Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [633,1,Mod(71,633)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(633, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 8]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("633.71");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 633 = 3 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 633.m (of order \(10\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.315908152997\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{10})\) |
Coefficient field: | \(\Q(\zeta_{20})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{6} + x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(A_{5}\) |
Projective field: | Galois closure of 5.1.17839074969.1 |
Embedding invariants
Embedding label | 188.1 | ||
Root | \(0.587785 + 0.809017i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 633.188 |
Dual form | 633.1.m.b.266.1 |
$q$-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 \(\left(\mathbb{Z}/633\mathbb{Z}\right)^\times\).
\(n\) | \(212\) | \(424\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.587785 | − | 0.190983i | −0.587785 | − | 0.190983i | − | 1.00000i | \(-0.5\pi\) | |
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(3\) | 0.809017 | − | 0.587785i | 0.809017 | − | 0.587785i | ||||
\(4\) | −0.500000 | − | 0.363271i | −0.500000 | − | 0.363271i | ||||
\(5\) | −0.587785 | + | 0.809017i | −0.587785 | + | 0.809017i | −0.994522 | − | 0.104528i | \(-0.966667\pi\) |
0.406737 | + | 0.913545i | \(0.366667\pi\) | |||||||
\(6\) | −0.587785 | + | 0.190983i | −0.587785 | + | 0.190983i | ||||
\(7\) | 0.309017 | + | 0.951057i | 0.309017 | + | 0.951057i | 0.978148 | + | 0.207912i | \(0.0666667\pi\) |
−0.669131 | + | 0.743145i | \(0.733333\pi\) | |||||||
\(8\) | 0.587785 | + | 0.809017i | 0.587785 | + | 0.809017i | ||||
\(9\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(10\) | 0.500000 | − | 0.363271i | 0.500000 | − | 0.363271i | ||||
\(11\) | 0.951057 | − | 1.30902i | 0.951057 | − | 1.30902i | − | 1.00000i | \(-0.5\pi\) | |
0.951057 | − | 0.309017i | \(-0.100000\pi\) | |||||||
\(12\) | −0.618034 | −0.618034 | ||||||||
\(13\) | −0.309017 | − | 0.951057i | −0.309017 | − | 0.951057i | −0.978148 | − | 0.207912i | \(-0.933333\pi\) |
0.669131 | − | 0.743145i | \(-0.266667\pi\) | |||||||
\(14\) | − | 0.618034i | − | 0.618034i | ||||||
\(15\) | 1.00000i | 1.00000i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.53884 | − | 0.500000i | 1.53884 | − | 0.500000i | 0.587785 | − | 0.809017i | \(-0.300000\pi\) |
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(18\) | −0.363271 | + | 0.500000i | −0.363271 | + | 0.500000i | ||||
\(19\) | 0.309017 | + | 0.951057i | 0.309017 | + | 0.951057i | 0.978148 | + | 0.207912i | \(0.0666667\pi\) |
−0.669131 | + | 0.743145i | \(0.733333\pi\) | |||||||
\(20\) | 0.587785 | − | 0.190983i | 0.587785 | − | 0.190983i | ||||
\(21\) | 0.809017 | + | 0.587785i | 0.809017 | + | 0.587785i | ||||
\(22\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(23\) | −0.951057 | − | 0.309017i | −0.951057 | − | 0.309017i | −0.207912 | − | 0.978148i | \(-0.566667\pi\) |
−0.743145 | + | 0.669131i | \(0.766667\pi\) | |||||||
\(24\) | 0.951057 | + | 0.309017i | 0.951057 | + | 0.309017i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.618034i | 0.618034i | ||||||||
\(27\) | −0.309017 | − | 0.951057i | −0.309017 | − | 0.951057i | ||||
\(28\) | 0.190983 | − | 0.587785i | 0.190983 | − | 0.587785i | ||||
\(29\) | −0.587785 | + | 0.190983i | −0.587785 | + | 0.190983i | −0.587785 | − | 0.809017i | \(-0.700000\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | 0.190983 | − | 0.587785i | 0.190983 | − | 0.587785i | ||||
\(31\) | 0.618034 | 0.618034 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(32\) | − | 1.00000i | − | 1.00000i | ||||||
\(33\) | − | 1.61803i | − | 1.61803i | ||||||
\(34\) | −1.00000 | −1.00000 | ||||||||
\(35\) | −0.951057 | − | 0.309017i | −0.951057 | − | 0.309017i | ||||
\(36\) | −0.500000 | + | 0.363271i | −0.500000 | + | 0.363271i | ||||
\(37\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(38\) | − | 0.618034i | − | 0.618034i | ||||||
\(39\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(40\) | −1.00000 | −1.00000 | ||||||||
\(41\) | −0.951057 | + | 1.30902i | −0.951057 | + | 1.30902i | 1.00000i | \(0.5\pi\) | ||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(42\) | −0.363271 | − | 0.500000i | −0.363271 | − | 0.500000i | ||||
\(43\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(44\) | −0.951057 | + | 0.309017i | −0.951057 | + | 0.309017i | ||||
\(45\) | 0.587785 | + | 0.809017i | 0.587785 | + | 0.809017i | ||||
\(46\) | 0.500000 | + | 0.363271i | 0.500000 | + | 0.363271i | ||||
\(47\) | 0.587785 | − | 0.190983i | 0.587785 | − | 0.190983i | − | 1.00000i | \(-0.5\pi\) | |
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.951057 | − | 1.30902i | 0.951057 | − | 1.30902i | ||||
\(52\) | −0.190983 | + | 0.587785i | −0.190983 | + | 0.587785i | ||||
\(53\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(54\) | 0.618034i | 0.618034i | ||||||||
\(55\) | 0.500000 | + | 1.53884i | 0.500000 | + | 1.53884i | ||||
\(56\) | −0.587785 | + | 0.809017i | −0.587785 | + | 0.809017i | ||||
\(57\) | 0.809017 | + | 0.587785i | 0.809017 | + | 0.587785i | ||||
\(58\) | 0.381966 | 0.381966 | ||||||||
\(59\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(60\) | 0.363271 | − | 0.500000i | 0.363271 | − | 0.500000i | ||||
\(61\) | −1.30902 | + | 0.951057i | −1.30902 | + | 0.951057i | −0.309017 | + | 0.951057i | \(0.600000\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(62\) | −0.363271 | − | 0.118034i | −0.363271 | − | 0.118034i | ||||
\(63\) | 1.00000 | 1.00000 | ||||||||
\(64\) | −0.190983 | + | 0.587785i | −0.190983 | + | 0.587785i | ||||
\(65\) | 0.951057 | + | 0.309017i | 0.951057 | + | 0.309017i | ||||
\(66\) | −0.309017 | + | 0.951057i | −0.309017 | + | 0.951057i | ||||
\(67\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(68\) | −0.951057 | − | 0.309017i | −0.951057 | − | 0.309017i | ||||
\(69\) | −0.951057 | + | 0.309017i | −0.951057 | + | 0.309017i | ||||
\(70\) | 0.500000 | + | 0.363271i | 0.500000 | + | 0.363271i | ||||
\(71\) | 0.363271 | + | 0.500000i | 0.363271 | + | 0.500000i | 0.951057 | − | 0.309017i | \(-0.100000\pi\) |
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(72\) | 0.951057 | − | 0.309017i | 0.951057 | − | 0.309017i | ||||
\(73\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.190983 | − | 0.587785i | 0.190983 | − | 0.587785i | ||||
\(77\) | 1.53884 | + | 0.500000i | 1.53884 | + | 0.500000i | ||||
\(78\) | 0.363271 | + | 0.500000i | 0.363271 | + | 0.500000i | ||||
\(79\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(82\) | 0.809017 | − | 0.587785i | 0.809017 | − | 0.587785i | ||||
\(83\) | 0.363271 | − | 0.500000i | 0.363271 | − | 0.500000i | −0.587785 | − | 0.809017i | \(-0.700000\pi\) |
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(84\) | −0.190983 | − | 0.587785i | −0.190983 | − | 0.587785i | ||||
\(85\) | −0.500000 | + | 1.53884i | −0.500000 | + | 1.53884i | ||||
\(86\) | 0.587785 | + | 0.190983i | 0.587785 | + | 0.190983i | ||||
\(87\) | −0.363271 | + | 0.500000i | −0.363271 | + | 0.500000i | ||||
\(88\) | 1.61803 | 1.61803 | ||||||||
\(89\) | 0.951057 | − | 0.309017i | 0.951057 | − | 0.309017i | 0.207912 | − | 0.978148i | \(-0.433333\pi\) |
0.743145 | + | 0.669131i | \(0.233333\pi\) | |||||||
\(90\) | −0.190983 | − | 0.587785i | −0.190983 | − | 0.587785i | ||||
\(91\) | 0.809017 | − | 0.587785i | 0.809017 | − | 0.587785i | ||||
\(92\) | 0.363271 | + | 0.500000i | 0.363271 | + | 0.500000i | ||||
\(93\) | 0.500000 | − | 0.363271i | 0.500000 | − | 0.363271i | ||||
\(94\) | −0.381966 | −0.381966 | ||||||||
\(95\) | −0.951057 | − | 0.309017i | −0.951057 | − | 0.309017i | ||||
\(96\) | −0.587785 | − | 0.809017i | −0.587785 | − | 0.809017i | ||||
