Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [197,10,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, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("197.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 197 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
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: | \(101.462059724\) |
Analytic rank: | \(0\) |
Dimension: | \(76\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −34.7070 | −1.53385 | −0.766924 | − | 0.641738i | \(-0.778214\pi\) | ||||
−0.766924 | + | 0.641738i | \(0.778214\pi\) | |||||||
\(3\) | −78.4883 | −0.559447 | −0.279724 | − | 0.960081i | \(-0.590243\pi\) | ||||
−0.279724 | + | 0.960081i | \(0.590243\pi\) | |||||||
\(4\) | 692.576 | 1.35269 | ||||||||
\(5\) | −317.779 | −0.227384 | −0.113692 | − | 0.993516i | \(-0.536268\pi\) | ||||
−0.113692 | + | 0.993516i | \(0.536268\pi\) | |||||||
\(6\) | 2724.09 | 0.858107 | ||||||||
\(7\) | −4384.10 | −0.690144 | −0.345072 | − | 0.938576i | \(-0.612145\pi\) | ||||
−0.345072 | + | 0.938576i | \(0.612145\pi\) | |||||||
\(8\) | −6267.25 | −0.540969 | ||||||||
\(9\) | −13522.6 | −0.687019 | ||||||||
\(10\) | 11029.1 | 0.348772 | ||||||||
\(11\) | 45420.7 | 0.935378 | 0.467689 | − | 0.883893i | \(-0.345087\pi\) | ||||
0.467689 | + | 0.883893i | \(0.345087\pi\) | |||||||
\(12\) | −54359.1 | −0.756757 | ||||||||
\(13\) | −31389.1 | −0.304813 | −0.152407 | − | 0.988318i | \(-0.548702\pi\) | ||||
−0.152407 | + | 0.988318i | \(0.548702\pi\) | |||||||
\(14\) | 152159. | 1.05858 | ||||||||
\(15\) | 24941.9 | 0.127209 | ||||||||
\(16\) | −137081. | −0.522924 | ||||||||
\(17\) | 85496.2 | 0.248271 | 0.124136 | − | 0.992265i | \(-0.460384\pi\) | ||||
0.124136 | + | 0.992265i | \(0.460384\pi\) | |||||||
\(18\) | 469329. | 1.05378 | ||||||||
\(19\) | −806441. | −1.41965 | −0.709825 | − | 0.704378i | \(-0.751226\pi\) | ||||
−0.709825 | + | 0.704378i | \(0.751226\pi\) | |||||||
\(20\) | −220086. | −0.307579 | ||||||||
\(21\) | 344101. | 0.386099 | ||||||||
\(22\) | −1.57642e6 | −1.43473 | ||||||||
\(23\) | 392444. | 0.292417 | 0.146208 | − | 0.989254i | \(-0.453293\pi\) | ||||
0.146208 | + | 0.989254i | \(0.453293\pi\) | |||||||
\(24\) | 491906. | 0.302644 | ||||||||
\(25\) | −1.85214e6 | −0.948297 | ||||||||
\(26\) | 1.08942e6 | 0.467537 | ||||||||
\(27\) | 2.60625e6 | 0.943798 | ||||||||
\(28\) | −3.03633e6 | −0.933549 | ||||||||
\(29\) | 5.91681e6 | 1.55345 | 0.776724 | − | 0.629842i | \(-0.216880\pi\) | ||||
0.776724 | + | 0.629842i | \(0.216880\pi\) | |||||||
\(30\) | −865659. | −0.195120 | ||||||||
\(31\) | 3.42516e6 | 0.666122 | 0.333061 | − | 0.942905i | \(-0.391919\pi\) | ||||
0.333061 | + | 0.942905i | \(0.391919\pi\) | |||||||
\(32\) | 7.96652e6 | 1.34305 | ||||||||
\(33\) | −3.56499e6 | −0.523294 | ||||||||
\(34\) | −2.96732e6 | −0.380810 | ||||||||
\(35\) | 1.39317e6 | 0.156928 | ||||||||
\(36\) | −9.36542e6 | −0.929322 | ||||||||
\(37\) | −3.26032e6 | −0.285991 | −0.142996 | − | 0.989723i | \(-0.545673\pi\) | ||||
−0.142996 | + | 0.989723i | \(0.545673\pi\) | |||||||
\(38\) | 2.79892e7 | 2.17753 | ||||||||
\(39\) | 2.46368e6 | 0.170527 | ||||||||
\(40\) | 1.99160e6 | 0.123008 | ||||||||
\(41\) | −1.26323e7 | −0.698159 | −0.349079 | − | 0.937093i | \(-0.613506\pi\) | ||||
−0.349079 | + | 0.937093i | \(0.613506\pi\) | |||||||
\(42\) | −1.19427e7 | −0.592217 | ||||||||
\(43\) | −1.66489e7 | −0.742638 | −0.371319 | − | 0.928505i | \(-0.621094\pi\) | ||||
−0.371319 | + | 0.928505i | \(0.621094\pi\) | |||||||
\(44\) | 3.14573e7 | 1.26527 | ||||||||
\(45\) | 4.29719e6 | 0.156217 | ||||||||
\(46\) | −1.36205e7 | −0.448522 | ||||||||
\(47\) | −1.60830e7 | −0.480759 | −0.240380 | − | 0.970679i | \(-0.577272\pi\) | ||||
−0.240380 | + | 0.970679i | \(0.577272\pi\) | |||||||
\(48\) | 1.07593e7 | 0.292548 | ||||||||
\(49\) | −2.11332e7 | −0.523701 | ||||||||
\(50\) | 6.42823e7 | 1.45454 | ||||||||
\(51\) | −6.71045e6 | −0.138895 | ||||||||
\(52\) | −2.17394e7 | −0.412317 | ||||||||
\(53\) | −4.29820e7 | −0.748247 | −0.374123 | − | 0.927379i | \(-0.622056\pi\) | ||||
−0.374123 | + | 0.927379i | \(0.622056\pi\) | |||||||
\(54\) | −9.04551e7 | −1.44764 | ||||||||
\(55\) | −1.44337e7 | −0.212690 | ||||||||
\(56\) | 2.74763e7 | 0.373346 | ||||||||
\(57\) | 6.32962e7 | 0.794220 | ||||||||
\(58\) | −2.05355e8 | −2.38275 | ||||||||
\(59\) | −4.18933e7 | −0.450102 | −0.225051 | − | 0.974347i | \(-0.572255\pi\) | ||||
−0.225051 | + | 0.974347i | \(0.572255\pi\) | |||||||
\(60\) | 1.72742e7 | 0.172074 | ||||||||
\(61\) | −5.02151e7 | −0.464355 | −0.232178 | − | 0.972673i | \(-0.574585\pi\) | ||||
−0.232178 | + | 0.972673i | \(0.574585\pi\) | |||||||
\(62\) | −1.18877e8 | −1.02173 | ||||||||
\(63\) | 5.92844e7 | 0.474142 | ||||||||
\(64\) | −2.06308e8 | −1.53712 | ||||||||
\(65\) | 9.97479e6 | 0.0693097 | ||||||||
\(66\) | 1.23730e8 | 0.802654 | ||||||||
\(67\) | −2.36103e8 | −1.43141 | −0.715707 | − | 0.698401i | \(-0.753895\pi\) | ||||
−0.715707 | + | 0.698401i | \(0.753895\pi\) | |||||||
\(68\) | 5.92126e7 | 0.335833 | ||||||||
\(69\) | −3.08022e7 | −0.163592 | ||||||||
\(70\) | −4.83529e7 | −0.240703 | ||||||||
\(71\) | −2.73121e8 | −1.27553 | −0.637767 | − | 0.770230i | \(-0.720142\pi\) | ||||
−0.637767 | + | 0.770230i | \(0.720142\pi\) | |||||||
\(72\) | 8.47495e7 | 0.371656 | ||||||||
\(73\) | 1.41037e7 | 0.0581274 | 0.0290637 | − | 0.999578i | \(-0.490747\pi\) | ||||
0.0290637 | + | 0.999578i | \(0.490747\pi\) | |||||||
\(74\) | 1.13156e8 | 0.438667 | ||||||||
\(75\) | 1.45371e8 | 0.530522 | ||||||||
\(76\) | −5.58522e8 | −1.92034 | ||||||||
\(77\) | −1.99129e8 | −0.645545 | ||||||||
\(78\) | −8.55069e7 | −0.261562 | ||||||||
\(79\) | −1.34719e8 | −0.389141 | −0.194570 | − | 0.980889i | \(-0.562331\pi\) | ||||
−0.194570 | + | 0.980889i | \(0.562331\pi\) | |||||||
\(80\) | 4.35615e7 | 0.118904 | ||||||||
\(81\) | 6.16051e7 | 0.159014 | ||||||||
\(82\) | 4.38428e8 | 1.07087 | ||||||||
\(83\) | −2.79556e8 | −0.646573 | −0.323286 | − | 0.946301i | \(-0.604788\pi\) | ||||
−0.323286 | + | 0.946301i | \(0.604788\pi\) | |||||||
\(84\) | 2.38316e8 | 0.522271 | ||||||||
\(85\) | −2.71689e7 | −0.0564529 | ||||||||
\(86\) | 5.77833e8 | 1.13909 | ||||||||
\(87\) | −4.64400e8 | −0.869072 | ||||||||
\(88\) | −2.84663e8 | −0.506010 | ||||||||
\(89\) | 1.92906e8 | 0.325905 | 0.162953 | − | 0.986634i | \(-0.447898\pi\) | ||||
0.162953 | + | 0.986634i | \(0.447898\pi\) | |||||||
\(90\) | −1.49143e8 | −0.239613 | ||||||||
\(91\) | 1.37613e8 | 0.210365 | ||||||||
\(92\) | 2.71797e8 | 0.395548 | ||||||||
\(93\) | −2.68835e8 | −0.372660 | ||||||||
\(94\) | 5.58194e8 | 0.737411 | ||||||||
\(95\) | 2.56270e8 | 0.322806 | ||||||||
\(96\) | −6.25278e8 | −0.751368 | ||||||||
\(97\) | −3.24674e8 | −0.372370 | −0.186185 | − | 0.982515i | \(-0.559612\pi\) | ||||
−0.186185 | + | 0.982515i | \(0.559612\pi\) | |||||||
\(98\) | 7.33471e8 | 0.803278 | ||||||||
\(99\) | −6.14206e8 | −0.642622 | ||||||||
\(100\) | −1.28275e9 | −1.28275 | ||||||||
\(101\) | −1.53343e9 | −1.46629 | −0.733143 | − | 0.680075i | \(-0.761947\pi\) | ||||
−0.733143 | + | 0.680075i | \(0.761947\pi\) | |||||||
\(102\) | 2.32899e8 | 0.213043 | ||||||||
\(103\) | −2.10185e8 | −0.184007 | −0.0920035 | − | 0.995759i | \(-0.529327\pi\) | ||||
−0.0920035 | + | 0.995759i | \(0.529327\pi\) | |||||||
\(104\) | 1.96724e8 | 0.164895 | ||||||||
\(105\) | −1.09348e8 | −0.0877927 | ||||||||
\(106\) | 1.49178e9 | 1.14770 | ||||||||
\(107\) | 6.24581e8 | 0.460640 | 0.230320 | − | 0.973115i | \(-0.426023\pi\) | ||||
