Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [648,1,Mod(43,648)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(648, base_ring=CyclotomicField(54))
chi = DirichletCharacter(H, H._module([27, 27, 22]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("648.43");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 648 = 2^{3} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 648.bf (of order \(54\), degree \(18\), 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: | \(0.323394128186\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\Q(\zeta_{54})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - x^{9} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{27}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{27} + \cdots)\) |
Embedding invariants
Embedding label | 403.1 | ||
Root | \(-0.973045 - 0.230616i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 648.403 |
Dual form | 648.1.bf.a.283.1 |
$q$-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 \(\left(\mathbb{Z}/648\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(487\) | \(569\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{14}{27}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.0581448 | + | 0.998308i | −0.0581448 | + | 0.998308i | ||||
\(3\) | −0.286803 | − | 0.957990i | −0.286803 | − | 0.957990i | ||||
\(4\) | −0.993238 | − | 0.116093i | −0.993238 | − | 0.116093i | ||||
\(5\) | 0 | 0 | 0.973045 | − | 0.230616i | \(-0.0740741\pi\) | ||||
−0.973045 | + | 0.230616i | \(0.925926\pi\) | |||||||
\(6\) | 0.973045 | − | 0.230616i | 0.973045 | − | 0.230616i | ||||
\(7\) | 0 | 0 | −0.597159 | − | 0.802123i | \(-0.703704\pi\) | ||||
0.597159 | + | 0.802123i | \(0.296296\pi\) | |||||||
\(8\) | 0.173648 | − | 0.984808i | 0.173648 | − | 0.984808i | ||||
\(9\) | −0.835488 | + | 0.549509i | −0.835488 | + | 0.549509i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.36320 | − | 1.44491i | 1.36320 | − | 1.44491i | 0.597159 | − | 0.802123i | \(-0.296296\pi\) |
0.766044 | − | 0.642788i | \(-0.222222\pi\) | |||||||
\(12\) | 0.173648 | + | 0.984808i | 0.173648 | + | 0.984808i | ||||
\(13\) | 0 | 0 | −0.893633 | − | 0.448799i | \(-0.851852\pi\) | ||||
0.893633 | + | 0.448799i | \(0.148148\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.973045 | + | 0.230616i | 0.973045 | + | 0.230616i | ||||
\(17\) | −1.67948 | − | 0.611281i | −1.67948 | − | 0.611281i | −0.686242 | − | 0.727374i | \(-0.740741\pi\) |
−0.993238 | + | 0.116093i | \(0.962963\pi\) | |||||||
\(18\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(19\) | 1.28971 | − | 0.469417i | 1.28971 | − | 0.469417i | 0.396080 | − | 0.918216i | \(-0.370370\pi\) |
0.893633 | + | 0.448799i | \(0.148148\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.36320 | + | 1.44491i | 1.36320 | + | 1.44491i | ||||
\(23\) | 0 | 0 | 0.597159 | − | 0.802123i | \(-0.296296\pi\) | ||||
−0.597159 | + | 0.802123i | \(0.703704\pi\) | |||||||
\(24\) | −0.993238 | + | 0.116093i | −0.993238 | + | 0.116093i | ||||
\(25\) | 0.893633 | − | 0.448799i | 0.893633 | − | 0.448799i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.766044 | + | 0.642788i | 0.766044 | + | 0.642788i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | −0.835488 | − | 0.549509i | \(-0.814815\pi\) | ||||
0.835488 | + | 0.549509i | \(0.185185\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | −0.396080 | − | 0.918216i | \(-0.629630\pi\) | ||||
0.396080 | + | 0.918216i | \(0.370370\pi\) | |||||||
\(32\) | −0.286803 | + | 0.957990i | −0.286803 | + | 0.957990i | ||||
\(33\) | −1.77518 | − | 0.891529i | −1.77518 | − | 0.891529i | ||||
\(34\) | 0.707900 | − | 1.64110i | 0.707900 | − | 1.64110i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.893633 | − | 0.448799i | 0.893633 | − | 0.448799i | ||||
\(37\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(38\) | 0.393633 | + | 1.31482i | 0.393633 | + | 1.31482i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.0333522 | + | 0.572636i | 0.0333522 | + | 0.572636i | 0.973045 | + | 0.230616i | \(0.0740741\pi\) |
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.0333522 | + | 0.111404i | 0.0333522 | + | 0.111404i | 0.973045 | − | 0.230616i | \(-0.0740741\pi\) |
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(44\) | −1.52173 | + | 1.27688i | −1.52173 | + | 1.27688i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.396080 | − | 0.918216i | \(-0.370370\pi\) | ||||
−0.396080 | + | 0.918216i | \(0.629630\pi\) | |||||||
\(48\) | −0.0581448 | − | 0.998308i | −0.0581448 | − | 0.998308i | ||||
\(49\) | −0.286803 | + | 0.957990i | −0.286803 | + | 0.957990i | ||||
\(50\) | 0.396080 | + | 0.918216i | 0.396080 | + | 0.918216i | ||||
\(51\) | −0.103920 | + | 1.78424i | −0.103920 | + | 1.78424i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(54\) | −0.686242 | + | 0.727374i | −0.686242 | + | 0.727374i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.819590 | − | 1.10090i | −0.819590 | − | 1.10090i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.33549 | − | 1.41553i | −1.33549 | − | 1.41553i | −0.835488 | − | 0.549509i | \(-0.814815\pi\) |
−0.500000 | − | 0.866025i | \(-0.666667\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 0.993238 | − | 0.116093i | \(-0.0370370\pi\) | ||||
−0.993238 | + | 0.116093i | \(0.962963\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.939693 | − | 0.342020i | −0.939693 | − | 0.342020i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.993238 | − | 1.72034i | 0.993238 | − | 1.72034i | ||||
\(67\) | −0.997837 | + | 0.656288i | −0.997837 | + | 0.656288i | −0.939693 | − | 0.342020i | \(-0.888889\pi\) |
−0.0581448 | + | 0.998308i | \(0.518519\pi\) | |||||||
\(68\) | 1.59716 | + | 0.802123i | 1.59716 | + | 0.802123i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(72\) | 0.396080 | + | 0.918216i | 0.396080 | + | 0.918216i | ||||
\(73\) | −0.290162 | + | 1.64559i | −0.290162 | + | 1.64559i | 0.396080 | + | 0.918216i | \(0.370370\pi\) |
−0.686242 | + | 0.727374i | \(0.740741\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.686242 | − | 0.727374i | −0.686242 | − | 0.727374i | ||||
\(76\) | −1.33549 | + | 0.316516i | −1.33549 | + | 0.316516i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | 0.0581448 | − | 0.998308i | \(-0.481481\pi\) | ||||
