Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3192,1,Mod(293,3192)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3192, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 3, 3, 1]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3192.293");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3192 = 2^{3} \cdot 3 \cdot 7 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3192.fm (of order \(6\), degree \(2\), 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: | \(1.59301552032\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{6}\) |
Projective field: | Galois closure of 6.2.209656254528.1 |
Embedding invariants
Embedding label | 293.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3192.293 |
Dual form | 3192.1.fm.d.1133.1 |
$q$-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 \(\left(\mathbb{Z}/3192\mathbb{Z}\right)^\times\).
\(n\) | \(799\) | \(913\) | \(1009\) | \(1597\) | \(2129\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(3\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(5\) | −1.50000 | − | 0.866025i | −1.50000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(6\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(7\) | −1.00000 | −1.00000 | ||||||||
\(8\) | −1.00000 | −1.00000 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(10\) | −1.50000 | + | 0.866025i | −1.50000 | + | 0.866025i | ||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | −1.00000 | −1.00000 | ||||||||
\(13\) | 1.50000 | − | 0.866025i | 1.50000 | − | 0.866025i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
1.00000 | \(0\) | |||||||||
\(14\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(15\) | −1.50000 | + | 0.866025i | −1.50000 | + | 0.866025i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(17\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(18\) | −1.00000 | −1.00000 | ||||||||
\(19\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(20\) | 1.73205i | 1.73205i | ||||||||
\(21\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.50000 | + | 0.866025i | −1.50000 | + | 0.866025i | −0.500000 | + | 0.866025i | \(0.666667\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(24\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(25\) | 1.00000 | + | 1.73205i | 1.00000 | + | 1.73205i | ||||
\(26\) | − | 1.73205i | − | 1.73205i | ||||||
\(27\) | −1.00000 | −1.00000 | ||||||||
\(28\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(29\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(30\) | 1.73205i | 1.73205i | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.50000 | + | 0.866025i | 1.50000 | + | 0.866025i | ||||
\(36\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(37\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(38\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(39\) | − | 1.73205i | − | 1.73205i | ||||||
\(40\) | 1.50000 | + | 0.866025i | 1.50000 | + | 0.866025i | ||||
\(41\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(42\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(43\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.73205i | 1.73205i | ||||||||
\(46\) | 1.73205i | 1.73205i | ||||||||
\(47\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(48\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(49\) | 1.00000 | 1.00000 | ||||||||
\(50\) | 2.00000 | 2.00000 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.50000 | − | 0.866025i | −1.50000 | − | 0.866025i | ||||
\(53\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(54\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.00000 | 1.00000 | ||||||||
\(57\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(60\) | 1.50000 | + | 0.866025i | 1.50000 | + | 0.866025i | ||||
\(61\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(64\) | 1.00000 | 1.00000 | ||||||||
\(65\) | −3.00000 | −3.00000 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.73205i | 1.73205i | ||||||||
\(70\) | 1.50000 | − | 0.866025i | 1.50000 | − | 0.866025i | ||||
\(71\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(72\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(73\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.00000 | 2.00000 | ||||||||
\(76\) | −1.00000 | −1.00000 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1.50000 | − | 0.866025i | −1.50000 | − | 0.866025i | ||||
\(79\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(80\) | 1.50000 | − | 0.866025i | 1.50000 | − | 0.866025i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.73205i | 1.73205i | 0.500000 | + | 0.866025i | \(0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(84\) | 1.00000 | 1.00000 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(90\) | 1.50000 | + | 0.866025i | 1.50000 | + | 0.866025i | ||||
\(91\) | −1.50000 | + | 0.866025i | −1.50000 | + | 0.866025i | ||||
\(92\) | 1.50000 | + | 0.866025i | 1.50000 | + | 0.866025i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.50000 | + | 0.866025i | −1.50000 | + | 0.866025i | ||||
\(96\) | 1.00000 | 1.00000 | ||||||||
\(97\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(98\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | − | 1.73205i | 1.00000 | − | 1.73205i | ||||
