Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1296,1,Mod(53,1296)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1296, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 10]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1296.53");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1296 = 2^{4} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1296.x (of order \(12\), degree \(4\), not 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: | \(0.646788256372\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 432) |
Projective image: | \(S_{4}\) |
Projective field: | Galois closure of 4.2.55296.2 |
Embedding invariants
Embedding label | 53.2 | ||
Root | \(-0.965926 - 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1296.53 |
Dual form | 1296.1.x.a.269.2 |
$q$-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 \(\left(\mathbb{Z}/1296\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(1135\) | \(1217\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.965926 | + | 0.258819i | 0.965926 | + | 0.258819i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(5\) | −0.258819 | − | 0.965926i | −0.258819 | − | 0.965926i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | − | 1.00000i | \(-0.5\pi\) | |
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(8\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − | 1.00000i | − | 1.00000i | ||||||
\(11\) | −0.965926 | − | 0.258819i | −0.965926 | − | 0.258819i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.366025 | − | 1.36603i | −0.366025 | − | 1.36603i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
0.500000 | − | 0.866025i | \(-0.333333\pi\) | |||||||
\(14\) | 0.965926 | − | 0.258819i | 0.965926 | − | 0.258819i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(17\) | 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 | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(20\) | 0.258819 | − | 0.965926i | 0.258819 | − | 0.965926i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(23\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 1.41421i | − | 1.41421i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.00000 | 1.00000 | ||||||||
\(29\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(32\) | 0.258819 | + | 0.965926i | 0.258819 | + | 0.965926i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.366025 | + | 1.36603i | −0.366025 | + | 1.36603i | ||||
\(35\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(41\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.366025 | + | 1.36603i | −0.366025 | + | 1.36603i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(44\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.22474 | + | 0.707107i | −1.22474 | + | 0.707107i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.366025 | − | 1.36603i | 0.366025 | − | 1.36603i | ||||
\(53\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.00000i | 1.00000i | ||||||||
\(56\) | 0.965926 | + | 0.258819i | 0.965926 | + | 0.258819i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(62\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000i | 1.00000i | ||||||||
\(65\) | −1.22474 | + | 0.707107i | −1.22474 | + | 0.707107i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.366025 | + | 1.36603i | 0.366025 | + | 1.36603i | 0.866025 | + | 0.500000i | \(0.166667\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(68\) | −0.707107 | + | 1.22474i | −0.707107 | + | 1.22474i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(71\) | 1.41421 | 1.41421 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 1.00000i | − | 1.00000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.965926 | + | 0.258819i | −0.965926 | + | 0.258819i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(80\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.258819 | − | 0.965926i | 0.258819 | − | 0.965926i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
0.965926 | − | 0.258819i | \(-0.0833333\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.36603 | − | 0.366025i | 1.36603 | − | 0.366025i | ||||
