Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [880,1,Mod(109,880)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(880, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 2, 2]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("880.109");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 880 = 2^{4} \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 880.x (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.439177211117\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{16})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{8}\) |
Projective field: | Galois closure of 8.0.7676100608000.1 |
Embedding invariants
Embedding label | 549.1 | ||
Root | \(-0.382683 - 0.923880i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 880.549 |
Dual form | 880.1.x.a.109.1 |
$q$-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 \(\left(\mathbb{Z}/880\mathbb{Z}\right)^\times\).
\(n\) | \(111\) | \(177\) | \(321\) | \(661\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.923880 | + | 0.382683i | −0.923880 | + | 0.382683i | ||||
\(3\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(4\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(5\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 0.765367i | − | 0.765367i | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||
0.923880 | − | 0.382683i | \(-0.125000\pi\) | |||||||
\(8\) | −0.382683 | + | 0.923880i | −0.382683 | + | 0.923880i | ||||
\(9\) | − | 1.00000i | − | 1.00000i | ||||||
\(10\) | −0.923880 | − | 0.382683i | −0.923880 | − | 0.382683i | ||||
\(11\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.30656 | − | 1.30656i | 1.30656 | − | 1.30656i | 0.382683 | − | 0.923880i | \(-0.375000\pi\) |
0.923880 | − | 0.382683i | \(-0.125000\pi\) | |||||||
\(14\) | 0.292893 | + | 0.707107i | 0.292893 | + | 0.707107i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | − | 1.00000i | − | 1.00000i | ||||||
\(17\) | −0.765367 | −0.765367 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(18\) | 0.382683 | + | 0.923880i | 0.382683 | + | 0.923880i | ||||
\(19\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(20\) | 1.00000 | 1.00000 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.923880 | + | 0.382683i | 0.923880 | + | 0.382683i | ||||
\(23\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000i | 1.00000i | ||||||||
\(26\) | −0.707107 | + | 1.70711i | −0.707107 | + | 1.70711i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.541196 | − | 0.541196i | −0.541196 | − | 0.541196i | ||||
\(29\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.41421 | −1.41421 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(32\) | 0.382683 | + | 0.923880i | 0.382683 | + | 0.923880i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.707107 | − | 0.292893i | 0.707107 | − | 0.292893i | ||||
\(35\) | 0.541196 | − | 0.541196i | 0.541196 | − | 0.541196i | ||||
\(36\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(37\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.923880 | + | 0.382683i | −0.923880 | + | 0.382683i | ||||
\(41\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.30656 | + | 1.30656i | 1.30656 | + | 1.30656i | 0.923880 | + | 0.382683i | \(0.125000\pi\) |
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(44\) | −1.00000 | −1.00000 | ||||||||
\(45\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.414214 | 0.414214 | ||||||||
\(50\) | −0.382683 | − | 0.923880i | −0.382683 | − | 0.923880i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 1.84776i | − | 1.84776i | ||||||
\(53\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1.00000i | − | 1.00000i | ||||||
\(56\) | 0.707107 | + | 0.292893i | 0.707107 | + | 0.292893i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | 1.00000 | \(0\) | ||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(62\) | 1.30656 | − | 0.541196i | 1.30656 | − | 0.541196i | ||||
\(63\) | −0.765367 | −0.765367 | ||||||||
\(64\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(65\) | 1.84776 | 1.84776 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(68\) | −0.541196 | + | 0.541196i | −0.541196 | + | 0.541196i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.292893 | + | 0.707107i | −0.292893 | + | 0.707107i | ||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 0.923880 | + | 0.382683i | 0.923880 | + | 0.382683i | ||||