0.230320 | + | 0.973115i | \(0.426023\pi\) | |||||||
\(108\) | 1.80503e9 | 1.27666 | ||||||||
\(109\) | 1.30462e9 | 0.885246 | 0.442623 | − | 0.896708i | \(-0.354048\pi\) | ||||
0.442623 | + | 0.896708i | \(0.354048\pi\) | |||||||
\(110\) | 5.00952e8 | 0.326234 | ||||||||
\(111\) | 2.55897e8 | 0.159997 | ||||||||
\(112\) | 6.00979e8 | 0.360893 | ||||||||
\(113\) | −2.65903e9 | −1.53416 | −0.767080 | − | 0.641551i | \(-0.778291\pi\) | ||||
−0.767080 | + | 0.641551i | \(0.778291\pi\) | |||||||
\(114\) | −2.19682e9 | −1.21821 | ||||||||
\(115\) | −1.24710e8 | −0.0664908 | ||||||||
\(116\) | 4.09784e9 | 2.10133 | ||||||||
\(117\) | 4.24462e8 | 0.209413 | ||||||||
\(118\) | 1.45399e9 | 0.690388 | ||||||||
\(119\) | −3.74824e8 | −0.171343 | ||||||||
\(120\) | −1.56317e8 | −0.0688163 | ||||||||
\(121\) | −2.94906e8 | −0.125069 | ||||||||
\(122\) | 1.74282e9 | 0.712250 | ||||||||
\(123\) | 9.91486e8 | 0.390583 | ||||||||
\(124\) | 2.37219e9 | 0.901054 | ||||||||
\(125\) | 1.20923e9 | 0.443011 | ||||||||
\(126\) | −2.05759e9 | −0.727261 | ||||||||
\(127\) | 1.09075e9 | 0.372057 | 0.186029 | − | 0.982544i | \(-0.440438\pi\) | ||||
0.186029 | + | 0.982544i | \(0.440438\pi\) | |||||||
\(128\) | 3.08148e9 | 1.01465 | ||||||||
\(129\) | 1.30674e9 | 0.415467 | ||||||||
\(130\) | −3.46195e8 | −0.106310 | ||||||||
\(131\) | 5.01286e8 | 0.148719 | 0.0743593 | − | 0.997232i | \(-0.476309\pi\) | ||||
0.0743593 | + | 0.997232i | \(0.476309\pi\) | |||||||
\(132\) | −2.46903e9 | −0.707854 | ||||||||
\(133\) | 3.53552e9 | 0.979763 | ||||||||
\(134\) | 8.19443e9 | 2.19557 | ||||||||
\(135\) | −8.28210e8 | −0.214604 | ||||||||
\(136\) | −5.35826e8 | −0.134307 | ||||||||
\(137\) | 5.81288e9 | 1.40977 | 0.704886 | − | 0.709320i | \(-0.250998\pi\) | ||||
0.704886 | + | 0.709320i | \(0.250998\pi\) | |||||||
\(138\) | 1.06905e9 | 0.250925 | ||||||||
\(139\) | 5.56713e9 | 1.26492 | 0.632462 | − | 0.774591i | \(-0.282044\pi\) | ||||
0.632462 | + | 0.774591i | \(0.282044\pi\) | |||||||
\(140\) | 9.64879e8 | 0.212274 | ||||||||
\(141\) | 1.26233e9 | 0.268960 | ||||||||
\(142\) | 9.47920e9 | 1.95647 | ||||||||
\(143\) | −1.42572e9 | −0.285116 | ||||||||
\(144\) | 1.85370e9 | 0.359259 | ||||||||
\(145\) | −1.88024e9 | −0.353229 | ||||||||
\(146\) | −4.89498e8 | −0.0891585 | ||||||||
\(147\) | 1.65871e9 | 0.292983 | ||||||||
\(148\) | −2.25802e9 | −0.386857 | ||||||||
\(149\) | −6.08351e9 | −1.01115 | −0.505576 | − | 0.862782i | \(-0.668720\pi\) | ||||
−0.505576 | + | 0.862782i | \(0.668720\pi\) | |||||||
\(150\) | −5.04541e9 | −0.813740 | ||||||||
\(151\) | −7.47140e8 | −0.116952 | −0.0584758 | − | 0.998289i | \(-0.518624\pi\) | ||||
−0.0584758 | + | 0.998289i | \(0.518624\pi\) | |||||||
\(152\) | 5.05417e9 | 0.767987 | ||||||||
\(153\) | −1.15613e9 | −0.170567 | ||||||||
\(154\) | 6.91118e9 | 0.990168 | ||||||||
\(155\) | −1.08844e9 | −0.151465 | ||||||||
\(156\) | 1.70628e9 | 0.230670 | ||||||||
\(157\) | −4.04825e8 | −0.0531764 | −0.0265882 | − | 0.999646i | \(-0.508464\pi\) | ||||
−0.0265882 | + | 0.999646i | \(0.508464\pi\) | |||||||
\(158\) | 4.67569e9 | 0.596882 | ||||||||
\(159\) | 3.37358e9 | 0.418605 | ||||||||
\(160\) | −2.53159e9 | −0.305389 | ||||||||
\(161\) | −1.72051e9 | −0.201809 | ||||||||
\(162\) | −2.13813e9 | −0.243902 | ||||||||
\(163\) | 4.12010e9 | 0.457155 | 0.228577 | − | 0.973526i | \(-0.426593\pi\) | ||||
0.228577 | + | 0.973526i | \(0.426593\pi\) | |||||||
\(164\) | −8.74881e9 | −0.944391 | ||||||||
\(165\) | 1.13288e9 | 0.118989 | ||||||||
\(166\) | 9.70255e9 | 0.991744 | ||||||||
\(167\) | −6.48009e9 | −0.644699 | −0.322350 | − | 0.946621i | \(-0.604473\pi\) | ||||
−0.322350 | + | 0.946621i | \(0.604473\pi\) | |||||||
\(168\) | −2.15657e9 | −0.208868 | ||||||||
\(169\) | −9.61922e9 | −0.907089 | ||||||||
\(170\) | 9.42950e8 | 0.0865901 | ||||||||
\(171\) | 1.09052e10 | 0.975327 | ||||||||
\(172\) | −1.15306e10 | −1.00456 | ||||||||
\(173\) | 1.65334e10 | 1.40332 | 0.701659 | − | 0.712513i | \(-0.252443\pi\) | ||||
0.701659 | + | 0.712513i | \(0.252443\pi\) | |||||||
\(174\) | 1.61179e10 | 1.33302 | ||||||||
\(175\) | 8.11998e9 | 0.654461 | ||||||||
\(176\) | −6.22634e9 | −0.489131 | ||||||||
\(177\) | 3.28814e9 | 0.251808 | ||||||||
\(178\) | −6.69520e9 | −0.499889 | ||||||||
\(179\) | −1.11447e10 | −0.811393 | −0.405696 | − | 0.914008i | \(-0.632971\pi\) | ||||
−0.405696 | + | 0.914008i | \(0.632971\pi\) | |||||||
\(180\) | 2.97613e9 | 0.211313 | ||||||||
\(181\) | 8.09522e9 | 0.560629 | 0.280314 | − | 0.959908i | \(-0.409561\pi\) | ||||
0.280314 | + | 0.959908i | \(0.409561\pi\) | |||||||
\(182\) | −4.77614e9 | −0.322668 | ||||||||
\(183\) | 3.94130e9 | 0.259782 | ||||||||
\(184\) | −2.45954e9 | −0.158188 | ||||||||
\(185\) | 1.03606e9 | 0.0650298 | ||||||||
\(186\) | 9.33046e9 | 0.571603 | ||||||||
\(187\) | 3.88330e9 | 0.232227 | ||||||||
\(188\) | −1.11387e10 | −0.650317 | ||||||||
\(189\) | −1.14261e10 | −0.651356 | ||||||||
\(190\) | −8.89436e9 | −0.495135 | ||||||||
\(191\) | 2.54043e10 | 1.38120 | 0.690600 | − | 0.723237i | \(-0.257346\pi\) | ||||
0.690600 | + | 0.723237i | \(0.257346\pi\) | |||||||
\(192\) | 1.61928e10 | 0.859936 | ||||||||
\(193\) | 2.69561e10 | 1.39846 | 0.699229 | − | 0.714898i | \(-0.253527\pi\) | ||||
0.699229 | + | 0.714898i | \(0.253527\pi\) | |||||||
\(194\) | 1.12685e10 | 0.571159 | ||||||||
\(195\) | −7.82904e8 | −0.0387751 | ||||||||
\(196\) | −1.46364e10 | −0.708404 | ||||||||
\(197\) | 1.50614e9 | 0.0712470 | ||||||||
\(198\) | 2.13172e10 | 0.985684 | ||||||||
\(199\) | −2.58701e10 | −1.16939 | −0.584695 | − | 0.811253i | \(-0.698786\pi\) | ||||
−0.584695 | + | 0.811253i | \(0.698786\pi\) | |||||||
\(200\) | 1.16078e10 | 0.512999 | ||||||||
\(201\) | 1.85313e10 | 0.800801 | ||||||||
\(202\) | 5.32209e10 | 2.24906 | ||||||||
\(203\) | −2.59399e10 | −1.07210 | ||||||||
\(204\) | −4.64749e9 | −0.187881 | ||||||||
\(205\) | 4.01427e9 | 0.158750 | ||||||||
\(206\) | 7.29489e9 | 0.282238 | ||||||||
\(207\) | −5.30685e9 | −0.200896 | ||||||||
\(208\) | 4.30286e9 | 0.159394 | ||||||||
\(209\) | −3.66291e10 | −1.32791 | ||||||||
\(210\) | 3.79514e9 | 0.134661 | ||||||||
\(211\) | −7.64852e9 | −0.265648 | −0.132824 | − | 0.991140i | \(-0.542405\pi\) | ||||
−0.132824 | + | 0.991140i | \(0.542405\pi\) | |||||||
\(212\) | −2.97683e10 | −1.01214 | ||||||||
\(213\) | 2.14368e10 | 0.713594 | ||||||||
\(214\) | −2.16773e10 | −0.706551 | ||||||||
\(215\) | 5.29066e9 | 0.168864 | ||||||||
\(216\) | −1.63340e10 | −0.510565 | ||||||||
\(217\) | −1.50163e10 | −0.459720 | ||||||||
\(218\) | −4.52794e10 | −1.35783 | ||||||||
\(219\) | −1.10698e9 | −0.0325192 | ||||||||
\(220\) | −9.99646e9 | −0.287703 | ||||||||
\(221\) | −2.68365e9 | −0.0756764 | ||||||||
\(222\) | −8.88142e9 | −0.245411 | ||||||||
\(223\) | −1.10676e10 | −0.299696 | −0.149848 | − | 0.988709i | \(-0.547878\pi\) | ||||
−0.149848 | + | 0.988709i | \(0.547878\pi\) | |||||||
\(224\) | −3.49260e10 | −0.926901 | ||||||||
\(225\) | 2.50458e10 | 0.651498 | ||||||||
\(226\) | 9.22871e10 | 2.35317 | ||||||||
\(227\) | 5.78204e9 | 0.144532 | 0.0722661 | − | 0.997385i | \(-0.476977\pi\) | ||||
0.0722661 | + | 0.997385i | \(0.476977\pi\) | |||||||
\(228\) | 4.38374e10 | 1.07433 | ||||||||
\(229\) | 3.22040e10 | 0.773837 | 0.386919 | − | 0.922114i | \(-0.373539\pi\) | ||||
0.386919 | + | 0.922114i | \(0.373539\pi\) | |||||||
\(230\) | 4.32832e9 | 0.101987 | ||||||||
\(231\) | 1.56293e10 | 0.361148 | ||||||||
\(232\) | −3.70821e10 | −0.840366 | ||||||||
\(233\) | 5.50337e10 | 1.22328 | 0.611642 | − | 0.791135i | \(-0.290510\pi\) | ||||
