Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3528,1,Mod(1733,3528)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3528, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 5, 4]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3528.1733");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3528 = 2^{3} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3528.db (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.76070136457\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{12}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
Embedding invariants
Embedding label | 2333.2 | ||
Root | \(-0.965926 + 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3528.2333 |
Dual form | 3528.1.db.a.1733.2 |
$q$-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 \(\left(\mathbb{Z}/3528\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) | \(1765\) | \(2647\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(3\) | 0.258819 | − | 0.965926i | 0.258819 | − | 0.965926i | ||||
\(4\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(5\) | −0.517638 | −0.517638 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(6\) | 0.258819 | + | 0.965926i | 0.258819 | + | 0.965926i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000i | 1.00000i | ||||||||
\(9\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(10\) | 0.448288 | − | 0.258819i | 0.448288 | − | 0.258819i | ||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(13\) | 1.22474 | − | 0.707107i | 1.22474 | − | 0.707107i | 0.258819 | − | 0.965926i | \(-0.416667\pi\) |
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.133975 | + | 0.500000i | −0.133975 | + | 0.500000i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(17\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(18\) | 1.00000 | 1.00000 | ||||||||
\(19\) | 1.67303 | + | 0.965926i | 1.67303 | + | 0.965926i | 0.965926 | + | 0.258819i | \(0.0833333\pi\) |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(20\) | −0.258819 | + | 0.448288i | −0.258819 | + | 0.448288i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 1.73205i | − | 1.73205i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||
0.500000 | − | 0.866025i | \(-0.333333\pi\) | |||||||
\(24\) | 0.965926 | + | 0.258819i | 0.965926 | + | 0.258819i | ||||
\(25\) | −0.732051 | −0.732051 | ||||||||
\(26\) | −0.707107 | + | 1.22474i | −0.707107 | + | 1.22474i | ||||
\(27\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(30\) | −0.133975 | − | 0.500000i | −0.133975 | − | 0.500000i | ||||
\(31\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(32\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(37\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(38\) | −1.93185 | −1.93185 | ||||||||
\(39\) | −0.366025 | − | 1.36603i | −0.366025 | − | 1.36603i | ||||
\(40\) | − | 0.517638i | − | 0.517638i | ||||||
\(41\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.448288 | + | 0.258819i | 0.448288 | + | 0.258819i | ||||
\(46\) | 0.866025 | + | 1.50000i | 0.866025 | + | 1.50000i | ||||
\(47\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(48\) | −0.965926 | + | 0.258819i | −0.965926 | + | 0.258819i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0.633975 | − | 0.366025i | 0.633975 | − | 0.366025i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 1.41421i | − | 1.41421i | ||||||
\(53\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(54\) | 0.258819 | − | 0.965926i | 0.258819 | − | 0.965926i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.36603 | − | 1.36603i | 1.36603 | − | 1.36603i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.707107 | + | 1.22474i | −0.707107 | + | 1.22474i | 0.258819 | + | 0.965926i | \(0.416667\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(60\) | 0.366025 | + | 0.366025i | 0.366025 | + | 0.366025i | ||||
\(61\) | 1.67303 | − | 0.965926i | 1.67303 | − | 0.965926i | 0.707107 | − | 0.707107i | \(-0.250000\pi\) |
0.965926 | − | 0.258819i | \(-0.0833333\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −1.00000 | ||||||||
\(65\) | −0.633975 | + | 0.366025i | −0.633975 | + | 0.366025i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.67303 | − | 0.448288i | −1.67303 | − | 0.448288i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 1.00000i | − | 1.00000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(72\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(73\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.189469 | + | 0.707107i | −0.189469 | + | 0.707107i | ||||
