Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [16,13,Mod(15,16)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(16, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 13, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("16.15");
S:= CuspForms(chi, 13);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 16 = 2^{4} \) |
Weight: | \( k \) | \(=\) | \( 13 \) |
Character orbit: | \([\chi]\) | \(=\) | 16.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: | \(14.6239010764\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-1155}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 289 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{4}\cdot 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 15.1 | ||
Root | \(0.500000 + 16.9926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 16.15 |
Dual form | 16.13.c.a.15.2 |
$q$-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 \(\left(\mathbb{Z}/16\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(15\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − 815.647i | − 1.11886i | −0.828879 | − | 0.559429i | \(-0.811021\pi\) | ||||
0.828879 | − | 0.559429i | \(-0.188979\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −270.000 | −0.0172800 | −0.00864000 | − | 0.999963i | \(-0.502750\pi\) | ||||
−0.00864000 | + | 0.999963i | \(0.502750\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 181074.i | − 1.53910i | −0.638586 | − | 0.769550i | \(-0.720480\pi\) | ||||
0.638586 | − | 0.769550i | \(-0.279520\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −133839. | −0.251842 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.65169e6i | 0.932333i | 0.884697 | + | 0.466167i | \(0.154365\pi\) | ||||
−0.884697 | + | 0.466167i | \(0.845635\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.38635e6 | −0.908747 | −0.454374 | − | 0.890811i | \(-0.650137\pi\) | ||||
−0.454374 | + | 0.890811i | \(0.650137\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 220225.i | 0.0193339i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.93836e7 | −1.63163 | −0.815814 | − | 0.578314i | \(-0.803711\pi\) | ||||
−0.815814 | + | 0.578314i | \(0.803711\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 5.42609e7i | − 1.15336i | −0.816970 | − | 0.576681i | \(-0.804348\pi\) | ||||
0.816970 | − | 0.576681i | \(-0.195652\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.47692e8 | −1.72203 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.40353e8i | 1.62361i | 0.583925 | + | 0.811807i | \(0.301516\pi\) | ||||
−0.583925 | + | 0.811807i | \(0.698484\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.44068e8 | −0.999701 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 3.24303e8i | − 0.837082i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.63561e8 | 0.274974 | 0.137487 | − | 0.990504i | \(-0.456097\pi\) | ||||
0.137487 | + | 0.990504i | \(0.456097\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 2.31481e8i | − 0.260822i | −0.991460 | − | 0.130411i | \(-0.958370\pi\) | ||||
0.991460 | − | 0.130411i | \(-0.0416297\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.34719e9 | 1.04315 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.88899e7i | 0.0265957i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.60002e9 | 1.40312 | 0.701560 | − | 0.712610i | \(-0.252487\pi\) | ||||
0.701560 | + | 0.712610i | \(0.252487\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.57771e9i | 1.01676i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.12486e9 | 0.447330 | 0.223665 | − | 0.974666i | \(-0.428198\pi\) | ||||
0.223665 | + | 0.974666i | \(0.428198\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 2.60465e9i | − 0.412040i | −0.978548 | − | 0.206020i | \(-0.933949\pi\) | ||||
0.978548 | − | 0.206020i | \(-0.0660512\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.61365e7 | 0.00435182 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 1.75816e10i | − 1.63106i | −0.578712 | − | 0.815532i | \(-0.696444\pi\) | ||||
0.578712 | − | 0.815532i | \(-0.303556\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.89464e10 | −1.36883 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.21231e10i | 1.82556i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.35853e10 | −0.612932 | −0.306466 | − | 0.951882i | \(-0.599147\pi\) | ||||
−0.306466 | + | 0.951882i | \(0.599147\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 4.45955e8i | − 0.0161107i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.42578e10 | −1.29045 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 2.48727e10i | − 0.589673i | −0.955548 | − | 0.294837i | \(-0.904735\pi\) | ||||
0.955548 | − | 0.294837i | \(-0.0952652\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.54966e10 | 0.688981 | 0.344490 | − | 0.938790i | \(-0.388052\pi\) | ||||
0.344490 | + | 0.938790i | \(0.388052\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.42347e10i | 0.387610i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.18431e9 | 0.0157032 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 1.21936e11i | − 1.34798i | −0.738741 | − | 0.673989i | \(-0.764579\pi\) | ||||
0.738741 | − | 0.673989i | \(-0.235421\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.96043e11 | 1.81659 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.24791e11i | 0.974170i | 0.873355 | + | 0.487085i | \(0.161940\pi\) | ||||
−0.873355 | + | 0.487085i | \(0.838060\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.98227e9 | −0.0395302 | −0.0197651 | − | 0.999805i | \(-0.506292\pi\) | ||||
−0.0197651 | + | 0.999805i | \(0.506292\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.99073e11i | 1.11852i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.99077e11 | 1.43495 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 1.21589e11i | − 0.500185i | −0.968222 | − | 0.250093i | \(-0.919539\pi\) | ||||
0.968222 | − | 0.250093i | \(-0.0804611\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.35644e11 | −1.18842 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 3.97309e11i | − 1.21523i | −0.794230 | − | 0.607617i | \(-0.792126\pi\) | ||||
0.794230 | − | 0.607617i | \(-0.207874\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.06336e10 | 0.0281945 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 1.33408e11i | − 0.307657i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.53989e11 | −1.51714 | −0.758569 | − | 0.651593i | \(-0.774101\pi\) | ||||
−0.758569 | + | 0.651593i | \(0.774101\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.94252e11i | 1.39865i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.88806e11 | −0.291823 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.46504e10i | 0.0199301i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.70604e11 | −1.16523 | −0.582615 | − | 0.812748i | \(-0.697970\pi\) | ||||
