Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1083,1,Mod(62,1083)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1083, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([9, 16]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1083.62");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1083 = 3 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1083.l (of order \(18\), degree \(6\), not 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: | \(0.540487408682\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\Q(\zeta_{18})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{3} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 57) |
Projective image: | \(D_{3}\) |
Projective field: | Galois closure of 3.1.1083.1 |
Artin image: | $S_3\times C_9$ |
Artin field: | Galois closure of \(\mathbb{Q}[x]/(x^{54} - \cdots)\) |
Embedding invariants
Embedding label | 776.1 | ||
Root | \(0.939693 + 0.342020i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1083.776 |
Dual form | 1083.1.l.a.956.1 |
$q$-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 \(\left(\mathbb{Z}/1083\mathbb{Z}\right)^\times\).
\(n\) | \(362\) | \(724\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{9}\right)\) |
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 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(3\) | −0.939693 | + | 0.342020i | −0.939693 | + | 0.342020i | ||||
\(4\) | 0.173648 | + | 0.984808i | 0.173648 | + | 0.984808i | ||||
\(5\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.766044 | − | 0.642788i | 0.766044 | − | 0.642788i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(12\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(13\) | 0.939693 | + | 0.342020i | 0.939693 | + | 0.342020i | 0.766044 | − | 0.642788i | \(-0.222222\pi\) |
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.939693 | + | 0.342020i | −0.939693 | + | 0.342020i | ||||
\(17\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.766044 | − | 0.642788i | −0.766044 | − | 0.642788i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.939693 | − | 0.342020i | −0.939693 | − | 0.342020i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(28\) | −0.766044 | + | 0.642788i | −0.766044 | + | 0.642788i | ||||
\(29\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.766044 | + | 0.642788i | 0.766044 | + | 0.642788i | ||||
\(37\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.00000 | −1.00000 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.173648 | + | 0.984808i | −0.173648 | + | 0.984808i | 0.766044 | + | 0.642788i | \(0.222222\pi\) |
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(48\) | 0.766044 | − | 0.642788i | 0.766044 | − | 0.642788i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.173648 | + | 0.984808i | −0.173648 | + | 0.984808i | ||||
\(53\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.173648 | − | 0.984808i | −0.173648 | − | 0.984808i | −0.939693 | − | 0.342020i | \(-0.888889\pi\) |
0.766044 | − | 0.642788i | \(-0.222222\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.939693 | + | 0.342020i | 0.939693 | + | 0.342020i | ||||
\(64\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.766044 | + | 0.642788i | −0.766044 | + | 0.642788i | −0.939693 | − | 0.342020i | \(-0.888889\pi\) |
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.939693 | − | 0.342020i | 0.939693 | − | 0.342020i | 0.173648 | − | 0.984808i | \(-0.444444\pi\) |
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 1.00000 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.939693 | − | 0.342020i | 0.939693 | − | 0.342020i | 0.173648 | − | 0.984808i | \(-0.444444\pi\) |
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.173648 | − | 0.984808i | 0.173648 | − | 0.984808i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(84\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.173648 | + | 0.984808i | 0.173648 | + | 0.984808i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.766044 | − | 0.642788i | −0.766044 | − | 0.642788i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.53209 | + | 1.28558i | 1.53209 | + | 1.28558i | 0.766044 | + | 0.642788i | \(0.222222\pi\) |
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.173648 | − | 0.984808i | 0.173648 | − | 0.984808i | ||||
\(101\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(108\) | −0.939693 | − | 0.342020i | −0.939693 | − | 0.342020i | ||||
\(109\) | 0.347296 | − | 1.96962i | 0.347296 | − | 1.96962i | 0.173648 | − | 0.984808i | \(-0.444444\pi\) |
0.173648 | − | 0.984808i | \(-0.444444\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.939693 | − | 0.342020i | 0.939693 | − | 0.342020i | ||||
\(112\) | −0.766044 | − | 0.642788i | −0.766044 | − | 0.642788i | ||||
