Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [812,1,Mod(307,812)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(812, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 2, 3]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("812.307");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 812 = 2^{2} \cdot 7 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 812.l (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.405240790258\) |
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 4.2.4780244.1 |
Embedding invariants
Embedding label | 447.1 | ||
Root | \(0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 812.447 |
Dual form | 812.1.l.d.307.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/812\mathbb{Z}\right)^\times\).
\(n\) | \(407\) | \(465\) | \(785\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(3\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(4\) | − | 1.00000i | − | 1.00000i | ||||||
\(5\) | 1.00000 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(6\) | −1.00000 | −1.00000 | ||||||||
\(7\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(8\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(11\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(12\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(13\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(14\) | 1.00000i | 1.00000i | ||||||||
\(15\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(16\) | −1.00000 | −1.00000 | ||||||||
\(17\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | − | 1.00000i | \(-0.5\pi\) | |
1.00000 | \(0\) | |||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(20\) | − | 1.00000i | − | 1.00000i | ||||||
\(21\) | 1.00000 | 1.00000 | ||||||||
\(22\) | − | 1.00000i | − | 1.00000i | ||||||
\(23\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(24\) | 1.00000i | 1.00000i | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(27\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(28\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(29\) | 1.00000i | 1.00000i | ||||||||
\(30\) | −1.00000 | −1.00000 | ||||||||
\(31\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | 0.258819 | − | 0.965926i | \(-0.416667\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(32\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(33\) | −1.00000 | −1.00000 | ||||||||
\(34\) | 1.41421i | 1.41421i | ||||||||
\(35\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | 1.00000i | \(0.5\pi\) | ||
−1.00000 | \(\pi\) | |||||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(40\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(41\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | 1.00000 | \(0\) | ||
1.00000i | \(0.5\pi\) | |||||||||
\(42\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(43\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(44\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(48\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(49\) | − | 1.00000i | − | 1.00000i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.41421 | 1.41421 | ||||||||
\(52\) | 1.00000i | 1.00000i | ||||||||
\(53\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(54\) | 1.00000i | 1.00000i | ||||||||
\(55\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(56\) | 1.00000 | 1.00000 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(59\) | −1.41421 | −1.41421 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(60\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(61\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(62\) | 1.00000 | 1.00000 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000i | 1.00000i | ||||||||
\(65\) | −1.00000 | −1.00000 | ||||||||
\(66\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(67\) | −1.41421 | −1.41421 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(68\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.00000i | 1.00000i | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(74\) | − | 1.41421i | − | 1.41421i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00000i | 1.00000i | ||||||||
\(78\) | 1.00000 | 1.00000 | ||||||||
\(79\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(80\) | −1.00000 | −1.00000 | ||||||||
\(81\) | 1.00000 | 1.00000 | ||||||||
\(82\) | −1.41421 | −1.41421 | ||||||||
\(83\) | 1.41421 | 1.41421 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(84\) | − | 1.00000i | − | 1.00000i | ||||||
\(85\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(86\) | − | 1.00000i | − | 1.00000i | ||||||
\(87\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(88\) | −1.00000 | −1.00000 | ||||||||
\(89\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 1.00000i | − | 1.00000i | ||||||
\(94\) | − | 1.00000i | − | 1.00000i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000 | 1.00000 | ||||||||
\(97\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | 1.00000 | \(0\) | ||
1.00000i | \(0.5\pi\) | |||||||||
\(98\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(102\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(103\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(104\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(105\) | 1.00000 | 1.00000 | ||||||||
\(106\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(107\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(108\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(109\) | − | 1.00000i | − | 1.00000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(110\) | − | 1.00000i | − | 1.00000i | ||||||
\(111\) | −1.41421 | −1.41421 | ||||||||
\(112\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(113\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.00000 | 1.00000 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(119\) | − | 1.41421i | − | 1.41421i | ||||||
\(120\) | 1.00000i | 1.00000i | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.41421i | 1.41421i | ||||||||
