Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1456,1,Mod(181,1456)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1456, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 2, 2]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1456.181");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1456 = 2^{4} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1456.bc (of order \(4\), 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: | \(0.726638658394\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(S_{4}\) |
Projective field: | Galois closure of 4.2.186368.2 |
Embedding invariants
Embedding label | 909.2 | ||
Root | \(-0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1456.909 |
Dual form | 1456.1.bc.b.181.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1456\mathbb{Z}\right)^\times\).
\(n\) | \(561\) | \(911\) | \(1093\) | \(1249\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(3\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(4\) | − | 1.00000i | − | 1.00000i | ||||||
\(5\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | − | 1.00000i | \(-0.5\pi\) | |
1.00000 | \(0\) | |||||||||
\(6\) | − | 1.00000i | − | 1.00000i | ||||||
\(7\) | 1.00000i | 1.00000i | ||||||||
\(8\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − | 1.41421i | − | 1.41421i | ||||||
\(11\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | 0.258819 | − | 0.965926i | \(-0.416667\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(12\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(13\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(14\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(15\) | − | 1.41421i | − | 1.41421i | ||||||
\(16\) | −1.00000 | −1.00000 | ||||||||
\(17\) | 1.41421i | 1.41421i | 0.707107 | + | 0.707107i | \(0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(20\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(21\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(22\) | −1.00000 | −1.00000 | ||||||||
\(23\) | − | 1.00000i | − | 1.00000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(24\) | −1.00000 | −1.00000 | ||||||||
\(25\) | − | 1.00000i | − | 1.00000i | ||||||
\(26\) | 1.00000i | 1.00000i | ||||||||
\(27\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(28\) | 1.00000 | 1.00000 | ||||||||
\(29\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | 1.00000 | \(0\) | ||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(31\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(33\) | −1.00000 | −1.00000 | ||||||||
\(34\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(35\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | 0.258819 | − | 0.965926i | \(-0.416667\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.00000i | 1.00000i | ||||||||
\(40\) | −1.41421 | −1.41421 | ||||||||
\(41\) | 1.00000i | 1.00000i | 0.866025 | + | 0.500000i | \(0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(42\) | 1.00000 | 1.00000 | ||||||||
\(43\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | − | 1.00000i | \(-0.5\pi\) | |
1.00000 | \(0\) | |||||||||
\(44\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(47\) | 1.00000 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(48\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(49\) | −1.00000 | −1.00000 | ||||||||
\(50\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(51\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(52\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(53\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | 1.00000i | \(0.5\pi\) | ||
−1.00000 | \(\pi\) | |||||||||
\(54\) | 1.00000 | 1.00000 | ||||||||
\(55\) | −1.41421 | −1.41421 | ||||||||
\(56\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.41421 | 1.41421 | ||||||||
\(59\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(60\) | −1.41421 | −1.41421 | ||||||||
\(61\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(62\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000i | 1.00000i | ||||||||
\(65\) | 1.41421i | 1.41421i | ||||||||
\(66\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(67\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(68\) | 1.41421 | 1.41421 | ||||||||
\(69\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(70\) | 1.41421 | 1.41421 | ||||||||
\(71\) | −1.41421 | −1.41421 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 1.00000i | − | 1.00000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(74\) | −1.00000 | −1.00000 | ||||||||
\(75\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(78\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(79\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(80\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(81\) | 1.00000 | 1.00000 | ||||||||
\(82\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(83\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(84\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(85\) | 1.41421 | + | 1.41421i | 1.41421 | + | 1.41421i | ||||
\(86\) | − | 1.41421i | − | 1.41421i | ||||||
\(87\) | 1.41421 | 1.41421 | ||||||||
\(88\) | 1.00000i | 1.00000i | ||||||||
\(89\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(92\) | −1.00000 | −1.00000 | ||||||||
\(93\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(94\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000i | 1.00000i | ||||||||
\(97\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(98\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.00000 | −1.00000 | ||||||||
\(101\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | 0.258819 | − | 0.965926i | \(-0.416667\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(102\) | 1.41421 | 1.41421 | ||||||||