\(73\) | 1.84776i | 1.84776i | 0.382683 | + | 0.923880i | \(0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.541196 | + | 0.541196i | −0.541196 | + | 0.541196i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(80\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(81\) | −1.00000 | −1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.30656 | − | 1.30656i | 1.30656 | − | 1.30656i | 0.382683 | − | 0.923880i | \(-0.375000\pi\) |
0.923880 | − | 0.382683i | \(-0.125000\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.541196 | − | 0.541196i | −0.541196 | − | 0.541196i | ||||
\(86\) | −1.70711 | − | 0.707107i | −1.70711 | − | 0.707107i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.923880 | − | 0.382683i | 0.923880 | − | 0.382683i | ||||
\(89\) | 1.41421i | 1.41421i | 0.707107 | + | 0.707107i | \(0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(90\) | −0.382683 | + | 0.923880i | −0.382683 | + | 0.923880i | ||||
\(91\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(98\) | −0.382683 | + | 0.158513i | −0.382683 | + | 0.158513i | ||||
\(99\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(100\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(101\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(104\) | 0.707107 | + | 1.70711i | 0.707107 | + | 1.70711i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.541196 | − | 0.541196i | −0.541196 | − | 0.541196i | 0.382683 | − | 0.923880i | \(-0.375000\pi\) |
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(110\) | 0.382683 | + | 0.923880i | 0.382683 | + | 0.923880i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.765367 | −0.765367 | ||||||||
\(113\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.30656 | − | 1.30656i | −1.30656 | − | 1.30656i | ||||
\(118\) | −1.30656 | − | 0.541196i | −1.30656 | − | 0.541196i | ||||
\(119\) | 0.585786i | 0.585786i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000i | 1.00000i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(125\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(126\) | 0.707107 | − | 0.292893i | 0.707107 | − | 0.292893i | ||||
\(127\) | −1.84776 | −1.84776 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(128\) | 0.923880 | + | 0.382683i | 0.923880 | + | 0.382683i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.70711 | + | 0.707107i | −1.70711 | + | 0.707107i | ||||
\(131\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.292893 | − | 0.707107i | 0.292893 | − | 0.707107i | ||||
\(137\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(140\) | − | 0.765367i | − | 0.765367i | ||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.84776 | −1.84776 | ||||||||
\(144\) | −1.00000 | −1.00000 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −0.707107 | − | 1.70711i | −0.707107 | − | 1.70711i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.765367i | 0.765367i | ||||||||
\(154\) | 0.292893 | − | 0.707107i | 0.292893 | − | 0.707107i | ||||
\(155\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.382683 | + | 0.923880i | −0.382683 | + | 0.923880i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.923880 | − | 0.382683i | 0.923880 | − | 0.382683i | ||||
\(163\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.707107 | + | 1.70711i | −0.707107 | + | 1.70711i | ||||
\(167\) | 1.84776i | 1.84776i | 0.382683 | + | 0.923880i | \(0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 2.41421i | − | 2.41421i | ||||||
\(170\) | 0.707107 | + | 0.292893i | 0.707107 | + | 0.292893i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.84776 | 1.84776 | ||||||||
\(173\) | 0.541196 | − | 0.541196i | 0.541196 | − | 0.541196i | −0.382683 | − | 0.923880i | \(-0.625000\pi\) |
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.765367 | 0.765367 | ||||||||
\(176\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.541196 | − | 1.30656i | −0.541196 | − | 1.30656i | ||||
\(179\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(180\) | − | 1.00000i | − | 1.00000i | ||||||
\(181\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(182\) | 1.30656 | + | 0.541196i | 1.30656 | + | 0.541196i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.541196 | + | 0.541196i | 0.541196 | + | 0.541196i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.41421 | 1.41421 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.84776 | −1.84776 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.292893 | − | 0.292893i | 0.292893 | − | 0.292893i | ||||
\(197\) | −0.541196 | − | 0.541196i | −0.541196 | − | 0.541196i | 0.382683 | − | 0.923880i | \(-0.375000\pi\) |
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(198\) | 0.382683 | − | 0.923880i | 0.382683 | − | 0.923880i | ||||
