4.94690e147 | −0.0195106 | ||||||||
\(493\) | −2.59041e148 | −0.0912775 | ||||||||
\(494\) | −3.11759e148 | −0.0981689 | ||||||||
\(495\) | −9.70300e148 | −0.273097 | ||||||||
\(496\) | −1.69948e149 | −0.427646 | ||||||||
\(497\) | 2.02426e148 | 0.0455499 | ||||||||
\(498\) | −7.89496e148 | −0.158899 | ||||||||
\(499\) | 4.92976e149 | 0.887658 | 0.443829 | − | 0.896111i | \(-0.353620\pi\) | ||||
0.443829 | + | 0.896111i | \(0.353620\pi\) | |||||||
\(500\) | 6.67071e148 | 0.107482 | ||||||||
\(501\) | −2.43479e148 | −0.0351130 | ||||||||
\(502\) | −8.53407e149 | −1.10179 | ||||||||
\(503\) | −1.94182e149 | −0.224484 | −0.112242 | − | 0.993681i | \(-0.535803\pi\) | ||||
−0.112242 | + | 0.993681i | \(0.535803\pi\) | |||||||
\(504\) | −2.69309e149 | −0.278841 | ||||||||
\(505\) | 2.91419e149 | 0.270301 | ||||||||
\(506\) | −1.77905e149 | −0.147855 | ||||||||
\(507\) | 1.58059e149 | 0.117728 | ||||||||
\(508\) | 1.86150e149 | 0.124287 | ||||||||
\(509\) | −7.85118e149 | −0.470000 | −0.235000 | − | 0.971995i | \(-0.575509\pi\) | ||||
−0.235000 | + | 0.971995i | \(0.575509\pi\) | |||||||
\(510\) | 2.96778e148 | 0.0159326 | ||||||||
\(511\) | −6.87769e149 | −0.331194 | ||||||||
\(512\) | −1.87783e150 | −0.811283 | ||||||||
\(513\) | 7.17304e149 | 0.278093 | ||||||||
\(514\) | 2.48245e150 | 0.863828 | ||||||||
\(515\) | 2.11422e150 | 0.660464 | ||||||||
\(516\) | −6.07805e148 | −0.0170493 | ||||||||
\(517\) | 2.43889e150 | 0.614423 | ||||||||
\(518\) | −8.10544e148 | −0.0183432 | ||||||||
\(519\) | 9.08936e149 | 0.184818 | ||||||||
\(520\) | −3.00623e149 | −0.0549334 | ||||||||
\(521\) | 1.11447e151 | 1.83052 | 0.915261 | − | 0.402861i | \(-0.131984\pi\) | ||||
0.915261 | + | 0.402861i | \(0.131984\pi\) | |||||||
\(522\) | 3.66468e150 | 0.541156 | ||||||||
\(523\) | −1.20337e151 | −1.59793 | −0.798964 | − | 0.601379i | \(-0.794618\pi\) | ||||
−0.798964 | + | 0.601379i | \(0.794618\pi\) | |||||||
\(524\) | −6.10749e149 | −0.0729418 | ||||||||
\(525\) | −1.51895e149 | −0.0163193 | ||||||||
\(526\) | −1.73382e151 | −1.67608 | ||||||||
\(527\) | 7.86546e149 | 0.0684282 | ||||||||
\(528\) | −6.21468e149 | −0.0486671 | ||||||||
\(529\) | −1.21989e151 | −0.860067 | ||||||||
\(530\) | −1.37419e151 | −0.872444 | ||||||||
\(531\) | 1.64880e151 | 0.942805 | ||||||||
\(532\) | −6.88758e149 | −0.0354790 | ||||||||
\(533\) | −2.80477e150 | −0.130178 | ||||||||
\(534\) | −3.59292e150 | −0.150282 | ||||||||
\(535\) | −2.18374e151 | −0.823314 | ||||||||
\(536\) | 3.22578e151 | 1.09645 | ||||||||
\(537\) | −2.93873e150 | −0.0900715 | ||||||||
\(538\) | 6.97429e151 | 1.92790 | ||||||||
\(539\) | 1.37551e151 | 0.342994 | ||||||||
\(540\) | −7.70025e149 | −0.0173241 | ||||||||
\(541\) | −1.79940e151 | −0.365324 | −0.182662 | − | 0.983176i | \(-0.558471\pi\) | ||||
−0.182662 | + | 0.983176i | \(0.558471\pi\) | |||||||
\(542\) | 5.20582e151 | 0.953958 | ||||||||
\(543\) | −5.32965e148 | −0.000881675 0 | ||||||||
\(544\) | −2.33117e150 | −0.0348205 | ||||||||
\(545\) | −8.85380e151 | −1.19433 | ||||||||
\(546\) | −2.41977e149 | −0.00294837 | ||||||||
\(547\) | −1.89946e151 | −0.209090 | −0.104545 | − | 0.994520i | \(-0.533339\pi\) | ||||
−0.104545 | + | 0.994520i | \(0.533339\pi\) | |||||||
\(548\) | 6.76925e150 | 0.0673317 | ||||||||
\(549\) | 2.49509e150 | 0.0224296 | ||||||||
\(550\) | 2.23609e151 | 0.181702 | ||||||||
\(551\) | −8.41884e151 | −0.618499 | ||||||||
\(552\) | 6.29620e150 | 0.0418273 | ||||||||
\(553\) | −5.96250e151 | −0.358248 | ||||||||
\(554\) | 1.05977e152 | 0.575999 | ||||||||
\(555\) | 1.03353e150 | 0.00508230 | ||||||||
\(556\) | −2.66306e151 | −0.118503 | ||||||||
\(557\) | −9.27529e151 | −0.373563 | −0.186782 | − | 0.982401i | \(-0.559806\pi\) | ||||
−0.186782 | + | 0.982401i | \(0.559806\pi\) | |||||||
\(558\) | −1.11274e152 | −0.405690 | ||||||||
