Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1932,1,Mod(275,1932)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1932, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 2, 3]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1932.275");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1932 = 2^{2} \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1932.w (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: | \(0.964193604407\) |
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: | \(D_{3}\) |
Projective field: | Galois closure of 3.1.13524.1 |
Artin image: | $C_3\times S_3$ |
Artin field: | Galois closure of 6.0.1030204224.1 |
Embedding invariants
Embedding label | 275.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1932.275 |
Dual form | 1932.1.w.b.1103.1 |
$q$-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 \(\left(\mathbb{Z}/1932\mathbb{Z}\right)^\times\).
\(n\) | \(829\) | \(925\) | \(967\) | \(1289\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(3\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(5\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(6\) | 1.00000 | 1.00000 | ||||||||
\(7\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(8\) | 1.00000 | 1.00000 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(10\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(11\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(12\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(13\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(14\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(15\) | −1.00000 | −1.00000 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(17\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(18\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(19\) | −1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | −0.500000 | + | 0.866025i | \(0.666667\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(20\) | −1.00000 | −1.00000 | ||||||||
\(21\) | 1.00000 | 1.00000 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(24\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(27\) | 1.00000 | 1.00000 | ||||||||
\(28\) | 1.00000 | 1.00000 | ||||||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(31\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.00000 | −1.00000 | ||||||||
\(35\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(36\) | 1.00000 | 1.00000 | ||||||||
\(37\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(38\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | ||||
\(39\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(40\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(41\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(42\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(43\) | 2.00000 | 2.00000 | 1.00000 | \(0\) | ||||||
1.00000 | \(0\) | |||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(46\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(47\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(48\) | 1.00000 | 1.00000 | ||||||||
\(49\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(52\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(53\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(54\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(57\) | 2.00000 | 2.00000 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
−0.500000 | − | 0.866025i | \(-0.666667\pi\) | |||||||
\(60\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(61\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(64\) | 1.00000 | 1.00000 | ||||||||
\(65\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(68\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(69\) | 1.00000 | 1.00000 | ||||||||
\(70\) | −1.00000 | −1.00000 | ||||||||
\(71\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(72\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(73\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.00000 | 2.00000 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1.00000 | −1.00000 | ||||||||
\(79\) | −1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | −0.500000 | + | 0.866025i | \(0.666667\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(80\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(84\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(85\) | 1.00000 | 1.00000 | ||||||||
\(86\) | −1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | −0.500000 | + | 0.866025i | \(0.666667\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(90\) | −1.00000 | −1.00000 | ||||||||
\(91\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(92\) | 1.00000 | 1.00000 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(95\) | 1.00000 | + | 1.73205i | 1.00000 | + | 1.73205i | ||||
\(96\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(97\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(98\) | 1.00000 | 1.00000 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(102\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(103\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(104\) | −1.00000 | −1.00000 | ||||||||
\(105\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(106\) | −1.00000 | −1.00000 | ||||||||
\(107\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(108\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(109\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(110\) | 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 | + | 1.73205i | −1.00000 | + | 1.73205i | ||||
\(115\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(118\) | 2.00000 | 2.00000 | ||||||||
\(119\) | −1.00000 | −1.00000 | ||||||||
\(120\) | −1.00000 | −1.00000 | ||||||||
\(121\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 1.00000 | ||||||||
\(126\) | 1.00000 | 1.00000 | ||||||||
\(127\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(128\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(129\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | ||||
\(130\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(131\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | ||||
\(134\) | −1.00000 | −1.00000 | ||||||||
\(135\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(136\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(137\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(138\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(139\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(140\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(141\) | −1.00000 | −1.00000 | ||||||||
\(142\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.00000 | −1.00000 | ||||||||
\(147\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(152\) | −1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | ||||
\(153\) | −1.00000 | −1.00000 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(157\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(158\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | ||||
\(159\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(160\) | −1.00000 | −1.00000 | ||||||||
\(161\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(162\) | 1.00000 | 1.00000 | ||||||||
\(163\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(168\) | 1.00000 | 1.00000 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(171\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | ||||
\(172\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | ||||
\(173\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | ||||
\(178\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | ||||