−0.0581448 | + | 0.998308i | \(0.518519\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.396080 | − | 0.918216i | 0.396080 | − | 0.918216i | ||||
\(82\) | −0.573606 | −0.573606 | ||||||||
\(83\) | −0.0890830 | + | 1.52950i | −0.0890830 | + | 1.52950i | 0.597159 | + | 0.802123i | \(0.296296\pi\) |
−0.686242 | + | 0.727374i | \(0.740741\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.113155 | + | 0.0268182i | −0.113155 | + | 0.0268182i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.18624 | − | 1.59340i | −1.18624 | − | 1.59340i | ||||
\(89\) | −0.326352 | + | 1.85083i | −0.326352 | + | 1.85083i | 0.173648 | + | 0.984808i | \(0.444444\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000 | 1.00000 | ||||||||
\(97\) | 0.770807 | + | 0.182685i | 0.770807 | + | 0.182685i | 0.597159 | − | 0.802123i | \(-0.296296\pi\) |
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(98\) | −0.939693 | − | 0.342020i | −0.939693 | − | 0.342020i | ||||
\(99\) | −0.344948 | + | 1.95630i | −0.344948 | + | 1.95630i | ||||
\(100\) | −0.939693 | + | 0.342020i | −0.939693 | + | 0.342020i | ||||
\(101\) | 0 | 0 | 0.993238 | − | 0.116093i | \(-0.0370370\pi\) | ||||
−0.993238 | + | 0.116093i | \(0.962963\pi\) | |||||||
\(102\) | −1.77518 | − | 0.207489i | −1.77518 | − | 0.207489i | ||||
\(103\) | 0 | 0 | −0.686242 | − | 0.727374i | \(-0.740741\pi\) | ||||
0.686242 | + | 0.727374i | \(0.259259\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.835488 | − | 1.44711i | 0.835488 | − | 1.44711i | −0.0581448 | − | 0.998308i | \(-0.518519\pi\) |
0.893633 | − | 0.448799i | \(-0.148148\pi\) | |||||||
\(108\) | −0.686242 | − | 0.727374i | −0.686242 | − | 0.727374i | ||||
\(109\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.0996057 | + | 0.332706i | −0.0996057 | + | 0.332706i | −0.993238 | − | 0.116093i | \(-0.962963\pi\) |
0.893633 | + | 0.448799i | \(0.148148\pi\) | |||||||
\(114\) | 1.14669 | − | 0.754192i | 1.14669 | − | 0.754192i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.49079 | − | 1.25092i | 1.49079 | − | 1.25092i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.171300 | − | 2.94111i | −0.171300 | − | 2.94111i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.539014 | − | 0.196185i | 0.539014 | − | 0.196185i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(128\) | 0.396080 | − | 0.918216i | 0.396080 | − | 0.918216i | ||||
\(129\) | 0.0971586 | − | 0.0639022i | 0.0971586 | − | 0.0639022i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.137557 | + | 0.318893i | 0.137557 | + | 0.318893i | 0.973045 | − | 0.230616i | \(-0.0740741\pi\) |
−0.835488 | + | 0.549509i | \(0.814815\pi\) | |||||||
\(132\) | 1.65968 | + | 1.09159i | 1.65968 | + | 1.09159i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −0.597159 | − | 1.03431i | −0.597159 | − | 1.03431i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.893633 | + | 1.54782i | −0.893633 | + | 1.54782i | ||||
\(137\) | 0.707900 | − | 0.355521i | 0.707900 | − | 0.355521i | −0.0581448 | − | 0.998308i | \(-0.518519\pi\) |
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.473045 | − | 0.635410i | 0.473045 | − | 0.635410i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
0.973045 | + | 0.230616i | \(0.0740741\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.939693 | + | 0.342020i | −0.939693 | + | 0.342020i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.62593 | − | 0.385353i | −1.62593 | − | 0.385353i | ||||
\(147\) | 1.00000 | 1.00000 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | −0.893633 | − | 0.448799i | \(-0.851852\pi\) | ||||
0.893633 | + | 0.448799i | \(0.148148\pi\) | |||||||
\(150\) | 0.766044 | − | 0.642788i | 0.766044 | − | 0.642788i | ||||
\(151\) | 0 | 0 | 0.686242 | − | 0.727374i | \(-0.259259\pi\) | ||||
−0.686242 | + | 0.727374i | \(0.740741\pi\) | |||||||
\(152\) | −0.238329 | − | 1.35163i | −0.238329 | − | 1.35163i | ||||
\(153\) | 1.73909 | − | 0.412172i | 1.73909 | − | 0.412172i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.973045 | − | 0.230616i | \(-0.0740741\pi\) | ||||
−0.973045 | + | 0.230616i | \(0.925926\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.893633 | + | 0.448799i | 0.893633 | + | 0.448799i | ||||
\(163\) | 0.347296 | 0.347296 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(164\) | 0.0333522 | − | 0.572636i | 0.0333522 | − | 0.572636i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.52173 | − | 0.177865i | −1.52173 | − | 0.177865i | ||||
\(167\) | 0 | 0 | 0.973045 | − | 0.230616i | \(-0.0740741\pi\) | ||||
−0.973045 | + | 0.230616i | \(0.925926\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.597159 | + | 0.802123i | 0.597159 | + | 0.802123i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.819590 | + | 1.10090i | −0.819590 | + | 1.10090i | ||||
\(172\) | −0.0201935 | − | 0.114523i | −0.0201935 | − | 0.114523i | ||||
\(173\) | 0 | 0 | 0.686242 | − | 0.727374i | \(-0.259259\pi\) | ||||
−0.686242 | + | 0.727374i | \(0.740741\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.65968 | − | 1.09159i | 1.65968 | − | 1.09159i | ||||
\(177\) | −0.973045 | + | 1.68536i | −0.973045 | + | 1.68536i | ||||
\(178\) | −1.82873 | − | 0.433416i | −1.82873 | − | 0.433416i | ||||
\(179\) | 1.76604 | + | 0.642788i | 1.76604 | + | 0.642788i | 1.00000 | \(0\) | ||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.17272 | + | 1.59340i | −3.17272 | + | 1.59340i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.835488 | − | 0.549509i | \(-0.814815\pi\) | ||||
0.835488 | + | 0.549509i | \(0.185185\pi\) | |||||||
\(192\) | −0.0581448 | + | 0.998308i | −0.0581448 | + | 0.998308i | ||||
\(193\) | −0.227194 | − | 0.526695i | −0.227194 | − | 0.526695i | 0.766044 | − | 0.642788i | \(-0.222222\pi\) |
−0.993238 | + | 0.116093i | \(0.962963\pi\) | |||||||
\(194\) | −0.227194 | + | 0.758881i | −0.227194 | + | 0.758881i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.396080 | − | 0.918216i | 0.396080 | − | 0.918216i | ||||
\(197\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(198\) | −1.93293 | − | 0.458113i | −1.93293 | − | 0.458113i | ||||
\(199\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(200\) | −0.286803 | − | 0.957990i | −0.286803 | − | 0.957990i | ||||