\(101\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(104\) | −1.50000 | + | 0.866025i | −1.50000 | + | 0.866025i | ||||
\(105\) | 1.50000 | − | 0.866025i | 1.50000 | − | 0.866025i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(108\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(109\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(113\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(114\) | −1.00000 | −1.00000 | ||||||||
\(115\) | 3.00000 | 3.00000 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.50000 | − | 0.866025i | −1.50000 | − | 0.866025i | ||||
\(118\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.50000 | − | 0.866025i | 1.50000 | − | 0.866025i | ||||
\(121\) | −1.00000 | −1.00000 | ||||||||
\(122\) | −1.00000 | −1.00000 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 1.73205i | − | 1.73205i | ||||||
\(126\) | 1.00000 | 1.00000 | ||||||||
\(127\) | −1.50000 | + | 0.866025i | −1.50000 | + | 0.866025i | −0.500000 | + | 0.866025i | \(0.666667\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(128\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.50000 | + | 2.59808i | −1.50000 | + | 2.59808i | ||||
\(131\) | −1.50000 | − | 0.866025i | −1.50000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.50000 | + | 0.866025i | 1.50000 | + | 0.866025i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.50000 | − | 0.866025i | 1.50000 | − | 0.866025i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
1.00000 | \(0\) | |||||||||
\(138\) | 1.50000 | + | 0.866025i | 1.50000 | + | 0.866025i | ||||
\(139\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
−0.500000 | − | 0.866025i | \(-0.666667\pi\) | |||||||
\(140\) | − | 1.73205i | − | 1.73205i | ||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 1.00000 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(150\) | 1.00000 | − | 1.73205i | 1.00000 | − | 1.73205i | ||||
\(151\) | 1.73205i | 1.73205i | 0.500000 | + | 0.866025i | \(0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(152\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.50000 | + | 0.866025i | −1.50000 | + | 0.866025i | ||||
\(157\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 1.73205i | − | 1.73205i | ||||||
\(161\) | 1.50000 | − | 0.866025i | 1.50000 | − | 0.866025i | ||||
\(162\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(163\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.50000 | + | 0.866025i | 1.50000 | + | 0.866025i | ||||
\(167\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(168\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(169\) | 1.00000 | − | 1.73205i | 1.00000 | − | 1.73205i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.00000 | −1.00000 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(180\) | 1.50000 | − | 0.866025i | 1.50000 | − | 0.866025i | ||||
\(181\) | −1.50000 | + | 0.866025i | −1.50000 | + | 0.866025i | −0.500000 | + | 0.866025i | \(0.666667\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(182\) | 1.73205i | 1.73205i | ||||||||
\(183\) | −1.00000 | −1.00000 | ||||||||
\(184\) | 1.50000 | − | 0.866025i | 1.50000 | − | 0.866025i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.00000 | 1.00000 | ||||||||
\(190\) | 1.73205i | 1.73205i | ||||||||
\(191\) | − | 1.73205i | − | 1.73205i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||
0.500000 | − | 0.866025i | \(-0.333333\pi\) | |||||||
\(192\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(193\) | −1.50000 | − | 0.866025i | −1.50000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.50000 | + | 2.59808i | −1.50000 | + | 2.59808i | ||||
\(196\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(197\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(200\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.50000 | + | 0.866025i | 1.50000 | + | 0.866025i | ||||
\(208\) | 1.73205i | 1.73205i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | − | 1.73205i | − | 1.73205i | ||||||
\(211\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000 | 1.00000 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(224\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(225\) | 1.00000 | − | 1.73205i | 1.00000 | − | 1.73205i | ||||
\(226\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(227\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(228\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(229\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(230\) | 1.50000 | − | 2.59808i | 1.50000 | − | 2.59808i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.50000 | + | 0.866025i | 1.50000 | + | 0.866025i | 1.00000 | \(0\) | ||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(234\) | −1.50000 | + | 0.866025i | −1.50000 | + | 0.866025i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.00000 | −1.00000 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 1.73205i | − | 1.73205i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||
0.500000 | − | 0.866025i | \(-0.333333\pi\) | |||||||
\(240\) | − | 1.73205i | − | 1.73205i | ||||||
