Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [48,22,Mod(47,48)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(48, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("48.47");
S:= CuspForms(chi, 22);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 48 = 2^{4} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 48.c (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(134.149125258\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6 x^{11} + \cdots + 19\!\cdots\!25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{68}\cdot 3^{56}\cdot 7^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 47.6 | ||
Root | \(0.500000 + 3.90105e7i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 48.47 |
Dual form | 48.22.c.b.47.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/48\mathbb{Z}\right)^\times\).
\(n\) | \(17\) | \(31\) | \(37\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −30363.0 | + | 97665.0i | −0.296873 | + | 0.954917i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 3.55520e7i | − | 1.62809i | −0.580799 | − | 0.814047i | \(-0.697260\pi\) | ||
0.580799 | − | 0.814047i | \(-0.302740\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.36883e9i | 1.83155i | 0.401692 | + | 0.915775i | \(0.368422\pi\) | ||||
−0.401692 | + | 0.915775i | \(0.631578\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −8.61653e9 | − | 5.93080e9i | −0.823732 | − | 0.566979i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −8.13058e10 | −0.945144 | −0.472572 | − | 0.881292i | \(-0.656674\pi\) | ||||
−0.472572 | + | 0.881292i | \(0.656674\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.01527e11 | −0.204257 | −0.102129 | − | 0.994771i | \(-0.532565\pi\) | ||||
−0.102129 | + | 0.994771i | \(0.532565\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.47219e12 | + | 1.07947e12i | 1.55469 | + | 0.483338i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.39503e13i | 1.67830i | 0.543900 | + | 0.839150i | \(0.316947\pi\) | ||||
−0.543900 | + | 0.839150i | \(0.683053\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 9.45210e12i | 0.353684i | 0.984239 | + | 0.176842i | \(0.0565882\pi\) | ||||
−0.984239 | + | 0.176842i | \(0.943412\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.33686e14 | − | 4.15616e13i | −1.74898 | − | 0.543738i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.97092e14 | 0.992035 | 0.496018 | − | 0.868313i | \(-0.334795\pi\) | ||||
0.496018 | + | 0.868313i | \(0.334795\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −7.87110e14 | −1.65069 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 8.40855e14 | − | 6.61456e14i | 0.785962 | − | 0.618275i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.11066e15i | 1.37301i | 0.727126 | + | 0.686504i | \(0.240856\pi\) | ||||
−0.727126 | + | 0.686504i | \(0.759144\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 3.21136e15i | − | 0.703706i | −0.936055 | − | 0.351853i | \(-0.885552\pi\) | ||
0.936055 | − | 0.351853i | \(-0.114448\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.46869e15 | − | 7.94072e15i | 0.280588 | − | 0.902534i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.86645e16 | 2.98193 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.51240e16 | 0.858954 | 0.429477 | − | 0.903078i | \(-0.358698\pi\) | ||||
0.429477 | + | 0.903078i | \(0.358698\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.08267e15 | − | 9.91566e15i | 0.0606386 | − | 0.195049i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 1.94790e16i | − | 0.226639i | −0.993559 | − | 0.113320i | \(-0.963852\pi\) | ||
0.993559 | − | 0.113320i | \(-0.0361484\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.27069e16i | 0.160228i | 0.996786 | + | 0.0801141i | \(0.0255285\pi\) | ||||
−0.996786 | + | 0.0801141i | \(0.974472\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.10852e17 | + | 3.06335e17i | −0.923095 | + | 1.34111i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.64317e17 | −0.732990 | −0.366495 | − | 0.930420i | \(-0.619442\pi\) | ||||
−0.366495 | + | 0.930420i | \(0.619442\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.31514e18 | −2.35457 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.36245e18 | − | 4.23573e17i | −1.60264 | − | 0.498243i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.40537e18i | 1.10381i | 0.833908 | + | 0.551903i | \(0.186098\pi\) | ||||
−0.833908 | + | 0.551903i | \(0.813902\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.89059e18i | 1.53878i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −9.23139e17 | − | 2.86994e17i | −0.337739 | − | 0.104999i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.50456e17 | 0.0383234 | 0.0191617 | − | 0.999816i | \(-0.493900\pi\) | ||||
0.0191617 | + | 0.999816i | \(0.493900\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.64227e17 | −0.0294769 | −0.0147384 | − | 0.999891i | \(-0.504692\pi\) | ||||
−0.0147384 | + | 0.999891i | \(0.504692\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 8.11823e18 | − | 1.17945e19i | 1.03845 | − | 1.50871i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.60950e18i | 0.332550i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.03110e19i | 0.691059i | 0.938408 | + | 0.345529i | \(0.112301\pi\) | ||||
−0.938408 | + | 0.345529i | \(0.887699\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.98430e18 | + | 1.92490e19i | −0.294509 | + | 0.947311i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.34577e19 | 0.490636 | 0.245318 | − | 0.969443i | \(-0.421108\pi\) | ||||
0.245318 | + | 0.969443i | \(0.421108\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.29171e19 | −1.16880 | −0.584401 | − | 0.811465i | \(-0.698670\pi\) | ||||
−0.584401 | + | 0.811465i | \(0.698670\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.38990e19 | − | 7.68731e19i | 0.490046 | − | 1.57627i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 1.11293e20i | − | 1.73108i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.61084e20i | 1.91411i | 0.289905 | + | 0.957055i | \(0.406376\pi\) | ||||
−0.289905 | + | 0.957055i | \(0.593624\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.90703e19 | + | 1.02206e20i | 0.357070 | + | 0.934078i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.59123e20 | −1.12568 | −0.562838 | − | 0.826567i | \(-0.690291\pi\) | ||||
−0.562838 | + | 0.826567i | \(0.690291\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.95961e20 | 2.73243 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.03802e20 | − | 9.44489e19i | −1.31111 | − | 0.407610i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 4.43760e20i | − | 1.50853i | −0.656571 | − | 0.754264i | \(-0.727994\pi\) | ||
0.656571 | − | 0.754264i | \(-0.272006\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 1.38973e20i | − | 0.374107i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.13637e20 | + | 9.75065e19i | 0.671981 | + | 0.208912i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.36042e20 | 0.575831 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.06077e21 | −1.46056 | −0.730278 | − | 0.683150i | \(-0.760610\pi\) | ||||
−0.730278 | + | 0.683150i | \(0.760610\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.00574e20 | + | 4.82208e20i | 0.778546 | + | 0.535877i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 1.15660e21i | − | 1.04185i | −0.853601 | − | 0.520927i | \(-0.825586\pi\) | ||
0.853601 | − | 0.520927i | \(-0.174414\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 1.98586e21i | − | 1.45598i | −0.685585 | − | 0.727992i | \(-0.740454\pi\) | ||