\(97\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.951057 | − | 1.30902i | −0.951057 | − | 1.30902i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(102\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(103\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(104\) | 0.587785 | − | 0.809017i | 0.587785 | − | 0.809017i | ||||
\(105\) | −0.951057 | + | 0.309017i | −0.951057 | + | 0.309017i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.17557 | + | 1.61803i | −1.17557 | + | 1.61803i | −0.587785 | + | 0.809017i | \(0.700000\pi\) |
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(108\) | −0.190983 | + | 0.587785i | −0.190983 | + | 0.587785i | ||||
\(109\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | −0.913545 | − | 0.406737i | \(-0.866667\pi\) |
0.104528 | + | 0.994522i | \(0.466667\pi\) | |||||||
\(110\) | − | 1.00000i | − | 1.00000i | ||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.951057 | + | 0.309017i | −0.951057 | + | 0.309017i | −0.743145 | − | 0.669131i | \(-0.766667\pi\) |
−0.207912 | + | 0.978148i | \(0.566667\pi\) | |||||||
\(114\) | −0.363271 | − | 0.500000i | −0.363271 | − | 0.500000i | ||||
\(115\) | 0.809017 | − | 0.587785i | 0.809017 | − | 0.587785i | ||||
\(116\) | 0.363271 | + | 0.118034i | 0.363271 | + | 0.118034i | ||||
\(117\) | −1.00000 | −1.00000 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.951057 | + | 1.30902i | 0.951057 | + | 1.30902i | ||||
\(120\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(121\) | −0.500000 | − | 1.53884i | −0.500000 | − | 1.53884i | ||||
\(122\) | 0.951057 | − | 0.309017i | 0.951057 | − | 0.309017i | ||||
\(123\) | 1.61803i | 1.61803i | ||||||||
\(124\) | −0.309017 | − | 0.224514i | −0.309017 | − | 0.224514i | ||||
\(125\) | −0.951057 | − | 0.309017i | −0.951057 | − | 0.309017i | ||||
\(126\) | −0.587785 | − | 0.190983i | −0.587785 | − | 0.190983i | ||||
\(127\) | −0.309017 | − | 0.951057i | −0.309017 | − | 0.951057i | −0.978148 | − | 0.207912i | \(-0.933333\pi\) |
0.669131 | − | 0.743145i | \(-0.266667\pi\) | |||||||
\(128\) | −0.363271 | + | 0.500000i | −0.363271 | + | 0.500000i | ||||
\(129\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(130\) | −0.500000 | − | 0.363271i | −0.500000 | − | 0.363271i | ||||
\(131\) | 1.53884 | + | 0.500000i | 1.53884 | + | 0.500000i | 0.951057 | − | 0.309017i | \(-0.100000\pi\) |
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(132\) | −0.587785 | + | 0.809017i | −0.587785 | + | 0.809017i | ||||
\(133\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.951057 | + | 0.309017i | 0.951057 | + | 0.309017i | ||||
\(136\) | 1.30902 | + | 0.951057i | 1.30902 | + | 0.951057i | ||||
\(137\) | −0.951057 | + | 0.309017i | −0.951057 | + | 0.309017i | −0.743145 | − | 0.669131i | \(-0.766667\pi\) |
−0.207912 | + | 0.978148i | \(0.566667\pi\) | |||||||
\(138\) | 0.618034 | 0.618034 | ||||||||
\(139\) | −0.309017 | − | 0.951057i | −0.309017 | − | 0.951057i | −0.978148 | − | 0.207912i | \(-0.933333\pi\) |
0.669131 | − | 0.743145i | \(-0.266667\pi\) | |||||||
\(140\) | 0.363271 | + | 0.500000i | 0.363271 | + | 0.500000i | ||||
\(141\) | 0.363271 | − | 0.500000i | 0.363271 | − | 0.500000i | ||||
\(142\) | −0.118034 | − | 0.363271i | −0.118034 | − | 0.363271i | ||||
\(143\) | −1.53884 | − | 0.500000i | −1.53884 | − | 0.500000i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.190983 | − | 0.587785i | 0.190983 | − | 0.587785i | ||||
\(146\) | 0.587785 | + | 0.190983i | 0.587785 | + | 0.190983i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.587785 | − | 0.190983i | −0.587785 | − | 0.190983i | − | 1.00000i | \(-0.5\pi\) | |
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.30902 | + | 0.951057i | 1.30902 | + | 0.951057i | 1.00000 | \(0\) | ||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(152\) | −0.587785 | + | 0.809017i | −0.587785 | + | 0.809017i | ||||
\(153\) | − | 1.61803i | − | 1.61803i | ||||||
\(154\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(155\) | −0.363271 | + | 0.500000i | −0.363271 | + | 0.500000i | ||||
\(156\) | 0.190983 | + | 0.587785i | 0.190983 | + | 0.587785i | ||||
\(157\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.809017 | + | 0.587785i | 0.809017 | + | 0.587785i | ||||
\(161\) | − | 1.00000i | − | 1.00000i | ||||||
\(162\) | 0.363271 | + | 0.500000i | 0.363271 | + | 0.500000i | ||||
\(163\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | 0.104528 | − | 0.994522i | \(-0.466667\pi\) |
−0.913545 | + | 0.406737i | \(0.866667\pi\) | |||||||
\(164\) | 0.951057 | − | 0.309017i | 0.951057 | − | 0.309017i | ||||
\(165\) | 1.30902 | + | 0.951057i | 1.30902 | + | 0.951057i | ||||
\(166\) | −0.309017 | + | 0.224514i | −0.309017 | + | 0.224514i | ||||
\(167\) | 0.587785 | − | 0.190983i | 0.587785 | − | 0.190983i | − | 1.00000i | \(-0.5\pi\) | |
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(168\) | 1.00000i | 1.00000i | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0.587785 | − | 0.809017i | 0.587785 | − | 0.809017i | ||||
\(171\) | 1.00000 | 1.00000 | ||||||||
\(172\) | 0.500000 | + | 0.363271i | 0.500000 | + | 0.363271i | ||||
\(173\) | − | 1.00000i | − | 1.00000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(174\) | 0.309017 | − | 0.224514i | 0.309017 | − | 0.224514i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.618034 | −0.618034 | ||||||||
\(179\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(180\) | − | 0.618034i | − | 0.618034i | ||||||
\(181\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(182\) | −0.587785 | + | 0.190983i | −0.587785 | + | 0.190983i | ||||
\(183\) | −0.500000 | + | 1.53884i | −0.500000 | + | 1.53884i | ||||
\(184\) | −0.309017 | − | 0.951057i | −0.309017 | − | 0.951057i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.363271 | + | 0.118034i | −0.363271 | + | 0.118034i | ||||
\(187\) | 0.809017 | − | 2.48990i | 0.809017 | − | 2.48990i | ||||
\(188\) | −0.363271 | − | 0.118034i | −0.363271 | − | 0.118034i | ||||
\(189\) | 0.809017 | − | 0.587785i | 0.809017 | − | 0.587785i | ||||
\(190\) | 0.500000 | + | 0.363271i | 0.500000 | + | 0.363271i | ||||
\(191\) | −0.951057 | + | 0.309017i | −0.951057 | + | 0.309017i | −0.743145 | − | 0.669131i | \(-0.766667\pi\) |
−0.207912 | + | 0.978148i | \(0.566667\pi\) | |||||||
\(192\) | 0.190983 | + | 0.587785i | 0.190983 | + | 0.587785i | ||||
\(193\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.951057 | − | 0.309017i | 0.951057 | − | 0.309017i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 0.618034i | − | 0.618034i | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||
0.951057 | − | 0.309017i | \(-0.100000\pi\) | |||||||
\(198\) | 0.309017 | + | 0.951057i | 0.309017 | + | 0.951057i | ||||
\(199\) | −0.618034 | −0.618034 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.363271 | − | 0.500000i | −0.363271 | − | 0.500000i | ||||
\(204\) | −0.951057 | + | 0.309017i | −0.951057 | + | 0.309017i | ||||
\(205\) | −0.500000 | − | 1.53884i | −0.500000 | − | 1.53884i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.587785 | + | 0.809017i | −0.587785 | + | 0.809017i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.53884 | + | 0.500000i | 1.53884 | + | 0.500000i | ||||
\(210\) | 0.618034 | 0.618034 | ||||||||
\(211\) | 0.309017 | + | 0.951057i | 0.309017 | + | 0.951057i | ||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.587785 | + | 0.190983i | 0.587785 | + | 0.190983i | ||||
\(214\) | 1.00000 | − | 0.726543i | 1.00000 | − | 0.726543i | ||||
\(215\) | 0.587785 | − | 0.809017i | 0.587785 | − | 0.809017i | ||||
\(216\) | 0.587785 | − | 0.809017i | 0.587785 | − | 0.809017i | ||||
\(217\) | 0.190983 | + | 0.587785i | 0.190983 | + | 0.587785i | ||||
\(218\) | 0.587785 | − | 0.190983i | 0.587785 | − | 0.190983i | ||||
