Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1620,1,Mod(79,1620)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1620, base_ring=CyclotomicField(54))
chi = DirichletCharacter(H, H._module([27, 28, 27]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1620.79");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1620.bp (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: | \(0.808485320465\) |
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 | 499.1 | ||
Root | \(-0.973045 + 0.230616i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1620.499 |
Dual form | 1620.1.bp.a.1159.1 |
$q$-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 \(\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times\).
\(n\) | \(811\) | \(1297\) | \(1541\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{4}{27}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.893633 | − | 0.448799i | −0.893633 | − | 0.448799i | ||||
\(3\) | −0.973045 | − | 0.230616i | −0.973045 | − | 0.230616i | ||||
\(4\) | 0.597159 | + | 0.802123i | 0.597159 | + | 0.802123i | ||||
\(5\) | −0.286803 | − | 0.957990i | −0.286803 | − | 0.957990i | ||||
\(6\) | 0.766044 | + | 0.642788i | 0.766044 | + | 0.642788i | ||||
\(7\) | 0.543613 | + | 1.26024i | 0.543613 | + | 1.26024i | 0.939693 | + | 0.342020i | \(0.111111\pi\) |
−0.396080 | + | 0.918216i | \(0.629630\pi\) | |||||||
\(8\) | −0.173648 | − | 0.984808i | −0.173648 | − | 0.984808i | ||||
\(9\) | 0.893633 | + | 0.448799i | 0.893633 | + | 0.448799i | ||||
\(10\) | −0.173648 | + | 0.984808i | −0.173648 | + | 0.984808i | ||||
\(11\) | 0 | 0 | 0.973045 | − | 0.230616i | \(-0.0740741\pi\) | ||||
−0.973045 | + | 0.230616i | \(0.925926\pi\) | |||||||
\(12\) | −0.396080 | − | 0.918216i | −0.396080 | − | 0.918216i | ||||
\(13\) | 0 | 0 | −0.835488 | − | 0.549509i | \(-0.814815\pi\) | ||||
0.835488 | + | 0.549509i | \(0.185185\pi\) | |||||||
\(14\) | 0.0798028 | − | 1.37016i | 0.0798028 | − | 1.37016i | ||||
\(15\) | 0.0581448 | + | 0.998308i | 0.0581448 | + | 0.998308i | ||||
\(16\) | −0.286803 | + | 0.957990i | −0.286803 | + | 0.957990i | ||||
\(17\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(18\) | −0.597159 | − | 0.802123i | −0.597159 | − | 0.802123i | ||||
\(19\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(20\) | 0.597159 | − | 0.802123i | 0.597159 | − | 0.802123i | ||||
\(21\) | −0.238329 | − | 1.35163i | −0.238329 | − | 1.35163i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.313758 | + | 0.727374i | −0.313758 | + | 0.727374i | 0.686242 | + | 0.727374i | \(0.259259\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(24\) | −0.0581448 | + | 0.998308i | −0.0581448 | + | 0.998308i | ||||
\(25\) | −0.835488 | + | 0.549509i | −0.835488 | + | 0.549509i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.766044 | − | 0.642788i | −0.766044 | − | 0.642788i | ||||
\(28\) | −0.686242 | + | 1.18861i | −0.686242 | + | 1.18861i | ||||
\(29\) | 0.115503 | + | 1.98312i | 0.115503 | + | 1.98312i | 0.173648 | + | 0.984808i | \(0.444444\pi\) |
−0.0581448 | + | 0.998308i | \(0.518519\pi\) | |||||||
\(30\) | 0.396080 | − | 0.918216i | 0.396080 | − | 0.918216i | ||||
\(31\) | 0 | 0 | 0.993238 | − | 0.116093i | \(-0.0370370\pi\) | ||||
−0.993238 | + | 0.116093i | \(0.962963\pi\) | |||||||
\(32\) | 0.686242 | − | 0.727374i | 0.686242 | − | 0.727374i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.05138 | − | 0.882215i | 1.05138 | − | 0.882215i | ||||
\(36\) | 0.173648 | + | 0.984808i | 0.173648 | + | 0.984808i | ||||
\(37\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.893633 | + | 0.448799i | −0.893633 | + | 0.448799i | ||||
\(41\) | −1.49324 | + | 0.749932i | −1.49324 | + | 0.749932i | −0.993238 | − | 0.116093i | \(-0.962963\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(42\) | −0.393633 | + | 1.31482i | −0.393633 | + | 1.31482i | ||||
\(43\) | 0.238329 | + | 0.252614i | 0.238329 | + | 0.252614i | 0.835488 | − | 0.549509i | \(-0.185185\pi\) |
−0.597159 | + | 0.802123i | \(0.703704\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.173648 | − | 0.984808i | 0.173648 | − | 0.984808i | ||||
\(46\) | 0.606829 | − | 0.509190i | 0.606829 | − | 0.509190i | ||||
\(47\) | 1.77518 | + | 0.207489i | 1.77518 | + | 0.207489i | 0.939693 | − | 0.342020i | \(-0.111111\pi\) |
0.835488 | + | 0.549509i | \(0.185185\pi\) | |||||||
\(48\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(49\) | −0.606439 | + | 0.642788i | −0.606439 | + | 0.642788i | ||||
