Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2205,1,Mod(67,2205)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2205, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([4, 3, 8]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2205.67");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 2205.ci (of order \(12\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.10043835286\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(S_{4}\) |
Projective field: | Galois closure of 4.2.3472875.1 |
Embedding invariants
Embedding label | 508.1 | ||
Root | \(0.965926 - 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2205.508 |
Dual form | 2205.1.ci.a.1402.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2205\mathbb{Z}\right)^\times\).
\(n\) | \(442\) | \(1081\) | \(1226\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.366025 | + | 1.36603i | 0.366025 | + | 1.36603i | 0.866025 | + | 0.500000i | \(0.166667\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(3\) | −0.965926 | + | 0.258819i | −0.965926 | + | 0.258819i | ||||
\(4\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(5\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(6\) | −0.707107 | − | 1.22474i | −0.707107 | − | 1.22474i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(10\) | 0.707107 | − | 1.22474i | 0.707107 | − | 1.22474i | ||||
\(11\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(12\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(13\) | 0.965926 | − | 0.258819i | 0.965926 | − | 0.258819i | 0.258819 | − | 0.965926i | \(-0.416667\pi\) |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(17\) | 0.258819 | + | 0.965926i | 0.258819 | + | 0.965926i | 0.965926 | + | 0.258819i | \(0.0833333\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(18\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(19\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(20\) | 0.965926 | + | 0.258819i | 0.965926 | + | 0.258819i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.366025 | − | 1.36603i | −0.366025 | − | 1.36603i | ||||
\(23\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | 1.00000 | \(0\) | ||
1.00000i | \(0.5\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000i | 1.00000i | ||||||||
\(26\) | 0.707107 | + | 1.22474i | 0.707107 | + | 1.22474i | ||||
\(27\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(30\) | −0.366025 | + | 1.36603i | −0.366025 | + | 1.36603i | ||||
\(31\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(32\) | −1.36603 | − | 0.366025i | −1.36603 | − | 0.366025i | ||||
\(33\) | 0.965926 | − | 0.258819i | 0.965926 | − | 0.258819i | ||||
\(34\) | −1.22474 | + | 0.707107i | −1.22474 | + | 0.707107i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(37\) | −1.36603 | − | 0.366025i | −1.36603 | − | 0.366025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.707107 | + | 1.22474i | −0.707107 | + | 1.22474i | 0.258819 | + | 0.965926i | \(0.416667\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(44\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(45\) | −0.965926 | − | 0.258819i | −0.965926 | − | 0.258819i | ||||
\(46\) | −1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | ||||
\(47\) | 0.258819 | + | 0.965926i | 0.258819 | + | 0.965926i | 0.965926 | + | 0.258819i | \(0.0833333\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(48\) | 0.258819 | − | 0.965926i | 0.258819 | − | 0.965926i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −1.36603 | + | 0.366025i | −1.36603 | + | 0.366025i | ||||
\(51\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(52\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(53\) | 1.36603 | − | 0.366025i | 1.36603 | − | 0.366025i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(54\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | ||||
\(55\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.22474 | + | 0.707107i | −1.22474 | + | 0.707107i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(60\) | −1.00000 | −1.00000 | ||||||||
\(61\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 1.00000i | − | 1.00000i | ||||||
\(65\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(66\) | 0.707107 | + | 1.22474i | 0.707107 | + | 1.22474i | ||||
\(67\) | 1.36603 | + | 0.366025i | 1.36603 | + | 0.366025i | 0.866025 | − | 0.500000i | \(-0.166667\pi\) |
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(68\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(69\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.965926 | − | 0.258819i | 0.965926 | − | 0.258819i | 0.258819 | − | 0.965926i | \(-0.416667\pi\) |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(74\) | − | 2.00000i | − | 2.00000i | ||||||
\(75\) | −0.258819 | − | 0.965926i | −0.258819 | − | 0.965926i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(79\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | 0.866025 | − | 0.500000i | \(-0.166667\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | 0.965926 | − | 0.258819i | 0.965926 | − | 0.258819i | ||||
\(81\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(82\) | −1.93185 | − | 0.517638i | −1.93185 | − | 0.517638i | ||||