\(241\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(242\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(243\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(244\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(245\) | −1.50000 | − | 0.866025i | −1.50000 | − | 0.866025i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 1.73205i | − | 1.73205i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.50000 | + | 0.866025i | 1.50000 | + | 0.866025i | ||||
\(250\) | −1.50000 | − | 0.866025i | −1.50000 | − | 0.866025i | ||||
\(251\) | −1.50000 | + | 0.866025i | −1.50000 | + | 0.866025i | −0.500000 | + | 0.866025i | \(0.666667\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(252\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 1.73205i | 1.73205i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(257\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.50000 | + | 2.59808i | 1.50000 | + | 2.59808i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.50000 | + | 0.866025i | −1.50000 | + | 0.866025i | ||||
\(263\) | 1.50000 | + | 0.866025i | 1.50000 | + | 0.866025i | 1.00000 | \(0\) | ||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.00000 | − | 1.73205i | 1.00000 | − | 1.73205i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
0.500000 | − | 0.866025i | \(-0.333333\pi\) | |||||||
\(270\) | 1.50000 | − | 0.866025i | 1.50000 | − | 0.866025i | ||||
\(271\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.73205i | 1.73205i | ||||||||
\(274\) | − | 1.73205i | − | 1.73205i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.50000 | − | 0.866025i | 1.50000 | − | 0.866025i | ||||
\(277\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(278\) | −2.00000 | −2.00000 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.50000 | − | 0.866025i | −1.50000 | − | 0.866025i | ||||
\(281\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
−0.500000 | − | 0.866025i | \(-0.666667\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(284\) | −1.00000 | −1.00000 | ||||||||
\(285\) | 1.73205i | 1.73205i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(289\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.00000 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(294\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(295\) | −1.50000 | + | 0.866025i | −1.50000 | + | 0.866025i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.50000 | + | 2.59808i | −1.50000 | + | 2.59808i | ||||
\(300\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1.50000 | + | 0.866025i | 1.50000 | + | 0.866025i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(305\) | 1.73205i | 1.73205i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.50000 | + | 0.866025i | 1.50000 | + | 0.866025i | 1.00000 | \(0\) | ||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(312\) | 1.73205i | 1.73205i | ||||||||
\(313\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(314\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(315\) | − | 1.73205i | − | 1.73205i | ||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.50000 | − | 0.866025i | −1.50000 | − | 0.866025i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − | 1.73205i | − | 1.73205i | ||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 1.00000 | 1.00000 | ||||||||
\(325\) | 3.00000 | + | 1.73205i | 3.00000 | + | 1.73205i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(332\) | 1.50000 | − | 0.866025i | 1.50000 | − | 0.866025i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(337\) | 1.50000 | + | 0.866025i | 1.50000 | + | 0.866025i | 1.00000 | \(0\) | ||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(338\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | ||||
\(339\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(343\) | −1.00000 | −1.00000 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.50000 | − | 2.59808i | 1.50000 | − | 2.59808i | ||||
\(346\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(347\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.00000 | 2.00000 | 1.00000 | \(0\) | ||||||
1.00000 | \(0\) | |||||||||
\(350\) | −2.00000 | −2.00000 | ||||||||
\(351\) | −1.50000 | + | 0.866025i | −1.50000 | + | 0.866025i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(354\) | −1.00000 | −1.00000 | ||||||||
\(355\) | −1.50000 | + | 0.866025i | −1.50000 | + | 0.866025i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(360\) | − | 1.73205i | − | 1.73205i | ||||||
\(361\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(362\) | 1.73205i | 1.73205i | ||||||||
\(363\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(364\) | 1.50000 | + | 0.866025i | 1.50000 | + | 0.866025i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(367\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(368\) | − | 1.73205i | − | 1.73205i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.50000 | − | 0.866025i | −1.50000 | − | 0.866025i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(379\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(380\) | 1.50000 | + | 0.866025i | 1.50000 | + | 0.866025i | ||||
\(381\) | 1.73205i | 1.73205i | ||||||||