0.685585 | − | 0.727992i | \(-0.259546\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.47760e21 | + | 4.75282e21i | −0.885257 | + | 2.84750i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.46370e21 | 1.21076 | 0.605380 | − | 0.795937i | \(-0.293021\pi\) | ||||
0.605380 | + | 0.795937i | \(0.293021\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.35594e20 | −0.0548609 | −0.0274304 | − | 0.999624i | \(-0.508732\pi\) | ||||
−0.0274304 | + | 0.999624i | \(0.508732\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.62838e20 | + | 2.45373e21i | −0.255001 | + | 0.820230i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 4.56440e21i | − | 1.26491i | −0.774596 | − | 0.632456i | \(-0.782047\pi\) | ||
0.774596 | − | 0.632456i | \(-0.217953\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 7.00703e21i | − | 1.61513i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 8.74813e20 | + | 6.02138e20i | 0.168253 | + | 0.115810i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.90955e22 | −3.07389 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.89623e20 | −0.106702 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.90241e21 | + | 5.91440e20i | 0.216422 | + | 0.0672832i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.10308e22i | 1.05938i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 3.26959e21i | − | 0.265800i | −0.991129 | − | 0.132900i | \(-0.957571\pi\) | ||
0.991129 | − | 0.132900i | \(-0.0424289\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.21767e21 | − | 6.89449e20i | −0.153005 | − | 0.0475675i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.36405e22 | 1.38774 | 0.693870 | − | 0.720100i | \(-0.255904\pi\) | ||||
0.693870 | + | 0.720100i | \(0.255904\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.29383e22 | −0.647790 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.35161e22 | − | 2.98941e22i | −1.00661 | − | 1.27962i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 2.16152e22i | − | 0.792854i | −0.918066 | − | 0.396427i | \(-0.870250\pi\) | ||
0.918066 | − | 0.396427i | \(-0.129750\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 3.40010e22i | − | 1.07111i | −0.844499 | − | 0.535557i | \(-0.820102\pi\) | ||
0.844499 | − | 0.535557i | \(-0.179898\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.02546e21 | − | 2.58145e22i | 0.217605 | − | 0.699944i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.25476e21 | 0.193053 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.10590e23 | 2.23539 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.99315e22 | − | 1.28443e23i | 0.699010 | − | 2.24842i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.03375e22i | 0.612708i | 0.951918 | + | 0.306354i | \(0.0991091\pi\) | ||||
−0.951918 | + | 0.306354i | \(0.900891\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 2.84800e22i | − | 0.376082i | −0.982161 | − | 0.188041i | \(-0.939786\pi\) | ||
0.982161 | − | 0.188041i | \(-0.0602138\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 8.27364e22 | − | 1.20203e23i | 0.951561 | − | 1.38247i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.14170e23 | −1.14570 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.30679e23 | −1.14619 | −0.573097 | − | 0.819488i | \(-0.694258\pi\) | ||||
−0.573097 | + | 0.819488i | \(0.694258\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.37255e23 | − | 4.26711e22i | −1.05404 | − | 0.327691i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.69785e23i | 1.81696i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 2.56766e23i | − | 1.51903i | −0.650487 | − | 0.759517i | \(-0.725435\pi\) | ||
0.650487 | − | 0.759517i | \(-0.274565\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.82309e23 | − | 8.77668e22i | −1.46941 | − | 0.456824i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.27675e23 | −1.50286 | −0.751432 | − | 0.659810i | \(-0.770637\pi\) | ||||
−0.751432 | + | 0.659810i | \(0.770637\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.36757e23 | −0.958279 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.60585e22 | − | 8.14444e22i | 0.200531 | − | 0.291341i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.54074e23i | 0.804408i | 0.915550 | + | 0.402204i | \(0.131756\pi\) | ||||
−0.915550 | + | 0.402204i | \(0.868244\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 1.07742e24i | − | 3.02332i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.56829e21 | + | 1.46943e22i | −0.0113772 | + | 0.0365956i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.15928e22 | −0.0920579 | −0.0460290 | − | 0.998940i | \(-0.514657\pi\) | ||||
−0.0460290 | + | 0.998940i | \(0.514657\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.99467e23 | 0.392867 | 0.196433 | − | 0.980517i | \(-0.437064\pi\) | ||||
0.196433 | + | 0.980517i | \(0.437064\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.98642e21 | − | 1.60392e22i | 0.00875090 | − | 0.0281480i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 8.93208e23i | − | 1.39846i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 1.13424e24i | − | 1.58624i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 9.05418e23 | + | 1.15098e24i | 1.13240 | + | 1.43953i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.63158e24 | 1.82708 | 0.913542 | − | 0.406745i | \(-0.133336\pi\) | ||||
0.913542 | + | 0.406745i | \(0.133336\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.17016e23 | 0.518982 | 0.259491 | − | 0.965746i | \(-0.416445\pi\) | ||||
0.259491 | + | 0.965746i | \(0.416445\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.52522e23 | − | 1.09595e23i | −0.317558 | − | 0.0987253i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 1.35824e24i | − | 1.09921i | −0.835424 | − | 0.549606i | \(-0.814778\pi\) | ||
0.835424 | − | 0.549606i | \(-0.185222\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 1.58981e24i | − | 1.15715i | −0.815631 | − | 0.578573i | \(-0.803610\pi\) | ||
0.815631 | − | 0.578573i | \(-0.196390\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.00702e24 | − | 3.13072e23i | −0.659903 | − | 0.205157i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.25795e24 | −2.51473 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.92517e23 | −0.368990 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.69825e24 | − | 1.16891e24i | −0.817171 | − | 0.562463i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 7.68511e23i | − | 0.334283i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.51376e24i | 1.38295i | 0.722400 | + | 0.691476i | \(0.243039\pi\) | ||||
−0.722400 | + | 0.691476i | \(0.756961\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.08617e23 | + | 1.31435e24i | −0.145657 | + | 0.468516i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.07277e23 | 0.260867 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.39579e24 | 1.28887 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.30309e24 | − | 4.19150e24i | 0.346986 | − | 1.11611i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 1.41634e24i | − | 0.342805i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.91484e24i | 0.862012i | 0.902349 | + | 0.431006i | \(0.141841\pi\) | ||||
−0.902349 | + | 0.431006i | \(0.858159\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.78216e24 | + | 4.66819e24i | 1.35973 | + | 0.935906i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.66708e24 | 0.487264 | 0.243632 | − | 0.969868i | \(-0.421661\pi\) | ||||