\(83\) | −0.258819 | + | 0.965926i | −0.258819 | + | 0.965926i | 0.707107 | + | 0.707107i | \(0.250000\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(90\) | − | 1.41421i | − | 1.41421i | ||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.36603 | − | 0.366025i | −1.36603 | − | 0.366025i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.22474 | + | 0.707107i | −1.22474 | + | 0.707107i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.41421 | 1.41421 | ||||||||
\(97\) | 0.965926 | + | 0.258819i | 0.965926 | + | 0.258819i | 0.707107 | − | 0.707107i | \(-0.250000\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(100\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(101\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(102\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(103\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.00000 | + | 1.73205i | 1.00000 | + | 1.73205i | ||||
\(107\) | −1.36603 | − | 0.366025i | −1.36603 | − | 0.366025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(108\) | 0.258819 | − | 0.965926i | 0.258819 | − | 0.965926i | ||||
\(109\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | − | 1.00000i | \(-0.5\pi\) | |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(110\) | −0.707107 | + | 1.22474i | −0.707107 | + | 1.22474i | ||||
\(111\) | 1.41421 | 1.41421 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 1.41421i | − | 1.41421i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(118\) | −1.41421 | − | 1.41421i | −1.41421 | − | 1.41421i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.366025 | − | 1.36603i | 0.366025 | − | 1.36603i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | 1.00000i | \(0.5\pi\) | ||
−1.00000 | \(\pi\) | |||||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.366025 | − | 1.36603i | 0.366025 | − | 1.36603i | ||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 2.00000i | 2.00000i | ||||||||
\(135\) | 1.00000 | 1.00000 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(138\) | 0.517638 | − | 1.93185i | 0.517638 | − | 1.93185i | ||||
\(139\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(142\) | −0.366025 | − | 1.36603i | −0.366025 | − | 1.36603i | ||||
\(143\) | −0.965926 | + | 0.258819i | −0.965926 | + | 0.258819i | ||||
\(144\) | 1.00000i | 1.00000i | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.707107 | + | 1.22474i | 0.707107 | + | 1.22474i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.36603 | − | 0.366025i | 1.36603 | − | 0.366025i | ||||
\(149\) | − | 1.00000i | − | 1.00000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(150\) | 1.22474 | − | 0.707107i | 1.22474 | − | 0.707107i | ||||
\(151\) | 1.00000 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(157\) | 0.965926 | + | 0.258819i | 0.965926 | + | 0.258819i | 0.707107 | − | 0.707107i | \(-0.250000\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(158\) | −0.366025 | + | 1.36603i | −0.366025 | + | 1.36603i | ||||
\(159\) | −1.22474 | + | 0.707107i | −1.22474 | + | 0.707107i | ||||
\(160\) | 0.707107 | + | 1.22474i | 0.707107 | + | 1.22474i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.36603 | + | 0.366025i | 1.36603 | + | 0.366025i | ||||
\(163\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(164\) | − | 1.41421i | − | 1.41421i | ||||||
\(165\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(166\) | −1.41421 | −1.41421 | ||||||||
\(167\) | −0.258819 | − | 0.965926i | −0.258819 | − | 0.965926i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 1.36603 | + | 0.366025i | 1.36603 | + | 0.366025i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.93185 | − | 0.517638i | 1.93185 | − | 0.517638i | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) |
0.965926 | − | 0.258819i | \(-0.0833333\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(177\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | 0.866025 | − | 0.500000i | \(-0.166667\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | 0.965926 | − | 0.258819i | 0.965926 | − | 0.258819i | ||||
\(181\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.707107 | + | 1.22474i | 0.707107 | + | 1.22474i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.258819 | − | 0.965926i | −0.258819 | − | 0.965926i | ||||
\(188\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(192\) | 0.258819 | + | 0.965926i | 0.258819 | + | 0.965926i | ||||
\(193\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(194\) | 1.41421i | 1.41421i | ||||||||
\(195\) | 0.965926 | + | 0.258819i | 0.965926 | + | 0.258819i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(198\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(199\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.41421 | −1.41421 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(205\) | 1.36603 | − | 0.366025i | 1.36603 | − | 0.366025i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.36603 | + | 0.366025i | 1.36603 | + | 0.366025i | ||||
\(208\) | −0.258819 | + | 0.965926i | −0.258819 | + | 0.965926i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(212\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(213\) | 0.965926 | − | 0.258819i | 0.965926 | − | 0.258819i | ||||
