Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2160,1,Mod(1187,2160)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2160, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 2, 1]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2160.1187");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 2160.be (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: | \(1.07798042729\) |
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 4.2.6912000.6 |
Embedding invariants
Embedding label | 1403.2 | ||
Root | \(0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2160.1403 |
Dual form | 2160.1.be.a.1187.2 |
$q$-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 \(\left(\mathbb{Z}/2160\mathbb{Z}\right)^\times\).
\(n\) | \(271\) | \(1297\) | \(1621\) | \(2081\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
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 | 0 | ||||||||
\(4\) | − | 1.00000i | − | 1.00000i | ||||||
\(5\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(8\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − | 1.00000i | − | 1.00000i | ||||||
\(11\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −1.00000 | ||||||||
\(17\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | 0.258819 | − | 0.965926i | \(-0.416667\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(20\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | 1.00000 | ||||||||
\(23\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 1.00000i | − | 1.00000i | ||||||
\(26\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.00000i | 1.00000i | 0.866025 | + | 0.500000i | \(0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.00000 | −1.00000 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.00000 | −1.00000 | ||||||||
\(41\) | −1.41421 | −1.41421 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.00000 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(44\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.00000i | 1.00000i | ||||||||
\(47\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000i | 1.00000i | ||||||||
\(50\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 1.00000i | − | 1.00000i | ||||||
\(53\) | −1.41421 | −1.41421 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.00000 | 1.00000 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 1.00000i | − | 1.00000i | ||||||
\(59\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | 1.00000i | \(0.5\pi\) | ||
−1.00000 | \(\pi\) | |||||||||
\(62\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000i | 1.00000i | ||||||||
\(65\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.00000 | −2.00000 | −1.00000 | \(\pi\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(68\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.00000 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(80\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(83\) | −1.41421 | −1.41421 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.00000 | −1.00000 | ||||||||
\(86\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 1.00000i | − | 1.00000i | ||||||
\(89\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 1.00000i | − | 1.00000i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | − | 1.00000i | \(-0.5\pi\) | |
1.00000 | \(0\) | |||||||||
\(98\) | 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 | \(-0.583333\pi\) |
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | 1.00000 | \(0\) | ||
1.00000i | \(0.5\pi\) | |||||||||
\(104\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | 1.00000 | \(0\) | ||
1.00000i | \(0.5\pi\) | |||||||||
\(110\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.00000i | 1.00000i | ||||||||
\(116\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 1.41421i | 1.41421i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.00000 | 1.00000 | ||||||||
\(125\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | 1.00000 | \(0\) | ||
1.00000i | \(0.5\pi\) | |||||||||
\(128\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | − | 1.00000i | − | 1.00000i | ||||||
\(131\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1.41421 | + | 1.41421i | −1.41421 | + | 1.41421i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.00000i | 1.00000i | ||||||||
\(137\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 1.00000i | − | 1.00000i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.00000i | 1.00000i | 0.866025 | + | 0.500000i | \(0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(158\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.00000i | 1.00000i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 1.00000i | − | 1.00000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(164\) | 1.41421i | 1.41421i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(167\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 1.00000i | − | 1.00000i | ||||||
\(173\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.41421 | + | 1.41421i | 1.41421 | + | 1.41421i | 0.707107 | + | 0.707107i | \(0.250000\pi\) |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.00000 | 1.00000 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 1.00000i | − | 1.00000i | ||||||
\(188\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(194\) | − | 1.41421i | − | 1.41421i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 1.00000 | ||||||||