\(199\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(200\) | −0.923880 | − | 0.382683i | −0.923880 | − | 0.382683i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.30656 | − | 1.30656i | −1.30656 | − | 1.30656i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.707107 | + | 0.292893i | 0.707107 | + | 0.292893i | ||||
\(215\) | 1.84776i | 1.84776i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.08239i | 1.08239i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(221\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(224\) | 0.707107 | − | 0.292893i | 0.707107 | − | 0.292893i | ||||
\(225\) | 1.00000 | 1.00000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.30656 | + | 1.30656i | −1.30656 | + | 1.30656i | −0.382683 | + | 0.923880i | \(0.625000\pi\) |
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | − | 1.00000i | \(-0.5\pi\) | |
−1.00000 | \(\pi\) | |||||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.765367i | 0.765367i | 0.923880 | + | 0.382683i | \(0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(234\) | 1.70711 | + | 0.707107i | 1.70711 | + | 0.707107i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.41421 | 1.41421 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.224171 | − | 0.541196i | −0.224171 | − | 0.541196i | ||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(242\) | −0.382683 | − | 0.923880i | −0.382683 | − | 0.923880i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.292893 | + | 0.292893i | 0.292893 | + | 0.292893i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0.541196 | − | 1.30656i | 0.541196 | − | 1.30656i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.382683 | − | 0.923880i | 0.382683 | − | 0.923880i | ||||
\(251\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | 1.00000 | \(0\) | ||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | −0.541196 | + | 0.541196i | −0.541196 | + | 0.541196i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 1.70711 | − | 0.707107i | 1.70711 | − | 0.707107i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.00000 | −1.00000 | ||||||||
\(257\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.30656 | − | 1.30656i | 1.30656 | − | 1.30656i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 1.84776i | − | 1.84776i | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||
0.382683 | − | 0.923880i | \(-0.375000\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | − | 1.00000i | \(-0.5\pi\) | |
1.00000 | \(0\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(272\) | 0.765367i | 0.765367i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.30656 | + | 1.30656i | 1.30656 | + | 1.30656i | 0.923880 | + | 0.382683i | \(0.125000\pi\) |
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.41421i | 1.41421i | ||||||||
\(280\) | 0.292893 | + | 0.707107i | 0.292893 | + | 0.707107i | ||||
\(281\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.30656 | + | 1.30656i | 1.30656 | + | 1.30656i | 0.923880 | + | 0.382683i | \(0.125000\pi\) |
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.70711 | − | 0.707107i | 1.70711 | − | 0.707107i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.923880 | − | 0.382683i | 0.923880 | − | 0.382683i | ||||
\(289\) | −0.414214 | −0.414214 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.30656 | + | 1.30656i | 1.30656 | + | 1.30656i | ||||
\(293\) | −1.30656 | − | 1.30656i | −1.30656 | − | 1.30656i | −0.923880 | − | 0.382683i | \(-0.875000\pi\) |
−0.382683 | − | 0.923880i | \(-0.625000\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.41421i | 1.41421i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.292893 | − | 0.707107i | −0.292893 | − | 0.707107i | ||||
\(307\) | 0.541196 | − | 0.541196i | 0.541196 | − | 0.541196i | −0.382683 | − | 0.923880i | \(-0.625000\pi\) |
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(308\) | 0.765367i | 0.765367i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.30656 | + | 0.541196i | 1.30656 | + | 0.541196i | ||||
\(311\) | − | 2.00000i | − | 2.00000i | − | 1.00000i | \(-0.5\pi\) | |||