\(50\) | 0.993238 | − | 0.116093i | 0.993238 | − | 0.116093i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(54\) | 0.396080 | + | 0.918216i | 0.396080 | + | 0.918216i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.14669 | − | 0.754192i | 1.14669 | − | 0.754192i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.786803 | − | 1.82401i | 0.786803 | − | 1.82401i | ||||
\(59\) | 0 | 0 | −0.973045 | − | 0.230616i | \(-0.925926\pi\) | ||||
0.973045 | + | 0.230616i | \(0.0740741\pi\) | |||||||
\(60\) | −0.766044 | + | 0.642788i | −0.766044 | + | 0.642788i | ||||
\(61\) | 1.16212 | − | 1.56100i | 1.16212 | − | 1.56100i | 0.396080 | − | 0.918216i | \(-0.370370\pi\) |
0.766044 | − | 0.642788i | \(-0.222222\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.0798028 | + | 1.37016i | −0.0798028 | + | 1.37016i | ||||
\(64\) | −0.939693 | + | 0.342020i | −0.939693 | + | 0.342020i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.00676164 | + | 0.116093i | −0.00676164 | + | 0.116093i | 0.993238 | + | 0.116093i | \(0.0370370\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.473045 | − | 0.635410i | 0.473045 | − | 0.635410i | ||||
\(70\) | −1.33549 | + | 0.316516i | −1.33549 | + | 0.316516i | ||||
\(71\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(72\) | 0.286803 | − | 0.957990i | 0.286803 | − | 0.957990i | ||||
\(73\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.939693 | − | 0.342020i | 0.939693 | − | 0.342020i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | −0.893633 | − | 0.448799i | \(-0.851852\pi\) | ||||
0.893633 | + | 0.448799i | \(0.148148\pi\) | |||||||
\(80\) | 1.00000 | 1.00000 | ||||||||
\(81\) | 0.597159 | + | 0.802123i | 0.597159 | + | 0.802123i | ||||
\(82\) | 1.67098 | 1.67098 | ||||||||
\(83\) | 1.49324 | + | 0.749932i | 1.49324 | + | 0.749932i | 0.993238 | − | 0.116093i | \(-0.0370370\pi\) |
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(84\) | 0.941855 | − | 0.998308i | 0.941855 | − | 0.998308i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.0996057 | − | 0.332706i | −0.0996057 | − | 0.332706i | ||||
\(87\) | 0.344948 | − | 1.95630i | 0.344948 | − | 1.95630i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.310355 | + | 1.76011i | 0.310355 | + | 1.76011i | 0.597159 | + | 0.802123i | \(0.296296\pi\) |
−0.286803 | + | 0.957990i | \(0.592593\pi\) | |||||||
\(90\) | −0.597159 | + | 0.802123i | −0.597159 | + | 0.802123i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.770807 | + | 0.182685i | −0.770807 | + | 0.182685i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.49324 | − | 0.982118i | −1.49324 | − | 0.982118i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.835488 | + | 0.549509i | −0.835488 | + | 0.549509i | ||||
\(97\) | 0 | 0 | 0.286803 | − | 0.957990i | \(-0.407407\pi\) | ||||
−0.286803 | + | 0.957990i | \(0.592593\pi\) | |||||||
\(98\) | 0.830416 | − | 0.302247i | 0.830416 | − | 0.302247i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.939693 | − | 0.342020i | −0.939693 | − | 0.342020i | ||||
\(101\) | 0.914900 | − | 1.22892i | 0.914900 | − | 1.22892i | −0.0581448 | − | 0.998308i | \(-0.518519\pi\) |
0.973045 | − | 0.230616i | \(-0.0740741\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.82873 | + | 0.433416i | 1.82873 | + | 0.433416i | 0.993238 | − | 0.116093i | \(-0.0370370\pi\) |
0.835488 | + | 0.549509i | \(0.185185\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.22650 | + | 0.615969i | −1.22650 | + | 0.615969i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.286803 | − | 0.496758i | −0.286803 | − | 0.496758i | 0.686242 | − | 0.727374i | \(-0.259259\pi\) |
−0.973045 | + | 0.230616i | \(0.925926\pi\) | |||||||
\(108\) | 0.0581448 | − | 0.998308i | 0.0581448 | − | 0.998308i | ||||
\(109\) | −0.597159 | + | 1.03431i | −0.597159 | + | 1.03431i | 0.396080 | + | 0.918216i | \(0.370370\pi\) |
−0.993238 | + | 0.116093i | \(0.962963\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.36320 | + | 0.159336i | −1.36320 | + | 0.159336i | ||||
\(113\) | 0 | 0 | 0.686242 | − | 0.727374i | \(-0.259259\pi\) | ||||
−0.686242 | + | 0.727374i | \(0.740741\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.786803 | + | 0.0919641i | 0.786803 | + | 0.0919641i | ||||
\(116\) | −1.52173 | + | 1.27688i | −1.52173 | + | 1.27688i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.973045 | − | 0.230616i | 0.973045 | − | 0.230616i | ||||
\(121\) | 0.893633 | − | 0.448799i | 0.893633 | − | 0.448799i | ||||