\(103\) | −1.41421 | −1.41421 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(104\) | 1.00000 | 1.00000 | ||||||||
\(105\) | 1.41421 | 1.41421 | ||||||||
\(106\) | 1.41421i | 1.41421i | ||||||||
\(107\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(108\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(109\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(110\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(111\) | −1.00000 | −1.00000 | ||||||||
\(112\) | − | 1.00000i | − | 1.00000i | ||||||
\(113\) | 1.00000 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(116\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.41421 | −1.41421 | ||||||||
\(120\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(121\) | 0 | 0 | ||||||||
\(122\) | − | 1.00000i | − | 1.00000i | ||||||
\(123\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(124\) | 1.00000i | 1.00000i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(129\) | − | 1.41421i | − | 1.41421i | ||||||
\(130\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(131\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(132\) | 1.00000i | 1.00000i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 1.00000i | − | 1.00000i | ||||||
\(135\) | 1.41421 | 1.41421 | ||||||||
\(136\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(137\) | 1.41421 | 1.41421 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(138\) | −1.00000 | −1.00000 | ||||||||
\(139\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(140\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(141\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(142\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(143\) | 1.00000 | 1.00000 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.00000 | 2.00000 | ||||||||
\(146\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(147\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(148\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(149\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | 0.258819 | − | 0.965926i | \(-0.416667\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(150\) | −1.00000 | −1.00000 | ||||||||
\(151\) | 1.41421 | 1.41421 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | − | 1.00000i | − | 1.00000i | ||||||
\(155\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(156\) | 1.00000 | 1.00000 | ||||||||
\(157\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(158\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(159\) | 1.41421i | 1.41421i | ||||||||
\(160\) | 1.41421i | 1.41421i | ||||||||
\(161\) | 1.00000 | 1.00000 | ||||||||
\(162\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(163\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(164\) | 1.00000 | 1.00000 | ||||||||
\(165\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(168\) | − | 1.00000i | − | 1.00000i | ||||||
\(169\) | − | 1.00000i | − | 1.00000i | ||||||
\(170\) | 2.00000 | 2.00000 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(173\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(174\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(175\) | 1.00000 | 1.00000 | ||||||||
\(176\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(182\) | −1.00000 | −1.00000 | ||||||||
\(183\) | − | 1.00000i | − | 1.00000i | ||||||
\(184\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(185\) | −1.41421 | −1.41421 | ||||||||
\(186\) | 1.00000i | 1.00000i | ||||||||
\(187\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(188\) | − | 1.00000i | − | 1.00000i | ||||||
\(189\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(192\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(193\) | 1.41421i | 1.41421i | 0.707107 | + | 0.707107i | \(0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(194\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(195\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(196\) | 1.00000i | 1.00000i | ||||||||
\(197\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(200\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(201\) | − | 1.00000i | − | 1.00000i | ||||||
\(202\) | −1.00000 | −1.00000 | ||||||||
\(203\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(204\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(205\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(206\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(211\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(212\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(213\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 2.00000i | − | 2.00000i | ||||||
\(216\) | − | 1.00000i | − | 1.00000i | ||||||
\(217\) | − | 1.00000i | − | 1.00000i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(220\) | 1.41421i | 1.41421i | ||||||||
\(221\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(222\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(223\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(224\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(227\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | 1.00000i | \(0.5\pi\) | ||
−1.00000 | \(\pi\) | |||||||||
\(230\) | −1.41421 | −1.41421 | ||||||||
\(231\) | − | 1.00000i | − | 1.00000i | ||||||
\(232\) | − | 1.41421i | − | 1.41421i | ||||||
\(233\) | − | 1.00000i | − | 1.00000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(238\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(239\) | 1.41421i | 1.41421i | 0.707107 | + | 0.707107i | \(0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(240\) | 1.41421i | 1.41421i | ||||||||