\(559\) | −3.44611e151 | −0.113756 | ||||||||
\(560\) | −8.03224e151 | −0.240105 | ||||||||
\(561\) | 2.87624e150 | 0.00778730 | ||||||||
\(562\) | 1.02704e152 | 0.251897 | ||||||||
\(563\) | 5.77012e151 | 0.128224 | 0.0641119 | − | 0.997943i | \(-0.479579\pi\) | ||||
0.0641119 | + | 0.997943i | \(0.479579\pi\) | |||||||
\(564\) | 9.60906e150 | 0.0193504 | ||||||||
\(565\) | 6.26615e152 | 1.14370 | ||||||||
\(566\) | −4.22387e152 | −0.698874 | ||||||||
\(567\) | −1.91370e152 | −0.287087 | ||||||||
\(568\) | 1.05464e152 | 0.143473 | ||||||||
\(569\) | 8.15675e152 | 1.00644 | 0.503218 | − | 0.864159i | \(-0.332149\pi\) | ||||
0.503218 | + | 0.864159i | \(0.332149\pi\) | |||||||
\(570\) | 9.64531e151 | 0.107960 | ||||||||
\(571\) | 1.62614e153 | 1.65141 | 0.825703 | − | 0.564106i | \(-0.190779\pi\) | ||||
0.825703 | + | 0.564106i | \(0.190779\pi\) | |||||||
\(572\) | 3.24351e150 | 0.00298907 | ||||||||
\(573\) | −1.95774e151 | −0.0163747 | ||||||||
\(574\) | −6.80534e152 | −0.516702 | ||||||||
\(575\) | −2.49466e152 | −0.171968 | ||||||||
\(576\) | −1.38729e153 | −0.868399 | ||||||||
\(577\) | −8.44089e152 | −0.479878 | −0.239939 | − | 0.970788i | \(-0.577127\pi\) | ||||
−0.239939 | + | 0.970788i | \(0.577127\pi\) | |||||||
\(578\) | −1.96927e153 | −1.01698 | ||||||||
\(579\) | −7.64172e150 | −0.00358534 | ||||||||
\(580\) | 9.03761e151 | 0.0385301 | ||||||||
\(581\) | −9.88923e152 | −0.383166 | ||||||||
\(582\) | 3.27169e152 | 0.115225 | ||||||||
\(583\) | −1.33181e153 | −0.426420 | ||||||||
\(584\) | −3.58326e153 | −1.04319 | ||||||||
\(585\) | −2.16750e152 | −0.0573864 | ||||||||
\(586\) | 5.52029e153 | 1.32937 | ||||||||
\(587\) | 2.52144e153 | 0.552374 | 0.276187 | − | 0.961104i | \(-0.410929\pi\) | ||||
0.276187 | + | 0.961104i | \(0.410929\pi\) | |||||||
\(588\) | 5.41940e151 | 0.0108021 | ||||||||
\(589\) | 2.55628e153 | 0.463671 | ||||||||
\(590\) | 4.46571e153 | 0.737231 | ||||||||
\(591\) | −1.28502e153 | −0.193110 | ||||||||
\(592\) | −4.65023e152 | −0.0636239 | ||||||||
\(593\) | 9.68298e153 | 1.20635 | 0.603176 | − | 0.797608i | \(-0.293902\pi\) | ||||
0.603176 | + | 0.797608i | \(0.293902\pi\) | |||||||
\(594\) | −8.19603e152 | −0.0929942 | ||||||||
\(595\) | 3.71744e152 | 0.0384195 | ||||||||
\(596\) | 6.38850e152 | 0.0601494 | ||||||||
\(597\) | −1.11395e153 | −0.0955635 | ||||||||
\(598\) | −3.97413e152 | −0.0310689 | ||||||||
\(599\) | −9.77515e153 | −0.696522 | −0.348261 | − | 0.937398i | \(-0.613228\pi\) | ||||
−0.348261 | + | 0.937398i | \(0.613228\pi\) | |||||||
\(600\) | −7.91370e152 | −0.0514026 | ||||||||
\(601\) | −2.68769e154 | −1.59164 | −0.795822 | − | 0.605531i | \(-0.792961\pi\) | ||||
−0.795822 | + | 0.605531i | \(0.792961\pi\) | |||||||
\(602\) | −8.36145e153 | −0.451519 | ||||||||
\(603\) | 2.32580e154 | 1.14541 | ||||||||
\(604\) | −3.88558e153 | −0.174544 | ||||||||
\(605\) | 1.53895e154 | 0.630667 | ||||||||
\(606\) | 1.22210e153 | 0.0456957 | ||||||||
\(607\) | −1.85080e154 | −0.631519 | −0.315759 | − | 0.948839i | \(-0.602259\pi\) | ||||
−0.315759 | + | 0.948839i | \(0.602259\pi\) | |||||||
\(608\) | −7.57632e153 | −0.235944 | ||||||||
\(609\) | −6.53442e152 | −0.0185758 | ||||||||
\(610\) | 6.75785e152 | 0.0175389 | ||||||||
\(611\) | 5.44811e153 | 0.129110 | ||||||||
\(612\) | −7.96077e152 | −0.0172287 | ||||||||
\(613\) | −6.56124e154 | −1.29697 | −0.648484 | − | 0.761228i | \(-0.724597\pi\) | ||||
−0.648484 | + | 0.761228i | \(0.724597\pi\) | |||||||
\(614\) | 6.96443e154 | 1.25760 | ||||||||
\(615\) | 8.67749e153 | 0.143161 | ||||||||
\(616\) | −7.06917e153 | −0.106571 | ||||||||
\(617\) | 1.91681e154 | 0.264090 | 0.132045 | − | 0.991244i | \(-0.457846\pi\) | ||||
0.132045 | + | 0.991244i | \(0.457846\pi\) | |||||||
\(618\) | 8.86620e153 | 0.111655 | ||||||||