0.611642 | + | 0.791135i | \(0.290510\pi\) | |||||||
\(234\) | −1.47318e10 | −0.321207 | ||||||||
\(235\) | 5.11085e9 | 0.109317 | ||||||||
\(236\) | −2.90143e10 | −0.608847 | ||||||||
\(237\) | 1.05739e10 | 0.217704 | ||||||||
\(238\) | 1.30090e10 | 0.262814 | ||||||||
\(239\) | 4.76937e10 | 0.945520 | 0.472760 | − | 0.881191i | \(-0.343258\pi\) | ||||
0.472760 | + | 0.881191i | \(0.343258\pi\) | |||||||
\(240\) | −3.41907e9 | −0.0665208 | ||||||||
\(241\) | −3.33763e10 | −0.637326 | −0.318663 | − | 0.947868i | \(-0.603234\pi\) | ||||
−0.318663 | + | 0.947868i | \(0.603234\pi\) | |||||||
\(242\) | 1.02353e10 | 0.191836 | ||||||||
\(243\) | −5.61341e10 | −1.03276 | ||||||||
\(244\) | −3.47778e10 | −0.628128 | ||||||||
\(245\) | 6.71569e9 | 0.119081 | ||||||||
\(246\) | −3.44115e10 | −0.599095 | ||||||||
\(247\) | 2.53135e10 | 0.432729 | ||||||||
\(248\) | −2.14664e10 | −0.360351 | ||||||||
\(249\) | 2.19419e10 | 0.361723 | ||||||||
\(250\) | −4.19688e10 | −0.679512 | ||||||||
\(251\) | −8.82721e10 | −1.40376 | −0.701878 | − | 0.712297i | \(-0.747655\pi\) | ||||
−0.701878 | + | 0.712297i | \(0.747655\pi\) | |||||||
\(252\) | 4.10590e10 | 0.641366 | ||||||||
\(253\) | 1.78251e10 | 0.273520 | ||||||||
\(254\) | −3.78568e10 | −0.570679 | ||||||||
\(255\) | 2.13244e9 | 0.0315824 | ||||||||
\(256\) | −1.31927e9 | −0.0191979 | ||||||||
\(257\) | −1.54597e9 | −0.0221056 | −0.0110528 | − | 0.999939i | \(-0.503518\pi\) | ||||
−0.0110528 | + | 0.999939i | \(0.503518\pi\) | |||||||
\(258\) | −4.53531e10 | −0.637263 | ||||||||
\(259\) | 1.42936e10 | 0.197375 | ||||||||
\(260\) | 6.90830e9 | 0.0937543 | ||||||||
\(261\) | −8.00106e10 | −1.06725 | ||||||||
\(262\) | −1.73982e10 | −0.228112 | ||||||||
\(263\) | −9.93743e10 | −1.28078 | −0.640388 | − | 0.768052i | \(-0.721226\pi\) | ||||
−0.640388 | + | 0.768052i | \(0.721226\pi\) | |||||||
\(264\) | 2.23427e10 | 0.283086 | ||||||||
\(265\) | 1.36587e10 | 0.170139 | ||||||||
\(266\) | −1.22707e11 | −1.50281 | ||||||||
\(267\) | −1.51409e10 | −0.182327 | ||||||||
\(268\) | −1.63519e11 | −1.93626 | ||||||||
\(269\) | 8.06972e10 | 0.939665 | 0.469833 | − | 0.882756i | \(-0.344314\pi\) | ||||
0.469833 | + | 0.882756i | \(0.344314\pi\) | |||||||
\(270\) | 2.87447e10 | 0.329170 | ||||||||
\(271\) | 7.06333e10 | 0.795514 | 0.397757 | − | 0.917491i | \(-0.369789\pi\) | ||||
0.397757 | + | 0.917491i | \(0.369789\pi\) | |||||||
\(272\) | −1.17199e10 | −0.129827 | ||||||||
\(273\) | −1.08010e10 | −0.117688 | ||||||||
\(274\) | −2.01748e11 | −2.16238 | ||||||||
\(275\) | −8.41256e10 | −0.887015 | ||||||||
\(276\) | −2.13329e10 | −0.221288 | ||||||||
\(277\) | 5.83837e10 | 0.595844 | 0.297922 | − | 0.954590i | \(-0.403706\pi\) | ||||
0.297922 | + | 0.954590i | \(0.403706\pi\) | |||||||
\(278\) | −1.93218e11 | −1.94020 | ||||||||
\(279\) | −4.63171e10 | −0.457638 | ||||||||
\(280\) | −8.73138e9 | −0.0848929 | ||||||||
\(281\) | −1.94254e10 | −0.185863 | −0.0929313 | − | 0.995673i | \(-0.529624\pi\) | ||||
−0.0929313 | + | 0.995673i | \(0.529624\pi\) | |||||||
\(282\) | −4.38117e10 | −0.412543 | ||||||||
\(283\) | −1.46775e11 | −1.36023 | −0.680117 | − | 0.733104i | \(-0.738071\pi\) | ||||
−0.680117 | + | 0.733104i | \(0.738071\pi\) | |||||||
\(284\) | −1.89157e11 | −1.72540 | ||||||||
\(285\) | −2.01142e10 | −0.180593 | ||||||||
\(286\) | 4.94823e10 | 0.437324 | ||||||||
\(287\) | 5.53812e10 | 0.481830 | ||||||||
\(288\) | −1.07728e11 | −0.922704 | ||||||||
\(289\) | −1.11278e11 | −0.938361 | ||||||||
\(290\) | 6.52573e10 | 0.541799 | ||||||||
\(291\) | 2.54831e10 | 0.208321 | ||||||||
\(292\) | 9.76790e9 | 0.0786282 | ||||||||
\(293\) | 6.43253e10 | 0.509891 | 0.254945 | − | 0.966955i | \(-0.417942\pi\) | ||||
0.254945 | + | 0.966955i | \(0.417942\pi\) | |||||||
\(294\) | −5.75689e10 | −0.449392 | ||||||||
\(295\) | 1.33128e10 | 0.102346 | ||||||||
\(296\) | 2.04333e10 | 0.154712 | ||||||||
\(297\) | 1.18378e11 | 0.882808 | ||||||||
\(298\) | 2.11140e11 | 1.55095 | ||||||||
\(299\) | −1.23185e10 | −0.0891325 | ||||||||
\(300\) | 1.00681e11 | 0.717630 | ||||||||
\(301\) | 7.29905e10 | 0.512527 | ||||||||
\(302\) | 2.59310e10 | 0.179386 | ||||||||
\(303\) | 1.20357e11 | 0.820310 | ||||||||
\(304\) | 1.10548e11 | 0.742369 | ||||||||
\(305\) | 1.59573e10 | 0.105587 | ||||||||
\(306\) | 4.01258e10 | 0.261624 | ||||||||
\(307\) | −1.07620e11 | −0.691468 | −0.345734 | − | 0.938333i | \(-0.612370\pi\) | ||||
−0.345734 | + | 0.938333i | \(0.612370\pi\) | |||||||
\(308\) | −1.37912e11 | −0.873221 | ||||||||
\(309\) | 1.64971e10 | 0.102942 | ||||||||
\(310\) | 3.77766e10 | 0.232325 | ||||||||
\(311\) | 2.54619e11 | 1.54337 | 0.771683 | − | 0.636007i | \(-0.219415\pi\) | ||||
0.771683 | + | 0.636007i | \(0.219415\pi\) | |||||||
\(312\) | −1.54405e10 | −0.0922498 | ||||||||
\(313\) | −9.85166e9 | −0.0580176 | −0.0290088 | − | 0.999579i | \(-0.509235\pi\) | ||||
−0.0290088 | + | 0.999579i | \(0.509235\pi\) | |||||||
\(314\) | 1.40503e10 | 0.0815644 | ||||||||
\(315\) | −1.88393e10 | −0.107812 | ||||||||
\(316\) | −9.33031e10 | −0.526386 | ||||||||
\(317\) | 1.38869e11 | 0.772395 | 0.386198 | − | 0.922416i | \(-0.373788\pi\) | ||||
0.386198 | + | 0.922416i | \(0.373788\pi\) | |||||||
\(318\) | −1.17087e11 | −0.642075 | ||||||||
\(319\) | 2.68746e11 | 1.45306 | ||||||||
\(320\) | 6.55604e10 | 0.349515 | ||||||||
\(321\) | −4.90223e10 | −0.257704 | ||||||||
\(322\) | 5.97139e10 | 0.309545 | ||||||||
\(323\) | −6.89476e10 | −0.352459 | ||||||||
\(324\) | 4.26662e10 | 0.215096 | ||||||||
\(325\) | 5.81371e10 | 0.289053 | ||||||||
\(326\) | −1.42996e11 | −0.701205 | ||||||||
\(327\) | −1.02397e11 | −0.495248 | ||||||||
\(328\) | 7.91697e10 | 0.377682 | ||||||||
\(329\) | 7.05097e10 | 0.331793 | ||||||||
\(330\) | −3.93188e10 | −0.182511 | ||||||||
\(331\) | 2.16628e11 | 0.991948 | 0.495974 | − | 0.868337i | \(-0.334811\pi\) | ||||
0.495974 | + | 0.868337i | \(0.334811\pi\) | |||||||
\(332\) | −1.93614e11 | −0.874611 | ||||||||
\(333\) | 4.40880e10 | 0.196481 | ||||||||
\(334\) | 2.24905e11 | 0.988870 | ||||||||
\(335\) | 7.50286e10 | 0.325480 | ||||||||
\(336\) | −4.71698e10 | −0.201900 | ||||||||
\(337\) | 2.71871e11 | 1.14823 | 0.574115 | − | 0.818775i | \(-0.305346\pi\) | ||||
0.574115 | + | 0.818775i | \(0.305346\pi\) | |||||||
\(338\) | 3.33854e11 | 1.39134 | ||||||||
\(339\) | 2.08703e11 | 0.858282 | ||||||||
\(340\) | −1.88165e10 | −0.0763631 | ||||||||
\(341\) | 1.55573e11 | 0.623075 | ||||||||
\(342\) | −3.78486e11 | −1.49600 | ||||||||
\(343\) | 2.69565e11 | 1.05157 | ||||||||
\(344\) | 1.04343e11 | 0.401744 | ||||||||
\(345\) | 9.78829e9 | 0.0371981 | ||||||||
\(346\) | −5.73826e11 | −2.15247 | ||||||||
\(347\) | 1.59007e11 | 0.588752 | 0.294376 | − | 0.955690i | \(-0.404888\pi\) | ||||
0.294376 | + | 0.955690i | \(0.404888\pi\) | |||||||
\(348\) | −3.21632e11 | −1.17558 | ||||||||
\(349\) | −3.98060e11 | −1.43626 | −0.718132 | − | 0.695907i | \(-0.755003\pi\) | ||||
−0.718132 | + | 0.695907i | \(0.755003\pi\) | |||||||
\(350\) | −2.81820e11 | −1.00384 | ||||||||
\(351\) | −8.18079e10 | −0.287682 | ||||||||
\(352\) | 3.61845e11 | 1.25626 | ||||||||
\(353\) | 3.42439e10 | 0.117381 | 0.0586903 | − | 0.998276i | \(-0.481308\pi\) | ||||
0.0586903 | + | 0.998276i | \(0.481308\pi\) | |||||||
\(354\) | −1.14121e11 | −0.386236 | ||||||||
\(355\) | 8.67919e10 | 0.290036 | ||||||||
\(356\) | 1.33602e11 | 0.440848 | ||||||||
\(357\) | 2.94193e10 | 0.0958573 | ||||||||
\(358\) | 3.86800e11 | 1.24455 | ||||||||
\(359\) | −2.17991e11 | −0.692649 | −0.346325 | − | 0.938115i | \(-0.612570\pi\) | ||||