\(197\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 1.00000i | − | 1.00000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(200\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 1.00000i | − | 1.00000i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(206\) | 1.41421 | 1.41421 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.00000 | −1.00000 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | − | 1.00000i | \(-0.5\pi\) | |
−1.00000 | \(\pi\) | |||||||||
\(212\) | 1.41421i | 1.41421i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1.41421 | 1.41421 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − | 1.00000i | − | 1.00000i | ||||||
\(221\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − | 1.00000i | − | 1.00000i | ||||||
\(227\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | 1.00000i | \(0.5\pi\) | ||
−1.00000 | \(\pi\) | |||||||||
\(230\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.00000 | −1.00000 | ||||||||
\(233\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 1.00000i | − | 1.00000i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.00000 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(245\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.00000 | −1.00000 | ||||||||
\(251\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.00000 | −1.00000 | ||||||||
\(254\) | 1.41421 | 1.41421 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 1.00000 | ||||||||
\(257\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | 0.258819 | − | 0.965926i | \(-0.416667\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.00000i | 1.00000i | ||||||||
\(263\) | −1.41421 | + | 1.41421i | −1.41421 | + | 1.41421i | −0.707107 | + | 0.707107i | \(0.750000\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.00000i | 2.00000i | ||||||||
\(269\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(272\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.41421 | 1.41421 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.00000 | 1.00000 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.00000 | 1.00000 | ||||||||
\(299\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.41421i | 1.41421i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.00000 | 1.00000 | ||||||||
\(311\) | 1.41421i | 1.41421i | 0.707107 | + | 0.707107i | \(0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | − | 1.00000i | \(-0.5\pi\) | |
1.00000 | \(0\) | |||||||||
\(314\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 1.00000i | − | 1.00000i | ||||||
\(317\) | −1.41421 | −1.41421 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.00000 | 1.00000 | ||||||||
\(320\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 1.00000i | − | 1.00000i | ||||||
\(326\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(332\) | 1.41421i | 1.41421i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.41421 | + | 1.41421i | −1.41421 | + | 1.41421i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | − | 1.00000i | \(-0.5\pi\) | |
1.00000 | \(0\) | |||||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.00000i | 1.00000i | ||||||||
\(341\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.41421 | −1.41421 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.00000 | −1.00000 | ||||||||
\(353\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.00000 | 2.00000 | ||||||||
\(359\) | 1.41421 | 1.41421 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000i | 1.00000i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(368\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 1.00000i | − | 1.00000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(374\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.00000 | −1.00000 | ||||||||
\(377\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(389\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.00000 | 1.00000 | ||||||||
\(392\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 1.00000i | − | 1.00000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(398\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000i | 1.00000i | ||||||||
\(401\) | 1.41421i | 1.41421i | 0.707107 | + | 0.707107i | \(0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.00000i | 1.00000i | ||||||||
\(404\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(410\) | 1.41421i | 1.41421i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(416\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | 0.258819 | − | 0.965926i | \(-0.416667\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | 1.00000 | \(0\) | ||
1.00000i | \(0.5\pi\) | |||||||||
\(422\) | −1.41421 | −1.41421 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(425\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − | 1.00000i | − | 1.00000i | ||||||
\(431\) | −1.41421 | −1.41421 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | − | 1.00000i | \(-0.5\pi\) | |
−1.00000 | \(\pi\) | |||||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 2.00000i | − | 2.00000i | − | 1.00000i | \(-0.5\pi\) | |||
− | 1.00000i | \(-0.5\pi\) | ||||||||
\(440\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.00000 | −1.00000 | ||||||||
\(443\) | − | 1.41421i | − | 1.41421i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(452\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | − | 1.00000i | \(-0.5\pi\) | |
−1.00000 | \(\pi\) | |||||||||
\(458\) | 1.41421i | 1.41421i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.00000 | 1.00000 | ||||||||
\(461\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | 1.00000i | \(0.5\pi\) | ||
−1.00000 | \(\pi\) | |||||||||