\(241\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(245\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(246\) | 1.00000 | 1.00000 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | 0.258819 | − | 0.965926i | \(-0.416667\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(254\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(255\) | 2.00000 | 2.00000 | ||||||||
\(256\) | 1.00000 | 1.00000 | ||||||||
\(257\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(258\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(259\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(260\) | 1.41421 | 1.41421 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(264\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(265\) | 2.00000i | 2.00000i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(269\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(270\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(271\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(272\) | − | 1.41421i | − | 1.41421i | ||||||
\(273\) | −1.00000 | −1.00000 | ||||||||
\(274\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(275\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(276\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(277\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | − | 1.41421i | − | 1.41421i | ||||||
\(281\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(282\) | − | 1.00000i | − | 1.00000i | ||||||
\(283\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(284\) | 1.41421i | 1.41421i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(287\) | −1.00000 | −1.00000 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.00000 | −1.00000 | ||||||||
\(290\) | 1.41421 | − | 1.41421i | 1.41421 | − | 1.41421i | ||||
\(291\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(292\) | −1.00000 | −1.00000 | ||||||||
\(293\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(294\) | 1.00000i | 1.00000i | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.00000i | 1.00000i | ||||||||
\(297\) | − | 1.00000i | − | 1.00000i | ||||||
\(298\) | −1.00000 | −1.00000 | ||||||||
\(299\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(300\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(301\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(302\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(303\) | −1.00000 | −1.00000 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 1.41421i | − | 1.41421i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | 1.00000 | \(0\) | ||
1.00000i | \(0.5\pi\) | |||||||||
\(308\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(309\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(310\) | 1.41421i | 1.41421i | ||||||||
\(311\) | 1.41421 | 1.41421 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(312\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(313\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(314\) | − | 1.00000i | − | 1.00000i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.00000i | 1.00000i | ||||||||
\(317\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(318\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(319\) | − | 1.41421i | − | 1.41421i | ||||||
\(320\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | − | 1.00000i | − | 1.00000i | ||||||
\(325\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(329\) | 1.00000i | 1.00000i | ||||||||
\(330\) | 1.41421i | 1.41421i | ||||||||
\(331\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 1.41421i | − | 1.41421i | ||||||
\(336\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(337\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(338\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(339\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(340\) | 1.41421 | − | 1.41421i | 1.41421 | − | 1.41421i | ||||
\(341\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 1.00000i | ||||||
\(344\) | −1.41421 | −1.41421 | ||||||||
\(345\) | −1.41421 | −1.41421 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | − | 1.00000i | \(-0.5\pi\) | |
1.00000 | \(0\) | |||||||||
\(348\) | − | 1.41421i | − | 1.41421i | ||||||
\(349\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(350\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(351\) | −1.00000 | −1.00000 | ||||||||
\(352\) | 1.00000 | 1.00000 | ||||||||
\(353\) | 1.00000 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.41421 | + | 1.41421i | −1.41421 | + | 1.41421i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 1.00000i | − | 1.00000i | ||||||
\(362\) | 1.00000 | 1.00000 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(365\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(366\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(367\) | − | 1.41421i | − | 1.41421i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(368\) | 1.00000i | 1.00000i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(371\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(372\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(373\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | − | 1.00000i | \(-0.5\pi\) | |
1.00000 | \(0\) | |||||||||
\(374\) | − | 1.41421i | − | 1.41421i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(377\) | −1.41421 | −1.41421 | ||||||||
\(378\) | 1.00000i | 1.00000i | ||||||||
\(379\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(384\) | 1.00000 | 1.00000 | ||||||||
\(385\) | − | 1.41421i | − | 1.41421i | ||||||
\(386\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.00000i | 1.00000i | ||||||||
\(389\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(390\) | 1.41421 | 1.41421 | ||||||||
\(391\) | 1.41421 | 1.41421 | ||||||||
\(392\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.00000 | 1.00000 | ||||||||
\(395\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | − | 1.00000i | \(-0.5\pi\) | |