0.243632 | + | 0.969868i | \(0.421661\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.18167e24 | −1.36323 | −0.681616 | − | 0.731711i | \(-0.738722\pi\) | ||||
−0.681616 | + | 0.731711i | \(0.738722\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.08695e25 | + | 3.37920e24i | 1.65304 | + | 0.513911i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 6.36272e24i | − | 0.883904i | −0.897039 | − | 0.441952i | \(-0.854286\pi\) | ||
0.897039 | − | 0.441952i | \(-0.145714\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.39701e24i | 1.19338i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.57322e25 | − | 4.89098e24i | −1.82782 | − | 0.568249i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.64315e24 | 0.813007 | 0.406504 | − | 0.913649i | \(-0.366748\pi\) | ||||
0.406504 | + | 0.913649i | \(0.366748\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.50959e24 | −0.244581 | −0.122291 | − | 0.992494i | \(-0.539024\pi\) | ||||
−0.122291 | + | 0.992494i | \(0.539024\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.11682e25 | + | 7.12520e23i | −0.997971 | + | 0.0636695i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.67558e25i | 3.83347i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 9.59647e23i | − | 0.0722426i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.83145e24 | − | 1.55408e25i | 0.334183 | − | 1.07493i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.37900e25 | 0.876984 | 0.438492 | − | 0.898735i | \(-0.355513\pi\) | ||||
0.438492 | + | 0.898735i | \(0.355513\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.60247e25 | −0.937616 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.50589e25 | + | 4.84380e25i | −0.811186 | + | 2.60924i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 1.53289e25i | − | 0.760701i | −0.924842 | − | 0.380350i | \(-0.875803\pi\) | ||
0.924842 | − | 0.380350i | \(-0.124197\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.43903e25i | 1.57322i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.84487e25 | − | 2.68031e25i | 0.778467 | − | 1.13099i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.28430e25 | −1.66857 | −0.834286 | − | 0.551332i | \(-0.814120\pi\) | ||||
−0.834286 | + | 0.551332i | \(0.814120\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.99636e25 | 1.79710 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.33398e25 | + | 1.34739e25i | 1.44052 | + | 0.447842i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 2.46839e25i | − | 0.758602i | −0.925273 | − | 0.379301i | \(-0.876164\pi\) | ||
0.925273 | − | 0.379301i | \(-0.123836\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 4.10139e24i | − | 0.116615i | −0.998299 | − | 0.0583073i | \(-0.981430\pi\) | ||
0.998299 | − | 0.0583073i | \(-0.0185703\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.35728e25 | + | 4.21964e24i | 0.357241 | + | 0.111063i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.39966e25 | 1.56014 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.49763e25 | 0.790199 | 0.395100 | − | 0.918638i | \(-0.370710\pi\) | ||||
0.395100 | + | 0.918638i | \(0.370710\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.90459e25 | + | 2.76708e25i | −0.398986 | + | 0.579666i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.73843e25i | 0.532212i | 0.963944 | + | 0.266106i | \(0.0857371\pi\) | ||||
−0.963944 | + | 0.266106i | \(0.914263\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.89255e25i | 0.882629i | 0.897353 | + | 0.441314i | \(0.145488\pi\) | ||||
−0.897353 | + | 0.441314i | \(0.854512\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.02032e25 | + | 3.28195e25i | −0.170949 | + | 0.549871i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.66633e25 | 0.415101 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.25519e26 | −1.81669 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.22082e25 | − | 1.03600e26i | 0.433600 | − | 1.39471i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 7.20642e25i | − | 0.902838i | −0.892312 | − | 0.451419i | \(-0.850918\pi\) | ||
0.892312 | − | 0.451419i | \(-0.149082\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 5.34902e24i | − | 0.0623940i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −6.83663e25 | + | 5.37802e25i | −0.742847 | + | 0.584359i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.00102e25 | −0.202630 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.10818e25 | −0.293466 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.12959e26 | + | 3.51177e25i | 0.994884 | + | 0.309299i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.83860e24i | 0.0479911i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.74780e26i | 1.34134i | 0.741755 | + | 0.670671i | \(0.233994\pi\) | ||||
−0.741755 | + | 0.670671i | \(0.766006\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.93948e26 | + | 6.02965e25i | 1.39034 | + | 0.432243i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.44780e26 | −0.969894 | −0.484947 | − | 0.874544i | \(-0.661161\pi\) | ||||
−0.484947 | + | 0.874544i | \(0.661161\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.52618e25 | −0.220846 | −0.110423 | − | 0.993885i | \(-0.535221\pi\) | ||||
−0.110423 | + | 0.993885i | \(0.535221\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.19319e26 | − | 2.88620e26i | −2.45632 | − | 1.69069i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 1.26009e25i | − | 0.0690686i | −0.999404 | − | 0.0345343i | \(-0.989005\pi\) | ||
0.999404 | − | 0.0345343i | \(-0.0109948\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 2.52914e26i | − | 1.29769i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.48052e25 | + | 2.40617e26i | −0.359442 | + | 1.15617i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.31860e26 | −0.593588 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.99132e25 | 0.337165 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.11704e24 | − | 1.32428e25i | 0.0162867 | − | 0.0523876i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 3.61804e26i | − | 1.34251i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 3.75401e26i | − | 1.30708i | −0.756892 | − | 0.653540i | \(-0.773283\pi\) | ||
0.756892 | − | 0.653540i | \(-0.226717\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.16481e26 | − | 1.49005e26i | −0.707548 | − | 0.487009i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.66577e26 | 1.12511 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.88457e26 | −0.831702 | −0.415851 | − | 0.909433i | \(-0.636516\pi\) | ||||
−0.415851 | + | 0.909433i | \(0.636516\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.45782e26 | + | 1.38589e26i | 1.20789 | + | 0.375519i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.61102e26i | 0.665104i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.03564e27i | − | 2.48097i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6.84341e26 | + | 2.12754e26i | 1.54231 | + | 0.479488i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.55460e26 | −0.753931 | −0.376965 | − | 0.926227i | \(-0.623032\pi\) | ||||
−0.376965 | + | 0.926227i | \(0.623032\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.03239e25 | −0.120454 | −0.0602272 | − | 0.998185i | \(-0.519183\pi\) | ||||
−0.0602272 | + | 0.998185i | \(0.519183\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.53697e25 | + | 6.71559e25i | −0.160538 | + | 0.126287i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.42270e25i | 0.0252046i | 0.999921 | + | 0.0126023i | \(0.00401155\pi\) | ||||
