Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2015,1,Mod(464,2015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2015, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 4, 3]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2015.464");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2015 = 5 \cdot 13 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 2015.bq (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: | \(1.00561600046\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(A_{4}\) |
Projective field: | Galois closure of 4.0.4060225.2 |
Embedding invariants
Embedding label | 464.1 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2015.464 |
Dual form | 2015.1.bq.e.1394.1 |
$q$-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 \(\left(\mathbb{Z}/2015\mathbb{Z}\right)^\times\).
\(n\) | \(716\) | \(807\) | \(1861\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | − | 1.00000i | \(-0.5\pi\) | |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(3\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 1.00000i | − | 1.00000i | ||||||
\(6\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(7\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | − | 1.00000i | \(-0.5\pi\) | |
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(8\) | 1.00000i | 1.00000i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(11\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | − | 1.00000i | \(-0.5\pi\) | |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 1.00000 | ||||||||
\(14\) | −1.00000 | −1.00000 | ||||||||
\(15\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(16\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(17\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 1.00000i | − | 1.00000i | ||||||
\(22\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(23\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(24\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(25\) | −1.00000 | −1.00000 | ||||||||
\(26\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(27\) | 1.00000 | 1.00000 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | − | 1.00000i | \(-0.5\pi\) | |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(30\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(31\) | −1.00000 | −1.00000 | ||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(34\) | 1.00000i | 1.00000i | ||||||||
\(35\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(38\) | − | 1.00000i | − | 1.00000i | ||||||
\(39\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(40\) | 1.00000 | 1.00000 | ||||||||
\(41\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(42\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(43\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(47\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(48\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(51\) | −1.00000 | −1.00000 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(54\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(55\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(56\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(57\) | 1.00000 | 1.00000 | ||||||||
\(58\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(59\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | − | 1.00000i | \(-0.5\pi\) | |
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(62\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −1.00000 | ||||||||
\(65\) | − | 1.00000i | − | 1.00000i | ||||||
\(66\) | 1.00000 | 1.00000 | ||||||||
\(67\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | 0.866025 | − | 0.500000i | \(-0.166667\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(70\) | 1.00000i | 1.00000i | ||||||||
\(71\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(74\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(75\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.00000 | −1.00000 | ||||||||
\(78\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(79\) | 2.00000i | 2.00000i | 1.00000i | \(0.5\pi\) | ||||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(81\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(82\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(83\) | −2.00000 | −2.00000 | −1.00000 | \(\pi\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(86\) | 1.00000i | 1.00000i | ||||||||
\(87\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(88\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(89\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | 0.866025 | − | 0.500000i | \(-0.166667\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(102\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(103\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(104\) | 1.00000i | 1.00000i | ||||||||
\(105\) | −1.00000 | −1.00000 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | 0.866025 | − | 0.500000i | \(-0.166667\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(110\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(111\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(112\) | − | 1.00000i | − | 1.00000i | ||||||
\(113\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | − | 1.00000i | \(-0.5\pi\) | |
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(114\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(115\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 1.00000i | − | 1.00000i | ||||||
\(119\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(120\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −1.00000 | −1.00000 | ||||||||
\(123\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000i | 1.00000i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(128\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(129\) | −1.00000 | −1.00000 | ||||||||
\(130\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(134\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(135\) | − | 1.00000i | − | 1.00000i | ||||||
\(136\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(137\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(138\) | 1.00000i | 1.00000i | ||||||||
\(139\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 1.00000i | − | 1.00000i | ||||||
\(143\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(150\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(151\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(152\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(155\) | 1.00000i | 1.00000i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 2.00000i | − | 2.00000i | − | 1.00000i | \(-0.5\pi\) | |||
− | 1.00000i | \(-0.5\pi\) | ||||||||
\(158\) | 1.00000 | − | 1.73205i | 1.00000 | − | 1.73205i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 1.00000i | − | 1.00000i | ||||||
\(162\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(163\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | − | 1.00000i | \(-0.5\pi\) | |
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(166\) | 1.73205 | + | 1.00000i | 1.73205 | + | 1.00000i | ||||