\(619\) | −3.47345e153 | −0.0399880 | −0.0199940 | − | 0.999800i | \(-0.506365\pi\) | ||||
−0.0199940 | + | 0.999800i | \(0.506365\pi\) | |||||||
\(620\) | −2.74417e153 | −0.0288849 | ||||||||
\(621\) | 9.14379e153 | 0.0880121 | ||||||||
\(622\) | 1.75410e155 | 1.54414 | ||||||||
\(623\) | −4.50049e154 | −0.362387 | ||||||||
\(624\) | −1.38826e153 | −0.0102265 | ||||||||
\(625\) | −4.88061e154 | −0.328952 | ||||||||
\(626\) | 1.52577e155 | 0.941051 | ||||||||
\(627\) | 9.34782e153 | 0.0527669 | ||||||||
\(628\) | −1.08875e154 | −0.0562557 | ||||||||
\(629\) | 2.15220e153 | 0.0101805 | ||||||||
\(630\) | −5.25910e154 | −0.227778 | ||||||||
\(631\) | −3.38805e155 | −1.34375 | −0.671877 | − | 0.740662i | \(-0.734512\pi\) | ||||
−0.671877 | + | 0.740662i | \(0.734512\pi\) | |||||||
\(632\) | −3.10645e155 | −1.12841 | ||||||||
\(633\) | −3.26573e154 | −0.108661 | ||||||||
\(634\) | 2.95104e154 | 0.0899543 | ||||||||
\(635\) | −3.26530e155 | −0.911972 | ||||||||
\(636\) | −5.24724e153 | −0.0134295 | ||||||||
\(637\) | 3.07268e154 | 0.0720739 | ||||||||
\(638\) | 9.61950e154 | 0.206826 | ||||||||
\(639\) | 7.60396e154 | 0.149880 | ||||||||
\(640\) | −4.56932e155 | −0.825778 | ||||||||
\(641\) | 1.01586e156 | 1.68350 | 0.841749 | − | 0.539869i | \(-0.181526\pi\) | ||||
0.841749 | + | 0.539869i | \(0.181526\pi\) | |||||||
\(642\) | −9.15773e154 | −0.139185 | ||||||||
\(643\) | 1.24375e156 | 1.73390 | 0.866950 | − | 0.498396i | \(-0.166077\pi\) | ||||
0.866950 | + | 0.498396i | \(0.166077\pi\) | |||||||
\(644\) | −8.77990e153 | −0.0112286 | ||||||||
\(645\) | 1.06617e155 | 0.125101 | ||||||||
\(646\) | 2.00852e155 | 0.216258 | ||||||||
\(647\) | 4.94606e155 | 0.488734 | 0.244367 | − | 0.969683i | \(-0.421420\pi\) | ||||
0.244367 | + | 0.969683i | \(0.421420\pi\) | |||||||
\(648\) | −9.97031e155 | −0.904266 | ||||||||
\(649\) | 4.32798e155 | 0.360333 | ||||||||
\(650\) | 4.99509e154 | 0.0381814 | ||||||||
\(651\) | 1.98410e154 | 0.0139257 | ||||||||
\(652\) | −7.52393e154 | −0.0484957 | ||||||||
\(653\) | −4.28612e155 | −0.253736 | −0.126868 | − | 0.991920i | \(-0.540493\pi\) | ||||
−0.126868 | + | 0.991920i | \(0.540493\pi\) | |||||||
\(654\) | −3.71293e155 | −0.201907 | ||||||||
\(655\) | 1.07133e156 | 0.535220 | ||||||||
\(656\) | −3.90434e156 | −1.79219 | ||||||||
\(657\) | −2.58354e156 | −1.08978 | ||||||||
\(658\) | 1.32190e156 | 0.512461 | ||||||||
\(659\) | −5.85902e155 | −0.208778 | −0.104389 | − | 0.994537i | \(-0.533289\pi\) | ||||
−0.104389 | + | 0.994537i | \(0.533289\pi\) | |||||||
\(660\) | −1.00349e154 | −0.00328718 | ||||||||
\(661\) | 2.07235e156 | 0.624142 | 0.312071 | − | 0.950059i | \(-0.398977\pi\) | ||||
0.312071 | + | 0.950059i | \(0.398977\pi\) | |||||||
\(662\) | 3.70809e156 | 1.02691 | ||||||||
\(663\) | 6.42509e153 | 0.00163636 | ||||||||
\(664\) | −5.15226e156 | −1.20690 | ||||||||
\(665\) | 1.20817e156 | 0.260332 | ||||||||
\(666\) | −3.04474e155 | −0.0603573 | ||||||||
\(667\) | −1.07319e156 | −0.195745 | ||||||||
\(668\) | 1.76892e155 | 0.0296903 | ||||||||
\(669\) | 1.48577e155 | 0.0229510 | ||||||||
\(670\) | 6.29933e156 | 0.895659 | ||||||||
\(671\) | 6.54942e154 | 0.00857241 | ||||||||
\(672\) | −5.88048e154 | −0.00708627 | ||||||||
\(673\) | −1.13628e157 | −1.26081 | −0.630406 | − | 0.776266i | \(-0.717111\pi\) | ||||
−0.630406 | + | 0.776266i | \(0.717111\pi\) | |||||||
\(674\) | 1.78224e157 | 1.82114 | ||||||||
\(675\) | −1.14928e156 | −0.108160 | ||||||||
\(676\) | −1.14833e156 | −0.0995463 | ||||||||
\(677\) | 2.68359e156 | 0.214311 | 0.107155 | − | 0.994242i | \(-0.465826\pi\) | ||||
0.107155 | + | 0.994242i | \(0.465826\pi\) | |||||||
\(678\) | 2.62778e156 | 0.193348 | ||||||||
\(679\) | 4.09812e156 | 0.277851 | ||||||||
\(680\) | 1.93678e156 | 0.121014 | ||||||||
\(681\) | 2.21647e156 | 0.127643 | ||||||||