\(124\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(125\) | −1.00000 | −1.00000 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(128\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(129\) | −1.00000 | −1.00000 | ||||||||
\(130\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(131\) | 1.41421 | − | 1.41421i | 1.41421 | − | 1.41421i | 0.707107 | − | 0.707107i | \(-0.250000\pi\) |
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(132\) | 1.00000i | 1.00000i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(135\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(136\) | 1.41421 | 1.41421 | ||||||||
\(137\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | 1.00000 | \(0\) | ||
1.00000i | \(0.5\pi\) | |||||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(140\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(141\) | −1.00000 | −1.00000 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.00000i | 1.00000i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(148\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(149\) | − | 1.00000i | − | 1.00000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(155\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(156\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(157\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | − | 1.00000i | \(-0.5\pi\) | |
−1.00000 | \(\pi\) | |||||||||
\(158\) | 1.00000i | 1.00000i | ||||||||
\(159\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(160\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(163\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | 0.258819 | − | 0.965926i | \(-0.416667\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(164\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(165\) | −1.00000 | −1.00000 | ||||||||
\(166\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(167\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(168\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 1.41421i | 1.41421i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(173\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(174\) | − | 1.00000i | − | 1.00000i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(177\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 1.00000i | − | 1.00000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(182\) | − | 1.00000i | − | 1.00000i | ||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(186\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(187\) | 1.41421i | 1.41421i | ||||||||
\(188\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(189\) | − | 1.00000i | − | 1.00000i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(192\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(193\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | − | 1.00000i | \(-0.5\pi\) | |
−1.00000 | \(\pi\) | |||||||||
\(194\) | −1.41421 | −1.41421 | ||||||||
\(195\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(196\) | −1.00000 | −1.00000 | ||||||||
\(197\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.41421 | 1.41421 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(204\) | − | 1.41421i | − | 1.41421i | ||||||
\(205\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.00000 | 1.00000 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(211\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(212\) | 1.00000i | 1.00000i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(216\) | 1.00000 | 1.00000 | ||||||||
\(217\) | −1.00000 | −1.00000 | ||||||||
\(218\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(221\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(222\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(223\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(224\) | − | 1.00000i | − | 1.00000i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.41421 | 1.41421 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(232\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(233\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(236\) | 1.41421i | 1.41421i | ||||||||
\(237\) | 1.00000 | 1.00000 | ||||||||
\(238\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(239\) | − | 1.41421i | − | 1.41421i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(240\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(241\) | 1.00000 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 1.00000i | − | 1.00000i | ||||||
\(246\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | − | 1.00000i | − | 1.00000i | ||||||
\(249\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(250\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(251\) | 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 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.41421 | 1.41421 | ||||||||
\(256\) | 1.00000 | 1.00000 | ||||||||
\(257\) | 1.00000i | 1.00000i | 0.866025 | + | 0.500000i | \(0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(258\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(259\) | 1.41421i | 1.41421i | ||||||||
\(260\) | 1.00000i | 1.00000i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.00000i | 2.00000i | ||||||||
\(263\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(264\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(265\) | −1.00000 | −1.00000 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.41421i | 1.41421i | ||||||||
\(269\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | 1.00000 | \(0\) | ||
1.00000i | \(0.5\pi\) | |||||||||
\(270\) | 1.00000i | 1.00000i | ||||||||
\(271\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(272\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(273\) | −1.00000 | −1.00000 | ||||||||
\(274\) | −1.41421 | −1.41421 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.00000 | 1.00000 | ||||||||
\(281\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(282\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(283\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.00000i | 1.00000i | ||||||||