\(214\) | − | 2.00000i | − | 2.00000i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0.366025 | − | 1.36603i | 0.366025 | − | 1.36603i | ||||
\(219\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(220\) | −0.965926 | − | 0.258819i | −0.965926 | − | 0.258819i | ||||
\(221\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(222\) | 0.517638 | + | 1.93185i | 0.517638 | + | 1.93185i | ||||
\(223\) | 0.258819 | − | 0.965926i | 0.258819 | − | 0.965926i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
0.965926 | − | 0.258819i | \(-0.0833333\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(230\) | 1.93185 | − | 0.517638i | 1.93185 | − | 0.517638i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(234\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | ||||
\(235\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(236\) | 0.707107 | − | 1.22474i | 0.707107 | − | 1.22474i | ||||
\(237\) | −0.965926 | − | 0.258819i | −0.965926 | − | 0.258819i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(240\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(241\) | −1.41421 | −1.41421 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.258819 | + | 0.965926i | −0.258819 | + | 0.965926i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.00000 | 2.00000 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 1.00000i | − | 1.00000i | ||||||
\(250\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | ||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(254\) | −1.73205 | − | 1.00000i | −1.73205 | − | 1.00000i | ||||
\(255\) | −0.258819 | + | 0.965926i | −0.258819 | + | 0.965926i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(257\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.00000 | 1.00000 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | 1.00000 | \(0\) | ||
1.00000i | \(0.5\pi\) | |||||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.36603 | + | 0.366025i | −1.36603 | + | 0.366025i | ||||
\(269\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(270\) | 0.366025 | + | 1.36603i | 0.366025 | + | 1.36603i | ||||
\(271\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(272\) | −0.965926 | − | 0.258819i | −0.965926 | − | 0.258819i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 1.00000i | − | 1.00000i | ||||||
\(276\) | 1.41421 | 1.41421 | ||||||||
\(277\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(278\) | −0.517638 | + | 1.93185i | −0.517638 | + | 1.93185i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(282\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(283\) | 0.258819 | − | 0.965926i | 0.258819 | − | 0.965926i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
0.965926 | − | 0.258819i | \(-0.0833333\pi\) | |||||||
\(284\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.707107 | − | 1.22474i | −0.707107 | − | 1.22474i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.36603 | + | 0.366025i | −1.36603 | + | 0.366025i | ||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.00000 | −1.00000 | ||||||||
\(292\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(293\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.36603 | + | 0.366025i | 1.36603 | + | 0.366025i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(298\) | 1.36603 | − | 0.366025i | 1.36603 | − | 0.366025i | ||||
\(299\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | ||||
\(300\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0.366025 | + | 1.36603i | 0.366025 | + | 1.36603i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.707107 | + | 1.22474i | −0.707107 | + | 1.22474i | ||||
\(307\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.707107 | − | 1.22474i | −0.707107 | − | 1.22474i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
0.258819 | − | 0.965926i | \(-0.416667\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(314\) | 1.41421i | 1.41421i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.00000 | −1.00000 | ||||||||
\(317\) | 0.366025 | + | 1.36603i | 0.366025 | + | 1.36603i | 0.866025 | + | 0.500000i | \(0.166667\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(318\) | −1.41421 | − | 1.41421i | −1.41421 | − | 1.41421i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(321\) | 1.41421 | 1.41421 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 1.00000i | 1.00000i | ||||||||
\(325\) | 0.258819 | + | 0.965926i | 0.258819 | + | 0.965926i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.965926 | + | 0.258819i | 0.965926 | + | 0.258819i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0.366025 | − | 1.36603i | 0.366025 | − | 1.36603i | ||||
\(331\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(332\) | −0.258819 | − | 0.965926i | −0.258819 | − | 0.965926i | ||||
\(333\) | −1.36603 | + | 0.366025i | −1.36603 | + | 0.366025i | ||||
\(334\) | 1.22474 | − | 0.707107i | 1.22474 | − | 0.707107i | ||||