\(201\) | 0.914900 | + | 0.767692i | 0.914900 | + | 0.767692i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.310355 | − | 1.76011i | 0.310355 | − | 1.76011i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.07987 | − | 2.50343i | 1.07987 | − | 2.50343i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.439408 | + | 1.46773i | −0.439408 | + | 1.46773i | 0.396080 | + | 0.918216i | \(0.370370\pi\) |
−0.835488 | + | 0.549509i | \(0.814815\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.39608 | + | 0.918216i | 1.39608 | + | 0.918216i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0.766044 | − | 0.642788i | 0.766044 | − | 0.642788i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.65968 | − | 0.193988i | 1.65968 | − | 0.193988i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.993238 | − | 0.116093i | \(-0.0370370\pi\) | ||||
−0.993238 | + | 0.116093i | \(0.962963\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(226\) | −0.326352 | − | 0.118782i | −0.326352 | − | 0.118782i | ||||
\(227\) | −0.113155 | − | 0.0268182i | −0.113155 | − | 0.0268182i | 0.173648 | − | 0.984808i | \(-0.444444\pi\) |
−0.286803 | + | 0.957990i | \(0.592593\pi\) | |||||||
\(228\) | 0.686242 | + | 1.18861i | 0.686242 | + | 1.18861i | ||||
\(229\) | 0 | 0 | 0.835488 | − | 0.549509i | \(-0.185185\pi\) | ||||
−0.835488 | + | 0.549509i | \(0.814815\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.337935 | + | 1.91652i | 0.337935 | + | 1.91652i | 0.396080 | + | 0.918216i | \(0.370370\pi\) |
−0.0581448 | + | 0.998308i | \(0.518519\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.16212 | + | 1.56100i | 1.16212 | + | 1.56100i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.993238 | − | 0.116093i | \(-0.962963\pi\) | ||||
0.993238 | + | 0.116093i | \(0.0370370\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.0694434 | + | 1.19230i | −0.0694434 | + | 1.19230i | 0.766044 | + | 0.642788i | \(0.222222\pi\) |
−0.835488 | + | 0.549509i | \(0.814815\pi\) | |||||||
\(242\) | 2.94609 | 2.94609 | ||||||||
\(243\) | −0.993238 | − | 0.116093i | −0.993238 | − | 0.116093i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.164512 | + | 0.549509i | 0.164512 | + | 0.549509i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.49079 | − | 0.353324i | 1.49079 | − | 0.353324i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.0201935 | + | 0.114523i | −0.0201935 | + | 0.114523i | −0.993238 | − | 0.116093i | \(-0.962963\pi\) |
0.973045 | + | 0.230616i | \(0.0740741\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.893633 | + | 0.448799i | 0.893633 | + | 0.448799i | ||||
\(257\) | −0.997837 | + | 0.656288i | −0.997837 | + | 0.656288i | −0.939693 | − | 0.342020i | \(-0.888889\pi\) |
−0.0581448 | + | 0.998308i | \(0.518519\pi\) | |||||||
\(258\) | 0.0581448 | + | 0.100710i | 0.0581448 | + | 0.100710i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −0.326352 | + | 0.118782i | −0.326352 | + | 0.118782i | ||||
\(263\) | 0 | 0 | 0.993238 | − | 0.116093i | \(-0.0370370\pi\) | ||||
−0.993238 | + | 0.116093i | \(0.962963\pi\) | |||||||
\(264\) | −1.18624 | + | 1.59340i | −1.18624 | + | 1.59340i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.86668 | − | 0.218183i | 1.86668 | − | 0.218183i | ||||
\(268\) | 1.06728 | − | 0.536009i | 1.06728 | − | 0.536009i | ||||
\(269\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(272\) | −1.49324 | − | 0.982118i | −1.49324 | − | 0.982118i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.313758 | + | 0.727374i | 0.313758 | + | 0.727374i | ||||
\(275\) | 0.569728 | − | 1.90302i | 0.569728 | − | 1.90302i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | 0.396080 | − | 0.918216i | \(-0.370370\pi\) | ||||
−0.396080 | + | 0.918216i | \(0.629630\pi\) | |||||||
\(278\) | 0.606829 | + | 0.509190i | 0.606829 | + | 0.509190i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.439408 | − | 1.46773i | −0.439408 | − | 1.46773i | −0.835488 | − | 0.549509i | \(-0.814815\pi\) |
0.396080 | − | 0.918216i | \(-0.370370\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.0890830 | − | 1.52950i | −0.0890830 | − | 1.52950i | −0.686242 | − | 0.727374i | \(-0.740741\pi\) |
0.597159 | − | 0.802123i | \(-0.296296\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −0.286803 | − | 0.957990i | −0.286803 | − | 0.957990i | ||||
\(289\) | 1.68094 | + | 1.41048i | 1.68094 | + | 1.41048i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.0460600 | − | 0.790819i | −0.0460600 | − | 0.790819i | ||||
\(292\) | 0.479241 | − | 1.60078i | 0.479241 | − | 1.60078i | ||||
\(293\) | 0 | 0 | −0.396080 | − | 0.918216i | \(-0.629630\pi\) | ||||
0.396080 | + | 0.918216i | \(0.370370\pi\) | |||||||
\(294\) | −0.0581448 | + | 0.998308i | −0.0581448 | + | 0.998308i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.97304 | − | 0.230616i | 1.97304 | − | 0.230616i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0.597159 | + | 0.802123i | 0.597159 | + | 0.802123i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.36320 | − | 0.159336i | 1.36320 | − | 0.159336i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.310355 | + | 1.76011i | 0.310355 | + | 1.76011i | ||||
\(307\) | −1.82873 | − | 0.665602i | −1.82873 | − | 0.665602i | −0.993238 | − | 0.116093i | \(-0.962963\pi\) |
−0.835488 | − | 0.549509i | \(-0.814815\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.893633 | − | 0.448799i | \(-0.851852\pi\) | ||||
0.893633 | + | 0.448799i | \(0.148148\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.393633 | − | 0.417226i | 0.393633 | − | 0.417226i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
0.893633 | + | 0.448799i | \(0.148148\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | −0.597159 | − | 0.802123i | \(-0.703704\pi\) | ||||
0.597159 | + | 0.802123i | \(0.296296\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.62593 | − | 0.385353i | −1.62593 | − | 0.385353i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.45299 | −2.45299 | ||||||||
\(324\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.0201935 | + | 0.346709i | −0.0201935 | + | 0.346709i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.569728 | + | 0.0665916i | 0.569728 | + | 0.0665916i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.12229 | − | 1.50750i | −1.12229 | − | 1.50750i | −0.835488 | − | 0.549509i | \(-0.814815\pi\) |
