Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1089,1,Mod(241,1089)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1089, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 3]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1089.241");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1089 = 3^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1089.h (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.543481798757\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(S_{4}\) |
Projective field: | Galois closure of 4.2.107811.1 |
Embedding invariants
Embedding label | 967.2 | ||
Root | \(1.22474 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1089.967 |
Dual form | 1089.1.h.a.241.2 |
$q$-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 \(\left(\mathbb{Z}/1089\mathbb{Z}\right)^\times\).
\(n\) | \(244\) | \(848\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.22474 | − | 0.707107i | 1.22474 | − | 0.707107i | 0.258819 | − | 0.965926i | \(-0.416667\pi\) |
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(3\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(4\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(5\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(6\) | − | 1.41421i | − | 1.41421i | ||||||
\(7\) | −1.22474 | + | 0.707107i | −1.22474 | + | 0.707107i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(10\) | − | 1.41421i | − | 1.41421i | ||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(13\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(14\) | −1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | ||||
\(15\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(16\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(17\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(18\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | ||||
\(19\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(20\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(21\) | 1.41421i | 1.41421i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −1.00000 | ||||||||
\(28\) | 1.41421i | 1.41421i | ||||||||
\(29\) | 1.22474 | − | 0.707107i | 1.22474 | − | 0.707107i | 0.258819 | − | 0.965926i | \(-0.416667\pi\) |
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(30\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | ||||
\(31\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(32\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.41421i | 1.41421i | ||||||||
\(36\) | −1.00000 | −1.00000 | ||||||||
\(37\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(42\) | 1.00000 | + | 1.73205i | 1.00000 | + | 1.73205i | ||||
\(43\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −1.00000 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(48\) | 1.00000 | 1.00000 | ||||||||
\(49\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.00000 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(54\) | −1.22474 | + | 0.707107i | −1.22474 | + | 0.707107i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.00000 | − | 1.73205i | 1.00000 | − | 1.73205i | ||||
\(59\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(60\) | −1.00000 | −1.00000 | ||||||||
\(61\) | −1.22474 | + | 0.707107i | −1.22474 | + | 0.707107i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(62\) | 1.41421i | 1.41421i | ||||||||
\(63\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | ||||
\(64\) | 1.00000 | 1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.00000 | + | 1.73205i | 1.00000 | + | 1.73205i | ||||
\(71\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 1.41421i | − | 1.41421i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(74\) | −1.22474 | + | 0.707107i | −1.22474 | + | 0.707107i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(80\) | 1.00000 | 1.00000 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.22474 | + | 0.707107i | −1.22474 | + | 0.707107i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(84\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 1.41421i | − | 1.41421i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(90\) | −1.22474 | + | 0.707107i | −1.22474 | + | 0.707107i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(94\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.22474 | − | 0.707107i | 1.22474 | − | 0.707107i | ||||
\(97\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(98\) | − | 1.41421i | − | 1.41421i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.22474 | + | 0.707107i | −1.22474 | + | 0.707107i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | ||||
\(106\) | 1.22474 | − | 0.707107i | 1.22474 | − | 0.707107i | ||||
\(107\) | − | 1.41421i | − | 1.41421i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(108\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(109\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(112\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | ||||
\(113\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 1.41421i | − | 1.41421i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.41421i | 1.41421i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(125\) | 1.00000 | 1.00000 | ||||||||
\(126\) | 2.00000 | 2.00000 | ||||||||
\(127\) | − | 1.41421i | − | 1.41421i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 1.41421i | − | 1.41421i | ||||||
\(135\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(140\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | ||||
\(141\) | 1.00000 | 1.00000 | ||||||||
\(142\) | −1.22474 | + | 0.707107i | −1.22474 | + | 0.707107i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(145\) | − | 1.41421i | − | 1.41421i | ||||||
\(146\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | ||||