−0.346325 | + | 0.938115i | \(0.612570\pi\) | |||||||
\(360\) | −2.69316e10 | −0.0845085 | ||||||||
\(361\) | 3.27660e11 | 1.01541 | ||||||||
\(362\) | −2.80961e11 | −0.859919 | ||||||||
\(363\) | 2.31466e10 | 0.0699694 | ||||||||
\(364\) | 9.53076e10 | 0.284558 | ||||||||
\(365\) | −4.48186e9 | −0.0132172 | ||||||||
\(366\) | −1.36791e11 | −0.398466 | ||||||||
\(367\) | 6.13834e11 | 1.76626 | 0.883128 | − | 0.469133i | \(-0.155433\pi\) | ||||
0.883128 | + | 0.469133i | \(0.155433\pi\) | |||||||
\(368\) | −5.37967e10 | −0.152912 | ||||||||
\(369\) | 1.70821e11 | 0.479648 | ||||||||
\(370\) | −3.59586e10 | −0.0997458 | ||||||||
\(371\) | 1.88437e11 | 0.516398 | ||||||||
\(372\) | −1.86189e11 | −0.504092 | ||||||||
\(373\) | 3.88866e11 | 1.04018 | 0.520092 | − | 0.854110i | \(-0.325897\pi\) | ||||
0.520092 | + | 0.854110i | \(0.325897\pi\) | |||||||
\(374\) | −1.34778e11 | −0.356201 | ||||||||
\(375\) | −9.49106e10 | −0.247841 | ||||||||
\(376\) | 1.00796e11 | 0.260076 | ||||||||
\(377\) | −1.85723e11 | −0.473511 | ||||||||
\(378\) | 3.96565e11 | 0.999081 | ||||||||
\(379\) | −4.00694e11 | −0.997553 | −0.498776 | − | 0.866731i | \(-0.666217\pi\) | ||||
−0.498776 | + | 0.866731i | \(0.666217\pi\) | |||||||
\(380\) | 1.77486e11 | 0.436655 | ||||||||
\(381\) | −8.56114e10 | −0.208147 | ||||||||
\(382\) | −8.81706e11 | −2.11855 | ||||||||
\(383\) | 5.44318e11 | 1.29258 | 0.646291 | − | 0.763091i | \(-0.276319\pi\) | ||||
0.646291 | + | 0.763091i | \(0.276319\pi\) | |||||||
\(384\) | −2.41860e11 | −0.567642 | ||||||||
\(385\) | 6.32790e10 | 0.146787 | ||||||||
\(386\) | −9.35566e11 | −2.14502 | ||||||||
\(387\) | 2.25136e11 | 0.510207 | ||||||||
\(388\) | −2.24862e11 | −0.503700 | ||||||||
\(389\) | −6.24163e11 | −1.38205 | −0.691027 | − | 0.722829i | \(-0.742841\pi\) | ||||
−0.691027 | + | 0.722829i | \(0.742841\pi\) | |||||||
\(390\) | 2.71723e10 | 0.0594751 | ||||||||
\(391\) | 3.35524e10 | 0.0725986 | ||||||||
\(392\) | 1.32447e11 | 0.283306 | ||||||||
\(393\) | −3.93451e10 | −0.0832002 | ||||||||
\(394\) | −5.22736e10 | −0.109282 | ||||||||
\(395\) | 4.28108e10 | 0.0884843 | ||||||||
\(396\) | −4.25384e11 | −0.869267 | ||||||||
\(397\) | 6.86003e10 | 0.138602 | 0.0693009 | − | 0.997596i | \(-0.477923\pi\) | ||||
0.0693009 | + | 0.997596i | \(0.477923\pi\) | |||||||
\(398\) | 8.97874e11 | 1.79367 | ||||||||
\(399\) | −2.77497e11 | −0.548126 | ||||||||
\(400\) | 2.53894e11 | 0.495887 | ||||||||
\(401\) | −9.20590e11 | −1.77794 | −0.888969 | − | 0.457968i | \(-0.848577\pi\) | ||||
−0.888969 | + | 0.457968i | \(0.848577\pi\) | |||||||
\(402\) | −6.43167e11 | −1.22831 | ||||||||
\(403\) | −1.07513e11 | −0.203043 | ||||||||
\(404\) | −1.06202e12 | −1.98343 | ||||||||
\(405\) | −1.95768e10 | −0.0361571 | ||||||||
\(406\) | 9.00296e11 | 1.64444 | ||||||||
\(407\) | −1.48086e11 | −0.267510 | ||||||||
\(408\) | 4.20561e10 | 0.0751377 | ||||||||
\(409\) | −4.77860e10 | −0.0844396 | −0.0422198 | − | 0.999108i | \(-0.513443\pi\) | ||||
−0.0422198 | + | 0.999108i | \(0.513443\pi\) | |||||||
\(410\) | −1.39323e11 | −0.243498 | ||||||||
\(411\) | −4.56243e11 | −0.788693 | ||||||||
\(412\) | −1.45569e11 | −0.248904 | ||||||||
\(413\) | 1.83665e11 | 0.310635 | ||||||||
\(414\) | 1.84185e11 | 0.308143 | ||||||||
\(415\) | 8.88369e10 | 0.147020 | ||||||||
\(416\) | −2.50062e11 | −0.409381 | ||||||||
\(417\) | −4.36954e11 | −0.707659 | ||||||||
\(418\) | 1.27129e12 | 2.03681 | ||||||||
\(419\) | −1.23633e11 | −0.195961 | −0.0979806 | − | 0.995188i | \(-0.531238\pi\) | ||||
−0.0979806 | + | 0.995188i | \(0.531238\pi\) | |||||||
\(420\) | −7.57317e10 | −0.118756 | ||||||||
\(421\) | −7.95967e11 | −1.23488 | −0.617442 | − | 0.786617i | \(-0.711831\pi\) | ||||
−0.617442 | + | 0.786617i | \(0.711831\pi\) | |||||||
\(422\) | 2.65457e11 | 0.407463 | ||||||||
\(423\) | 2.17484e11 | 0.330291 | ||||||||
\(424\) | 2.69379e11 | 0.404778 | ||||||||
\(425\) | −1.58351e11 | −0.235435 | ||||||||
\(426\) | −7.44006e11 | −1.09454 | ||||||||
\(427\) | 2.20148e11 | 0.320472 | ||||||||
\(428\) | 4.32570e11 | 0.623102 | ||||||||
\(429\) | 1.11902e11 | 0.159507 | ||||||||
\(430\) | −1.83623e11 | −0.259012 | ||||||||
\(431\) | 5.29976e11 | 0.739790 | 0.369895 | − | 0.929074i | \(-0.379394\pi\) | ||||
0.369895 | + | 0.929074i | \(0.379394\pi\) | |||||||
\(432\) | −3.57268e11 | −0.493535 | ||||||||
\(433\) | 8.23521e10 | 0.112585 | 0.0562923 | − | 0.998414i | \(-0.482072\pi\) | ||||
0.0562923 | + | 0.998414i | \(0.482072\pi\) | |||||||
\(434\) | 5.21170e11 | 0.705140 | ||||||||
\(435\) | 1.47576e11 | 0.197613 | ||||||||
\(436\) | 9.03547e11 | 1.19746 | ||||||||
\(437\) | −3.16483e11 | −0.415129 | ||||||||
\(438\) | 3.84198e10 | 0.0498795 | ||||||||
\(439\) | 2.06575e11 | 0.265453 | 0.132727 | − | 0.991153i | \(-0.457627\pi\) | ||||
0.132727 | + | 0.991153i | \(0.457627\pi\) | |||||||
\(440\) | 9.04599e10 | 0.115059 | ||||||||
\(441\) | 2.85776e11 | 0.359793 | ||||||||
\(442\) | 9.31414e10 | 0.116076 | ||||||||
\(443\) | 3.89537e11 | 0.480543 | 0.240271 | − | 0.970706i | \(-0.422764\pi\) | ||||
0.240271 | + | 0.970706i | \(0.422764\pi\) | |||||||
\(444\) | 1.77228e11 | 0.216426 | ||||||||
\(445\) | −6.13015e10 | −0.0741056 | ||||||||
\(446\) | 3.84122e11 | 0.459688 | ||||||||
\(447\) | 4.77484e11 | 0.565686 | ||||||||
\(448\) | 9.04477e11 | 1.06083 | ||||||||
\(449\) | −1.16999e12 | −1.35854 | −0.679271 | − | 0.733887i | \(-0.737704\pi\) | ||||
−0.679271 | + | 0.733887i | \(0.737704\pi\) | |||||||
\(450\) | −8.69263e11 | −0.999298 | ||||||||
\(451\) | −5.73767e11 | −0.653042 | ||||||||
\(452\) | −1.84158e12 | −2.07524 | ||||||||
\(453\) | 5.86417e10 | 0.0654282 | ||||||||
\(454\) | −2.00677e11 | −0.221690 | ||||||||
\(455\) | −4.37305e10 | −0.0478336 | ||||||||
\(456\) | −3.96693e11 | −0.429648 | ||||||||
\(457\) | 1.55946e12 | 1.67244 | 0.836221 | − | 0.548392i | \(-0.184760\pi\) | ||||
0.836221 | + | 0.548392i | \(0.184760\pi\) | |||||||
\(458\) | −1.11770e12 | −1.18695 | ||||||||
\(459\) | 2.22824e11 | 0.234318 | ||||||||
\(460\) | −8.63713e10 | −0.0899413 | ||||||||
\(461\) | 7.18326e11 | 0.740742 | 0.370371 | − | 0.928884i | \(-0.379230\pi\) | ||||
0.370371 | + | 0.928884i | \(0.379230\pi\) | |||||||
\(462\) | −5.42446e11 | −0.553947 | ||||||||
\(463\) | 7.79371e11 | 0.788188 | 0.394094 | − | 0.919070i | \(-0.371058\pi\) | ||||
0.394094 | + | 0.919070i | \(0.371058\pi\) | |||||||
\(464\) | −8.11084e11 | −0.812335 | ||||||||
\(465\) | 8.54300e10 | 0.0847369 | ||||||||
\(466\) | −1.91005e12 | −1.87633 | ||||||||
\(467\) | 1.68439e12 | 1.63876 | 0.819381 | − | 0.573250i | \(-0.194318\pi\) | ||||
0.819381 | + | 0.573250i | \(0.194318\pi\) | |||||||
\(468\) | 2.93972e11 | 0.283270 | ||||||||
\(469\) | 1.03510e12 | 0.987882 | ||||||||
\(470\) | −1.77382e11 | −0.167675 | ||||||||
\(471\) | 3.17740e10 | 0.0297494 | ||||||||
\(472\) | 2.62556e11 | 0.243491 | ||||||||
\(473\) | −7.56205e11 | −0.694647 | ||||||||
\(474\) | −3.66987e11 | −0.333924 | ||||||||
\(475\) | 1.49364e12 | 1.34625 | ||||||||
\(476\) | −2.59594e11 | −0.231773 | ||||||||
\(477\) | 5.81227e11 | 0.514060 | ||||||||
\(478\) | −1.65531e12 | −1.45028 | ||||||||
\(479\) | 4.99339e11 | 0.433396 | 0.216698 | − | 0.976239i | \(-0.430471\pi\) | ||||
0.216698 | + | 0.976239i | \(0.430471\pi\) | |||||||
\(480\) | 1.98700e11 | 0.170849 | ||||||||
\(481\) | 1.02339e11 | 0.0871740 | ||||||||
\(482\) | 1.15839e12 | 0.977560 | ||||||||
\(483\) | 1.35040e11 | 0.112902 | ||||||||
\(484\) | −2.04245e11 | −0.169179 | ||||||||
\(485\) | 1.03175e11 | 0.0846710 | ||||||||