\(122\) | −1.73909 | + | 0.873403i | −1.73909 | + | 0.873403i | ||||
\(123\) | 1.62593 | − | 0.385353i | 1.62593 | − | 0.385353i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.766044 | + | 0.642788i | 0.766044 | + | 0.642788i | ||||
\(126\) | 0.686242 | − | 1.18861i | 0.686242 | − | 1.18861i | ||||
\(127\) | −0.914900 | + | 0.767692i | −0.914900 | + | 0.767692i | −0.973045 | − | 0.230616i | \(-0.925926\pi\) |
0.0581448 | + | 0.998308i | \(0.481481\pi\) | |||||||
\(128\) | 0.993238 | + | 0.116093i | 0.993238 | + | 0.116093i | ||||
\(129\) | −0.173648 | − | 0.300767i | −0.173648 | − | 0.300767i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.993238 | − | 0.116093i | \(-0.0370370\pi\) | ||||
−0.993238 | + | 0.116093i | \(0.962963\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.0581448 | − | 0.100710i | 0.0581448 | − | 0.100710i | ||||
\(135\) | −0.396080 | + | 0.918216i | −0.396080 | + | 0.918216i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.835488 | − | 0.549509i | \(-0.185185\pi\) | ||||
−0.835488 | + | 0.549509i | \(0.814815\pi\) | |||||||
\(138\) | −0.707900 | + | 0.355521i | −0.707900 | + | 0.355521i | ||||
\(139\) | 0 | 0 | 0.396080 | − | 0.918216i | \(-0.370370\pi\) | ||||
−0.396080 | + | 0.918216i | \(0.629630\pi\) | |||||||
\(140\) | 1.33549 | + | 0.316516i | 1.33549 | + | 0.316516i | ||||
\(141\) | −1.67948 | − | 0.611281i | −1.67948 | − | 0.611281i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.686242 | + | 0.727374i | −0.686242 | + | 0.727374i | ||||
\(145\) | 1.86668 | − | 0.679415i | 1.86668 | − | 0.679415i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.738329 | − | 0.485607i | 0.738329 | − | 0.485607i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.997837 | − | 0.656288i | −0.997837 | − | 0.656288i | −0.0581448 | − | 0.998308i | \(-0.518519\pi\) |
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(150\) | −0.993238 | − | 0.116093i | −0.993238 | − | 0.116093i | ||||
\(151\) | 0 | 0 | 0.973045 | − | 0.230616i | \(-0.0740741\pi\) | ||||
−0.973045 | + | 0.230616i | \(0.925926\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | −0.286803 | − | 0.957990i | \(-0.592593\pi\) | ||||
0.286803 | + | 0.957990i | \(0.407407\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.893633 | − | 0.448799i | −0.893633 | − | 0.448799i | ||||
\(161\) | −1.08723 | −1.08723 | ||||||||
\(162\) | −0.173648 | − | 0.984808i | −0.173648 | − | 0.984808i | ||||
\(163\) | −1.53209 | −1.53209 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(164\) | −1.49324 | − | 0.749932i | −1.49324 | − | 0.749932i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.997837 | − | 1.34033i | −0.997837 | − | 1.34033i | ||||
\(167\) | −0.569728 | − | 1.90302i | −0.569728 | − | 1.90302i | −0.396080 | − | 0.918216i | \(-0.629630\pi\) |
−0.173648 | − | 0.984808i | \(-0.555556\pi\) | |||||||
\(168\) | −1.28971 | + | 0.469417i | −1.28971 | + | 0.469417i | ||||
\(169\) | 0.396080 | + | 0.918216i | 0.396080 | + | 0.918216i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.0603074 | + | 0.342020i | −0.0603074 | + | 0.342020i | ||||
\(173\) | 0 | 0 | 0.973045 | − | 0.230616i | \(-0.0740741\pi\) | ||||
−0.973045 | + | 0.230616i | \(0.925926\pi\) | |||||||
\(174\) | −1.18624 | + | 1.59340i | −1.18624 | + | 1.59340i | ||||
\(175\) | −1.14669 | − | 0.754192i | −1.14669 | − | 0.754192i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.512593 | − | 1.71218i | 0.512593 | − | 1.71218i | ||||
\(179\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(180\) | 0.893633 | − | 0.448799i | 0.893633 | − | 0.448799i | ||||
\(181\) | 0.539014 | + | 0.196185i | 0.539014 | + | 0.196185i | 0.597159 | − | 0.802123i | \(-0.296296\pi\) |
−0.0581448 | + | 0.998308i | \(0.518519\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.49079 | + | 1.25092i | −1.49079 | + | 1.25092i | ||||
\(184\) | 0.770807 | + | 0.182685i | 0.770807 | + | 0.182685i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0.893633 | + | 1.54782i | 0.893633 | + | 1.54782i | ||||
\(189\) | 0.393633 | − | 1.31482i | 0.393633 | − | 1.31482i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.0581448 | − | 0.998308i | \(-0.518519\pi\) | ||||
0.0581448 | + | 0.998308i | \(0.481481\pi\) | |||||||
\(192\) | 0.993238 | − | 0.116093i | 0.993238 | − | 0.116093i | ||||
\(193\) | 0 | 0 | 0.993238 | − | 0.116093i | \(-0.0370370\pi\) | ||||
−0.993238 | + | 0.116093i | \(0.962963\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.877735 | − | 0.102593i | −0.877735 | − | 0.102593i | ||||
