Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2151,1,Mod(238,2151)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2151, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 3]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2151.238");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2151 = 3^{2} \cdot 239 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 2151.f (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.07348884217\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{18})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{3} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Projective image: | \(D_{9}\) |
Projective field: | Galois closure of 9.1.1733990286981681.1 |
Embedding invariants
Embedding label | 238.3 | ||
Root | \(-0.173648 + 0.984808i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2151.238 |
Dual form | 2151.1.f.a.1672.3 |
$q$-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 \(\left(\mathbb{Z}/2151\mathbb{Z}\right)^\times\).
\(n\) | \(479\) | \(1441\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.939693 | + | 1.62760i | 0.939693 | + | 1.62760i | 0.766044 | + | 0.642788i | \(0.222222\pi\) |
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(3\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(4\) | −1.26604 | + | 2.19285i | −1.26604 | + | 2.19285i | ||||
\(5\) | −0.173648 | + | 0.300767i | −0.173648 | + | 0.300767i | −0.939693 | − | 0.342020i | \(-0.888889\pi\) |
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(6\) | −1.87939 | −1.87939 | ||||||||
\(7\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(8\) | −2.87939 | −2.87939 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(10\) | −0.652704 | −0.652704 | ||||||||
\(11\) | −0.173648 | − | 0.300767i | −0.173648 | − | 0.300767i | 0.766044 | − | 0.642788i | \(-0.222222\pi\) |
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(12\) | −1.26604 | − | 2.19285i | −1.26604 | − | 2.19285i | ||||
\(13\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.173648 | − | 0.300767i | −0.173648 | − | 0.300767i | ||||
\(16\) | −1.43969 | − | 2.49362i | −1.43969 | − | 2.49362i | ||||
\(17\) | −1.87939 | −1.87939 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(18\) | 0.939693 | − | 1.62760i | 0.939693 | − | 1.62760i | ||||
\(19\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(20\) | −0.439693 | − | 0.761570i | −0.439693 | − | 0.761570i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.326352 | − | 0.565258i | 0.326352 | − | 0.565258i | ||||
\(23\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(24\) | 1.43969 | − | 2.49362i | 1.43969 | − | 2.49362i | ||||
\(25\) | 0.439693 | + | 0.761570i | 0.439693 | + | 0.761570i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 1.00000 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.173648 | − | 0.300767i | −0.173648 | − | 0.300767i | 0.766044 | − | 0.642788i | \(-0.222222\pi\) |
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(30\) | 0.326352 | − | 0.565258i | 0.326352 | − | 0.565258i | ||||
\(31\) | −0.766044 | + | 1.32683i | −0.766044 | + | 1.32683i | 0.173648 | + | 0.984808i | \(0.444444\pi\) |
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(32\) | 1.26604 | − | 2.19285i | 1.26604 | − | 2.19285i | ||||
\(33\) | 0.347296 | 0.347296 | ||||||||
\(34\) | −1.76604 | − | 3.05888i | −1.76604 | − | 3.05888i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.53209 | 2.53209 | ||||||||
\(37\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(41\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(44\) | 0.879385 | 0.879385 | ||||||||
\(45\) | 0.347296 | 0.347296 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(48\) | 2.87939 | 2.87939 | ||||||||
\(49\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(50\) | −0.826352 | + | 1.43128i | −0.826352 | + | 1.43128i | ||||
\(51\) | 0.939693 | − | 1.62760i | 0.939693 | − | 1.62760i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(54\) | 0.939693 | + | 1.62760i | 0.939693 | + | 1.62760i | ||||
\(55\) | 0.120615 | 0.120615 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.326352 | − | 0.565258i | 0.326352 | − | 0.565258i | ||||
\(59\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(60\) | 0.879385 | 0.879385 | ||||||||
\(61\) | 0.939693 | + | 1.62760i | 0.939693 | + | 1.62760i | 0.766044 | + | 0.642788i | \(0.222222\pi\) |
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(62\) | −2.87939 | −2.87939 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.87939 | 1.87939 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.326352 | + | 0.565258i | 0.326352 | + | 0.565258i | ||||
\(67\) | −0.766044 | + | 1.32683i | −0.766044 | + | 1.32683i | 0.173648 | + | 0.984808i | \(0.444444\pi\) |