\(86\) | −0.707107 | + | 1.22474i | −0.707107 | + | 1.22474i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(89\) | −1.41421 | −1.41421 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.36603 | + | 0.366025i | −1.36603 | + | 0.366025i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.965926 | + | 0.258819i | 0.965926 | + | 0.258819i | 0.707107 | − | 0.707107i | \(-0.250000\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(104\) | 0.707107 | − | 1.22474i | 0.707107 | − | 1.22474i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(107\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(110\) | −0.258819 | + | 0.965926i | −0.258819 | + | 0.965926i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(113\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.707107 | + | 1.22474i | 0.707107 | + | 1.22474i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(125\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(128\) | −0.258819 | + | 0.965926i | −0.258819 | + | 0.965926i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.36603 | + | 0.366025i | −1.36603 | + | 0.366025i | ||||
\(131\) | −0.965926 | + | 0.258819i | −0.965926 | + | 0.258819i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.41421i | 1.41421i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(137\) | −0.707107 | − | 1.22474i | −0.707107 | − | 1.22474i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
0.258819 | − | 0.965926i | \(-0.416667\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(140\) | −0.258819 | − | 0.965926i | −0.258819 | − | 0.965926i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.36603 | + | 0.366025i | 1.36603 | + | 0.366025i | ||||
\(143\) | 1.41421i | 1.41421i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.258819 | − | 0.965926i | 0.258819 | − | 0.965926i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.258819 | + | 0.965926i | 0.258819 | + | 0.965926i | 0.965926 | + | 0.258819i | \(0.0833333\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.00000 | −1.00000 | ||||||||
\(155\) | 0.965926 | + | 0.258819i | 0.965926 | + | 0.258819i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | 1.00000i | \(0.5\pi\) | ||
−1.00000 | \(\pi\) | |||||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(167\) | 0.707107 | − | 1.22474i | 0.707107 | − | 1.22474i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
0.965926 | − | 0.258819i | \(-0.0833333\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(170\) | 1.41421 | 1.41421 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(173\) | 0.258819 | − | 0.965926i | 0.258819 | − | 0.965926i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
0.965926 | − | 0.258819i | \(-0.0833333\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.258819 | − | 0.965926i | −0.258819 | − | 0.965926i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.36603 | − | 0.366025i | −1.36603 | − | 0.366025i | ||||
\(179\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | 0.258819 | − | 0.965926i | \(-0.416667\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(182\) | −0.707107 | − | 1.22474i | −0.707107 | − | 1.22474i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.366025 | − | 1.36603i | 0.366025 | − | 1.36603i | ||||
\(188\) | −1.41421 | −1.41421 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.22474 | − | 0.707107i | 1.22474 | − | 0.707107i | 0.258819 | − | 0.965926i | \(-0.416667\pi\) |
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(194\) | −0.258819 | − | 0.965926i | −0.258819 | − | 0.965926i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 1.00000i | − | 1.00000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(212\) | 0.965926 | − | 0.258819i | 0.965926 | − | 0.258819i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(215\) | 1.41421 | 1.41421 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.00000i | 1.00000i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(221\) | 1.93185 | − | 0.517638i | 1.93185 | − | 0.517638i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(224\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.36603 | + | 0.366025i | −1.36603 | + | 0.366025i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.41421 | 1.41421 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.366025 | + | 1.36603i | 0.366025 | + | 1.36603i | ||||
\(239\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −0.965926 | + | 0.258819i | −0.965926 | + | 0.258819i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(251\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −0.965926 | − | 0.258819i | −0.965926 | − | 0.258819i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(257\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −1.41421 | −1.41421 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.00000 | −1.00000 | ||||||||
\(263\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.366025 | + | 1.36603i | −0.366025 | + | 1.36603i | ||||
\(269\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.00000 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(272\) | −1.22474 | + | 0.707107i | −1.22474 | + | 0.707107i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.366025 | − | 1.36603i | −0.366025 | − | 1.36603i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | − | 1.00000i | − | 1.00000i | ||||||