\(464\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 1.41421i | − | 1.41421i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 1.41421i | − | 1.41421i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 1.41421i | − | 1.41421i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(488\) | 1.41421 | 1.41421 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.00000 | 1.00000 | ||||||||
\(491\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.00000 | −1.00000 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 1.00000i | − | 1.00000i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | − | 1.00000i | \(-0.5\pi\) | |
1.00000 | \(0\) | |||||||||
\(500\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.00000 | 1.00000 | ||||||||
\(503\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 1.00000i | − | 1.00000i | ||||||
\(506\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(509\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.00000 | −1.00000 | ||||||||
\(515\) | 1.41421 | 1.41421 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.00000 | 1.00000 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.00000 | −1.00000 | ||||||||
\(521\) | −1.41421 | −1.41421 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(524\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.00000i | 2.00000i | ||||||||
\(527\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0 | 0 | ||||||||
\(530\) | 1.41421i | 1.41421i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.41421 | −1.41421 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.41421 | + | 1.41421i | 1.41421 | + | 1.41421i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.00000i | 1.00000i | ||||||||
\(539\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.00000 | 1.00000 | ||||||||
\(545\) | 1.41421 | 1.41421 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.00000 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | − | 1.00000i | − | 1.00000i | ||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.41421 | 1.41421 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.00000 | 1.00000 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(563\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 1.00000i | − | 1.00000i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | 1.00000i | \(0.5\pi\) | ||
−1.00000 | \(\pi\) | |||||||||
\(572\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.00000 | −1.00000 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.41421 | −1.41421 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.00000i | 1.00000i | ||||||||
\(599\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 1.00000i | − | 1.00000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.00000i | 1.00000i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | − | 1.00000i | \(-0.5\pi\) | |
−1.00000 | \(\pi\) | |||||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(611\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 1.00000i | − | 1.00000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(614\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | − | 1.00000i | \(-0.5\pi\) | |
−1.00000 | \(\pi\) | |||||||||
\(620\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.00000 | −1.00000 | ||||||||
\(626\) | − | 1.41421i | − | 1.41421i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.00000 | 1.00000 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 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 | ||||||||
\(634\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(635\) | 1.41421 | 1.41421 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.00000i | 1.00000i | ||||||||
\(638\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.00000 | 1.00000 | ||||||||
\(641\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.00000i | 1.00000i | 0.866025 | + | 0.500000i | \(0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.00000 | −1.00000 | ||||||||
\(653\) | 1.41421i | 1.41421i | 0.707107 | + | 0.707107i | \(0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.00000i | 1.00000i | ||||||||
\(656\) | 1.41421 | 1.41421 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.41421 | − | 1.41421i | −1.41421 | − | 1.41421i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
−0.707107 | − | 0.707107i | \(-0.750000\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | − | 1.00000i | \(-0.5\pi\) | |
−1.00000 | \(\pi\) | |||||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.00000i | 1.00000i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2.00000i | 2.00000i | ||||||||
\(671\) | −1.41421 | −1.41421 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | 1.00000 | \(0\) | ||
1.00000i | \(0.5\pi\) | |||||||||
\(674\) | − | 1.41421i | − | 1.41421i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.00000i | 1.00000i | ||||||||
\(683\) | − | 1.41421i | − | 1.41421i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.00000 | −1.00000 | ||||||||
\(689\) | −1.41421 | −1.41421 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 1.00000i | − | 1.00000i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | 1.00000i | \(0.5\pi\) | ||
−1.00000 | \(\pi\) | |||||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.00000 | 1.00000 | ||||||||
\(716\) | 1.41421 | − | 1.41421i | 1.41421 | − | 1.41421i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(719\) | − | 1.41421i | − | 1.41421i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | 1.00000i | \(0.5\pi\) | ||
−1.00000 | \(\pi\) | |||||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 1.00000i | − | 1.00000i | ||||||
\(737\) | −1.41421 | − | 1.41421i | −1.41421 | − | 1.41421i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.00000 | 1.00000 | ||||||||