\(76\) | 1.67303 | − | 0.965926i | 1.67303 | − | 0.965926i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(79\) | −0.866025 | − | 1.50000i | −0.866025 | − | 1.50000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
− | 1.00000i | \(-0.5\pi\) | ||||||||
\(80\) | 0.258819 | + | 0.448288i | 0.258819 | + | 0.448288i | ||||
\(81\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.707107 | − | 1.22474i | 0.707107 | − | 1.22474i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
0.965926 | − | 0.258819i | \(-0.0833333\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(90\) | −0.517638 | −0.517638 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.50000 | − | 0.866025i | −1.50000 | − | 0.866025i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(96\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(97\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.366025 | + | 0.633975i | −0.366025 | + | 0.633975i | ||||
\(101\) | 1.93185 | 1.93185 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(104\) | 0.707107 | + | 1.22474i | 0.707107 | + | 1.22474i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(108\) | 0.258819 | + | 0.965926i | 0.258819 | + | 0.965926i | ||||
\(109\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | − | 1.00000i | \(-0.5\pi\) | |
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(114\) | −0.500000 | + | 1.86603i | −0.500000 | + | 1.86603i | ||||
\(115\) | 0.896575i | 0.896575i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.41421 | −1.41421 | ||||||||
\(118\) | − | 1.41421i | − | 1.41421i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −0.500000 | − | 0.133975i | −0.500000 | − | 0.133975i | ||||
\(121\) | −1.00000 | −1.00000 | ||||||||
\(122\) | −0.965926 | + | 1.67303i | −0.965926 | + | 1.67303i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.896575 | 0.896575 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(128\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.366025 | − | 0.633975i | 0.366025 | − | 0.633975i | ||||
\(131\) | −1.93185 | −1.93185 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.366025 | − | 0.366025i | 0.366025 | − | 0.366025i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(138\) | 1.67303 | − | 0.448288i | 1.67303 | − | 0.448288i | ||||
\(139\) | −0.448288 | + | 0.258819i | −0.448288 | + | 0.258819i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000i | 1.00000i | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(150\) | −0.189469 | − | 0.707107i | −0.189469 | − | 0.707107i | ||||
\(151\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(152\) | −0.965926 | + | 1.67303i | −0.965926 | + | 1.67303i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.36603 | − | 0.366025i | −1.36603 | − | 0.366025i | ||||
\(157\) | −1.67303 | − | 0.965926i | −1.67303 | − | 0.965926i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
−0.707107 | − | 0.707107i | \(-0.750000\pi\) | |||||||
\(158\) | 1.50000 | + | 0.866025i | 1.50000 | + | 0.866025i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.448288 | − | 0.258819i | −0.448288 | − | 0.258819i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(163\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.41421i | 1.41421i | ||||||||
\(167\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.965926 | − | 1.67303i | −0.965926 | − | 1.67303i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.707107 | − | 1.22474i | −0.707107 | − | 1.22474i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
0.258819 | − | 0.965926i | \(-0.416667\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(180\) | 0.448288 | − | 0.258819i | 0.448288 | − | 0.258819i | ||||
\(181\) | − | 0.517638i | − | 0.517638i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||
0.965926 | − | 0.258819i | \(-0.0833333\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.500000 | − | 1.86603i | −0.500000 | − | 1.86603i | ||||
\(184\) | 1.73205 | 1.73205 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.00000 | 1.00000 | ||||||||
\(191\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(192\) | −0.258819 | + | 0.965926i | −0.258819 | + | 0.965926i | ||||
\(193\) | 0.866025 | − | 1.50000i | 0.866025 | − | 1.50000i | − | 1.00000i | \(-0.5\pi\) | |
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.189469 | + | 0.707107i | 0.189469 | + | 0.707107i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(200\) | − | 0.732051i | − | 0.732051i | ||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.67303 | + | 0.965926i | −1.67303 | + | 0.965926i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.866025 | + | 1.50000i | −0.866025 | + | 1.50000i | ||||