\(167\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(168\) | 1.00000 | 1.00000 | ||||||||
\(169\) | 1.00000 | 1.00000 | ||||||||
\(170\) | 1.00000 | 1.00000 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | − | 1.00000i | \(-0.5\pi\) | |
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(174\) | 1.00000 | 1.00000 | ||||||||
\(175\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(176\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(177\) | 1.00000 | 1.00000 | ||||||||
\(178\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(179\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | 0.866025 | − | 0.500000i | \(-0.166667\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(182\) | −1.00000 | −1.00000 | ||||||||
\(183\) | − | 1.00000i | − | 1.00000i | ||||||
\(184\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(185\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(186\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(187\) | 1.00000i | 1.00000i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(190\) | −1.00000 | −1.00000 | ||||||||
\(191\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(192\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(193\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | − | 1.00000i | \(-0.5\pi\) | |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(194\) | 1.00000 | 1.00000 | ||||||||
\(195\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(200\) | − | 1.00000i | − | 1.00000i | ||||||
\(201\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(202\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(203\) | −1.00000 | −1.00000 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(209\) | − | 1.00000i | − | 1.00000i | ||||||
\(210\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(211\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.00000 | 1.00000 | ||||||||
\(214\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(215\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(216\) | 1.00000i | 1.00000i | ||||||||
\(217\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(222\) | − | 1.00000i | − | 1.00000i | ||||||
\(223\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.00000 | −1.00000 | ||||||||
\(227\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(230\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(231\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(232\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(233\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.73205 | + | 1.00000i | 1.73205 | + | 1.00000i | ||||
\(238\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(241\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | − | 1.00000i | \(-0.5\pi\) | |
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.00000i | 1.00000i | ||||||||
\(247\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(248\) | − | 1.00000i | − | 1.00000i | ||||||
\(249\) | −1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | ||||
\(250\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(251\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | − | 1.00000i | \(-0.5\pi\) | |
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(254\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(255\) | 1.00000i | 1.00000i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | − | 1.00000i | \(-0.5\pi\) | |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(258\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(259\) | 1.00000i | 1.00000i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(264\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(267\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | − | 1.00000i | \(-0.5\pi\) | |
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(270\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(271\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | 0.866025 | − | 0.500000i | \(-0.166667\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(272\) | −1.00000 | −1.00000 | ||||||||
\(273\) | − | 1.00000i | − | 1.00000i | ||||||
\(274\) | 1.00000i | 1.00000i | ||||||||
\(275\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(278\) | 1.00000 | 1.00000 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(281\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | 0.866025 | − | 0.500000i | \(-0.166667\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − | 1.00000i | − | 1.00000i | ||||||
\(286\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(287\) | − | 1.00000i | − | 1.00000i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(291\) | 1.00000i | 1.00000i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(296\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(297\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(298\) | − | 1.00000i | − | 1.00000i | ||||||
\(299\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(304\) | 1.00000 | 1.00000 | ||||||||
\(305\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(311\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(312\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(313\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(314\) | −1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(320\) | 1.00000i | 1.00000i | ||||||||
\(321\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(322\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(323\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.00000 | −1.00000 | ||||||||
\(326\) | −1.00000 | −1.00000 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | − | 1.00000i | − | 1.00000i | ||||||
\(331\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(335\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(336\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(337\) | 2.00000 | 2.00000 | 1.00000 | \(0\) | ||||||
1.00000 | \(0\) | |||||||||
\(338\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(339\) | − | 1.00000i | − | 1.00000i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 1.00000i | ||||||||
\(344\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(345\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(346\) | −1.00000 | −1.00000 | ||||||||
\(347\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(350\) | 1.00000 | 1.00000 | ||||||||
\(351\) | 1.00000 | 1.00000 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(354\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(355\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(358\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(359\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(367\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(368\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(374\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(375\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(378\) | −1.00000 | −1.00000 | ||||||||
\(379\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(382\) | 1.00000i | 1.00000i | ||||||||
\(383\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(384\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(385\) | 1.00000i | 1.00000i | ||||||||