\(197\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(200\) | 0.686242 | + | 0.727374i | 0.686242 | + | 0.727374i | ||||
\(201\) | 0.0333522 | − | 0.111404i | 0.0333522 | − | 0.111404i | ||||
\(202\) | −1.36912 | + | 0.687600i | −1.36912 | + | 0.687600i | ||||
\(203\) | −2.43641 | + | 1.22361i | −2.43641 | + | 1.22361i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.14669 | + | 1.21542i | 1.14669 | + | 1.21542i | ||||
\(206\) | −1.43969 | − | 1.20805i | −1.43969 | − | 1.20805i | ||||
\(207\) | −0.606829 | + | 0.509190i | −0.606829 | + | 0.509190i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 1.37248 | 1.37248 | ||||||||
\(211\) | 0 | 0 | 0.686242 | − | 0.727374i | \(-0.259259\pi\) | ||||
−0.686242 | + | 0.727374i | \(0.740741\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.0333522 | + | 0.572636i | 0.0333522 | + | 0.572636i | ||||
\(215\) | 0.173648 | − | 0.300767i | 0.173648 | − | 0.300767i | ||||
\(216\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0.997837 | − | 0.656288i | 0.997837 | − | 0.656288i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.06728 | + | 1.43361i | −1.06728 | + | 1.43361i | −0.173648 | + | 0.984808i | \(0.555556\pi\) |
−0.893633 | + | 0.448799i | \(0.851852\pi\) | |||||||
\(224\) | 1.28971 | + | 0.469417i | 1.28971 | + | 0.469417i | ||||
\(225\) | −0.993238 | + | 0.116093i | −0.993238 | + | 0.116093i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.539014 | + | 1.80043i | −0.539014 | + | 1.80043i | 0.0581448 | + | 0.998308i | \(0.481481\pi\) |
−0.597159 | + | 0.802123i | \(0.703704\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.115503 | − | 1.98312i | 0.115503 | − | 1.98312i | −0.0581448 | − | 0.998308i | \(-0.518519\pi\) |
0.173648 | − | 0.984808i | \(-0.444444\pi\) | |||||||
\(230\) | −0.661840 | − | 0.435299i | −0.661840 | − | 0.435299i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.93293 | − | 0.458113i | 1.93293 | − | 0.458113i | ||||
\(233\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.310355 | − | 1.76011i | −0.310355 | − | 1.76011i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.597159 | − | 0.802123i | \(-0.703704\pi\) | ||||
0.597159 | + | 0.802123i | \(0.296296\pi\) | |||||||
\(240\) | −0.973045 | − | 0.230616i | −0.973045 | − | 0.230616i | ||||
\(241\) | −0.512593 | − | 0.257434i | −0.512593 | − | 0.257434i | 0.173648 | − | 0.984808i | \(-0.444444\pi\) |
−0.686242 | + | 0.727374i | \(0.740741\pi\) | |||||||
\(242\) | −1.00000 | −1.00000 | ||||||||
\(243\) | −0.396080 | − | 0.918216i | −0.396080 | − | 0.918216i | ||||
\(244\) | 1.94609 | 1.94609 | ||||||||
\(245\) | 0.789712 | + | 0.396608i | 0.789712 | + | 0.396608i | ||||
\(246\) | −1.62593 | − | 0.385353i | −1.62593 | − | 0.385353i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.28004 | − | 1.07408i | −1.28004 | − | 1.07408i | ||||
\(250\) | −0.396080 | − | 0.918216i | −0.396080 | − | 0.918216i | ||||
\(251\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(252\) | −1.14669 | + | 0.754192i | −1.14669 | + | 0.754192i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 1.16212 | − | 0.275428i | 1.16212 | − | 0.275428i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.835488 | − | 0.549509i | −0.835488 | − | 0.549509i | ||||
\(257\) | 0 | 0 | 0.0581448 | − | 0.998308i | \(-0.481481\pi\) | ||||
−0.0581448 | + | 0.998308i | \(0.518519\pi\) | |||||||
\(258\) | 0.0201935 | + | 0.346709i | 0.0201935 | + | 0.346709i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.786803 | + | 1.82401i | −0.786803 | + | 1.82401i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.12229 | − | 1.50750i | 1.12229 | − | 1.50750i | 0.286803 | − | 0.957990i | \(-0.407407\pi\) |
0.835488 | − | 0.549509i | \(-0.185185\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.103920 | − | 1.78424i | 0.103920 | − | 1.78424i | ||||
\(268\) | −0.0971586 | + | 0.0639022i | −0.0971586 | + | 0.0639022i | ||||
\(269\) | 0.286803 | + | 0.496758i | 0.286803 | + | 0.496758i | 0.973045 | − | 0.230616i | \(-0.0740741\pi\) |
−0.686242 | + | 0.727374i | \(0.740741\pi\) | |||||||
\(270\) | 0.766044 | − | 0.642788i | 0.766044 | − | 0.642788i | ||||
\(271\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.792160 | 0.792160 | ||||||||
\(277\) | 0 | 0 | −0.993238 | − | 0.116093i | \(-0.962963\pi\) | ||||
0.993238 | + | 0.116093i | \(0.0370370\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.05138 | − | 0.882215i | −1.05138 | − | 0.882215i | ||||