\(287\) | 1.41421 | 1.41421 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 1.00000i | − | 1.00000i | ||||||
\(290\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(291\) | 1.41421i | 1.41421i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | 1.00000i | \(0.5\pi\) | ||
−1.00000 | \(\pi\) | |||||||||
\(294\) | 1.00000i | 1.00000i | ||||||||
\(295\) | −1.41421 | −1.41421 | ||||||||
\(296\) | −1.41421 | −1.41421 | ||||||||
\(297\) | 1.00000i | 1.00000i | ||||||||
\(298\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.00000i | 1.00000i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(308\) | 1.00000 | 1.00000 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.00000 | 1.00000 | ||||||||
\(311\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(312\) | − | 1.00000i | − | 1.00000i | ||||||
\(313\) | − | 1.00000i | − | 1.00000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(314\) | 1.41421 | 1.41421 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(317\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(318\) | 1.00000 | 1.00000 | ||||||||
\(319\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(320\) | 1.00000i | 1.00000i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | − | 1.00000i | − | 1.00000i | ||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.00000 | 1.00000 | ||||||||
\(327\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(328\) | 1.41421i | 1.41421i | ||||||||
\(329\) | 1.00000i | 1.00000i | ||||||||
\(330\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(331\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(332\) | − | 1.41421i | − | 1.41421i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.41421 | −1.41421 | ||||||||
\(336\) | −1.00000 | −1.00000 | ||||||||
\(337\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(341\) | 1.00000 | 1.00000 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(344\) | −1.00000 | −1.00000 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.41421 | 1.41421 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(348\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(349\) | − | 1.00000i | − | 1.00000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(352\) | 1.00000i | 1.00000i | ||||||||
\(353\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(354\) | 1.41421 | 1.41421 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 1.00000i | − | 1.00000i | ||||||
\(362\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.41421 | − | 1.41421i | −1.41421 | − | 1.41421i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
−0.707107 | − | 0.707107i | \(-0.750000\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 1.41421i | − | 1.41421i | ||||||
\(371\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(372\) | −1.00000 | −1.00000 | ||||||||
\(373\) | 1.00000 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(374\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(375\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(376\) | −1.00000 | −1.00000 | ||||||||
\(377\) | − | 1.00000i | − | 1.00000i | ||||||
\(378\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(379\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(384\) | − | 1.00000i | − | 1.00000i | ||||||
\(385\) | 1.00000i | 1.00000i | ||||||||
\(386\) | 1.41421 | 1.41421 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(389\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(390\) | 1.00000 | 1.00000 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(393\) | 2.00000 | 2.00000 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.00000i | 1.00000i | 0.866025 | + | 0.500000i | \(0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(398\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.00000 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(402\) | 1.41421 | 1.41421 | ||||||||
\(403\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 1.00000 | ||||||||
\(406\) | −1.00000 | −1.00000 | ||||||||
\(407\) | − | 1.41421i | − | 1.41421i | ||||||
\(408\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(409\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(410\) | −1.41421 | −1.41421 | ||||||||
\(411\) | 1.41421i | 1.41421i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.41421 | 1.41421 | ||||||||
\(416\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(420\) | − | 1.00000i | − | 1.00000i | ||||||
\(421\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(422\) | −1.00000 | −1.00000 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.00000 | 1.00000 | ||||||||
\(430\) | − | 1.00000i | − | 1.00000i | ||||||
\(431\) | 1.41421i | 1.41421i | 0.707107 | + | 0.707107i | \(0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(432\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(433\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | − | 1.00000i | \(-0.5\pi\) | |
−1.00000 | \(\pi\) | |||||||||
\(434\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(435\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(436\) | −1.00000 | −1.00000 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(440\) | −1.00000 | −1.00000 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 1.41421i | − | 1.41421i | ||||||
\(443\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(444\) | 1.41421i | 1.41421i | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(448\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(449\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.41421 | −1.41421 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(455\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.00000i | 2.00000i | 1.00000i | \(0.5\pi\) | ||||||
1.00000i | \(0.5\pi\) | |||||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 1.41421i | − | 1.41421i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(462\) | − | 1.00000i | − | 1.00000i | ||||||