−0.582615 | + | 0.812748i | \(0.697970\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 2.21060e11i | − 0.234800i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.00753e12 | 0.949142 | 0.474571 | − | 0.880217i | \(-0.342603\pi\) | ||||
0.474571 | + | 0.880217i | \(0.342603\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 1.35534e9i | − 0.00113507i | −1.00000 | 0.000567536i | \(-0.999819\pi\) | |||||
1.00000 | 0.000567536i | \(-0.000180652\pi\) | ||||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.98769e10 | 0.0297567 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.20319e11i | 0.213442i | 0.994289 | + | 0.106721i | \(0.0340352\pi\) | ||||
−0.994289 | + | 0.106721i | \(0.965965\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.23486e12 | 0.736309 | 0.368154 | − | 0.929765i | \(-0.379990\pi\) | ||||
0.368154 | + | 0.929765i | \(0.379990\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 2.93635e12i | − 1.56989i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.02216e12 | 1.45160 | 0.725800 | − | 0.687905i | \(-0.241470\pi\) | ||||
0.725800 | + | 0.687905i | \(0.241470\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 6.48954e10i | − 0.0280561i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.87065e11 | 0.228860 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.13132e12i | 2.51124i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.10365e11 | 0.130755 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 1.73314e12i | − 0.500499i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.31816e11 | 0.0345548 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 9.15391e11i | − 0.218165i | −0.994033 | − | 0.109082i | \(-0.965209\pi\) | ||||
0.994033 | − | 0.109082i | \(-0.0347912\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.12448e12 | −0.461014 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 7.42385e12i | − 1.46893i | −0.678646 | − | 0.734466i | \(-0.737433\pi\) | ||||
0.678646 | − | 0.734466i | \(-0.262567\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9.82522e12 | −1.77514 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 8.75618e10i | 0.0144648i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.33044e12 | 0.654950 | 0.327475 | − | 0.944860i | \(-0.393802\pi\) | ||||
0.327475 | + | 0.944860i | \(0.393802\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.77715e12i | 1.07828i | 0.842216 | + | 0.539140i | \(0.181251\pi\) | ||||
−0.842216 | + | 0.539140i | \(0.818749\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.43404e13 | −1.82493 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 7.24487e12i | − 0.847255i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.41615e10 | −0.00475155 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.54536e13i | 1.53153i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.12754e12 | 0.651361 | 0.325681 | − | 0.945480i | \(-0.394407\pi\) | ||||
0.325681 | + | 0.945480i | \(0.394407\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 8.27460e12i | − 0.698048i | −0.937114 | − | 0.349024i | \(-0.886513\pi\) | ||||
0.937114 | − | 0.349024i | \(-0.113487\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.27105e12 | 0.410912 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.24998e10i | 0.00450701i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.93139e12 | −0.396058 | −0.198029 | − | 0.980196i | \(-0.563454\pi\) | ||||
−0.198029 | + | 0.980196i | \(0.563454\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.10808e13i | 0.685784i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.35216e13 | 2.49891 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 2.97063e13i | − 1.58388i | −0.610599 | − | 0.791940i | \(-0.709071\pi\) | ||||
0.610599 | − | 0.791940i | \(-0.290929\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.63742e11 | −0.0180256 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 1.32583e13i | − 0.611208i | −0.952159 | − | 0.305604i | \(-0.901142\pi\) | ||||
0.952159 | − | 0.305604i | \(-0.0988584\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.05802e12 | −0.174178 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.26223e12i | 0.290465i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.75686e13 | 1.02834 | 0.514171 | − | 0.857688i | \(-0.328100\pi\) | ||||
0.514171 | + | 0.857688i | \(0.328100\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.41942e13i | 1.53864i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.02874e13 | −0.659760 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.86049e13i | 1.17361i | 0.809728 | + | 0.586805i | \(0.199614\pi\) | ||||
−0.809728 | + | 0.586805i | \(0.800386\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.74367e13 | −0.780297 | −0.390148 | − | 0.920752i | \(-0.627576\pi\) | ||||
−0.390148 | + | 0.920752i | \(0.627576\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 2.89527e13i | − 0.770871i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −9.72006e11 | −0.0242459 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 6.50492e13i | − 1.52122i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.87227e13 | −1.28835 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 2.46619e12i | − 0.0507956i | −0.999677 | − | 0.0253978i | \(-0.991915\pi\) | ||||
0.999677 | − | 0.0253978i | \(-0.00808525\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.51237e13 | −1.45356 | −0.726780 | − | 0.686871i | \(-0.758984\pi\) | ||||
−0.726780 | + | 0.686871i | \(0.758984\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 9.65983e11i | − 0.0175696i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.83661e13 | 1.51178 | 0.755890 | − | 0.654699i | \(-0.227204\pi\) | ||||
0.755890 | + | 0.654699i | \(0.227204\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.96844e13i | 0.800022i | 0.916510 | + | 0.400011i | \(0.130994\pi\) | ||||
−0.916510 | + | 0.400011i | \(0.869006\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.94567e13 | −1.50820 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 2.96166e13i | − 0.423213i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.73713e11 | −0.00772986 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 3.21686e13i | − 0.408894i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.96219e13 | 1.07532 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.28031e14i | 1.45085i | 0.688303 | + | 0.725423i | \(0.258356\pi\) | ||||
−0.688303 | + | 0.725423i | \(0.741644\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.01786e14 | 1.08996 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.03256e11i | 0.00712005i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.19150e13 | −0.401431 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.87942e12i | 0.0442286i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.72750e14 | 1.48274 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 8.64588e13i | − 0.703040i | −0.936180 | − | 0.351520i | \(-0.885665\pi\) | ||||