−0.999921 | + | 0.0126023i | \(0.995988\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 4.78450e26i | − | 0.798801i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.79797e26 | − | 1.86496e27i | 0.912556 | − | 2.93531i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.85469e26 | 0.275283 | 0.137641 | − | 0.990482i | \(-0.456048\pi\) | ||||
0.137641 | + | 0.990482i | \(0.456048\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.24867e26 | 0.874907 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.39753e25 | − | 7.71185e25i | 0.0316770 | − | 0.101892i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.52579e27i | 1.90292i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 5.69151e26i | − | 0.670246i | −0.942174 | − | 0.335123i | \(-0.891222\pi\) | ||
0.942174 | − | 0.335123i | \(-0.108778\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.15526e26 | + | 1.67841e26i | −0.128500 | + | 0.186690i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.92370e27 | −2.02167 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.39733e26 | −0.138789 | −0.0693945 | − | 0.997589i | \(-0.522107\pi\) | ||||
−0.0693945 | + | 0.997589i | \(0.522107\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.07733e27 | − | 3.34929e26i | −1.01162 | − | 0.314503i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 3.15817e26i | − | 0.280447i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.28970e27i | 1.08337i | 0.840581 | + | 0.541686i | \(0.182214\pi\) | ||||
−0.840581 | + | 0.541686i | \(0.817786\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.19325e26 | + | 9.92746e25i | 0.253817 | + | 0.0789089i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.08252e25 | −0.00814420 | −0.00407210 | − | 0.999992i | \(-0.501296\pi\) | ||||
−0.00407210 | + | 0.999992i | \(0.501296\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.95671e27 | −2.81836 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.34670e26 | − | 1.95655e26i | 0.0908460 | − | 0.131985i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.32643e25i | 0.0468190i | 0.999726 | + | 0.0234095i | \(0.00745215\pi\) | ||||
−0.999726 | + | 0.0234095i | \(0.992548\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.74949e27i | 1.66493i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.17796e26 | + | 2.30885e27i | −0.411983 | + | 1.32518i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.72685e27 | 3.11635 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.26195e27 | −1.16730 | −0.583650 | − | 0.812006i | \(-0.698376\pi\) | ||||
−0.583650 | + | 0.812006i | \(0.698376\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.92845e26 | − | 1.26362e27i | 0.192312 | − | 0.618586i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.07907e26i | 0.235922i | 0.993018 | + | 0.117961i | \(0.0376358\pi\) | ||||
−0.993018 | + | 0.117961i | \(0.962364\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.26041e26i | 0.143737i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.63363e27 | − | 1.38903e27i | 1.52077 | − | 0.581344i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.04272e27 | −0.811835 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.42237e27 | 0.536928 | 0.268464 | − | 0.963290i | \(-0.413484\pi\) | ||||
0.268464 | + | 0.963290i | \(0.413484\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.11105e27 | + | 6.56302e26i | 0.757109 | + | 0.235377i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.05948e26i | 0.0701911i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.65715e27i | 1.83271i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.32070e27 | + | 1.03237e27i | 1.02283 | + | 0.317986i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.74722e26 | −0.168349 | −0.0841745 | − | 0.996451i | \(-0.526825\pi\) | ||||
−0.0841745 | + | 0.996451i | \(0.526825\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.15296e27 | 0.878531 | 0.439265 | − | 0.898357i | \(-0.355239\pi\) | ||||
0.439265 | + | 0.898357i | \(0.355239\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.27750e27 | + | 1.56761e27i | 0.603787 | + | 0.415590i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 1.09804e28i | − | 2.77035i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 2.24798e26i | − | 0.0539883i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.50639e26 | + | 8.06200e26i | −0.0573122 | + | 0.184349i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.60602e26 | 0.122080 | 0.0610398 | − | 0.998135i | \(-0.480558\pi\) | ||||
0.0610398 | + | 0.998135i | \(0.480558\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.72416e27 | −0.979945 | −0.489973 | − | 0.871738i | \(-0.662993\pi\) | ||||
−0.489973 | + | 0.871738i | \(0.662993\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.35785e27 | + | 1.08008e28i | −0.663627 | + | 2.13461i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.86294e27i | 0.350867i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.42156e27i | 0.793776i | 0.917867 | + | 0.396888i | \(0.129910\pi\) | ||||
−0.917867 | + | 0.396888i | \(0.870090\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.13319e28 | + | 7.79981e27i | 1.93954 | + | 1.33499i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.39591e26 | −0.0880695 | −0.0440347 | − | 0.999030i | \(-0.514021\pi\) | ||||
−0.0440347 | + | 0.999030i | \(0.514021\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.57766e28 | −2.45603 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.93956e27 | − | 1.22477e27i | −0.585085 | − | 0.181897i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 2.75637e27i | − | 0.390617i | −0.980742 | − | 0.195309i | \(-0.937429\pi\) | ||
0.980742 | − | 0.195309i | \(-0.0625709\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.58375e27i | 0.214207i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.78150e27 | + | 8.64739e26i | 0.359127 | + | 0.111649i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.94078e27 | −0.609082 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.15103e27 | 0.370964 | 0.185482 | − | 0.982648i | \(-0.440615\pi\) | ||||
0.185482 | + | 0.982648i | \(0.440615\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 9.22751e27 | + | 1.17302e28i | 1.03765 | + | 1.31908i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.89127e27i | 0.847788i | 0.905712 | + | 0.423894i | \(0.139337\pi\) | ||||
−0.905712 | + | 0.423894i | \(0.860663\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 1.39692e28i | − | 1.43407i | −0.697035 | − | 0.717037i | \(-0.745498\pi\) | ||
0.697035 | − | 0.717037i | \(-0.254502\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.46655e27 | − | 1.11504e28i | 0.340128 | − | 1.09405i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.34461e27 | 0.876463 | 0.438232 | − | 0.898862i | \(-0.355605\pi\) | ||||
0.438232 | + | 0.898862i | \(0.355605\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.41139e28 | −1.26571 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.96779e27 | − | 1.27627e28i | 0.340274 | − | 1.09452i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 1.84620e27i | − | 0.151439i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 7.43985e27i | − | 0.583823i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.33494e27 | − | 1.21094e28i | 0.625834 | − | 0.909241i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.21401e28 | 1.59095 | 0.795477 | − | 0.605984i | \(-0.207220\pi\) | ||||