− | 1.00000i | \(-0.5\pi\) | ||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.541196 | − | 0.541196i | −0.541196 | − | 0.541196i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | − | 1.00000i | − | 1.00000i | ||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(325\) | 1.30656 | + | 1.30656i | 1.30656 | + | 1.30656i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.41421 | + | 1.41421i | 1.41421 | + | 1.41421i | 0.707107 | + | 0.707107i | \(0.250000\pi\) |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(332\) | − | 1.84776i | − | 1.84776i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −0.707107 | − | 1.70711i | −0.707107 | − | 1.70711i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.765367 | 0.765367 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(338\) | 0.923880 | + | 2.23044i | 0.923880 | + | 2.23044i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.765367 | −0.765367 | ||||||||
\(341\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.08239i | − | 1.08239i | ||||||
\(344\) | −1.70711 | + | 0.707107i | −1.70711 | + | 0.707107i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.292893 | + | 0.707107i | −0.292893 | + | 0.707107i | ||||
\(347\) | −1.30656 | − | 1.30656i | −1.30656 | − | 1.30656i | −0.923880 | − | 0.382683i | \(-0.875000\pi\) |
−0.382683 | − | 0.923880i | \(-0.625000\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(350\) | −0.707107 | + | 0.292893i | −0.707107 | + | 0.292893i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.382683 | − | 0.923880i | 0.382683 | − | 0.923880i | ||||
\(353\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(360\) | 0.382683 | + | 0.923880i | 0.382683 | + | 0.923880i | ||||
\(361\) | − | 1.00000i | − | 1.00000i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.41421 | −1.41421 | ||||||||
\(365\) | −1.30656 | + | 1.30656i | −1.30656 | + | 1.30656i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.541196 | + | 0.541196i | 0.541196 | + | 0.541196i | 0.923880 | − | 0.382683i | \(-0.125000\pi\) |
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(374\) | −0.707107 | − | 0.292893i | −0.707107 | − | 0.292893i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | 1.00000 | \(0\) | ||
1.00000i | \(0.5\pi\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.30656 | + | 0.541196i | −1.30656 | + | 0.541196i | ||||
\(383\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.765367 | −0.765367 | ||||||||
\(386\) | 1.70711 | − | 0.707107i | 1.70711 | − | 0.707107i | ||||
\(387\) | 1.30656 | − | 1.30656i | 1.30656 | − | 1.30656i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | − | 1.00000i | \(-0.5\pi\) | |
−1.00000 | \(\pi\) | |||||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −0.158513 | + | 0.382683i | −0.158513 | + | 0.382683i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.707107 | + | 0.292893i | 0.707107 | + | 0.292893i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.00000i | 1.00000i | ||||||||
\(397\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 1.00000 | ||||||||
\(401\) | −1.41421 | −1.41421 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.84776 | + | 1.84776i | −1.84776 | + | 1.84776i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.765367 | − | 0.765367i | 0.765367 | − | 0.765367i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.84776 | 1.84776 | ||||||||
\(416\) | 1.70711 | + | 0.707107i | 1.70711 | + | 0.707107i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.41421 | − | 1.41421i | 1.41421 | − | 1.41421i | 0.707107 | − | 0.707107i | \(-0.250000\pi\) |
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 0.765367i | − | 0.765367i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −0.765367 | −0.765367 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.707107 | − | 1.70711i | −0.707107 | − | 1.70711i | ||||
\(431\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(434\) | −0.414214 | − | 1.00000i | −0.414214 | − | 1.00000i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(440\) | 0.923880 | + | 0.382683i | 0.923880 | + | 0.382683i | ||||
\(441\) | − | 0.414214i | − | 0.414214i | ||||||
\(442\) | 0.541196 | − | 1.30656i | 0.541196 | − | 1.30656i | ||||
\(443\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.541196 | + | 0.541196i | −0.541196 | + | 0.541196i | ||||
\(449\) | −1.41421 | −1.41421 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(450\) | −0.923880 | + | 0.382683i | −0.923880 | + | 0.382683i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0.707107 | − | 1.70711i | 0.707107 | − | 1.70711i | ||||
\(455\) | − | 1.41421i | − | 1.41421i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 1.84776i | − | 1.84776i | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||
0.382683 | − | 0.923880i | \(-0.375000\pi\) | |||||||
\(458\) | 1.30656 | + | 0.541196i | 1.30656 | + | 0.541196i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.292893 | − | 0.707107i | −0.292893 | − | 0.707107i | ||||