−0.286803 | − | 0.957990i | \(-0.592593\pi\) | |||||||
\(332\) | 0.266044 | − | 1.50881i | 0.266044 | − | 1.50881i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.103920 | − | 0.0521907i | −0.103920 | − | 0.0521907i | 0.396080 | − | 0.918216i | \(-0.370370\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(338\) | −0.835488 | + | 0.549509i | −0.835488 | + | 0.549509i | ||||
\(339\) | 0.347296 | 0.347296 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −1.05138 | − | 0.882215i | −1.05138 | − | 0.882215i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0.115503 | − | 0.0135004i | 0.115503 | − | 0.0135004i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.819590 | + | 1.10090i | −0.819590 | + | 1.10090i | 0.173648 | + | 0.984808i | \(0.444444\pi\) |
−0.993238 | + | 0.116093i | \(0.962963\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 0.893633 | − | 0.448799i | \(-0.148148\pi\) | ||||
−0.893633 | + | 0.448799i | \(0.851852\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.993238 | + | 1.72034i | 0.993238 | + | 1.72034i | ||||
\(353\) | 1.39608 | + | 0.918216i | 1.39608 | + | 0.918216i | 1.00000 | \(0\) | ||
0.396080 | + | 0.918216i | \(0.370370\pi\) | |||||||
\(354\) | −1.62593 | − | 1.06939i | −1.62593 | − | 1.06939i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0.539014 | − | 1.80043i | 0.539014 | − | 1.80043i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.744386 | + | 1.72568i | −0.744386 | + | 1.72568i | ||||
\(359\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.676961 | − | 0.568038i | 0.676961 | − | 0.568038i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.76842 | + | 1.00762i | −2.76842 | + | 1.00762i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | −0.286803 | − | 0.957990i | \(-0.592593\pi\) | ||||
0.286803 | + | 0.957990i | \(0.407407\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.342534 | − | 0.460103i | −0.342534 | − | 0.460103i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | 0.286803 | − | 0.957990i | \(-0.407407\pi\) | ||||
−0.286803 | + | 0.957990i | \(0.592593\pi\) | |||||||
\(374\) | −1.40623 | − | 3.26000i | −1.40623 | − | 3.26000i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.286803 | − | 0.496758i | 0.286803 | − | 0.496758i | −0.686242 | − | 0.727374i | \(-0.740741\pi\) |
0.973045 | + | 0.230616i | \(0.0740741\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.686242 | − | 0.727374i | \(-0.740741\pi\) | ||||
0.686242 | + | 0.727374i | \(0.259259\pi\) | |||||||
\(384\) | −0.993238 | − | 0.116093i | −0.993238 | − | 0.116093i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.539014 | − | 0.196185i | 0.539014 | − | 0.196185i | ||||
\(387\) | −0.0890830 | − | 0.0747496i | −0.0890830 | − | 0.0747496i | ||||
\(388\) | −0.744386 | − | 0.270935i | −0.744386 | − | 0.270935i | ||||
\(389\) | 0 | 0 | −0.973045 | − | 0.230616i | \(-0.925926\pi\) | ||||
0.973045 | + | 0.230616i | \(0.0740741\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0.893633 | + | 0.448799i | 0.893633 | + | 0.448799i | ||||
\(393\) | 0.266044 | − | 0.223238i | 0.266044 | − | 0.223238i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.569728 | − | 1.90302i | 0.569728 | − | 1.90302i | ||||
\(397\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.973045 | − | 0.230616i | 0.973045 | − | 0.230616i | ||||
\(401\) | 1.36320 | + | 0.159336i | 1.36320 | + | 0.159336i | 0.766044 | − | 0.642788i | \(-0.222222\pi\) |
0.597159 | + | 0.802123i | \(0.296296\pi\) | |||||||
\(402\) | −0.819590 | + | 0.868715i | −0.819590 | + | 0.868715i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 1.73909 | + | 0.412172i | 1.73909 | + | 0.412172i | ||||
\(409\) | −1.77518 | − | 0.207489i | −1.77518 | − | 0.207489i | −0.835488 | − | 0.549509i | \(-0.814815\pi\) |
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.543613 | − | 0.576196i | −0.543613 | − | 0.576196i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.744386 | − | 0.270935i | −0.744386 | − | 0.270935i | ||||
\(418\) | 2.43641 | + | 1.22361i | 2.43641 | + | 1.22361i | ||||
\(419\) | −0.290162 | + | 0.190842i | −0.290162 | + | 0.190842i | −0.686242 | − | 0.727374i | \(-0.740741\pi\) |
0.396080 | + | 0.918216i | \(0.370370\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | −0.973045 | − | 0.230616i | \(-0.925926\pi\) | ||||
0.973045 | + | 0.230616i | \(0.0740741\pi\) | |||||||
\(422\) | −1.43969 | − | 0.524005i | −1.43969 | − | 0.524005i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.77518 | + | 0.207489i | −1.77518 | + | 0.207489i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −0.997837 | + | 1.34033i | −0.997837 | + | 1.34033i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(432\) | 0.597159 | + | 0.802123i | 0.597159 | + | 0.802123i | ||||
\(433\) | −0.893633 | − | 1.54782i | −0.893633 | − | 1.54782i | −0.835488 | − | 0.549509i | \(-0.814815\pi\) |
−0.0581448 | − | 0.998308i | \(-0.518519\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0.0971586 | + | 1.66815i | 0.0971586 | + | 1.66815i | ||||
\(439\) | 0 | 0 | 0.396080 | − | 0.918216i | \(-0.370370\pi\) | ||||
−0.396080 | + | 0.918216i | \(0.629630\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.286803 | − | 0.957990i | −0.286803 | − | 0.957990i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.164512 | + | 0.549509i | 0.164512 | + | 0.549509i | 1.00000 | \(0\) | ||
−0.835488 | + | 0.549509i | \(0.814815\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.606829 | − | 0.509190i | 0.606829 | − | 0.509190i | −0.286803 | − | 0.957990i | \(-0.592593\pi\) |
0.893633 | + | 0.448799i | \(0.148148\pi\) | |||||||
\(450\) | −0.835488 | − | 0.549509i | −0.835488 | − | 0.549509i | ||||
\(451\) | 0.872874 | + | 0.732428i | 0.872874 | + | 0.732428i | ||||
\(452\) | 0.137557 | − | 0.318893i | 0.137557 | − | 0.318893i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0.0333522 | − | 0.111404i | 0.0333522 | − | 0.111404i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.22650 | + | 0.615969i | −1.22650 | + | 0.615969i | ||||