\(219\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(220\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(221\) | −0.951057 | − | 1.30902i | −0.951057 | − | 1.30902i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.00000 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(224\) | 0.951057 | − | 0.309017i | 0.951057 | − | 0.309017i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.618034 | 0.618034 | ||||||||
\(227\) | −0.951057 | + | 0.309017i | −0.951057 | + | 0.309017i | −0.743145 | − | 0.669131i | \(-0.766667\pi\) |
−0.207912 | + | 0.978148i | \(0.566667\pi\) | |||||||
\(228\) | −0.190983 | − | 0.587785i | −0.190983 | − | 0.587785i | ||||
\(229\) | −0.500000 | − | 0.363271i | −0.500000 | − | 0.363271i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(230\) | −0.587785 | + | 0.190983i | −0.587785 | + | 0.190983i | ||||
\(231\) | 1.53884 | − | 0.500000i | 1.53884 | − | 0.500000i | ||||
\(232\) | −0.500000 | − | 0.363271i | −0.500000 | − | 0.363271i | ||||
\(233\) | 0.363271 | + | 0.500000i | 0.363271 | + | 0.500000i | 0.951057 | − | 0.309017i | \(-0.100000\pi\) |
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(234\) | 0.587785 | + | 0.190983i | 0.587785 | + | 0.190983i | ||||
\(235\) | −0.190983 | + | 0.587785i | −0.190983 | + | 0.587785i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.309017 | − | 0.951057i | −0.309017 | − | 0.951057i | ||||
\(239\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.500000 | − | 1.53884i | 0.500000 | − | 1.53884i | −0.309017 | − | 0.951057i | \(-0.600000\pi\) |
0.809017 | − | 0.587785i | \(-0.200000\pi\) | |||||||
\(242\) | 1.00000i | 1.00000i | ||||||||
\(243\) | −1.00000 | −1.00000 | ||||||||
\(244\) | 1.00000 | 1.00000 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(247\) | 0.809017 | − | 0.587785i | 0.809017 | − | 0.587785i | ||||
\(248\) | 0.363271 | + | 0.500000i | 0.363271 | + | 0.500000i | ||||
\(249\) | − | 0.618034i | − | 0.618034i | ||||||
\(250\) | 0.500000 | + | 0.363271i | 0.500000 | + | 0.363271i | ||||
\(251\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(252\) | −0.500000 | − | 0.363271i | −0.500000 | − | 0.363271i | ||||
\(253\) | −1.30902 | + | 0.951057i | −1.30902 | + | 0.951057i | ||||
\(254\) | 0.618034i | 0.618034i | ||||||||
\(255\) | 0.500000 | + | 1.53884i | 0.500000 | + | 1.53884i | ||||
\(256\) | 0.809017 | − | 0.587785i | 0.809017 | − | 0.587785i | ||||
\(257\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(258\) | 0.587785 | − | 0.190983i | 0.587785 | − | 0.190983i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −0.363271 | − | 0.500000i | −0.363271 | − | 0.500000i | ||||
\(261\) | 0.618034i | 0.618034i | ||||||||
\(262\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(263\) | 0.951057 | + | 0.309017i | 0.951057 | + | 0.309017i | 0.743145 | − | 0.669131i | \(-0.233333\pi\) |
0.207912 | + | 0.978148i | \(0.433333\pi\) | |||||||
\(264\) | 1.30902 | − | 0.951057i | 1.30902 | − | 0.951057i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.587785 | − | 0.190983i | 0.587785 | − | 0.190983i | ||||
\(267\) | 0.587785 | − | 0.809017i | 0.587785 | − | 0.809017i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(270\) | −0.500000 | − | 0.363271i | −0.500000 | − | 0.363271i | ||||
\(271\) | 1.30902 | + | 0.951057i | 1.30902 | + | 0.951057i | 1.00000 | \(0\) | ||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(274\) | 0.618034 | 0.618034 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.587785 | + | 0.190983i | 0.587785 | + | 0.190983i | ||||
\(277\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(278\) | 0.618034i | 0.618034i | ||||||||
\(279\) | 0.190983 | − | 0.587785i | 0.190983 | − | 0.587785i | ||||
\(280\) | −0.309017 | − | 0.951057i | −0.309017 | − | 0.951057i | ||||
\(281\) | −0.951057 | + | 1.30902i | −0.951057 | + | 1.30902i | 1.00000i | \(0.5\pi\) | ||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(282\) | −0.309017 | + | 0.224514i | −0.309017 | + | 0.224514i | ||||
\(283\) | 0.309017 | + | 0.951057i | 0.309017 | + | 0.951057i | 0.978148 | + | 0.207912i | \(0.0666667\pi\) |
−0.669131 | + | 0.743145i | \(0.733333\pi\) | |||||||
\(284\) | − | 0.381966i | − | 0.381966i | ||||||
\(285\) | −0.951057 | + | 0.309017i | −0.951057 | + | 0.309017i | ||||
\(286\) | 0.809017 | + | 0.587785i | 0.809017 | + | 0.587785i | ||||
\(287\) | −1.53884 | − | 0.500000i | −1.53884 | − | 0.500000i | ||||
\(288\) | −0.951057 | − | 0.309017i | −0.951057 | − | 0.309017i | ||||
\(289\) | 1.30902 | − | 0.951057i | 1.30902 | − | 0.951057i | ||||
\(290\) | −0.224514 | + | 0.309017i | −0.224514 | + | 0.309017i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.500000 | + | 0.363271i | 0.500000 | + | 0.363271i | ||||
\(293\) | 0.587785 | + | 0.809017i | 0.587785 | + | 0.809017i | 0.994522 | − | 0.104528i | \(-0.0333333\pi\) |
−0.406737 | + | 0.913545i | \(0.633333\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.53884 | − | 0.500000i | −1.53884 | − | 0.500000i | ||||
\(298\) | 0.309017 | + | 0.224514i | 0.309017 | + | 0.224514i | ||||
\(299\) | 1.00000i | 1.00000i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.309017 | − | 0.951057i | −0.309017 | − | 0.951057i | ||||
\(302\) | −0.587785 | − | 0.809017i | −0.587785 | − | 0.809017i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 1.61803i | − | 1.61803i | ||||||
\(306\) | −0.309017 | + | 0.951057i | −0.309017 | + | 0.951057i | ||||
\(307\) | 0.809017 | − | 0.587785i | 0.809017 | − | 0.587785i | −0.104528 | − | 0.994522i | \(-0.533333\pi\) |
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(308\) | −0.587785 | − | 0.809017i | −0.587785 | − | 0.809017i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.309017 | − | 0.224514i | 0.309017 | − | 0.224514i | ||||
\(311\) | −0.951057 | − | 0.309017i | −0.951057 | − | 0.309017i | −0.207912 | − | 0.978148i | \(-0.566667\pi\) |
−0.743145 | + | 0.669131i | \(0.766667\pi\) | |||||||
\(312\) | − | 1.00000i | − | 1.00000i | ||||||
\(313\) | −0.500000 | + | 0.363271i | −0.500000 | + | 0.363271i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(314\) | 0.587785 | + | 0.190983i | 0.587785 | + | 0.190983i | ||||
\(315\) | −0.587785 | + | 0.809017i | −0.587785 | + | 0.809017i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.951057 | − | 0.309017i | 0.951057 | − | 0.309017i | 0.207912 | − | 0.978148i | \(-0.433333\pi\) |
0.743145 | + | 0.669131i | \(0.233333\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.309017 | + | 0.951057i | −0.309017 | + | 0.951057i | ||||
\(320\) | −0.363271 | − | 0.500000i | −0.363271 | − | 0.500000i | ||||
\(321\) | 2.00000i | 2.00000i | ||||||||
\(322\) | −0.190983 | + | 0.587785i | −0.190983 | + | 0.587785i | ||||
\(323\) | 0.951057 | + | 1.30902i | 0.951057 | + | 1.30902i | ||||
\(324\) | 0.190983 | + | 0.587785i | 0.190983 | + | 0.587785i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0.363271 | + | 0.500000i | 0.363271 | + | 0.500000i | ||||
\(327\) | −0.309017 | + | 0.951057i | −0.309017 | + | 0.951057i | ||||
\(328\) | −1.61803 | −1.61803 | ||||||||
\(329\) | 0.363271 | + | 0.500000i | 0.363271 | + | 0.500000i | ||||
\(330\) | −0.587785 | − | 0.809017i | −0.587785 | − | 0.809017i | ||||
\(331\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(332\) | −0.363271 | + | 0.118034i | −0.363271 | + | 0.118034i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −0.381966 | −0.381966 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.309017 | + | 0.951057i | −0.309017 | + | 0.951057i | 0.669131 | + | 0.743145i | \(0.266667\pi\) |
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.587785 | + | 0.809017i | −0.587785 | + | 0.809017i | ||||
\(340\) | 0.809017 | − | 0.587785i | 0.809017 | − | 0.587785i | ||||
\(341\) | 0.587785 | − | 0.809017i | 0.587785 | − | 0.809017i | ||||
\(342\) | −0.587785 | − | 0.190983i | −0.587785 | − | 0.190983i | ||||
\(343\) | 0.809017 | + | 0.587785i | 0.809017 | + | 0.587785i | ||||
\(344\) | −0.587785 | − | 0.809017i | −0.587785 | − | 0.809017i | ||||
\(345\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(346\) | −0.190983 | + | 0.587785i | −0.190983 | + | 0.587785i | ||||