\(208\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.965926 | − | 0.258819i | −0.965926 | − | 0.258819i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.633975 | + | 0.366025i | 0.633975 | + | 0.366025i | ||||
\(226\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(227\) | −0.517638 | −0.517638 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(228\) | −0.500000 | − | 1.86603i | −0.500000 | − | 1.86603i | ||||
\(229\) | 0.517638i | 0.517638i | 0.965926 | + | 0.258819i | \(0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(230\) | −0.448288 | − | 0.776457i | −0.448288 | − | 0.776457i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.50000 | + | 0.866025i | 1.50000 | + | 0.866025i | 1.00000 | \(0\) | ||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(234\) | 1.22474 | − | 0.707107i | 1.22474 | − | 0.707107i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0.707107 | + | 1.22474i | 0.707107 | + | 1.22474i | ||||
\(237\) | −1.67303 | + | 0.448288i | −1.67303 | + | 0.448288i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.50000 | + | 0.866025i | −1.50000 | + | 0.866025i | −0.500000 | + | 0.866025i | \(0.666667\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(240\) | 0.500000 | − | 0.133975i | 0.500000 | − | 0.133975i | ||||
\(241\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(242\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(243\) | 0.965926 | − | 0.258819i | 0.965926 | − | 0.258819i | ||||
\(244\) | − | 1.93185i | − | 1.93185i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.73205 | 2.73205 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(250\) | −0.776457 | + | 0.448288i | −0.776457 | + | 0.448288i | ||||
\(251\) | 0.517638 | 0.517638 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(257\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0.732051i | 0.732051i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.67303 | − | 0.965926i | 1.67303 | − | 0.965926i | ||||
\(263\) | − | 1.00000i | − | 1.00000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.965926 | + | 1.67303i | 0.965926 | + | 1.67303i | 0.707107 | + | 0.707107i | \(0.250000\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(270\) | −0.133975 | + | 0.500000i | −0.133975 | + | 0.500000i | ||||
\(271\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.22474 | + | 1.22474i | −1.22474 | + | 1.22474i | ||||
\(277\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(278\) | 0.258819 | − | 0.448288i | 0.258819 | − | 0.448288i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.50000 | + | 0.866025i | 1.50000 | + | 0.866025i | 1.00000 | \(0\) | ||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.67303 | + | 0.965926i | 1.67303 | + | 0.965926i | 0.965926 | + | 0.258819i | \(0.0833333\pi\) |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(284\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(285\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(289\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.965926 | + | 1.67303i | 0.965926 | + | 1.67303i | 0.707107 | + | 0.707107i | \(0.250000\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.366025 | − | 0.633975i | 0.366025 | − | 0.633975i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.22474 | − | 2.12132i | −1.22474 | − | 2.12132i | ||||
\(300\) | 0.517638 | + | 0.517638i | 0.517638 | + | 0.517638i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(303\) | 0.500000 | − | 1.86603i | 0.500000 | − | 1.86603i | ||||
\(304\) | − | 1.93185i | − | 1.93185i | ||||||
\(305\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.517638i | 0.517638i | 0.965926 | + | 0.258819i | \(0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(312\) | 1.36603 | − | 0.366025i | 1.36603 | − | 0.366025i | ||||
\(313\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(314\) | 1.93185 | 1.93185 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.73205 | −1.73205 | ||||||||
\(317\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0.517638 | 0.517638 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 1.00000 | 1.00000 | ||||||||
\(325\) | −0.896575 | + | 0.517638i | −0.896575 | + | 0.517638i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(332\) | −0.707107 | − | 1.22474i | −0.707107 | − | 1.22474i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(338\) | 1.00000i | 1.00000i | ||||||||
\(339\) | −0.258819 | − | 0.965926i | −0.258819 | − | 0.965926i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 1.67303 | + | 0.965926i | 1.67303 | + | 0.965926i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.866025 | + | 0.232051i | 0.866025 | + | 0.232051i | ||||
\(346\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | ||||