\(486\) | 1.94825e12 | 1.58409 | ||||||||
\(487\) | 1.78158e12 | 1.43524 | 0.717619 | − | 0.696436i | \(-0.245232\pi\) | ||||
0.717619 | + | 0.696436i | \(0.245232\pi\) | |||||||
\(488\) | 3.14711e11 | 0.251202 | ||||||||
\(489\) | −3.23379e11 | −0.255754 | ||||||||
\(490\) | −2.33082e11 | −0.182652 | ||||||||
\(491\) | −5.85711e11 | −0.454796 | −0.227398 | − | 0.973802i | \(-0.573022\pi\) | ||||
−0.227398 | + | 0.973802i | \(0.573022\pi\) | |||||||
\(492\) | 6.86679e11 | 0.528337 | ||||||||
\(493\) | 5.05864e11 | 0.385676 | ||||||||
\(494\) | −8.78555e11 | −0.663740 | ||||||||
\(495\) | 1.95181e11 | 0.146122 | ||||||||
\(496\) | −4.69526e11 | −0.348331 | ||||||||
\(497\) | 1.19739e12 | 0.880302 | ||||||||
\(498\) | −7.61537e11 | −0.554828 | ||||||||
\(499\) | 3.39368e11 | 0.245030 | 0.122515 | − | 0.992467i | \(-0.460904\pi\) | ||||
0.122515 | + | 0.992467i | \(0.460904\pi\) | |||||||
\(500\) | 8.37485e11 | 0.599256 | ||||||||
\(501\) | 5.08611e11 | 0.360675 | ||||||||
\(502\) | 3.06366e12 | 2.15315 | ||||||||
\(503\) | 1.15682e12 | 0.805769 | 0.402884 | − | 0.915251i | \(-0.368008\pi\) | ||||
0.402884 | + | 0.915251i | \(0.368008\pi\) | |||||||
\(504\) | −3.71551e11 | −0.256496 | ||||||||
\(505\) | 4.87292e11 | 0.333410 | ||||||||
\(506\) | −6.18655e11 | −0.419538 | ||||||||
\(507\) | 7.54996e11 | 0.507468 | ||||||||
\(508\) | 7.55430e11 | 0.503277 | ||||||||
\(509\) | −2.22385e11 | −0.146850 | −0.0734251 | − | 0.997301i | \(-0.523393\pi\) | ||||
−0.0734251 | + | 0.997301i | \(0.523393\pi\) | |||||||
\(510\) | −7.40105e10 | −0.0484426 | ||||||||
\(511\) | −6.18322e10 | −0.0401163 | ||||||||
\(512\) | −1.53193e12 | −0.985201 | ||||||||
\(513\) | −2.10179e12 | −1.33986 | ||||||||
\(514\) | 5.36560e10 | 0.0339066 | ||||||||
\(515\) | 6.67923e10 | 0.0418402 | ||||||||
\(516\) | 9.05019e11 | 0.561997 | ||||||||
\(517\) | −7.30503e11 | −0.449692 | ||||||||
\(518\) | −4.96088e11 | −0.302743 | ||||||||
\(519\) | −1.29768e12 | −0.785082 | ||||||||
\(520\) | −6.25145e10 | −0.0374944 | ||||||||
\(521\) | 3.85547e11 | 0.229249 | 0.114625 | − | 0.993409i | \(-0.463433\pi\) | ||||
0.114625 | + | 0.993409i | \(0.463433\pi\) | |||||||
\(522\) | 2.77693e12 | 1.63699 | ||||||||
\(523\) | −1.73676e12 | −1.01504 | −0.507518 | − | 0.861641i | \(-0.669437\pi\) | ||||
−0.507518 | + | 0.861641i | \(0.669437\pi\) | |||||||
\(524\) | 3.47179e11 | 0.201170 | ||||||||
\(525\) | −6.37323e11 | −0.366136 | ||||||||
\(526\) | 3.44898e12 | 1.96451 | ||||||||
\(527\) | 2.92838e11 | 0.165379 | ||||||||
\(528\) | 4.88694e11 | 0.273643 | ||||||||
\(529\) | −1.64714e12 | −0.914493 | ||||||||
\(530\) | −4.74054e11 | −0.260968 | ||||||||
\(531\) | 5.66507e11 | 0.309229 | ||||||||
\(532\) | 2.44862e12 | 1.32531 | ||||||||
\(533\) | 3.96516e11 | 0.212808 | ||||||||
\(534\) | 5.25495e11 | 0.279662 | ||||||||
\(535\) | −1.98478e11 | −0.104742 | ||||||||
\(536\) | 1.47972e12 | 0.774350 | ||||||||
\(537\) | 8.74731e11 | 0.453932 | ||||||||
\(538\) | −2.80076e12 | −1.44130 | ||||||||
\(539\) | −9.59887e11 | −0.489859 | ||||||||
\(540\) | −5.73599e11 | −0.290293 | ||||||||
\(541\) | 1.77719e12 | 0.891964 | 0.445982 | − | 0.895042i | \(-0.352855\pi\) | ||||
0.445982 | + | 0.895042i | \(0.352855\pi\) | |||||||
\(542\) | −2.45147e12 | −1.22020 | ||||||||
\(543\) | −6.35380e11 | −0.313642 | ||||||||
\(544\) | 6.81107e11 | 0.333442 | ||||||||
\(545\) | −4.14580e11 | −0.201291 | ||||||||
\(546\) | 3.74871e11 | 0.180516 | ||||||||
\(547\) | −3.93472e12 | −1.87919 | −0.939595 | − | 0.342289i | \(-0.888798\pi\) | ||||
−0.939595 | + | 0.342289i | \(0.888798\pi\) | |||||||
\(548\) | 4.02586e12 | 1.90698 | ||||||||
\(549\) | 6.79039e11 | 0.319021 | ||||||||
\(550\) | 2.91975e12 | 1.36055 | ||||||||
\(551\) | −4.77156e12 | −2.20535 | ||||||||
\(552\) | 1.93045e11 | 0.0884980 | ||||||||
\(553\) | 5.90622e11 | 0.268563 | ||||||||
\(554\) | −2.02632e12 | −0.913934 | ||||||||
\(555\) | −8.13186e10 | −0.0363807 | ||||||||
\(556\) | 3.85566e12 | 1.71105 | ||||||||
\(557\) | 1.79477e12 | 0.790061 | 0.395031 | − | 0.918668i | \(-0.370734\pi\) | ||||
0.395031 | + | 0.918668i | \(0.370734\pi\) | |||||||
\(558\) | 1.60753e12 | 0.701947 | ||||||||
\(559\) | 5.22594e11 | 0.226366 | ||||||||
\(560\) | −1.90978e11 | −0.0820612 | ||||||||
\(561\) | −3.04793e11 | −0.129919 | ||||||||
\(562\) | 6.74198e11 | 0.285085 | ||||||||
\(563\) | 1.89933e12 | 0.796731 | 0.398365 | − | 0.917227i | \(-0.369578\pi\) | ||||
0.398365 | + | 0.917227i | \(0.369578\pi\) | |||||||
\(564\) | 8.74260e11 | 0.363818 | ||||||||
\(565\) | 8.44984e11 | 0.348843 | ||||||||
\(566\) | 5.09413e12 | 2.08639 | ||||||||
\(567\) | −2.70083e11 | −0.109742 | ||||||||
\(568\) | 1.71172e12 | 0.690024 | ||||||||
\(569\) | −2.64265e12 | −1.05690 | −0.528451 | − | 0.848964i | \(-0.677227\pi\) | ||||
−0.528451 | + | 0.848964i | \(0.677227\pi\) | |||||||
\(570\) | 6.98103e11 | 0.277002 | ||||||||
\(571\) | 2.85690e12 | 1.12469 | 0.562344 | − | 0.826903i | \(-0.309900\pi\) | ||||
0.562344 | + | 0.826903i | \(0.309900\pi\) | |||||||
\(572\) | −9.87417e11 | −0.385672 | ||||||||
\(573\) | −1.99394e12 | −0.772709 | ||||||||
\(574\) | −1.92212e12 | −0.739054 | ||||||||
\(575\) | −7.26861e11 | −0.277298 | ||||||||
\(576\) | 2.78982e12 | 1.05603 | ||||||||
\(577\) | 2.44238e12 | 0.917323 | 0.458662 | − | 0.888611i | \(-0.348329\pi\) | ||||
0.458662 | + | 0.888611i | \(0.348329\pi\) | |||||||
\(578\) | 3.86214e12 | 1.43930 | ||||||||
\(579\) | −2.11574e12 | −0.782363 | ||||||||
\(580\) | −1.30221e12 | −0.477808 | ||||||||
\(581\) | 1.22560e12 | 0.446228 | ||||||||
\(582\) | −8.84442e11 | −0.319533 | ||||||||
\(583\) | −1.95227e12 | −0.699893 | ||||||||
\(584\) | −8.83916e10 | −0.0314451 | ||||||||
\(585\) | −1.34885e11 | −0.0476170 | ||||||||
\(586\) | −2.23254e12 | −0.782095 | ||||||||
\(587\) | −4.14506e12 | −1.44098 | −0.720492 | − | 0.693463i | \(-0.756084\pi\) | ||||
−0.720492 | + | 0.693463i | \(0.756084\pi\) | |||||||
\(588\) | 1.14878e12 | 0.396315 | ||||||||
\(589\) | −2.76219e12 | −0.945660 | ||||||||
\(590\) | −4.62048e11 | −0.156983 | ||||||||
\(591\) | −1.18214e11 | −0.0398590 | ||||||||
\(592\) | 4.46929e11 | 0.149552 | ||||||||
\(593\) | 2.78764e12 | 0.925742 | 0.462871 | − | 0.886426i | \(-0.346819\pi\) | ||||
0.462871 | + | 0.886426i | \(0.346819\pi\) | |||||||
\(594\) | −4.10854e12 | −1.35409 | ||||||||
\(595\) | 1.19111e11 | 0.0389606 | ||||||||
\(596\) | −4.21330e12 | −1.36777 | ||||||||
\(597\) | 2.03050e12 | 0.654212 | ||||||||
\(598\) | 4.27537e11 | 0.136716 | ||||||||
\(599\) | 5.47204e11 | 0.173672 | 0.0868358 | − | 0.996223i | \(-0.472324\pi\) | ||||
0.0868358 | + | 0.996223i | \(0.472324\pi\) | |||||||
\(600\) | −9.11079e11 | −0.286996 | ||||||||
\(601\) | −2.82471e12 | −0.883160 | −0.441580 | − | 0.897222i | \(-0.645582\pi\) | ||||
−0.441580 | + | 0.897222i | \(0.645582\pi\) | |||||||
\(602\) | −2.53328e12 | −0.786139 | ||||||||
\(603\) | 3.19273e12 | 0.983408 | ||||||||
\(604\) | −5.17451e11 | −0.158199 | ||||||||
\(605\) | 9.37147e10 | 0.0284386 | ||||||||
\(606\) | −4.17721e12 | −1.25823 | ||||||||
\(607\) | −3.14194e12 | −0.939397 | −0.469699 | − | 0.882827i | \(-0.655637\pi\) | ||||
−0.469699 | + | 0.882827i | \(0.655637\pi\) | |||||||
\(608\) | −6.42453e12 | −1.90667 | ||||||||
\(609\) | 2.03598e12 | 0.599785 | ||||||||
\(610\) | −5.53830e11 | −0.161954 | ||||||||
\(611\) | 5.04832e11 | 0.146542 | ||||||||
\(612\) | −8.00708e11 | −0.230724 | ||||||||
\(613\) | −4.73278e12 | −1.35377 | −0.676885 | − | 0.736089i | \(-0.736670\pi\) | ||||
−0.676885 | + | 0.736089i | \(0.736670\pi\) | |||||||