\(179\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(180\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(181\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(182\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −1.00000 | −1.00000 | ||||||||
\(189\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(190\) | −2.00000 | −2.00000 | ||||||||
\(191\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(192\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(193\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.00000 | 1.00000 | ||||||||
\(196\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(197\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
−0.500000 | − | 0.866025i | \(-0.666667\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −1.00000 | −1.00000 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(207\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(208\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(211\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(212\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(213\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.00000 | − | 1.73205i | 1.00000 | − | 1.73205i | ||||
\(216\) | 1.00000 | 1.00000 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(224\) | 1.00000 | 1.00000 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(227\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(228\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | ||||
\(229\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(230\) | −1.00000 | −1.00000 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(234\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(235\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(236\) | −1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | ||||
\(237\) | 2.00000 | 2.00000 | ||||||||
\(238\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(239\) | 2.00000 | 2.00000 | 1.00000 | \(0\) | ||||||
1.00000 | \(0\) | |||||||||
\(240\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(241\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(242\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(243\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.00000 | −1.00000 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.00000 | − | 1.73205i | 1.00000 | − | 1.73205i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(251\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(252\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(257\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(258\) | 2.00000 | 2.00000 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.00000 | 1.00000 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(263\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.00000 | 1.00000 | ||||||||
\(266\) | 2.00000 | 2.00000 | ||||||||
\(267\) | 2.00000 | 2.00000 | ||||||||
\(268\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(269\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(270\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(271\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(272\) | −1.00000 | −1.00000 | ||||||||
\(273\) | −1.00000 | −1.00000 | ||||||||
\(274\) | −1.00000 | −1.00000 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(277\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(281\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(282\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(283\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(284\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(285\) | 1.00000 | − | 1.73205i | 1.00000 | − | 1.73205i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000 | 1.00000 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(293\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(294\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(295\) | −2.00000 | −2.00000 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(299\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(307\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.00000 | −1.00000 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(312\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(313\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.00000 | −1.00000 | ||||||||
\(316\) | 2.00000 | 2.00000 | ||||||||
\(317\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(318\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.00000 | 1.00000 | ||||||||
\(323\) | −2.00000 | −2.00000 | ||||||||
\(324\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(335\) | 1.00000 | 1.00000 | ||||||||
\(336\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(337\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(340\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 2.00000 | 2.00000 | ||||||||
\(343\) | 1.00000 | 1.00000 | ||||||||
\(344\) | 2.00000 | 2.00000 | ||||||||
\(345\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −1.00000 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(354\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | ||||
\(355\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(356\) | 2.00000 | 2.00000 | ||||||||
\(357\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(358\) | −1.00000 | −1.00000 | ||||||||
\(359\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(360\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(361\) | −1.50000 | − | 2.59808i | −1.50000 | − | 2.59808i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.00000 | 1.00000 | ||||||||
\(364\) | −1.00000 | −1.00000 | ||||||||
\(365\) | 1.00000 | 1.00000 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(368\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.00000 | −1.00000 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(376\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(379\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(380\) | 1.00000 | − | 1.73205i | 1.00000 | − | 1.73205i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(384\) | 1.00000 | 1.00000 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.00000 | −1.00000 | ||||||||
\(387\) | −1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
−0.500000 | − | 0.866025i | \(-0.666667\pi\) | |||||||
\(390\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(391\) | −1.00000 | −1.00000 | ||||||||
\(392\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(393\) | −1.00000 | −1.00000 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.00000 | + | 1.73205i | 1.00000 | + | 1.73205i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(398\) | 2.00000 | 2.00000 | ||||||||
\(399\) | −1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(402\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −1.00000 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(409\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(412\) | −1.00000 | −1.00000 | ||||||||
\(413\) | 2.00000 | 2.00000 | ||||||||
\(414\) | 1.00000 | 1.00000 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(420\) | −1.00000 | −1.00000 | ||||||||
\(421\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(424\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.00000 | −1.00000 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.00000 | + | 1.73205i | 1.00000 | + | 1.73205i | ||||
\(431\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(432\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(433\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | ||||
\(438\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(439\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 1.00000 | ||||||||
\(442\) | 1.00000 | 1.00000 | ||||||||