\(347\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.366025 | + | 1.36603i | −0.366025 | + | 1.36603i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(354\) | −1.36603 | − | 0.366025i | −1.36603 | − | 0.366025i | ||||
\(355\) | 0.517638i | 0.517638i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.50000 | + | 0.866025i | 1.50000 | + | 0.866025i | 1.00000 | \(0\) | ||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(360\) | −0.258819 | + | 0.448288i | −0.258819 | + | 0.448288i | ||||
\(361\) | 1.36603 | + | 2.36603i | 1.36603 | + | 2.36603i | ||||
\(362\) | 0.258819 | + | 0.448288i | 0.258819 | + | 0.448288i | ||||
\(363\) | −0.258819 | + | 0.965926i | −0.258819 | + | 0.965926i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.36603 | + | 1.36603i | 1.36603 | + | 1.36603i | ||||
\(367\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(368\) | −1.50000 | + | 0.866025i | −1.50000 | + | 0.866025i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.232051 | − | 0.866025i | 0.232051 | − | 0.866025i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(380\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(381\) | −0.258819 | + | 0.965926i | −0.258819 | + | 0.965926i | ||||
\(382\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(383\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(384\) | −0.258819 | − | 0.965926i | −0.258819 | − | 0.965926i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.73205i | 1.73205i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(390\) | −0.517638 | − | 0.517638i | −0.517638 | − | 0.517638i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.500000 | + | 1.86603i | −0.500000 | + | 1.86603i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.448288 | + | 0.776457i | 0.448288 | + | 0.776457i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.366025 | + | 0.633975i | 0.366025 | + | 0.633975i | ||||
\(401\) | − | 1.00000i | − | 1.00000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0.965926 | − | 1.67303i | 0.965926 | − | 1.67303i | ||||
\(405\) | −0.258819 | − | 0.448288i | −0.258819 | − | 0.448288i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | − | 1.73205i | − | 1.73205i | ||||||
\(415\) | −0.366025 | + | 0.633975i | −0.366025 | + | 0.633975i | ||||
\(416\) | 1.41421 | 1.41421 | ||||||||
\(417\) | 0.133975 | + | 0.500000i | 0.133975 | + | 0.500000i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.258819 | − | 0.448288i | −0.258819 | − | 0.448288i | 0.707107 | − | 0.707107i | \(-0.250000\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0.965926 | − | 0.258819i | 0.965926 | − | 0.258819i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(432\) | 0.965926 | + | 0.258819i | 0.965926 | + | 0.258819i | ||||
\(433\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.67303 | − | 2.89778i | 1.67303 | − | 2.89778i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 1.73205i | − | 1.73205i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||
0.500000 | − | 0.866025i | \(-0.333333\pi\) | |||||||
\(450\) | −0.732051 | −0.732051 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | − | 1.00000i | − | 1.00000i | ||||||
\(453\) | −0.258819 | + | 0.965926i | −0.258819 | + | 0.965926i | ||||
\(454\) | 0.448288 | − | 0.258819i | 0.448288 | − | 0.258819i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.36603 | + | 1.36603i | 1.36603 | + | 1.36603i | ||||
\(457\) | 0.866025 | + | 1.50000i | 0.866025 | + | 1.50000i | 0.866025 | + | 0.500000i | \(0.166667\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(458\) | −0.258819 | − | 0.448288i | −0.258819 | − | 0.448288i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.776457 | + | 0.448288i | 0.776457 | + | 0.448288i | ||||
\(461\) | −0.965926 | + | 1.67303i | −0.965926 | + | 1.67303i | −0.258819 | + | 0.965926i | \(0.583333\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.866025 | + | 1.50000i | 0.866025 | + | 1.50000i | 0.866025 | + | 0.500000i | \(0.166667\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.73205 | −1.73205 | ||||||||
\(467\) | 0.707107 | − | 1.22474i | 0.707107 | − | 1.22474i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
0.965926 | − | 0.258819i | \(-0.0833333\pi\) | |||||||
\(468\) | −0.707107 | + | 1.22474i | −0.707107 | + | 1.22474i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.36603 | + | 1.36603i | −1.36603 | + | 1.36603i | ||||
\(472\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 1.22474 | − | 1.22474i | 1.22474 | − | 1.22474i | ||||
\(475\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0.866025 | − | 1.50000i | 0.866025 | − | 1.50000i | ||||