\(281\) | −1.33549 | − | 1.41553i | −1.33549 | − | 1.41553i | −0.835488 | − | 0.549509i | \(-0.814815\pi\) |
−0.500000 | − | 0.866025i | \(-0.666667\pi\) | |||||||
\(282\) | 1.22650 | + | 1.30001i | 1.22650 | + | 1.30001i | ||||
\(283\) | −1.06728 | + | 0.536009i | −1.06728 | + | 0.536009i | −0.893633 | − | 0.448799i | \(-0.851852\pi\) |
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.75684 | − | 1.47416i | −1.75684 | − | 1.47416i | ||||
\(288\) | 0.939693 | − | 0.342020i | 0.939693 | − | 0.342020i | ||||
\(289\) | 0.766044 | − | 0.642788i | 0.766044 | − | 0.642788i | ||||
\(290\) | −1.97304 | − | 0.230616i | −1.97304 | − | 0.230616i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | 0.993238 | − | 0.116093i | \(-0.0370370\pi\) | ||||
−0.993238 | + | 0.116093i | \(0.962963\pi\) | |||||||
\(294\) | −0.877735 | + | 0.102593i | −0.877735 | + | 0.102593i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.597159 | + | 1.03431i | 0.597159 | + | 1.03431i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0.835488 | + | 0.549509i | 0.835488 | + | 0.549509i | ||||
\(301\) | −0.188795 | + | 0.437675i | −0.188795 | + | 0.437675i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.17365 | + | 0.984808i | −1.17365 | + | 0.984808i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.82873 | − | 0.665602i | −1.82873 | − | 0.665602i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.744386 | − | 0.270935i | 0.744386 | − | 0.270935i | 0.0581448 | − | 0.998308i | \(-0.481481\pi\) |
0.686242 | + | 0.727374i | \(0.259259\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.67948 | − | 0.843467i | −1.67948 | − | 0.843467i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.835488 | − | 0.549509i | \(-0.814815\pi\) | ||||
0.835488 | + | 0.549509i | \(0.185185\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | 0.973045 | − | 0.230616i | \(-0.0740741\pi\) | ||||
−0.973045 | + | 0.230616i | \(0.925926\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.33549 | − | 0.316516i | 1.33549 | − | 0.316516i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | −0.396080 | − | 0.918216i | \(-0.629630\pi\) | ||||
0.396080 | + | 0.918216i | \(0.370370\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0.597159 | + | 0.802123i | 0.597159 | + | 0.802123i | ||||
\(321\) | 0.164512 | + | 0.549509i | 0.164512 | + | 0.549509i | ||||
\(322\) | 0.971580 | + | 0.487946i | 0.971580 | + | 0.487946i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −0.286803 | + | 0.957990i | −0.286803 | + | 0.957990i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.36912 | + | 0.687600i | 1.36912 | + | 0.687600i | ||||
\(327\) | 0.819590 | − | 0.868715i | 0.819590 | − | 0.868715i | ||||
\(328\) | 0.997837 | + | 1.34033i | 0.997837 | + | 1.34033i | ||||
\(329\) | 0.703526 | + | 2.34994i | 0.703526 | + | 2.34994i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | −0.396080 | − | 0.918216i | \(-0.629630\pi\) | ||||
0.396080 | + | 0.918216i | \(0.370370\pi\) | |||||||
\(332\) | 0.290162 | + | 1.64559i | 0.290162 | + | 1.64559i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −0.344948 | + | 1.95630i | −0.344948 | + | 1.95630i | ||||
\(335\) | 0.113155 | − | 0.0268182i | 0.113155 | − | 0.0268182i | ||||
\(336\) | 1.36320 | + | 0.159336i | 1.36320 | + | 0.159336i | ||||
\(337\) | 0 | 0 | −0.835488 | − | 0.549509i | \(-0.814815\pi\) | ||||
0.835488 | + | 0.549509i | \(0.185185\pi\) | |||||||
\(338\) | 0.0581448 | − | 0.998308i | 0.0581448 | − | 0.998308i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.149980 | + | 0.0545883i | 0.149980 | + | 0.0545883i | ||||
\(344\) | 0.207391 | − | 0.278574i | 0.207391 | − | 0.278574i | ||||
\(345\) | −0.744386 | − | 0.270935i | −0.744386 | − | 0.270935i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.606829 | + | 1.40679i | −0.606829 | + | 1.40679i | 0.286803 | + | 0.957990i | \(0.407407\pi\) |
−0.893633 | + | 0.448799i | \(0.851852\pi\) | |||||||
\(348\) | 1.77518 | − | 0.891529i | 1.77518 | − | 0.891529i | ||||
\(349\) | −1.49324 | + | 0.982118i | −1.49324 | + | 0.982118i | −0.500000 | + | 0.866025i | \(0.666667\pi\) |
−0.993238 | + | 0.116093i | \(0.962963\pi\) | |||||||
\(350\) | 0.686242 | + | 1.18861i | 0.686242 | + | 1.18861i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | −0.0581448 | − | 0.998308i | \(-0.518519\pi\) | ||||
0.0581448 | + | 0.998308i | \(0.481481\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.22650 | + | 1.30001i | −1.22650 | + | 1.30001i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(360\) | −1.00000 | −1.00000 | ||||||||