−1.00000 | \(\pi\) | |||||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000i | 1.00000i | ||||||||
\(401\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(402\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(403\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(404\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(405\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(406\) | 1.41421i | 1.41421i | ||||||||
\(407\) | 1.00000i | 1.00000i | ||||||||
\(408\) | − | 1.41421i | − | 1.41421i | ||||||
\(409\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(410\) | 1.41421 | 1.41421 | ||||||||
\(411\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(412\) | 1.41421i | 1.41421i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − | 1.00000i | − | 1.00000i | ||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(420\) | − | 1.41421i | − | 1.41421i | ||||||
\(421\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | 0.258819 | − | 0.965926i | \(-0.416667\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.41421 | 1.41421 | ||||||||
\(425\) | 1.41421 | 1.41421 | ||||||||
\(426\) | 1.41421i | 1.41421i | ||||||||
\(427\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(430\) | −1.41421 | − | 1.41421i | −1.41421 | − | 1.41421i | ||||
\(431\) | 1.41421i | 1.41421i | 0.707107 | + | 0.707107i | \(0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(432\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(433\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(434\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(435\) | 1.41421 | − | 1.41421i | 1.41421 | − | 1.41421i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −1.00000 | −1.00000 | ||||||||
\(439\) | 1.41421 | 1.41421 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(440\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.41421 | −1.41421 | ||||||||
\(443\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(444\) | 1.00000i | 1.00000i | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(447\) | −1.00000 | −1.00000 | ||||||||
\(448\) | −1.00000 | −1.00000 | ||||||||
\(449\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(452\) | − | 1.00000i | − | 1.00000i | ||||||
\(453\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.41421 | −1.41421 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.41421 | 1.41421 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(458\) | 1.41421i | 1.41421i | ||||||||
\(459\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(460\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(461\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | − | 1.00000i | \(-0.5\pi\) | |
−1.00000 | \(\pi\) | |||||||||
\(462\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(463\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(464\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(465\) | 1.41421i | 1.41421i | ||||||||
\(466\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(467\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(470\) | − | 1.41421i | − | 1.41421i | ||||||
\(471\) | − | 1.00000i | − | 1.00000i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.41421 | −1.41421 | ||||||||
\(474\) | 1.00000i | 1.00000i | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.41421i | 1.41421i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(479\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(480\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(481\) | 1.00000 | 1.00000 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.41421 | −1.41421 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(488\) | −1.00000 | −1.00000 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.41421i | 1.41421i | ||||||||
\(491\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | 1.00000i | \(0.5\pi\) | ||
−1.00000 | \(\pi\) | |||||||||
\(492\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(493\) | −1.41421 | + | 1.41421i | −1.41421 | + | 1.41421i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.00000 | 1.00000 | ||||||||
\(497\) | − | 1.41421i | − | 1.41421i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.00000 | −1.00000 | ||||||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.41421 | −1.41421 | ||||||||
\(506\) | 1.00000i | 1.00000i | ||||||||
\(507\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(508\) | 1.00000i | 1.00000i | ||||||||
\(509\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(510\) | 1.41421 | − | 1.41421i | 1.41421 | − | 1.41421i | ||||
\(511\) | 1.00000 | 1.00000 | ||||||||
\(512\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.41421 | + | 1.41421i | −1.41421 | + | 1.41421i | ||||
\(516\) | −1.41421 | −1.41421 | ||||||||
\(517\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(518\) | − | 1.00000i | − | 1.00000i | ||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(521\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | 0.258819 | − | 0.965926i | \(-0.416667\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 1.41421i | − | 1.41421i | ||||||
\(528\) | 1.00000 | 1.00000 | ||||||||
\(529\) | 0 | 0 | ||||||||
\(530\) | 1.41421 | + | 1.41421i | 1.41421 | + | 1.41421i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.00000 | −1.00000 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.00000i | 1.00000i | ||||||||
\(539\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(540\) | − | 1.41421i | − | 1.41421i | ||||||
\(541\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(542\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(543\) | 1.00000 | 1.00000 | ||||||||
\(544\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(547\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | − | 1.00000i | \(-0.5\pi\) | |