\(281\) | 0.707107 | + | 1.22474i | 0.707107 | + | 1.22474i | 0.965926 | + | 0.258819i | \(0.0833333\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(284\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.366025 | + | 1.36603i | −0.366025 | + | 1.36603i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.00000 | −1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(293\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.00000i | 1.00000i | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.366025 | + | 1.36603i | 0.366025 | + | 1.36603i | ||||
\(302\) | −0.965926 | + | 0.258819i | −0.965926 | + | 0.258819i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | − | 1.00000i | \(-0.5\pi\) | |
1.00000 | \(0\) | |||||||||
\(308\) | −0.965926 | − | 0.258819i | −0.965926 | − | 0.258819i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(311\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | − | 1.00000i | \(-0.5\pi\) | |
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.258819 | + | 0.965926i | −0.258819 | + | 0.965926i | 0.707107 | + | 0.707107i | \(0.250000\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0.965926 | − | 0.258819i | 0.965926 | − | 0.258819i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.22474 | + | 0.707107i | −1.22474 | + | 0.707107i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.707107 | + | 1.22474i | −0.707107 | + | 1.22474i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.366025 | − | 1.36603i | 0.366025 | − | 1.36603i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(332\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(335\) | 1.22474 | − | 0.707107i | 1.22474 | − | 0.707107i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(338\) | −0.965926 | + | 0.258819i | −0.965926 | + | 0.258819i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.36603 | + | 0.366025i | 1.36603 | + | 0.366025i | ||||
\(341\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 1.00000i | ||||||||
\(344\) | −1.22474 | + | 0.707107i | −1.22474 | + | 0.707107i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(347\) | 0.258819 | + | 0.965926i | 0.258819 | + | 0.965926i | 0.965926 | + | 0.258819i | \(0.0833333\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 1.00000i | − | 1.00000i | ||||||
\(353\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.366025 | − | 1.36603i | −0.366025 | − | 1.36603i | ||||
\(356\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(359\) | −1.41421 | −1.41421 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000i | 1.00000i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.366025 | − | 1.36603i | −0.366025 | − | 1.36603i | ||||
\(365\) | −0.965926 | + | 0.258819i | −0.965926 | + | 0.258819i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.258819 | − | 0.965926i | 0.258819 | − | 0.965926i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.36603 | + | 0.366025i | −1.36603 | + | 0.366025i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(374\) | 0.707107 | − | 1.22474i | 0.707107 | − | 1.22474i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.36603 | − | 0.366025i | −1.36603 | − | 0.366025i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 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 | ||||||||
\(382\) | 1.36603 | − | 0.366025i | 1.36603 | − | 0.366025i | ||||
\(383\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(386\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 1.00000i | − | 1.00000i | ||||||
\(389\) | 0.965926 | + | 0.258819i | 0.965926 | + | 0.258819i | 0.707107 | − | 0.707107i | \(-0.250000\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | − | 1.00000i | \(-0.5\pi\) | |
1.00000 | \(0\) | |||||||||
\(398\) | 0.258819 | − | 0.965926i | 0.258819 | − | 0.965926i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.36603 | + | 0.366025i | 1.36603 | + | 0.366025i | ||||
\(404\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | 0.866025 | − | 0.500000i | \(-0.166667\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.00000 | −1.00000 | ||||||||
\(416\) | 1.22474 | − | 0.707107i | 1.22474 | − | 0.707107i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.00000 | 1.00000 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −0.965926 | + | 0.258819i | −0.965926 | + | 0.258819i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.36603 | + | 0.366025i | 1.36603 | + | 0.366025i | ||||