0.795477 | + | 0.605984i | \(0.207220\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.55077e27 | −0.175448 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.63485e28 | − | 8.19147e27i | −1.73505 | − | 0.539407i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.77126e28i | 2.37792i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.55360e28i | 0.938180i | 0.883150 | + | 0.469090i | \(0.155418\pi\) | ||||
−0.883150 | + | 0.469090i | \(0.844582\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.50770e28 | + | 7.79618e27i | 1.45055 | + | 0.450961i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.88611e27 | −0.492443 | −0.246222 | − | 0.969214i | \(-0.579189\pi\) | ||||
−0.246222 | + | 0.969214i | \(0.579189\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.33946e28 | −2.30432 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.71435e28 | − | 2.49068e28i | 0.872458 | − | 1.26755i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.84213e28i | 0.898624i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.00716e27i | 0.374475i | 0.982315 | + | 0.187237i | \(0.0599534\pi\) | ||||
−0.982315 | + | 0.187237i | \(0.940047\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.94918e27 | − | 3.20023e28i | 0.446160 | − | 1.43511i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.50080e28 | −1.93565 | −0.967824 | − | 0.251629i | \(-0.919034\pi\) | ||||
−0.967824 | + | 0.251629i | \(0.919034\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.11193e28 | −1.69624 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.18864e27 | − | 2.31228e28i | 0.284488 | − | 0.915077i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 3.13277e28i | − | 1.18957i | −0.803883 | − | 0.594787i | \(-0.797236\pi\) | ||
0.803883 | − | 0.594787i | \(-0.202764\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 5.87461e28i | − | 2.14072i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.25216e27 | + | 7.94785e27i | 0.218674 | + | 0.277982i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.06012e28 | −2.37048 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.14905e28 | 0.692781 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.48142e28 | − | 7.71445e27i | −0.768143 | − | 0.238807i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 4.52720e28i | − | 1.34597i | −0.739658 | − | 0.672983i | \(-0.765013\pi\) | ||
0.739658 | − | 0.672983i | \(-0.234987\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.14432e28i | 0.612382i | 0.951970 | + | 0.306191i | \(0.0990547\pi\) | ||||
−0.951970 | + | 0.306191i | \(0.900945\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.05226e29 | + | 3.27136e28i | 2.88702 | + | 0.897543i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.47994e28 | 1.18103 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.26278e26 | −0.0158665 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.29641e27 | − | 8.92324e26i | −0.0315682 | − | 0.0217285i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.97765e27i | 0.0462928i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 8.75895e28i | − | 1.97123i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.26288e27 | − | 4.06216e27i | 0.0273295 | − | 0.0879076i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.06928e29 | 2.22541 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.03725e28 | 1.20856 | 0.604279 | − | 0.796773i | \(-0.293461\pi\) | ||||
0.604279 | + | 0.796773i | \(0.293461\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6.05640e27 | + | 1.94809e28i | −0.116632 | + | 0.375155i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.82065e27i | 0.0893186i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 4.25089e28i | − | 0.757901i | −0.925417 | − | 0.378951i | \(-0.876285\pi\) | ||
0.925417 | − | 0.378951i | \(-0.123715\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.41507e27 | + | 9.73997e26i | 0.0242810 | + | 0.0167128i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.94023e28 | −0.485612 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.20495e29 | −3.50579 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8.72351e28 | + | 2.71204e28i | 1.33541 | + | 0.415165i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 8.71218e28i | − | 1.28424i | −0.766603 | − | 0.642122i | \(-0.778054\pi\) | ||
0.766603 | − | 0.642122i | \(-0.221946\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 2.30537e27i | − | 0.0327278i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.10775e29 | + | 3.44389e28i | 1.51472 | + | 0.470911i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.63734e28 | 0.215676 | 0.107838 | − | 0.994168i | \(-0.465607\pi\) | ||||
0.107838 | + | 0.994168i | \(0.465607\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.62274e29 | −2.05940 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.39902e29 | + | 5.34804e28i | −1.71081 | + | 0.653992i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.60930e29i | 1.89653i | 0.317487 | + | 0.948263i | \(0.397161\pi\) | ||||
−0.317487 | + | 0.948263i | \(0.602839\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.06590e28i | 0.575411i | 0.957719 | + | 0.287705i | \(0.0928924\pi\) | ||||
−0.957719 | + | 0.287705i | \(0.907108\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.95397e28 | + | 1.59348e29i | −0.542413 | + | 1.74471i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.55133e29 | −1.63754 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.67417e27 | 0.0272171 | 0.0136086 | − | 0.999907i | \(-0.495668\pi\) | ||||
0.0136086 | + | 0.999907i | \(0.495668\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.56981e28 | + | 5.04943e28i | −0.154072 | + | 0.495585i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 2.17812e29i | − | 2.06173i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 1.14264e29i | − | 1.04326i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.14072e28 | − | 3.11014e28i | 0.188549 | − | 0.273932i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.08450e29 | 0.921575 | 0.460787 | − | 0.887511i | \(-0.347567\pi\) | ||||
0.460787 | + | 0.887511i | \(0.347567\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.03541e28 | 0.248890 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.32653e29 | + | 4.12403e28i | 1.04966 | + | 0.326327i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.92155e28i | 0.604973i | 0.953154 | + | 0.302486i | \(0.0978166\pi\) | ||||
−0.953154 | + | 0.302486i | \(0.902183\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.78885e29i | 5.00458i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.55269e29 | + | 4.82714e28i | 1.10498 | + | 0.343526i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.02774e28 | −0.551584 | −0.275792 | − | 0.961217i | \(-0.588940\pi\) | ||||
−0.275792 | + | 0.961217i | \(0.588940\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.12347e29 | 0.745383 | 0.372692 | − | 0.927955i | \(-0.378435\pi\) | ||||
0.372692 | + | 0.927955i | \(0.378435\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.11524e28 | − | 8.88450e28i | 0.391816 | − | 0.569247i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.80727e28i | 0.173721i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 7.77330e28i | − | 0.464648i | −0.972638 | − | 0.232324i | \(-0.925367\pi\) | ||
0.972638 | − | 0.232324i | \(-0.0746330\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.29284e29 | − | 4.15852e29i | 0.746558 | − | 2.40136i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.68354e28 | 0.149719 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.58302e29 | −1.39249 | −0.696247 | − | 0.717802i | \(-0.745148\pi\) | ||||