\(386\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 2.00000i | − | 2.00000i | − | 1.00000i | \(-0.5\pi\) | |||
− | 1.00000i | \(-0.5\pi\) | ||||||||
\(390\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(391\) | −1.00000 | −1.00000 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(395\) | 2.00000 | 2.00000 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | − | 1.00000i | \(-0.5\pi\) | |
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(398\) | 1.00000 | 1.00000 | ||||||||
\(399\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(400\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(401\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | 0.866025 | − | 0.500000i | \(-0.166667\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(402\) | −1.00000 | −1.00000 | ||||||||
\(403\) | −1.00000 | −1.00000 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(406\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(407\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(408\) | − | 1.00000i | − | 1.00000i | ||||||
\(409\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(410\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(411\) | −1.00000 | −1.00000 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.00000i | 2.00000i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.00000i | 1.00000i | ||||||||
\(418\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(419\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(422\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(426\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(427\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(430\) | 1.00000 | 1.00000 | ||||||||
\(431\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(432\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(433\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(434\) | 1.00000 | 1.00000 | ||||||||
\(435\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.00000 | 1.00000 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(440\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.00000i | 1.00000i | ||||||||
\(443\) | 2.00000i | 2.00000i | 1.00000i | \(0.5\pi\) | ||||||
1.00000i | \(0.5\pi\) | |||||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(446\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(447\) | 1.00000 | 1.00000 | ||||||||
\(448\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(449\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | − | 1.00000i | \(-0.5\pi\) | |
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.00000 | 1.00000 | ||||||||
\(455\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(456\) | 1.00000i | 1.00000i | ||||||||
\(457\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(462\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(463\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(464\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(465\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.00000 | 1.00000 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.73205 | − | 1.00000i | −1.73205 | − | 1.00000i | ||||
\(472\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(473\) | 1.00000i | 1.00000i | ||||||||
\(474\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | ||||
\(475\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(482\) | −1.00000 | −1.00000 | ||||||||
\(483\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(488\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(489\) | − | 1.00000i | − | 1.00000i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | − | 1.00000i | \(-0.5\pi\) | |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.00000i | 1.00000i | ||||||||
\(494\) | − | 1.00000i | − | 1.00000i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(497\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(498\) | 1.73205 | − | 1.00000i | 1.73205 | − | 1.00000i | ||||
\(499\) | 2.00000i | 2.00000i | 1.00000i | \(0.5\pi\) | ||||||
1.00000i | \(0.5\pi\) | |||||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(502\) | −1.00000 | −1.00000 | ||||||||
\(503\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | − | 1.00000i | \(-0.5\pi\) | |
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(506\) | 1.00000 | 1.00000 | ||||||||
\(507\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | − | 1.00000i | \(-0.5\pi\) | |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(510\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 1.00000i | − | 1.00000i | ||||||
\(513\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(514\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(519\) | − | 1.00000i | − | 1.00000i | ||||||
\(520\) | 1.00000 | 1.00000 | ||||||||
\(521\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.00000i | 1.00000i | ||||||||
\(526\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(527\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(528\) | 1.00000i | 1.00000i | ||||||||
\(529\) | 0 | 0 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(534\) | −1.00000 | −1.00000 | ||||||||
\(535\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(536\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(537\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(538\) | −1.00000 | −1.00000 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(542\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(547\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(551\) | − | 1.00000i | − | 1.00000i | ||||||
\(552\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(553\) | 1.00000 | + | 1.73205i | 1.00000 | + | 1.73205i | ||||
\(554\) | − | 1.00000i | − | 1.00000i | ||||||
\(555\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(560\) | −1.00000 | −1.00000 | ||||||||
\(561\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(566\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(567\) | − | 1.00000i | − | 1.00000i | ||||||
\(568\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(569\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | 0.866025 | − | 0.500000i | \(-0.166667\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(570\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(571\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.00000 | −1.00000 | ||||||||
\(574\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(575\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.73205 | + | 1.00000i | −1.73205 | + | 1.00000i | ||||
\(582\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.00000 | 1.00000 | ||||||||
\(587\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(590\) | −1.00000 | −1.00000 | ||||||||
\(591\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(592\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(593\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(594\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(595\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.00000i | 1.00000i | ||||||||