\(457\) | −1.62593 | − | 1.06939i | −1.62593 | − | 1.06939i | −0.939693 | − | 0.342020i | \(-0.888889\pi\) |
−0.686242 | − | 0.727374i | \(-0.740741\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.893633 | − | 1.54782i | −0.893633 | − | 1.54782i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 0.893633 | − | 0.448799i | \(-0.148148\pi\) | ||||
−0.893633 | + | 0.448799i | \(0.851852\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | 0.597159 | − | 0.802123i | \(-0.296296\pi\) | ||||
−0.597159 | + | 0.802123i | \(0.703704\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.93293 | + | 0.225927i | −1.93293 | + | 0.225927i | ||||
\(467\) | 1.28971 | − | 0.469417i | 1.28971 | − | 0.469417i | 0.396080 | − | 0.918216i | \(-0.370370\pi\) |
0.893633 | + | 0.448799i | \(0.148148\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.62593 | + | 1.06939i | −1.62593 | + | 1.06939i | ||||
\(473\) | 0.206435 | + | 0.103676i | 0.206435 | + | 0.103676i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.941855 | − | 0.998308i | 0.941855 | − | 0.998308i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.597159 | − | 0.802123i | \(-0.703704\pi\) | ||||
0.597159 | + | 0.802123i | \(0.296296\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −1.18624 | − | 0.138652i | −1.18624 | − | 0.138652i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.171300 | + | 2.94111i | −0.171300 | + | 2.94111i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.173648 | − | 0.984808i | 0.173648 | − | 0.984808i | ||||
\(487\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.0996057 | − | 0.332706i | −0.0996057 | − | 0.332706i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.62593 | + | 0.385353i | −1.62593 | + | 0.385353i | −0.939693 | − | 0.342020i | \(-0.888889\pi\) |
−0.686242 | + | 0.727374i | \(0.740741\pi\) | |||||||
\(492\) | −0.558145 | + | 0.132283i | −0.558145 | + | 0.132283i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0.266044 | + | 1.50881i | 0.266044 | + | 1.50881i | ||||
\(499\) | 1.59716 | + | 0.802123i | 1.59716 | + | 0.802123i | 1.00000 | \(0\) | ||
0.597159 | + | 0.802123i | \(0.296296\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −0.113155 | − | 0.0268182i | −0.113155 | − | 0.0268182i | ||||
\(503\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.597159 | − | 0.802123i | 0.597159 | − | 0.802123i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | 0.597159 | − | 0.802123i | \(-0.296296\pi\) | ||||
−0.597159 | + | 0.802123i | \(0.703704\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(513\) | 1.28971 | + | 0.469417i | 1.28971 | + | 0.469417i | ||||
\(514\) | −0.597159 | − | 1.03431i | −0.597159 | − | 1.03431i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.103920 | + | 0.0521907i | −0.103920 | + | 0.0521907i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.0890830 | − | 0.0747496i | −0.0890830 | − | 0.0747496i | 0.597159 | − | 0.802123i | \(-0.296296\pi\) |
−0.686242 | + | 0.727374i | \(0.740741\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.266044 | − | 0.223238i | 0.266044 | − | 0.223238i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(524\) | −0.0996057 | − | 0.332706i | −0.0996057 | − | 0.332706i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −1.52173 | − | 1.27688i | −1.52173 | − | 1.27688i | ||||
\(529\) | −0.286803 | − | 0.957990i | −0.286803 | − | 0.957990i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.89363 | + | 0.448799i | 1.89363 | + | 0.448799i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0.109277 | + | 1.87621i | 0.109277 | + | 1.87621i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0.473045 | + | 1.09664i | 0.473045 | + | 1.09664i | ||||
\(537\) | 0.109277 | − | 1.87621i | 0.109277 | − | 1.87621i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.993238 | + | 1.72034i | 0.993238 | + | 1.72034i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.06728 | − | 1.43361i | 1.06728 | − | 1.43361i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.77518 | + | 0.207489i | −1.77518 | + | 0.207489i | −0.939693 | − | 0.342020i | \(-0.888889\pi\) |
−0.835488 | + | 0.549509i | \(0.814815\pi\) | |||||||
\(548\) | −0.744386 | + | 0.270935i | −0.744386 | + | 0.270935i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.86668 | + | 0.679415i | 1.86668 | + | 0.679415i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.543613 | + | 0.576196i | −0.543613 | + | 0.576196i | ||||
\(557\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.43641 | + | 2.58244i | 2.43641 | + | 2.58244i | ||||
\(562\) | 1.49079 | − | 0.353324i | 1.49079 | − | 0.353324i | ||||
\(563\) | −0.786803 | − | 0.0919641i | −0.786803 | − | 0.0919641i | −0.286803 | − | 0.957990i | \(-0.592593\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.53209 | 1.53209 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −0.113155 | + | 1.94280i | −0.113155 | + | 1.94280i | 0.173648 | + | 0.984808i | \(0.444444\pi\) |
−0.286803 | + | 0.957990i | \(0.592593\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.65968 | + | 0.193988i | 1.65968 | + | 0.193988i | 0.893633 | − | 0.448799i | \(-0.148148\pi\) |
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.973045 | − | 0.230616i | 0.973045 | − | 0.230616i | ||||
\(577\) | 0.137557 | + | 0.780125i | 0.137557 | + | 0.780125i | 0.973045 | + | 0.230616i | \(0.0740741\pi\) |
−0.835488 | + | 0.549509i | \(0.814815\pi\) | |||||||
\(578\) | −1.50583 | + | 1.59609i | −1.50583 | + | 1.59609i | ||||
\(579\) | −0.439408 | + | 0.368707i | −0.439408 | + | 0.368707i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0.792160 | 0.792160 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 1.57020 | + | 0.571507i | 1.57020 | + | 0.571507i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.18624 | + | 0.138652i | −1.18624 | + | 0.138652i | −0.686242 | − | 0.727374i | \(-0.740741\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(588\) | −0.993238 | − | 0.116093i | −0.993238 | − | 0.116093i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.939693 | − | 1.62760i | 0.939693 | − | 1.62760i | 0.173648 | − | 0.984808i | \(-0.444444\pi\) |
0.766044 | − | 0.642788i | \(-0.222222\pi\) | |||||||
