Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2448,1,Mod(319,2448)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2448, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([6, 0, 4, 3]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2448.319");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2448 = 2^{4} \cdot 3^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 2448.de (of order \(12\), degree \(4\), 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: | \(1.22171115093\) |
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 4.2.1591812.1 |
Embedding invariants
Embedding label | 2095.2 | ||
Root | \(-0.258819 + 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2448.2095 |
Dual form | 2448.1.de.a.319.2 |
$q$-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 \(\left(\mathbb{Z}/2448\mathbb{Z}\right)^\times\).
\(n\) | \(613\) | \(1361\) | \(1873\) | \(2143\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
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 | 0 | ||||||||
\(3\) | 0.258819 | − | 0.965926i | 0.258819 | − | 0.965926i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.258819 | + | 0.965926i | 0.258819 | + | 0.965926i | 0.965926 | + | 0.258819i | \(0.0833333\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 1.00000i | − | 1.00000i | ||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.41421 | 1.41421 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.965926 | + | 0.258819i | 0.965926 | + | 0.258819i | 0.707107 | − | 0.707107i | \(-0.250000\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.366025 | − | 1.36603i | −0.366025 | − | 1.36603i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
0.500000 | − | 0.866025i | \(-0.333333\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.258819 | − | 0.965926i | 0.258819 | − | 0.965926i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
0.965926 | − | 0.258819i | \(-0.0833333\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.00000 | 1.00000 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.965926 | + | 0.258819i | −0.965926 | + | 0.258819i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.707107 | − | 1.22474i | 0.707107 | − | 1.22474i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
0.965926 | − | 0.258819i | \(-0.0833333\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.965926 | − | 0.258819i | −0.965926 | − | 0.258819i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.00000i | 1.00000i | 0.866025 | + | 0.500000i | \(0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.366025 | − | 1.36603i | 0.366025 | − | 1.36603i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.707107 | + | 1.22474i | 0.707107 | + | 1.22474i | 0.965926 | + | 0.258819i | \(0.0833333\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.36603 | + | 0.366025i | −1.36603 | + | 0.366025i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.258819 | − | 0.965926i | −0.258819 | − | 0.965926i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.707107 | + | 1.22474i | −0.707107 | + | 1.22474i | 0.258819 | + | 0.965926i | \(0.416667\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.41421 | −1.41421 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.00000 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.258819 | − | 0.965926i | 0.258819 | − | 0.965926i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.22474 | + | 0.707107i | −1.22474 | + | 0.707107i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | 1.00000 | \(0\) | ||
1.00000i | \(0.5\pi\) | |||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.00000i | 1.00000i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.258819 | + | 0.965926i | −0.258819 | + | 0.965926i | 0.707107 | + | 0.707107i | \(0.250000\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.258819 | + | 0.965926i | −0.258819 | + | 0.965926i | 0.707107 | + | 0.707107i | \(0.250000\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.258819 | − | 0.965926i | −0.258819 | − | 0.965926i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.707107 | − | 1.22474i | 0.707107 | − | 1.22474i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
0.965926 | − | 0.258819i | \(-0.0833333\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.965926 | + | 0.258819i | 0.965926 | + | 0.258819i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.366025 | + | 1.36603i | 0.366025 | + | 1.36603i | 0.866025 | + | 0.500000i | \(0.166667\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.36603 | − | 0.366025i | 1.36603 | − | 0.366025i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.41421 | −1.41421 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.41421i | 1.41421i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.965926 | − | 0.258819i | 0.965926 | − | 0.258819i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | − | 1.00000i | \(-0.5\pi\) | |
−1.00000 | \(\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.366025 | + | 1.36603i | 0.366025 | + | 1.36603i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.93185 | + | 0.517638i | 1.93185 | + | 0.517638i | 0.965926 | + | 0.258819i | \(0.0833333\pi\) |