\(614\) | 3.73518e12 | 1.06061 | ||||||||
\(615\) | −3.15073e11 | −0.0888123 | ||||||||
\(616\) | 1.24799e12 | 0.349220 | ||||||||
\(617\) | −1.65834e12 | −0.460671 | −0.230335 | − | 0.973111i | \(-0.573982\pi\) | ||||
−0.230335 | + | 0.973111i | \(0.573982\pi\) | |||||||
\(618\) | −5.72563e11 | −0.157898 | ||||||||
\(619\) | 3.65341e12 | 1.00021 | 0.500105 | − | 0.865965i | \(-0.333295\pi\) | ||||
0.500105 | + | 0.865965i | \(0.333295\pi\) | |||||||
\(620\) | −7.53830e11 | −0.204885 | ||||||||
\(621\) | 1.02281e12 | 0.275982 | ||||||||
\(622\) | −8.83706e12 | −2.36729 | ||||||||
\(623\) | −8.45721e11 | −0.224922 | ||||||||
\(624\) | −3.37724e11 | −0.0891727 | ||||||||
\(625\) | 3.23320e12 | 0.847563 | ||||||||
\(626\) | 3.41922e11 | 0.0889901 | ||||||||
\(627\) | 2.87496e12 | 0.742895 | ||||||||
\(628\) | −2.80372e11 | −0.0719310 | ||||||||
\(629\) | −2.78745e11 | −0.0710034 | ||||||||
\(630\) | 6.53857e11 | 0.165367 | ||||||||
\(631\) | −3.13554e12 | −0.787373 | −0.393687 | − | 0.919245i | \(-0.628800\pi\) | ||||
−0.393687 | + | 0.919245i | \(0.628800\pi\) | |||||||
\(632\) | 8.44317e11 | 0.210513 | ||||||||
\(633\) | 6.00319e11 | 0.148616 | ||||||||
\(634\) | −4.81974e12 | −1.18474 | ||||||||
\(635\) | −3.46618e11 | −0.0845999 | ||||||||
\(636\) | 2.33646e12 | 0.566241 | ||||||||
\(637\) | 6.63354e11 | 0.159631 | ||||||||
\(638\) | −9.32736e12 | −2.22877 | ||||||||
\(639\) | 3.69330e12 | 0.876315 | ||||||||
\(640\) | −9.79230e11 | −0.230714 | ||||||||
\(641\) | 3.92823e12 | 0.919042 | 0.459521 | − | 0.888167i | \(-0.348021\pi\) | ||||
0.459521 | + | 0.888167i | \(0.348021\pi\) | |||||||
\(642\) | 1.70142e12 | 0.395278 | ||||||||
\(643\) | −2.71651e11 | −0.0626702 | −0.0313351 | − | 0.999509i | \(-0.509976\pi\) | ||||
−0.0313351 | + | 0.999509i | \(0.509976\pi\) | |||||||
\(644\) | −1.19159e12 | −0.272985 | ||||||||
\(645\) | −4.15255e11 | −0.0944705 | ||||||||
\(646\) | 2.39297e12 | 0.540618 | ||||||||
\(647\) | −4.95489e12 | −1.11164 | −0.555821 | − | 0.831302i | \(-0.687596\pi\) | ||||
−0.555821 | + | 0.831302i | \(0.687596\pi\) | |||||||
\(648\) | −3.86095e11 | −0.0860214 | ||||||||
\(649\) | −1.90283e12 | −0.421015 | ||||||||
\(650\) | −2.01776e12 | −0.443364 | ||||||||
\(651\) | 1.17860e12 | 0.257189 | ||||||||
\(652\) | 2.85348e12 | 0.618387 | ||||||||
\(653\) | −1.24814e11 | −0.0268629 | −0.0134314 | − | 0.999910i | \(-0.504275\pi\) | ||||
−0.0134314 | + | 0.999910i | \(0.504275\pi\) | |||||||
\(654\) | 3.55390e12 | 0.759635 | ||||||||
\(655\) | −1.59298e11 | −0.0338162 | ||||||||
\(656\) | 1.73165e12 | 0.365084 | ||||||||
\(657\) | −1.90719e11 | −0.0399346 | ||||||||
\(658\) | −2.44718e12 | −0.508920 | ||||||||
\(659\) | 6.61121e12 | 1.36552 | 0.682758 | − | 0.730645i | \(-0.260780\pi\) | ||||
0.682758 | + | 0.730645i | \(0.260780\pi\) | |||||||
\(660\) | 7.84605e11 | 0.160955 | ||||||||
\(661\) | −1.86809e12 | −0.380620 | −0.190310 | − | 0.981724i | \(-0.560949\pi\) | ||||
−0.190310 | + | 0.981724i | \(0.560949\pi\) | |||||||
\(662\) | −7.51851e12 | −1.52150 | ||||||||
\(663\) | 2.10635e11 | 0.0423370 | ||||||||
\(664\) | 1.75205e12 | 0.349776 | ||||||||
\(665\) | −1.12351e12 | −0.222782 | ||||||||
\(666\) | −1.53016e12 | −0.301372 | ||||||||
\(667\) | 2.32201e12 | 0.454254 | ||||||||
\(668\) | −4.48796e12 | −0.872076 | ||||||||
\(669\) | 8.68675e11 | 0.167664 | ||||||||
\(670\) | −2.60402e12 | −0.499237 | ||||||||
\(671\) | −2.28081e12 | −0.434348 | ||||||||
\(672\) | 2.74128e12 | 0.518552 | ||||||||
\(673\) | −7.86777e12 | −1.47837 | −0.739186 | − | 0.673501i | \(-0.764790\pi\) | ||||
−0.739186 | + | 0.673501i | \(0.764790\pi\) | |||||||
\(674\) | −9.43584e12 | −1.76121 | ||||||||
\(675\) | −4.82714e12 | −0.895000 | ||||||||
\(676\) | −6.66204e12 | −1.22701 | ||||||||
\(677\) | −2.30065e12 | −0.420922 | −0.210461 | − | 0.977602i | \(-0.567496\pi\) | ||||
−0.210461 | + | 0.977602i | \(0.567496\pi\) | |||||||
\(678\) | −7.24346e12 | −1.31647 | ||||||||
\(679\) | 1.42341e12 | 0.256989 | ||||||||
\(680\) | 1.70274e11 | 0.0305393 | ||||||||
\(681\) | −4.53822e11 | −0.0808582 | ||||||||
\(682\) | −5.39948e12 | −0.955702 | ||||||||
\(683\) | −1.72763e12 | −0.303779 | −0.151889 | − | 0.988397i | \(-0.548536\pi\) | ||||
−0.151889 | + | 0.988397i | \(0.548536\pi\) | |||||||
\(684\) | 7.55266e12 | 1.31931 | ||||||||
\(685\) | −1.84721e12 | −0.320560 | ||||||||
\(686\) | −9.35578e12 | −1.61295 | ||||||||
\(687\) | −2.52763e12 | −0.432921 | ||||||||
\(688\) | 2.28225e12 | 0.388343 | ||||||||
\(689\) | 1.34917e12 | 0.228076 | ||||||||
\(690\) | −3.39722e11 | −0.0570562 | ||||||||
\(691\) | −6.13080e12 | −1.02298 | −0.511489 | − | 0.859290i | \(-0.670906\pi\) | ||||
−0.511489 | + | 0.859290i | \(0.670906\pi\) | |||||||
\(692\) | 1.14507e13 | 1.89825 | ||||||||
\(693\) | 2.69274e12 | 0.443502 | ||||||||
\(694\) | −5.51864e12 | −0.903055 | ||||||||
\(695\) | −1.76911e12 | −0.287623 | ||||||||
\(696\) | 2.91051e12 | 0.470141 | ||||||||
\(697\) | −1.08001e12 | −0.173333 | ||||||||
\(698\) | 1.38155e13 | 2.20301 | ||||||||
\(699\) | −4.31950e12 | −0.684362 | ||||||||
\(700\) | 5.62370e12 | 0.885281 | ||||||||
\(701\) | 3.06258e12 | 0.479024 | 0.239512 | − | 0.970893i | \(-0.423013\pi\) | ||||
0.239512 | + | 0.970893i | \(0.423013\pi\) | |||||||
\(702\) | 2.83931e12 | 0.441261 | ||||||||
\(703\) | 2.62926e12 | 0.406008 | ||||||||
\(704\) | −9.37067e12 | −1.43778 | ||||||||
\(705\) | −4.01142e11 | −0.0611571 | ||||||||
\(706\) | −1.18850e12 | −0.180044 | ||||||||
\(707\) | 6.72273e12 | 1.01195 | ||||||||
\(708\) | 2.27728e12 | 0.340618 | ||||||||
\(709\) | 7.23288e12 | 1.07499 | 0.537493 | − | 0.843268i | \(-0.319371\pi\) | ||||
0.537493 | + | 0.843268i | \(0.319371\pi\) | |||||||
\(710\) | −3.01229e12 | −0.444871 | ||||||||
\(711\) | 1.82175e12 | 0.267347 | ||||||||
\(712\) | −1.20899e12 | −0.176305 | ||||||||
\(713\) | 1.34418e12 | 0.194785 | ||||||||
\(714\) | −1.02106e12 | −0.147030 | ||||||||
\(715\) | 4.53062e11 | 0.0648307 | ||||||||
\(716\) | −7.71858e12 | −1.09756 | ||||||||
\(717\) | −3.74340e12 | −0.528969 | ||||||||
\(718\) | 7.56581e12 | 1.06242 | ||||||||
\(719\) | 1.09651e13 | 1.53014 | 0.765072 | − | 0.643944i | \(-0.222703\pi\) | ||||
0.765072 | + | 0.643944i | \(0.222703\pi\) | |||||||
\(720\) | −5.89065e11 | −0.0816896 | ||||||||
\(721\) | 9.21473e11 | 0.126991 | ||||||||
\(722\) | −1.13721e13 | −1.55748 | ||||||||
\(723\) | 2.61965e12 | 0.356550 | ||||||||
\(724\) | 5.60656e12 | 0.758355 | ||||||||
\(725\) | −1.09588e13 | −1.47313 | ||||||||
\(726\) | −8.03350e11 | −0.107322 | ||||||||
\(727\) | 1.30404e13 | 1.73135 | 0.865676 | − | 0.500604i | \(-0.166889\pi\) | ||||
0.865676 | + | 0.500604i | \(0.166889\pi\) | |||||||
\(728\) | −8.62456e11 | −0.113801 | ||||||||
\(729\) | 3.19329e12 | 0.418760 | ||||||||
\(730\) | 1.55552e11 | 0.0202732 | ||||||||
\(731\) | −1.42342e12 | −0.184376 | ||||||||
\(732\) | 2.72965e12 | 0.351404 | ||||||||
\(733\) | −1.43509e12 | −0.183616 | −0.0918080 | − | 0.995777i | \(-0.529265\pi\) | ||||
−0.0918080 | + | 0.995777i | \(0.529265\pi\) | |||||||
\(734\) | −2.13043e13 | −2.70917 | ||||||||
\(735\) | −5.27103e11 | −0.0666197 | ||||||||
\(736\) | 3.12641e12 | 0.392731 | ||||||||
\(737\) | −1.07240e13 | −1.33891 | ||||||||
\(738\) | −5.92869e12 | −0.735707 | ||||||||
\(739\) | −9.09373e12 | −1.12161 | −0.560805 | − | 0.827948i | \(-0.689508\pi\) | ||||
−0.560805 | + | 0.827948i | \(0.689508\pi\) | |||||||
\(740\) | 7.17551e11 | 0.0879650 | ||||||||
\(741\) | −1.98681e12 | −0.242089 | ||||||||
\(742\) | −6.54010e12 | −0.792076 | ||||||||