\(594\) | 0.115503 | + | 1.98312i | 0.115503 | + | 1.98312i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.286803 | − | 0.957990i | \(-0.407407\pi\) | ||||
−0.286803 | + | 0.957990i | \(0.592593\pi\) | |||||||
\(600\) | −0.835488 | + | 0.549509i | −0.835488 | + | 0.549509i | ||||
\(601\) | −0.786803 | + | 1.82401i | −0.786803 | + | 1.82401i | −0.286803 | + | 0.957990i | \(0.592593\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.473045 | − | 1.09664i | 0.473045 | − | 1.09664i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | −0.0581448 | − | 0.998308i | \(-0.518519\pi\) | ||||
0.0581448 | + | 0.998308i | \(0.481481\pi\) | |||||||
\(608\) | 0.0798028 | + | 1.37016i | 0.0798028 | + | 1.37016i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −1.77518 | + | 0.207489i | −1.77518 | + | 0.207489i | ||||
\(613\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(614\) | 0.770807 | − | 1.78693i | 0.770807 | − | 1.78693i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.313758 | + | 0.727374i | 0.313758 | + | 0.727374i | 1.00000 | \(0\) | ||
−0.686242 | + | 0.727374i | \(0.740741\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.479241 | + | 0.315202i | 0.479241 | + | 0.315202i | 0.766044 | − | 0.642788i | \(-0.222222\pi\) |
−0.286803 | + | 0.957990i | \(0.592593\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.597159 | − | 0.802123i | 0.597159 | − | 0.802123i | ||||
\(626\) | 0.393633 | + | 0.417226i | 0.393633 | + | 0.417226i | ||||
\(627\) | −2.70797 | − | 0.316516i | −2.70797 | − | 0.316516i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.53209 | 1.53209 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.819590 | − | 1.10090i | −0.819590 | − | 1.10090i | −0.993238 | − | 0.116093i | \(-0.962963\pi\) |
0.173648 | − | 0.984808i | \(-0.444444\pi\) | |||||||
\(642\) | 0.479241 | − | 1.60078i | 0.479241 | − | 1.60078i | ||||
\(643\) | −1.93293 | + | 0.458113i | −1.93293 | + | 0.458113i | −0.939693 | + | 0.342020i | \(0.888889\pi\) |
−0.993238 | + | 0.116093i | \(0.962963\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.142629 | − | 2.44884i | 0.142629 | − | 2.44884i | ||||
\(647\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(648\) | −0.835488 | − | 0.549509i | −0.835488 | − | 0.549509i | ||||
\(649\) | −3.86586 | −3.86586 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.344948 | − | 0.0403186i | −0.344948 | − | 0.0403186i | ||||
\(653\) | 0 | 0 | 0.973045 | − | 0.230616i | \(-0.0740741\pi\) | ||||
−0.973045 | + | 0.230616i | \(0.925926\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −0.0996057 | + | 0.564892i | −0.0996057 | + | 0.564892i | ||||
\(657\) | −0.661840 | − | 1.53432i | −0.661840 | − | 1.53432i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.05138 | + | 1.11440i | −1.05138 | + | 1.11440i | −0.0581448 | + | 0.998308i | \(0.518519\pi\) |
−0.993238 | + | 0.116093i | \(0.962963\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | −0.893633 | − | 0.448799i | \(-0.851852\pi\) | ||||
0.893633 | + | 0.448799i | \(0.148148\pi\) | |||||||
\(662\) | 1.57020 | − | 1.03274i | 1.57020 | − | 1.03274i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.49079 | + | 0.353324i | 1.49079 | + | 0.353324i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.36912 | − | 0.687600i | 1.36912 | − | 0.687600i | 0.396080 | − | 0.918216i | \(-0.370370\pi\) |
0.973045 | + | 0.230616i | \(0.0740741\pi\) | |||||||
\(674\) | 0.0581448 | − | 0.100710i | 0.0581448 | − | 0.100710i | ||||
\(675\) | 0.973045 | + | 0.230616i | 0.973045 | + | 0.230616i | ||||
\(676\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(677\) | 0 | 0 | −0.835488 | − | 0.549509i | \(-0.814815\pi\) | ||||
0.835488 | + | 0.549509i | \(0.185185\pi\) | |||||||
\(678\) | −0.0201935 | + | 0.346709i | −0.0201935 | + | 0.346709i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.00676164 | + | 0.116093i | 0.00676164 | + | 0.116093i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.914900 | + | 0.767692i | 0.914900 | + | 0.767692i | 0.973045 | − | 0.230616i | \(-0.0740741\pi\) |
−0.0581448 | + | 0.998308i | \(0.518519\pi\) | |||||||
\(684\) | 0.941855 | − | 0.998308i | 0.941855 | − | 0.998308i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.00676164 | + | 0.116093i | 0.00676164 | + | 0.116093i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.539014 | + | 1.80043i | 0.539014 | + | 1.80043i | 0.597159 | + | 0.802123i | \(0.296296\pi\) |
−0.0581448 | + | 0.998308i | \(0.518519\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.05138 | − | 0.882215i | −1.05138 | − | 0.882215i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.294027 | − | 0.982118i | 0.294027 | − | 0.982118i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.73909 | − | 0.873403i | 1.73909 | − | 0.873403i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −1.77518 | + | 0.891529i | −1.77518 | + | 0.891529i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −0.997837 | + | 1.34033i | −0.997837 | + | 1.34033i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 1.16212 | − | 1.56100i | 1.16212 | − | 1.56100i | ||||
\(709\) | 0 | 0 | 0.993238 | − | 0.116093i | \(-0.0370370\pi\) | ||||
−0.993238 | + | 0.116093i | \(0.962963\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.76604 | + | 0.642788i | 1.76604 | + | 0.642788i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.67948 | − | 0.843467i | −1.67948 | − | 0.843467i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0.527715 | + | 0.708845i | 0.527715 | + | 0.708845i | ||||
\(723\) | 1.16212 | − | 0.275428i | 1.16212 | − | 0.275428i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −0.844948 | − | 2.82232i | −0.844948 | − | 2.82232i | ||||
\(727\) | 0 | 0 | 0.0581448 | − | 0.998308i | \(-0.481481\pi\) | ||||
−0.0581448 | + | 0.998308i | \(0.518519\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.173648 | + | 0.984808i | 0.173648 | + | 0.984808i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.0120848 | − | 0.207489i | 0.0120848 | − | 0.207489i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | −0.993238 | − | 0.116093i | \(-0.962963\pi\) | ||||
0.993238 | + | 0.116093i | \(0.0370370\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.411977 | + | 2.33644i | −0.411977 | + | 2.33644i | ||||