0.936180 | − | 0.351520i | \(-0.114335\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.26658e13 | 0.251766 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 5.88647e12i | − 0.0430229i | −0.999769 | − | 0.0215115i | \(-0.993152\pi\) | ||||
0.999769 | − | 0.0215115i | \(-0.00684784\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.06405e13 | 0.628506 | 0.314253 | − | 0.949339i | \(-0.398246\pi\) | ||||
0.314253 | + | 0.949339i | \(0.398246\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − 2.43941e14i | − 1.60551i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.58282e13 | −0.223918 | −0.111959 | − | 0.993713i | \(-0.535713\pi\) | ||||
−0.111959 | + | 0.993713i | \(0.535713\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.74703e12i | 0.0281848i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −9.91735e13 | −0.559636 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.86133e14i | 1.53525i | 0.640897 | + | 0.767627i | \(0.278562\pi\) | ||||
−0.640897 | + | 0.767627i | \(0.721438\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.33804e13 | −0.272446 | −0.136223 | − | 0.990678i | \(-0.543496\pi\) | ||||
−0.136223 | + | 0.990678i | \(0.543496\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.01419e14i | 0.492587i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.11552e12 | 0.0236534 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.38007e14i | 1.04811i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.24064e14 | −1.35967 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 1.92417e14i | − 0.769488i | −0.923023 | − | 0.384744i | \(-0.874290\pi\) | ||||
0.923023 | − | 0.384744i | \(-0.125710\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.96988e14 | −1.51375 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − 8.67323e12i | − 0.0315457i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.57922e14 | 0.548079 | 0.274039 | − | 0.961719i | \(-0.411640\pi\) | ||||
0.274039 | + | 0.961719i | \(0.411640\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 6.51869e14i | − 2.15954i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.18908e13 | −0.0692499 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.95937e13i | 0.300952i | 0.988614 | + | 0.150476i | \(0.0480806\pi\) | ||||
−0.988614 | + | 0.150476i | \(0.951919\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.66802e12 | 0.0105915 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.14989e14i | 1.69746i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.38111e14 | −1.42023 | −0.710114 | − | 0.704087i | \(-0.751357\pi\) | ||||
−0.710114 | + | 0.704087i | \(0.751357\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 2.33208e14i | − 0.588746i | −0.955691 | − | 0.294373i | \(-0.904889\pi\) | ||||
0.955691 | − | 0.294373i | \(-0.0951108\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.47830e14 | 1.56489 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 4.03123e14i | − 0.932055i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.76832e14 | 1.27694 | 0.638470 | − | 0.769647i | \(-0.279568\pi\) | ||||
0.638470 | + | 0.769647i | \(0.279568\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.09811e13i | 0.0656859i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.02774e13 | 0.0615008 | 0.0307504 | − | 0.999527i | \(-0.490210\pi\) | ||||
0.0307504 | + | 0.999527i | \(0.490210\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.61277e14i | 1.67658i | 0.545225 | + | 0.838290i | \(0.316444\pi\) | ||||
−0.545225 | + | 0.838290i | \(0.683556\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.19496e13 | 0.0222989 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 3.84757e14i | − 0.688486i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.68442e14 | 1.66221 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.91670e14i | 1.30373i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.10405e14 | −0.332545 | −0.166273 | − | 0.986080i | \(-0.553173\pi\) | ||||
−0.166273 | + | 0.986080i | \(0.553173\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.71564e12i | 0.0101896i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.35646e14 | 0.780440 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 1.05427e15i | − 1.47546i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.71634e14 | −0.634171 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 8.21792e14i | − 1.06195i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.58407e12 | −0.0119056 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 7.57481e14i | − 0.904777i | −0.891821 | − | 0.452389i | \(-0.850572\pi\) | ||||
0.891821 | − | 0.452389i | \(-0.149428\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.10548e12 | −0.00126998 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.39394e15i | 1.54057i | 0.637702 | + | 0.770283i | \(0.279885\pi\) | ||||
−0.637702 | + | 0.770283i | \(0.720115\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.80830e14 | −0.936755 | −0.468378 | − | 0.883528i | \(-0.655161\pi\) | ||||
−0.468378 | + | 0.883528i | \(0.655161\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 6.54337e12i | − 0.00669789i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.75062e15 | −1.72518 | −0.862592 | − | 0.505901i | \(-0.831160\pi\) | ||||
−0.862592 | + | 0.505901i | \(0.831160\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.70151e14i | 0.256367i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.61267e14 | 0.238811 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.13699e15i | 1.88186i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.07057e15 | 0.908476 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 1.00721e15i | − 0.823824i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.18356e15 | −2.51037 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 2.85677e14i | − 0.217224i | −0.994084 | − | 0.108612i | \(-0.965359\pi\) | ||||
0.994084 | − | 0.108612i | \(-0.0346406\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.81824e14 | −0.353364 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.29227e13i | 0.0232931i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.86299e15 | 1.27184 | 0.635918 | − | 0.771757i | \(-0.280622\pi\) | ||||
0.635918 | + | 0.771757i | \(0.280622\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 2.46502e15i | − 1.62413i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.82333e14 | 0.243173 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.24396e14i | 0.567667i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.29317e13 | −0.0313907 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 5.35266e14i | − 0.306615i | −0.988179 | − | 0.153307i | \(-0.951008\pi\) | ||||
0.988179 | − | 0.153307i | \(-0.0489925\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.28497e14 | 0.237135 | 0.118567 | − | 0.992946i | \(-0.462170\pi\) | ||||