−1.00000 | \(\pi\) | |||||||||
\(548\) | − | 1.41421i | − | 1.41421i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.00000i | 1.00000i | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 1.00000i | 1.00000i | ||||||||
\(553\) | − | 1.00000i | − | 1.00000i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.41421i | 1.41421i | ||||||||
\(560\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(561\) | − | 1.41421i | − | 1.41421i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(564\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(565\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(566\) | 1.00000 | 1.00000 | ||||||||
\(567\) | 1.00000i | 1.00000i | ||||||||
\(568\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(569\) | 1.00000i | 1.00000i | 0.866025 | + | 0.500000i | \(0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(572\) | − | 1.00000i | − | 1.00000i | ||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(575\) | −1.00000 | −1.00000 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(578\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(579\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(580\) | − | 2.00000i | − | 2.00000i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 1.00000i | 1.00000i | ||||||||
\(583\) | 1.41421 | 1.41421 | ||||||||
\(584\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(588\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.00000 | 1.00000 | ||||||||
\(592\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(593\) | −2.00000 | −2.00000 | −1.00000 | \(\pi\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(594\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(595\) | −1.41421 | + | 1.41421i | −1.41421 | + | 1.41421i | ||||
\(596\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.00000 | 1.00000 | ||||||||
\(599\) | 1.00000i | 1.00000i | 0.866025 | + | 0.500000i | \(0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(600\) | 1.00000i | 1.00000i | ||||||||
\(601\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(602\) | 1.41421 | 1.41421 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 1.41421i | − | 1.41421i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(607\) | − | 1.41421i | − | 1.41421i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.41421i | 1.41421i | ||||||||
\(610\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(611\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | 0.258819 | − | 0.965926i | \(-0.416667\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(614\) | 1.41421 | 1.41421 | ||||||||
\(615\) | 1.41421 | 1.41421 | ||||||||
\(616\) | −1.00000 | −1.00000 | ||||||||
\(617\) | 1.41421 | 1.41421 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(618\) | 1.41421i | 1.41421i | ||||||||
\(619\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | − | 1.00000i | \(-0.5\pi\) | |
1.00000 | \(0\) | |||||||||
\(620\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(621\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(622\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | − | 1.00000i | − | 1.00000i | ||||||
\(625\) | 1.00000 | 1.00000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(629\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(632\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 1.00000i | − | 1.00000i | ||||||
\(635\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(636\) | 1.41421 | 1.41421 | ||||||||
\(637\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(638\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.41421 | 1.41421 | ||||||||
\(641\) | 1.00000 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | 1.00000 | \(0\) | ||
1.00000i | \(0.5\pi\) | |||||||||
\(644\) | − | 1.00000i | − | 1.00000i | ||||||
\(645\) | −1.41421 | − | 1.41421i | −1.41421 | − | 1.41421i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(648\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 1.00000 | 1.00000 | ||||||||
\(651\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 1.00000i | − | 1.00000i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(659\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(660\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(661\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(662\) | 1.00000 | 1.00000 | ||||||||
\(663\) | −1.41421 | −1.41421 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(670\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(671\) | −1.00000 | −1.00000 | ||||||||
\(672\) | −1.00000 | −1.00000 | ||||||||
\(673\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(674\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(675\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(676\) | −1.00000 | −1.00000 | ||||||||
\(677\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(678\) | − | 1.00000i | − | 1.00000i | ||||||
\(679\) | − | 1.00000i | − | 1.00000i | ||||||
\(680\) | − | 2.00000i | − | 2.00000i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.00000 | 1.00000 | ||||||||
\(683\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | 0.258819 | − | 0.965926i | \(-0.416667\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.41421 | − | 1.41421i | 1.41421 | − | 1.41421i | ||||
\(686\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(687\) | 1.41421i | 1.41421i | ||||||||
\(688\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(689\) | − | 1.41421i | − | 1.41421i | ||||||
\(690\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(691\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | − | 1.00000i | \(-0.5\pi\) | |