\(431\) | − | 1.41421i | − | 1.41421i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(434\) | −0.258819 | + | 0.965926i | −0.258819 | + | 0.965926i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(440\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.00000 | 2.00000 | ||||||||
\(443\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.366025 | + | 1.36603i | 0.366025 | + | 1.36603i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(449\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.707107 | + | 1.22474i | −0.707107 | + | 1.22474i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | − | 1.00000i | \(-0.5\pi\) | |
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(458\) | −1.41421 | −1.41421 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.258819 | − | 0.965926i | 0.258819 | − | 0.965926i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
0.965926 | − | 0.258819i | \(-0.0833333\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.36603 | + | 0.366025i | 1.36603 | + | 0.366025i | ||||
\(467\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | 0.258819 | − | 0.965926i | \(-0.416667\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(470\) | 0.707107 | + | 1.22474i | 0.707107 | + | 1.22474i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.707107 | − | 1.22474i | 0.707107 | − | 1.22474i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.41421i | 1.41421i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.22474 | + | 0.707107i | −1.22474 | + | 0.707107i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 2.00000i | − | 2.00000i | − | 1.00000i | \(-0.5\pi\) | |||
− | 1.00000i | \(-0.5\pi\) | ||||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.258819 | − | 0.965926i | −0.258819 | − | 0.965926i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.00000 | −1.00000 | ||||||||
\(497\) | 1.22474 | − | 0.707107i | 1.22474 | − | 0.707107i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.366025 | − | 1.36603i | −0.366025 | − | 1.36603i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
0.500000 | − | 0.866025i | \(-0.333333\pi\) | |||||||
\(500\) | −0.258819 | − | 0.965926i | −0.258819 | − | 0.965926i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 1.00000i | − | 1.00000i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(509\) | −0.965926 | + | 0.258819i | −0.965926 | + | 0.258819i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(512\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.36603 | − | 0.366025i | 1.36603 | − | 0.366025i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.36603 | − | 0.366025i | −1.36603 | − | 0.366025i | ||||
\(521\) | −1.41421 | −1.41421 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | 1.00000 | \(0\) | ||
1.00000i | \(0.5\pi\) | |||||||||
\(524\) | −0.965926 | − | 0.258819i | −0.965926 | − | 0.258819i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(530\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(536\) | −0.707107 | + | 1.22474i | −0.707107 | + | 1.22474i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(542\) | 0.965926 | + | 0.258819i | 0.965926 | + | 0.258819i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.36603 | + | 0.366025i | −1.36603 | + | 0.366025i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.36603 | − | 0.366025i | −1.36603 | − | 0.366025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(548\) | − | 1.41421i | − | 1.41421i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.00000 | 2.00000 | ||||||||
\(560\) | 0.258819 | − | 0.965926i | 0.258819 | − | 0.965926i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.366025 | + | 1.36603i | 0.366025 | + | 1.36603i | ||||
\(563\) | 0.965926 | − | 0.258819i | 0.965926 | − | 0.258819i | 0.258819 | − | 0.965926i | \(-0.416667\pi\) |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(569\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.36603 | + | 0.366025i | −1.36603 | + | 0.366025i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(572\) | −0.707107 | + | 1.22474i | −0.707107 | + | 1.22474i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(578\) | −0.965926 | − | 0.258819i | −0.965926 | − | 0.258819i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.258819 | − | 0.965926i | −0.258819 | − | 0.965926i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(584\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.965926 | + | 0.258819i | 0.965926 | + | 0.258819i | 0.707107 | − | 0.707107i | \(-0.250000\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.41421i | 1.41421i | 0.707107 | + | 0.707107i | \(0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(596\) | −0.258819 | + | 0.965926i | −0.258819 | + | 0.965926i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.707107 | + | 1.22474i | −0.707107 | + | 1.22474i | 0.258819 | + | 0.965926i | \(0.416667\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(602\) | 1.41421i | 1.41421i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.00000 | −1.00000 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.00000 | − | 1.73205i | 1.00000 | − | 1.73205i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