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(68\) | 2.37939 | − | 4.12122i | 2.37939 | − | 4.12122i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.00000 | 2.00000 | 1.00000 | \(0\) | ||||||
1.00000 | \(0\) | |||||||||
\(72\) | 1.43969 | + | 2.49362i | 1.43969 | + | 2.49362i | ||||
\(73\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.879385 | −0.879385 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(80\) | 1.00000 | 1.00000 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.939693 | + | 1.62760i | 0.939693 | + | 1.62760i | 0.766044 | + | 0.642788i | \(0.222222\pi\) |
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.326352 | − | 0.565258i | 0.326352 | − | 0.565258i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.347296 | 0.347296 | ||||||||
\(88\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(89\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(90\) | 0.326352 | + | 0.565258i | 0.326352 | + | 0.565258i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.766044 | − | 1.32683i | −0.766044 | − | 1.32683i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.26604 | + | 2.19285i | 1.26604 | + | 2.19285i | ||||
\(97\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(98\) | −1.87939 | −1.87939 | ||||||||
\(99\) | −0.173648 | + | 0.300767i | −0.173648 | + | 0.300767i | ||||
\(100\) | −2.22668 | −2.22668 | ||||||||
\(101\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
−0.500000 | − | 0.866025i | \(-0.666667\pi\) | |||||||
\(102\) | 3.53209 | 3.53209 | ||||||||
\(103\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(108\) | −1.26604 | + | 2.19285i | −1.26604 | + | 2.19285i | ||||
\(109\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(110\) | 0.113341 | + | 0.196312i | 0.113341 | + | 0.196312i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.879385 | 0.879385 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(121\) | 0.439693 | − | 0.761570i | 0.439693 | − | 0.761570i | ||||
\(122\) | −1.76604 | + | 3.05888i | −1.76604 | + | 3.05888i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.93969 | − | 3.35965i | −1.93969 | − | 3.35965i | ||||
\(125\) | −0.652704 | −0.652704 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.53209 | 1.53209 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(132\) | −0.439693 | + | 0.761570i | −0.439693 | + | 0.761570i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −2.87939 | −2.87939 | ||||||||
\(135\) | −0.173648 | + | 0.300767i | −0.173648 | + | 0.300767i | ||||
\(136\) | 5.41147 | 5.41147 | ||||||||
\(137\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.87939 | + | 3.25519i | 1.87939 | + | 3.25519i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.43969 | + | 2.49362i | −1.43969 | + | 2.49362i | ||||
\(145\) | 0.120615 | 0.120615 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(150\) | −0.826352 | − | 1.43128i | −0.826352 | − | 1.43128i | ||||
\(151\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.939693 | + | 1.62760i | 0.939693 | + | 1.62760i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.266044 | − | 0.460802i | −0.266044 | − | 0.460802i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.173648 | + | 0.300767i | −0.173648 | + | 0.300767i | −0.939693 | − | 0.342020i | \(-0.888889\pi\) |
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.439693 | + | 0.761570i | 0.439693 | + | 0.761570i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.87939 | −1.87939 | ||||||||
\(163\) | 1.53209 | 1.53209 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.0603074 | + | 0.104455i | −0.0603074 | + | 0.104455i | ||||
\(166\) | −1.76604 | + | 3.05888i | −1.76604 | + | 3.05888i | ||||
\(167\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(170\) | 1.22668 | 1.22668 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(174\) | 0.326352 | + | 0.565258i | 0.326352 | + | 0.565258i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(180\) | −0.439693 | + | 0.761570i | −0.439693 | + | 0.761570i | ||||
\(181\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.87939 | −1.87939 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.43969 | − | 2.49362i | 1.43969 | − | 2.49362i | ||||
\(187\) | 0.326352 | + | 0.565258i | 0.326352 | + | 0.565258i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(192\) | −0.939693 | + | 1.62760i | −0.939693 | + | 1.62760i | ||||
\(193\) | −0.766044 | + | 1.32683i | −0.766044 | + | 1.32683i | 0.173648 | + | 0.984808i | \(0.444444\pi\) |
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.26604 | − | 2.19285i | −1.26604 | − | 2.19285i | ||||
\(197\) | −1.87939 | −1.87939 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(198\) | −0.652704 | −0.652704 | ||||||||