\(335\) | −0.707107 | − | 1.22474i | −0.707107 | − | 1.22474i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.366025 | + | 1.36603i | 0.366025 | + | 1.36603i | 0.866025 | + | 0.500000i | \(0.166667\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.00000i | 1.00000i | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.366025 | + | 1.36603i | 0.366025 | + | 1.36603i | ||||
\(346\) | 1.41421 | + | 2.44949i | 1.41421 | + | 2.44949i | ||||
\(347\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(352\) | 1.36603 | + | 0.366025i | 1.36603 | + | 0.366025i | ||||
\(353\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(354\) | 1.73205 | + | 1.00000i | 1.73205 | + | 1.00000i | ||||
\(355\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.366025 | + | 1.36603i | −0.366025 | + | 1.36603i | ||||
\(359\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(368\) | −1.36603 | + | 0.366025i | −1.36603 | + | 0.366025i | ||||
\(369\) | 1.41421i | 1.41421i | ||||||||
\(370\) | −1.41421 | + | 1.41421i | −1.41421 | + | 1.41421i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(374\) | 1.22474 | − | 0.707107i | 1.22474 | − | 0.707107i | ||||
\(375\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 1.00000i | − | 1.00000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.707107 | − | 1.22474i | 0.707107 | − | 1.22474i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | 0.258819 | − | 0.965926i | \(-0.416667\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.965926 | + | 0.258819i | −0.965926 | + | 0.258819i | ||||
\(389\) | − | 1.00000i | − | 1.00000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(390\) | 1.41421i | 1.41421i | ||||||||
\(391\) | −0.707107 | + | 1.22474i | −0.707107 | + | 1.22474i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.258819 | − | 0.965926i | −0.258819 | − | 0.965926i | ||||
\(396\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(397\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(398\) | 0.517638 | − | 1.93185i | 0.517638 | − | 1.93185i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(401\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(402\) | −0.517638 | − | 1.93185i | −0.517638 | − | 1.93185i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.965926 | + | 0.258819i | −0.965926 | + | 0.258819i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.36603 | + | 0.366025i | 1.36603 | + | 0.366025i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.22474 | − | 0.707107i | 1.22474 | − | 0.707107i | 0.258819 | − | 0.965926i | \(-0.416667\pi\) |
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(410\) | 1.00000 | + | 1.73205i | 1.00000 | + | 1.73205i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 2.00000i | 2.00000i | ||||||||
\(415\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(416\) | −1.41421 | −1.41421 | ||||||||
\(417\) | −1.36603 | − | 0.366025i | −1.36603 | − | 0.366025i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(422\) | 1.36603 | + | 0.366025i | 1.36603 | + | 0.366025i | ||||
\(423\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.965926 | + | 0.258819i | −0.965926 | + | 0.258819i | ||||
\(426\) | 0.707107 | + | 1.22474i | 0.707107 | + | 1.22474i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 1.36603 | − | 0.366025i | 1.36603 | − | 0.366025i | ||||
\(429\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(432\) | −0.258819 | − | 0.965926i | −0.258819 | − | 0.965926i | ||||
\(433\) | −1.41421 | − | 1.41421i | −1.41421 | − | 1.41421i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
−0.707107 | − | 0.707107i | \(-0.750000\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.00000 | 1.00000 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(439\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(443\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(444\) | −1.22474 | + | 0.707107i | −1.22474 | + | 0.707107i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.41421 | 1.41421 | ||||||||
\(447\) | 0.258819 | + | 0.965926i | 0.258819 | + | 0.965926i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 2.00000i | − | 2.00000i | − | 1.00000i | \(-0.5\pi\) | |||
− | 1.00000i | \(-0.5\pi\) | ||||||||
\(450\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(451\) | 0.707107 | − | 1.22474i | 0.707107 | − | 1.22474i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.965926 | + | 0.258819i | −0.965926 | + | 0.258819i | ||||
\(454\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(460\) | 0.707107 | + | 1.22474i | 0.707107 | + | 1.22474i | ||||
\(461\) | −0.707107 | − | 1.22474i | −0.707107 | − | 1.22474i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
0.258819 | − | 0.965926i | \(-0.416667\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.965926 | − | 0.258819i | −0.965926 | − | 0.258819i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(468\) | −0.258819 | + | 0.965926i | −0.258819 | + | 0.965926i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 1.36603 | + | 0.366025i | 1.36603 | + | 0.366025i | ||||
\(471\) | −1.00000 | −1.00000 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | − | 1.41421i | − | 1.41421i | ||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(480\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(481\) | −1.41421 | −1.41421 | ||||||||