\(361\) | 0.766044 | + | 0.642788i | 0.766044 | + | 0.642788i | ||||
\(362\) | −0.393633 | − | 0.417226i | −0.393633 | − | 0.417226i | ||||
\(363\) | −0.973045 | + | 0.230616i | −0.973045 | + | 0.230616i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.89363 | − | 0.448799i | 1.89363 | − | 0.448799i | ||||
\(367\) | −0.686242 | − | 0.727374i | −0.686242 | − | 0.727374i | 0.286803 | − | 0.957990i | \(-0.407407\pi\) |
−0.973045 | + | 0.230616i | \(0.925926\pi\) | |||||||
\(368\) | −0.606829 | − | 0.509190i | −0.606829 | − | 0.509190i | ||||
\(369\) | −1.67098 | −1.67098 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | 0.686242 | − | 0.727374i | \(-0.259259\pi\) | ||||
−0.686242 | + | 0.727374i | \(0.740741\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.597159 | − | 0.802123i | −0.597159 | − | 0.802123i | ||||
\(376\) | −0.103920 | − | 1.78424i | −0.103920 | − | 1.78424i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −0.941855 | + | 0.998308i | −0.941855 | + | 0.998308i | ||||
\(379\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.06728 | − | 0.536009i | 1.06728 | − | 0.536009i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.49079 | − | 0.353324i | −1.49079 | − | 0.353324i | −0.597159 | − | 0.802123i | \(-0.703704\pi\) |
−0.893633 | + | 0.448799i | \(0.851852\pi\) | |||||||
\(384\) | −0.939693 | − | 0.342020i | −0.939693 | − | 0.342020i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.0996057 | + | 0.332706i | 0.0996057 | + | 0.332706i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.0333522 | − | 0.111404i | 0.0333522 | − | 0.111404i | −0.939693 | − | 0.342020i | \(-0.888889\pi\) |
0.973045 | + | 0.230616i | \(0.0740741\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0.738329 | + | 0.485607i | 0.738329 | + | 0.485607i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.286803 | − | 0.957990i | −0.286803 | − | 0.957990i | ||||
\(401\) | 0.207391 | + | 0.278574i | 0.207391 | + | 0.278574i | 0.893633 | − | 0.448799i | \(-0.148148\pi\) |
−0.686242 | + | 0.727374i | \(0.740741\pi\) | |||||||
\(402\) | −0.0798028 | + | 0.0845860i | −0.0798028 | + | 0.0845860i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 1.53209 | 1.53209 | ||||||||
\(405\) | 0.597159 | − | 0.802123i | 0.597159 | − | 0.802123i | ||||
\(406\) | 2.72641 | 2.72641 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.12229 | − | 1.50750i | −1.12229 | − | 1.50750i | −0.835488 | − | 0.549509i | \(-0.814815\pi\) |
−0.286803 | − | 0.957990i | \(-0.592593\pi\) | |||||||
\(410\) | −0.479241 | − | 1.60078i | −0.479241 | − | 1.60078i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.744386 | + | 1.72568i | 0.744386 | + | 1.72568i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0.770807 | − | 0.182685i | 0.770807 | − | 0.182685i | ||||
\(415\) | 0.290162 | − | 1.64559i | 0.290162 | − | 1.64559i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.0581448 | − | 0.998308i | \(-0.481481\pi\) | ||||
−0.0581448 | + | 0.998308i | \(0.518519\pi\) | |||||||
\(420\) | −1.22650 | − | 0.615969i | −1.22650 | − | 0.615969i | ||||
\(421\) | −0.0996057 | + | 0.332706i | −0.0996057 | + | 0.332706i | −0.993238 | − | 0.116093i | \(-0.962963\pi\) |
0.893633 | + | 0.448799i | \(0.148148\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.49324 | + | 0.982118i | 1.49324 | + | 0.982118i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.59898 | + | 0.615969i | 2.59898 | + | 0.615969i | ||||
\(428\) | 0.227194 | − | 0.526695i | 0.227194 | − | 0.526695i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.290162 | + | 0.190842i | −0.290162 | + | 0.190842i | ||||
\(431\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(432\) | 0.835488 | − | 0.549509i | 0.835488 | − | 0.549509i | ||||
\(433\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.97304 | + | 0.230616i | −1.97304 | + | 0.230616i | ||||
\(436\) | −1.18624 | + | 0.138652i | −1.18624 | + | 0.138652i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | −0.993238 | − | 0.116093i | \(-0.962963\pi\) | ||||
0.993238 | + | 0.116093i | \(0.0370370\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.830416 | + | 0.302247i | −0.830416 | + | 0.302247i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.0798028 | − | 0.0845860i | −0.0798028 | − | 0.0845860i | 0.686242 | − | 0.727374i | \(-0.259259\pi\) |
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.59716 | − | 0.802123i | 1.59716 | − | 0.802123i | ||||