\(199\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(200\) | −1.26604 | − | 2.19285i | −1.26604 | − | 2.19285i | ||||
\(201\) | −0.766044 | − | 1.32683i | −0.766044 | − | 1.32683i | ||||
\(202\) | 1.87939 | − | 3.25519i | 1.87939 | − | 3.25519i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 2.37939 | + | 4.12122i | 2.37939 | + | 4.12122i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.939693 | − | 1.62760i | 0.939693 | − | 1.62760i | 0.173648 | − | 0.984808i | \(-0.444444\pi\) |
0.766044 | − | 0.642788i | \(-0.222222\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.87939 | −2.87939 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −0.939693 | − | 1.62760i | −0.939693 | − | 1.62760i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.152704 | + | 0.264490i | −0.152704 | + | 0.264490i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.439693 | − | 0.761570i | 0.439693 | − | 0.761570i | ||||
\(226\) | 1.87939 | 1.87939 | ||||||||
\(227\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(233\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(240\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(241\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(242\) | 1.65270 | 1.65270 | ||||||||
\(243\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(244\) | −4.75877 | −4.75877 | ||||||||
\(245\) | −0.173648 | − | 0.300767i | −0.173648 | − | 0.300767i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 2.20574 | − | 3.82045i | 2.20574 | − | 3.82045i | ||||
\(249\) | −1.87939 | −1.87939 | ||||||||
\(250\) | −0.613341 | − | 1.06234i | −0.613341 | − | 1.06234i | ||||
\(251\) | 0.347296 | 0.347296 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 1.43969 | + | 2.49362i | 1.43969 | + | 2.49362i | ||||
\(255\) | 0.326352 | + | 0.565258i | 0.326352 | + | 0.565258i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.766044 | + | 1.32683i | −0.766044 | + | 1.32683i | 0.173648 | + | 0.984808i | \(0.444444\pi\) |
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.173648 | + | 0.300767i | −0.173648 | + | 0.300767i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.766044 | − | 1.32683i | −0.766044 | − | 1.32683i | −0.939693 | − | 0.342020i | \(-0.888889\pi\) |
0.173648 | − | 0.984808i | \(-0.444444\pi\) | |||||||
\(264\) | −1.00000 | −1.00000 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.93969 | − | 3.35965i | −1.93969 | − | 3.35965i | ||||
\(269\) | 1.53209 | 1.53209 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(270\) | −0.652704 | −0.652704 | ||||||||
\(271\) | 0.347296 | 0.347296 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(272\) | 2.70574 | + | 4.68647i | 2.70574 | + | 4.68647i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.152704 | − | 0.264490i | 0.152704 | − | 0.264490i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.53209 | 1.53209 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.939693 | − | 1.62760i | 0.939693 | − | 1.62760i | 0.173648 | − | 0.984808i | \(-0.444444\pi\) |
0.766044 | − | 0.642788i | \(-0.222222\pi\) | |||||||
\(284\) | −2.53209 | + | 4.38571i | −2.53209 | + | 4.38571i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −2.53209 | −2.53209 | ||||||||
\(289\) | 2.53209 | 2.53209 | ||||||||
\(290\) | 0.113341 | + | 0.196312i | 0.113341 | + | 0.196312i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | −0.500000 | + | 0.866025i | \(0.666667\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(294\) | 0.939693 | − | 1.62760i | 0.939693 | − | 1.62760i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.173648 | − | 0.300767i | −0.173648 | − | 0.300767i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 1.11334 | − | 1.92836i | 1.11334 | − | 1.92836i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.00000 | 2.00000 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.652704 | −0.652704 | ||||||||
\(306\) | −1.76604 | + | 3.05888i | −1.76604 | + | 3.05888i | ||||
\(307\) | 0.347296 | 0.347296 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(311\) | −0.173648 | + | 0.300767i | −0.173648 | + | 0.300767i | −0.939693 | − | 0.342020i | \(-0.888889\pi\) |
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(314\) | −0.652704 | −0.652704 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.0603074 | + | 0.104455i | −0.0603074 | + | 0.104455i | ||||
\(320\) | −0.326352 | + | 0.565258i | −0.326352 | + | 0.565258i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −1.26604 | − | 2.19285i | −1.26604 | − | 2.19285i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.43969 | + | 2.49362i | 1.43969 | + | 2.49362i | ||||
\(327\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −0.226682 | −0.226682 | ||||||||