\(467\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(468\) | −1.84776 | −1.84776 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.30656 | + | 0.541196i | −1.30656 | + | 0.541196i | ||||
\(473\) | − | 1.84776i | − | 1.84776i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.414214 | + | 0.414214i | 0.414214 | + | 0.414214i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.382683 | − | 0.158513i | −0.382683 | − | 0.158513i | ||||
\(491\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.00000 | −1.00000 | ||||||||
\(496\) | 1.41421i | 1.41421i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | 1.00000i | \(0.5\pi\) | ||
−1.00000 | \(\pi\) | |||||||||
\(500\) | 1.00000i | 1.00000i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.30656 | − | 0.541196i | −1.30656 | − | 0.541196i | ||||
\(503\) | − | 0.765367i | − | 0.765367i | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||
0.923880 | − | 0.382683i | \(-0.125000\pi\) | |||||||
\(504\) | 0.292893 | − | 0.707107i | 0.292893 | − | 0.707107i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.30656 | + | 1.30656i | −1.30656 | + | 1.30656i | ||||
\(509\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | 1.00000i | \(0.5\pi\) | ||
−1.00000 | \(\pi\) | |||||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.41421 | 1.41421 | ||||||||
\(512\) | 0.923880 | − | 0.382683i | 0.923880 | − | 0.382683i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.707107 | + | 1.70711i | −0.707107 | + | 1.70711i | ||||
\(521\) | 1.41421i | 1.41421i | 0.707107 | + | 0.707107i | \(0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.541196 | + | 0.541196i | 0.541196 | + | 0.541196i | 0.923880 | − | 0.382683i | \(-0.125000\pi\) |
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.707107 | + | 1.70711i | 0.707107 | + | 1.70711i | ||||
\(527\) | 1.08239 | 1.08239 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | −1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 0.765367i | − | 0.765367i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −0.541196 | + | 1.30656i | −0.541196 | + | 1.30656i | ||||
\(539\) | −0.292893 | − | 0.292893i | −0.292893 | − | 0.292893i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.292893 | − | 0.707107i | −0.292893 | − | 0.707107i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.541196 | + | 0.541196i | −0.541196 | + | 0.541196i | −0.923880 | − | 0.382683i | \(-0.875000\pi\) |
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.382683 | + | 0.923880i | −0.382683 | + | 0.923880i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −1.70711 | − | 0.707107i | −1.70711 | − | 0.707107i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.30656 | + | 1.30656i | −1.30656 | + | 1.30656i | −0.382683 | + | 0.923880i | \(0.625000\pi\) |
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(558\) | −0.541196 | − | 1.30656i | −0.541196 | − | 1.30656i | ||||
\(559\) | 3.41421 | 3.41421 | ||||||||
\(560\) | −0.541196 | − | 0.541196i | −0.541196 | − | 0.541196i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −0.541196 | + | 0.541196i | −0.541196 | + | 0.541196i | −0.923880 | − | 0.382683i | \(-0.875000\pi\) |
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.70711 | − | 0.707107i | −1.70711 | − | 0.707107i | ||||
\(567\) | 0.765367i | 0.765367i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(572\) | −1.30656 | + | 1.30656i | −1.30656 | + | 1.30656i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(577\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(578\) | 0.382683 | − | 0.158513i | 0.382683 | − | 0.158513i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −1.70711 | − | 0.707107i | −1.70711 | − | 0.707107i | ||||
\(585\) | − | 1.84776i | − | 1.84776i | ||||||
\(586\) | 1.70711 | + | 0.707107i | 1.70711 | + | 0.707107i | ||||
\(587\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −0.541196 | − | 1.30656i | −0.541196 | − | 1.30656i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.765367 | 0.765367 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.414214 | + | 0.414214i | −0.414214 | + | 0.414214i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.41421i | 1.41421i | 0.707107 | + | 0.707107i | \(0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(602\) | −0.541196 | + | 1.30656i | −0.541196 | + | 1.30656i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.765367 | 0.765367 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0.541196 | + | 0.541196i | 0.541196 | + | 0.541196i | ||||