\(482\) | −0.517638 | − | 1.93185i | −0.517638 | − | 1.93185i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(486\) | −1.41421 | −1.41421 | ||||||||
\(487\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(492\) | 0.366025 | + | 1.36603i | 0.366025 | + | 1.36603i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.965926 | + | 0.258819i | 0.965926 | + | 0.258819i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 1.36603 | − | 0.366025i | 1.36603 | − | 0.366025i | ||||
\(499\) | 1.00000i | 1.00000i | 0.866025 | + | 0.500000i | \(0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(500\) | −0.258819 | + | 0.965926i | −0.258819 | + | 0.965926i | ||||
\(501\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.00000 | − | 1.73205i | 1.00000 | − | 1.73205i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.366025 | − | 1.36603i | 0.366025 | − | 1.36603i | ||||
\(509\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(510\) | −1.41421 | −1.41421 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.258819 | − | 0.965926i | −0.258819 | − | 0.965926i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.73205 | + | 1.00000i | −1.73205 | + | 1.00000i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.707107 | − | 1.22474i | 0.707107 | − | 1.22474i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
0.965926 | − | 0.258819i | \(-0.0833333\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.258819 | − | 0.965926i | 0.258819 | − | 0.965926i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
0.965926 | − | 0.258819i | \(-0.0833333\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −0.258819 | + | 0.965926i | −0.258819 | + | 0.965926i | ||||
\(529\) | 1.00000i | 1.00000i | ||||||||
\(530\) | 0.517638 | − | 1.93185i | 0.517638 | − | 1.93185i | ||||
\(531\) | −0.707107 | + | 1.22474i | −0.707107 | + | 1.22474i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.366025 | + | 1.36603i | −0.366025 | + | 1.36603i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.707107 | + | 1.22474i | 0.707107 | + | 1.22474i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.965926 | − | 0.258819i | −0.965926 | − | 0.258819i | ||||
\(538\) | −0.517638 | + | 1.93185i | −0.517638 | + | 1.93185i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(541\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 1.41421i | − | 1.41421i | ||||||
\(545\) | 0.258819 | + | 0.965926i | 0.258819 | + | 0.965926i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.36603 | − | 0.366025i | −1.36603 | − | 0.366025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.36603 | − | 0.366025i | 1.36603 | − | 0.366025i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(556\) | −1.41421 | −1.41421 | ||||||||
\(557\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(562\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(563\) | 0.258819 | − | 0.965926i | 0.258819 | − | 0.965926i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
0.965926 | − | 0.258819i | \(-0.0833333\pi\) | |||||||
\(564\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.41421 | 1.41421 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | 0.866025 | − | 0.500000i | \(-0.166667\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(572\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(576\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(577\) | 0.258819 | + | 0.965926i | 0.258819 | + | 0.965926i | 0.965926 | + | 0.258819i | \(0.0833333\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −0.366025 | − | 1.36603i | −0.366025 | − | 1.36603i | ||||
\(583\) | −1.36603 | + | 0.366025i | −1.36603 | + | 0.366025i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.00000 | −1.00000 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 2.00000i | 2.00000i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(593\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(594\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(597\) | 1.36603 | + | 0.366025i | 1.36603 | + | 0.366025i | ||||
\(598\) | −0.517638 | + | 1.93185i | −0.517638 | + | 1.93185i | ||||
\(599\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | − | 1.00000i | \(-0.5\pi\) | |
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.36603 | − | 0.366025i | 1.36603 | − | 0.366025i | ||||
\(604\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(612\) | −0.965926 | − | 0.258819i | −0.965926 | − | 0.258819i | ||||
\(613\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(614\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | ||||
\(615\) | −1.22474 | + | 0.707107i | −1.22474 | + | 0.707107i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.41421i | 1.41421i | 0.707107 | + | 0.707107i | \(0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.41421 | −1.41421 | ||||||||
\(622\) | 1.41421 | − | 1.41421i | 1.41421 | − | 1.41421i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | − | 1.00000i | − | 1.00000i | ||||||
\(625\) | −1.00000 | −1.00000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.965926 | + | 0.258819i | −0.965926 | + | 0.258819i | ||||