\(331\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(332\) | −4.75877 | −4.75877 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.266044 | − | 0.460802i | −0.266044 | − | 0.460802i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.173648 | + | 0.300767i | −0.173648 | + | 0.300767i | −0.939693 | − | 0.342020i | \(-0.888889\pi\) |
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(338\) | 0.939693 | − | 1.62760i | 0.939693 | − | 1.62760i | ||||
\(339\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(340\) | 0.826352 | + | 1.43128i | 0.826352 | + | 1.43128i | ||||
\(341\) | 0.532089 | 0.532089 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.766044 | + | 1.32683i | −0.766044 | + | 1.32683i | 0.173648 | + | 0.984808i | \(0.444444\pi\) |
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(348\) | −0.439693 | + | 0.761570i | −0.439693 | + | 0.761570i | ||||
\(349\) | −0.766044 | − | 1.32683i | −0.766044 | − | 1.32683i | −0.939693 | − | 0.342020i | \(-0.888889\pi\) |
0.173648 | − | 0.984808i | \(-0.444444\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.879385 | −0.879385 | ||||||||
\(353\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.347296 | + | 0.601535i | −0.347296 | + | 0.601535i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.00000 | 2.00000 | 1.00000 | \(0\) | ||||||
1.00000 | \(0\) | |||||||||
\(360\) | −1.00000 | −1.00000 | ||||||||
\(361\) | 1.00000 | 1.00000 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.439693 | + | 0.761570i | 0.439693 | + | 0.761570i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.76604 | − | 3.05888i | −1.76604 | − | 3.05888i | ||||
\(367\) | 0.939693 | + | 1.62760i | 0.939693 | + | 1.62760i | 0.766044 | + | 0.642788i | \(0.222222\pi\) |
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 3.87939 | 3.87939 | ||||||||
\(373\) | −1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | −0.500000 | + | 0.866025i | \(0.666667\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(374\) | −0.613341 | + | 1.06234i | −0.613341 | + | 1.06234i | ||||
\(375\) | 0.326352 | − | 0.565258i | 0.326352 | − | 0.565258i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.766044 | + | 1.32683i | −0.766044 | + | 1.32683i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(384\) | −1.00000 | −1.00000 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.87939 | −2.87939 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.173648 | − | 0.300767i | −0.173648 | − | 0.300767i | 0.766044 | − | 0.642788i | \(-0.222222\pi\) |
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 1.43969 | − | 2.49362i | 1.43969 | − | 2.49362i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.76604 | − | 3.05888i | −1.76604 | − | 3.05888i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.439693 | − | 0.761570i | −0.439693 | − | 0.761570i | ||||
\(397\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.26604 | − | 2.19285i | 1.26604 | − | 2.19285i | ||||
\(401\) | 0.939693 | − | 1.62760i | 0.939693 | − | 1.62760i | 0.173648 | − | 0.984808i | \(-0.444444\pi\) |
0.766044 | − | 0.642788i | \(-0.222222\pi\) | |||||||
\(402\) | 1.43969 | − | 2.49362i | 1.43969 | − | 2.49362i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 5.06418 | 5.06418 | ||||||||
\(405\) | −0.173648 | − | 0.300767i | −0.173648 | − | 0.300767i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −2.70574 | + | 4.68647i | −2.70574 | + | 4.68647i | ||||
\(409\) | 0.939693 | − | 1.62760i | 0.939693 | − | 1.62760i | 0.173648 | − | 0.984808i | \(-0.444444\pi\) |
0.766044 | − | 0.642788i | \(-0.222222\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.652704 | −0.652704 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.766044 | + | 1.32683i | −0.766044 | + | 1.32683i | 0.173648 | + | 0.984808i | \(0.444444\pi\) |
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(422\) | 3.53209 | 3.53209 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.826352 | − | 1.43128i | −0.826352 | − | 1.43128i | ||||
\(426\) | −3.75877 | −3.75877 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.53209 | 1.53209 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(432\) | −1.43969 | − | 2.49362i | −1.43969 | − | 2.49362i | ||||
\(433\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.0603074 | + | 0.104455i | −0.0603074 | + | 0.104455i | ||||
\(436\) | 1.26604 | − | 2.19285i | 1.26604 | − | 2.19285i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(440\) | −0.347296 | −0.347296 | ||||||||
\(441\) | 1.00000 | 1.00000 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.939693 | + | 1.62760i | 0.939693 | + | 1.62760i | 0.766044 | + | 0.642788i | \(0.222222\pi\) |