\(147\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(148\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(149\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(160\) | 1.22474 | − | 0.707107i | 1.22474 | − | 0.707107i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.41421i | 1.41421i | ||||||||
\(163\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | ||||
\(167\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(174\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(180\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(181\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.41421i | 1.41421i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(186\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 1.00000 | 1.00000 | ||||||||
\(189\) | 1.22474 | − | 0.707107i | 1.22474 | − | 0.707107i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(192\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(193\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(194\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(197\) | 1.41421i | 1.41421i | 0.707107 | + | 0.707107i | \(0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(202\) | −1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | ||||
\(203\) | −1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 1.41421i | − | 1.41421i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 2.00000 | 2.00000 | ||||||||
\(211\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(212\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(213\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(214\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 1.41421i | − | 1.41421i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 1.41421i | 1.41421i | ||||||||
\(223\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(224\) | −2.00000 | −2.00000 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − | 1.41421i | − | 1.41421i | ||||||
\(227\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 1.41421i | − | 1.41421i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.00000 | 1.00000 | ||||||||
\(236\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(240\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(241\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(244\) | 1.41421i | 1.41421i | ||||||||
\(245\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.41421i | 1.41421i | ||||||||
\(250\) | 1.22474 | − | 0.707107i | 1.22474 | − | 0.707107i | ||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 1.22474 | − | 0.707107i | 1.22474 | − | 0.707107i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(257\) | 1.00000 | − | 1.73205i | 1.00000 | − | 1.73205i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
0.500000 | − | 0.866025i | \(-0.333333\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.22474 | − | 0.707107i | 1.22474 | − | 0.707107i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(269\) | 1.00000 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(270\) | 1.41421i | 1.41421i | ||||||||
\(271\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(278\) | 2.00000 | 2.00000 | ||||||||
\(279\) | 1.00000 | 1.00000 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(282\) | 1.22474 | − | 0.707107i | 1.22474 | − | 0.707107i | ||||
\(283\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(284\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | − | 1.41421i | − | 1.41421i | ||||||
\(289\) | 1.00000 | 1.00000 | ||||||||
\(290\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | ||||
\(291\) | −1.00000 | −1.00000 | ||||||||
\(292\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | ||||
\(293\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(294\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | ||||
\(295\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.41421i | 1.41421i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.41421i | 1.41421i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(310\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | ||||
\(311\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(314\) | 1.41421i | 1.41421i | ||||||||
\(315\) | 1.22474 | − | 0.707107i | 1.22474 | − | 0.707107i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(318\) | − | 1.41421i | − | 1.41421i | ||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(321\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.22474 | + | 0.707107i | −1.22474 | + | 0.707107i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(332\) | 1.41421i | 1.41421i | ||||||||
\(333\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(336\) | −1.22474 | + | 0.707107i | −1.22474 | + | 0.707107i | ||||
\(337\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(338\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | ||||
\(339\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(348\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | ||||
\(349\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(354\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | ||||
\(355\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.22474 | + | 0.707107i | −1.22474 | + | 0.707107i | ||||
\(359\) | − | 1.41421i | − | 1.41421i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 1.00000 | ||||||||
\(362\) | −1.22474 | + | 0.707107i | −1.22474 | + | 0.707107i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | ||||
\(366\) | 1.00000 | + | 1.73205i | 1.00000 | + | 1.73205i | ||||
\(367\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.41421i | 1.41421i | ||||||||
\(371\) | −1.22474 | + | 0.707107i | −1.22474 | + | 0.707107i | ||||
\(372\) | 1.00000 | 1.00000 | ||||||||
\(373\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 1.00000 | − | 1.73205i | 1.00000 | − | 1.73205i | ||||