0.500000 | − | 0.866025i | \(-0.333333\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.41421 | + | 1.41421i | 1.41421 | + | 1.41421i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | − | 1.00000i | \(-0.5\pi\) | |
−1.00000 | \(\pi\) | |||||||||
\(614\) | 1.22474 | − | 0.707107i | 1.22474 | − | 0.707107i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(617\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.366025 | + | 1.36603i | −0.366025 | + | 1.36603i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(620\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.22474 | + | 0.707107i | −1.22474 | + | 0.707107i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(626\) | 0.965926 | − | 0.258819i | 0.965926 | − | 0.258819i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 1.00000i | − | 1.00000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(635\) | 0.258819 | + | 0.965926i | 0.258819 | + | 0.965926i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.00000 | 1.00000 | ||||||||
\(641\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.36603 | + | 0.366025i | −1.36603 | + | 0.366025i | ||||
\(653\) | 0.965926 | − | 0.258819i | 0.965926 | − | 0.258819i | 0.258819 | − | 0.965926i | \(-0.416667\pi\) |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(659\) | −0.258819 | + | 0.965926i | −0.258819 | + | 0.965926i | 0.707107 | + | 0.707107i | \(0.250000\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(662\) | 0.707107 | − | 1.22474i | 0.707107 | − | 1.22474i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 1.22474 | − | 0.707107i | 1.22474 | − | 0.707107i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.36603 | − | 0.366025i | 1.36603 | − | 0.366025i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.00000 | −1.00000 | ||||||||
\(677\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(680\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(683\) | 1.41421 | − | 1.41421i | 1.41421 | − | 1.41421i | 0.707107 | − | 0.707107i | \(-0.250000\pi\) |
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(686\) | −0.258819 | + | 0.965926i | −0.258819 | + | 0.965926i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.36603 | + | 0.366025i | −1.36603 | + | 0.366025i | ||||
\(689\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(692\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.00000i | 1.00000i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | 0.258819 | − | 0.965926i | \(-0.416667\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0.258819 | − | 0.965926i | 0.258819 | − | 0.965926i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.965926 | − | 0.258819i | 0.965926 | − | 0.258819i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(710\) | − | 1.41421i | − | 1.41421i | ||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.36603 | − | 0.366025i | 1.36603 | − | 0.366025i | ||||
\(716\) | −0.258819 | − | 0.965926i | −0.258819 | − | 0.965926i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.36603 | − | 0.366025i | −1.36603 | − | 0.366025i | ||||
\(719\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −0.258819 | + | 0.965926i | −0.258819 | + | 0.965926i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | − | 1.00000i | \(-0.5\pi\) | |
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(728\) | − | 1.41421i | − | 1.41421i | ||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.00000 | −1.00000 | ||||||||
\(731\) | −1.93185 | − | 0.517638i | −1.93185 | − | 0.517638i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(734\) | 0.258819 | + | 0.965926i | 0.258819 | + | 0.965926i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 1.41421i | − | 1.41421i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | 1.00000i | \(0.5\pi\) | ||
−1.00000 | \(\pi\) | |||||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(743\) | 0.707107 | − | 1.22474i | 0.707107 | − | 1.22474i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