\(479\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(480\) | −0.366025 | + | 0.366025i | −0.366025 | + | 0.366025i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(487\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(488\) | 0.965926 | + | 1.67303i | 0.965926 | + | 1.67303i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −2.36603 | + | 1.36603i | −2.36603 | + | 1.36603i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 1.36603 | + | 0.366025i | 1.36603 | + | 0.366025i | ||||
\(499\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(500\) | 0.448288 | − | 0.776457i | 0.448288 | − | 0.776457i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −0.448288 | + | 0.258819i | −0.448288 | + | 0.258819i | ||||
\(503\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.00000 | −1.00000 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(508\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(509\) | 1.41421 | 1.41421 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 1.00000i | − | 1.00000i | ||||||
\(513\) | −1.86603 | + | 0.500000i | −1.86603 | + | 0.500000i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.36603 | + | 0.366025i | −1.36603 | + | 0.366025i | ||||
\(520\) | −0.366025 | − | 0.633975i | −0.366025 | − | 0.633975i | ||||
\(521\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.448288 | + | 0.258819i | 0.448288 | + | 0.258819i | 0.707107 | − | 0.707107i | \(-0.250000\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(524\) | −0.965926 | + | 1.67303i | −0.965926 | + | 1.67303i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.00000 | −2.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.22474 | − | 0.707107i | 1.22474 | − | 0.707107i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1.67303 | − | 0.965926i | −1.67303 | − | 0.965926i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −0.133975 | − | 0.500000i | −0.133975 | − | 0.500000i | ||||
\(541\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.500000 | − | 0.133975i | −0.500000 | − | 0.133975i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.93185 | −1.93185 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0.448288 | − | 1.67303i | 0.448288 | − | 1.67303i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.517638i | 0.517638i | ||||||||
\(557\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.73205 | −1.73205 | ||||||||
\(563\) | 0.258819 | − | 0.448288i | 0.258819 | − | 0.448288i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.448288 | + | 0.258819i | −0.448288 | + | 0.258819i | ||||
\(566\) | −1.93185 | −1.93185 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.00000 | 1.00000 | ||||||||
\(569\) | −1.73205 | + | 1.00000i | −1.73205 | + | 1.00000i | −0.866025 | + | 0.500000i | \(0.833333\pi\) |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(570\) | 0.258819 | − | 0.965926i | 0.258819 | − | 0.965926i | ||||
\(571\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.258819 | + | 0.965926i | 0.258819 | + | 0.965926i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.26795i | 1.26795i | ||||||||
\(576\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(577\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(578\) | − | 1.00000i | − | 1.00000i | ||||||
\(579\) | −1.22474 | − | 1.22474i | −1.22474 | − | 1.22474i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.732051 | 0.732051 | ||||||||
\(586\) | −1.67303 | − | 0.965926i | −1.67303 | − | 0.965926i | ||||
\(587\) | 0.965926 | − | 1.67303i | 0.965926 | − | 1.67303i | 0.258819 | − | 0.965926i | \(-0.416667\pi\) |
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0.732051i | 0.732051i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.12132 | + | 1.22474i | 2.12132 | + | 1.22474i | ||||
\(599\) | 1.73205 | + | 1.00000i | 1.73205 | + | 1.00000i | 0.866025 | + | 0.500000i | \(0.166667\pi\) |
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(600\) | −0.707107 | − | 0.189469i | −0.707107 | − | 0.189469i | ||||
\(601\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(605\) | 0.517638 | 0.517638 | ||||||||
\(606\) | 0.500000 | + | 1.86603i | 0.500000 | + | 1.86603i | ||||