−1.00000 | \(\pi\) | |||||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 1.41421i | − | 1.41421i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(697\) | −1.41421 | −1.41421 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(700\) | − | 1.00000i | − | 1.00000i | ||||||
\(701\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(702\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(705\) | − | 1.41421i | − | 1.41421i | ||||||
\(706\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(707\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | 0.258819 | − | 0.965926i | \(-0.416667\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(710\) | 2.00000i | 2.00000i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.00000i | 1.00000i | ||||||||
\(714\) | 1.41421i | 1.41421i | ||||||||
\(715\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 1.41421i | − | 1.41421i | ||||||
\(722\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(725\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(728\) | 1.00000i | 1.00000i | ||||||||
\(729\) | 1.00000i | 1.00000i | ||||||||
\(730\) | −1.41421 | −1.41421 | ||||||||
\(731\) | 1.41421 | + | 1.41421i | 1.41421 | + | 1.41421i | ||||
\(732\) | −1.00000 | −1.00000 | ||||||||
\(733\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | 1.00000 | \(0\) | ||
1.00000i | \(0.5\pi\) | |||||||||
\(734\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(735\) | 1.41421i | 1.41421i | ||||||||
\(736\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(737\) | −1.00000 | −1.00000 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(740\) | 1.41421i | 1.41421i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.41421 | −1.41421 | ||||||||
\(743\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(744\) | 1.00000 | 1.00000 | ||||||||
\(745\) | −1.41421 | −1.41421 | ||||||||
\(746\) | − | 1.41421i | − | 1.41421i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.00000 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(752\) | −1.00000 | −1.00000 | ||||||||
\(753\) | −1.00000 | −1.00000 | ||||||||
\(754\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(755\) | 1.41421 | − | 1.41421i | 1.41421 | − | 1.41421i | ||||
\(756\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(757\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.00000i | 1.00000i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.00000i | 1.00000i | 0.866025 | + | 0.500000i | \(0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(762\) | 1.00000i | 1.00000i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(769\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(770\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.41421 | 1.41421 | ||||||||
\(773\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.00000i | 1.00000i | ||||||||
\(776\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(777\) | − | 1.00000i | − | 1.00000i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(781\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(782\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(783\) | 1.41421i | 1.41421i | ||||||||
\(784\) | 1.00000 | 1.00000 | ||||||||
\(785\) | − | 1.41421i | − | 1.41421i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(788\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.41421i | 1.41421i | ||||||||
\(791\) | 1.00000i | 1.00000i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.00000i | 1.00000i | ||||||||
\(794\) | −1.41421 | −1.41421 | ||||||||
\(795\) | 1.41421 | + | 1.41421i | 1.41421 | + | 1.41421i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.41421i | 1.41421i | ||||||||
\(800\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(804\) | −1.00000 | −1.00000 | ||||||||
\(805\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(806\) | − | 1.00000i | − | 1.00000i | ||||||
\(807\) | 1.00000i | 1.00000i | ||||||||
\(808\) | 1.00000i | 1.00000i | ||||||||
\(809\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(810\) | − | 1.41421i | − | 1.41421i | ||||||
\(811\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | 1.00000i | \(0.5\pi\) | ||
−1.00000 | \(\pi\) | |||||||||
\(812\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(813\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(814\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(821\) | 1.41421 | + | 1.41421i | 1.41421 | + | 1.41421i | 0.707107 | + | 0.707107i | \(0.250000\pi\) |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(822\) | − | 1.41421i | − | 1.41421i | ||||||
\(823\) | 1.00000i | 1.00000i | 0.866025 | + | 0.500000i | \(0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(824\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(825\) | 1.00000i | 1.00000i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(833\) | − | 1.41421i | − | 1.41421i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(838\) | 1.00000i | 1.00000i | ||||||||
\(839\) | 1.00000i | 1.00000i | 0.866025 | + | 0.500000i | \(0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(840\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(841\) | 1.00000i | 1.00000i | ||||||||
\(842\) | −1.00000 | −1.00000 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(849\) | 1.00000 | 1.00000 | ||||||||
\(850\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(851\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(852\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(853\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | − | 1.00000i | \(-0.5\pi\) | |
1.00000 | \(0\) | |||||||||
\(854\) | 1.00000 | 1.00000 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(858\) | − | 1.00000i | − | 1.00000i | ||||||
\(859\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | 0.258819 | − | 0.965926i | \(-0.416667\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(860\) | −2.00000 | −2.00000 | ||||||||