\(347\) | 0.951057 | − | 1.30902i | 0.951057 | − | 1.30902i | − | 1.00000i | \(-0.5\pi\) | |
0.951057 | − | 0.309017i | \(-0.100000\pi\) | |||||||
\(348\) | 0.363271 | − | 0.118034i | 0.363271 | − | 0.118034i | ||||
\(349\) | 1.00000 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(352\) | −1.30902 | − | 0.951057i | −1.30902 | − | 0.951057i | ||||
\(353\) | −1.53884 | + | 0.500000i | −1.53884 | + | 0.500000i | −0.951057 | − | 0.309017i | \(-0.900000\pi\) |
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.618034 | −0.618034 | ||||||||
\(356\) | −0.587785 | − | 0.190983i | −0.587785 | − | 0.190983i | ||||
\(357\) | 1.53884 | + | 0.500000i | 1.53884 | + | 0.500000i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 1.61803i | − | 1.61803i | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||
0.587785 | − | 0.809017i | \(-0.300000\pi\) | |||||||
\(360\) | −0.309017 | + | 0.951057i | −0.309017 | + | 0.951057i | ||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.30902 | − | 0.951057i | −1.30902 | − | 0.951057i | ||||
\(364\) | −0.618034 | −0.618034 | ||||||||
\(365\) | 0.587785 | − | 0.809017i | 0.587785 | − | 0.809017i | ||||
\(366\) | 0.587785 | − | 0.809017i | 0.587785 | − | 0.809017i | ||||
\(367\) | −0.309017 | − | 0.951057i | −0.309017 | − | 0.951057i | −0.978148 | − | 0.207912i | \(-0.933333\pi\) |
0.669131 | − | 0.743145i | \(-0.266667\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.951057 | + | 1.30902i | 0.951057 | + | 1.30902i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −0.381966 | −0.381966 | ||||||||
\(373\) | −1.30902 | + | 0.951057i | −1.30902 | + | 0.951057i | −0.309017 | + | 0.951057i | \(0.600000\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(374\) | −0.951057 | + | 1.30902i | −0.951057 | + | 1.30902i | ||||
\(375\) | −0.951057 | + | 0.309017i | −0.951057 | + | 0.309017i | ||||
\(376\) | 0.500000 | + | 0.363271i | 0.500000 | + | 0.363271i | ||||
\(377\) | 0.363271 | + | 0.500000i | 0.363271 | + | 0.500000i | ||||
\(378\) | −0.587785 | + | 0.190983i | −0.587785 | + | 0.190983i | ||||
\(379\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(380\) | 0.363271 | + | 0.500000i | 0.363271 | + | 0.500000i | ||||
\(381\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(382\) | 0.618034 | 0.618034 | ||||||||
\(383\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(384\) | 0.618034i | 0.618034i | ||||||||
\(385\) | −1.30902 | + | 0.951057i | −1.30902 | + | 0.951057i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.309017 | + | 0.951057i | −0.309017 | + | 0.951057i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 1.00000i | − | 1.00000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(390\) | −0.618034 | −0.618034 | ||||||||
\(391\) | −1.61803 | −1.61803 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.53884 | − | 0.500000i | 1.53884 | − | 0.500000i | ||||
\(394\) | −0.118034 | + | 0.363271i | −0.118034 | + | 0.363271i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.00000i | 1.00000i | ||||||||
\(397\) | −0.500000 | − | 1.53884i | −0.500000 | − | 1.53884i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.309017 | − | 0.951057i | \(-0.400000\pi\) | |||||||
\(398\) | 0.363271 | + | 0.118034i | 0.363271 | + | 0.118034i | ||||
\(399\) | −0.309017 | + | 0.951057i | −0.309017 | + | 0.951057i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.190983 | − | 0.587785i | −0.190983 | − | 0.587785i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.951057 | − | 0.309017i | 0.951057 | − | 0.309017i | ||||
\(406\) | 0.118034 | + | 0.363271i | 0.118034 | + | 0.363271i | ||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 1.61803 | 1.61803 | ||||||||
\(409\) | 0.190983 | + | 0.587785i | 0.190983 | + | 0.587785i | 1.00000 | \(0\) | ||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(410\) | 1.00000i | 1.00000i | ||||||||
\(411\) | −0.587785 | + | 0.809017i | −0.587785 | + | 0.809017i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0.500000 | − | 0.363271i | 0.500000 | − | 0.363271i | ||||
\(415\) | 0.190983 | + | 0.587785i | 0.190983 | + | 0.587785i | ||||
\(416\) | −0.951057 | + | 0.309017i | −0.951057 | + | 0.309017i | ||||
\(417\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(418\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(419\) | 0.363271 | + | 0.500000i | 0.363271 | + | 0.500000i | 0.951057 | − | 0.309017i | \(-0.100000\pi\) |
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(420\) | 0.587785 | + | 0.190983i | 0.587785 | + | 0.190983i | ||||
\(421\) | 1.61803 | 1.61803 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(422\) | − | 0.618034i | − | 0.618034i | ||||||
\(423\) | − | 0.618034i | − | 0.618034i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −0.309017 | − | 0.224514i | −0.309017 | − | 0.224514i | ||||
\(427\) | −1.30902 | − | 0.951057i | −1.30902 | − | 0.951057i | ||||
\(428\) | 1.17557 | − | 0.381966i | 1.17557 | − | 0.381966i | ||||
\(429\) | −1.53884 | + | 0.500000i | −1.53884 | + | 0.500000i | ||||
\(430\) | −0.500000 | + | 0.363271i | −0.500000 | + | 0.363271i | ||||
\(431\) | 0.951057 | + | 0.309017i | 0.951057 | + | 0.309017i | 0.743145 | − | 0.669131i | \(-0.233333\pi\) |
0.207912 | + | 0.978148i | \(0.433333\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | 0.104528 | − | 0.994522i | \(-0.466667\pi\) |
−0.913545 | + | 0.406737i | \(0.866667\pi\) | |||||||
\(434\) | − | 0.381966i | − | 0.381966i | ||||||
\(435\) | −0.190983 | − | 0.587785i | −0.190983 | − | 0.587785i | ||||
\(436\) | 0.618034 | 0.618034 | ||||||||
\(437\) | − | 1.00000i | − | 1.00000i | ||||||
\(438\) | 0.587785 | − | 0.190983i | 0.587785 | − | 0.190983i | ||||
\(439\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(440\) | −0.951057 | + | 1.30902i | −0.951057 | + | 1.30902i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.309017 | + | 0.951057i | 0.309017 | + | 0.951057i | ||||
\(443\) | 0.587785 | − | 0.809017i | 0.587785 | − | 0.809017i | −0.406737 | − | 0.913545i | \(-0.633333\pi\) |
0.994522 | + | 0.104528i | \(0.0333333\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.309017 | + | 0.951057i | −0.309017 | + | 0.951057i | ||||
\(446\) | −0.587785 | − | 0.190983i | −0.587785 | − | 0.190983i | ||||
\(447\) | −0.587785 | + | 0.190983i | −0.587785 | + | 0.190983i | ||||
\(448\) | −0.618034 | −0.618034 | ||||||||
\(449\) | −0.951057 | + | 0.309017i | −0.951057 | + | 0.309017i | −0.743145 | − | 0.669131i | \(-0.766667\pi\) |
−0.207912 | + | 0.978148i | \(0.566667\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.809017 | + | 2.48990i | 0.809017 | + | 2.48990i | ||||
\(452\) | 0.587785 | + | 0.190983i | 0.587785 | + | 0.190983i | ||||
\(453\) | 1.61803 | 1.61803 | ||||||||
\(454\) | 0.618034 | 0.618034 | ||||||||
\(455\) | 1.00000i | 1.00000i | ||||||||
\(456\) | 1.00000i | 1.00000i | ||||||||
\(457\) | −0.190983 | + | 0.587785i | −0.190983 | + | 0.587785i | 0.809017 | + | 0.587785i | \(0.200000\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(458\) | 0.224514 | + | 0.309017i | 0.224514 | + | 0.309017i | ||||
\(459\) | −0.951057 | − | 1.30902i | −0.951057 | − | 1.30902i | ||||
\(460\) | −0.618034 | −0.618034 | ||||||||
\(461\) | −0.587785 | + | 0.809017i | −0.587785 | + | 0.809017i | −0.994522 | − | 0.104528i | \(-0.966667\pi\) |
0.406737 | + | 0.913545i | \(0.366667\pi\) | |||||||
\(462\) | −1.00000 | −1.00000 | ||||||||
\(463\) | 0.809017 | + | 0.587785i | 0.809017 | + | 0.587785i | 0.913545 | − | 0.406737i | \(-0.133333\pi\) |
−0.104528 | + | 0.994522i | \(0.533333\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.618034i | 0.618034i | ||||||||
\(466\) | −0.118034 | − | 0.363271i | −0.118034 | − | 0.363271i | ||||
\(467\) | 0.587785 | + | 0.809017i | 0.587785 | + | 0.809017i | 0.994522 | − | 0.104528i | \(-0.0333333\pi\) |
−0.406737 | + | 0.913545i | \(0.633333\pi\) | |||||||