\(607\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(608\) | 0.965926 | + | 1.67303i | 0.965926 | + | 1.67303i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(614\) | −0.258819 | − | 0.448288i | −0.258819 | − | 0.448288i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.73205 | + | 1.00000i | −1.73205 | + | 1.00000i | −0.866025 | + | 0.500000i | \(0.833333\pi\) |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.93185i | 1.93185i | 0.258819 | + | 0.965926i | \(0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.22474 | + | 1.22474i | 1.22474 | + | 1.22474i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(625\) | 0.267949 | 0.267949 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.67303 | + | 0.965926i | −1.67303 | + | 0.965926i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.73205 | −1.73205 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(632\) | 1.50000 | − | 0.866025i | 1.50000 | − | 0.866025i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.517638 | 0.517638 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(640\) | −0.448288 | + | 0.258819i | −0.448288 | + | 0.258819i | ||||
\(641\) | 1.00000i | 1.00000i | 0.866025 | + | 0.500000i | \(0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.22474 | + | 0.707107i | −1.22474 | + | 0.707107i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(648\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0.517638 | − | 0.896575i | 0.517638 | − | 0.896575i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.00000 | 1.00000 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.448288 | − | 0.258819i | −0.448288 | − | 0.258819i | 0.258819 | − | 0.965926i | \(-0.416667\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.517638 | − | 0.517638i | 0.517638 | − | 0.517638i | ||||
\(676\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(677\) | 0.707107 | + | 1.22474i | 0.707107 | + | 1.22474i | 0.965926 | + | 0.258819i | \(0.0833333\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(678\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.133975 | + | 0.500000i | −0.133975 | + | 0.500000i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(684\) | −1.93185 | −1.93185 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.500000 | + | 0.133975i | 0.500000 | + | 0.133975i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −0.866025 | + | 0.232051i | −0.866025 | + | 0.232051i | ||||
\(691\) | 0.448288 | − | 0.258819i | 0.448288 | − | 0.258819i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(692\) | −1.41421 | −1.41421 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.232051 | − | 0.133975i | 0.232051 | − | 0.133975i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −1.41421 | −1.41421 | ||||||||
\(699\) | 1.22474 | − | 1.22474i | 1.22474 | − | 1.22474i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(702\) | −0.366025 | − | 1.36603i | −0.366025 | − | 1.36603i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 1.36603 | − | 0.366025i | 1.36603 | − | 0.366025i | ||||
\(709\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(710\) | −0.258819 | − | 0.448288i | −0.258819 | − | 0.448288i | ||||
\(711\) | 1.73205i | 1.73205i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.448288 | + | 1.67303i | 0.448288 | + | 1.67303i | ||||
\(718\) | −1.73205 | −1.73205 | ||||||||
\(719\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(720\) | − | 0.517638i | − | 0.517638i | ||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −2.36603 | − | 1.36603i | −2.36603 | − | 1.36603i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −0.448288 | − | 0.258819i | −0.448288 | − | 0.258819i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −0.258819 | − | 0.965926i | −0.258819 | − | 0.965926i | ||||
\(727\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 1.00000i | − | 1.00000i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −1.86603 | − | 0.500000i | −1.86603 | − | 0.500000i | ||||
\(733\) | − | 1.93185i | − | 1.93185i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||
0.258819 | − | 0.965926i | \(-0.416667\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.866025 | − | 1.50000i | 0.866025 | − | 1.50000i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.707107 | − | 2.63896i | 0.707107 | − | 2.63896i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.22474 | + | 0.707107i | −1.22474 | + | 0.707107i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0.232051 | + | 0.866025i | 0.232051 | + | 0.866025i | ||||
\(751\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.133975 | − | 0.500000i | 0.133975 | − | 0.500000i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.517638 | 0.517638 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(761\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(762\) | −0.258819 | − | 0.965926i | −0.258819 | − | 0.965926i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 1.00000i | 1.00000i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.00000i | 2.00000i | ||||||||
\(768\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(769\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −0.866025 | − | 1.50000i | −0.866025 | − | 1.50000i | ||||