−0.696247 | + | 0.717802i | \(0.745148\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.10269e28 | − | 6.76346e28i | 0.109543 | − | 0.352355i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.88675e29i | 0.949995i | 0.879987 | + | 0.474997i | \(0.157551\pi\) | ||||
−0.879987 | + | 0.474997i | \(0.842449\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.62056e28i | 0.370881i | 0.982655 | + | 0.185441i | \(0.0593713\pi\) | ||||
−0.982655 | + | 0.185441i | \(0.940629\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.65726e29 | − | 1.30368e29i | 0.779702 | − | 0.613350i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.07431e29 | 2.76294 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.68452e28 | 0.0740860 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.50565e28 | + | 2.33343e28i | 0.319212 | + | 0.0992396i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.50487e29i | 1.44158i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.16492e29i | 1.25909i | 0.776966 | + | 0.629543i | \(0.216758\pi\) | ||||
−0.776966 | + | 0.629543i | \(0.783242\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.43172e29 | − | 1.06688e29i | −1.32060 | − | 0.410561i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.16241e29 | −0.432747 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.33522e29 | 0.480939 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.15959e29 | − | 7.98151e28i | −0.404153 | − | 0.278180i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 3.12846e29i | − | 1.05517i | −0.849504 | − | 0.527583i | \(-0.823098\pi\) | ||
0.849504 | − | 0.527583i | \(-0.176902\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.05138e29i | 0.669624i | 0.942285 | + | 0.334812i | \(0.108673\pi\) | ||||
−0.942285 | + | 0.334812i | \(0.891327\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.45113e28 | + | 7.88426e28i | −0.0774444 | + | 0.249106i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.82322e29 | −1.16932 | −0.584661 | − | 0.811278i | \(-0.698772\pi\) | ||||
−0.584661 | + | 0.811278i | \(0.698772\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.22329e28 | −0.0362211 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.33469e29 | + | 4.29315e29i | −0.382632 | + | 1.23077i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 1.78353e29i | − | 0.495099i | −0.968875 | − | 0.247549i | \(-0.920375\pi\) | ||
0.968875 | − | 0.247549i | \(-0.0796252\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 8.40468e29i | − | 2.25937i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.69797e29 | + | 2.54533e29i | 0.962779 | + | 0.662685i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.40298e28 | −0.161467 | −0.0807337 | − | 0.996736i | \(-0.525726\pi\) | ||||
−0.0807337 | + | 0.996736i | \(0.525726\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.51347e29 | 1.10254 | 0.551271 | − | 0.834327i | \(-0.314143\pi\) | ||||
0.551271 | + | 0.834327i | \(0.314143\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.38326e29 | + | 4.30042e28i | 0.327350 | + | 0.101770i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.59982e29i | 1.05466i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.13086e29i | 1.36207i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.82343e29 | − | 1.18866e29i | −0.823150 | − | 0.255909i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.33526e28 | 0.0278599 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.16425e29 | −0.639901 | −0.319951 | − | 0.947434i | \(-0.603666\pi\) | ||||
−0.319951 | + | 0.947434i | \(0.603666\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −6.61845e29 | + | 5.20639e29i | −1.29738 | + | 1.02058i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 5.55817e29i | − | 1.05621i | −0.849178 | − | 0.528106i | \(-0.822902\pi\) | ||
0.849178 | − | 0.528106i | \(-0.177098\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 1.45201e30i | − | 2.67508i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.09805e28 | + | 2.60480e29i | −0.144656 | + | 0.465297i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.76496e26 | −0.00117179 | −0.000585893 | − | 1.00000i | \(-0.500186\pi\) | ||||
−0.000585893 | 1.00000i | \(0.500186\pi\) | ||||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.68464e29 | −1.29084 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.48420e29 | − | 7.99063e29i | 0.404707 | − | 1.30177i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 1.42683e29i | − | 0.225460i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 1.14106e30i | − | 1.74900i | −0.485023 | − | 0.874501i | \(-0.661189\pi\) | ||
0.485023 | − | 0.874501i | \(-0.338811\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6.60059e29 | + | 9.58963e29i | −0.981485 | + | 1.42595i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.20880e30 | −1.74388 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.71737e29 | 0.380369 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.21414e29 | + | 1.93191e29i | 0.844055 | + | 0.262408i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.98936e29i | 0.921294i | 0.887584 | + | 0.460647i | \(0.152383\pi\) | ||||
−0.887584 | + | 0.460647i | \(0.847617\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.37474e29i | 0.303798i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −9.17759e29 | − | 2.85321e29i | −1.13957 | − | 0.354282i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.58318e30 | 1.90821 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.53396e29 | 0.998539 | 0.499270 | − | 0.866447i | \(-0.333602\pi\) | ||||
0.499270 | + | 0.866447i | \(0.333602\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.55355e29 | − | 1.38798e30i | 1.08526 | − | 1.57672i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 6.32934e29i | − | 0.698101i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 2.93473e29i | − | 0.314308i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2.32069e29 | + | 7.46468e29i | −0.241360 | + | 0.776354i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.51890e29 | −0.456435 | −0.228218 | − | 0.973610i | \(-0.573290\pi\) | ||||
−0.228218 | + | 0.973610i | \(0.573290\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.71829e30 | 2.66671 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.61986e28 | − | 2.45099e29i | 0.0726097 | − | 0.233555i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 2.44843e30i | − | 2.26641i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 5.79335e29i | − | 0.520977i | −0.965477 | − | 0.260488i | \(-0.916116\pi\) | ||
0.965477 | − | 0.260488i | \(-0.0838835\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.69512e29 | − | 1.11238e30i | 0.235472 | − | 0.971881i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.16768e29 | −0.268911 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.47112e29 | 0.121354 | 0.0606772 | − | 0.998157i | \(-0.480674\pi\) | ||||
0.0606772 | + | 0.998157i | \(0.480674\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.56640e30 | − | 1.41965e30i | −3.66064 | − | 1.13805i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 8.38343e29i | − | 0.653150i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.59263e30i | 1.20600i | 0.797741 | + | 0.603000i | \(0.206028\pi\) | ||||
−0.797741 | + | 0.603000i | \(0.793972\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.37238e28 | + | 2.91377e28i | 0.0689857 | + | 0.0214469i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.91119e29 | −0.422953 | −0.211477 | − | 0.977383i | \(-0.567827\pi\) | ||||