\(468\) | 0.500000 | + | 0.363271i | 0.500000 | + | 0.363271i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0.224514 | − | 0.309017i | 0.224514 | − | 0.309017i | ||||
\(471\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.951057 | + | 1.30902i | −0.951057 | + | 1.30902i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 1.00000i | − | 1.00000i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0.951057 | − | 1.30902i | 0.951057 | − | 1.30902i | − | 1.00000i | \(-0.5\pi\) | |
0.951057 | − | 0.309017i | \(-0.100000\pi\) | |||||||
\(480\) | 1.00000 | 1.00000 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −0.587785 | + | 0.809017i | −0.587785 | + | 0.809017i | ||||
\(483\) | −0.587785 | − | 0.809017i | −0.587785 | − | 0.809017i | ||||
\(484\) | −0.309017 | + | 0.951057i | −0.309017 | + | 0.951057i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.587785 | + | 0.190983i | 0.587785 | + | 0.190983i | ||||
\(487\) | −0.190983 | + | 0.587785i | −0.190983 | + | 0.587785i | 0.809017 | + | 0.587785i | \(0.200000\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(488\) | −1.53884 | − | 0.500000i | −1.53884 | − | 0.500000i | ||||
\(489\) | −1.00000 | −1.00000 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(492\) | 0.587785 | − | 0.809017i | 0.587785 | − | 0.809017i | ||||
\(493\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(494\) | −0.587785 | + | 0.190983i | −0.587785 | + | 0.190983i | ||||
\(495\) | 1.61803 | 1.61803 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.363271 | + | 0.500000i | −0.363271 | + | 0.500000i | ||||
\(498\) | −0.118034 | + | 0.363271i | −0.118034 | + | 0.363271i | ||||
\(499\) | −0.309017 | + | 0.951057i | −0.309017 | + | 0.951057i | 0.669131 | + | 0.743145i | \(0.266667\pi\) |
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(500\) | 0.363271 | + | 0.500000i | 0.363271 | + | 0.500000i | ||||
\(501\) | 0.363271 | − | 0.500000i | 0.363271 | − | 0.500000i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0.363271 | − | 0.500000i | 0.363271 | − | 0.500000i | −0.587785 | − | 0.809017i | \(-0.700000\pi\) |
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(504\) | 0.587785 | + | 0.809017i | 0.587785 | + | 0.809017i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.951057 | − | 0.309017i | 0.951057 | − | 0.309017i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.190983 | + | 0.587785i | −0.190983 | + | 0.587785i | ||||
\(509\) | 0.587785 | − | 0.809017i | 0.587785 | − | 0.809017i | −0.406737 | − | 0.913545i | \(-0.633333\pi\) |
0.994522 | + | 0.104528i | \(0.0333333\pi\) | |||||||
\(510\) | − | 1.00000i | − | 1.00000i | ||||||
\(511\) | −0.309017 | − | 0.951057i | −0.309017 | − | 0.951057i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.809017 | − | 0.587785i | 0.809017 | − | 0.587785i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.618034 | 0.618034 | ||||||||
\(517\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.587785 | − | 0.809017i | −0.587785 | − | 0.809017i | ||||
\(520\) | 0.309017 | + | 0.951057i | 0.309017 | + | 0.951057i | ||||
\(521\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(522\) | 0.118034 | − | 0.363271i | 0.118034 | − | 0.363271i | ||||
\(523\) | 0.618034 | 0.618034 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(524\) | −0.587785 | − | 0.809017i | −0.587785 | − | 0.809017i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.500000 | − | 0.363271i | −0.500000 | − | 0.363271i | ||||
\(527\) | 0.951057 | − | 0.309017i | 0.951057 | − | 0.309017i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0 | 0 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.618034 | 0.618034 | ||||||||
\(533\) | 1.53884 | + | 0.500000i | 1.53884 | + | 0.500000i | ||||
\(534\) | −0.500000 | + | 0.363271i | −0.500000 | + | 0.363271i | ||||
\(535\) | −0.618034 | − | 1.90211i | −0.618034 | − | 1.90211i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −0.363271 | − | 0.500000i | −0.363271 | − | 0.500000i | ||||
\(541\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(542\) | −0.587785 | − | 0.809017i | −0.587785 | − | 0.809017i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.500000 | − | 1.53884i | −0.500000 | − | 1.53884i | ||||
\(545\) | − | 1.00000i | − | 1.00000i | ||||||
\(546\) | −0.363271 | + | 0.500000i | −0.363271 | + | 0.500000i | ||||
\(547\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(548\) | 0.587785 | + | 0.190983i | 0.587785 | + | 0.190983i | ||||
\(549\) | 0.500000 | + | 1.53884i | 0.500000 | + | 1.53884i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.363271 | − | 0.500000i | −0.363271 | − | 0.500000i | ||||
\(552\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.190983 | + | 0.587785i | −0.190983 | + | 0.587785i | ||||
\(557\) | −1.53884 | − | 0.500000i | −1.53884 | − | 0.500000i | −0.587785 | − | 0.809017i | \(-0.700000\pi\) |
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(558\) | −0.224514 | + | 0.309017i | −0.224514 | + | 0.309017i | ||||
\(559\) | 0.309017 | + | 0.951057i | 0.309017 | + | 0.951057i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.809017 | − | 2.48990i | −0.809017 | − | 2.48990i | ||||
\(562\) | 0.809017 | − | 0.587785i | 0.809017 | − | 0.587785i | ||||
\(563\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(564\) | −0.363271 | + | 0.118034i | −0.363271 | + | 0.118034i | ||||
\(565\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(566\) | − | 0.618034i | − | 0.618034i | ||||||
\(567\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(568\) | −0.190983 | + | 0.587785i | −0.190983 | + | 0.587785i | ||||
\(569\) | 0.587785 | + | 0.190983i | 0.587785 | + | 0.190983i | 0.587785 | − | 0.809017i | \(-0.300000\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(570\) | 0.618034 | 0.618034 | ||||||||
\(571\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(572\) | 0.587785 | + | 0.809017i | 0.587785 | + | 0.809017i | ||||
\(573\) | −0.587785 | + | 0.809017i | −0.587785 | + | 0.809017i | ||||
\(574\) | 0.809017 | + | 0.587785i | 0.809017 | + | 0.587785i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.500000 | + | 0.363271i | 0.500000 | + | 0.363271i | ||||
\(577\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | 0.104528 | − | 0.994522i | \(-0.466667\pi\) |
−0.913545 | + | 0.406737i | \(0.866667\pi\) | |||||||
\(578\) | −0.951057 | + | 0.309017i | −0.951057 | + | 0.309017i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.309017 | + | 0.224514i | −0.309017 | + | 0.224514i | ||||
\(581\) | 0.587785 | + | 0.190983i | 0.587785 | + | 0.190983i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −0.587785 | − | 0.809017i | −0.587785 | − | 0.809017i | ||||
\(585\) | 0.587785 | − | 0.809017i | 0.587785 | − | 0.809017i | ||||
\(586\) | −0.190983 | − | 0.587785i | −0.190983 | − | 0.587785i | ||||
\(587\) | 0.587785 | − | 0.809017i | 0.587785 | − | 0.809017i | −0.406737 | − | 0.913545i | \(-0.633333\pi\) |
0.994522 | + | 0.104528i | \(0.0333333\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.190983 | + | 0.587785i | 0.190983 | + | 0.587785i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.363271 | − | 0.500000i | −0.363271 | − | 0.500000i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(594\) | 0.809017 | + | 0.587785i | 0.809017 | + | 0.587785i | ||||
\(595\) | −1.61803 | −1.61803 | ||||||||
\(596\) | 0.224514 | + | 0.309017i | 0.224514 | + | 0.309017i | ||||
\(597\) | −0.500000 | + | 0.363271i | −0.500000 | + | 0.363271i | ||||
\(598\) | 0.190983 | − | 0.587785i | 0.190983 | − | 0.587785i | ||||
\(599\) | 1.00000i | 1.00000i | 0.866025 | + | 0.500000i | \(0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(602\) | 0.618034i | 0.618034i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −0.309017 | − | 0.951057i | −0.309017 | − | 0.951057i | ||||
\(605\) | 1.53884 | + | 0.500000i | 1.53884 | + | 0.500000i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.00000 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(608\) | 0.951057 | − | 0.309017i | 0.951057 | − | 0.309017i | ||||