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(450\) | 1.65270 | 1.65270 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 1.26604 | + | 2.19285i | 1.26604 | + | 2.19285i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
−0.500000 | − | 0.866025i | \(-0.666667\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.87939 | −1.87939 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(464\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(465\) | 0.532089 | 0.532089 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.173648 | − | 0.300767i | −0.173648 | − | 0.300767i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.87939 | −1.87939 | ||||||||
\(479\) | −0.173648 | − | 0.300767i | −0.173648 | − | 0.300767i | 0.766044 | − | 0.642788i | \(-0.222222\pi\) |
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(480\) | −0.879385 | −0.879385 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −0.939693 | + | 1.62760i | −0.939693 | + | 1.62760i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.11334 | + | 1.92836i | 1.11334 | + | 1.92836i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.939693 | − | 1.62760i | 0.939693 | − | 1.62760i | ||||
\(487\) | 0.347296 | 0.347296 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(488\) | −2.70574 | − | 4.68647i | −2.70574 | − | 4.68647i | ||||
\(489\) | −0.766044 | + | 1.32683i | −0.766044 | + | 1.32683i | ||||
\(490\) | 0.326352 | − | 0.565258i | 0.326352 | − | 0.565258i | ||||
\(491\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.326352 | + | 0.565258i | 0.326352 | + | 0.565258i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.0603074 | − | 0.104455i | −0.0603074 | − | 0.104455i | ||||
\(496\) | 4.41147 | 4.41147 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −1.76604 | − | 3.05888i | −1.76604 | − | 3.05888i | ||||
\(499\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(500\) | 0.826352 | − | 1.43128i | 0.826352 | − | 1.43128i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0.326352 | + | 0.565258i | 0.326352 | + | 0.565258i | ||||
\(503\) | 1.53209 | 1.53209 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.694593 | 0.694593 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.00000 | 1.00000 | ||||||||
\(508\) | −1.93969 | + | 3.35965i | −1.93969 | + | 3.35965i | ||||
\(509\) | −0.766044 | + | 1.32683i | −0.766044 | + | 1.32683i | 0.173648 | + | 0.984808i | \(0.444444\pi\) |
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(510\) | −0.613341 | + | 1.06234i | −0.613341 | + | 1.06234i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 1.00000 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2.87939 | −2.87939 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(522\) | −0.652704 | −0.652704 | ||||||||
\(523\) | −1.87939 | −1.87939 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.43969 | − | 2.49362i | 1.43969 | − | 2.49362i | ||||
\(527\) | 1.43969 | − | 2.49362i | 1.43969 | − | 2.49362i | ||||
\(528\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(529\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.20574 | − | 3.82045i | 2.20574 | − | 3.82045i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.43969 | + | 2.49362i | 1.43969 | + | 2.49362i | ||||
\(539\) | 0.347296 | 0.347296 | ||||||||
\(540\) | −0.439693 | − | 0.761570i | −0.439693 | − | 0.761570i | ||||
\(541\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(542\) | 0.326352 | + | 0.565258i | 0.326352 | + | 0.565258i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.37939 | + | 4.12122i | −2.37939 | + | 4.12122i | ||||
\(545\) | 0.173648 | − | 0.300767i | 0.173648 | − | 0.300767i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.939693 | − | 1.62760i | 0.939693 | − | 1.62760i | ||||
\(550\) | 0.573978 | 0.573978 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(558\) | 1.43969 | + | 2.49362i | 1.43969 | + | 2.49362i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.652704 | −0.652704 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | −0.500000 | + | 0.866025i | \(0.666667\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.173648 | + | 0.300767i | 0.173648 | + | 0.300767i | ||||
\(566\) | 3.53209 | 3.53209 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.75877 | −5.75877 | ||||||||
\(569\) | −0.766044 | − | 1.32683i | −0.766044 | − | 1.32683i | −0.939693 | − | 0.342020i | \(-0.888889\pi\) |
0.173648 | − | 0.984808i | \(-0.444444\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.939693 | − | 1.62760i | −0.939693 | − | 1.62760i | ||||
\(577\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(578\) | 2.37939 | + | 4.12122i | 2.37939 | + | 4.12122i | ||||
\(579\) | −0.766044 | − | 1.32683i | −0.766044 | − | 1.32683i | ||||
\(580\) | −0.152704 | + | 0.264490i | −0.152704 | + | 0.264490i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.75877 | −3.75877 | ||||||||