\(379\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | ||||
\(382\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | ||||
\(383\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.00000 | −1.00000 | ||||||||
\(389\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.00000 | + | 1.73205i | 1.00000 | + | 1.73205i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(398\) | −1.22474 | + | 0.707107i | −1.22474 | + | 0.707107i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(402\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 1.41421i | 1.41421i | ||||||||
\(405\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(406\) | 2.82843i | 2.82843i | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.00000 | 1.00000 | ||||||||
\(412\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(413\) | − | 1.41421i | − | 1.41421i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.41421i | 1.41421i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.22474 | − | 0.707107i | 1.22474 | − | 0.707107i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(420\) | 1.22474 | − | 0.707107i | 1.22474 | − | 0.707107i | ||||
\(421\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(422\) | 2.00000 | 2.00000 | ||||||||
\(423\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.41421i | 1.41421i | ||||||||
\(427\) | 1.00000 | − | 1.73205i | 1.00000 | − | 1.73205i | ||||
\(428\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.41421i | 1.41421i | 0.707107 | + | 0.707107i | \(0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(432\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(433\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(434\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | ||||
\(435\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −2.00000 | −2.00000 | ||||||||
\(439\) | 1.22474 | − | 0.707107i | 1.22474 | − | 0.707107i | 0.258819 | − | 0.965926i | \(-0.416667\pi\) |
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.00000 | −1.00000 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(444\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.22474 | + | 0.707107i | −1.22474 | + | 0.707107i | ||||
\(449\) | 1.00000 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.22474 | + | 0.707107i | −1.22474 | + | 0.707107i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.22474 | − | 0.707107i | 1.22474 | − | 0.707107i | 0.258819 | − | 0.965926i | \(-0.416667\pi\) |
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(464\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | ||||
\(465\) | 1.00000 | 1.00000 | ||||||||
\(466\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | ||||
\(467\) | 1.00000 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.41421i | 1.41421i | ||||||||
\(470\) | 1.22474 | − | 0.707107i | 1.22474 | − | 0.707107i | ||||
\(471\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(478\) | 2.00000 | 2.00000 | ||||||||
\(479\) | 1.22474 | − | 0.707107i | 1.22474 | − | 0.707107i | 0.258819 | − | 0.965926i | \(-0.416667\pi\) |
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(480\) | − | 1.41421i | − | 1.41421i | ||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.00000 | −1.00000 | ||||||||
\(486\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | ||||
\(487\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(490\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | ||||
\(491\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(492\) | 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 | ||||
\(498\) | 1.00000 | + | 1.73205i | 1.00000 | + | 1.73205i | ||||
\(499\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(500\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 1.41421i | − | 1.41421i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.41421i | 1.41421i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.00000 | −1.00000 | ||||||||
\(508\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | ||||
\(509\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.00000 | + | 1.73205i | 1.00000 | + | 1.73205i | ||||
\(512\) | 1.41421i | 1.41421i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 2.82843i | − | 2.82843i | ||||||
\(515\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 1.00000 | − | 1.73205i | 1.00000 | − | 1.73205i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(522\) | −2.00000 | −2.00000 | ||||||||
\(523\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(530\) | − | 1.41421i | − | 1.41421i | ||||||
\(531\) | 1.00000 | 1.00000 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(538\) | 1.22474 | − | 0.707107i | 1.22474 | − | 0.707107i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(541\) | 1.41421i | 1.41421i | 0.707107 | + | 0.707107i | \(0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.22474 | + | 0.707107i | −1.22474 | + | 0.707107i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(548\) | 1.00000 | 1.00000 | ||||||||
\(549\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(556\) | 1.22474 | − | 0.707107i | 1.22474 | − | 0.707107i | ||||
\(557\) | 1.41421i | 1.41421i | 0.707107 | + | 0.707107i | \(0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(558\) | 1.22474 | − | 0.707107i | 1.22474 | − | 0.707107i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −1.22474 | + | 0.707107i | −1.22474 | + | 0.707107i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(564\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(565\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(566\) | −2.00000 | −2.00000 | ||||||||
\(567\) | − | 1.41421i | − | 1.41421i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.22474 | − | 0.707107i | 1.22474 | − | 0.707107i | 0.258819 | − | 0.965926i | \(-0.416667\pi\) |