\(743\) | −1.54607e12 | −0.186115 | −0.0930573 | − | 0.995661i | \(-0.529664\pi\) | ||||
−0.0930573 | + | 0.995661i | \(0.529664\pi\) | |||||||
\(744\) | 1.68486e12 | 0.201597 | ||||||||
\(745\) | 1.93321e12 | 0.229920 | ||||||||
\(746\) | −1.34964e13 | −1.59548 | ||||||||
\(747\) | 3.78032e12 | 0.444208 | ||||||||
\(748\) | 2.68948e12 | 0.314131 | ||||||||
\(749\) | −2.73823e12 | −0.317908 | ||||||||
\(750\) | 3.29406e12 | 0.380151 | ||||||||
\(751\) | −5.99142e12 | −0.687306 | −0.343653 | − | 0.939097i | \(-0.611664\pi\) | ||||
−0.343653 | + | 0.939097i | \(0.611664\pi\) | |||||||
\(752\) | 2.20469e12 | 0.251401 | ||||||||
\(753\) | 6.92832e12 | 0.785328 | ||||||||
\(754\) | 6.44590e12 | 0.726294 | ||||||||
\(755\) | 2.37425e11 | 0.0265929 | ||||||||
\(756\) | −7.91342e12 | −0.881082 | ||||||||
\(757\) | 9.68176e12 | 1.07158 | 0.535788 | − | 0.844353i | \(-0.320015\pi\) | ||||
0.535788 | + | 0.844353i | \(0.320015\pi\) | |||||||
\(758\) | 1.39069e13 | 1.53009 | ||||||||
\(759\) | −1.39906e12 | −0.153020 | ||||||||
\(760\) | −1.60611e12 | −0.174628 | ||||||||
\(761\) | 9.51077e12 | 1.02798 | 0.513990 | − | 0.857796i | \(-0.328167\pi\) | ||||
0.513990 | + | 0.857796i | \(0.328167\pi\) | |||||||
\(762\) | 2.97131e12 | 0.319265 | ||||||||
\(763\) | −5.71958e12 | −0.610947 | ||||||||
\(764\) | 1.75944e13 | 1.86833 | ||||||||
\(765\) | 3.67393e11 | 0.0387842 | ||||||||
\(766\) | −1.88916e13 | −1.98262 | ||||||||
\(767\) | 1.31500e12 | 0.137197 | ||||||||
\(768\) | 1.03547e11 | 0.0107402 | ||||||||
\(769\) | −5.53577e12 | −0.570834 | −0.285417 | − | 0.958403i | \(-0.592132\pi\) | ||||
−0.285417 | + | 0.958403i | \(0.592132\pi\) | |||||||
\(770\) | −2.19622e12 | −0.225148 | ||||||||
\(771\) | 1.21341e11 | 0.0123669 | ||||||||
\(772\) | 1.86692e13 | 1.89168 | ||||||||
\(773\) | −2.03244e12 | −0.204744 | −0.102372 | − | 0.994746i | \(-0.532643\pi\) | ||||
−0.102372 | + | 0.994746i | \(0.532643\pi\) | |||||||
\(774\) | −7.81380e12 | −0.782579 | ||||||||
\(775\) | −6.34389e12 | −0.631681 | ||||||||
\(776\) | 2.03481e12 | 0.201441 | ||||||||
\(777\) | −1.12188e12 | −0.110421 | ||||||||
\(778\) | 2.16628e13 | 2.11986 | ||||||||
\(779\) | 1.01872e13 | 0.991142 | ||||||||
\(780\) | −5.42221e11 | −0.0524506 | ||||||||
\(781\) | −1.24053e13 | −1.19311 | ||||||||
\(782\) | −1.16450e12 | −0.111355 | ||||||||
\(783\) | 1.54207e13 | 1.46614 | ||||||||
\(784\) | 2.89697e12 | 0.273856 | ||||||||
\(785\) | 1.28645e11 | 0.0120914 | ||||||||
\(786\) | 1.36555e12 | 0.127616 | ||||||||
\(787\) | 1.56177e13 | 1.45121 | 0.725607 | − | 0.688110i | \(-0.241559\pi\) | ||||
0.725607 | + | 0.688110i | \(0.241559\pi\) | |||||||
\(788\) | 1.04312e12 | 0.0963750 | ||||||||
\(789\) | 7.79971e12 | 0.716526 | ||||||||
\(790\) | −1.48583e12 | −0.135721 | ||||||||
\(791\) | 1.16575e13 | 1.05879 | ||||||||
\(792\) | 3.84938e12 | 0.347638 | ||||||||
\(793\) | 1.57621e12 | 0.141542 | ||||||||
\(794\) | −2.38091e12 | −0.212594 | ||||||||
\(795\) | −1.07205e12 | −0.0951839 | ||||||||
\(796\) | −1.79170e13 | −1.58182 | ||||||||
\(797\) | −1.65794e13 | −1.45548 | −0.727742 | − | 0.685851i | \(-0.759430\pi\) | ||||
−0.727742 | + | 0.685851i | \(0.759430\pi\) | |||||||
\(798\) | 9.63109e12 | 0.840741 | ||||||||
\(799\) | −1.37504e12 | −0.119359 | ||||||||
\(800\) | −1.47551e13 | −1.27361 | ||||||||
\(801\) | −2.60859e12 | −0.223903 | ||||||||
\(802\) | 3.19509e13 | 2.72708 | ||||||||
\(803\) | 6.40601e11 | 0.0543711 | ||||||||
\(804\) | 1.28344e13 | 1.08323 | ||||||||
\(805\) | 5.46742e11 | 0.0458882 | ||||||||
\(806\) | 3.73145e12 | 0.311437 | ||||||||
\(807\) | −6.33378e12 | −0.525693 | ||||||||
\(808\) | 9.61041e12 | 0.793215 | ||||||||
\(809\) | −6.70961e12 | −0.550717 | −0.275359 | − | 0.961342i | \(-0.588797\pi\) | ||||
−0.275359 | + | 0.961342i | \(0.588797\pi\) | |||||||
\(810\) | 6.79452e11 | 0.0554595 | ||||||||
\(811\) | −9.43966e12 | −0.766236 | −0.383118 | − | 0.923699i | \(-0.625150\pi\) | ||||
−0.383118 | + | 0.923699i | \(0.625150\pi\) | |||||||
\(812\) | −1.79654e13 | −1.45022 | ||||||||
\(813\) | −5.54389e12 | −0.445048 | ||||||||
\(814\) | 5.13963e12 | 0.410319 | ||||||||
\(815\) | −1.30928e12 | −0.103950 | ||||||||
\(816\) | 9.19877e11 | 0.0726314 | ||||||||
\(817\) | 1.34264e13 | 1.05429 | ||||||||
\(818\) | 1.65851e12 | 0.129517 | ||||||||
\(819\) | −1.86089e12 | −0.144525 | ||||||||
\(820\) | 2.78019e12 | 0.214739 | ||||||||
\(821\) | 5.58747e12 | 0.429211 | 0.214606 | − | 0.976701i | \(-0.431153\pi\) | ||||
0.214606 | + | 0.976701i | \(0.431153\pi\) | |||||||
\(822\) | 1.58348e13 | 1.20974 | ||||||||
\(823\) | −1.54375e12 | −0.117294 | −0.0586472 | − | 0.998279i | \(-0.518679\pi\) | ||||
−0.0586472 | + | 0.998279i | \(0.518679\pi\) | |||||||
\(824\) | 1.31728e12 | 0.0995420 | ||||||||
\(825\) | 6.60287e12 | 0.496238 | ||||||||
\(826\) | −6.37445e12 | −0.476467 | ||||||||
\(827\) | 1.60862e13 | 1.19585 | 0.597926 | − | 0.801551i | \(-0.295992\pi\) | ||||
0.597926 | + | 0.801551i | \(0.295992\pi\) | |||||||
\(828\) | −3.67540e12 | −0.271749 | ||||||||
\(829\) | 2.18581e13 | 1.60738 | 0.803689 | − | 0.595050i | \(-0.202868\pi\) | ||||
0.803689 | + | 0.595050i | \(0.202868\pi\) | |||||||
\(830\) | −3.08326e12 | −0.225507 | ||||||||
\(831\) | −4.58244e12 | −0.333343 | ||||||||
\(832\) | 6.47583e12 | 0.468534 | ||||||||
\(833\) | −1.80681e12 | −0.130020 | ||||||||
\(834\) | 1.51654e13 | 1.08544 | ||||||||
\(835\) | 2.05923e12 | 0.146594 | ||||||||
\(836\) | −2.53685e13 | −1.79625 | ||||||||
\(837\) | 8.92683e12 | 0.628684 | ||||||||
\(838\) | 4.29092e12 | 0.300574 | ||||||||
\(839\) | 1.41779e13 | 0.987831 | 0.493915 | − | 0.869510i | \(-0.335565\pi\) | ||||
0.493915 | + | 0.869510i | \(0.335565\pi\) | |||||||
\(840\) | 6.85311e11 | 0.0474931 | ||||||||
\(841\) | 2.05015e13 | 1.41320 | ||||||||
\(842\) | 2.76256e13 | 1.89412 | ||||||||
\(843\) | 1.52467e12 | 0.103980 | ||||||||
\(844\) | −5.29718e12 | −0.359339 | ||||||||
\(845\) | 3.05678e12 | 0.206257 | ||||||||
\(846\) | −7.54823e12 | −0.506616 | ||||||||
\(847\) | 1.29290e12 | 0.0863154 | ||||||||
\(848\) | 5.89203e12 | 0.391276 | ||||||||
\(849\) | 1.15201e13 | 0.760979 | ||||||||
\(850\) | 5.49589e12 | 0.361121 | ||||||||
\(851\) | −1.27949e12 | −0.0836286 | ||||||||
\(852\) | 1.48466e13 | 0.965269 | ||||||||
\(853\) | 8.74262e12 | 0.565420 | 0.282710 | − | 0.959205i | \(-0.408767\pi\) | ||||
0.282710 | + | 0.959205i | \(0.408767\pi\) | |||||||
\(854\) | −7.64069e12 | −0.491555 | ||||||||
\(855\) | −3.46543e12 | −0.221774 | ||||||||
\(856\) | −3.91441e12 | −0.249192 | ||||||||
\(857\) | 1.69587e13 | 1.07394 | 0.536969 | − | 0.843602i | \(-0.319569\pi\) | ||||
0.536969 | + | 0.843602i | \(0.319569\pi\) | |||||||
\(858\) | −3.88378e12 | −0.244660 | ||||||||
\(859\) | 2.06546e13 | 1.29434 | 0.647169 | − | 0.762346i | \(-0.275953\pi\) | ||||
0.647169 | + | 0.762346i | \(0.275953\pi\) | |||||||
\(860\) | 3.66419e12 | 0.228420 | ||||||||
\(861\) | −4.34678e12 | −0.269559 | ||||||||
\(862\) | −1.83939e13 | −1.13473 | ||||||||
\(863\) | −1.47651e13 | −0.906126 | −0.453063 | − | 0.891478i | \(-0.649669\pi\) | ||||
−0.453063 | + | 0.891478i | \(0.649669\pi\) | |||||||
\(864\) | 2.07627e13 | 1.26757 | ||||||||
\(865\) | −5.25398e12 | −0.319092 | ||||||||
\(866\) | −2.85819e12 | −0.172688 | ||||||||
\(867\) | 8.73404e12 | 0.524964 | ||||||||
\(868\) | −1.03999e13 | −0.621857 | ||||||||
\(869\) | −6.11903e12 | −0.363993 | ||||||||
\(870\) | −5.12194e12 | −0.303108 | ||||||||
\(871\) | 7.41107e12 | 0.436314 | ||||||||
\(872\) | −8.17637e12 | −0.478890 | ||||||||