\(609\) | −0.587785 | − | 0.190983i | −0.587785 | − | 0.190983i | ||||
\(610\) | −0.309017 | + | 0.951057i | −0.309017 | + | 0.951057i | ||||
\(611\) | −0.363271 | − | 0.500000i | −0.363271 | − | 0.500000i | ||||
\(612\) | −0.587785 | + | 0.809017i | −0.587785 | + | 0.809017i | ||||
\(613\) | −0.309017 | − | 0.951057i | −0.309017 | − | 0.951057i | −0.978148 | − | 0.207912i | \(-0.933333\pi\) |
0.669131 | − | 0.743145i | \(-0.266667\pi\) | |||||||
\(614\) | −0.587785 | + | 0.190983i | −0.587785 | + | 0.190983i | ||||
\(615\) | −1.30902 | − | 0.951057i | −1.30902 | − | 0.951057i | ||||
\(616\) | 0.500000 | + | 1.53884i | 0.500000 | + | 1.53884i | ||||
\(617\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.61803 | 1.61803 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(620\) | 0.363271 | − | 0.118034i | 0.363271 | − | 0.118034i | ||||
\(621\) | 1.00000i | 1.00000i | ||||||||
\(622\) | 0.500000 | + | 0.363271i | 0.500000 | + | 0.363271i | ||||
\(623\) | 0.587785 | + | 0.809017i | 0.587785 | + | 0.809017i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.809017 | − | 0.587785i | 0.809017 | − | 0.587785i | ||||
\(626\) | 0.363271 | − | 0.118034i | 0.363271 | − | 0.118034i | ||||
\(627\) | 1.53884 | − | 0.500000i | 1.53884 | − | 0.500000i | ||||
\(628\) | 0.500000 | + | 0.363271i | 0.500000 | + | 0.363271i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0.500000 | − | 0.363271i | 0.500000 | − | 0.363271i | ||||
\(631\) | −0.190983 | + | 0.587785i | −0.190983 | + | 0.587785i | 0.809017 | + | 0.587785i | \(0.200000\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.809017 | + | 0.587785i | 0.809017 | + | 0.587785i | ||||
\(634\) | −0.618034 | −0.618034 | ||||||||
\(635\) | 0.951057 | + | 0.309017i | 0.951057 | + | 0.309017i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0.363271 | − | 0.500000i | 0.363271 | − | 0.500000i | ||||
\(639\) | 0.587785 | − | 0.190983i | 0.587785 | − | 0.190983i | ||||
\(640\) | −0.190983 | − | 0.587785i | −0.190983 | − | 0.587785i | ||||
\(641\) | −0.587785 | − | 0.809017i | −0.587785 | − | 0.809017i | 0.406737 | − | 0.913545i | \(-0.366667\pi\) |
−0.994522 | + | 0.104528i | \(0.966667\pi\) | |||||||
\(642\) | 0.381966 | − | 1.17557i | 0.381966 | − | 1.17557i | ||||
\(643\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(644\) | −0.363271 | + | 0.500000i | −0.363271 | + | 0.500000i | ||||
\(645\) | − | 1.00000i | − | 1.00000i | ||||||
\(646\) | −0.309017 | − | 0.951057i | −0.309017 | − | 0.951057i | ||||
\(647\) | 1.00000i | 1.00000i | 0.866025 | + | 0.500000i | \(0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(648\) | − | 1.00000i | − | 1.00000i | ||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.500000 | + | 0.363271i | 0.500000 | + | 0.363271i | ||||
\(652\) | 0.190983 | + | 0.587785i | 0.190983 | + | 0.587785i | ||||
\(653\) | −1.53884 | + | 0.500000i | −1.53884 | + | 0.500000i | −0.951057 | − | 0.309017i | \(-0.900000\pi\) |
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(654\) | 0.363271 | − | 0.500000i | 0.363271 | − | 0.500000i | ||||
\(655\) | −1.30902 | + | 0.951057i | −1.30902 | + | 0.951057i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.309017 | + | 0.951057i | −0.309017 | + | 0.951057i | ||||
\(658\) | −0.118034 | − | 0.363271i | −0.118034 | − | 0.363271i | ||||
\(659\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(660\) | −0.309017 | − | 0.951057i | −0.309017 | − | 0.951057i | ||||
\(661\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.53884 | − | 0.500000i | −1.53884 | − | 0.500000i | ||||
\(664\) | 0.618034 | 0.618034 | ||||||||
\(665\) | − | 1.00000i | − | 1.00000i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.618034 | 0.618034 | ||||||||
\(668\) | −0.363271 | − | 0.118034i | −0.363271 | − | 0.118034i | ||||
\(669\) | 0.809017 | − | 0.587785i | 0.809017 | − | 0.587785i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.61803i | 2.61803i | ||||||||
\(672\) | 0.587785 | − | 0.809017i | 0.587785 | − | 0.809017i | ||||
\(673\) | 0.618034 | 0.618034 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(674\) | 0.363271 | − | 0.500000i | 0.363271 | − | 0.500000i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −0.951057 | + | 0.309017i | −0.951057 | + | 0.309017i | −0.743145 | − | 0.669131i | \(-0.766667\pi\) |
−0.207912 | + | 0.978148i | \(0.566667\pi\) | |||||||
\(678\) | 0.500000 | − | 0.363271i | 0.500000 | − | 0.363271i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −1.53884 | + | 0.500000i | −1.53884 | + | 0.500000i | ||||
\(681\) | −0.587785 | + | 0.809017i | −0.587785 | + | 0.809017i | ||||
\(682\) | −0.500000 | + | 0.363271i | −0.500000 | + | 0.363271i | ||||
\(683\) | − | 0.618034i | − | 0.618034i | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||
0.951057 | − | 0.309017i | \(-0.100000\pi\) | |||||||
\(684\) | −0.500000 | − | 0.363271i | −0.500000 | − | 0.363271i | ||||
\(685\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(686\) | −0.363271 | − | 0.500000i | −0.363271 | − | 0.500000i | ||||
\(687\) | −0.618034 | −0.618034 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −0.363271 | + | 0.500000i | −0.363271 | + | 0.500000i | ||||
\(691\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(692\) | −0.363271 | + | 0.500000i | −0.363271 | + | 0.500000i | ||||
\(693\) | 0.951057 | − | 1.30902i | 0.951057 | − | 1.30902i | ||||
\(694\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(695\) | 0.951057 | + | 0.309017i | 0.951057 | + | 0.309017i | ||||
\(696\) | −0.618034 | −0.618034 | ||||||||
\(697\) | −0.809017 | + | 2.48990i | −0.809017 | + | 2.48990i | ||||
\(698\) | −0.587785 | − | 0.190983i | −0.587785 | − | 0.190983i | ||||
\(699\) | 0.587785 | + | 0.190983i | 0.587785 | + | 0.190983i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.951057 | + | 0.309017i | 0.951057 | + | 0.309017i | 0.743145 | − | 0.669131i | \(-0.233333\pi\) |
0.207912 | + | 0.978148i | \(0.433333\pi\) | |||||||
\(702\) | 0.587785 | − | 0.190983i | 0.587785 | − | 0.190983i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0.587785 | + | 0.809017i | 0.587785 | + | 0.809017i | ||||
\(705\) | 0.190983 | + | 0.587785i | 0.190983 | + | 0.587785i | ||||
\(706\) | 1.00000 | 1.00000 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.500000 | + | 1.53884i | −0.500000 | + | 1.53884i | 0.309017 | + | 0.951057i | \(0.400000\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(710\) | 0.363271 | + | 0.118034i | 0.363271 | + | 0.118034i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0.809017 | + | 0.587785i | 0.809017 | + | 0.587785i | ||||
\(713\) | −0.587785 | − | 0.190983i | −0.587785 | − | 0.190983i | ||||
\(714\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(715\) | 1.30902 | − | 0.951057i | 1.30902 | − | 0.951057i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −0.309017 | + | 0.951057i | −0.309017 | + | 0.951057i | ||||
\(719\) | 0.587785 | + | 0.190983i | 0.587785 | + | 0.190983i | 0.587785 | − | 0.809017i | \(-0.300000\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.500000 | − | 1.53884i | −0.500000 | − | 1.53884i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0.587785 | + | 0.809017i | 0.587785 | + | 0.809017i | ||||
\(727\) | 1.00000 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(728\) | 0.951057 | + | 0.309017i | 0.951057 | + | 0.309017i | ||||
\(729\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(730\) | −0.500000 | + | 0.363271i | −0.500000 | + | 0.363271i | ||||
\(731\) | −1.53884 | + | 0.500000i | −1.53884 | + | 0.500000i | ||||
\(732\) | 0.809017 | − | 0.587785i | 0.809017 | − | 0.587785i | ||||
\(733\) | 0.500000 | − | 1.53884i | 0.500000 | − | 1.53884i | −0.309017 | − | 0.951057i | \(-0.600000\pi\) |
0.809017 | − | 0.587785i | \(-0.200000\pi\) | |||||||