\(113\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.939693 | − | 0.342020i | 0.939693 | − | 0.342020i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.766044 | + | 0.642788i | −0.766044 | + | 0.642788i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.87939 | − | 0.684040i | −1.87939 | − | 0.684040i | −0.939693 | − | 0.342020i | \(-0.888889\pi\) |
−0.939693 | − | 0.342020i | \(-0.888889\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.173648 | − | 0.984808i | −0.173648 | − | 0.984808i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.939693 | + | 0.342020i | 0.939693 | + | 0.342020i | 0.766044 | − | 0.642788i | \(-0.222222\pi\) |
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.173648 | − | 0.984808i | −0.173648 | − | 0.984808i | ||||
\(149\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.00000 | 2.00000 | 1.00000 | \(0\) | ||||||
1.00000 | \(0\) | |||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.173648 | − | 0.984808i | −0.173648 | − | 0.984808i | ||||
\(157\) | −0.173648 | + | 0.984808i | −0.173648 | + | 0.984808i | 0.766044 | + | 0.642788i | \(0.222222\pi\) |
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.00000 | −1.00000 | ||||||||
\(173\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.173648 | − | 0.984808i | −0.173648 | − | 0.984808i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.53209 | − | 1.28558i | 1.53209 | − | 1.28558i | 0.766044 | − | 0.642788i | \(-0.222222\pi\) |
0.766044 | − | 0.642788i | \(-0.222222\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.00000 | −1.00000 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(192\) | 0.766044 | + | 0.642788i | 0.766044 | + | 0.642788i | ||||
\(193\) | 0.939693 | − | 0.342020i | 0.939693 | − | 0.342020i | 0.173648 | − | 0.984808i | \(-0.444444\pi\) |
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.766044 | + | 0.642788i | −0.766044 | + | 0.642788i | −0.939693 | − | 0.342020i | \(-0.888889\pi\) |
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.00000 | −1.00000 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.766044 | − | 0.642788i | −0.766044 | − | 0.642788i | 0.173648 | − | 0.984808i | \(-0.444444\pi\) |
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.766044 | + | 0.642788i | −0.766044 | + | 0.642788i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.173648 | + | 0.984808i | −0.173648 | + | 0.984808i | 0.766044 | + | 0.642788i | \(0.222222\pi\) |
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.939693 | + | 0.342020i | −0.939693 | + | 0.342020i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.766044 | + | 0.642788i | −0.766044 | + | 0.642788i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.939693 | + | 0.342020i | 0.939693 | + | 0.342020i | 0.766044 | − | 0.642788i | \(-0.222222\pi\) |
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.173648 | + | 0.984808i | 0.173648 | + | 0.984808i | ||||
\(244\) | 0.939693 | − | 0.342020i | 0.939693 | − | 0.342020i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(252\) | −0.173648 | + | 0.984808i | −0.173648 | + | 0.984808i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.766044 | − | 0.642788i | 0.766044 | − | 0.642788i | ||||
\(257\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.766044 | − | 0.642788i | −0.766044 | − | 0.642788i | ||||
\(269\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.347296 | − | 1.96962i | 0.347296 | − | 1.96962i | 0.173648 | − | 0.984808i | \(-0.444444\pi\) |
0.173648 | − | 0.984808i | \(-0.444444\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | −0.500000 | + | 0.866025i | \(0.666667\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.939693 | + | 0.342020i | 0.939693 | + | 0.342020i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.53209 | + | 1.28558i | 1.53209 | + | 1.28558i | 0.766044 | + | 0.642788i | \(0.222222\pi\) |
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.173648 | + | 0.984808i | 0.173648 | + | 0.984808i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.87939 | − | 0.684040i | −1.87939 | − | 0.684040i | ||||
\(292\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(293\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0.173648 | + | 0.984808i | 0.173648 | + | 0.984808i | ||||
\(301\) | −0.939693 | + | 0.342020i | −0.939693 | + | 0.342020i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.87939 | + | 0.684040i | −1.87939 | + | 0.684040i | −0.939693 | + | 0.342020i | \(0.888889\pi\) |
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.173648 | + | 0.984808i | −0.173648 | + | 0.984808i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.53209 | − | 1.28558i | 1.53209 | − | 1.28558i | 0.766044 | − | 0.642788i | \(-0.222222\pi\) |
0.766044 | − | 0.642788i | \(-0.222222\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(317\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 1.00000 | 1.00000 | ||||||||