\(587\) | −0.766044 | − | 1.32683i | −0.766044 | − | 1.32683i | −0.939693 | − | 0.342020i | \(-0.888889\pi\) |
0.173648 | − | 0.984808i | \(-0.444444\pi\) | |||||||
\(588\) | 2.53209 | 2.53209 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.939693 | − | 1.62760i | 0.939693 | − | 1.62760i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(594\) | 0.326352 | − | 0.565258i | 0.326352 | − | 0.565258i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(600\) | 2.53209 | 2.53209 | ||||||||
\(601\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.53209 | 1.53209 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.152704 | + | 0.264490i | 0.152704 | + | 0.264490i | ||||
\(606\) | 1.87939 | + | 3.25519i | 1.87939 | + | 3.25519i | ||||
\(607\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.613341 | − | 1.06234i | −0.613341 | − | 1.06234i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −4.75877 | −4.75877 | ||||||||
\(613\) | 2.00000 | 2.00000 | 1.00000 | \(0\) | ||||||
1.00000 | \(0\) | |||||||||
\(614\) | 0.326352 | + | 0.565258i | 0.326352 | + | 0.565258i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(620\) | 1.34730 | 1.34730 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −0.652704 | −0.652704 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.326352 | + | 0.565258i | −0.326352 | + | 0.565258i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.439693 | − | 0.761570i | −0.439693 | − | 0.761570i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.347296 | 0.347296 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.939693 | + | 1.62760i | 0.939693 | + | 1.62760i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.266044 | + | 0.460802i | −0.266044 | + | 0.460802i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −0.226682 | −0.226682 | ||||||||
\(639\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | ||||
\(640\) | −0.347296 | −0.347296 | ||||||||
\(641\) | 0.939693 | + | 1.62760i | 0.939693 | + | 1.62760i | 0.766044 | + | 0.642788i | \(0.222222\pi\) |
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.766044 | + | 1.32683i | −0.766044 | + | 1.32683i | 0.173648 | + | 0.984808i | \(0.444444\pi\) |
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.347296 | 0.347296 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(648\) | 1.43969 | − | 2.49362i | 1.43969 | − | 2.49362i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.93969 | + | 3.35965i | −1.93969 | + | 3.35965i | ||||
\(653\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(654\) | 1.87939 | 1.87939 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(660\) | −0.152704 | − | 0.264490i | −0.152704 | − | 0.264490i | ||||
\(661\) | −0.173648 | + | 0.300767i | −0.173648 | + | 0.300767i | −0.939693 | − | 0.342020i | \(-0.888889\pi\) |
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.70574 | − | 4.68647i | −2.70574 | − | 4.68647i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(671\) | 0.326352 | − | 0.565258i | 0.326352 | − | 0.565258i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(674\) | −0.652704 | −0.652704 | ||||||||
\(675\) | 0.439693 | + | 0.761570i | 0.439693 | + | 0.761570i | ||||
\(676\) | 2.53209 | 2.53209 | ||||||||
\(677\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(678\) | −0.939693 | + | 1.62760i | −0.939693 | + | 1.62760i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −0.939693 | + | 1.62760i | −0.939693 | + | 1.62760i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(683\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.173648 | − | 0.300767i | −0.173648 | − | 0.300767i | 0.766044 | − | 0.642788i | \(-0.222222\pi\) |
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.87939 | −2.87939 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.00000 | −1.00000 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 1.43969 | − | 2.49362i | 1.43969 | − | 2.49362i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −0.326352 | − | 0.565258i | −0.326352 | − | 0.565258i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(710\) | −1.30541 | −1.30541 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(718\) | 1.87939 | + | 3.25519i | 1.87939 | + | 3.25519i | ||||
\(719\) | −1.87939 | −1.87939 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(720\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0.939693 | + | 1.62760i | 0.939693 | + | 1.62760i | ||||
\(723\) | −1.00000 | −1.00000 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.152704 | − | 0.264490i | 0.152704 | − | 0.264490i | ||||
\(726\) | −0.826352 | + | 1.43128i | −0.826352 | + | 1.43128i | ||||