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.707107 | + | 1.22474i | −0.707107 | + | 1.22474i | 0.258819 | + | 0.965926i | \(0.416667\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.258819 | + | 0.965926i | 0.258819 | + | 0.965926i | 0.965926 | + | 0.258819i | \(0.0833333\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | − | 1.00000i | \(-0.5\pi\) | |
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.00000 | −1.00000 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.366025 | + | 1.36603i | 0.366025 | + | 1.36603i | 0.866025 | + | 0.500000i | \(0.166667\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.965926 | − | 0.258819i | 0.965926 | − | 0.258819i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.707107 | − | 1.22474i | −0.707107 | − | 1.22474i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.00000i | 1.00000i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | − | 1.00000i | \(-0.5\pi\) | |
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.366025 | + | 1.36603i | −0.366025 | + | 1.36603i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.258819 | − | 0.965926i | 0.258819 | − | 0.965926i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | 1.00000i | \(0.5\pi\) | ||
−1.00000 | \(\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.258819 | − | 0.965926i | 0.258819 | − | 0.965926i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.366025 | + | 1.36603i | 0.366025 | + | 1.36603i | 0.866025 | + | 0.500000i | \(0.166667\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | − | 1.00000i | \(-0.5\pi\) | |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.965926 | − | 0.258819i | −0.965926 | − | 0.258819i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.00000 | −1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.258819 | − | 0.965926i | −0.258819 | − | 0.965926i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.366025 | + | 1.36603i | 0.366025 | + | 1.36603i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.258819 | + | 0.965926i | −0.258819 | + | 0.965926i | 0.707107 | + | 0.707107i | \(0.250000\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.36603 | − | 0.366025i | 1.36603 | − | 0.366025i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.22474 | − | 0.707107i | 1.22474 | − | 0.707107i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 1.41421i | − | 1.41421i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.00000i | 1.00000i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.22474 | − | 0.707107i | 1.22474 | − | 0.707107i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.00000 | 1.00000 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | − | 1.00000i | \(-0.5\pi\) | |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.965926 | + | 0.258819i | 0.965926 | + | 0.258819i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.41421 | 1.41421 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 1.00000 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.258819 | + | 0.965926i | 0.258819 | + | 0.965926i | 0.965926 | + | 0.258819i | \(0.0833333\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.22474 | + | 0.707107i | −1.22474 | + | 0.707107i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | 0.866025 | − | 0.500000i | \(-0.166667\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.258819 | − | 0.965926i | 0.258819 | − | 0.965926i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | 1.00000 | \(0\) | ||
1.00000i | \(0.5\pi\) | |||||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.366025 | + | 1.36603i | −0.366025 | + | 1.36603i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.965926 | + | 0.258819i | −0.965926 | + | 0.258819i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.707107 | + | 1.22474i | 0.707107 | + | 1.22474i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 1.00000i | − | 1.00000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.36603 | + | 0.366025i | 1.36603 | + | 0.366025i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.965926 | − | 0.258819i | 0.965926 | − | 0.258819i | 0.258819 | − | 0.965926i | \(-0.416667\pi\) |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.00000 | −1.00000 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | − | 1.00000i | \(-0.5\pi\) | |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.22474 | + | 0.707107i | −1.22474 | + | 0.707107i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.41421 | −1.41421 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.965926 | + | 0.258819i | −0.965926 | + | 0.258819i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.36603 | + | 0.366025i | 1.36603 | + | 0.366025i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.93185 | − | 0.517638i | 1.93185 | − | 0.517638i | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) |