\(382\) | −1.50000 | − | 0.866025i | −1.50000 | − | 0.866025i | ||||
\(383\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(384\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.50000 | + | 0.866025i | −1.50000 | + | 0.866025i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(390\) | 1.50000 | + | 2.59808i | 1.50000 | + | 2.59808i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −1.00000 | −1.00000 | ||||||||
\(393\) | −1.50000 | + | 0.866025i | −1.50000 | + | 0.866025i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.00000 | − | 1.73205i | 1.00000 | − | 1.73205i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
0.500000 | − | 0.866025i | \(-0.333333\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(400\) | −2.00000 | −2.00000 | ||||||||
\(401\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.50000 | − | 0.866025i | 1.50000 | − | 0.866025i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 1.73205i | − | 1.73205i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(414\) | 1.50000 | − | 0.866025i | 1.50000 | − | 0.866025i | ||||
\(415\) | 1.50000 | − | 2.59808i | 1.50000 | − | 2.59808i | ||||
\(416\) | 1.50000 | + | 0.866025i | 1.50000 | + | 0.866025i | ||||
\(417\) | −2.00000 | −2.00000 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(420\) | −1.50000 | − | 0.866025i | −1.50000 | − | 0.866025i | ||||
\(421\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.00000 | −1.00000 | ||||||||
\(427\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.00000 | + | 1.73205i | 1.00000 | + | 1.73205i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(432\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(433\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.73205i | 1.73205i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.00000 | −1.00000 | ||||||||
\(449\) | 1.00000 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(450\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(453\) | 1.50000 | + | 0.866025i | 1.50000 | + | 0.866025i | ||||
\(454\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(455\) | 3.00000 | 3.00000 | ||||||||
\(456\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(457\) | 1.00000 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(458\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.50000 | − | 2.59808i | −1.50000 | − | 2.59808i | ||||
\(461\) | 1.50000 | + | 0.866025i | 1.50000 | + | 0.866025i | 1.00000 | \(0\) | ||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.00000 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.50000 | − | 0.866025i | 1.50000 | − | 0.866025i | ||||
\(467\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(468\) | 1.73205i | 1.73205i | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(472\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.00000 | 2.00000 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.50000 | − | 0.866025i | −1.50000 | − | 0.866025i | ||||
\(479\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(480\) | −1.50000 | − | 0.866025i | −1.50000 | − | 0.866025i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 1.73205i | − | 1.73205i | ||||||
\(484\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000 | 1.00000 | ||||||||
\(487\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(488\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.50000 | + | 0.866025i | −1.50000 | + | 0.866025i | ||||
\(491\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −1.50000 | − | 0.866025i | −1.50000 | − | 0.866025i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(498\) | 1.50000 | − | 0.866025i | 1.50000 | − | 0.866025i | ||||
\(499\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(500\) | −1.50000 | + | 0.866025i | −1.50000 | + | 0.866025i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.73205i | 1.73205i | ||||||||
\(503\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(504\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | ||||
\(508\) | 1.50000 | + | 0.866025i | 1.50000 | + | 0.866025i | ||||
\(509\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −1.00000 | ||||||||
\(513\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(520\) | 3.00000 | 3.00000 | ||||||||
\(521\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(524\) | 1.73205i | 1.73205i | ||||||||
\(525\) | −2.00000 | −2.00000 | ||||||||
\(526\) | 1.50000 | − | 0.866025i | 1.50000 | − | 0.866025i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | − | 1.73205i | 1.00000 | − | 1.73205i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.00000 | −1.00000 | ||||||||
\(532\) | 1.00000 | 1.00000 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | − | 1.73205i | − | 1.73205i | ||||||
\(541\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.73205i | 1.73205i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.50000 | + | 0.866025i | 1.50000 | + | 0.866025i | ||||
\(547\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(548\) | −1.50000 | − | 0.866025i | −1.50000 | − | 0.866025i | ||||
\(549\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | − | 1.73205i | − | 1.73205i | ||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | ||||