\(325\) | −0.766044 | − | 0.642788i | −0.766044 | − | 0.642788i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.347296 | + | 1.96962i | 0.347296 | + | 1.96962i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.766044 | + | 0.642788i | −0.766044 | + | 0.642788i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.939693 | + | 0.342020i | 0.939693 | + | 0.342020i | ||||
\(337\) | −0.173648 | + | 0.984808i | −0.173648 | + | 0.984808i | 0.766044 | + | 0.642788i | \(0.222222\pi\) |
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 1.00000 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.766044 | + | 0.642788i | −0.766044 | + | 0.642788i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.766044 | + | 0.642788i | 0.766044 | + | 0.642788i | ||||
\(364\) | −0.939693 | + | 0.342020i | −0.939693 | + | 0.342020i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.939693 | + | 0.342020i | 0.939693 | + | 0.342020i | 0.766044 | − | 0.642788i | \(-0.222222\pi\) |
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(373\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
−0.500000 | − | 0.866025i | \(-0.666667\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.00000 | 2.00000 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(388\) | −1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | ||||
\(389\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.766044 | − | 0.642788i | −0.766044 | − | 0.642788i | 0.173648 | − | 0.984808i | \(-0.444444\pi\) |
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 1.00000 | ||||||||
\(401\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.173648 | + | 0.984808i | 0.173648 | + | 0.984808i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.53209 | − | 1.28558i | 1.53209 | − | 1.28558i | 0.766044 | − | 0.642788i | \(-0.222222\pi\) |
0.766044 | − | 0.642788i | \(-0.222222\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.939693 | + | 0.342020i | 0.939693 | + | 0.342020i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.00000 | −1.00000 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.87939 | + | 0.684040i | −1.87939 | + | 0.684040i | −0.939693 | + | 0.342020i | \(0.888889\pi\) |
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.766044 | − | 0.642788i | 0.766044 | − | 0.642788i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(432\) | 0.173648 | − | 0.984808i | 0.173648 | − | 0.984808i | ||||
\(433\) | −0.173648 | − | 0.984808i | −0.173648 | − | 0.984808i | −0.939693 | − | 0.342020i | \(-0.888889\pi\) |
0.766044 | − | 0.642788i | \(-0.222222\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.00000 | 2.00000 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.766044 | − | 0.642788i | −0.766044 | − | 0.642788i | 0.173648 | − | 0.984808i | \(-0.444444\pi\) |
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(444\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(449\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.87939 | + | 0.684040i | −1.87939 | + | 0.684040i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(468\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(469\) | −0.939693 | − | 0.342020i | −0.939693 | − | 0.342020i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.173648 | − | 0.984808i | −0.173648 | − | 0.984808i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.939693 | − | 0.342020i | −0.939693 | − | 0.342020i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.766044 | − | 0.642788i | 0.766044 | − | 0.642788i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
−0.500000 | − | 0.866025i | \(-0.666667\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.173648 | + | 0.984808i | −0.173648 | + | 0.984808i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.766044 | − | 0.642788i | −0.766044 | − | 0.642788i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.173648 | + | 0.984808i | −0.173648 | + | 0.984808i | 0.766044 | + | 0.642788i | \(0.222222\pi\) |
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.347296 | − | 1.96962i | 0.347296 | − | 1.96962i | ||||
\(509\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.766044 | + | 0.642788i | 0.766044 | + | 0.642788i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.939693 | − | 0.342020i | 0.939693 | − | 0.342020i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.766044 | + | 0.642788i | −0.766044 | + | 0.642788i | −0.939693 | − | 0.342020i | \(-0.888889\pi\) |
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.939693 | + | 0.342020i | −0.939693 | + | 0.342020i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.766044 | + | 0.642788i | −0.766044 | + | 0.642788i | −0.939693 | − | 0.342020i | \(-0.888889\pi\) |
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.173648 | − | 0.984808i | −0.173648 | − | 0.984808i | −0.939693 | − | 0.342020i | \(-0.888889\pi\) |