0.965926 | − | 0.258819i | \(-0.0833333\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(746\) | −1.41421 | −1.41421 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(749\) | −0.258819 | + | 0.965926i | −0.258819 | + | 0.965926i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(752\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | − | 1.00000i | \(-0.5\pi\) | |
−1.00000 | \(\pi\) | |||||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 1.41421 | 1.41421 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(770\) | 0.258819 | + | 0.965926i | 0.258819 | + | 0.965926i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(773\) | −1.41421 | + | 1.41421i | −1.41421 | + | 1.41421i | −0.707107 | + | 0.707107i | \(0.750000\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0.258819 | − | 0.965926i | 0.258819 | − | 0.965926i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.36603 | − | 0.366025i | −1.36603 | − | 0.366025i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(788\) | 0.965926 | − | 0.258819i | 0.965926 | − | 0.258819i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 1.22474 | − | 0.707107i | 1.22474 | − | 0.707107i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(797\) | −0.965926 | + | 0.258819i | −0.965926 | + | 0.258819i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.258819 | + | 0.965926i | −0.258819 | + | 0.965926i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(809\) | 1.41421 | 1.41421 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.93185 | − | 0.517638i | −1.93185 | − | 0.517638i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
−0.965926 | − | 0.258819i | \(-0.916667\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | 0.866025 | − | 0.500000i | \(-0.166667\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | 1.00000i | \(0.5\pi\) | ||
−1.00000 | \(\pi\) | |||||||||
\(830\) | −0.965926 | − | 0.258819i | −0.965926 | − | 0.258819i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.36603 | − | 0.366025i | 1.36603 | − | 0.366025i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.36603 | − | 0.366025i | −1.36603 | − | 0.366025i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −0.707107 | − | 1.22474i | −0.707107 | − | 1.22474i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
0.258819 | − | 0.965926i | \(-0.416667\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0.965926 | + | 0.258819i | 0.965926 | + | 0.258819i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.366025 | − | 1.36603i | 0.366025 | − | 1.36603i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.00000 | −1.00000 | ||||||||
\(857\) | −0.707107 | − | 1.22474i | −0.707107 | − | 1.22474i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
0.258819 | − | 0.965926i | \(-0.416667\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(860\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.366025 | − | 1.36603i | 0.366025 | − | 1.36603i | ||||
\(863\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.00000 | −1.00000 | ||||||||
\(866\) | −0.965926 | − | 0.258819i | −0.965926 | − | 0.258819i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.73205 | − | 1.00000i | 1.73205 | − | 1.00000i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.965926 | − | 0.258819i | −0.965926 | − | 0.258819i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.366025 | + | 1.36603i | 0.366025 | + | 1.36603i | 0.866025 | + | 0.500000i | \(0.166667\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(878\) | −0.965926 | + | 0.258819i | −0.965926 | + | 0.258819i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(881\) | − | 1.41421i | − | 1.41421i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(884\) | 1.93185 | + | 0.517638i | 1.93185 | + | 0.517638i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0.707107 | − | 1.22474i | 0.707107 | − | 1.22474i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
0.965926 | − | 0.258819i | \(-0.0833333\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(890\) | 1.41421i | 1.41421i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(896\) | 0.258819 | + | 0.965926i | 0.258819 | + | 0.965926i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(911\) | 1.22474 | − | 0.707107i | 1.22474 | − | 0.707107i | 0.258819 | − | 0.965926i | \(-0.416667\pi\) |
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(914\) | 0.965926 | − | 0.258819i | 0.965926 | − | 0.258819i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.36603 | − | 0.366025i | −1.36603 | − | 0.366025i | ||||