\(557\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −1.50000 | + | 0.866025i | −1.50000 | + | 0.866025i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.00000 | −2.00000 | ||||||||
\(563\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.50000 | + | 0.866025i | 1.50000 | + | 0.866025i | ||||
\(566\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(567\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(568\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(569\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(570\) | 1.50000 | + | 0.866025i | 1.50000 | + | 0.866025i | ||||
\(571\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.50000 | − | 0.866025i | −1.50000 | − | 0.866025i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.00000 | − | 1.73205i | −3.00000 | − | 1.73205i | ||||
\(576\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(577\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(578\) | 1.00000 | 1.00000 | ||||||||
\(579\) | −1.50000 | + | 0.866025i | −1.50000 | + | 0.866025i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 1.73205i | − | 1.73205i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.50000 | + | 2.59808i | 1.50000 | + | 2.59808i | ||||
\(586\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(587\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(588\) | −1.00000 | −1.00000 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 1.73205i | 1.73205i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.50000 | + | 2.59808i | 1.50000 | + | 2.59808i | ||||
\(599\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(600\) | −2.00000 | −2.00000 | ||||||||
\(601\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.50000 | − | 0.866025i | 1.50000 | − | 0.866025i | ||||
\(605\) | 1.50000 | + | 0.866025i | 1.50000 | + | 0.866025i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(608\) | 1.00000 | 1.00000 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.50000 | + | 0.866025i | 1.50000 | + | 0.866025i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(614\) | 1.50000 | − | 0.866025i | 1.50000 | − | 0.866025i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.50000 | − | 0.866025i | 1.50000 | − | 0.866025i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
1.00000 | \(0\) | |||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.50000 | − | 0.866025i | 1.50000 | − | 0.866025i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1.50000 | + | 0.866025i | 1.50000 | + | 0.866025i | ||||
\(625\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.00000 | −1.00000 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −1.50000 | − | 0.866025i | −1.50000 | − | 0.866025i | ||||
\(631\) | 1.00000 | + | 1.73205i | 1.00000 | + | 1.73205i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.00000 | 3.00000 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.50000 | − | 0.866025i | 1.50000 | − | 0.866025i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.00000 | −1.00000 | ||||||||
\(640\) | −1.50000 | + | 0.866025i | −1.50000 | + | 0.866025i | ||||
\(641\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(644\) | −1.50000 | − | 0.866025i | −1.50000 | − | 0.866025i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(648\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 3.00000 | − | 1.73205i | 3.00000 | − | 1.73205i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.50000 | + | 2.59808i | 1.50000 | + | 2.59808i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.50000 | + | 0.866025i | −1.50000 | + | 0.866025i | −0.500000 | + | 0.866025i | \(0.666667\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 1.73205i | − | 1.73205i | ||||||
\(665\) | 1.50000 | − | 0.866025i | 1.50000 | − | 0.866025i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −1.00000 | −1.00000 | ||||||||
\(673\) | − | 1.73205i | − | 1.73205i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||
0.500000 | − | 0.866025i | \(-0.333333\pi\) | |||||||
\(674\) | 1.50000 | − | 0.866025i | 1.50000 | − | 0.866025i | ||||
\(675\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | ||||
\(676\) | −2.00000 | −2.00000 | ||||||||
\(677\) | 2.00000 | 2.00000 | 1.00000 | \(0\) | ||||||
1.00000 | \(0\) | |||||||||
\(678\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(684\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(685\) | −3.00000 | −3.00000 | ||||||||
\(686\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(687\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −1.50000 | − | 2.59808i | −1.50000 | − | 2.59808i | ||||
\(691\) | 1.00000 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(692\) | −1.00000 | −1.00000 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.46410i | 3.46410i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 1.00000 | − | 1.73205i | 1.00000 | − | 1.73205i | ||||
\(699\) | 1.50000 | − | 0.866025i | 1.50000 | − | 0.866025i | ||||
\(700\) | −1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | ||||