\(727\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 2.37939 | − | 4.12122i | 2.37939 | − | 4.12122i | ||||
\(733\) | −0.766044 | + | 1.32683i | −0.766044 | + | 1.32683i | 0.173648 | + | 0.984808i | \(0.444444\pi\) |
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(734\) | −1.76604 | + | 3.05888i | −1.76604 | + | 3.05888i | ||||
\(735\) | 0.347296 | 0.347296 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.532089 | 0.532089 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(744\) | 2.20574 | + | 3.82045i | 2.20574 | + | 3.82045i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −3.75877 | −3.75877 | ||||||||
\(747\) | 0.939693 | − | 1.62760i | 0.939693 | − | 1.62760i | ||||
\(748\) | −1.65270 | −1.65270 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 1.22668 | 1.22668 | ||||||||
\(751\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.173648 | + | 0.300767i | −0.173648 | + | 0.300767i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.87939 | −1.87939 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(762\) | −2.87939 | −2.87939 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.652704 | −0.652704 | ||||||||
\(766\) | 1.87939 | 1.87939 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.766044 | − | 1.32683i | −0.766044 | − | 1.32683i | ||||
\(772\) | −1.93969 | − | 3.35965i | −1.93969 | − | 3.35965i | ||||
\(773\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.34730 | −1.34730 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.326352 | − | 0.565258i | 0.326352 | − | 0.565258i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.347296 | − | 0.601535i | −0.347296 | − | 0.601535i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.173648 | − | 0.300767i | −0.173648 | − | 0.300767i | ||||
\(784\) | 2.87939 | 2.87939 | ||||||||
\(785\) | −0.0603074 | − | 0.104455i | −0.0603074 | − | 0.104455i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(788\) | 2.37939 | − | 4.12122i | 2.37939 | − | 4.12122i | ||||
\(789\) | 1.53209 | 1.53209 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −0.173648 | + | 0.300767i | −0.173648 | + | 0.300767i | −0.939693 | − | 0.342020i | \(-0.888889\pi\) |
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 2.22668 | 2.22668 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 3.53209 | 3.53209 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 3.87939 | 3.87939 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.766044 | + | 1.32683i | −0.766044 | + | 1.32683i | ||||
\(808\) | 2.87939 | + | 4.98724i | 2.87939 | + | 4.98724i | ||||
\(809\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(810\) | 0.326352 | − | 0.565258i | 0.326352 | − | 0.565258i | ||||
\(811\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.173648 | + | 0.300767i | −0.173648 | + | 0.300767i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.266044 | + | 0.460802i | −0.266044 | + | 0.460802i | ||||
\(816\) | −5.41147 | −5.41147 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 3.53209 | 3.53209 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.152704 | + | 0.264490i | 0.152704 | + | 0.264490i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.347296 | 0.347296 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(830\) | −0.613341 | − | 1.06234i | −0.613341 | − | 1.06234i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.939693 | − | 1.62760i | 0.939693 | − | 1.62760i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.766044 | + | 1.32683i | −0.766044 | + | 1.32683i | ||||
\(838\) | −2.87939 | −2.87939 | ||||||||
\(839\) | 0.939693 | + | 1.62760i | 0.939693 | + | 1.62760i | 0.766044 | + | 0.642788i | \(0.222222\pi\) |
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.439693 | − | 0.761570i | 0.439693 | − | 0.761570i | ||||
\(842\) | −0.939693 | + | 1.62760i | −0.939693 | + | 1.62760i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.37939 | + | 4.12122i | 2.37939 | + | 4.12122i | ||||
\(845\) | 0.347296 | 0.347296 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.939693 | + | 1.62760i | 0.939693 | + | 1.62760i | ||||
\(850\) | 1.55303 | − | 2.68993i | 1.55303 | − | 2.68993i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −2.53209 | − | 4.38571i | −2.53209 | − | 4.38571i | ||||
\(853\) | 0.939693 | + | 1.62760i | 0.939693 | + | 1.62760i | 0.766044 | + | 0.642788i | \(0.222222\pi\) |
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.939693 | − | 1.62760i | 0.939693 | − | 1.62760i | 0.173648 | − | 0.984808i | \(-0.444444\pi\) |
0.766044 | − | 0.642788i | \(-0.222222\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.43969 | + | 2.49362i | 1.43969 | + | 2.49362i | ||||