\(629\) | − | 1.41421i | − | 1.41421i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.258819 | + | 0.965926i | −0.258819 | + | 0.965926i | ||||
\(634\) | −1.73205 | + | 1.00000i | −1.73205 | + | 1.00000i | ||||
\(635\) | 1.41421 | 1.41421 | ||||||||
\(636\) | 0.707107 | − | 1.22474i | 0.707107 | − | 1.22474i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(642\) | 0.517638 | + | 1.93185i | 0.517638 | + | 1.93185i | ||||
\(643\) | 0.965926 | − | 0.258819i | 0.965926 | − | 0.258819i | 0.258819 | − | 0.965926i | \(-0.416667\pi\) |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.22474 | − | 0.707107i | 1.22474 | − | 0.707107i | ||||
\(650\) | −1.22474 | + | 0.707107i | −1.22474 | + | 0.707107i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(654\) | 1.41421i | 1.41421i | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −0.707107 | − | 1.22474i | −0.707107 | − | 1.22474i | ||||
\(657\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | − | 1.00000i | \(-0.5\pi\) | |
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(660\) | 1.00000 | 1.00000 | ||||||||
\(661\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(662\) | −1.36603 | − | 0.366025i | −1.36603 | − | 0.366025i | ||||
\(663\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | ||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(669\) | 1.00000i | 1.00000i | ||||||||
\(670\) | 1.41421 | − | 1.41421i | 1.41421 | − | 1.41421i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.366025 | + | 1.36603i | −0.366025 | + | 1.36603i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(674\) | −1.73205 | + | 1.00000i | −1.73205 | + | 1.00000i | ||||
\(675\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −0.258819 | − | 0.965926i | −0.258819 | − | 0.965926i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.22474 | − | 0.707107i | 1.22474 | − | 0.707107i | ||||
\(690\) | −1.73205 | + | 1.00000i | −1.73205 | + | 1.00000i | ||||
\(691\) | 0.707107 | − | 1.22474i | 0.707107 | − | 1.22474i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
0.965926 | − | 0.258819i | \(-0.0833333\pi\) | |||||||
\(692\) | −1.41421 | + | 1.41421i | −1.41421 | + | 1.41421i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.366025 | − | 1.36603i | −0.366025 | − | 1.36603i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.36603 | − | 0.366025i | −1.36603 | − | 0.366025i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.00000 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(702\) | −1.36603 | − | 0.366025i | −1.36603 | − | 0.366025i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 1.00000i | 1.00000i | ||||||||
\(705\) | −0.258819 | + | 0.965926i | −0.258819 | + | 0.965926i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −0.366025 | + | 1.36603i | −0.366025 | + | 1.36603i | ||||
\(709\) | −1.73205 | − | 1.00000i | −1.73205 | − | 1.00000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
−0.866025 | − | 0.500000i | \(-0.833333\pi\) | |||||||
\(710\) | −0.707107 | + | 1.22474i | −0.707107 | + | 1.22474i | ||||
\(711\) | 1.00000 | 1.00000 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(716\) | −1.00000 | −1.00000 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(720\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −1.36603 | − | 0.366025i | −1.36603 | − | 0.366025i | ||||
\(723\) | 1.36603 | − | 0.366025i | 1.36603 | − | 0.366025i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.965926 | + | 0.258819i | 0.965926 | + | 0.258819i | 0.707107 | − | 0.707107i | \(-0.250000\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 1.00000i | − | 1.00000i | ||||||
\(730\) | 0.366025 | − | 1.36603i | 0.366025 | − | 1.36603i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.41421 | + | 1.41421i | 1.41421 | + | 1.41421i | 0.707107 | + | 0.707107i | \(0.250000\pi\) |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(734\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | ||||
\(737\) | −1.36603 | − | 0.366025i | −1.36603 | − | 0.366025i | ||||
\(738\) | −1.93185 | + | 0.517638i | −1.93185 | + | 0.517638i | ||||
\(739\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(740\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.258819 | + | 0.965926i | 0.258819 | + | 0.965926i | ||||
\(748\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1.36603 | − | 0.366025i | −1.36603 | − | 0.366025i | ||||
\(751\) | 2.00000 | 2.00000 | 1.00000 | \(0\) | ||||||
1.00000 | \(0\) | |||||||||
\(752\) | −0.965926 | − | 0.258819i | −0.965926 | − | 0.258819i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | − | 1.00000i | \(-0.5\pi\) | |
1.00000 | \(0\) | |||||||||
\(758\) | 1.36603 | − | 0.366025i | 1.36603 | − | 0.366025i | ||||
\(759\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(762\) | 1.93185 | + | 0.517638i | 1.93185 | + | 0.517638i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − | 1.00000i | − | 1.00000i | ||||||
\(766\) | 0.707107 | − | 1.22474i | 0.707107 | − | 1.22474i | ||||
\(767\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(768\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(769\) | 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 | ||||||||