0.965926 | − | 0.258819i | \(-0.0833333\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.36603 | + | 0.366025i | −1.36603 | + | 0.366025i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.366025 | − | 1.36603i | 0.366025 | − | 1.36603i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.41421 | 1.41421 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.965926 | − | 0.258819i | −0.965926 | − | 0.258819i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0 | 0 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 1.41421i | − | 1.41421i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.366025 | + | 1.36603i | −0.366025 | + | 1.36603i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.965926 | + | 0.258819i | −0.965926 | + | 0.258819i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.36603 | + | 0.366025i | 1.36603 | + | 0.366025i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.517638 | − | 1.93185i | −0.517638 | − | 1.93185i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.00000 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.41421 | −1.41421 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 1.00000i | − | 1.00000i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −0.707107 | − | 1.22474i | −0.707107 | − | 1.22474i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
0.258819 | − | 0.965926i | \(-0.416667\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | − | 1.00000i | \(-0.5\pi\) | |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.965926 | + | 0.258819i | 0.965926 | + | 0.258819i | 0.707107 | − | 0.707107i | \(-0.250000\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.965926 | + | 0.258819i | −0.965926 | + | 0.258819i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −0.707107 | + | 1.22474i | −0.707107 | + | 1.22474i | 0.258819 | + | 0.965926i | \(0.416667\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.366025 | − | 1.36603i | 0.366025 | − | 1.36603i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.22474 | + | 0.707107i | −1.22474 | + | 0.707107i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.00000i | 1.00000i | 0.866025 | + | 0.500000i | \(0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.258819 | + | 0.965926i | −0.258819 | + | 0.965926i | 0.707107 | + | 0.707107i | \(0.250000\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.41421i | 1.41421i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.00000 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.36603 | − | 0.366025i | −1.36603 | − | 0.366025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.258819 | + | 0.965926i | 0.258819 | + | 0.965926i | 0.965926 | + | 0.258819i | \(0.0833333\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.41421 | 1.41421 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.41421 | −1.41421 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.00000 | − | 1.73205i | 1.00000 | − | 1.73205i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.258819 | − | 0.965926i | −0.258819 | − | 0.965926i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.258819 | + | 0.965926i | −0.258819 | + | 0.965926i | 0.707107 | + | 0.707107i | \(0.250000\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.41421i | 1.41421i | 0.707107 | + | 0.707107i | \(0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.258819 | + | 0.965926i | 0.258819 | + | 0.965926i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 1.41421i | − | 1.41421i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.707107 | − | 1.22474i | −0.707107 | − | 1.22474i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.965926 | − | 0.258819i | 0.965926 | − | 0.258819i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −0.366025 | − | 1.36603i | −0.366025 | − | 1.36603i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
0.500000 | − | 0.866025i | \(-0.333333\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.00000 | 1.00000 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.258819 | − | 0.965926i | −0.258819 | − | 0.965926i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.258819 | + | 0.965926i | 0.258819 | + | 0.965926i | 0.965926 | + | 0.258819i | \(0.0833333\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.366025 | − | 1.36603i | −0.366025 | − | 1.36603i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
0.500000 | − | 0.866025i | \(-0.333333\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.258819 | + | 0.965926i | −0.258819 | + | 0.965926i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | 0.258819 | − | 0.965926i | \(-0.416667\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.41421 | 1.41421 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.366025 | + | 1.36603i | −0.366025 | + | 1.36603i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 1.00000i | − | 1.00000i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.22474 | − | 0.707107i | −1.22474 | − | 0.707107i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | − | 1.00000i | \(-0.5\pi\) | |
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.36603 | + | 0.366025i | −1.36603 | + | 0.366025i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0.517638 | − | 1.93185i | 0.517638 | − | 1.93185i | 0.258819 | − | 0.965926i | \(-0.416667\pi\) |
0.258819 | − | 0.965926i | \(-0.416667\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.22474 | − | 0.707107i | 1.22474 | − | 0.707107i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.258819 | + | 0.965926i | −0.258819 | + | 0.965926i | 0.707107 | + | 0.707107i | \(0.250000\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 1.00000i | − | 1.00000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.965926 | + | 0.258819i | 0.965926 | + | 0.258819i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.707107 | − | 1.22474i | 0.707107 | − | 1.22474i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.258819 | − | 0.965926i | −0.258819 | − | 0.965926i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 2.00000i | − | 2.00000i | − | 1.00000i | \(-0.5\pi\) | |||