\(738\) | 0.479241 | − | 0.315202i | 0.479241 | − | 0.315202i | ||||
\(739\) | −0.344948 | − | 1.95630i | −0.344948 | − | 1.95630i | −0.286803 | − | 0.957990i | \(-0.592593\pi\) |
−0.0581448 | − | 0.998308i | \(-0.518519\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.835488 | − | 0.549509i | \(-0.185185\pi\) | ||||
−0.835488 | + | 0.549509i | \(0.814815\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.766044 | − | 1.32683i | −0.766044 | − | 1.32683i | ||||
\(748\) | 3.33625 | − | 1.21429i | 3.33625 | − | 1.21429i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | −0.686242 | − | 0.727374i | \(-0.740741\pi\) | ||||
0.686242 | + | 0.727374i | \(0.259259\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.115503 | − | 0.0135004i | 0.115503 | − | 0.0135004i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(758\) | 0.479241 | + | 0.315202i | 0.479241 | + | 0.315202i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.286803 | − | 0.957990i | 0.286803 | − | 0.957990i | −0.686242 | − | 0.727374i | \(-0.740741\pi\) |
0.973045 | − | 0.230616i | \(-0.0740741\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0.173648 | − | 0.984808i | 0.173648 | − | 0.984808i | ||||
\(769\) | −0.0201935 | − | 0.346709i | −0.0201935 | − | 0.346709i | −0.993238 | − | 0.116093i | \(-0.962963\pi\) |
0.973045 | − | 0.230616i | \(-0.0740741\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.914900 | + | 0.767692i | 0.914900 | + | 0.767692i | ||||
\(772\) | 0.164512 | + | 0.549509i | 0.164512 | + | 0.549509i | ||||
\(773\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(774\) | 0.0798028 | − | 0.0845860i | 0.0798028 | − | 0.0845860i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0.313758 | − | 0.727374i | 0.313758 | − | 0.727374i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.311820 | + | 0.722880i | 0.311820 | + | 0.722880i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0.207391 | + | 0.278574i | 0.207391 | + | 0.278574i | ||||
\(787\) | 0.914900 | − | 1.22892i | 0.914900 | − | 1.22892i | −0.0581448 | − | 0.998308i | \(-0.518519\pi\) |
0.973045 | − | 0.230616i | \(-0.0740741\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.86668 | + | 0.679415i | 1.86668 | + | 0.679415i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | −0.893633 | − | 0.448799i | \(-0.851852\pi\) | ||||
0.893633 | + | 0.448799i | \(0.148148\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0.173648 | + | 0.984808i | 0.173648 | + | 0.984808i | ||||
\(801\) | −0.744386 | − | 1.72568i | −0.744386 | − | 1.72568i | ||||
\(802\) | −0.238329 | + | 1.35163i | −0.238329 | + | 1.35163i | ||||
\(803\) | 1.98218 | + | 2.66253i | 1.98218 | + | 2.66253i | ||||
\(804\) | −0.819590 | − | 0.868715i | −0.819590 | − | 0.868715i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.67098 | −1.67098 | −0.835488 | − | 0.549509i | \(-0.814815\pi\) | ||||
−0.835488 | + | 0.549509i | \(0.814815\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.19432 | 1.19432 | 0.597159 | − | 0.802123i | \(-0.296296\pi\) | ||||
0.597159 | + | 0.802123i | \(0.296296\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.512593 | + | 1.71218i | −0.512593 | + | 1.71218i | ||||
\(817\) | 0.0953099 | + | 0.128023i | 0.0953099 | + | 0.128023i | ||||
\(818\) | 0.310355 | − | 1.76011i | 0.310355 | − | 1.76011i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.686242 | − | 0.727374i | \(-0.259259\pi\) | ||||
−0.686242 | + | 0.727374i | \(0.740741\pi\) | |||||||
\(822\) | 0.606829 | − | 0.509190i | 0.606829 | − | 0.509190i | ||||
\(823\) | 0 | 0 | −0.893633 | − | 0.448799i | \(-0.851852\pi\) | ||||
0.893633 | + | 0.448799i | \(0.148148\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.98648 | −1.98648 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.939693 | + | 0.342020i | 0.939693 | + | 0.342020i | 0.766044 | − | 0.642788i | \(-0.222222\pi\) |
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.06728 | − | 1.43361i | 1.06728 | − | 1.43361i | ||||
\(834\) | 0.313758 | − | 0.727374i | 0.313758 | − | 0.727374i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.36320 | + | 2.36114i | −1.36320 | + | 2.36114i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −0.173648 | − | 0.300767i | −0.173648 | − | 0.300767i | ||||
\(839\) | 0 | 0 | −0.835488 | − | 0.549509i | \(-0.814815\pi\) | ||||
0.835488 | + | 0.549509i | \(0.185185\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.396080 | + | 0.918216i | 0.396080 | + | 0.918216i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.28004 | + | 0.841897i | −1.28004 | + | 0.841897i | ||||
\(844\) | 0.606829 | − | 1.40679i | 0.606829 | − | 1.40679i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.43969 | + | 0.524005i | −1.43969 | + | 0.524005i | ||||
\(850\) | −0.103920 | − | 1.78424i | −0.103920 | − | 1.78424i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | −0.286803 | − | 0.957990i | \(-0.592593\pi\) | ||||
0.286803 | + | 0.957990i | \(0.407407\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.28004 | − | 1.07408i | −1.28004 | − | 1.07408i | ||||
\(857\) | −0.396080 | + | 0.918216i | −0.396080 | + | 0.918216i | 0.597159 | + | 0.802123i | \(0.296296\pi\) |
−0.993238 | + | 0.116093i | \(0.962963\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.569728 | − | 1.90302i | 0.569728 | − | 1.90302i | 0.173648 | − | 0.984808i | \(-0.444444\pi\) |
0.396080 | − | 0.918216i | \(-0.370370\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(864\) | −0.835488 | + | 0.549509i | −0.835488 | + | 0.549509i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.59716 | − | 0.802123i | 1.59716 | − | 0.802123i | ||||
\(867\) | 0.869125 | − | 2.01486i | 0.869125 | − | 2.01486i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.744386 | + | 0.270935i | −0.744386 | + | 0.270935i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.67098 | −1.67098 | ||||||||
\(877\) | 0 | 0 | 0.835488 | − | 0.549509i | \(-0.185185\pi\) | ||||
−0.835488 | + | 0.549509i | \(0.814815\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −0.326352 | − | 1.85083i | −0.326352 | − | 1.85083i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
0.173648 | − | 0.984808i | \(-0.444444\pi\) | |||||||
\(882\) | 0.973045 | − | 0.230616i | 0.973045 | − | 0.230616i | ||||