\(682\) | −2.92085e156 | −0.155052 | ||||||||
\(683\) | −7.20565e156 | −0.352634 | −0.176317 | − | 0.984333i | \(-0.556418\pi\) | ||||
−0.176317 | + | 0.984333i | \(0.556418\pi\) | |||||||
\(684\) | −2.58726e156 | −0.116742 | ||||||||
\(685\) | −1.18741e157 | −0.494055 | ||||||||
\(686\) | 1.56461e157 | 0.600370 | ||||||||
\(687\) | −8.74435e154 | −0.00309477 | ||||||||
\(688\) | −4.79711e157 | −1.56611 | ||||||||
\(689\) | −2.97506e156 | −0.0896044 | ||||||||
\(690\) | 1.22953e156 | 0.0341676 | ||||||||
\(691\) | −5.23321e157 | −1.34195 | −0.670975 | − | 0.741480i | \(-0.734124\pi\) | ||||
−0.670975 | + | 0.741480i | \(0.734124\pi\) | |||||||
\(692\) | −6.60359e156 | −0.156276 | ||||||||
\(693\) | −5.09690e156 | −0.111330 | ||||||||
\(694\) | −3.71448e156 | −0.0748942 | ||||||||
\(695\) | 4.67135e157 | 0.869533 | ||||||||
\(696\) | −3.40442e156 | −0.0585100 | ||||||||
\(697\) | 1.80699e157 | 0.286771 | ||||||||
\(698\) | 1.41243e158 | 2.07009 | ||||||||
\(699\) | −1.15331e157 | −0.156121 | ||||||||
\(700\) | 1.10355e156 | 0.0137991 | ||||||||
\(701\) | 8.30755e157 | 0.959673 | 0.479836 | − | 0.877358i | \(-0.340696\pi\) | ||||
0.479836 | + | 0.877358i | \(0.340696\pi\) | |||||||
\(702\) | −1.83087e156 | −0.0195410 | ||||||||
\(703\) | 6.99466e156 | 0.0689836 | ||||||||
\(704\) | −3.64153e157 | −0.331896 | ||||||||
\(705\) | −1.68555e157 | −0.141986 | ||||||||
\(706\) | 5.94791e157 | 0.463131 | ||||||||
\(707\) | 1.53080e157 | 0.110190 | ||||||||
\(708\) | 1.70519e156 | 0.0113482 | ||||||||
\(709\) | −1.08796e158 | −0.669494 | −0.334747 | − | 0.942308i | \(-0.608651\pi\) | ||||
−0.334747 | + | 0.942308i | \(0.608651\pi\) | |||||||
\(710\) | 2.05950e157 | 0.117199 | ||||||||
\(711\) | −2.23976e158 | −1.17880 | ||||||||
\(712\) | −2.34474e158 | −1.14145 | ||||||||
\(713\) | 3.25860e157 | 0.146745 | ||||||||
\(714\) | 1.55895e156 | 0.00649502 | ||||||||
\(715\) | −5.68953e156 | −0.0219327 | ||||||||
\(716\) | 2.13504e157 | 0.0761613 | ||||||||
\(717\) | −1.37707e157 | −0.0454615 | ||||||||
\(718\) | −2.61302e158 | −0.798429 | ||||||||
\(719\) | 5.50384e158 | 1.55673 | 0.778363 | − | 0.627814i | \(-0.216050\pi\) | ||||
0.778363 | + | 0.627814i | \(0.216050\pi\) | |||||||
\(720\) | −3.01724e158 | −0.790053 | ||||||||
\(721\) | 1.11058e158 | 0.269242 | ||||||||
\(722\) | 1.85526e158 | 0.416477 | ||||||||
\(723\) | 5.32823e157 | 0.110766 | ||||||||
\(724\) | 3.87209e155 | 0.000745513 0 | ||||||||
\(725\) | 1.34889e158 | 0.240556 | ||||||||
\(726\) | 6.45373e157 | 0.106617 | ||||||||
\(727\) | 4.79637e158 | 0.734096 | 0.367048 | − | 0.930202i | \(-0.380368\pi\) | ||||
0.367048 | + | 0.930202i | \(0.380368\pi\) | |||||||
\(728\) | −1.57915e157 | −0.0223939 | ||||||||
\(729\) | −6.97652e158 | −0.916771 | ||||||||
\(730\) | −6.99742e158 | −0.852156 | ||||||||
\(731\) | 2.22017e158 | 0.250595 | ||||||||
\(732\) | 2.58042e155 | 0.000269977 0 | ||||||||
\(733\) | 1.24852e159 | 1.21094 | 0.605471 | − | 0.795867i | \(-0.292985\pi\) | ||||
0.605471 | + | 0.795867i | \(0.292985\pi\) | |||||||
\(734\) | 1.30542e159 | 1.17387 | ||||||||
\(735\) | −9.50633e157 | −0.0792621 | ||||||||
\(736\) | −9.65785e157 | −0.0746727 | ||||||||
\(737\) | 6.10505e158 | 0.437767 | ||||||||
\(738\) | −2.55637e159 | −1.70018 | ||||||||
\(739\) | 6.30540e158 | 0.388997 | 0.194498 | − | 0.980903i | \(-0.437692\pi\) | ||||
0.194498 | + | 0.980903i | \(0.437692\pi\) | |||||||
\(740\) | −7.50875e156 | −0.00429741 | ||||||||
\(741\) | 2.08816e157 | 0.0110880 | ||||||||
\(742\) | −7.21852e158 | −0.355657 | ||||||||
\(743\) | −7.63977e158 | −0.349302 | −0.174651 | − | 0.984630i | \(-0.555880\pi\) | ||||
−0.174651 | + | 0.984630i | \(0.555880\pi\) | |||||||
\(744\) | 1.03371e158 | 0.0438633 | ||||||||
\(745\) | −1.12062e159 | −0.441354 | ||||||||