\(613\) | 0.541196 | + | 0.541196i | 0.541196 | + | 0.541196i | 0.923880 | − | 0.382683i | \(-0.125000\pi\) |
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(614\) | −0.292893 | + | 0.707107i | −0.292893 | + | 0.707107i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.292893 | − | 0.707107i | −0.292893 | − | 0.707107i | ||||
\(617\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(620\) | −1.41421 | −1.41421 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0.765367 | + | 1.84776i | 0.765367 | + | 1.84776i | ||||
\(623\) | 1.08239 | 1.08239 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.00000 | −1.00000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0.707107 | + | 0.292893i | 0.707107 | + | 0.292893i | ||||
\(631\) | 2.00000i | 2.00000i | 1.00000i | \(0.5\pi\) | ||||||
1.00000i | \(0.5\pi\) | |||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.30656 | − | 1.30656i | −1.30656 | − | 1.30656i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.541196 | − | 0.541196i | 0.541196 | − | 0.541196i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.382683 | + | 0.923880i | 0.382683 | + | 0.923880i | ||||
\(641\) | 1.41421 | 1.41421 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(648\) | 0.382683 | − | 0.923880i | 0.382683 | − | 0.923880i | ||||
\(649\) | − | 1.41421i | − | 1.41421i | ||||||
\(650\) | −1.70711 | − | 0.707107i | −1.70711 | − | 0.707107i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.84776 | 1.84776 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | 1.00000 | \(0\) | ||
1.00000i | \(0.5\pi\) | |||||||||
\(662\) | −1.84776 | − | 0.765367i | −1.84776 | − | 0.765367i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.707107 | + | 1.70711i | 0.707107 | + | 1.70711i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 1.30656 | + | 1.30656i | 1.30656 | + | 1.30656i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.765367 | −0.765367 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(674\) | −0.707107 | + | 0.292893i | −0.707107 | + | 0.292893i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.70711 | − | 1.70711i | −1.70711 | − | 1.70711i | ||||
\(677\) | 0.541196 | + | 0.541196i | 0.541196 | + | 0.541196i | 0.923880 | − | 0.382683i | \(-0.125000\pi\) |
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0.707107 | − | 0.292893i | 0.707107 | − | 0.292893i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.30656 | − | 0.541196i | −1.30656 | − | 0.541196i | ||||
\(683\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0.414214 | + | 1.00000i | 0.414214 | + | 1.00000i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.30656 | − | 1.30656i | 1.30656 | − | 1.30656i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | 1.00000i | \(0.5\pi\) | ||
−1.00000 | \(\pi\) | |||||||||
\(692\) | − | 0.765367i | − | 0.765367i | ||||||
\(693\) | 0.541196 | + | 0.541196i | 0.541196 | + | 0.541196i | ||||
\(694\) | 1.70711 | + | 0.707107i | 1.70711 | + | 0.707107i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.541196 | − | 0.541196i | 0.541196 | − | 0.541196i | ||||
\(701\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 1.00000i | 1.00000i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.41421 | − | 1.41421i | −1.41421 | − | 1.41421i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
−0.707107 | − | 0.707107i | \(-0.750000\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.30656 | − | 0.541196i | −1.30656 | − | 0.541196i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.30656 | − | 1.30656i | −1.30656 | − | 1.30656i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.41421 | −1.41421 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(720\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0.382683 | + | 0.923880i | 0.382683 | + | 0.923880i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(728\) | 1.30656 | − | 0.541196i | 1.30656 | − | 0.541196i | ||||
\(729\) | 1.00000i | 1.00000i | ||||||||
\(730\) | 0.707107 | − | 1.70711i | 0.707107 | − | 1.70711i | ||||
\(731\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.541196 | − | 0.541196i | 0.541196 | − | 0.541196i | −0.382683 | − | 0.923880i | \(-0.625000\pi\) |
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0.765367i | 0.765367i | 0.923880 | + | 0.382683i | \(0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −0.707107 | − | 0.292893i | −0.707107 | − | 0.292893i | ||||
\(747\) | −1.30656 | − | 1.30656i | −1.30656 | − | 1.30656i | ||||
\(748\) | 0.765367 | 0.765367 | ||||||||