\(873\) | 4.39044e12 | 0.255825 | ||||||||
\(874\) | 1.09842e13 | 0.636745 | ||||||||
\(875\) | −5.30140e12 | −0.305742 | ||||||||
\(876\) | −7.66666e11 | −0.0439883 | ||||||||
\(877\) | 1.84154e13 | 1.05119 | 0.525597 | − | 0.850734i | \(-0.323842\pi\) | ||||
0.525597 | + | 0.850734i | \(0.323842\pi\) | |||||||
\(878\) | −7.16961e12 | −0.407165 | ||||||||
\(879\) | −5.04878e12 | −0.285257 | ||||||||
\(880\) | 1.97860e12 | 0.111221 | ||||||||
\(881\) | 4.40458e9 | 0.000246328 0 | 0.000123164 | − | 1.00000i | \(-0.499961\pi\) | ||||
0.000123164 | 1.00000i | \(0.499961\pi\) | ||||||||
\(882\) | −9.91843e12 | −0.551867 | ||||||||
\(883\) | −2.14276e13 | −1.18618 | −0.593090 | − | 0.805136i | \(-0.702092\pi\) | ||||
−0.593090 | + | 0.805136i | \(0.702092\pi\) | |||||||
\(884\) | −1.85863e12 | −0.102367 | ||||||||
\(885\) | −1.04490e12 | −0.0572572 | ||||||||
\(886\) | −1.35197e13 | −0.737079 | ||||||||
\(887\) | −1.16483e13 | −0.631836 | −0.315918 | − | 0.948786i | \(-0.602312\pi\) | ||||
−0.315918 | + | 0.948786i | \(0.602312\pi\) | |||||||
\(888\) | −1.60377e12 | −0.0865534 | ||||||||
\(889\) | −4.78198e12 | −0.256773 | ||||||||
\(890\) | 2.12759e12 | 0.113667 | ||||||||
\(891\) | 2.79815e12 | 0.148738 | ||||||||
\(892\) | −7.66514e12 | −0.405395 | ||||||||
\(893\) | 1.29700e13 | 0.682510 | ||||||||
\(894\) | −1.65721e13 | −0.867676 | ||||||||
\(895\) | 3.54156e12 | 0.184498 | ||||||||
\(896\) | −1.35095e13 | −0.700253 | ||||||||
\(897\) | 9.66855e11 | 0.0498649 | ||||||||
\(898\) | 4.06068e13 | 2.08380 | ||||||||
\(899\) | 2.02660e13 | 1.03478 | ||||||||
\(900\) | 1.73461e13 | 0.881273 | ||||||||
\(901\) | −3.67479e12 | −0.185768 | ||||||||
\(902\) | 1.99137e13 | 1.00167 | ||||||||
\(903\) | −5.72890e12 | −0.286732 | ||||||||
\(904\) | 1.66648e13 | 0.829933 | ||||||||
\(905\) | −2.57249e12 | −0.127478 | ||||||||
\(906\) | −2.03528e12 | −0.100357 | ||||||||
\(907\) | 1.69591e13 | 0.832088 | 0.416044 | − | 0.909344i | \(-0.363416\pi\) | ||||
0.416044 | + | 0.909344i | \(0.363416\pi\) | |||||||
\(908\) | 4.00450e12 | 0.195507 | ||||||||
\(909\) | 2.07360e13 | 1.00737 | ||||||||
\(910\) | 1.51776e12 | 0.0733695 | ||||||||
\(911\) | −1.52448e13 | −0.733310 | −0.366655 | − | 0.930357i | \(-0.619497\pi\) | ||||
−0.366655 | + | 0.930357i | \(0.619497\pi\) | |||||||
\(912\) | −8.67673e12 | −0.415317 | ||||||||
\(913\) | −1.26976e13 | −0.604790 | ||||||||
\(914\) | −5.41242e13 | −2.56527 | ||||||||
\(915\) | −1.25246e12 | −0.0590703 | ||||||||
\(916\) | 2.23037e13 | 1.04676 | ||||||||
\(917\) | −2.19769e12 | −0.102637 | ||||||||
\(918\) | −7.73357e12 | −0.359408 | ||||||||
\(919\) | 1.71192e13 | 0.791704 | 0.395852 | − | 0.918314i | \(-0.370449\pi\) | ||||
0.395852 | + | 0.918314i | \(0.370449\pi\) | |||||||
\(920\) | 7.81590e11 | 0.0359695 | ||||||||
\(921\) | 8.44694e12 | 0.386840 | ||||||||
\(922\) | −2.49309e13 | −1.13619 | ||||||||
\(923\) | 8.57301e12 | 0.388800 | ||||||||
\(924\) | 1.08245e13 | 0.488521 | ||||||||
\(925\) | 6.03858e12 | 0.271204 | ||||||||
\(926\) | −2.70496e13 | −1.20896 | ||||||||
\(927\) | 2.84225e12 | 0.126416 | ||||||||
\(928\) | 4.71363e13 | 2.08636 | ||||||||
\(929\) | −2.10069e13 | −0.925318 | −0.462659 | − | 0.886536i | \(-0.653105\pi\) | ||||
−0.462659 | + | 0.886536i | \(0.653105\pi\) | |||||||
\(930\) | −2.96502e12 | −0.129973 | ||||||||
\(931\) | 1.70427e13 | 0.743473 | ||||||||
\(932\) | 3.81150e13 | 1.65472 | ||||||||
\(933\) | −1.99846e13 | −0.863432 | ||||||||
\(934\) | −5.84600e13 | −2.51361 | ||||||||
\(935\) | −1.23403e12 | −0.0528048 | ||||||||
\(936\) | −2.66021e12 | −0.113286 | ||||||||
\(937\) | 1.95899e13 | 0.830240 | 0.415120 | − | 0.909767i | \(-0.363740\pi\) | ||||
0.415120 | + | 0.909767i | \(0.363740\pi\) | |||||||
\(938\) | −3.59253e13 | −1.51526 | ||||||||
\(939\) | 7.73240e11 | 0.0324578 | ||||||||
\(940\) | 3.53965e12 | 0.147872 | ||||||||
\(941\) | −4.14361e13 | −1.72276 | −0.861382 | − | 0.507957i | \(-0.830401\pi\) | ||||
−0.861382 | + | 0.507957i | \(0.830401\pi\) | |||||||
\(942\) | −1.10278e12 | −0.0456310 | ||||||||
\(943\) | −4.95746e12 | −0.204153 | ||||||||
\(944\) | 5.74280e12 | 0.235369 | ||||||||
\(945\) | 3.63096e12 | 0.148108 | ||||||||
\(946\) | 2.62456e13 | 1.06548 | ||||||||
\(947\) | −5.17476e12 | −0.209081 | −0.104541 | − | 0.994521i | \(-0.533337\pi\) | ||||
−0.104541 | + | 0.994521i | \(0.533337\pi\) | |||||||
\(948\) | 7.32320e12 | 0.294485 | ||||||||
\(949\) | −4.42703e11 | −0.0177180 | ||||||||
\(950\) | −5.18399e13 | −2.06494 | ||||||||
\(951\) | −1.08996e13 | −0.432114 | ||||||||
\(952\) | 2.34912e12 | 0.0926912 | ||||||||
\(953\) | −2.26576e13 | −0.889808 | −0.444904 | − | 0.895578i | \(-0.646762\pi\) | ||||
−0.444904 | + | 0.895578i | \(0.646762\pi\) | |||||||
\(954\) | −2.01727e13 | −0.788489 | ||||||||
\(955\) | −8.07294e12 | −0.314063 | ||||||||
\(956\) | 3.30315e13 | 1.27899 | ||||||||
\(957\) | −2.10934e13 | −0.812910 | ||||||||
\(958\) | −1.73305e13 | −0.664764 | ||||||||
\(959\) | −2.54843e13 | −0.972946 | ||||||||
\(960\) | −5.14572e12 | −0.195535 | ||||||||
\(961\) | −1.47079e13 | −0.556282 | ||||||||
\(962\) | −3.55187e12 | −0.133712 | ||||||||
\(963\) | −8.44595e12 | −0.316468 | ||||||||
\(964\) | −2.31156e13 | −0.862103 | ||||||||
\(965\) | −8.56608e12 | −0.317987 | ||||||||
\(966\) | −4.68684e12 | −0.173174 | ||||||||
\(967\) | 4.77063e13 | 1.75451 | 0.877257 | − | 0.480021i | \(-0.159371\pi\) | ||||
0.877257 | + | 0.480021i | \(0.159371\pi\) | |||||||
\(968\) | 1.84825e12 | 0.0676583 | ||||||||
\(969\) | 5.41158e12 | 0.197182 | ||||||||
\(970\) | −3.58088e12 | −0.129872 | ||||||||
\(971\) | −2.95828e13 | −1.06796 | −0.533978 | − | 0.845498i | \(-0.679304\pi\) | ||||
−0.533978 | + | 0.845498i | \(0.679304\pi\) | |||||||
\(972\) | −3.88771e13 | −1.39700 | ||||||||
\(973\) | −2.44069e13 | −0.872980 | ||||||||
\(974\) | −6.18332e13 | −2.20144 | ||||||||
\(975\) | −4.56308e12 | −0.161710 | ||||||||
\(976\) | 6.88356e12 | 0.242823 | ||||||||
\(977\) | 4.08329e13 | 1.43379 | 0.716893 | − | 0.697183i | \(-0.245564\pi\) | ||||
0.716893 | + | 0.697183i | \(0.245564\pi\) | |||||||
\(978\) | 1.12235e13 | 0.392287 | ||||||||
\(979\) | 8.76195e12 | 0.304845 | ||||||||
\(980\) | 4.65113e12 | 0.161080 | ||||||||
\(981\) | −1.76418e13 | −0.608181 | ||||||||
\(982\) | 2.03283e13 | 0.697587 | ||||||||
\(983\) | 2.71445e13 | 0.927239 | 0.463619 | − | 0.886034i | \(-0.346551\pi\) | ||||
0.463619 | + | 0.886034i | \(0.346551\pi\) | |||||||
\(984\) | −6.21389e12 | −0.211293 | ||||||||
\(985\) | −4.78619e11 | −0.0162004 | ||||||||
\(986\) | −1.75570e13 | −0.591569 | ||||||||
\(987\) | −5.53419e12 | −0.185621 | ||||||||
\(988\) | 1.75315e13 | 0.585347 | ||||||||
\(989\) | −6.53375e12 | −0.217160 | ||||||||
\(990\) | −6.77416e12 | −0.224129 | ||||||||
\(991\) | 3.58312e13 | 1.18013 | 0.590064 | − | 0.807356i | \(-0.299102\pi\) | ||||
0.590064 | + | 0.807356i | \(0.299102\pi\) | |||||||
\(992\) | 2.72866e13 | 0.894637 | ||||||||
\(993\) | −1.70028e13 | −0.554942 | ||||||||
\(994\) | −4.15578e13 | −1.35025 | ||||||||
\(995\) | 8.22097e12 | 0.265901 | ||||||||
\(996\) | 1.51964e13 | 0.489299 | ||||||||
\(997\) | 5.01617e12 | 0.160785 | 0.0803923 | − | 0.996763i | \(-0.474383\pi\) | ||||
0.0803923 | + | 0.996763i | \(0.474383\pi\) | |||||||
\(998\) | −1.17785e13 | −0.375838 | ||||||||
\(999\) | −8.49721e12 | −0.269918 |
(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 | 197.10.a.b.1.13 | ✓ | 76 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
197.10.a.b.1.13 | ✓ | 76 | 1.1 | even | 1 | trivial |