\(463\) | 1.41421 | 1.41421 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(464\) | − | 1.00000i | − | 1.00000i | ||||||
\(465\) | − | 1.00000i | − | 1.00000i | ||||||
\(466\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(467\) | −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 | ||||
\(470\) | − | 1.00000i | − | 1.00000i | ||||||
\(471\) | − | 1.41421i | − | 1.41421i | ||||||
\(472\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(473\) | − | 1.00000i | − | 1.00000i | ||||||
\(474\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.41421 | −1.41421 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(479\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(480\) | 1.00000 | 1.00000 | ||||||||
\(481\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(482\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.41421i | 1.41421i | 0.707107 | + | 0.707107i | \(0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 1.00000i | − | 1.00000i | ||||||
\(490\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(491\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | 0.258819 | − | 0.965926i | \(-0.416667\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(492\) | 1.41421 | 1.41421 | ||||||||
\(493\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −1.41421 | −1.41421 | ||||||||
\(499\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(500\) | 1.00000i | 1.00000i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.00000 | −1.00000 | ||||||||
\(503\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 1.00000i | − | 1.00000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(510\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.00000i | 1.00000i | ||||||||
\(517\) | − | 1.00000i | − | 1.00000i | ||||||
\(518\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(521\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.41421 | 1.41421 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(524\) | −1.41421 | − | 1.41421i | −1.41421 | − | 1.41421i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 1.00000i | − | 1.00000i | ||||||
\(527\) | −1.41421 | −1.41421 | ||||||||
\(528\) | 1.00000 | 1.00000 | ||||||||
\(529\) | 1.00000 | 1.00000 | ||||||||
\(530\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1.41421 | −1.41421 | ||||||||
\(539\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(540\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(541\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(542\) | 1.00000i | 1.00000i | ||||||||
\(543\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(544\) | − | 1.41421i | − | 1.41421i | ||||||
\(545\) | − | 1.00000i | − | 1.00000i | ||||||
\(546\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(547\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(548\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 1.00000i | − | 1.00000i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.41421 | −1.41421 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(560\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(561\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(562\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(563\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(564\) | 1.00000i | 1.00000i | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | 1.00000i | \(0.5\pi\) | ||
−1.00000 | \(\pi\) | |||||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 1.41421i | − | 1.41421i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(572\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(578\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(579\) | − | 1.41421i | − | 1.41421i | ||||||
\(580\) | 1.00000 | 1.00000 | ||||||||
\(581\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(582\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(583\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 1.41421i | − | 1.41421i | ||||||
\(587\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(588\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(593\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(594\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(595\) | − | 1.41421i | − | 1.41421i | ||||||
\(596\) | −1.00000 | −1.00000 | ||||||||
\(597\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | − | 1.00000i | \(-0.5\pi\) | |
1.00000 | \(0\) | |||||||||
\(602\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.00000i | 1.00000i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 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 | \(-0.166667\pi\) | |||||||
\(614\) | −1.00000 | −1.00000 | ||||||||
\(615\) | 1.41421i | 1.41421i | ||||||||
\(616\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(617\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(620\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(625\) | −1.00000 | −1.00000 | ||||||||
\(626\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(629\) | 2.00000i | 2.00000i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(632\) | 1.00000 | 1.00000 | ||||||||
\(633\) | 1.00000i | 1.00000i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(637\) | 1.00000i | 1.00000i | ||||||||
\(638\) | 1.00000 | 1.00000 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(641\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | 1.00000 | \(0\) | ||
1.00000i | \(0.5\pi\) | |||||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 1.41421i | − | 1.41421i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.00000 | −1.00000 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.41421i | 1.41421i | 0.707107 | + | 0.707107i | \(0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(648\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(649\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(652\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(653\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | − | 1.00000i | \(-0.5\pi\) | |
1.00000 | \(0\) | |||||||||