\(749\) | −0.414214 | + | 0.414214i | −0.414214 | + | 0.414214i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.00000 | −2.00000 | −1.00000 | \(\pi\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(758\) | −1.30656 | − | 0.541196i | −1.30656 | − | 0.541196i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(765\) | −0.541196 | + | 0.541196i | −0.541196 | + | 0.541196i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.61313 | 2.61313 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(770\) | 0.707107 | − | 0.292893i | 0.707107 | − | 0.292893i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.30656 | + | 1.30656i | −1.30656 | + | 1.30656i | ||||
\(773\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(774\) | −0.707107 | + | 1.70711i | −0.707107 | + | 1.70711i | ||||
\(775\) | − | 1.41421i | − | 1.41421i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.30656 | + | 0.541196i | 1.30656 | + | 0.541196i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 0.414214i | − | 0.414214i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.541196 | − | 0.541196i | 0.541196 | − | 0.541196i | −0.382683 | − | 0.923880i | \(-0.625000\pi\) |
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(788\) | −0.765367 | −0.765367 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −0.382683 | − | 0.923880i | −0.382683 | − | 0.923880i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −0.923880 | + | 0.382683i | −0.923880 | + | 0.382683i | ||||
\(801\) | 1.41421 | 1.41421 | ||||||||
\(802\) | 1.30656 | − | 0.541196i | 1.30656 | − | 0.541196i | ||||
\(803\) | 1.30656 | − | 1.30656i | 1.30656 | − | 1.30656i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.00000 | − | 2.41421i | 1.00000 | − | 2.41421i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(810\) | 0.923880 | + | 0.382683i | 0.923880 | + | 0.382683i | ||||
\(811\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.414214 | + | 1.00000i | −0.414214 | + | 1.00000i | ||||
\(827\) | 1.30656 | + | 1.30656i | 1.30656 | + | 1.30656i | 0.923880 | + | 0.382683i | \(0.125000\pi\) |
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.41421 | − | 1.41421i | 1.41421 | − | 1.41421i | 0.707107 | − | 0.707107i | \(-0.250000\pi\) |
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(830\) | −1.70711 | + | 0.707107i | −1.70711 | + | 0.707107i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.84776 | −1.84776 | ||||||||
\(833\) | −0.317025 | −0.317025 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.30656 | + | 1.30656i | −1.30656 | + | 1.30656i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −0.765367 | + | 1.84776i | −0.765367 | + | 1.84776i | ||||
\(839\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 1.00000i | − | 1.00000i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.70711 | − | 1.70711i | 1.70711 | − | 1.70711i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.765367 | 0.765367 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0.292893 | + | 0.707107i | 0.292893 | + | 0.707107i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.30656 | + | 1.30656i | 1.30656 | + | 1.30656i | 0.923880 | + | 0.382683i | \(0.125000\pi\) |
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.707107 | − | 0.292893i | 0.707107 | − | 0.292893i | ||||
\(857\) | − | 1.84776i | − | 1.84776i | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||
0.382683 | − | 0.923880i | \(-0.375000\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.41421 | − | 1.41421i | −1.41421 | − | 1.41421i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
−0.707107 | − | 0.707107i | \(-0.750000\pi\) | |||||||
\(860\) | 1.30656 | + | 1.30656i | 1.30656 | + | 1.30656i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.765367 | 0.765367 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.765367 | + | 0.765367i | 0.765367 | + | 0.765367i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.541196 | + | 0.541196i | 0.541196 | + | 0.541196i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.541196 | − | 0.541196i | 0.541196 | − | 0.541196i | −0.382683 | − | 0.923880i | \(-0.625000\pi\) |
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.00000 | −1.00000 | ||||||||
\(881\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(882\) | 0.158513 | + | 0.382683i | 0.158513 | + | 0.382683i | ||||
\(883\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(884\) | 1.41421i | 1.41421i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 1.84776i | − | 1.84776i | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||