\(446\) | 1.59716 | − | 0.802123i | 1.59716 | − | 0.802123i | ||||
\(447\) | 0.819590 | + | 0.868715i | 0.819590 | + | 0.868715i | ||||
\(448\) | −0.941855 | − | 0.998308i | −0.941855 | − | 0.998308i | ||||
\(449\) | 1.17365 | + | 0.984808i | 1.17365 | + | 0.984808i | 1.00000 | \(0\) | ||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(450\) | 0.939693 | + | 0.342020i | 0.939693 | + | 0.342020i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.28971 | − | 1.36702i | 1.28971 | − | 1.36702i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | −0.0581448 | − | 0.998308i | \(-0.518519\pi\) | ||||
0.0581448 | + | 0.998308i | \(0.481481\pi\) | |||||||
\(458\) | −0.993238 | + | 1.72034i | −0.993238 | + | 1.72034i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.396080 | + | 0.686030i | 0.396080 | + | 0.686030i | ||||
\(461\) | 0.479241 | − | 0.315202i | 0.479241 | − | 0.315202i | −0.286803 | − | 0.957990i | \(-0.592593\pi\) |
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.744386 | − | 1.72568i | 0.744386 | − | 1.72568i | 0.0581448 | − | 0.998308i | \(-0.481481\pi\) |
0.686242 | − | 0.727374i | \(-0.259259\pi\) | |||||||
\(464\) | −1.93293 | − | 0.458113i | −1.93293 | − | 0.458113i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.326352 | + | 0.118782i | 0.326352 | + | 0.118782i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.149980 | + | 0.0545883i | −0.149980 | + | 0.0545883i | ||||
\(470\) | −0.512593 | + | 1.71218i | −0.512593 | + | 1.71218i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.396080 | − | 0.918216i | \(-0.629630\pi\) | ||||
0.396080 | + | 0.918216i | \(0.370370\pi\) | |||||||
\(480\) | 0.766044 | + | 0.642788i | 0.766044 | + | 0.642788i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0.342534 | + | 0.460103i | 0.342534 | + | 0.460103i | ||||
\(483\) | 1.05792 | + | 0.250732i | 1.05792 | + | 0.250732i | ||||
\(484\) | 0.893633 | + | 0.448799i | 0.893633 | + | 0.448799i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.0581448 | + | 0.998308i | −0.0581448 | + | 0.998308i | ||||
\(487\) | 1.00000 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(488\) | −1.73909 | − | 0.873403i | −1.73909 | − | 0.873403i | ||||
\(489\) | 1.49079 | + | 0.353324i | 1.49079 | + | 0.353324i | ||||
\(490\) | −0.527715 | − | 0.708845i | −0.527715 | − | 0.708845i | ||||
\(491\) | 0 | 0 | −0.286803 | − | 0.957990i | \(-0.592593\pi\) | ||||
0.286803 | + | 0.957990i | \(0.407407\pi\) | |||||||
\(492\) | 1.28004 | + | 1.07408i | 1.28004 | + | 1.07408i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0.661840 | + | 1.53432i | 0.661840 | + | 1.53432i | ||||
\(499\) | 0 | 0 | −0.835488 | − | 0.549509i | \(-0.814815\pi\) | ||||
0.835488 | + | 0.549509i | \(0.185185\pi\) | |||||||
\(500\) | −0.0581448 | + | 0.998308i | −0.0581448 | + | 0.998308i | ||||
\(501\) | 0.115503 | + | 1.98312i | 0.115503 | + | 1.98312i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.82873 | − | 0.665602i | 1.82873 | − | 0.665602i | 0.835488 | − | 0.549509i | \(-0.185185\pi\) |
0.993238 | − | 0.116093i | \(-0.0370370\pi\) | |||||||
\(504\) | 1.36320 | − | 0.159336i | 1.36320 | − | 0.159336i | ||||
\(505\) | −1.43969 | − | 0.524005i | −1.43969 | − | 0.524005i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.173648 | − | 0.984808i | −0.173648 | − | 0.984808i | ||||
\(508\) | −1.16212 | − | 0.275428i | −1.16212 | − | 0.275428i | ||||
\(509\) | 0.770807 | − | 1.78693i | 0.770807 | − | 1.78693i | 0.173648 | − | 0.984808i | \(-0.444444\pi\) |
0.597159 | − | 0.802123i | \(-0.296296\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.109277 | − | 1.87621i | −0.109277 | − | 1.87621i | ||||
\(516\) | 0.137557 | − | 0.318893i | 0.137557 | − | 0.318893i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.606829 | − | 0.509190i | 0.606829 | − | 0.509190i | −0.286803 | − | 0.957990i | \(-0.592593\pi\) |
0.893633 | + | 0.448799i | \(0.148148\pi\) | |||||||
\(522\) | 1.52173 | − | 1.27688i | 1.52173 | − | 1.27688i | ||||
\(523\) | −1.49079 | − | 1.25092i | −1.49079 | − | 1.25092i | −0.893633 | − | 0.448799i | \(-0.851852\pi\) |
−0.597159 | − | 0.802123i | \(-0.703704\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.941855 | + | 0.998308i | 0.941855 | + | 0.998308i | ||||
\(526\) | −1.67948 | + | 0.843467i | −1.67948 | + | 0.843467i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.255614 | + | 0.270935i | 0.255614 | + | 0.270935i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −0.893633 | + | 1.54782i | −0.893633 | + | 1.54782i | ||||