\(654\) | 1.00000i | 1.00000i | ||||||||
\(655\) | 1.41421 | − | 1.41421i | 1.41421 | − | 1.41421i | ||||
\(656\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(659\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(660\) | 1.00000i | 1.00000i | ||||||||
\(661\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(662\) | −1.00000 | −1.00000 | ||||||||
\(663\) | −1.41421 | −1.41421 | ||||||||
\(664\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(673\) | 1.00000i | 1.00000i | 0.866025 | + | 0.500000i | \(0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.41421 | 1.41421 | ||||||||
\(680\) | 1.41421 | 1.41421 | ||||||||
\(681\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(682\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(683\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(686\) | 1.00000 | 1.00000 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(689\) | 1.00000 | 1.00000 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.00000 | −1.00000 | ||||||||
\(697\) | 2.00000 | 2.00000 | ||||||||
\(698\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(699\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.00000i | 1.00000i | 0.866025 | + | 0.500000i | \(0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(702\) | − | 1.00000i | − | 1.00000i | ||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(705\) | −1.00000 | −1.00000 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(709\) | − | 1.00000i | − | 1.00000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 1.41421i | 1.41421i | ||||||||
\(715\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(718\) | − | 1.00000i | − | 1.00000i | ||||||
\(719\) | 1.41421 | 1.41421 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(723\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(724\) | −1.00000 | −1.00000 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(728\) | −1.00000 | −1.00000 | ||||||||
\(729\) | − | 1.00000i | − | 1.00000i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.41421i | 1.41421i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | 1.00000 | \(0\) | ||
1.00000i | \(0.5\pi\) | |||||||||
\(734\) | 2.00000 | 2.00000 | ||||||||
\(735\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(740\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 1.00000i | − | 1.00000i | ||||||
\(743\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(744\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(745\) | − | 1.00000i | − | 1.00000i | ||||||
\(746\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.41421 | 1.41421 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 1.00000 | 1.00000 | ||||||||
\(751\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(752\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(753\) | 1.00000i | 1.00000i | ||||||||
\(754\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.00000 | −1.00000 | ||||||||
\(757\) | −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 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.41421 | 1.41421 | ||||||||
\(768\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(769\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | 1.00000 | \(0\) | ||
1.00000i | \(0.5\pi\) | |||||||||
\(770\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(771\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(772\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(773\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | 1.00000i | \(0.5\pi\) | ||
−1.00000 | \(\pi\) | |||||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.41421i | 1.41421i | ||||||||
\(777\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(784\) | 1.00000i | 1.00000i | ||||||||
\(785\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(786\) | −1.41421 | + | 1.41421i | −1.41421 | + | 1.41421i | ||||
\(787\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.00000 | −1.00000 | ||||||||
\(790\) | 1.00000i | 1.00000i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(795\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(796\) | − | 1.41421i | − | 1.41421i | ||||||
\(797\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | − | 1.00000i | \(-0.5\pi\) | |
1.00000 | \(0\) | |||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.41421i | 1.41421i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.00000 | −1.00000 | ||||||||
\(807\) | 1.41421i | 1.41421i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | 1.00000i | \(0.5\pi\) | ||
−1.00000 | \(\pi\) | |||||||||
\(810\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(811\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(812\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(813\) | 1.00000 | 1.00000 | ||||||||
\(814\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(815\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(816\) | −1.41421 | −1.41421 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(821\) | 1.00000i | 1.00000i | 0.866025 | + | 0.500000i | \(0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(822\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(823\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | − | 1.41421i | − | 1.41421i | ||||||
\(827\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | 1.00000i | \(0.5\pi\) | ||
−1.00000 | \(\pi\) | |||||||||
\(830\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 1.00000i | − | 1.00000i | ||||||
\(833\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.00000 | −1.00000 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(840\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(841\) | −1.00000 | −1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(844\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.00000 | 1.00000 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | 1.00000 | \(0\) | ||