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.00000 | 1.00000 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(577\) | 1.00000 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(578\) | 1.22474 | − | 0.707107i | 1.22474 | − | 0.707107i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | ||||
\(581\) | 1.00000 | − | 1.73205i | 1.00000 | − | 1.73205i | ||||
\(582\) | −1.22474 | + | 0.707107i | −1.22474 | + | 0.707107i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.00000 | −2.00000 | ||||||||
\(587\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(588\) | −1.00000 | −1.00000 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | ||||
\(591\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | ||||
\(592\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(593\) | − | 1.41421i | − | 1.41421i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.00000 | −1.00000 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.00000 | + | 1.73205i | 1.00000 | + | 1.73205i | ||||
\(607\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.00000 | + | 1.73205i | 1.00000 | + | 1.73205i | ||||
\(610\) | 1.00000 | + | 1.73205i | 1.00000 | + | 1.73205i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(618\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | ||||
\(619\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(620\) | 1.00000 | 1.00000 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.41421i | 1.41421i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 1.00000 | − | 1.73205i | 1.00000 | − | 1.73205i | ||||
\(631\) | 1.00000 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.22474 | − | 0.707107i | 1.22474 | − | 0.707107i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | ||||
\(636\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.00000 | + | 1.73205i | 1.00000 | + | 1.73205i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(642\) | −2.00000 | −2.00000 | ||||||||
\(643\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.00000 | −2.00000 | −1.00000 | \(\pi\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | ||||
\(652\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(653\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.22474 | + | 0.707107i | −1.22474 | + | 0.707107i | ||||
\(658\) | −2.00000 | −2.00000 | ||||||||
\(659\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(662\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | ||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | ||||
\(673\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(674\) | −2.00000 | −2.00000 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.00000 | −1.00000 | ||||||||
\(677\) | 1.22474 | − | 0.707107i | 1.22474 | − | 0.707107i | 0.258819 | − | 0.965926i | \(-0.416667\pi\) |
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(678\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | ||||
\(679\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.00000 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.00000 | 1.00000 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.00000 | 2.00000 | ||||||||
\(695\) | 1.22474 | − | 0.707107i | 1.22474 | − | 0.707107i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.00000 | − | 1.73205i | 1.00000 | − | 1.73205i | ||||
\(708\) | 1.00000 | 1.00000 | ||||||||
\(709\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(710\) | 1.41421i | 1.41421i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(717\) | 1.22474 | − | 0.707107i | 1.22474 | − | 0.707107i | ||||
\(718\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | ||||
\(719\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(720\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(721\) | 1.41421i | 1.41421i | ||||||||
\(722\) | 1.22474 | − | 0.707107i | 1.22474 | − | 0.707107i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 1.00000 | ||||||||
\(730\) | −2.00000 | −2.00000 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | ||||
\(733\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(734\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | ||||
\(735\) | −1.00000 | −1.00000 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(740\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | ||||
\(743\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.00000 | + | 1.73205i | 1.00000 | + | 1.73205i | ||||
\(750\) | − | 1.41421i | − | 1.41421i | ||||||
\(751\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(752\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | − | 1.41421i | − | 1.41421i | ||||||
\(757\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(762\) | −2.00000 | −2.00000 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 1.00000 | 1.00000 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.41421i | 1.41421i | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(769\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 1.41421i | − | 1.41421i | ||||||
\(778\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.22474 | + | 0.707107i | −1.22474 | + | 0.707107i | ||||
\(784\) | 1.00000 | 1.00000 | ||||||||
\(785\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(788\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.41421i | 1.41421i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −1.22474 | + | 0.707107i | −1.22474 | + | 0.707107i | ||||
\(795\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(796\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(797\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − | 1.41421i | − | 1.41421i | ||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −1.00000 | −1.00000 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 1.41421i | − | 1.41421i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(810\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | ||||