0.118567 | + | 0.992946i | \(0.462170\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.42251e15i | 0.760696i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.03428e13 | −0.0208506 | −0.0104253 | − | 0.999946i | \(-0.503319\pi\) | ||||
−0.0104253 | + | 0.999946i | \(0.503319\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 3.36937e13i | − 0.0168337i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.81664e15 | 2.80972 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 2.04103e15i | − 0.953417i | −0.879061 | − | 0.476709i | \(-0.841830\pi\) | ||||
0.879061 | − | 0.476709i | \(-0.158170\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.30932e14 | −0.330243 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 3.34713e14i | − 0.146296i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.61521e12 | 0.000683082 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.14353e15i | 1.28653i | 0.765642 | + | 0.643266i | \(0.222421\pi\) | ||||
−0.765642 | + | 0.643266i | \(0.777579\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.84390e14 | −0.112656 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.45993e15i | 0.943364i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.60286e15 | 0.966492 | 0.483246 | − | 0.875485i | \(-0.339458\pi\) | ||||
0.483246 | + | 0.875485i | \(0.339458\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − 1.07516e14i | − 0.0386619i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7.17436e14 | −0.249882 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.15054e15i | 0.725624i | 0.931862 | + | 0.362812i | \(0.118183\pi\) | ||||
−0.931862 | + | 0.362812i | \(0.881817\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.46636e14 | −0.244095 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 5.24573e15i | − 1.66193i | −0.556324 | − | 0.830966i | \(-0.687789\pi\) | ||||
0.556324 | − | 0.830966i | \(-0.312211\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.07507e13 | −0.0247960 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.48604e14i | 0.103769i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.40137e15 | −0.981649 | −0.490824 | − | 0.871259i | \(-0.663304\pi\) | ||||
−0.490824 | + | 0.871259i | \(0.663304\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 9.46596e15i | − 2.64914i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.05524e15 | −1.64352 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.28290e13i | 0.00864320i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.10617e14 | 0.130422 | 0.0652112 | − | 0.997871i | \(-0.479228\pi\) | ||||
0.0652112 | + | 0.997871i | \(0.479228\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8.01391e15i | 1.98613i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.14473e12 | −0.00195889 | −0.000979446 | − | 1.00000i | \(-0.500312\pi\) | ||||
−0.000979446 | 1.00000i | \(0.500312\pi\) | ||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.01535e15i | 0.237021i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 9.06239e13 | 0.0205359 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.94611e15i | 1.30818i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.52561e15 | −1.39406 | −0.697030 | − | 0.717042i | \(-0.745496\pi\) | ||||
−0.697030 | + | 0.717042i | \(0.745496\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 3.53211e15i | − 0.732796i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.50379e15 | −0.907566 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.07273e14i | 0.0209992i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.34341e15 | 1.20644 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.75593e14i | 0.161815i | 0.996722 | + | 0.0809073i | \(0.0257818\pi\) | ||||
−0.996722 | + | 0.0809073i | \(0.974218\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.20280e14 | −0.129363 | −0.0646813 | − | 0.997906i | \(-0.520603\pi\) | ||||
−0.0646813 | + | 0.997906i | \(0.520603\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.35310e15i | 0.410770i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9.61225e15 | 1.63114 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 6.42749e15i | − 1.06041i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.90926e15 | −0.947958 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 3.23527e15i | − 0.504717i | −0.967634 | − | 0.252358i | \(-0.918794\pi\) | ||||
0.967634 | − | 0.252358i | \(-0.0812061\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.88418e15 | 0.285888 | 0.142944 | − | 0.989731i | \(-0.454343\pi\) | ||||
0.142944 | + | 0.989731i | \(0.454343\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.60202e13i | 0.00531631i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.30418e16 | 1.87261 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.20354e15i | 0.866667i | 0.901234 | + | 0.433333i | \(0.142663\pi\) | ||||
−0.901234 | + | 0.433333i | \(0.857337\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.53576e15 | 0.344729 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 6.29203e15i | − 0.832470i | −0.909257 | − | 0.416235i | \(-0.863349\pi\) | ||||
0.909257 | − | 0.416235i | \(-0.136651\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.03577e14 | 0.0262161 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 5.81355e15i | − 0.728780i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.72941e15 | 0.821295 | 0.410647 | − | 0.911794i | \(-0.365303\pi\) | ||||
0.410647 | + | 0.911794i | \(0.365303\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.50961e15i | 0.417061i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.74915e15 | −0.781016 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 2.14448e14i | − 0.0241687i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.09987e16 | 1.20738 | 0.603690 | − | 0.797219i | \(-0.293696\pi\) | ||||
0.603690 | + | 0.797219i | \(0.293696\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.27722e16i | 1.36581i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.49346e15 | −0.155592 | −0.0777961 | − | 0.996969i | \(-0.524788\pi\) | ||||
−0.0777961 | + | 0.996969i | \(0.524788\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 2.15660e15i | − 0.218920i | −0.993991 | − | 0.109460i | \(-0.965088\pi\) | ||||
0.993991 | − | 0.109460i | \(-0.0349121\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.09777e13 | 0.00504270 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.54346e15i | 0.341606i | 0.985305 | + | 0.170803i | \(0.0546362\pi\) | ||||
−0.985305 | + | 0.170803i | \(0.945364\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.20794e16 | −2.07467 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.83792e15i | 0.443132i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.30207e15 | 0.384158 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.32433e16i | 1.15302i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.81824e15 | 0.154362 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 8.95923e15i | − 0.741750i | −0.928683 | − | 0.370875i | \(-0.879058\pi\) | ||||