\(861\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(862\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(863\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(864\) | −1.00000 | −1.00000 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(868\) | −1.00000 | −1.00000 | ||||||||
\(869\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(870\) | − | 2.00000i | − | 2.00000i | ||||||
\(871\) | 1.00000i | 1.00000i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(877\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(878\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.41421 | 1.41421 | ||||||||
\(881\) | 1.41421i | 1.41421i | 0.707107 | + | 0.707107i | \(0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(884\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.41421 | −1.41421 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(888\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(889\) | − | 1.00000i | − | 1.00000i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(892\) | 1.00000i | 1.00000i | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(897\) | 1.00000 | 1.00000 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.41421 | − | 1.41421i | −1.41421 | − | 1.41421i | ||||
\(902\) | − | 1.00000i | − | 1.00000i | ||||||
\(903\) | 1.41421 | 1.41421 | ||||||||
\(904\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(905\) | 1.41421 | 1.41421 | ||||||||
\(906\) | − | 1.41421i | − | 1.41421i | ||||||
\(907\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(911\) | 2.00000 | 2.00000 | 1.00000 | \(0\) | ||||||
1.00000 | \(0\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(915\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(916\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 1.41421i | 1.41421i | ||||||||
\(919\) | 1.00000i | 1.00000i | 0.866025 | + | 0.500000i | \(0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(920\) | 1.41421i | 1.41421i | ||||||||
\(921\) | 1.41421 | 1.41421 | ||||||||
\(922\) | −1.41421 | −1.41421 | ||||||||
\(923\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(924\) | −1.00000 | −1.00000 | ||||||||
\(925\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.41421 | −1.41421 | ||||||||
\(929\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(930\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1.00000 | −1.00000 | ||||||||
\(933\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 2.00000i | − | 2.00000i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.41421 | −1.41421 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(938\) | 1.00000 | 1.00000 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(941\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | 1.00000 | \(0\) | ||
1.00000i | \(0.5\pi\) | |||||||||
\(942\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(943\) | 1.00000 | 1.00000 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.41421i | 1.41421i | ||||||||
\(946\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(947\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(948\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(949\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 1.00000i | − | 1.00000i | ||||||
\(952\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(953\) | − | 2.00000i | − | 2.00000i | − | 1.00000i | \(-0.5\pi\) | |||
− | 1.00000i | \(-0.5\pi\) | ||||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.41421 | 1.41421 | ||||||||
\(957\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.41421i | 1.41421i | ||||||||
\(960\) | 1.41421 | 1.41421 | ||||||||
\(961\) | 0 | 0 | ||||||||
\(962\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.41421 | + | 1.41421i | 1.41421 | + | 1.41421i | ||||
\(966\) | − | 1.00000i | − | 1.00000i | ||||||
\(967\) | 1.41421 | 1.41421 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.41421i | 1.41421i | ||||||||
\(971\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(975\) | 1.00000 | 1.00000 | ||||||||
\(976\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(977\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.41421i | 1.41421i | ||||||||
\(983\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(984\) | − | 1.00000i | − | 1.00000i | ||||||
\(985\) | 1.41421 | 1.41421 | ||||||||
\(986\) | 2.00000i | 2.00000i | ||||||||
\(987\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.00000 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(992\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(993\) | 1.00000 | 1.00000 | ||||||||
\(994\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | 0.258819 | − | 0.965926i | \(-0.416667\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(998\) | 1.00000i | 1.00000i | ||||||||
\(999\) | − | 1.00000i | − | 1.00000i |
(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 | 1456.1.bc.b.909.2 | yes | 4 | |
7.6 | odd | 2 | 1456.1.bc.a.909.2 | yes | 4 | ||
13.12 | even | 2 | 1456.1.bc.a.909.1 | yes | 4 | ||
16.5 | even | 4 | inner | 1456.1.bc.b.181.1 | yes | 4 | |
91.90 | odd | 2 | inner | 1456.1.bc.b.909.1 | yes | 4 | |
112.69 | odd | 4 | 1456.1.bc.a.181.1 | ✓ | 4 | ||
208.181 | even | 4 | 1456.1.bc.a.181.2 | yes | 4 | ||
1456.181 | odd | 4 | inner | 1456.1.bc.b.181.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1456.1.bc.a.181.1 | ✓ | 4 | 112.69 | odd | 4 | ||
1456.1.bc.a.181.2 | yes | 4 | 208.181 | even | 4 | ||
1456.1.bc.a.909.1 | yes | 4 | 13.12 | even | 2 | ||
1456.1.bc.a.909.2 | yes | 4 | 7.6 | odd | 2 | ||
1456.1.bc.b.181.1 | yes | 4 | 16.5 | even | 4 | inner | |
1456.1.bc.b.181.2 | yes | 4 | 1456.181 | odd | 4 | inner | |
1456.1.bc.b.909.1 | yes | 4 | 91.90 | odd | 2 | inner | |
1456.1.bc.b.909.2 | yes | 4 | 1.1 | even | 1 | trivial |