\(773\) | −0.965926 | − | 1.67303i | −0.965926 | − | 1.67303i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
−0.258819 | − | 0.965926i | \(-0.583333\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0.707107 | + | 0.189469i | 0.707107 | + | 0.189469i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(786\) | −0.500000 | − | 1.86603i | −0.500000 | − | 1.86603i | ||||
\(787\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.965926 | − | 0.258819i | −0.965926 | − | 0.258819i | ||||
\(790\) | −0.776457 | − | 0.448288i | −0.776457 | − | 0.448288i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.36603 | − | 2.36603i | 1.36603 | − | 2.36603i | ||||
\(794\) | −1.41421 | −1.41421 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −0.965926 | − | 1.67303i | −0.965926 | − | 1.67303i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
−0.258819 | − | 0.965926i | \(-0.583333\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −0.633975 | − | 0.366025i | −0.633975 | − | 0.366025i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.86603 | − | 0.500000i | 1.86603 | − | 0.500000i | ||||
\(808\) | 1.93185i | 1.93185i | ||||||||
\(809\) | 1.73205 | − | 1.00000i | 1.73205 | − | 1.00000i | 0.866025 | − | 0.500000i | \(-0.166667\pi\) |
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(810\) | 0.448288 | + | 0.258819i | 0.448288 | + | 0.258819i | ||||
\(811\) | 1.41421i | 1.41421i | 0.707107 | + | 0.707107i | \(0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(828\) | 0.866025 | + | 1.50000i | 0.866025 | + | 1.50000i | ||||
\(829\) | −1.22474 | + | 0.707107i | −1.22474 | + | 0.707107i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(830\) | − | 0.732051i | − | 0.732051i | ||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.22474 | + | 0.707107i | −1.22474 | + | 0.707107i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −0.366025 | − | 0.366025i | −0.366025 | − | 0.366025i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0.448288 | + | 0.258819i | 0.448288 | + | 0.258819i | ||||
\(839\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.22474 | − | 1.22474i | 1.22474 | − | 1.22474i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.258819 | + | 0.448288i | −0.258819 | + | 0.448288i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.36603 | − | 1.36603i | 1.36603 | − | 1.36603i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(853\) | −0.448288 | − | 0.258819i | −0.448288 | − | 0.258819i | 0.258819 | − | 0.965926i | \(-0.416667\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.41421i | 1.41421i | 0.707107 | + | 0.707107i | \(0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | − | 1.00000i | \(-0.5\pi\) | |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(864\) | −0.965926 | + | 0.258819i | −0.965926 | + | 0.258819i | ||||
\(865\) | 0.366025 | + | 0.633975i | 0.366025 | + | 0.633975i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 3.34607i | 3.34607i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.86603 | − | 0.500000i | 1.86603 | − | 0.500000i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.517638 | − | 0.517638i | −0.517638 | − | 0.517638i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.36603 | + | 0.633975i | −2.36603 | + | 0.633975i | ||||
\(898\) | 0.866025 | + | 1.50000i | 0.866025 | + | 1.50000i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0.633975 | − | 0.366025i | 0.633975 | − | 0.366025i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(905\) | 0.267949i | 0.267949i | ||||||||
\(906\) | −0.258819 | − | 0.965926i | −0.258819 | − | 0.965926i | ||||
\(907\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(908\) | −0.258819 | + | 0.448288i | −0.258819 | + | 0.448288i | ||||
\(909\) | −1.67303 | − | 0.965926i | −1.67303 | − | 0.965926i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.50000 | + | 0.866025i | 1.50000 | + | 0.866025i | 1.00000 | \(0\) | ||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(912\) | −1.86603 | − | 0.500000i | −1.86603 | − | 0.500000i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −1.50000 | − | 0.866025i | −1.50000 | − | 0.866025i | ||||
\(915\) | 0.258819 | + | 0.965926i | 0.258819 | + | 0.965926i | ||||
\(916\) | 0.448288 | + | 0.258819i | 0.448288 | + | 0.258819i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.866025 | + | 1.50000i | −0.866025 | + | 1.50000i | 1.00000i | \(0.5\pi\) | ||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(920\) | −0.896575 | −0.896575 | ||||||||
\(921\) | 0.500000 | + | 0.133975i | 0.500000 | + | 0.133975i | ||||