\(734\) | 0.618034i | 0.618034i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.309017 | + | 0.951057i | −0.309017 | + | 0.951057i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −0.309017 | − | 0.951057i | −0.309017 | − | 0.951057i | ||||
\(739\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(744\) | 0.587785 | + | 0.190983i | 0.587785 | + | 0.190983i | ||||
\(745\) | 0.500000 | − | 0.363271i | 0.500000 | − | 0.363271i | ||||
\(746\) | 0.951057 | − | 0.309017i | 0.951057 | − | 0.309017i | ||||
\(747\) | −0.363271 | − | 0.500000i | −0.363271 | − | 0.500000i | ||||
\(748\) | −1.30902 | + | 0.951057i | −1.30902 | + | 0.951057i | ||||
\(749\) | −1.90211 | − | 0.618034i | −1.90211 | − | 0.618034i | ||||
\(750\) | 0.618034 | 0.618034 | ||||||||
\(751\) | 1.30902 | − | 0.951057i | 1.30902 | − | 0.951057i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
1.00000 | \(0\) | |||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.118034 | − | 0.363271i | −0.118034 | − | 0.363271i | ||||
\(755\) | −1.53884 | + | 0.500000i | −1.53884 | + | 0.500000i | ||||
\(756\) | −0.618034 | −0.618034 | ||||||||
\(757\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | 0.104528 | − | 0.994522i | \(-0.466667\pi\) |
−0.913545 | + | 0.406737i | \(0.866667\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.500000 | + | 1.53884i | −0.500000 | + | 1.53884i | ||||
\(760\) | −0.309017 | − | 0.951057i | −0.309017 | − | 0.951057i | ||||
\(761\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(762\) | 0.363271 | + | 0.500000i | 0.363271 | + | 0.500000i | ||||
\(763\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(764\) | 0.587785 | + | 0.190983i | 0.587785 | + | 0.190983i | ||||
\(765\) | 1.30902 | + | 0.951057i | 1.30902 | + | 0.951057i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(769\) | 0.500000 | + | 0.363271i | 0.500000 | + | 0.363271i | 0.809017 | − | 0.587785i | \(-0.200000\pi\) |
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(770\) | 0.951057 | − | 0.309017i | 0.951057 | − | 0.309017i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(774\) | 0.363271 | − | 0.500000i | 0.363271 | − | 0.500000i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −0.190983 | + | 0.587785i | −0.190983 | + | 0.587785i | ||||
\(779\) | −1.53884 | − | 0.500000i | −1.53884 | − | 0.500000i | ||||
\(780\) | −0.587785 | − | 0.190983i | −0.587785 | − | 0.190983i | ||||
\(781\) | 1.00000 | 1.00000 | ||||||||
\(782\) | 0.951057 | + | 0.309017i | 0.951057 | + | 0.309017i | ||||
\(783\) | 0.363271 | + | 0.500000i | 0.363271 | + | 0.500000i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.587785 | − | 0.809017i | 0.587785 | − | 0.809017i | ||||
\(786\) | −1.00000 | −1.00000 | ||||||||
\(787\) | −1.30902 | − | 0.951057i | −1.30902 | − | 0.951057i | −0.309017 | − | 0.951057i | \(-0.600000\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(788\) | −0.224514 | + | 0.309017i | −0.224514 | + | 0.309017i | ||||
\(789\) | 0.951057 | − | 0.309017i | 0.951057 | − | 0.309017i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.587785 | − | 0.809017i | −0.587785 | − | 0.809017i | ||||
\(792\) | 0.500000 | − | 1.53884i | 0.500000 | − | 1.53884i | ||||
\(793\) | 1.30902 | + | 0.951057i | 1.30902 | + | 0.951057i | ||||
\(794\) | 1.00000i | 1.00000i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.309017 | + | 0.224514i | 0.309017 | + | 0.224514i | ||||
\(797\) | 0.587785 | − | 0.190983i | 0.587785 | − | 0.190983i | − | 1.00000i | \(-0.5\pi\) | |
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(798\) | 0.363271 | − | 0.500000i | 0.363271 | − | 0.500000i | ||||
\(799\) | 0.809017 | − | 0.587785i | 0.809017 | − | 0.587785i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 1.00000i | − | 1.00000i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.951057 | + | 1.30902i | −0.951057 | + | 1.30902i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.809017 | + | 0.587785i | 0.809017 | + | 0.587785i | ||||
\(806\) | 0.381966i | 0.381966i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −0.587785 | − | 0.190983i | −0.587785 | − | 0.190983i | − | 1.00000i | \(-0.5\pi\) | |
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(810\) | −0.618034 | −0.618034 | ||||||||
\(811\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(812\) | 0.381966i | 0.381966i | ||||||||
\(813\) | 1.61803 | 1.61803 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.951057 | − | 0.309017i | 0.951057 | − | 0.309017i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.309017 | − | 0.951057i | −0.309017 | − | 0.951057i | ||||
\(818\) | − | 0.381966i | − | 0.381966i | ||||||
\(819\) | −0.309017 | − | 0.951057i | −0.309017 | − | 0.951057i | ||||
\(820\) | −0.309017 | + | 0.951057i | −0.309017 | + | 0.951057i | ||||
\(821\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(822\) | 0.500000 | − | 0.363271i | 0.500000 | − | 0.363271i | ||||
\(823\) | −0.500000 | − | 0.363271i | −0.500000 | − | 0.363271i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(828\) | 0.587785 | − | 0.190983i | 0.587785 | − | 0.190983i | ||||
\(829\) | 1.61803 | 1.61803 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(830\) | − | 0.381966i | − | 0.381966i | ||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.618034 | 0.618034 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0.363271 | + | 0.500000i | 0.363271 | + | 0.500000i | ||||
\(835\) | −0.190983 | + | 0.587785i | −0.190983 | + | 0.587785i | ||||
\(836\) | −0.587785 | − | 0.809017i | −0.587785 | − | 0.809017i | ||||
\(837\) | −0.190983 | − | 0.587785i | −0.190983 | − | 0.587785i | ||||
\(838\) | −0.118034 | − | 0.363271i | −0.118034 | − | 0.363271i | ||||
\(839\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(840\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(841\) | −0.500000 | + | 0.363271i | −0.500000 | + | 0.363271i | ||||
\(842\) | −0.951057 | − | 0.309017i | −0.951057 | − | 0.309017i | ||||
\(843\) | 1.61803i | 1.61803i | ||||||||
\(844\) | 0.190983 | − | 0.587785i | 0.190983 | − | 0.587785i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −0.118034 | + | 0.363271i | −0.118034 | + | 0.363271i | ||||
\(847\) | 1.30902 | − | 0.951057i | 1.30902 | − | 0.951057i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.809017 | + | 0.587785i | 0.809017 | + | 0.587785i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −0.224514 | − | 0.309017i | −0.224514 | − | 0.309017i | ||||
\(853\) | −0.190983 | + | 0.587785i | −0.190983 | + | 0.587785i | 0.809017 | + | 0.587785i | \(0.200000\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(854\) | 0.587785 | + | 0.809017i | 0.587785 | + | 0.809017i | ||||
\(855\) | −0.587785 | + | 0.809017i | −0.587785 | + | 0.809017i | ||||
\(856\) | −2.00000 | −2.00000 | ||||||||
\(857\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(858\) | 1.00000 | 1.00000 | ||||||||
\(859\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(860\) | −0.587785 | + | 0.190983i | −0.587785 | + | 0.190983i | ||||
\(861\) | −1.53884 | + | 0.500000i | −1.53884 | + | 0.500000i | ||||
\(862\) | −0.500000 | − | 0.363271i | −0.500000 | − | 0.363271i | ||||
\(863\) | −1.53884 | + | 0.500000i | −1.53884 | + | 0.500000i | −0.951057 | − | 0.309017i | \(-0.900000\pi\) |
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(864\) | −0.951057 | + | 0.309017i | −0.951057 | + | 0.309017i | ||||
\(865\) | 0.809017 | + | 0.587785i | 0.809017 | + | 0.587785i | ||||
\(866\) | 0.363271 | + | 0.500000i | 0.363271 | + | 0.500000i | ||||
\(867\) | 0.500000 | − | 1.53884i | 0.500000 | − | 1.53884i | ||||
\(868\) | 0.118034 | − | 0.363271i | 0.118034 | − | 0.363271i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0.381966i | 0.381966i | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −0.951057 | − | 0.309017i | −0.951057 | − | 0.309017i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.190983 | + | 0.587785i | −0.190983 | + | 0.587785i | ||||
\(875\) | − | 1.00000i | − | 1.00000i | ||||||
\(876\) | 0.618034 | 0.618034 | ||||||||