\(771\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −0.965926 | + | 0.258819i | −0.965926 | + | 0.258819i | −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 | ||||||||
\(778\) | 1.36603 | − | 0.366025i | 1.36603 | − | 0.366025i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −0.965926 | + | 0.258819i | −0.965926 | + | 0.258819i | ||||
\(781\) | 1.00000 | 1.00000 | ||||||||
\(782\) | −1.93185 | − | 0.517638i | −1.93185 | − | 0.517638i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.965926 | − | 0.258819i | −0.965926 | − | 0.258819i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | ||||
\(790\) | 1.22474 | − | 0.707107i | 1.22474 | − | 0.707107i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.36603 | + | 0.366025i | 1.36603 | + | 0.366025i | ||||
\(796\) | 1.41421 | 1.41421 | ||||||||
\(797\) | 0.258819 | + | 0.965926i | 0.258819 | + | 0.965926i | 0.965926 | + | 0.258819i | \(0.0833333\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(800\) | 0.366025 | − | 1.36603i | 0.366025 | − | 1.36603i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.965926 | + | 0.258819i | −0.965926 | + | 0.258819i | ||||
\(804\) | 1.22474 | − | 0.707107i | 1.22474 | − | 0.707107i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.36603 | − | 0.366025i | −1.36603 | − | 0.366025i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | − | 1.00000i | \(-0.5\pi\) | |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(810\) | −0.707107 | − | 1.22474i | −0.707107 | − | 1.22474i | ||||
\(811\) | 1.41421 | 1.41421 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.00000i | 2.00000i | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.00000 | 1.00000 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 1.41421 | + | 1.41421i | 1.41421 | + | 1.41421i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(821\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.366025 | + | 1.36603i | −0.366025 | + | 1.36603i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.258819 | + | 0.965926i | 0.258819 | + | 0.965926i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(828\) | −1.36603 | + | 0.366025i | −1.36603 | + | 0.366025i | ||||
\(829\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(830\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −0.258819 | − | 0.965926i | −0.258819 | − | 0.965926i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | − | 2.00000i | − | 2.00000i | ||||||
\(835\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(842\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(843\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(844\) | 1.00000i | 1.00000i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −0.707107 | + | 1.22474i | −0.707107 | + | 1.22474i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −0.366025 | + | 1.36603i | −0.366025 | + | 1.36603i | ||||
\(849\) | 1.00000i | 1.00000i | ||||||||
\(850\) | −0.707107 | − | 1.22474i | −0.707107 | − | 1.22474i | ||||
\(851\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | ||||
\(852\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(853\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(858\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(859\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.36603 | + | 0.366025i | 1.36603 | + | 0.366025i | ||||
\(863\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(864\) | 1.22474 | − | 0.707107i | 1.22474 | − | 0.707107i | ||||
\(865\) | −1.73205 | − | 1.00000i | −1.73205 | − | 1.00000i | ||||
\(866\) | 1.41421 | − | 2.44949i | 1.41421 | − | 2.44949i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.41421 | 1.41421 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.965926 | − | 0.258819i | 0.965926 | − | 0.258819i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(877\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.965926 | + | 0.258819i | −0.965926 | + | 0.258819i | ||||
\(881\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(884\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(885\) | −1.41421 | −1.41421 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(892\) | 0.258819 | + | 0.965926i | 0.258819 | + | 0.965926i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −1.22474 | + | 0.707107i | −1.22474 | + | 0.707107i | ||||
\(895\) | −0.258819 | − | 0.965926i | −0.258819 | − | 0.965926i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.36603 | − | 0.366025i | −1.36603 | − | 0.366025i | ||||
\(898\) | 2.73205 | − | 0.732051i | 2.73205 | − | 0.732051i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(901\) | 0.707107 | + | 1.22474i | 0.707107 | + | 1.22474i | ||||
\(902\) | 1.93185 | + | 0.517638i | 1.93185 | + | 0.517638i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −0.707107 | − | 1.22474i | −0.707107 | − | 1.22474i | ||||
\(907\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | 1.00000i | \(0.5\pi\) | ||
−1.00000 | \(\pi\) | |||||||||
\(908\) | 0.258819 | − | 0.965926i | 0.258819 | − | 0.965926i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.258819 | − | 0.965926i | 0.258819 | − | 0.965926i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0.366025 | − | 1.36603i | 0.366025 | − | 1.36603i | ||||