\(922\) | − | 1.93185i | − | 1.93185i | ||||||
\(923\) | −0.707107 | − | 1.22474i | −0.707107 | − | 1.22474i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −1.50000 | − | 0.866025i | −1.50000 | − | 0.866025i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1.50000 | − | 0.866025i | 1.50000 | − | 0.866025i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.41421i | 1.41421i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | − | 1.41421i | − | 1.41421i | ||||||
\(937\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −0.258819 | + | 0.448288i | −0.258819 | + | 0.448288i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(942\) | 0.500000 | − | 1.86603i | 0.500000 | − | 1.86603i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 1.41421 | 1.41421 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(948\) | −0.448288 | + | 1.67303i | −0.448288 | + | 1.67303i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 1.41421 | 1.41421 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.448288 | − | 0.258819i | 0.448288 | − | 0.258819i | ||||
\(956\) | 1.73205i | 1.73205i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0.133975 | − | 0.500000i | 0.133975 | − | 0.500000i | ||||
\(961\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.448288 | + | 0.776457i | −0.448288 | + | 0.776457i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(968\) | − | 1.00000i | − | 1.00000i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.258819 | + | 0.448288i | −0.258819 | + | 0.448288i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(972\) | 0.258819 | − | 0.965926i | 0.258819 | − | 0.965926i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(975\) | 0.267949 | + | 1.00000i | 0.267949 | + | 1.00000i | ||||
\(976\) | −1.67303 | − | 0.965926i | −1.67303 | − | 0.965926i | ||||
\(977\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.36603 | − | 2.36603i | 1.36603 | − | 2.36603i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.36603 | + | 0.366025i | −1.36603 | + | 0.366025i | ||||
\(997\) | 0.517638i | 0.517638i | 0.965926 | + | 0.258819i | \(0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3528.1.db.a.2333.2 | 8 | ||
7.2 | even | 3 | 3528.1.bg.a.2549.4 | yes | 8 | ||
7.3 | odd | 6 | 3528.1.bi.a.2909.2 | 8 | |||
7.4 | even | 3 | 3528.1.bi.a.2909.1 | 8 | |||
7.5 | odd | 6 | 3528.1.bg.a.2549.3 | yes | 8 | ||
7.6 | odd | 2 | inner | 3528.1.db.a.2333.1 | 8 | ||
8.5 | even | 2 | inner | 3528.1.db.a.2333.1 | 8 | ||
9.5 | odd | 6 | 3528.1.bi.a.1157.4 | 8 | |||
56.5 | odd | 6 | 3528.1.bg.a.2549.4 | yes | 8 | ||
56.13 | odd | 2 | CM | 3528.1.db.a.2333.2 | 8 | ||
56.37 | even | 6 | 3528.1.bg.a.2549.3 | yes | 8 | ||
56.45 | odd | 6 | 3528.1.bi.a.2909.1 | 8 | |||
56.53 | even | 6 | 3528.1.bi.a.2909.2 | 8 | |||
63.5 | even | 6 | 3528.1.bg.a.1373.4 | yes | 8 | ||
63.23 | odd | 6 | 3528.1.bg.a.1373.3 | ✓ | 8 | ||
63.32 | odd | 6 | inner | 3528.1.db.a.1733.1 | 8 | ||
63.41 | even | 6 | 3528.1.bi.a.1157.3 | 8 | |||
63.59 | even | 6 | inner | 3528.1.db.a.1733.2 | 8 | ||
72.5 | odd | 6 | 3528.1.bi.a.1157.3 | 8 | |||
504.5 | even | 6 | 3528.1.bg.a.1373.3 | ✓ | 8 | ||
504.149 | odd | 6 | 3528.1.bg.a.1373.4 | yes | 8 | ||
504.221 | odd | 6 | inner | 3528.1.db.a.1733.2 | 8 | ||
504.293 | even | 6 | 3528.1.bi.a.1157.4 | 8 | |||
504.437 | even | 6 | inner | 3528.1.db.a.1733.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3528.1.bg.a.1373.3 | ✓ | 8 | 63.23 | odd | 6 | ||
3528.1.bg.a.1373.3 | ✓ | 8 | 504.5 | even | 6 | ||
3528.1.bg.a.1373.4 | yes | 8 | 63.5 | even | 6 | ||
3528.1.bg.a.1373.4 | yes | 8 | 504.149 | odd | 6 | ||
3528.1.bg.a.2549.3 | yes | 8 | 7.5 | odd | 6 | ||
3528.1.bg.a.2549.3 | yes | 8 | 56.37 | even | 6 | ||
3528.1.bg.a.2549.4 | yes | 8 | 7.2 | even | 3 | ||
3528.1.bg.a.2549.4 | yes | 8 | 56.5 | odd | 6 | ||
3528.1.bi.a.1157.3 | 8 | 63.41 | even | 6 | |||
3528.1.bi.a.1157.3 | 8 | 72.5 | odd | 6 | |||
3528.1.bi.a.1157.4 | 8 | 9.5 | odd | 6 | |||
3528.1.bi.a.1157.4 | 8 | 504.293 | even | 6 | |||
3528.1.bi.a.2909.1 | 8 | 7.4 | even | 3 | |||
3528.1.bi.a.2909.1 | 8 | 56.45 | odd | 6 | |||
3528.1.bi.a.2909.2 | 8 | 7.3 | odd | 6 | |||
3528.1.bi.a.2909.2 | 8 | 56.53 | even | 6 | |||
3528.1.db.a.1733.1 | 8 | 63.32 | odd | 6 | inner | ||
3528.1.db.a.1733.1 | 8 | 504.437 | even | 6 | inner | ||
3528.1.db.a.1733.2 | 8 | 63.59 | even | 6 | inner | ||
3528.1.db.a.1733.2 | 8 | 504.221 | odd | 6 | inner | ||
3528.1.db.a.2333.1 | 8 | 7.6 | odd | 2 | inner | ||
3528.1.db.a.2333.1 | 8 | 8.5 | even | 2 | inner | ||
3528.1.db.a.2333.2 | 8 | 1.1 | even | 1 | trivial | ||
3528.1.db.a.2333.2 | 8 | 56.13 | odd | 2 | CM |