− | 1.00000i | \(-0.5\pi\) | ||||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.22474 | + | 0.707107i | 1.22474 | + | 0.707107i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.707107 | + | 1.22474i | −0.707107 | + | 1.22474i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.707107 | + | 1.22474i | 0.707107 | + | 1.22474i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | − | 1.00000i | \(-0.5\pi\) | |
−1.00000 | \(\pi\) | |||||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.00000 | − | 1.73205i | 1.00000 | − | 1.73205i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.366025 | + | 1.36603i | 0.366025 | + | 1.36603i | 0.866025 | + | 0.500000i | \(0.166667\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.965926 | + | 0.258819i | 0.965926 | + | 0.258819i | 0.707107 | − | 0.707107i | \(-0.250000\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.00000 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.41421 | 1.41421 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −0.258819 | − | 0.965926i | −0.258819 | − | 0.965926i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.36603 | − | 0.366025i | 1.36603 | − | 0.366025i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.707107 | − | 1.22474i | −0.707107 | − | 1.22474i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
0.258819 | − | 0.965926i | \(-0.416667\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 1.41421i | − | 1.41421i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.258819 | + | 0.965926i | −0.258819 | + | 0.965926i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.366025 | − | 1.36603i | 0.366025 | − | 1.36603i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.965926 | + | 0.258819i | −0.965926 | + | 0.258819i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | − | 1.00000i | \(-0.5\pi\) | |
1.00000 | \(0\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.41421i | 1.41421i | 0.707107 | + | 0.707107i | \(0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.73205 | − | 1.00000i | −1.73205 | − | 1.00000i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.00000 | −1.00000 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.41421 | −1.41421 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.00000 | 1.00000 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.36603 | − | 0.366025i | −1.36603 | − | 0.366025i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 1.41421i | − | 1.41421i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.258819 | − | 0.965926i | 0.258819 | − | 0.965926i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.41421 | 1.41421 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.22474 | − | 0.707107i | 1.22474 | − | 0.707107i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1.00000i | − | 1.00000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.93185 | − | 0.517638i | 1.93185 | − | 0.517638i | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) |
0.965926 | − | 0.258819i | \(-0.0833333\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 1.41421i | − | 1.41421i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.366025 | − | 1.36603i | −0.366025 | − | 1.36603i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0 | 0 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.707107 | − | 1.22474i | −0.707107 | − | 1.22474i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
0.258819 | − | 0.965926i | \(-0.416667\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.36603 | − | 0.366025i | −1.36603 | − | 0.366025i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.965926 | + | 0.258819i | 0.965926 | + | 0.258819i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.258819 | + | 0.965926i | 0.258819 | + | 0.965926i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.366025 | − | 1.36603i | −0.366025 | − | 1.36603i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | 0.258819 | − | 0.965926i | \(-0.416667\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(998\) | 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 | 2448.1.de.a.2095.2 | yes | 8 | |
4.3 | odd | 2 | inner | 2448.1.de.a.2095.1 | yes | 8 | |
9.4 | even | 3 | inner | 2448.1.de.a.463.1 | yes | 8 | |
17.13 | even | 4 | inner | 2448.1.de.a.1951.2 | yes | 8 | |
36.31 | odd | 6 | inner | 2448.1.de.a.463.2 | yes | 8 | |
68.47 | odd | 4 | inner | 2448.1.de.a.1951.1 | yes | 8 | |
153.13 | even | 12 | inner | 2448.1.de.a.319.1 | ✓ | 8 | |
612.319 | odd | 12 | inner | 2448.1.de.a.319.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2448.1.de.a.319.1 | ✓ | 8 | 153.13 | even | 12 | inner | |
2448.1.de.a.319.2 | yes | 8 | 612.319 | odd | 12 | inner | |
2448.1.de.a.463.1 | yes | 8 | 9.4 | even | 3 | inner | |
2448.1.de.a.463.2 | yes | 8 | 36.31 | odd | 6 | inner | |
2448.1.de.a.1951.1 | yes | 8 | 68.47 | odd | 4 | inner | |
2448.1.de.a.1951.2 | yes | 8 | 17.13 | even | 4 | inner | |
2448.1.de.a.2095.1 | yes | 8 | 4.3 | odd | 2 | inner | |
2448.1.de.a.2095.2 | yes | 8 | 1.1 | even | 1 | trivial |