0.382683 | − | 0.923880i | \(-0.375000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.41421i | 1.41421i | ||||||||
\(890\) | 0.541196 | − | 1.30656i | 0.541196 | − | 1.30656i | ||||
\(891\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.292893 | − | 0.707107i | 0.292893 | − | 0.707107i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.30656 | − | 0.541196i | 1.30656 | − | 0.541196i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(908\) | 1.84776i | 1.84776i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0.541196 | + | 1.30656i | 0.541196 | + | 1.30656i | ||||
\(911\) | 1.41421 | 1.41421 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.84776 | −1.84776 | ||||||||
\(914\) | 0.707107 | + | 1.70711i | 0.707107 | + | 1.70711i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.41421 | −1.41421 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0.541196 | + | 0.541196i | 0.541196 | + | 0.541196i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.765367i | 0.765367i | ||||||||
\(936\) | 1.70711 | − | 0.707107i | 1.70711 | − | 0.707107i | ||||
\(937\) | − | 0.765367i | − | 0.765367i | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||
0.923880 | − | 0.382683i | \(-0.125000\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.707107 | + | 1.70711i | 0.707107 | + | 1.70711i | ||||
\(947\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.41421 | + | 2.41421i | 2.41421 | + | 2.41421i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.541196 | − | 0.224171i | −0.541196 | − | 0.224171i | ||||
\(953\) | 1.84776i | 1.84776i | 0.382683 | + | 0.923880i | \(0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.00000 | 1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.541196 | + | 0.541196i | −0.541196 | + | 0.541196i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.30656 | − | 1.30656i | −1.30656 | − | 1.30656i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.765367i | 0.765367i | 0.923880 | + | 0.382683i | \(0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(968\) | −0.923880 | − | 0.382683i | −0.923880 | − | 0.382683i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(980\) | 0.414214 | 0.414214 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 0.765367i | − | 0.765367i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0.923880 | − | 0.382683i | 0.923880 | − | 0.382683i | ||||
\(991\) | −1.41421 | −1.41421 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(992\) | −0.541196 | − | 1.30656i | −0.541196 | − | 1.30656i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.541196 | − | 0.541196i | −0.541196 | − | 0.541196i | 0.382683 | − | 0.923880i | \(-0.375000\pi\) |
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(998\) | 0.541196 | − | 1.30656i | 0.541196 | − | 1.30656i | ||||
\(999\) | 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 | 880.1.x.a.549.1 | yes | 8 | |
4.3 | odd | 2 | 3520.1.x.a.1649.4 | 8 | |||
5.4 | even | 2 | inner | 880.1.x.a.549.4 | yes | 8 | |
11.10 | odd | 2 | inner | 880.1.x.a.549.4 | yes | 8 | |
16.3 | odd | 4 | 3520.1.x.a.3409.3 | 8 | |||
16.13 | even | 4 | inner | 880.1.x.a.109.1 | ✓ | 8 | |
20.19 | odd | 2 | 3520.1.x.a.1649.3 | 8 | |||
44.43 | even | 2 | 3520.1.x.a.1649.3 | 8 | |||
55.54 | odd | 2 | CM | 880.1.x.a.549.1 | yes | 8 | |
80.19 | odd | 4 | 3520.1.x.a.3409.4 | 8 | |||
80.29 | even | 4 | inner | 880.1.x.a.109.4 | yes | 8 | |
176.109 | odd | 4 | inner | 880.1.x.a.109.4 | yes | 8 | |
176.131 | even | 4 | 3520.1.x.a.3409.4 | 8 | |||
220.219 | even | 2 | 3520.1.x.a.1649.4 | 8 | |||
880.109 | odd | 4 | inner | 880.1.x.a.109.1 | ✓ | 8 | |
880.659 | even | 4 | 3520.1.x.a.3409.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
880.1.x.a.109.1 | ✓ | 8 | 16.13 | even | 4 | inner | |
880.1.x.a.109.1 | ✓ | 8 | 880.109 | odd | 4 | inner | |
880.1.x.a.109.4 | yes | 8 | 80.29 | even | 4 | inner | |
880.1.x.a.109.4 | yes | 8 | 176.109 | odd | 4 | inner | |
880.1.x.a.549.1 | yes | 8 | 1.1 | even | 1 | trivial | |
880.1.x.a.549.1 | yes | 8 | 55.54 | odd | 2 | CM | |
880.1.x.a.549.4 | yes | 8 | 5.4 | even | 2 | inner | |
880.1.x.a.549.4 | yes | 8 | 11.10 | odd | 2 | inner | |
3520.1.x.a.1649.3 | 8 | 20.19 | odd | 2 | |||
3520.1.x.a.1649.3 | 8 | 44.43 | even | 2 | |||
3520.1.x.a.1649.4 | 8 | 4.3 | odd | 2 | |||
3520.1.x.a.1649.4 | 8 | 220.219 | even | 2 | |||
3520.1.x.a.3409.3 | 8 | 16.3 | odd | 4 | |||
3520.1.x.a.3409.3 | 8 | 880.659 | even | 4 | |||
3520.1.x.a.3409.4 | 8 | 80.19 | odd | 4 | |||
3520.1.x.a.3409.4 | 8 | 176.131 | even | 4 |