\(919\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(922\) | 1.41421 | − | 1.41421i | 1.41421 | − | 1.41421i | ||||
\(923\) | −0.965926 | + | 0.258819i | −0.965926 | + | 0.258819i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.366025 | − | 1.36603i | 0.366025 | − | 1.36603i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(934\) | − | 1.41421i | − | 1.41421i | ||||||
\(935\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.00000i | 1.00000i | ||||||||
\(941\) | 0.707107 | + | 1.22474i | 0.707107 | + | 1.22474i | 0.965926 | + | 0.258819i | \(0.0833333\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(942\) | −0.366025 | − | 1.36603i | −0.366025 | − | 1.36603i | ||||
\(943\) | −1.93185 | + | 0.517638i | −1.93185 | + | 0.517638i | ||||
\(944\) | − | 1.41421i | − | 1.41421i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(948\) | 0.965926 | − | 0.258819i | 0.965926 | − | 0.258819i | ||||
\(949\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.707107 | − | 1.22474i | −0.707107 | − | 1.22474i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | − | 1.00000i | \(-0.5\pi\) | |
−1.00000 | \(\pi\) | |||||||||
\(954\) | 1.73205 | + | 1.00000i | 1.73205 | + | 1.00000i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(961\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(962\) | −0.517638 | − | 1.93185i | −0.517638 | − | 1.93185i | ||||
\(963\) | −1.36603 | + | 0.366025i | −1.36603 | + | 0.366025i | ||||
\(964\) | 1.22474 | − | 0.707107i | 1.22474 | − | 0.707107i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(971\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(972\) | −0.258819 | − | 0.965926i | −0.258819 | − | 0.965926i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.00000 | −1.00000 | ||||||||
\(982\) | 1.36603 | + | 0.366025i | 1.36603 | + | 0.366025i | ||||
\(983\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 1.41421i | 1.41421i | ||||||||
\(991\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.258819 | − | 0.965926i | 0.258819 | − | 0.965926i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.366025 | + | 1.36603i | 0.366025 | + | 1.36603i | ||||
\(996\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(997\) | −1.41421 | + | 1.41421i | −1.41421 | + | 1.41421i | −0.707107 | + | 0.707107i | \(0.750000\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(998\) | −1.36603 | + | 0.366025i | −1.36603 | + | 0.366025i | ||||
\(999\) | 1.22474 | − | 0.707107i | 1.22474 | − | 0.707107i |
(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 | 2205.1.ci.a.508.1 | 8 | ||
5.2 | odd | 4 | inner | 2205.1.ci.a.67.2 | 8 | ||
7.2 | even | 3 | 2205.1.bu.a.373.2 | 8 | |||
7.3 | odd | 6 | 2205.1.bz.a.148.1 | ✓ | 8 | ||
7.4 | even | 3 | 2205.1.bz.a.148.2 | yes | 8 | ||
7.5 | odd | 6 | 2205.1.bu.a.373.1 | 8 | |||
7.6 | odd | 2 | inner | 2205.1.ci.a.508.2 | 8 | ||
9.7 | even | 3 | 2205.1.bu.a.1978.1 | 8 | |||
35.2 | odd | 12 | 2205.1.bu.a.2137.1 | 8 | |||
35.12 | even | 12 | 2205.1.bu.a.2137.2 | 8 | |||
35.17 | even | 12 | 2205.1.bz.a.1912.1 | yes | 8 | ||
35.27 | even | 4 | inner | 2205.1.ci.a.67.1 | 8 | ||
35.32 | odd | 12 | 2205.1.bz.a.1912.2 | yes | 8 | ||
45.7 | odd | 12 | 2205.1.bu.a.1537.2 | 8 | |||
63.16 | even | 3 | inner | 2205.1.ci.a.1843.2 | 8 | ||
63.25 | even | 3 | 2205.1.bz.a.1618.2 | yes | 8 | ||
63.34 | odd | 6 | 2205.1.bu.a.1978.2 | 8 | |||
63.52 | odd | 6 | 2205.1.bz.a.1618.1 | yes | 8 | ||
63.61 | odd | 6 | inner | 2205.1.ci.a.1843.1 | 8 | ||
315.52 | even | 12 | 2205.1.bz.a.1177.1 | yes | 8 | ||
315.97 | even | 12 | 2205.1.bu.a.1537.1 | 8 | |||
315.142 | odd | 12 | inner | 2205.1.ci.a.1402.1 | 8 | ||
315.187 | even | 12 | inner | 2205.1.ci.a.1402.2 | 8 | ||
315.277 | odd | 12 | 2205.1.bz.a.1177.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2205.1.bu.a.373.1 | 8 | 7.5 | odd | 6 | |||
2205.1.bu.a.373.2 | 8 | 7.2 | even | 3 | |||
2205.1.bu.a.1537.1 | 8 | 315.97 | even | 12 | |||
2205.1.bu.a.1537.2 | 8 | 45.7 | odd | 12 | |||
2205.1.bu.a.1978.1 | 8 | 9.7 | even | 3 | |||
2205.1.bu.a.1978.2 | 8 | 63.34 | odd | 6 | |||
2205.1.bu.a.2137.1 | 8 | 35.2 | odd | 12 | |||
2205.1.bu.a.2137.2 | 8 | 35.12 | even | 12 | |||
2205.1.bz.a.148.1 | ✓ | 8 | 7.3 | odd | 6 | ||
2205.1.bz.a.148.2 | yes | 8 | 7.4 | even | 3 | ||
2205.1.bz.a.1177.1 | yes | 8 | 315.52 | even | 12 | ||
2205.1.bz.a.1177.2 | yes | 8 | 315.277 | odd | 12 | ||
2205.1.bz.a.1618.1 | yes | 8 | 63.52 | odd | 6 | ||
2205.1.bz.a.1618.2 | yes | 8 | 63.25 | even | 3 | ||
2205.1.bz.a.1912.1 | yes | 8 | 35.17 | even | 12 | ||
2205.1.bz.a.1912.2 | yes | 8 | 35.32 | odd | 12 | ||
2205.1.ci.a.67.1 | 8 | 35.27 | even | 4 | inner | ||
2205.1.ci.a.67.2 | 8 | 5.2 | odd | 4 | inner | ||
2205.1.ci.a.508.1 | 8 | 1.1 | even | 1 | trivial | ||
2205.1.ci.a.508.2 | 8 | 7.6 | odd | 2 | inner | ||
2205.1.ci.a.1402.1 | 8 | 315.142 | odd | 12 | inner | ||
2205.1.ci.a.1402.2 | 8 | 315.187 | even | 12 | inner | ||
2205.1.ci.a.1843.1 | 8 | 63.61 | odd | 6 | inner | ||
2205.1.ci.a.1843.2 | 8 | 63.16 | even | 3 | inner |