\(746\) | 1.71210e159 | 0.625929 | ||||||||
\(747\) | −3.71480e159 | −1.26079 | ||||||||
\(748\) | −2.08964e157 | −0.00658466 | ||||||||
\(749\) | −1.14710e159 | −0.335629 | ||||||||
\(750\) | −4.90705e158 | −0.133328 | ||||||||
\(751\) | −6.80212e159 | −1.71644 | −0.858219 | − | 0.513284i | \(-0.828429\pi\) | ||||
−0.858219 | + | 0.513284i | \(0.828429\pi\) | |||||||
\(752\) | 7.58396e159 | 1.77748 | ||||||||
\(753\) | 5.71611e158 | 0.124445 | ||||||||
\(754\) | 2.14885e158 | 0.0434607 | ||||||||
\(755\) | 6.81581e159 | 1.28074 | ||||||||
\(756\) | −4.04487e157 | −0.00706228 | ||||||||
\(757\) | −5.64569e159 | −0.916000 | −0.458000 | − | 0.888952i | \(-0.651434\pi\) | ||||
−0.458000 | + | 0.888952i | \(0.651434\pi\) | |||||||
\(758\) | 1.10223e160 | 1.66199 | ||||||||
\(759\) | 1.19161e158 | 0.0166999 | ||||||||
\(760\) | 6.29454e159 | 0.819992 | ||||||||
\(761\) | 7.75612e159 | 0.939282 | 0.469641 | − | 0.882857i | \(-0.344383\pi\) | ||||
0.469641 | + | 0.882857i | \(0.344383\pi\) | |||||||
\(762\) | −1.36934e159 | −0.154174 | ||||||||
\(763\) | −4.65082e159 | −0.486875 | ||||||||
\(764\) | 1.42233e158 | 0.0138459 | ||||||||
\(765\) | 1.39642e159 | 0.126417 | ||||||||
\(766\) | −1.13769e160 | −0.957914 | ||||||||
\(767\) | 9.66804e158 | 0.0757174 | ||||||||
\(768\) | −4.83952e158 | −0.0352578 | ||||||||
\(769\) | −2.50815e160 | −1.69997 | −0.849986 | − | 0.526804i | \(-0.823390\pi\) | ||||
−0.849986 | + | 0.526804i | \(0.823390\pi\) | |||||||
\(770\) | −1.38048e159 | −0.0870549 | ||||||||
\(771\) | −1.66274e159 | −0.0975678 | ||||||||
\(772\) | 5.55185e157 | 0.00303164 | ||||||||
\(773\) | 9.78960e159 | 0.497511 | 0.248756 | − | 0.968566i | \(-0.419978\pi\) | ||||
0.248756 | + | 0.968566i | \(0.419978\pi\) | |||||||
\(774\) | −3.14090e160 | −1.48570 | ||||||||
\(775\) | −4.09574e159 | −0.180338 | ||||||||
\(776\) | 2.13511e160 | 0.875175 | ||||||||
\(777\) | 5.42901e157 | 0.00207183 | ||||||||
\(778\) | −3.59715e160 | −1.27818 | ||||||||
\(779\) | 5.87273e160 | 1.94317 | ||||||||
\(780\) | −2.24164e157 | −0.000690740 0 | ||||||||
\(781\) | 1.99598e159 | 0.0572829 | ||||||||
\(782\) | 2.56035e159 | 0.0684423 | ||||||||
\(783\) | −4.94413e159 | −0.123115 | ||||||||
\(784\) | 4.27727e160 | 0.992259 | ||||||||
\(785\) | 1.90980e160 | 0.412784 | ||||||||
\(786\) | 4.49275e159 | 0.0904816 | ||||||||
\(787\) | −2.42415e160 | −0.454948 | −0.227474 | − | 0.973784i | \(-0.573047\pi\) | ||||
−0.227474 | + | 0.973784i | \(0.573047\pi\) | |||||||
\(788\) | 9.33590e159 | 0.163287 | ||||||||
\(789\) | 1.16131e160 | 0.189310 | ||||||||
\(790\) | −6.06630e160 | −0.921765 | ||||||||
\(791\) | 3.29155e160 | 0.466236 | ||||||||
\(792\) | −2.65547e160 | −0.350666 | ||||||||
\(793\) | 1.46304e158 | 0.00180133 | ||||||||
\(794\) | −6.89184e159 | −0.0791220 | ||||||||
\(795\) | 9.20433e159 | 0.0985409 | ||||||||
\(796\) | 8.09308e159 | 0.0808051 | ||||||||
\(797\) | 1.35987e161 | 1.26637 | 0.633184 | − | 0.774001i | \(-0.281748\pi\) | ||||
0.633184 | + | 0.774001i | \(0.281748\pi\) | |||||||
\(798\) | 5.06659e159 | 0.0440104 | ||||||||
\(799\) | −3.50997e160 | −0.284418 | ||||||||
\(800\) | 1.21390e160 | 0.0917672 | ||||||||
\(801\) | −1.69057e161 | −1.19242 | ||||||||
\(802\) | −8.00190e160 | −0.526642 | ||||||||
\(803\) | −6.78160e160 | −0.416504 | ||||||||
\(804\) | 2.40534e159 | 0.0137869 | ||||||||
\(805\) | 1.54011e160 | 0.0823910 | ||||||||
\(806\) | −6.52473e159 | −0.0325813 | ||||||||
\(807\) | −4.67137e160 | −0.217753 | ||||||||
\(808\) | 7.97543e160 | 0.347075 | ||||||||
\(809\) | −1.20710e161 | −0.490456 | −0.245228 | − | 0.969465i | \(-0.578863\pi\) | ||||
−0.245228 | + | 0.969465i | \(0.578863\pi\) | |||||||
\(810\) | −1.94701e161 | −0.738669 | ||||||||
\(811\) | 1.32817e161 | 0.470541 | 0.235271 | − | 0.971930i | \(-0.424402\pi\) | ||||