1.00000i | \(0.5\pi\) | |||||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 1.00000i | − | 1.00000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(858\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(859\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(860\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(861\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(862\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(863\) | −1.41421 | −1.41421 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(864\) | − | 1.00000i | − | 1.00000i | ||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.41421 | 1.41421 | ||||||||
\(867\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(868\) | 1.00000i | 1.00000i | ||||||||
\(869\) | 1.00000i | 1.00000i | ||||||||
\(870\) | − | 1.00000i | − | 1.00000i | ||||||
\(871\) | 1.41421 | 1.41421 | ||||||||
\(872\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.00000 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.41421 | −1.41421 | ||||||||
\(880\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(881\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | − | 1.00000i | \(-0.5\pi\) | |
1.00000 | \(0\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(884\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(885\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | 0.258819 | − | 0.965926i | \(-0.416667\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(888\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 1.00000i | 1.00000i | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.00000 | −1.00000 | ||||||||
\(897\) | 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 | ||||
\(902\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(903\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 1.00000i | − | 1.00000i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.41421 | − | 1.41421i | −1.41421 | − | 1.41421i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
−0.707107 | − | 0.707107i | \(-0.750000\pi\) | |||||||
\(908\) | − | 1.41421i | − | 1.41421i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | − | 1.00000i | − | 1.00000i | ||||||
\(911\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | 0.258819 | − | 0.965926i | \(-0.416667\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(914\) | −1.41421 | − | 1.41421i | −1.41421 | − | 1.41421i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 2.00000i | − | 2.00000i | ||||||
\(918\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(919\) | 1.41421i | 1.41421i | 0.707107 | + | 0.707107i | \(0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.00000i | 1.00000i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(929\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(930\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1.00000i | 1.00000i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.00000 | 1.00000 | ||||||||
\(935\) | 1.41421i | 1.41421i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.00000 | −2.00000 | −1.00000 | \(\pi\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(938\) | − | 1.41421i | − | 1.41421i | ||||||
\(939\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(940\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(941\) | 1.00000 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(942\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 1.41421 | 1.41421 | ||||||||
\(945\) | − | 1.00000i | − | 1.00000i | ||||||
\(946\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(947\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(948\) | − | 1.00000i | − | 1.00000i | ||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(953\) | 1.00000 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.41421 | −1.41421 | ||||||||
\(957\) | − | 1.00000i | − | 1.00000i | ||||||
\(958\) | − | 1.00000i | − | 1.00000i | ||||||
\(959\) | 1.41421 | 1.41421 | ||||||||
\(960\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(961\) | 0 | 0 | ||||||||
\(962\) | 1.41421i | 1.41421i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 1.00000i | − | 1.00000i | ||||||
\(965\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1.41421 | −1.41421 | ||||||||
\(971\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.00000 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(978\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −1.00000 | −1.00000 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.00000 | 1.00000 | ||||||||
\(983\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(984\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −1.41421 | −1.41421 | ||||||||
\(987\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.41421 | 1.41421 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(992\) | −1.00000 | −1.00000 | ||||||||
\(993\) | 1.00000i | 1.00000i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.41421 | 1.41421 | ||||||||
\(996\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(997\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | − | 1.00000i | \(-0.5\pi\) | |
1.00000 | \(0\) | |||||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.41421i | 1.41421i |
(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 | 812.1.l.d.447.1 | yes | 4 | |
4.3 | odd | 2 | inner | 812.1.l.d.447.2 | yes | 4 | |
7.6 | odd | 2 | 812.1.l.c.447.1 | yes | 4 | ||
28.27 | even | 2 | 812.1.l.c.447.2 | yes | 4 | ||
29.17 | odd | 4 | 812.1.l.c.307.2 | yes | 4 | ||
116.75 | even | 4 | 812.1.l.c.307.1 | ✓ | 4 | ||
203.104 | even | 4 | inner | 812.1.l.d.307.2 | yes | 4 | |
812.307 | odd | 4 | inner | 812.1.l.d.307.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
812.1.l.c.307.1 | ✓ | 4 | 116.75 | even | 4 | ||
812.1.l.c.307.2 | yes | 4 | 29.17 | odd | 4 | ||
812.1.l.c.447.1 | yes | 4 | 7.6 | odd | 2 | ||
812.1.l.c.447.2 | yes | 4 | 28.27 | even | 2 | ||
812.1.l.d.307.1 | yes | 4 | 812.307 | odd | 4 | inner | |
812.1.l.d.307.2 | yes | 4 | 203.104 | even | 4 | inner | |
812.1.l.d.447.1 | yes | 4 | 1.1 | even | 1 | trivial | |
812.1.l.d.447.2 | yes | 4 | 4.3 | odd | 2 | inner |