−0.211477 | + | 0.977383i | \(0.567827\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.43408e30 | 0.997546 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.37109e30 | + | 9.43727e29i | 0.927256 | + | 0.638234i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.37237e30i | 2.21757i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 3.06438e29i | − | 0.195940i | −0.995189 | − | 0.0979701i | \(-0.968765\pi\) | ||
0.995189 | − | 0.0979701i | \(-0.0312349\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.18707e29 | + | 1.34680e30i | −0.260353 | + | 0.837447i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.01252e30 | −0.612297 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.30557e30 | 0.767881 | 0.383940 | − | 0.923358i | \(-0.374567\pi\) | ||||
0.383940 | + | 0.923358i | \(0.374567\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.86558e29 | − | 1.56505e30i | 0.278353 | − | 0.895346i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 5.41042e29i | − | 0.301087i | −0.988603 | − | 0.150544i | \(-0.951898\pi\) | ||
0.988603 | − | 0.150544i | \(-0.0481024\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 1.85605e29i | − | 0.100480i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.27347e30 | − | 2.94145e30i | −2.25079 | − | 1.54923i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.52754e28 | −0.00782783 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.95470e29 | −0.496366 | −0.248183 | − | 0.968713i | \(-0.579833\pi\) | ||||
−0.248183 | + | 0.968713i | \(0.579833\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.49710e30 | + | 4.65432e29i | 0.726406 | + | 0.225832i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.95905e30i | 1.39723i | 0.715498 | + | 0.698615i | \(0.246200\pi\) | ||||
−0.715498 | + | 0.698615i | \(0.753800\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.52769e30i | 1.16160i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.35873e30 | − | 1.04419e30i | −1.50229 | − | 0.467046i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.84117e29 | 0.0801588 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.09419e30 | −0.463722 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.05757e30 | + | 2.61561e30i | 0.848897 | + | 1.07913i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.64589e30i | 1.86611i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.17587e29i | 0.0459859i | 0.999736 | + | 0.0229930i | \(0.00731953\pi\) | ||||
−0.999736 | + | 0.0229930i | \(0.992680\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.30084e30 | − | 4.18426e30i | 0.495354 | − | 1.59335i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.24787e30 | 2.31675 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.66735e28 | 0.00602087 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.51704e30 | + | 4.87969e30i | −0.533511 | + | 1.71608i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 2.73219e30i | − | 0.935835i | −0.883772 | − | 0.467917i | \(-0.845004\pi\) | ||
0.883772 | − | 0.467917i | \(-0.154996\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 3.68730e30i | − | 1.23018i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.63185e30 | + | 3.82368e30i | −0.855304 | + | 1.24262i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.48941e30 | 1.10469 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.59140e30 | 2.95818 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.41075e30 | + | 7.49476e29i | 0.724402 | + | 0.225209i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.64561e30i | 0.481801i | 0.970550 | + | 0.240901i | \(0.0774428\pi\) | ||||
−0.970550 | + | 0.240901i | \(0.922557\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.93458e30i | 1.12248i | 0.827652 | + | 0.561241i | \(0.189676\pi\) | ||||
−0.827652 | + | 0.561241i | \(0.810324\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.00562e29 | + | 1.24530e29i | 0.111357 | + | 0.0346198i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.12855e30 | −2.47313 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.14628e29 | −0.0566702 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −8.24222e29 | + | 1.19747e30i | −0.212111 | + | 0.308164i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 1.85981e28i | − | 0.00466515i | −0.999997 | − | 0.00233257i | \(-0.999258\pi\) | ||
0.999997 | − | 0.00233257i | \(-0.000742482\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 2.35040e29i | − | 0.0574702i | −0.999587 | − | 0.0287351i | \(-0.990852\pi\) | ||
0.999587 | − | 0.0287351i | \(-0.00914792\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.94313e30 | + | 6.25022e30i | −0.463164 | + | 1.48980i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.97803e30 | −0.692025 | −0.346012 | − | 0.938230i | \(-0.612464\pi\) | ||||
−0.346012 | + | 0.938230i | \(0.612464\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.27916e30 | 0.289803 | 0.144902 | − | 0.989446i | \(-0.453713\pi\) | ||||
0.144902 | + | 0.989446i | \(0.453713\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.06199e30 | + | 3.41596e30i | −0.234589 | + | 0.754574i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 1.83466e31i | − | 3.95168i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.16495e31i | 2.44680i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.12418e30 | − | 2.70029e30i | −0.435084 | − | 0.553086i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.30738e30 | 0.660668 | 0.330334 | − | 0.943864i | \(-0.392839\pi\) | ||||
0.330334 | + | 0.943864i | \(0.392839\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.54335e30 | −0.885154 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.67448e30 | − | 8.31468e29i | −0.508218 | − | 0.158000i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8.41718e30i | 1.56017i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 1.08086e30i | − | 0.195430i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.77831e30 | − | 1.48553e30i | −0.842837 | − | 0.262029i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.95173e30 | 0.852112 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.54603e30 | 1.60272 | 0.801361 | − | 0.598182i | \(-0.204110\pi\) | ||||
0.801361 | + | 0.598182i | \(0.204110\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.89551e30 | − | 1.99299e30i | −0.474331 | − | 0.326484i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.28873e30i | 1.00523i | 0.864511 | + | 0.502614i | \(0.167628\pi\) | ||||
−0.864511 | + | 0.502614i | \(0.832372\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.97554e30i | 1.08805i | 0.839069 | + | 0.544026i | \(0.183101\pi\) | ||||
−0.839069 | + | 0.544026i | \(0.816899\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.09578e29 | + | 2.60407e30i | −0.123233 | + | 0.396387i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.06325e31 | 1.57951 | 0.789755 | − | 0.613422i | \(-0.210207\pi\) | ||||
0.789755 | + | 0.613422i | \(0.210207\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.03286e30 | 1.30965 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.81113e30 | − | 1.22588e31i | 0.539328 | − | 1.73479i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 1.30970e31i | − | 1.80911i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 1.04685e30i | − | 0.141154i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 9.14016e30 | + | 6.29122e30i | 1.20311 | + | 0.828104i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.50993e31 | −1.94031 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.26733e30 | −1.16268 | −0.581338 | − | 0.813662i | \(-0.697471\pi\) | ||||