0.235271 | + | 0.971930i | \(0.424402\pi\) | |||||||
\(812\) | 4.74737e159 | 0.0157070 | ||||||||
\(813\) | −3.48685e160 | −0.107748 | ||||||||
\(814\) | −7.99221e159 | −0.0230681 | ||||||||
\(815\) | 1.31979e161 | 0.355843 | ||||||||
\(816\) | 8.94394e159 | 0.0225281 | ||||||||
\(817\) | 7.21558e161 | 1.69804 | ||||||||
\(818\) | 4.03765e161 | 0.887810 | ||||||||
\(819\) | −1.13857e160 | −0.0233939 | ||||||||
\(820\) | −6.30436e160 | −0.121052 | ||||||||
\(821\) | −3.08347e160 | −0.0553344 | −0.0276672 | − | 0.999617i | \(-0.508808\pi\) | ||||
−0.0276672 | + | 0.999617i | \(0.508808\pi\) | |||||||
\(822\) | −4.97954e160 | −0.0835225 | ||||||||
\(823\) | 2.46013e161 | 0.385716 | 0.192858 | − | 0.981227i | \(-0.438224\pi\) | ||||
0.192858 | + | 0.981227i | \(0.438224\pi\) | |||||||
\(824\) | 5.78610e161 | 0.848058 | ||||||||
\(825\) | −1.49773e160 | −0.0205230 | ||||||||
\(826\) | 2.34580e161 | 0.300537 | ||||||||
\(827\) | −1.38302e162 | −1.65681 | −0.828403 | − | 0.560133i | \(-0.810750\pi\) | ||||
−0.828403 | + | 0.560133i | \(0.810750\pi\) | |||||||
\(828\) | −3.29809e160 | −0.0369470 | ||||||||
\(829\) | −1.17575e162 | −1.23180 | −0.615900 | − | 0.787824i | \(-0.711207\pi\) | ||||
−0.615900 | + | 0.787824i | \(0.711207\pi\) | |||||||
\(830\) | −1.00614e162 | −0.985880 | ||||||||
\(831\) | −7.09835e160 | −0.0650580 | ||||||||
\(832\) | −8.13463e160 | −0.0697418 | ||||||||
\(833\) | −1.97958e161 | −0.158773 | ||||||||
\(834\) | 1.95898e161 | 0.146999 | ||||||||
\(835\) | −3.10292e161 | −0.217856 | ||||||||
\(836\) | −6.79136e160 | −0.0446178 | ||||||||
\(837\) | 1.50123e161 | 0.0922962 | ||||||||
\(838\) | 1.23034e162 | 0.707917 | ||||||||
\(839\) | −2.36082e161 | −0.127138 | −0.0635689 | − | 0.997977i | \(-0.520248\pi\) | ||||
−0.0635689 | + | 0.997977i | \(0.520248\pi\) | |||||||
\(840\) | 4.88561e160 | 0.0246274 | ||||||||
\(841\) | −1.53895e162 | −0.726183 | ||||||||
\(842\) | 2.31852e162 | 1.02421 | ||||||||
\(843\) | −6.87911e160 | −0.0284513 | ||||||||
\(844\) | 2.37261e161 | 0.0918799 | ||||||||
\(845\) | 2.01432e162 | 0.730434 | ||||||||
\(846\) | 4.96559e162 | 1.68623 | ||||||||
\(847\) | 8.08394e161 | 0.257095 | ||||||||
\(848\) | −4.14139e162 | −1.23360 | ||||||||
\(849\) | 2.82914e161 | 0.0789366 | ||||||||
\(850\) | −3.21811e161 | −0.0841105 | ||||||||
\(851\) | 8.91639e160 | 0.0218323 | ||||||||
\(852\) | 7.86404e159 | 0.00180405 | ||||||||
\(853\) | −2.28041e162 | −0.490164 | −0.245082 | − | 0.969502i | \(-0.578815\pi\) | ||||
−0.245082 | + | 0.969502i | \(0.578815\pi\) | |||||||
\(854\) | 3.54984e160 | 0.00714984 | ||||||||
\(855\) | 4.53839e162 | 0.856608 | ||||||||
\(856\) | −5.97635e162 | −1.05716 | ||||||||
\(857\) | −3.75863e162 | −0.623151 | −0.311576 | − | 0.950221i | \(-0.600857\pi\) | ||||
−0.311576 | + | 0.950221i | \(0.600857\pi\) | |||||||
\(858\) | −2.38597e160 | −0.00370783 | ||||||||
\(859\) | 4.18442e162 | 0.609558 | 0.304779 | − | 0.952423i | \(-0.401417\pi\) | ||||
0.304779 | + | 0.952423i | \(0.401417\pi\) | |||||||
\(860\) | −7.74591e161 | −0.105781 | ||||||||
\(861\) | 4.55821e161 | 0.0583605 | ||||||||
\(862\) | −2.33309e162 | −0.280077 | ||||||||
\(863\) | −7.54580e161 | −0.0849388 | −0.0424694 | − | 0.999098i | \(-0.513522\pi\) | ||||
−0.0424694 | + | 0.999098i | \(0.513522\pi\) | |||||||
\(864\) | −4.44934e161 | −0.0469659 | ||||||||
\(865\) | 1.15835e163 | 1.14669 | ||||||||
\(866\) | −1.59887e163 | −1.48446 | ||||||||
\(867\) | 1.31902e162 | 0.114866 | ||||||||
\(868\) | −1.44148e161 | −0.0117751 | ||||||||
\(869\) | −5.87920e162 | −0.450527 | ||||||||
\(870\) | −6.64818e161 | −0.0477952 | ||||||||
\(871\) | 1.36377e162 | 0.0919888 | ||||||||
\(872\) | −2.42307e163 | −1.53356 | ||||||||
\(873\) | 1.53942e163 | 0.914254 | ||||||||
\(874\) | 8.32116e162 | 0.463767 | ||||||||