\(701\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(702\) | 1.73205i | 1.73205i | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(709\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(710\) | 1.73205i | 1.73205i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.50000 | − | 0.866025i | −1.50000 | − | 0.866025i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(720\) | −1.50000 | − | 0.866025i | −1.50000 | − | 0.866025i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −1.00000 | −1.00000 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.50000 | + | 0.866025i | 1.50000 | + | 0.866025i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(727\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(728\) | 1.50000 | − | 0.866025i | 1.50000 | − | 0.866025i | ||||
\(729\) | 1.00000 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(733\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.50000 | + | 0.866025i | −1.50000 | + | 0.866025i | ||||
\(736\) | −1.50000 | − | 0.866025i | −1.50000 | − | 0.866025i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.50000 | − | 0.866025i | −1.50000 | − | 0.866025i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.50000 | − | 0.866025i | 1.50000 | − | 0.866025i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1.50000 | + | 0.866025i | −1.50000 | + | 0.866025i | ||||
\(751\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.73205i | 1.73205i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.50000 | − | 2.59808i | 1.50000 | − | 2.59808i | ||||
\(756\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(757\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.50000 | − | 0.866025i | 1.50000 | − | 0.866025i | ||||
\(761\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(762\) | 1.50000 | + | 0.866025i | 1.50000 | + | 0.866025i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −1.50000 | + | 0.866025i | −1.50000 | + | 0.866025i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 1.73205i | − | 1.73205i | ||||||
\(768\) | −1.00000 | −1.00000 | ||||||||
\(769\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.73205i | 1.73205i | ||||||||
\(773\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 3.00000 | 3.00000 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(785\) | −1.50000 | + | 0.866025i | −1.50000 | + | 0.866025i | ||||
\(786\) | 1.73205i | 1.73205i | ||||||||
\(787\) | − | 1.73205i | − | 1.73205i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||
0.500000 | − | 0.866025i | \(-0.333333\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.50000 | − | 0.866025i | 1.50000 | − | 0.866025i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.00000 | 1.00000 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.50000 | − | 0.866025i | −1.50000 | − | 0.866025i | ||||
\(794\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(798\) | 1.00000 | 1.00000 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.00000 | −3.00000 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 1.73205i | − | 1.73205i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||
0.500000 | − | 0.866025i | \(-0.333333\pi\) | |||||||
\(810\) | − | 1.73205i | − | 1.73205i | ||||||
\(811\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.50000 | + | 0.866025i | 1.50000 | + | 0.866025i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(822\) | −1.50000 | − | 0.866025i | −1.50000 | − | 0.866025i | ||||
\(823\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(827\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(828\) | − | 1.73205i | − | 1.73205i | ||||||
\(829\) | − | 1.73205i | − | 1.73205i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||
0.500000 | − | 0.866025i | \(-0.333333\pi\) | |||||||
\(830\) | −1.50000 | − | 2.59808i | −1.50000 | − | 2.59808i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.50000 | − | 0.866025i | 1.50000 | − | 0.866025i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(840\) | −1.50000 | + | 0.866025i | −1.50000 | + | 0.866025i | ||||
\(841\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.00000 | −2.00000 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.00000 | + | 1.73205i | −3.00000 | + | 1.73205i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.00000 | 1.00000 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(853\) | 1.00000 | − | 1.73205i | 1.00000 | − | 1.73205i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
0.500000 | − | 0.866025i | \(-0.333333\pi\) | |||||||
\(854\) | 1.00000 | 1.00000 | ||||||||
\(855\) | 1.50000 | + | 0.866025i | 1.50000 | + | 0.866025i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
−0.500000 | − | 0.866025i | \(-0.666667\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.00000 | 2.00000 | ||||||||
\(863\) | 2.00000 | 2.00000 | 1.00000 | \(0\) | ||||||
1.00000 | \(0\) | |||||||||
\(864\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(865\) | −1.50000 | + | 0.866025i | −1.50000 | + | 0.866025i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.00000 | 1.00000 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.50000 | + | 0.866025i | 1.50000 | + | 0.866025i | ||||