\(746\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.00000 | −1.00000 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.00000i | 1.00000i | 0.866025 | + | 0.500000i | \(0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(752\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 1.00000i | − | 1.00000i | ||||||
\(755\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.41421 | 1.41421 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.00000 | 1.00000 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 1.00000i | − | 1.00000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.00000 | 1.00000 | ||||||||
\(776\) | −1.41421 | −1.41421 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.00000 | 1.00000 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 1.00000i | − | 1.00000i | ||||||
\(785\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 1.00000i | − | 1.00000i | ||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(794\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.00000 | −1.00000 | ||||||||
\(797\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.00000 | −1.00000 | ||||||||
\(800\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.00000 | −1.00000 | ||||||||
\(809\) | − | 1.41421i | − | 1.41421i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(821\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(824\) | − | 1.41421i | − | 1.41421i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(830\) | 1.41421i | 1.41421i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.00000i | 1.00000i | ||||||||
\(833\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.00000 | −1.00000 | ||||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0 | 0 | ||||||||
\(842\) | 1.41421 | 1.41421 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.41421 | 1.41421 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.00000i | 1.00000i | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.00000i | 1.00000i | 0.866025 | + | 0.500000i | \(0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | − | 1.00000i | \(-0.5\pi\) | |
−1.00000 | \(\pi\) | |||||||||
\(860\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(863\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.41421 | −1.41421 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.00000 | −2.00000 | ||||||||
\(872\) | − | 1.41421i | − | 1.41421i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 1.00000i | − | 1.00000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(878\) | −1.41421 | − | 1.41421i | −1.41421 | − | 1.41421i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.00000 | −1.00000 | ||||||||
\(881\) | 1.41421i | 1.41421i | 0.707107 | + | 0.707107i | \(0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(884\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(887\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | 0.258819 | − | 0.965926i | \(-0.416667\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.00000 | 2.00000 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(902\) | −1.41421 | −1.41421 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.00000 | −1.00000 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.00000i | 1.00000i | 0.866025 | + | 0.500000i | \(0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.41421 | 1.41421 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(914\) | −1.41421 | −1.41421 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.00000i | 1.00000i | 0.866025 | + | 0.500000i | \(0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(920\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1.41421i | 1.41421i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.00000i | 1.00000i | ||||||||
\(929\) | −1.41421 | −1.41421 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(935\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.00000 | −1.00000 | ||||||||
\(941\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.00000 | 1.00000 | ||||||||
\(947\) | 1.41421i | 1.41421i | 0.707107 | + | 0.707107i | \(0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0 | 0 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 1.00000i | − | 1.00000i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(971\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | 0.258819 | − | 0.965926i | \(-0.416667\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(977\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1.00000i | − | 1.00000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(992\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.00000 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(998\) | − | 1.41421i | − | 1.41421i | ||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2160.1.be.a.1403.2 | yes | 4 | |
3.2 | odd | 2 | inner | 2160.1.be.a.1403.1 | yes | 4 | |
5.2 | odd | 4 | 2160.1.ba.a.107.2 | yes | 4 | ||
15.2 | even | 4 | 2160.1.ba.a.107.1 | ✓ | 4 | ||
16.3 | odd | 4 | 2160.1.ba.a.323.1 | yes | 4 | ||
48.35 | even | 4 | 2160.1.ba.a.323.2 | yes | 4 | ||
80.67 | even | 4 | inner | 2160.1.be.a.1187.1 | yes | 4 | |
240.227 | odd | 4 | inner | 2160.1.be.a.1187.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2160.1.ba.a.107.1 | ✓ | 4 | 15.2 | even | 4 | ||
2160.1.ba.a.107.2 | yes | 4 | 5.2 | odd | 4 | ||
2160.1.ba.a.323.1 | yes | 4 | 16.3 | odd | 4 | ||
2160.1.ba.a.323.2 | yes | 4 | 48.35 | even | 4 | ||
2160.1.be.a.1187.1 | yes | 4 | 80.67 | even | 4 | inner | |
2160.1.be.a.1187.2 | yes | 4 | 240.227 | odd | 4 | inner | |
2160.1.be.a.1403.1 | yes | 4 | 3.2 | odd | 2 | inner | |
2160.1.be.a.1403.2 | yes | 4 | 1.1 | even | 1 | trivial |