\(875\) | −6.14657e162 | −0.321504 | ||||||||
\(876\) | −2.67190e161 | −0.0131173 | ||||||||
\(877\) | 3.14908e163 | 1.45113 | 0.725566 | − | 0.688153i | \(-0.241578\pi\) | ||||
0.725566 | + | 0.688153i | \(0.241578\pi\) | |||||||
\(878\) | 1.94264e163 | 0.840324 | ||||||||
\(879\) | −3.69748e162 | −0.150149 | ||||||||
\(880\) | −7.92003e162 | −0.301952 | ||||||||
\(881\) | −9.12306e162 | −0.326571 | −0.163285 | − | 0.986579i | \(-0.552209\pi\) | ||||
−0.163285 | + | 0.986579i | \(0.552209\pi\) | |||||||
\(882\) | 2.80054e163 | 0.941316 | ||||||||
\(883\) | 3.44556e162 | 0.108753 | 0.0543764 | − | 0.998521i | \(-0.482683\pi\) | ||||
0.0543764 | + | 0.998521i | \(0.482683\pi\) | |||||||
\(884\) | −4.66795e160 | −0.00138365 | ||||||||
\(885\) | −2.99112e162 | −0.0832689 | ||||||||
\(886\) | 5.05170e163 | 1.32089 | ||||||||
\(887\) | −4.40074e162 | −0.108085 | −0.0540424 | − | 0.998539i | \(-0.517211\pi\) | ||||
−0.0540424 | + | 0.998539i | \(0.517211\pi\) | |||||||
\(888\) | 2.82850e161 | 0.00652585 | ||||||||
\(889\) | −1.71523e163 | −0.371771 | ||||||||
\(890\) | −4.57884e163 | −0.932416 | ||||||||
\(891\) | −1.88696e163 | −0.361036 | ||||||||
\(892\) | −1.07944e162 | −0.0194066 | ||||||||
\(893\) | −1.14074e164 | −1.92722 | ||||||||
\(894\) | −4.69946e162 | −0.0746131 | ||||||||
\(895\) | −3.74514e163 | −0.558843 | ||||||||
\(896\) | −2.40022e163 | −0.336633 | ||||||||
\(897\) | 2.66187e161 | 0.00350918 | ||||||||
\(898\) | 7.47596e163 | 0.926468 | ||||||||
\(899\) | −1.76196e163 | −0.205273 | ||||||||
\(900\) | 4.14537e162 | 0.0454051 | ||||||||
\(901\) | 1.91670e163 | 0.197391 | ||||||||
\(902\) | −6.71027e163 | −0.649796 | ||||||||
\(903\) | 5.60048e162 | 0.0509983 | ||||||||
\(904\) | 1.71489e164 | 1.46855 | ||||||||
\(905\) | −6.79215e161 | −0.00547030 | ||||||||
\(906\) | 2.85828e163 | 0.216516 | ||||||||
\(907\) | 2.00931e164 | 1.43167 | 0.715835 | − | 0.698269i | \(-0.246046\pi\) | ||||
0.715835 | + | 0.698269i | \(0.246046\pi\) | |||||||
\(908\) | −1.61031e163 | −0.107931 | ||||||||
\(909\) | 5.75031e163 | 0.362573 | ||||||||
\(910\) | −3.08377e162 | −0.0182930 | ||||||||
\(911\) | −6.02724e163 | −0.336394 | −0.168197 | − | 0.985753i | \(-0.553795\pi\) | ||||
−0.168197 | + | 0.985753i | \(0.553795\pi\) | |||||||
\(912\) | 2.90679e163 | 0.152651 | ||||||||
\(913\) | −9.75107e163 | −0.481864 | ||||||||
\(914\) | 2.55811e163 | 0.118961 | ||||||||
\(915\) | −4.52640e161 | −0.00198099 | ||||||||
\(916\) | 6.35293e161 | 0.00261683 | ||||||||
\(917\) | 5.62761e163 | 0.218186 | ||||||||
\(918\) | 1.17954e163 | 0.0430473 | ||||||||
\(919\) | −2.55068e164 | −0.876284 | −0.438142 | − | 0.898906i | \(-0.644363\pi\) | ||||
−0.438142 | + | 0.898906i | \(0.644363\pi\) | |||||||
\(920\) | 8.02392e163 | 0.259515 | ||||||||
\(921\) | −4.66476e163 | −0.142043 | ||||||||
\(922\) | −4.16262e164 | −1.19344 | ||||||||
\(923\) | 4.45872e162 | 0.0120369 | ||||||||
\(924\) | −5.27122e161 | −0.00134004 | ||||||||
\(925\) | −1.12070e163 | −0.0268302 | ||||||||
\(926\) | −3.19645e164 | −0.720705 | ||||||||
\(927\) | 4.17180e164 | 0.885927 | ||||||||
\(928\) | 5.22209e163 | 0.104456 | ||||||||
\(929\) | 5.00935e164 | 0.943864 | 0.471932 | − | 0.881635i | \(-0.343557\pi\) | ||||
0.471932 | + | 0.881635i | \(0.343557\pi\) | |||||||
\(930\) | 2.01864e163 | 0.0358307 | ||||||||
\(931\) | −6.43367e164 | −1.07585 | ||||||||
\(932\) | 8.37900e163 | 0.132011 | ||||||||
\(933\) | −1.17489e164 | −0.174408 | ||||||||
\(934\) | −1.83054e164 | −0.256052 | ||||||||
\(935\) | 3.66550e163 | 0.0483158 | ||||||||
\(936\) | −5.93192e163 | −0.0736861 | ||||||||
\(937\) | −1.01592e164 | −0.118936 | −0.0594678 | − | 0.998230i | \(-0.518940\pi\) | ||||
−0.0594678 | + | 0.998230i | \(0.518940\pi\) | |||||||
\(938\) | 3.30898e164 | 0.365121 | ||||||||