0.928683 | − | 0.370875i | \(-0.120942\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.57910e16 | −1.27508 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 3.54983e16i | − 2.79592i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.62063e14 | 0.0201352 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 1.24818e16i | − 0.935631i | −0.883826 | − | 0.467815i | \(-0.845041\pi\) | ||||
0.883826 | − | 0.467815i | \(-0.154959\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.42298e16 | −1.77214 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.05874e16i | 0.755618i | 0.925884 | + | 0.377809i | \(0.123322\pi\) | ||||
−0.925884 | + | 0.377809i | \(0.876678\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.44161e15 | −0.448656 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.96862e13i | 0.00405735i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.25964e16 | 1.49935 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.22201e15i | 0.597341i | 0.954356 | + | 0.298670i | \(0.0965432\pi\) | ||||
−0.954356 | + | 0.298670i | \(0.903457\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.08141e16 | −0.683855 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.52282e16i | 1.55768i | 0.627224 | + | 0.778839i | \(0.284191\pi\) | ||||
−0.627224 | + | 0.778839i | \(0.715809\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.72034e14 | −0.0164012 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.30991e15i | 0.194881i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.27357e14 | 0.0475758 | 0.0237879 | − | 0.999717i | \(-0.492427\pi\) | ||||
0.0237879 | + | 0.999717i | \(0.492427\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.08323e15i | 0.0608409i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.75970e16 | −0.965459 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.65941e11i | 0 1.96141e-5i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.90393e16 | 1.52070 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − 2.24862e16i | − 1.15057i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.03033e16 | 1.51518 | 0.757590 | − | 0.652731i | \(-0.226377\pi\) | ||||
0.757590 | + | 0.652731i | \(0.226377\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.35359e15i | 0.163870i | 0.996638 | + | 0.0819350i | \(0.0261100\pi\) | ||||
−0.996638 | + | 0.0819350i | \(0.973890\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.60469e16 | 1.72152 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9.11653e15i | 0.425565i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.58550e16 | −1.63612 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.32894e15i | 0.148504i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9.32040e15 | −0.406510 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 8.64862e13i | − 0.00368828i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.14879e16 | 1.31310 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 3.12934e16i | − 1.27621i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.49714e16 | 1.39486 | 0.697429 | − | 0.716654i | \(-0.254327\pi\) | ||||
0.697429 | + | 0.716654i | \(0.254327\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.23786e16i | 0.873041i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.33413e14 | −0.0127234 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 3.12824e16i | − 1.16782i | −0.811818 | − | 0.583910i | \(-0.801522\pi\) | ||||
0.811818 | − | 0.583910i | \(-0.198478\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.75082e15 | −0.173514 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 8.87497e15i | − 0.317145i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.20165e16 | −0.769835 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 7.92814e14i | 0.0271277i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.39444e16 | 0.801811 | 0.400906 | − | 0.916119i | \(-0.368695\pi\) | ||||
0.400906 | + | 0.916119i | \(0.368695\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.14249e16i | 0.374440i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.30572e16 | −1.70203 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.34970e16i | 0.737841i | 0.929461 | + | 0.368920i | \(0.120272\pi\) | ||||
−0.929461 | + | 0.368920i | \(0.879728\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.15984e14 | −0.0250837 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 6.07763e16i | 1.82909i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.58337e16 | −0.761224 | −0.380612 | − | 0.924735i | \(-0.624287\pi\) | ||||
−0.380612 | + | 0.924735i | \(0.624287\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.10927e15i | 0.0897101i | 0.998994 | + | 0.0448550i | \(0.0142826\pi\) | ||||
−0.998994 | + | 0.0448550i | \(0.985717\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.01154e15 | −0.0568331 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 5.86625e16i | − 1.62313i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.04365e15 | 0.163774 | 0.0818869 | − | 0.996642i | \(-0.473905\pi\) | ||||
0.0818869 | + | 0.996642i | \(0.473905\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.12744e16i | 1.62633i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.19422e16 | −1.87037 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 2.24386e16i | − 0.571457i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.58507e14 | −0.00395471 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 1.81607e16i | − 0.443919i | −0.975056 | − | 0.221959i | \(-0.928755\pi\) | ||||
0.975056 | − | 0.221959i | \(-0.0712452\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.25604e16 | −0.300822 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − 7.20756e16i | − 1.69147i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.44671e16 | −0.792641 | −0.396320 | − | 0.918112i | \(-0.629713\pi\) | ||||
−0.396320 | + | 0.918112i | \(0.629713\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 1.92546e15i | − 0.0433942i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.05250e16 | 0.895110 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 6.45268e16i | − 1.39694i | −0.715637 | − | 0.698472i | \(-0.753863\pi\) | ||||
0.715637 | − | 0.698472i | \(-0.246137\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.99244e16 | 0.422804 | 0.211402 | − | 0.977399i | \(-0.432197\pi\) | ||||
0.211402 | + | 0.977399i | \(0.432197\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.63198e16i | 0.339477i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.10798e14 | −0.00225944 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.82361e16i | 1.56414i | 0.623192 | + | 0.782069i | \(0.285836\pi\) | ||||
−0.623192 | + | 0.782069i | \(0.714164\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.41567e16 | −0.473515 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.71190e16i | 1.48223i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.30905e15 | 0.0623650 | 0.0311825 | − | 0.999514i | \(-0.490073\pi\) | ||||