\(875\) | 1.73205i | 1.73205i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(882\) | −1.00000 | −1.00000 | ||||||||
\(883\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.73205i | 1.73205i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.50000 | − | 0.866025i | 1.50000 | − | 0.866025i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(897\) | 1.50000 | + | 2.59808i | 1.50000 | + | 2.59808i | ||||
\(898\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −2.00000 | −2.00000 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.00000 | 1.00000 | ||||||||
\(905\) | 3.00000 | 3.00000 | ||||||||
\(906\) | 1.50000 | − | 0.866025i | 1.50000 | − | 0.866025i | ||||
\(907\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(908\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.50000 | − | 2.59808i | 1.50000 | − | 2.59808i | ||||
\(911\) | 1.00000 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(912\) | 1.00000 | 1.00000 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(915\) | 1.50000 | + | 0.866025i | 1.50000 | + | 0.866025i | ||||
\(916\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(917\) | 1.50000 | + | 0.866025i | 1.50000 | + | 0.866025i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(920\) | −3.00000 | −3.00000 | ||||||||
\(921\) | 1.50000 | − | 0.866025i | 1.50000 | − | 0.866025i | ||||
\(922\) | 1.50000 | − | 0.866025i | 1.50000 | − | 0.866025i | ||||
\(923\) | − | 1.73205i | − | 1.73205i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(932\) | − | 1.73205i | − | 1.73205i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.50000 | + | 0.866025i | 1.50000 | + | 0.866025i | ||||
\(937\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(942\) | −1.00000 | −1.00000 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(945\) | −1.50000 | − | 0.866025i | −1.50000 | − | 0.866025i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 1.00000 | − | 1.73205i | 1.00000 | − | 1.73205i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | −0.500000 | + | 0.866025i | \(0.666667\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.50000 | + | 2.59808i | −1.50000 | + | 2.59808i | ||||
\(956\) | −1.50000 | + | 0.866025i | −1.50000 | + | 0.866025i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.50000 | + | 0.866025i | −1.50000 | + | 0.866025i | ||||
\(960\) | −1.50000 | + | 0.866025i | −1.50000 | + | 0.866025i | ||||
\(961\) | −1.00000 | −1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.50000 | + | 2.59808i | 1.50000 | + | 2.59808i | ||||
\(966\) | −1.50000 | − | 0.866025i | −1.50000 | − | 0.866025i | ||||
\(967\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(968\) | 1.00000 | 1.00000 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(972\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(973\) | 1.00000 | + | 1.73205i | 1.00000 | + | 1.73205i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.00000 | − | 1.73205i | 3.00000 | − | 1.73205i | ||||
\(976\) | 1.00000 | 1.00000 | ||||||||
\(977\) | 1.00000 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 1.73205i | 1.73205i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.50000 | + | 0.866025i | −1.50000 | + | 0.866025i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.50000 | − | 0.866025i | −1.50000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | − | 1.73205i | − | 1.73205i | ||||||
\(997\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 3192.1.fm.d.293.1 | yes | 2 | |
3.2 | odd | 2 | 3192.1.fm.a.293.1 | ✓ | 2 | ||
7.6 | odd | 2 | 3192.1.fm.c.293.1 | yes | 2 | ||
8.5 | even | 2 | 3192.1.fm.c.293.1 | yes | 2 | ||
19.12 | odd | 6 | 3192.1.fm.a.1133.1 | yes | 2 | ||
21.20 | even | 2 | 3192.1.fm.b.293.1 | yes | 2 | ||
24.5 | odd | 2 | 3192.1.fm.b.293.1 | yes | 2 | ||
56.13 | odd | 2 | CM | 3192.1.fm.d.293.1 | yes | 2 | |
57.50 | even | 6 | inner | 3192.1.fm.d.1133.1 | yes | 2 | |
133.69 | even | 6 | 3192.1.fm.b.1133.1 | yes | 2 | ||
152.69 | odd | 6 | 3192.1.fm.b.1133.1 | yes | 2 | ||
168.125 | even | 2 | 3192.1.fm.a.293.1 | ✓ | 2 | ||
399.335 | odd | 6 | 3192.1.fm.c.1133.1 | yes | 2 | ||
456.221 | even | 6 | 3192.1.fm.c.1133.1 | yes | 2 | ||
1064.69 | even | 6 | 3192.1.fm.a.1133.1 | yes | 2 | ||
3192.1133 | odd | 6 | inner | 3192.1.fm.d.1133.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3192.1.fm.a.293.1 | ✓ | 2 | 3.2 | odd | 2 | ||
3192.1.fm.a.293.1 | ✓ | 2 | 168.125 | even | 2 | ||
3192.1.fm.a.1133.1 | yes | 2 | 19.12 | odd | 6 | ||
3192.1.fm.a.1133.1 | yes | 2 | 1064.69 | even | 6 | ||
3192.1.fm.b.293.1 | yes | 2 | 21.20 | even | 2 | ||
3192.1.fm.b.293.1 | yes | 2 | 24.5 | odd | 2 | ||
3192.1.fm.b.1133.1 | yes | 2 | 133.69 | even | 6 | ||
3192.1.fm.b.1133.1 | yes | 2 | 152.69 | odd | 6 | ||
3192.1.fm.c.293.1 | yes | 2 | 7.6 | odd | 2 | ||
3192.1.fm.c.293.1 | yes | 2 | 8.5 | even | 2 | ||
3192.1.fm.c.1133.1 | yes | 2 | 399.335 | odd | 6 | ||
3192.1.fm.c.1133.1 | yes | 2 | 456.221 | even | 6 | ||
3192.1.fm.d.293.1 | yes | 2 | 1.1 | even | 1 | trivial | |
3192.1.fm.d.293.1 | yes | 2 | 56.13 | odd | 2 | CM | |
3192.1.fm.d.1133.1 | yes | 2 | 57.50 | even | 6 | inner | |
3192.1.fm.d.1133.1 | yes | 2 | 3192.1133 | odd | 6 | inner |