\(939\) | −1.02196e164 | −0.106290 | ||||||||
\(940\) | 1.22458e164 | 0.120059 | ||||||||
\(941\) | 2.65618e164 | 0.245489 | 0.122745 | − | 0.992438i | \(-0.460830\pi\) | ||||
0.122745 | + | 0.992438i | \(0.460830\pi\) | |||||||
\(942\) | 8.00896e163 | 0.0697832 | ||||||||
\(943\) | 7.48622e164 | 0.614983 | ||||||||
\(944\) | 1.34582e165 | 1.04242 | ||||||||
\(945\) | 7.09522e163 | 0.0518204 | ||||||||
\(946\) | −8.24464e164 | −0.567824 | ||||||||
\(947\) | 1.23281e165 | 0.800707 | 0.400353 | − | 0.916361i | \(-0.368887\pi\) | ||||
0.400353 | + | 0.916361i | \(0.368887\pi\) | |||||||
\(948\) | −2.31636e163 | −0.0141887 | ||||||||
\(949\) | −1.51491e164 | −0.0875208 | ||||||||
\(950\) | −1.04589e165 | −0.569935 | ||||||||
\(951\) | −1.97661e163 | −0.0101602 | ||||||||
\(952\) | 1.01737e164 | 0.0493320 | ||||||||
\(953\) | 2.31069e165 | 1.05703 | 0.528513 | − | 0.848925i | \(-0.322750\pi\) | ||||
0.528513 | + | 0.848925i | \(0.322750\pi\) | |||||||
\(954\) | −2.71157e165 | −1.17027 | ||||||||
\(955\) | −2.49496e164 | −0.101596 | ||||||||
\(956\) | 1.00047e164 | 0.0384407 | ||||||||
\(957\) | −6.44313e163 | −0.0233606 | ||||||||
\(958\) | −4.10479e165 | −1.40445 | ||||||||
\(959\) | −6.23737e164 | −0.201404 | ||||||||
\(960\) | 2.51672e164 | 0.0766974 | ||||||||
\(961\) | −2.94155e165 | −0.846112 | ||||||||
\(962\) | −1.78534e163 | −0.00484734 | ||||||||
\(963\) | −4.30897e165 | −1.10437 | ||||||||
\(964\) | −3.87106e164 | −0.0936600 | ||||||||
\(965\) | −9.73866e163 | −0.0222450 | ||||||||
\(966\) | 6.45860e163 | 0.0139286 | ||||||||
\(967\) | 8.08781e165 | 1.64688 | 0.823440 | − | 0.567404i | \(-0.192052\pi\) | ||||
0.823440 | + | 0.567404i | \(0.192052\pi\) | |||||||
\(968\) | 4.21171e165 | 0.809798 | ||||||||
\(969\) | −1.34531e164 | −0.0244259 | ||||||||
\(970\) | 4.16946e165 | 0.714906 | ||||||||
\(971\) | −2.32857e165 | −0.377069 | −0.188535 | − | 0.982067i | \(-0.560374\pi\) | ||||
−0.188535 | + | 0.982067i | \(0.560374\pi\) | |||||||
\(972\) | −2.28450e164 | −0.0349392 | ||||||||
\(973\) | 2.45382e165 | 0.354470 | ||||||||
\(974\) | 1.38868e166 | 1.89487 | ||||||||
\(975\) | −3.34570e163 | −0.00431252 | ||||||||
\(976\) | 2.03660e164 | 0.0247994 | ||||||||
\(977\) | −1.26993e165 | −0.146093 | −0.0730467 | − | 0.997329i | \(-0.523272\pi\) | ||||
−0.0730467 | + | 0.997329i | \(0.523272\pi\) | |||||||
\(978\) | 5.53470e164 | 0.0601572 | ||||||||
\(979\) | −4.43761e165 | −0.455733 | ||||||||
\(980\) | 6.90653e164 | 0.0670212 | ||||||||
\(981\) | −1.74704e166 | −1.60204 | ||||||||
\(982\) | 1.62783e165 | 0.141065 | ||||||||
\(983\) | 5.21648e165 | 0.427226 | 0.213613 | − | 0.976918i | \(-0.431477\pi\) | ||||
0.213613 | + | 0.976918i | \(0.431477\pi\) | |||||||
\(984\) | 2.37482e165 | 0.183824 | ||||||||
\(985\) | −1.63764e166 | −1.19814 | ||||||||
\(986\) | −1.38441e165 | −0.0957402 | ||||||||
\(987\) | −8.85405e164 | −0.0578816 | ||||||||
\(988\) | −1.51709e164 | −0.00937562 | ||||||||
\(989\) | 9.19801e165 | 0.537402 | ||||||||
\(990\) | −5.18563e165 | −0.286450 | ||||||||
\(991\) | −1.65064e166 | −0.862115 | −0.431058 | − | 0.902324i | \(-0.641859\pi\) | ||||
−0.431058 | + | 0.902324i | \(0.641859\pi\) | |||||||
\(992\) | −1.58563e165 | −0.0783075 | ||||||||
\(993\) | −2.48368e165 | −0.115988 | ||||||||
\(994\) | 1.08184e165 | 0.0477769 | ||||||||
\(995\) | −1.41963e166 | −0.592918 | ||||||||
\(996\) | −3.84185e164 | −0.0151757 | ||||||||
\(997\) | 4.67878e166 | 1.74804 | 0.874021 | − | 0.485888i | \(-0.161504\pi\) | ||||
0.874021 | + | 0.485888i | \(0.161504\pi\) | |||||||
\(998\) | 2.63464e166 | 0.931058 | ||||||||
\(999\) | 4.10775e164 | 0.0137315 |
(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 | 1.112.a.a.1.7 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.112.a.a.1.7 | ✓ | 9 | 1.1 | even | 1 | trivial |