0.0311825 | + | 0.999514i | \(0.490073\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.67948e14i | 0.00864862i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.04322e16 | 1.45787 | 0.728936 | − | 0.684582i | \(-0.240015\pi\) | ||||
0.728936 | + | 0.684582i | \(0.240015\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 8.90694e16i | − 1.58338i | −0.610924 | − | 0.791689i | \(-0.709202\pi\) | ||||
0.610924 | − | 0.791689i | \(-0.290798\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.79472e16 | 1.35910 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.36528e17i | 2.33503i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.95513e16 | 0.999104 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 7.30999e16i | − 1.20313i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.41782e17 | −2.28937 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 1.93551e16i | − 0.306634i | −0.988177 | − | 0.153317i | \(-0.951004\pi\) | ||||
0.988177 | − | 0.153317i | \(-0.0489955\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.04428e17 | 1.62329 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.47156e14i | 0.00376988i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.31054e16 | 1.24392 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − 1.67020e16i | − 0.245337i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.07240e15 | −0.130790 | −0.0653949 | − | 0.997859i | \(-0.520831\pi\) | ||||
−0.0653949 | + | 0.997859i | \(0.520831\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.47136e16i | 0.208186i | 0.994568 | + | 0.104093i | \(0.0331940\pi\) | ||||
−0.994568 | + | 0.104093i | \(0.966806\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.73609e14 | 0.00796632 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.15025e16i | 0.156807i | 0.996922 | + | 0.0784037i | \(0.0249823\pi\) | ||||
−0.996922 | + | 0.0784037i | \(0.975018\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.10819e16 | 0.549772 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.41879e16i | 0.449145i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.02325e17 | −1.31979 | −0.659893 | − | 0.751359i | \(-0.729399\pi\) | ||||
−0.659893 | + | 0.751359i | \(0.729399\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.00444e15i | 0.0253831i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.00661e14 | 0.00995535 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 1.35977e17i | − 1.66017i | −0.557639 | − | 0.830084i | \(-0.688293\pi\) | ||||
0.557639 | − | 0.830084i | \(-0.311707\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.02702e15 | −0.0123132 | −0.00615660 | − | 0.999981i | \(-0.501960\pi\) | ||||
−0.00615660 | + | 0.999981i | \(0.501960\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 1.40903e17i | − 1.65897i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.65281e15 | 0.0306744 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.93124e16i | 0.446452i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7.05199e16 | −0.786601 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.86291e16i | 0.642360i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.35963e16 | −1.00732 | −0.503661 | − | 0.863902i | \(-0.668014\pi\) | ||||
−0.503661 | + | 0.863902i | \(0.668014\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 7.91519e16i | 0.836832i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.23322e17 | −1.28088 | −0.640442 | − | 0.768006i | \(-0.721249\pi\) | ||||
−0.640442 | + | 0.768006i | \(0.721249\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.75751e17i | 1.79341i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.80128e15 | −0.0481365 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.82799e16i | 0.377091i | 0.982064 | + | 0.188546i | \(0.0603774\pi\) | ||||
−0.982064 | + | 0.188546i | \(0.939623\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.16922e15 | −0.0113175 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 7.39307e16i | − 0.703209i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.95897e16 | 0.557001 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.37695e16i | 0.585794i | 0.956144 | + | 0.292897i | \(0.0946193\pi\) | ||||
−0.956144 | + | 0.292897i | \(0.905381\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.00281e16 | −0.361381 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 2.09983e15i | − 0.0186327i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.36847e16 | −0.729877 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.92231e16i | 0.250532i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.51420e17 | −1.27607 | −0.638036 | − | 0.770007i | \(-0.720253\pi\) | ||||
−0.638036 | + | 0.770007i | \(0.720253\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 1.95341e17i | − 1.61831i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.87190e15 | 0.0315348 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 1.82438e17i | − 1.46083i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.73160e17 | 1.36323 | 0.681615 | − | 0.731711i | \(-0.261278\pi\) | ||||
0.681615 | + | 0.731711i | \(0.261278\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.62733e16i | 0.125967i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.56371e16 | 0.423475 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.95611e15i | 0.0146406i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.33383e17 | 1.71773 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.06527e16i | 0.149487i | 0.997203 | + | 0.0747437i | \(0.0238139\pi\) | ||||
−0.997203 | + | 0.0747437i | \(0.976186\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.45416e14 | −0.00174699 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.35396e16i | 0.304828i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.99200e16 | −0.274892 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.17858e15i | 0.0147559i | 0.999973 | + | 0.00737797i | \(0.00234850\pi\) | ||||
−0.999973 | + | 0.00737797i | \(0.997651\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −9.56527e16 | −0.637283 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.02581e17i | 0.672296i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.40075e17 | 0.903105 | 0.451553 | − | 0.892245i | \(-0.350870\pi\) | ||||
0.451553 | + | 0.892245i | \(0.350870\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − 4.17246e15i | − 0.0264648i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.01400e17 | 1.25677 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.13793e16i | 0.561023i | 0.959851 | + | 0.280512i | \(0.0905042\pi\) | ||||
−0.959851 | + | 0.280512i | \(0.909496\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.94130e17 | 1.17269 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.19217e17i | 0.708608i | 0.935130 | + | 0.354304i | \(0.115282\pi\) | ||||