\(443\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.00000 | + | 1.73205i | 1.00000 | + | 1.73205i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.00000 | −1.00000 | ||||||||
\(448\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(449\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(456\) | 2.00000 | 2.00000 | ||||||||
\(457\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(460\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(461\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(468\) | −1.00000 | −1.00000 | ||||||||
\(469\) | −1.00000 | −1.00000 | ||||||||
\(470\) | 1.00000 | 1.00000 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(477\) | −1.00000 | −1.00000 | ||||||||
\(478\) | −1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | ||||
\(479\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(480\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(484\) | 1.00000 | 1.00000 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(487\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(491\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 1.00000 | + | 1.73205i | 1.00000 | + | 1.73205i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(500\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(501\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(504\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(510\) | 1.00000 | 1.00000 | ||||||||
\(511\) | −1.00000 | −1.00000 | ||||||||
\(512\) | 1.00000 | 1.00000 | ||||||||
\(513\) | −1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(516\) | −1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(521\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(524\) | −1.00000 | −1.00000 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(530\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(531\) | 2.00000 | 2.00000 | ||||||||
\(532\) | −1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(537\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.00000 | −1.00000 | ||||||||
\(541\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(547\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(548\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 1.00000 | 1.00000 | ||||||||
\(553\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | ||||
\(554\) | −1.00000 | −1.00000 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
−0.500000 | − | 0.866025i | \(-0.666667\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.00000 | −2.00000 | ||||||||
\(560\) | −1.00000 | −1.00000 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(563\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(564\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(565\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(566\) | −1.00000 | −1.00000 | ||||||||
\(567\) | 1.00000 | 1.00000 | ||||||||
\(568\) | −1.00000 | −1.00000 | ||||||||
\(569\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(570\) | 1.00000 | + | 1.73205i | 1.00000 | + | 1.73205i | ||||
\(571\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(577\) | −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 | ||||||||
\(579\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(585\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(586\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(587\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(588\) | 1.00000 | 1.00000 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 1.00000 | − | 1.73205i | 1.00000 | − | 1.73205i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(596\) | −1.00000 | −1.00000 | ||||||||
\(597\) | −1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | ||||
\(598\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(599\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.00000 | 2.00000 | 1.00000 | \(0\) | ||||||
1.00000 | \(0\) | |||||||||
\(602\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | ||||
\(603\) | −1.00000 | −1.00000 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(608\) | 2.00000 | 2.00000 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(612\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(613\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(618\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(619\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(622\) | −1.00000 | −1.00000 | ||||||||
\(623\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | ||||
\(624\) | −1.00000 | −1.00000 | ||||||||
\(625\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(631\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(632\) | −1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.00000 | −1.00000 | ||||||||
\(637\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(640\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(641\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.00000 | 2.00000 | 1.00000 | \(0\) | ||||||
1.00000 | \(0\) | |||||||||
\(644\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(645\) | −2.00000 | −2.00000 | ||||||||
\(646\) | 1.00000 | − | 1.73205i | 1.00000 | − | 1.73205i | ||||
\(647\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
−0.500000 | − | 0.866025i | \(-0.666667\pi\) | |||||||
\(648\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.00000 | −1.00000 | ||||||||
\(658\) | −1.00000 | −1.00000 | ||||||||
\(659\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.00000 | −2.00000 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(673\) | 2.00000 | 2.00000 | 1.00000 | \(0\) | ||||||
1.00000 | \(0\) | |||||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(678\) | −1.00000 | −1.00000 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1.00000 | 1.00000 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(684\) | −1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | ||||
\(685\) | 1.00000 | 1.00000 | ||||||||
\(686\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | ||||
\(689\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(690\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(691\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.00000 | −1.00000 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(702\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 2.00000 | 2.00000 | ||||||||
\(709\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(710\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(711\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | ||||
\(712\) | −1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | −1.00000 | −1.00000 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(717\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(720\) | −1.00000 | −1.00000 | ||||||||
\(721\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(722\) | 3.00000 | 3.00000 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(727\) | 2.00000 | 2.00000 | 1.00000 | \(0\) | ||||||
1.00000 | \(0\) | |||||||||
\(728\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(729\) | 1.00000 | 1.00000 | ||||||||
\(730\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(731\) | 1.00000 | + | 1.73205i | 1.00000 | + | 1.73205i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(734\) | −1.00000 | −1.00000 | ||||||||
\(735\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(736\) | 1.00000 | 1.00000 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.00000 | −2.00000 | ||||||||
\(742\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(743\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 1.00000 | 1.00000 | ||||||||