\(811\) | 1.41421i | 1.41421i | 0.707107 | + | 0.707107i | \(0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(812\) | 1.00000 | + | 1.73205i | 1.00000 | + | 1.73205i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(822\) | 1.22474 | − | 0.707107i | 1.22474 | − | 0.707107i | ||||
\(823\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | ||||
\(827\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.00000 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(830\) | 1.00000 | + | 1.73205i | 1.00000 | + | 1.73205i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 1.00000 | − | 1.73205i | 1.00000 | − | 1.73205i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(838\) | − | 1.41421i | − | 1.41421i | ||||||
\(839\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(842\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.22474 | − | 0.707107i | 1.22474 | − | 0.707107i | ||||
\(845\) | −1.00000 | −1.00000 | ||||||||
\(846\) | − | 1.41421i | − | 1.41421i | ||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(849\) | −1.22474 | + | 0.707107i | −1.22474 | + | 0.707107i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(853\) | 1.22474 | − | 0.707107i | 1.22474 | − | 0.707107i | 0.258819 | − | 0.965926i | \(-0.416667\pi\) |
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(854\) | − | 2.82843i | − | 2.82843i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.22474 | + | 0.707107i | −1.22474 | + | 0.707107i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.00000 | + | 1.73205i | 1.00000 | + | 1.73205i | ||||
\(863\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(864\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(868\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −2.00000 | −2.00000 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.22474 | + | 0.707107i | −1.22474 | + | 0.707107i | ||||
\(876\) | −1.22474 | + | 0.707107i | −1.22474 | + | 0.707107i | ||||
\(877\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(878\) | 1.00000 | − | 1.73205i | 1.00000 | − | 1.73205i | ||||
\(879\) | −1.22474 | + | 0.707107i | −1.22474 | + | 0.707107i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(882\) | −1.22474 | + | 0.707107i | −1.22474 | + | 0.707107i | ||||
\(883\) | 1.00000 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.00000 | 1.00000 | ||||||||
\(886\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | ||||
\(887\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00000 | + | 1.73205i | 1.00000 | + | 1.73205i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.22474 | − | 0.707107i | 1.22474 | − | 0.707107i | ||||
\(899\) | 1.41421i | 1.41421i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | ||||
\(915\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.00000 | − | 1.73205i | 1.00000 | − | 1.73205i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.00000 | −1.00000 | ||||||||
\(928\) | 2.00000 | 2.00000 | ||||||||
\(929\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(930\) | 1.22474 | − | 0.707107i | 1.22474 | − | 0.707107i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | ||||
\(933\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(934\) | 1.22474 | − | 0.707107i | 1.22474 | − | 0.707107i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.41421i | 1.41421i | 0.707107 | + | 0.707107i | \(0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(938\) | 1.00000 | + | 1.73205i | 1.00000 | + | 1.73205i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(941\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(942\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −1.00000 | −1.00000 | ||||||||
\(945\) | − | 1.41421i | − | 1.41421i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.41421i | 1.41421i | 0.707107 | + | 0.707107i | \(0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(954\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | ||||
\(955\) | 1.00000 | 1.00000 | ||||||||
\(956\) | 1.22474 | − | 0.707107i | 1.22474 | − | 0.707107i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.00000 | − | 1.73205i | 1.00000 | − | 1.73205i | ||||
\(959\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | ||||
\(960\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(961\) | 0 | 0 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.22474 | + | 0.707107i | −1.22474 | + | 0.707107i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1.22474 | + | 0.707107i | −1.22474 | + | 0.707107i | ||||
\(971\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(972\) | 1.00000 | 1.00000 | ||||||||
\(973\) | −2.00000 | −2.00000 | ||||||||
\(974\) | −1.22474 | + | 0.707107i | −1.22474 | + | 0.707107i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | ||||
\(977\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(978\) | 1.41421i | 1.41421i | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −1.00000 | −1.00000 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2.00000 | 2.00000 | ||||||||
\(983\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.22474 | + | 0.707107i | −1.22474 | + | 0.707107i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(992\) | −1.22474 | + | 0.707107i | −1.22474 | + | 0.707107i | ||||
\(993\) | −1.00000 | −1.00000 | ||||||||
\(994\) | 1.00000 | − | 1.73205i | 1.00000 | − | 1.73205i | ||||
\(995\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(996\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | ||||
\(997\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(998\) | 1.41421i | 1.41421i | ||||||||
\(999\) | 1.00000 | 1.00000 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))