−0.935130 | + | 0.354304i | \(0.884718\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.92443e15 | −0.0112555 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.31755e16i | 0.306047i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.80014e16 | 0.328509 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 3.29458e17i | − 1.83637i | −0.396148 | − | 0.918187i | \(-0.629653\pi\) | ||||
0.396148 | − | 0.918187i | \(-0.370347\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.56945e17 | −0.860947 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.23414e15i | 0.0120623i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.24096e16 | −0.384787 | −0.192394 | − | 0.981318i | \(-0.561625\pi\) | ||||
−0.192394 | + | 0.981318i | \(0.561625\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.23802e17i | 1.69367i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.80979e16 | 0.453584 | 0.226792 | − | 0.973943i | \(-0.427176\pi\) | ||||
0.226792 | + | 0.973943i | \(0.427176\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 2.23601e17i | − 1.13325i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.42318e15 | −0.00710056 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.09100e17i | 0.535864i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.19640e17 | −1.06207 | −0.531036 | − | 0.847349i | \(-0.678197\pi\) | ||||
−0.531036 | + | 0.847349i | \(0.678197\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 1.28808e17i | − 0.613222i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.36479e17 | 1.57718 | 0.788589 | − | 0.614921i | \(-0.210812\pi\) | ||||
0.788589 | + | 0.614921i | \(0.210812\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.64969e16i | 0.260744i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.31695e17 | −2.41622 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 1.15297e17i | − 0.515933i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.06116e17 | −0.908251 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 5.30433e16i | − 0.230176i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.60147e15 | 0.00684388 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 8.11217e16i | − 0.341420i | −0.985321 | − | 0.170710i | \(-0.945394\pi\) | ||||
0.985321 | − | 0.170710i | \(-0.0546061\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8.12333e16 | 0.336722 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 5.47234e17i | − 2.23416i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.55700e17 | −0.626110 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 2.99181e15i | − 0.0118503i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4.21727e17 | −1.64544 | −0.822719 | − | 0.568448i | \(-0.807544\pi\) | ||||
−0.822719 | + | 0.568448i | \(0.807544\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.92426e17i | 2.66129i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.00913e17 | 0.382079 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 9.88083e15i | − 0.0368553i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.17508e16 | −0.0431811 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.38908e17i | 1.58903i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.89060e17 | 0.674385 | 0.337193 | − | 0.941436i | \(-0.390523\pi\) | ||||
0.337193 | + | 0.941436i | \(0.390523\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.86016e17i | 1.00523i | 0.864510 | + | 0.502615i | \(0.167629\pi\) | ||||
−0.864510 | + | 0.502615i | \(0.832371\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.90215e17 | −0.658723 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.02069e15i | 0.0273695i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.41331e17 | −0.475231 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 1.06302e17i | − 0.352239i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.69622e17 | 0.880435 | 0.440217 | − | 0.897891i | \(-0.354901\pi\) | ||||
0.440217 | + | 0.897891i | \(0.354901\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 5.35943e17i | − 1.72473i | −0.506291 | − | 0.862363i | \(-0.668984\pi\) | ||||
0.506291 | − | 0.862363i | \(-0.331016\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.28806e17 | −1.04284 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.10780e17i | 0.971449i | 0.874112 | + | 0.485724i | \(0.161444\pi\) | ||||
−0.874112 | + | 0.485724i | \(0.838556\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.99181e17 | 1.53791 | 0.768955 | − | 0.639303i | \(-0.220777\pi\) | ||||
0.768955 | + | 0.639303i | \(0.220777\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 4.70491e17i | − 1.42871i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.46175e17 | 2.23342 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.57974e15i | 0.0105617i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.50698e16 | −0.218330 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 5.10671e17i | − 1.46409i | −0.681254 | − | 0.732047i | \(-0.738565\pi\) | ||||
0.681254 | − | 0.732047i | \(-0.261435\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.27063e17 | −0.924389 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 2.46957e16i | − 0.0688107i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.09567e15 | 0.00300980 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 7.43062e16i | − 0.201245i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7.02498e17 | 1.87585 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.65277e17i | 2.27813i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.26560e16 | −0.162656 | −0.0813278 | − | 0.996687i | \(-0.525916\pi\) | ||||
−0.0813278 | + | 0.996687i | \(0.525916\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − 1.96080e15i | − 0.00501923i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.64927e17 | 1.42596 | 0.712980 | − | 0.701184i | \(-0.247345\pi\) | ||||
0.712980 | + | 0.701184i | \(0.247345\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 3.44043e17i | − 0.856355i | −0.903695 | − | 0.428178i | \(-0.859156\pi\) | ||||
0.903695 | − | 0.428178i | \(-0.140844\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.13826e17 | −0.770318 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.90262e17i | 1.18676i | 0.804922 | + | 0.593381i | \(0.202207\pi\) | ||||
−0.804922 | + | 0.593381i | \(0.797793\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.44352e15 | −0.0177698 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 7.89907e17i | − 1.85978i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.00826e17 | 0.466339 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.34854e17i | 1.22497i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.29905e17 | 0.293453 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 2.38684e16i | − 0.0531834i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.61799e17 | −1.23476 | −0.617382 | − | 0.786664i | \(-0.711807\pi\) | ||||