\(751\) | −1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | −0.500000 | + | 0.866025i | \(0.666667\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(752\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.00000 | 1.00000 | ||||||||
\(757\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(758\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.00000 | + | 1.73205i | 1.00000 | + | 1.73205i | ||||
\(761\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.00000 | + | 1.73205i | 1.00000 | + | 1.73205i | ||||
\(768\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(769\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(773\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(774\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.00000 | 2.00000 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000 | 1.00000 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(787\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2.00000 | −2.00000 | ||||||||
\(791\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(795\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(796\) | −1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | ||||
\(797\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(798\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | ||||
\(799\) | 1.00000 | 1.00000 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | ||||
\(802\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −1.00000 | −1.00000 | ||||||||
\(805\) | −1.00000 | −1.00000 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(810\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(811\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(817\) | −2.00000 | + | 3.46410i | −2.00000 | + | 3.46410i | ||||
\(818\) | −1.00000 | −1.00000 | ||||||||
\(819\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(822\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(823\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(824\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | ||||
\(827\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(828\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(829\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(832\) | −1.00000 | −1.00000 | ||||||||
\(833\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(840\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(841\) | 1.00000 | 1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.00000 | −1.00000 | ||||||||
\(847\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(848\) | −1.00000 | −1.00000 | ||||||||
\(849\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(853\) | 2.00000 | 2.00000 | 1.00000 | \(0\) | ||||||
1.00000 | \(0\) | |||||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.00000 | −2.00000 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(860\) | −2.00000 | −2.00000 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(864\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.00000 | 2.00000 | ||||||||
\(875\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(876\) | −1.00000 | −1.00000 | ||||||||
\(877\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(882\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(883\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(884\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(885\) | 1.00000 | + | 1.73205i | 1.00000 | + | 1.73205i | ||||
\(886\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(887\) | −1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | −0.500000 | + | 0.866025i | \(0.666667\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −2.00000 | −2.00000 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.00000 | + | 1.73205i | 1.00000 | + | 1.73205i | ||||
\(894\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(895\) | 1.00000 | 1.00000 | ||||||||
\(896\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(897\) | −1.00000 | −1.00000 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.00000 | 2.00000 | ||||||||
\(904\) | −1.00000 | −1.00000 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.00000 | 1.00000 | ||||||||
\(911\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(912\) | −1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(918\) | −1.00000 | −1.00000 | ||||||||
\(919\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(920\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.00000 | 1.00000 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.00000 | 2.00000 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(937\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(938\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(941\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
−0.500000 | − | 0.866025i | \(-0.666667\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 2.00000 | 2.00000 | ||||||||
\(945\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(948\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | ||||
\(949\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.00000 | −1.00000 | ||||||||
\(953\) | 2.00000 | 2.00000 | 1.00000 | \(0\) | ||||||
1.00000 | \(0\) | |||||||||
\(954\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.00000 | −1.00000 | ||||||||
\(960\) | −1.00000 | −1.00000 | ||||||||
\(961\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.00000 | 1.00000 | ||||||||
\(966\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(967\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(968\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(969\) | 1.00000 | + | 1.73205i | 1.00000 | + | 1.73205i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(972\) | 1.00000 | 1.00000 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(983\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(988\) | −2.00000 | −2.00000 | ||||||||
\(989\) | −1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(995\) | −2.00000 | −2.00000 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
−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 | 1932.1.w.b.275.1 | yes | 2 | |
3.2 | odd | 2 | 1932.1.w.c.275.1 | yes | 2 | ||
4.3 | odd | 2 | 1932.1.w.d.275.1 | yes | 2 | ||
7.4 | even | 3 | inner | 1932.1.w.b.1103.1 | yes | 2 | |
12.11 | even | 2 | 1932.1.w.a.275.1 | ✓ | 2 | ||
21.11 | odd | 6 | 1932.1.w.c.1103.1 | yes | 2 | ||
23.22 | odd | 2 | 1932.1.w.a.275.1 | ✓ | 2 | ||
28.11 | odd | 6 | 1932.1.w.d.1103.1 | yes | 2 | ||
69.68 | even | 2 | 1932.1.w.d.275.1 | yes | 2 | ||
84.11 | even | 6 | 1932.1.w.a.1103.1 | yes | 2 | ||
92.91 | even | 2 | 1932.1.w.c.275.1 | yes | 2 | ||
161.137 | odd | 6 | 1932.1.w.a.1103.1 | yes | 2 | ||
276.275 | odd | 2 | CM | 1932.1.w.b.275.1 | yes | 2 | |
483.137 | even | 6 | 1932.1.w.d.1103.1 | yes | 2 | ||
644.459 | even | 6 | 1932.1.w.c.1103.1 | yes | 2 | ||
1932.1103 | odd | 6 | inner | 1932.1.w.b.1103.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1932.1.w.a.275.1 | ✓ | 2 | 12.11 | even | 2 | ||
1932.1.w.a.275.1 | ✓ | 2 | 23.22 | odd | 2 | ||
1932.1.w.a.1103.1 | yes | 2 | 84.11 | even | 6 | ||
1932.1.w.a.1103.1 | yes | 2 | 161.137 | odd | 6 | ||
1932.1.w.b.275.1 | yes | 2 | 1.1 | even | 1 | trivial | |
1932.1.w.b.275.1 | yes | 2 | 276.275 | odd | 2 | CM | |
1932.1.w.b.1103.1 | yes | 2 | 7.4 | even | 3 | inner | |
1932.1.w.b.1103.1 | yes | 2 | 1932.1103 | odd | 6 | inner | |
1932.1.w.c.275.1 | yes | 2 | 3.2 | odd | 2 | ||
1932.1.w.c.275.1 | yes | 2 | 92.91 | even | 2 | ||
1932.1.w.c.1103.1 | yes | 2 | 21.11 | odd | 6 | ||
1932.1.w.c.1103.1 | yes | 2 | 644.459 | even | 6 | ||
1932.1.w.d.275.1 | yes | 2 | 4.3 | odd | 2 | ||
1932.1.w.d.275.1 | yes | 2 | 69.68 | even | 2 | ||
1932.1.w.d.1103.1 | yes | 2 | 28.11 | odd | 6 | ||
1932.1.w.d.1103.1 | yes | 2 | 483.137 | even | 6 |