\(598\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(599\) | −2.00000 | −2.00000 | −1.00000 | \(\pi\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(600\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(601\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | 0.866025 | − | 0.500000i | \(-0.166667\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(602\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | − | 1.00000i | − | 1.00000i | ||||||
\(607\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(610\) | 1.00000i | 1.00000i | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(616\) | − | 1.00000i | − | 1.00000i | ||||||
\(617\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | − | 1.00000i | \(-0.5\pi\) | |
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 2.00000i | − | 2.00000i | − | 1.00000i | \(-0.5\pi\) | |||
− | 1.00000i | \(-0.5\pi\) | ||||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.00000 | 1.00000 | ||||||||
\(624\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(625\) | 1.00000 | 1.00000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.00000 | 1.00000 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | − | 1.00000i | \(-0.5\pi\) | |
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(632\) | −2.00000 | −2.00000 | ||||||||
\(633\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 1.00000i | − | 1.00000i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(641\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(642\) | −1.00000 | −1.00000 | ||||||||
\(643\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.00000i | 1.00000i | ||||||||
\(646\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(647\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(648\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(649\) | − | 1.00000i | − | 1.00000i | ||||||
\(650\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(651\) | 1.00000i | 1.00000i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | − | 1.00000i | \(-0.5\pi\) | |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(662\) | 1.00000 | 1.00000 | ||||||||
\(663\) | −1.00000 | −1.00000 | ||||||||
\(664\) | − | 2.00000i | − | 2.00000i | ||||||
\(665\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(670\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(671\) | −1.00000 | −1.00000 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(674\) | −1.73205 | − | 1.00000i | −1.73205 | − | 1.00000i | ||||
\(675\) | −1.00000 | −1.00000 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(678\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(679\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(680\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(681\) | 1.00000i | 1.00000i | ||||||||
\(682\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(683\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(686\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.00000 | −1.00000 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 1.00000 | 1.00000 | ||||||||
\(691\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 1.00000i | − | 1.00000i | ||||||
\(695\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(696\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(697\) | −1.00000 | −1.00000 | ||||||||
\(698\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.00000 | −2.00000 | −1.00000 | \(\pi\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(702\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(703\) | −1.00000 | −1.00000 | ||||||||
\(704\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(707\) | 1.00000i | 1.00000i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(710\) | −1.00000 | −1.00000 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(713\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(714\) | 1.00000 | 1.00000 | ||||||||
\(715\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 1.00000i | − | 1.00000i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 2.00000i | − | 2.00000i | − | 1.00000i | \(-0.5\pi\) | |||
− | 1.00000i | \(-0.5\pi\) | ||||||||
\(728\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(729\) | 1.00000 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 2.00000i | − | 2.00000i | − | 1.00000i | \(-0.5\pi\) | |||
− | 1.00000i | \(-0.5\pi\) | ||||||||
\(734\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | − | 1.00000i | \(-0.5\pi\) | |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.00000 | 1.00000 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(744\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(745\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(746\) | 1.00000 | 1.00000 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.00000 | 1.00000 | ||||||||
\(750\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(751\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 1.00000i | − | 1.00000i | ||||||
\(754\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(758\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(759\) | 1.00000i | 1.00000i | ||||||||
\(760\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(761\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | − | 1.00000i | \(-0.5\pi\) | |
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(762\) | 1.00000i | 1.00000i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 1.00000i | − | 1.00000i | ||||||
\(767\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(770\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(771\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.00000 | 1.00000 | ||||||||
\(776\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(777\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(778\) | −1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | ||||
\(779\) | 1.00000 | 1.00000 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 1.00000i | − | 1.00000i | ||||||
\(782\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(783\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.00000 | −2.00000 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(790\) | −1.73205 | − | 1.00000i | −1.73205 | − | 1.00000i | ||||
\(791\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(794\) | −1.00000 | −1.00000 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(798\) | −1.00000 | −1.00000 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.00000 | −1.00000 | ||||||||
\(806\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(807\) | − | 1.00000i | − | 1.00000i | ||||||
\(808\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(809\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | 0.866025 | − | 0.500000i | \(-0.166667\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(810\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(811\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(814\) | −1.00000 | −1.00000 | ||||||||