−0.581338 | + | 0.813662i | \(0.697471\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 7.03815e30 | + | 2.18809e30i | 0.862135 | + | 0.268029i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 5.29699e29i | − | 0.0633552i | −0.999498 | − | 0.0316776i | \(-0.989915\pi\) | ||
0.999498 | − | 0.0316776i | \(-0.0100850\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 1.17325e31i | − | 1.37026i | −0.728421 | − | 0.685130i | \(-0.759746\pi\) | ||
0.728421 | − | 0.685130i | \(-0.240254\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.22412e29 | + | 1.62412e29i | 0.0595811 | + | 0.0185231i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.21463e30 | 0.358041 | 0.179020 | − | 0.983845i | \(-0.442707\pi\) | ||||
0.179020 | + | 0.983845i | \(0.442707\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.47550e30 | 0.486826 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.17664e30 | − | 8.30992e30i | −0.337483 | − | 0.882838i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 2.49835e30i | − | 0.259247i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.47871e30i | 0.149879i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.07570e29 | − | 1.95430e30i | 0.0601556 | − | 0.193495i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.98945e30 | 0.966195 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.96053e31 | −1.85252 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9.43736e29 | − | 3.03560e30i | 0.0871222 | − | 0.280236i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 7.09144e30i | − | 0.639624i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 1.03172e31i | − | 0.909251i | −0.890683 | − | 0.454626i | \(-0.849773\pi\) | ||
0.890683 | − | 0.454626i | \(-0.150227\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.85953e30 | + | 9.96584e30i | −0.590709 | + | 0.858209i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.92471e31 | −1.61966 | −0.809829 | − | 0.586666i | \(-0.800440\pi\) | ||||
−0.809829 | + | 0.586666i | \(0.800440\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.29376e31 | 1.06393 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5.70227e29 | − | 1.77277e29i | −0.0458275 | − | 0.0142473i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.23597e31i | 2.54172i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 1.58189e31i | − | 1.21441i | −0.794546 | − | 0.607204i | \(-0.792291\pi\) | ||
0.794546 | − | 0.607204i | \(-0.207709\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.70699e31 | − | 5.30685e30i | −1.28087 | − | 0.398208i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.36633e30 | −0.100216 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.97753e31 | −1.41787 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.17777e31 | + | 1.71112e31i | −0.825512 | + | 1.19934i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.61527e31i | 1.10683i | 0.832906 | + | 0.553414i | \(0.186675\pi\) | ||||
−0.832906 | + | 0.553414i | \(0.813325\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 1.24308e31i | − | 0.832776i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.39595e30 | − | 1.41399e31i | 0.287936 | − | 0.926168i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.03245e31 | −2.58254 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.33084e31 | −1.45964 | −0.729822 | − | 0.683637i | \(-0.760397\pi\) | ||||
−0.729822 | + | 0.683637i | \(0.760397\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.07065e30 | − | 3.44384e30i | 0.0655632 | − | 0.210889i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 9.65228e30i | − | 0.578015i | −0.957327 | − | 0.289007i | \(-0.906675\pi\) | ||
0.957327 | − | 0.289007i | \(-0.0933252\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 3.83915e30i | − | 0.224834i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.09198e31 | − | 3.21895e31i | 2.34369 | − | 1.84366i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.47142e31 | 0.824258 | 0.412129 | − | 0.911125i | \(-0.364785\pi\) | ||||
0.412129 | + | 0.911125i | \(0.364785\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.35726e30 | 0.238736 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.23067e30 | + | 3.82602e29i | 0.0659548 | + | 0.0205046i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.06433e31i | 1.08219i | 0.840961 | + | 0.541096i | \(0.181990\pi\) | ||||
−0.840961 | + | 0.541096i | \(0.818010\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 5.80061e31i | − | 2.97466i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.47009e31 | + | 7.67924e30i | 1.23919 | + | 0.385250i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.95874e31 | 1.45215 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.05127e31 | 0.504798 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.12285e31 | − | 1.46117e31i | −0.997342 | − | 0.686475i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 1.83810e31i | − | 0.844951i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.75379e31i | 0.788860i | 0.918926 | + | 0.394430i | \(0.129058\pi\) | ||||
−0.918926 | + | 0.394430i | \(0.870942\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.00365e30 | − | 1.28781e31i | 0.176221 | − | 0.566828i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.39045e31 | 0.598899 | 0.299449 | − | 0.954112i | \(-0.403197\pi\) | ||||
0.299449 | + | 0.954112i | \(0.403197\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.65414e31 | 1.96180 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.42640e30 | + | 7.80471e30i | −0.100095 | + | 0.321965i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 2.26862e31i | − | 0.915942i | −0.888967 | − | 0.457971i | \(-0.848576\pi\) | ||
0.888967 | − | 0.457971i | \(-0.151424\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.60803e31i | 1.42578i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.16835e30 | + | 8.04181e29i | 0.0451907 | + | 0.0311049i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.70993e31 | 1.78321 | 0.891606 | − | 0.452813i | \(-0.149579\pi\) | ||||
0.891606 | + | 0.452813i | \(0.149579\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.82883e31 | −1.78962 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.53356e31 | + | 1.09855e31i | 1.28198 | + | 0.398555i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.47535e30i | 0.158952i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1.02957e31i | − | 0.357999i | −0.983849 | − | 0.179000i | \(-0.942714\pi\) | ||
0.983849 | − | 0.179000i | \(-0.0572861\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.66636e31 | + | 1.13983e31i | 1.24815 | + | 0.388037i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.65210e31 | −1.88394 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.94089e31 | −1.61252 | −0.806262 | − | 0.591558i | \(-0.798513\pi\) | ||||
−0.806262 | + | 0.591558i | \(0.798513\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.11256e31 | − | 1.66184e31i | 0.675105 | − | 0.531070i |
(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 | 48.22.c.b.47.6 | yes | 12 | |
3.2 | odd | 2 | inner | 48.22.c.b.47.8 | yes | 12 | |
4.3 | odd | 2 | inner | 48.22.c.b.47.7 | yes | 12 | |
12.11 | even | 2 | inner | 48.22.c.b.47.5 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.22.c.b.47.5 | ✓ | 12 | 12.11 | even | 2 | inner | |
48.22.c.b.47.6 | yes | 12 | 1.1 | even | 1 | trivial | |
48.22.c.b.47.7 | yes | 12 | 4.3 | odd | 2 | inner | |
48.22.c.b.47.8 | yes | 12 | 3.2 | odd | 2 | inner |