\(877\) | 0.618034 | 0.618034 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.951057 | + | 0.309017i | 0.951057 | + | 0.309017i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −0.363271 | − | 0.500000i | −0.363271 | − | 0.500000i | 0.587785 | − | 0.809017i | \(-0.300000\pi\) |
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(884\) | 1.00000i | 1.00000i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.500000 | + | 0.363271i | −0.500000 | + | 0.363271i | ||||
\(887\) | − | 1.00000i | − | 1.00000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.809017 | − | 0.587785i | 0.809017 | − | 0.587785i | ||||
\(890\) | 0.363271 | − | 0.500000i | 0.363271 | − | 0.500000i | ||||
\(891\) | −1.53884 | + | 0.500000i | −1.53884 | + | 0.500000i | ||||
\(892\) | −0.500000 | − | 0.363271i | −0.500000 | − | 0.363271i | ||||
\(893\) | 0.363271 | + | 0.500000i | 0.363271 | + | 0.500000i | ||||
\(894\) | 0.381966 | 0.381966 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.587785 | − | 0.190983i | −0.587785 | − | 0.190983i | ||||
\(897\) | 0.587785 | + | 0.809017i | 0.587785 | + | 0.809017i | ||||
\(898\) | 0.618034 | 0.618034 | ||||||||
\(899\) | −0.363271 | + | 0.118034i | −0.363271 | + | 0.118034i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | − | 1.61803i | − | 1.61803i | ||||||
\(903\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(904\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −0.951057 | − | 0.309017i | −0.951057 | − | 0.309017i | ||||
\(907\) | −1.61803 | −1.61803 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(908\) | 0.587785 | + | 0.190983i | 0.587785 | + | 0.190983i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0.190983 | − | 0.587785i | 0.190983 | − | 0.587785i | ||||
\(911\) | − | 1.61803i | − | 1.61803i | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||
0.587785 | − | 0.809017i | \(-0.300000\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.309017 | − | 0.951057i | −0.309017 | − | 0.951057i | ||||
\(914\) | 0.224514 | − | 0.309017i | 0.224514 | − | 0.309017i | ||||
\(915\) | −0.951057 | − | 1.30902i | −0.951057 | − | 1.30902i | ||||
\(916\) | 0.118034 | + | 0.363271i | 0.118034 | + | 0.363271i | ||||
\(917\) | 1.61803i | 1.61803i | ||||||||
\(918\) | 0.309017 | + | 0.951057i | 0.309017 | + | 0.951057i | ||||
\(919\) | 1.30902 | + | 0.951057i | 1.30902 | + | 0.951057i | 1.00000 | \(0\) | ||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(920\) | 0.951057 | + | 0.309017i | 0.951057 | + | 0.309017i | ||||
\(921\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(922\) | 0.500000 | − | 0.363271i | 0.500000 | − | 0.363271i | ||||
\(923\) | 0.363271 | − | 0.500000i | 0.363271 | − | 0.500000i | ||||
\(924\) | −0.951057 | − | 0.309017i | −0.951057 | − | 0.309017i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −0.363271 | − | 0.500000i | −0.363271 | − | 0.500000i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0.190983 | + | 0.587785i | 0.190983 | + | 0.587785i | ||||
\(929\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(930\) | 0.118034 | − | 0.363271i | 0.118034 | − | 0.363271i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 0.381966i | − | 0.381966i | ||||||
\(933\) | −0.951057 | + | 0.309017i | −0.951057 | + | 0.309017i | ||||
\(934\) | −0.190983 | − | 0.587785i | −0.190983 | − | 0.587785i | ||||
\(935\) | 1.53884 | + | 2.11803i | 1.53884 | + | 2.11803i | ||||
\(936\) | −0.587785 | − | 0.809017i | −0.587785 | − | 0.809017i | ||||
\(937\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | −0.913545 | − | 0.406737i | \(-0.866667\pi\) |
0.104528 | + | 0.994522i | \(0.466667\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.190983 | + | 0.587785i | −0.190983 | + | 0.587785i | ||||
\(940\) | 0.309017 | − | 0.224514i | 0.309017 | − | 0.224514i | ||||
\(941\) | 0.951057 | + | 1.30902i | 0.951057 | + | 1.30902i | 0.951057 | + | 0.309017i | \(0.100000\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(942\) | 0.587785 | − | 0.190983i | 0.587785 | − | 0.190983i | ||||
\(943\) | 1.30902 | − | 0.951057i | 1.30902 | − | 0.951057i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.00000i | 1.00000i | ||||||||
\(946\) | 0.809017 | − | 0.587785i | 0.809017 | − | 0.587785i | ||||
\(947\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.309017 | + | 0.951057i | 0.309017 | + | 0.951057i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.587785 | − | 0.809017i | 0.587785 | − | 0.809017i | ||||
\(952\) | −0.500000 | + | 1.53884i | −0.500000 | + | 1.53884i | ||||
\(953\) | 0.951057 | + | 1.30902i | 0.951057 | + | 1.30902i | 0.951057 | + | 0.309017i | \(0.100000\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.309017 | + | 0.951057i | 0.309017 | + | 0.951057i | ||||
\(958\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(959\) | −0.587785 | − | 0.809017i | −0.587785 | − | 0.809017i | ||||
\(960\) | −0.587785 | − | 0.190983i | −0.587785 | − | 0.190983i | ||||
\(961\) | −0.618034 | −0.618034 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.17557 | + | 1.61803i | 1.17557 | + | 1.61803i | ||||
\(964\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.190983 | + | 0.587785i | 0.190983 | + | 0.587785i | ||||
\(967\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(968\) | 0.951057 | − | 1.30902i | 0.951057 | − | 1.30902i | ||||
\(969\) | 1.53884 | + | 0.500000i | 1.53884 | + | 0.500000i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.951057 | − | 0.309017i | 0.951057 | − | 0.309017i | 0.207912 | − | 0.978148i | \(-0.433333\pi\) |
0.743145 | + | 0.669131i | \(0.233333\pi\) | |||||||
\(972\) | 0.500000 | + | 0.363271i | 0.500000 | + | 0.363271i | ||||
\(973\) | 0.809017 | − | 0.587785i | 0.809017 | − | 0.587785i | ||||
\(974\) | 0.224514 | − | 0.309017i | 0.224514 | − | 0.309017i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0.587785 | + | 0.809017i | 0.587785 | + | 0.809017i | 0.994522 | − | 0.104528i | \(-0.0333333\pi\) |
−0.406737 | + | 0.913545i | \(0.633333\pi\) | |||||||
\(978\) | 0.587785 | + | 0.190983i | 0.587785 | + | 0.190983i | ||||
\(979\) | 0.500000 | − | 1.53884i | 0.500000 | − | 1.53884i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.309017 | + | 0.951057i | 0.309017 | + | 0.951057i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.53884 | − | 0.500000i | 1.53884 | − | 0.500000i | 0.587785 | − | 0.809017i | \(-0.300000\pi\) |
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(984\) | −1.30902 | + | 0.951057i | −1.30902 | + | 0.951057i | ||||
\(985\) | 0.500000 | + | 0.363271i | 0.500000 | + | 0.363271i | ||||
\(986\) | 0.587785 | − | 0.190983i | 0.587785 | − | 0.190983i | ||||
\(987\) | 0.587785 | + | 0.190983i | 0.587785 | + | 0.190983i | ||||
\(988\) | −0.618034 | −0.618034 | ||||||||
\(989\) | 0.951057 | + | 0.309017i | 0.951057 | + | 0.309017i | ||||
\(990\) | −0.951057 | − | 0.309017i | −0.951057 | − | 0.309017i | ||||
\(991\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(992\) | − | 0.618034i | − | 0.618034i | ||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0.309017 | − | 0.224514i | 0.309017 | − | 0.224514i | ||||
\(995\) | 0.363271 | − | 0.500000i | 0.363271 | − | 0.500000i | ||||
\(996\) | −0.224514 | + | 0.309017i | −0.224514 | + | 0.309017i | ||||
\(997\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(998\) | 0.363271 | − | 0.500000i | 0.363271 | − | 0.500000i | ||||
\(999\) | 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 | 633.1.m.b.188.1 | ✓ | 8 | |
3.2 | odd | 2 | inner | 633.1.m.b.188.2 | yes | 8 | |
211.55 | even | 5 | inner | 633.1.m.b.266.2 | yes | 8 | |
633.266 | odd | 10 | inner | 633.1.m.b.266.1 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
633.1.m.b.188.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
633.1.m.b.188.2 | yes | 8 | 3.2 | odd | 2 | inner | |
633.1.m.b.266.1 | yes | 8 | 633.266 | odd | 10 | inner | |
633.1.m.b.266.2 | yes | 8 | 211.55 | even | 5 | inner |