\(815\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(816\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(817\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(818\) | 1.00000 | 1.00000 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | − | 1.00000i | \(-0.5\pi\) | |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(822\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(823\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(826\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(827\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | − | 1.00000i | \(-0.5\pi\) | |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(830\) | 1.00000 | − | 1.73205i | 1.00000 | − | 1.73205i | ||||
\(831\) | 1.00000 | 1.00000 | ||||||||
\(832\) | −1.00000 | −1.00000 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(835\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.00000 | −1.00000 | ||||||||
\(838\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(839\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(840\) | − | 1.00000i | − | 1.00000i | ||||||
\(841\) | 0 | 0 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 1.00000i | − | 1.00000i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(850\) | − | 1.00000i | − | 1.00000i | ||||||
\(851\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(854\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(857\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(858\) | 1.00000 | 1.00000 | ||||||||
\(859\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(862\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(863\) | −2.00000 | −2.00000 | −1.00000 | \(\pi\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(866\) | 1.00000i | 1.00000i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.00000 | − | 1.73205i | 1.00000 | − | 1.73205i | ||||
\(870\) | − | 1.00000i | − | 1.00000i | ||||||
\(871\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(875\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(878\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(879\) | 1.00000i | 1.00000i | ||||||||
\(880\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(881\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | 0.866025 | − | 0.500000i | \(-0.166667\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 1.00000i | − | 1.00000i | ||||||
\(886\) | 1.00000 | − | 1.73205i | 1.00000 | − | 1.73205i | ||||
\(887\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | − | 1.00000i | \(-0.5\pi\) | |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(888\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(889\) | − | 1.00000i | − | 1.00000i | ||||||
\(890\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(891\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(895\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(896\) | 1.00000 | 1.00000 | ||||||||
\(897\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(898\) | −1.00000 | −1.00000 | ||||||||
\(899\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 1.00000 | 1.00000 | ||||||||
\(903\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(904\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | 0.866025 | − | 0.500000i | \(-0.166667\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.00000i | 1.00000i | ||||||||
\(911\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(912\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(913\) | 1.73205 | + | 1.00000i | 1.73205 | + | 1.00000i | ||||
\(914\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(915\) | −1.00000 | −1.00000 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 1.00000i | 1.00000i | ||||||||
\(919\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(920\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.00000 | 1.00000 | ||||||||
\(923\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | − | 1.00000i | \(-0.5\pi\) | |
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(930\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.00000 | 1.00000 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 2.00000i | − | 2.00000i | − | 1.00000i | \(-0.5\pi\) | |||
− | 1.00000i | \(-0.5\pi\) | ||||||||
\(938\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(942\) | 1.00000 | + | 1.73205i | 1.00000 | + | 1.73205i | ||||
\(943\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(944\) | 1.00000 | 1.00000 | ||||||||
\(945\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(946\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(947\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 1.00000i | 1.00000i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(953\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.00000 | 1.00000 | ||||||||
\(958\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(959\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(960\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(961\) | 1.00000 | 1.00000 | ||||||||
\(962\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(966\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(967\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(970\) | − | 1.00000i | − | 1.00000i | ||||||
\(971\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(974\) | 1.00000i | 1.00000i | ||||||||
\(975\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(976\) | − | 1.00000i | − | 1.00000i | ||||||
\(977\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | 0.866025 | − | 0.500000i | \(-0.166667\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(978\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(979\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(983\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(984\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(985\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(986\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.00000 | −1.00000 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | 0.866025 | − | 0.500000i | \(-0.166667\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.00000i | 1.00000i | ||||||||
\(994\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(995\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(998\) | 1.00000 | − | 1.73205i | 1.00000 | − | 1.73205i | ||||
\(999\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i |
(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 | 2015.1.bq.e.464.1 | yes | 4 | |
5.4 | even | 2 | 2015.1.bq.c.464.2 | yes | 4 | ||
13.3 | even | 3 | inner | 2015.1.bq.e.1394.2 | yes | 4 | |
31.30 | odd | 2 | 2015.1.bq.c.464.1 | ✓ | 4 | ||
65.29 | even | 6 | 2015.1.bq.c.1394.1 | yes | 4 | ||
155.154 | odd | 2 | inner | 2015.1.bq.e.464.2 | yes | 4 | |
403.185 | odd | 6 | 2015.1.bq.c.1394.2 | yes | 4 | ||
2015.1394 | odd | 6 | inner | 2015.1.bq.e.1394.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2015.1.bq.c.464.1 | ✓ | 4 | 31.30 | odd | 2 | ||
2015.1.bq.c.464.2 | yes | 4 | 5.4 | even | 2 | ||
2015.1.bq.c.1394.1 | yes | 4 | 65.29 | even | 6 | ||
2015.1.bq.c.1394.2 | yes | 4 | 403.185 | odd | 6 | ||
2015.1.bq.e.464.1 | yes | 4 | 1.1 | even | 1 | trivial | |
2015.1.bq.e.464.2 | yes | 4 | 155.154 | odd | 2 | inner | |
2015.1.bq.e.1394.1 | yes | 4 | 2015.1394 | odd | 6 | inner | |
2015.1.bq.e.1394.2 | yes | 4 | 13.3 | even | 3 | inner |