\(863\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(864\) | 1.26604 | − | 2.19285i | 1.26604 | − | 2.19285i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.26604 | + | 2.19285i | −1.26604 | + | 2.19285i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −0.226682 | −0.226682 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 2.87939 | 2.87939 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.939693 | − | 1.62760i | 0.939693 | − | 1.62760i | 0.173648 | − | 0.984808i | \(-0.444444\pi\) |
0.766044 | − | 0.642788i | \(-0.222222\pi\) | |||||||
\(878\) | −0.939693 | + | 1.62760i | −0.939693 | + | 1.62760i | ||||
\(879\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | ||||
\(880\) | −0.173648 | − | 0.300767i | −0.173648 | − | 0.300767i | ||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | 0.939693 | + | 1.62760i | 0.939693 | + | 1.62760i | ||||
\(883\) | 0.347296 | 0.347296 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.76604 | + | 3.05888i | −1.76604 | + | 3.05888i | ||||
\(887\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.347296 | 0.347296 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.532089 | 0.532089 | ||||||||
\(900\) | 1.11334 | + | 1.92836i | 1.11334 | + | 1.92836i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.43969 | + | 2.49362i | −1.43969 | + | 2.49362i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.326352 | − | 0.565258i | 0.326352 | − | 0.565258i | ||||
\(914\) | 1.87939 | − | 3.25519i | 1.87939 | − | 3.25519i | ||||
\(915\) | 0.326352 | − | 0.565258i | 0.326352 | − | 0.565258i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −1.76604 | − | 3.05888i | −1.76604 | − | 3.05888i | ||||
\(919\) | 1.53209 | 1.53209 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.173648 | + | 0.300767i | −0.173648 | + | 0.300767i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.879385 | −0.879385 | ||||||||
\(929\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(930\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −0.173648 | − | 0.300767i | −0.173648 | − | 0.300767i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.226682 | −0.226682 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.347296 | 0.347296 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(942\) | 0.326352 | − | 0.565258i | 0.326352 | − | 0.565258i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.26604 | − | 2.19285i | −1.26604 | − | 2.19285i | ||||
\(957\) | −0.0603074 | − | 0.104455i | −0.0603074 | − | 0.104455i | ||||
\(958\) | 0.326352 | − | 0.565258i | 0.326352 | − | 0.565258i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −0.326352 | − | 0.565258i | −0.326352 | − | 0.565258i | ||||
\(961\) | −0.673648 | − | 1.16679i | −0.673648 | − | 1.16679i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.53209 | −2.53209 | ||||||||
\(965\) | −0.266044 | − | 0.460802i | −0.266044 | − | 0.460802i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(968\) | −1.26604 | + | 2.19285i | −1.26604 | + | 2.19285i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.87939 | −1.87939 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(972\) | 2.53209 | 2.53209 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0.326352 | + | 0.565258i | 0.326352 | + | 0.565258i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.70574 | − | 4.68647i | 2.70574 | − | 4.68647i | ||||
\(977\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(978\) | −2.87939 | −2.87939 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0.879385 | 0.879385 | ||||||||
\(981\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −0.766044 | − | 1.32683i | −0.766044 | − | 1.32683i | −0.939693 | − | 0.342020i | \(-0.888889\pi\) |
0.173648 | − | 0.984808i | \(-0.444444\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.326352 | − | 0.565258i | 0.326352 | − | 0.565258i | ||||
\(986\) | −0.613341 | + | 1.06234i | −0.613341 | + | 1.06234i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0.113341 | − | 0.196312i | 0.113341 | − | 0.196312i | ||||
\(991\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(992\) | 1.93969 | + | 3.35965i | 1.93969 | + | 3.35965i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 2.37939 | − | 4.12122i | 2.37939 | − | 4.12122i | ||||
\(997\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(998\) | 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 | 2151.1.f.a.238.3 | ✓ | 6 | |
9.7 | even | 3 | inner | 2151.1.f.a.1672.3 | yes | 6 | |
239.238 | odd | 2 | CM | 2151.1.f.a.238.3 | ✓ | 6 | |
2151.1672 | odd | 6 | inner | 2151.1.f.a.1672.3 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2151.1.f.a.238.3 | ✓ | 6 | 1.1 | even | 1 | trivial | |
2151.1.f.a.238.3 | ✓ | 6 | 239.238 | odd | 2 | CM | |
2151.1.f.a.1672.3 | yes | 6 | 9.7 | even | 3 | inner | |
2151.1.f.a.1672.3 | yes | 6 | 2151.1672 | odd | 6 | inner |