−0.617382 | + | 0.786664i | \(0.711807\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.71616e17i | 0.372071i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.27518e17 | 0.700455 | 0.350228 | − | 0.936665i | \(-0.386104\pi\) | ||||
0.350228 | + | 0.936665i | \(0.386104\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.81950e17i | 1.22778i | 0.789391 | + | 0.613891i | \(0.210397\pi\) | ||||
−0.789391 | + | 0.613891i | \(0.789603\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.47759e15 | 0.0114007 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 4.36465e16i | − 0.0896205i | −0.998996 | − | 0.0448103i | \(-0.985732\pi\) | ||||
0.998996 | − | 0.0448103i | \(-0.0142683\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.65753e17 | −0.335777 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 5.54379e17i | − 1.10800i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9.53993e17 | −1.88121 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 1.04233e16i | − 0.0202800i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.59915e17 | −1.65082 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 3.78612e16i | − 0.0717193i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.35035e17 | 1.00008 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.84687e17i | 0.709547i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.40790e15 | 0.0134835 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 4.66428e17i | − 0.837800i | −0.908032 | − | 0.418900i | \(-0.862416\pi\) | ||||
0.908032 | − | 0.418900i | \(-0.137584\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.34847e17 | −0.239034 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.31660e16i | 0.0230326i | 0.999934 | + | 0.0115163i | \(0.00366584\pi\) | ||||
−0.999934 | + | 0.0115163i | \(0.996334\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.56230e17 | 1.13300 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 7.81722e15i | 0.0133207i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.34426e18 | −2.26083 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 1.06905e18i | − 1.77462i | −0.461171 | − | 0.887311i | \(-0.652571\pi\) | ||||
0.461171 | − | 0.887311i | \(-0.347429\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.17837e17 | −1.01232 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 5.47379e17i | − 0.885274i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.78650e17 | −1.40270 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.81397e14i | 0 0.000285859i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.94106e17 | 1.07977 | 0.539886 | − | 0.841738i | \(-0.318467\pi\) | ||||
0.539886 | + | 0.841738i | \(0.318467\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.02805e18i | 1.57876i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.13696e18 | 1.72367 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.75633e16i | 0.0262867i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5.34686e17 | −0.790062 | −0.395031 | − | 0.918668i | \(-0.629266\pi\) | ||||
−0.395031 | + | 0.918668i | \(0.629266\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.18447e17i | 1.04810i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.45210e17 | 1.21738 | 0.608691 | − | 0.793408i | \(-0.291695\pi\) | ||||
0.608691 | + | 0.793408i | \(0.291695\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.10718e17i | 0.726292i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.58551e16 | 0.0222628 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 2.47183e17i | − 0.342703i | −0.985210 | − | 0.171352i | \(-0.945187\pi\) | ||||
0.985210 | − | 0.171352i | \(-0.0548134\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.62403e16 | 0.0359229 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.42788e18i | 1.93023i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.88377e17 | −0.384949 | −0.192475 | − | 0.981302i | \(-0.561651\pi\) | ||||
−0.192475 | + | 0.981302i | \(0.561651\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.65871e14i | 0 0.000877749i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.20348e17 | 0.286839 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 7.84128e17i | − 1.00803i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.34080e17 | 0.931972 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 4.28712e16i | − 0.0537536i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.02834e16 | 0.0251175 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 5.78010e17i | − 0.706930i | −0.935448 | − | 0.353465i | \(-0.885003\pi\) | ||||
0.935448 | − | 0.353465i | \(-0.114997\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.74303e18 | 2.10553 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 9.64225e17i | − 1.15044i | −0.818000 | − | 0.575219i | \(-0.804917\pi\) | ||||
0.818000 | − | 0.575219i | \(-0.195083\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.40824e18 | 1.65958 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − 8.73204e17i | − 1.01646i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.54758e18 | −1.77945 | −0.889727 | − | 0.456494i | \(-0.849105\pi\) | ||||
−0.889727 | + | 0.456494i | \(0.849105\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 1.24535e18i | − 1.41448i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.65273e17 | −0.185433 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 7.20190e17i | 0.798227i | 0.916902 | + | 0.399113i | \(0.130682\pi\) | ||||
−0.916902 | + | 0.399113i | \(0.869318\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.38589e16 | −0.0261236 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.59666e18i | 2.80875i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.26037e17 | 0.668994 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 5.74291e17i | − 0.606303i | −0.952942 | − | 0.303152i | \(-0.901961\pi\) | ||||
0.952942 | − | 0.303152i | \(-0.0980388\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.33012e17 | −0.243043 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 1.34148e16i | − 0.0138244i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.64429e18 | 1.67420 | 0.837099 | − | 0.547052i | \(-0.184250\pi\) | ||||
0.837099 | + | 0.547052i | \(0.184250\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − 1.16750e18i | − 1.17453i |
(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 | 16.13.c.a.15.1 | ✓ | 2 | |
3.2 | odd | 2 | 144.13.g.d.127.1 | 2 | |||
4.3 | odd | 2 | inner | 16.13.c.a.15.2 | yes | 2 | |
8.3 | odd | 2 | 64.13.c.b.63.1 | 2 | |||
8.5 | even | 2 | 64.13.c.b.63.2 | 2 | |||
12.11 | even | 2 | 144.13.g.d.127.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
16.13.c.a.15.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
16.13.c.a.15.2 | yes | 2 | 4.3 | odd | 2 | inner | |
64.13.c.b.63.1 | 2 | 8.3 | odd | 2 | |||
64.13.c.b.63.2 | 2 | 8.5 | even | 2 | |||
144.13.g.d.127.1 | 2 | 3.2 | odd | 2 | |||
144.13.g.d.127.2 | 2 | 12.11 | even | 2 |