\(917\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.00000i | 1.00000i | 0.866025 | + | 0.500000i | \(0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(923\) | −0.517638 | − | 1.93185i | −0.517638 | − | 1.93185i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(935\) | −1.41421 | −1.41421 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.00000i | 1.00000i | 0.866025 | + | 0.500000i | \(0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(938\) | 0.707107 | + | 1.22474i | 0.707107 | + | 1.22474i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.366025 | + | 1.36603i | 0.366025 | + | 1.36603i | ||||
\(941\) | 0.965926 | − | 0.258819i | 0.965926 | − | 0.258819i | 0.258819 | − | 0.965926i | \(-0.416667\pi\) |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(947\) | −0.258819 | + | 0.965926i | −0.258819 | + | 0.965926i | 0.707107 | + | 0.707107i | \(0.250000\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.36603 | + | 0.366025i | −1.36603 | + | 0.366025i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.366025 | + | 1.36603i | −0.366025 | + | 1.36603i | ||||
\(953\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.36603 | + | 0.366025i | −1.36603 | + | 0.366025i | ||||
\(959\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0 | 0 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.965926 | − | 0.258819i | −0.965926 | − | 0.258819i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | − | 1.00000i | \(-0.5\pi\) | |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(971\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0.517638 | − | 1.93185i | 0.517638 | − | 1.93185i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.36603 | + | 0.366025i | 1.36603 | + | 0.366025i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 1.00000i | − | 1.00000i | ||||||
\(983\) | −0.707107 | − | 1.22474i | −0.707107 | − | 1.22474i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
0.258819 | − | 0.965926i | \(-0.416667\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(992\) | −0.965926 | − | 0.258819i | −0.965926 | − | 0.258819i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.36603 | − | 0.366025i | 1.36603 | − | 0.366025i | ||||
\(995\) | −0.965926 | + | 0.258819i | −0.965926 | + | 0.258819i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.366025 | + | 1.36603i | −0.366025 | + | 1.36603i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(998\) | − | 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 | 1296.1.x.a.53.2 | 8 | ||
3.2 | odd | 2 | inner | 1296.1.x.a.53.1 | 8 | ||
9.2 | odd | 6 | inner | 1296.1.x.a.917.2 | 8 | ||
9.4 | even | 3 | 432.1.j.a.53.1 | ✓ | 4 | ||
9.5 | odd | 6 | 432.1.j.a.53.2 | yes | 4 | ||
9.7 | even | 3 | inner | 1296.1.x.a.917.1 | 8 | ||
16.13 | even | 4 | inner | 1296.1.x.a.701.2 | 8 | ||
36.23 | even | 6 | 1728.1.j.a.1457.2 | 4 | |||
36.31 | odd | 6 | 1728.1.j.a.1457.1 | 4 | |||
48.29 | odd | 4 | inner | 1296.1.x.a.701.1 | 8 | ||
72.5 | odd | 6 | 3456.1.j.b.1889.1 | 4 | |||
72.13 | even | 6 | 3456.1.j.b.1889.2 | 4 | |||
72.59 | even | 6 | 3456.1.j.a.1889.1 | 4 | |||
72.67 | odd | 6 | 3456.1.j.a.1889.2 | 4 | |||
144.5 | odd | 12 | 3456.1.j.b.161.2 | 4 | |||
144.13 | even | 12 | 432.1.j.a.269.2 | yes | 4 | ||
144.29 | odd | 12 | inner | 1296.1.x.a.269.2 | 8 | ||
144.59 | even | 12 | 3456.1.j.a.161.2 | 4 | |||
144.61 | even | 12 | inner | 1296.1.x.a.269.1 | 8 | ||
144.67 | odd | 12 | 1728.1.j.a.593.2 | 4 | |||
144.77 | odd | 12 | 432.1.j.a.269.1 | yes | 4 | ||
144.85 | even | 12 | 3456.1.j.b.161.1 | 4 | |||
144.131 | even | 12 | 1728.1.j.a.593.1 | 4 | |||
144.139 | odd | 12 | 3456.1.j.a.161.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
432.1.j.a.53.1 | ✓ | 4 | 9.4 | even | 3 | ||
432.1.j.a.53.2 | yes | 4 | 9.5 | odd | 6 | ||
432.1.j.a.269.1 | yes | 4 | 144.77 | odd | 12 | ||
432.1.j.a.269.2 | yes | 4 | 144.13 | even | 12 | ||
1296.1.x.a.53.1 | 8 | 3.2 | odd | 2 | inner | ||
1296.1.x.a.53.2 | 8 | 1.1 | even | 1 | trivial | ||
1296.1.x.a.269.1 | 8 | 144.61 | even | 12 | inner | ||
1296.1.x.a.269.2 | 8 | 144.29 | odd | 12 | inner | ||
1296.1.x.a.701.1 | 8 | 48.29 | odd | 4 | inner | ||
1296.1.x.a.701.2 | 8 | 16.13 | even | 4 | inner | ||
1296.1.x.a.917.1 | 8 | 9.7 | even | 3 | inner | ||
1296.1.x.a.917.2 | 8 | 9.2 | odd | 6 | inner | ||
1728.1.j.a.593.1 | 4 | 144.131 | even | 12 | |||
1728.1.j.a.593.2 | 4 | 144.67 | odd | 12 | |||
1728.1.j.a.1457.1 | 4 | 36.31 | odd | 6 | |||
1728.1.j.a.1457.2 | 4 | 36.23 | even | 6 | |||
3456.1.j.a.161.1 | 4 | 144.139 | odd | 12 | |||
3456.1.j.a.161.2 | 4 | 144.59 | even | 12 | |||
3456.1.j.a.1889.1 | 4 | 72.59 | even | 6 | |||
3456.1.j.a.1889.2 | 4 | 72.67 | odd | 6 | |||
3456.1.j.b.161.1 | 4 | 144.85 | even | 12 | |||
3456.1.j.b.161.2 | 4 | 144.5 | odd | 12 | |||
3456.1.j.b.1889.1 | 4 | 72.5 | odd | 6 | |||
3456.1.j.b.1889.2 | 4 | 72.13 | even | 6 |