\(883\) | 0.310355 | − | 1.76011i | 0.310355 | − | 1.76011i | −0.286803 | − | 0.957990i | \(-0.592593\pi\) |
0.597159 | − | 0.802123i | \(-0.296296\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.558145 | + | 0.132283i | −0.558145 | + | 0.132283i | ||||
\(887\) | 0 | 0 | −0.993238 | − | 0.116093i | \(-0.962963\pi\) | ||||
0.993238 | + | 0.116093i | \(0.0370370\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.786803 | − | 1.82401i | −0.786803 | − | 1.82401i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0.473045 | + | 0.635410i | 0.473045 | + | 0.635410i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0.597159 | − | 0.802123i | 0.597159 | − | 0.802123i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −0.781942 | + | 0.828810i | −0.781942 | + | 0.828810i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.310355 | + | 0.155866i | 0.310355 | + | 0.155866i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.16212 | + | 0.275428i | 1.16212 | + | 0.275428i | 0.766044 | − | 0.642788i | \(-0.222222\pi\) |
0.396080 | + | 0.918216i | \(0.370370\pi\) | |||||||
\(908\) | 0.109277 | + | 0.0397734i | 0.109277 | + | 0.0397734i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 0.993238 | − | 0.116093i | \(-0.0370370\pi\) | ||||
−0.993238 | + | 0.116093i | \(0.962963\pi\) | |||||||
\(912\) | −0.543613 | − | 1.26024i | −0.543613 | − | 1.26024i | ||||
\(913\) | 2.08855 | + | 2.21373i | 2.08855 | + | 2.21373i | ||||
\(914\) | 1.16212 | − | 1.56100i | 1.16212 | − | 1.56100i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 1.59716 | − | 0.802123i | 1.59716 | − | 0.802123i | ||||
\(919\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.113155 | + | 1.94280i | −0.113155 | + | 1.94280i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0.286803 | + | 0.957990i | 0.286803 | + | 0.957990i | 0.973045 | + | 0.230616i | \(0.0740741\pi\) |
−0.686242 | + | 0.727374i | \(0.740741\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.0798028 | + | 1.37016i | 0.0798028 | + | 1.37016i | ||||
\(932\) | −0.113155 | − | 1.94280i | −0.113155 | − | 1.94280i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0.393633 | + | 1.31482i | 0.393633 | + | 1.31482i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.43969 | − | 1.20805i | −1.43969 | − | 1.20805i | −0.939693 | − | 0.342020i | \(-0.888889\pi\) |
−0.500000 | − | 0.866025i | \(-0.666667\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.512593 | − | 0.257434i | −0.512593 | − | 0.257434i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.396080 | − | 0.918216i | \(-0.629630\pi\) | ||||
0.396080 | + | 0.918216i | \(0.370370\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −0.973045 | − | 1.68536i | −0.973045 | − | 1.68536i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.115503 | + | 0.200058i | −0.115503 | + | 0.200058i | ||||
\(947\) | −1.49324 | + | 0.749932i | −1.49324 | + | 0.749932i | −0.993238 | − | 0.116093i | \(-0.962963\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0.941855 | + | 0.998308i | 0.941855 | + | 0.998308i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.12229 | + | 0.408481i | −1.12229 | + | 0.408481i | −0.835488 | − | 0.549509i | \(-0.814815\pi\) |
−0.286803 | + | 0.957990i | \(0.592593\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.686242 | + | 0.727374i | −0.686242 | + | 0.727374i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.0971586 | + | 1.66815i | 0.0971586 | + | 1.66815i | ||||
\(964\) | 0.207391 | − | 1.17617i | 0.207391 | − | 1.17617i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | 0.973045 | − | 0.230616i | \(-0.0740741\pi\) | ||||
−0.973045 | + | 0.230616i | \(0.925926\pi\) | |||||||
\(968\) | −2.92617 | − | 0.342020i | −2.92617 | − | 0.342020i | ||||
\(969\) | 0.703526 | + | 2.34994i | 0.703526 | + | 2.34994i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(972\) | 0.973045 | + | 0.230616i | 0.973045 | + | 0.230616i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.89363 | − | 0.448799i | 1.89363 | − | 0.448799i | 0.893633 | − | 0.448799i | \(-0.148148\pi\) |
1.00000 | \(0\) | |||||||||
\(978\) | 0.337935 | − | 0.0800921i | 0.337935 | − | 0.0800921i | ||||
\(979\) | 2.22941 | + | 2.99461i | 2.22941 | + | 2.99461i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −0.290162 | − | 1.64559i | −0.290162 | − | 1.64559i | ||||
\(983\) | 0 | 0 | 0.686242 | − | 0.727374i | \(-0.259259\pi\) | ||||
−0.686242 | + | 0.727374i | \(0.740741\pi\) | |||||||
\(984\) | −0.0996057 | − | 0.564892i | −0.0996057 | − | 0.564892i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.12229 | + | 1.50750i | −1.12229 | + | 1.50750i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.52173 | + | 0.177865i | −1.52173 | + | 0.177865i | ||||
\(997\) | 0 | 0 | 0.893633 | − | 0.448799i | \(-0.148148\pi\) | ||||
−0.893633 | + | 0.448799i | \(0.851852\pi\) | |||||||
\(998\) | −0.893633 | + | 1.54782i | −0.893633 | + | 1.54782i | ||||
\(999\) | 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 | 648.1.bf.a.403.1 | yes | 18 | |
3.2 | odd | 2 | 1944.1.bf.a.235.1 | 18 | |||
4.3 | odd | 2 | 2592.1.bz.a.79.1 | 18 | |||
8.3 | odd | 2 | CM | 648.1.bf.a.403.1 | yes | 18 | |
8.5 | even | 2 | 2592.1.bz.a.79.1 | 18 | |||
24.11 | even | 2 | 1944.1.bf.a.235.1 | 18 | |||
81.40 | even | 27 | inner | 648.1.bf.a.283.1 | ✓ | 18 | |
81.41 | odd | 54 | 1944.1.bf.a.91.1 | 18 | |||
324.283 | odd | 54 | 2592.1.bz.a.1903.1 | 18 | |||
648.203 | even | 54 | 1944.1.bf.a.91.1 | 18 | |||
648.283 | odd | 54 | inner | 648.1.bf.a.283.1 | ✓ | 18 | |
648.445 | even | 54 | 2592.1.bz.a.1903.1 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
648.1.bf.a.283.1 | ✓ | 18 | 81.40 | even | 27 | inner | |
648.1.bf.a.283.1 | ✓ | 18 | 648.283 | odd | 54 | inner | |
648.1.bf.a.403.1 | yes | 18 | 1.1 | even | 1 | trivial | |
648.1.bf.a.403.1 | yes | 18 | 8.3 | odd | 2 | CM | |
1944.1.bf.a.91.1 | 18 | 81.41 | odd | 54 | |||
1944.1.bf.a.91.1 | 18 | 648.203 | even | 54 | |||
1944.1.bf.a.235.1 | 18 | 3.2 | odd | 2 | |||
1944.1.bf.a.235.1 | 18 | 24.11 | even | 2 | |||
2592.1.bz.a.79.1 | 18 | 4.3 | odd | 2 | |||
2592.1.bz.a.79.1 | 18 | 8.5 | even | 2 | |||
2592.1.bz.a.1903.1 | 18 | 324.283 | odd | 54 | |||
2592.1.bz.a.1903.1 | 18 | 648.445 | even | 54 |