0.766044 | − | 0.642788i | \(-0.222222\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.766044 | − | 0.642788i | −0.766044 | − | 0.642788i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.766044 | + | 0.642788i | 0.766044 | + | 0.642788i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.173648 | + | 0.984808i | −0.173648 | + | 0.984808i | ||||
\(557\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.939693 | − | 0.342020i | 0.939693 | − | 0.342020i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.939693 | − | 0.342020i | −0.939693 | − | 0.342020i | ||||
\(577\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
−0.500000 | − | 0.866025i | \(-0.666667\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.766044 | + | 0.642788i | −0.766044 | + | 0.642788i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.939693 | − | 0.342020i | 0.939693 | − | 0.342020i | ||||
\(593\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.173648 | + | 0.984808i | −0.173648 | + | 0.984808i | ||||
\(604\) | 0.347296 | + | 1.96962i | 0.347296 | + | 1.96962i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.347296 | − | 1.96962i | 0.347296 | − | 1.96962i | 0.173648 | − | 0.984808i | \(-0.444444\pi\) |
0.173648 | − | 0.984808i | \(-0.444444\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0.939693 | − | 0.342020i | 0.939693 | − | 0.342020i | ||||
\(625\) | 0.766044 | + | 0.642788i | 0.766044 | + | 0.642788i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.00000 | −1.00000 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.173648 | − | 0.984808i | −0.173648 | − | 0.984808i | −0.939693 | − | 0.342020i | \(-0.888889\pi\) |
0.766044 | − | 0.642788i | \(-0.222222\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.939693 | + | 0.342020i | 0.939693 | + | 0.342020i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.939693 | − | 0.342020i | 0.939693 | − | 0.342020i | 0.173648 | − | 0.984808i | \(-0.444444\pi\) |
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.173648 | − | 0.984808i | 0.173648 | − | 0.984808i | ||||
\(652\) | 0.939693 | + | 0.342020i | 0.939693 | + | 0.342020i | ||||
\(653\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.347296 | + | 1.96962i | 0.347296 | + | 1.96962i | 0.173648 | + | 0.984808i | \(0.444444\pi\) |
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.173648 | − | 0.984808i | −0.173648 | − | 0.984808i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.766044 | − | 0.642788i | 0.766044 | − | 0.642788i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.347296 | + | 1.96962i | −0.347296 | + | 1.96962i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.939693 | − | 0.342020i | 0.939693 | − | 0.342020i | ||||
\(688\) | −0.173648 | − | 0.984808i | −0.173648 | − | 0.984808i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
−0.500000 | − | 0.866025i | \(-0.666667\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.939693 | − | 0.342020i | 0.939693 | − | 0.342020i | ||||
\(701\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.939693 | + | 0.342020i | 0.939693 | + | 0.342020i | 0.766044 | − | 0.642788i | \(-0.222222\pi\) |
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.00000 | 1.00000 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.00000 | −1.00000 | ||||||||
\(724\) | 1.53209 | + | 1.28558i | 1.53209 | + | 1.28558i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.173648 | + | 0.984808i | −0.173648 | + | 0.984808i | 0.766044 | + | 0.642788i | \(0.222222\pi\) |
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −0.766044 | + | 0.642788i | −0.766044 | + | 0.642788i | ||||
\(733\) | −1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | −0.500000 | + | 0.866025i | \(0.666667\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.766044 | − | 0.642788i | −0.766044 | − | 0.642788i | 0.173648 | − | 0.984808i | \(-0.444444\pi\) |
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.766044 | + | 0.642788i | −0.766044 | + | 0.642788i | −0.939693 | − | 0.342020i | \(-0.888889\pi\) |
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.173648 | − | 0.984808i | −0.173648 | − | 0.984808i | ||||
\(757\) | 0.939693 | − | 0.342020i | 0.939693 | − | 0.342020i | 0.173648 | − | 0.984808i | \(-0.444444\pi\) |
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.87939 | − | 0.684040i | 1.87939 | − | 0.684040i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(769\) | −0.766044 | + | 0.642788i | −0.766044 | + | 0.642788i | −0.939693 | − | 0.342020i | \(-0.888889\pi\) |
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(773\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.173648 | − | 0.984808i | −0.173648 | − | 0.984808i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.766044 | + | 0.642788i | 0.766044 | + | 0.642788i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.173648 | − | 0.984808i | 0.173648 | − | 0.984808i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.766044 | − | 0.642788i | −0.766044 | − | 0.642788i | ||||
\(797\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 |