\(535\) | −0.393633 | + | 0.417226i | −0.393633 | + | 0.417226i | ||||
\(536\) | 0.115503 | − | 0.0135004i | 0.115503 | − | 0.0135004i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −0.0333522 | − | 0.572636i | −0.0333522 | − | 0.572636i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −0.973045 | + | 0.230616i | −0.973045 | + | 0.230616i | ||||
\(541\) | −0.973045 | − | 1.68536i | −0.973045 | − | 1.68536i | −0.686242 | − | 0.727374i | \(-0.740741\pi\) |
−0.286803 | − | 0.957990i | \(-0.592593\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.479241 | − | 0.315202i | −0.479241 | − | 0.315202i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.16212 | + | 0.275428i | 1.16212 | + | 0.275428i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.0694434 | − | 0.0932786i | 0.0694434 | − | 0.0932786i | −0.766044 | − | 0.642788i | \(-0.777778\pi\) |
0.835488 | + | 0.549509i | \(0.185185\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.73909 | − | 0.873403i | 1.73909 | − | 0.873403i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −0.707900 | − | 0.355521i | −0.707900 | − | 0.355521i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0.543613 | + | 1.26024i | 0.543613 | + | 1.26024i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.558145 | + | 1.86433i | 0.558145 | + | 1.86433i | ||||
\(563\) | 0.997837 | + | 1.34033i | 0.997837 | + | 1.34033i | 0.939693 | + | 0.342020i | \(0.111111\pi\) |
0.0581448 | + | 0.998308i | \(0.481481\pi\) | |||||||
\(564\) | −0.512593 | − | 1.71218i | −0.512593 | − | 1.71218i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.19432 | 1.19432 | ||||||||
\(567\) | −0.686242 | + | 1.18861i | −0.686242 | + | 1.18861i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0.310355 | + | 0.155866i | 0.310355 | + | 0.155866i | 0.597159 | − | 0.802123i | \(-0.296296\pi\) |
−0.286803 | + | 0.957990i | \(0.592593\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | −0.597159 | − | 0.802123i | \(-0.703704\pi\) | ||||
0.597159 | + | 0.802123i | \(0.296296\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.908364 | + | 2.10582i | 0.908364 | + | 2.10582i | ||||
\(575\) | −0.137557 | − | 0.780125i | −0.137557 | − | 0.780125i | ||||
\(576\) | −0.993238 | − | 0.116093i | −0.993238 | − | 0.116093i | ||||
\(577\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(578\) | −0.973045 | + | 0.230616i | −0.973045 | + | 0.230616i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.65968 | + | 1.09159i | 1.65968 | + | 1.09159i | ||||
\(581\) | −0.133349 | + | 2.28951i | −0.133349 | + | 2.28951i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.16212 | + | 1.56100i | −1.16212 | + | 1.56100i | −0.396080 | + | 0.918216i | \(0.629630\pi\) |
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(588\) | 0.830416 | + | 0.302247i | 0.830416 | + | 0.302247i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.0694434 | − | 1.19230i | −0.0694434 | − | 1.19230i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.686242 | − | 0.727374i | \(-0.259259\pi\) | ||||
−0.686242 | + | 0.727374i | \(0.740741\pi\) | |||||||
\(600\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(601\) | −0.344948 | − | 0.0403186i | −0.344948 | − | 0.0403186i | −0.0581448 | − | 0.998308i | \(-0.518519\pi\) |
−0.286803 | + | 0.957990i | \(0.592593\pi\) | |||||||
\(602\) | 0.365142 | − | 0.306390i | 0.365142 | − | 0.306390i | ||||
\(603\) | −0.0581448 | + | 0.100710i | −0.0581448 | + | 0.100710i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.686242 | − | 0.727374i | −0.686242 | − | 0.727374i | ||||
\(606\) | 1.49079 | − | 0.353324i | 1.49079 | − | 0.353324i | ||||
\(607\) | 1.77518 | − | 0.891529i | 1.77518 | − | 0.891529i | 0.835488 | − | 0.549509i | \(-0.185185\pi\) |
0.939693 | − | 0.342020i | \(-0.111111\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.65292 | − | 0.628753i | 2.65292 | − | 0.628753i | ||||
\(610\) | 1.33549 | + | 1.41553i | 1.33549 | + | 1.41553i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(614\) | −0.786803 | − | 0.0919641i | −0.786803 | − | 0.0919641i | ||||
\(615\) | −0.835488 | − | 1.44711i | −0.835488 | − | 1.44711i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 0.993238 | − | 0.116093i | \(-0.0370370\pi\) | ||||
−0.993238 | + | 0.116093i | \(0.962963\pi\) | |||||||
\(618\) | 1.12229 | + | 1.50750i | 1.12229 | + | 1.50750i | ||||
\(619\) | 0 | 0 | −0.0581448 | − | 0.998308i | \(-0.518519\pi\) | ||||
0.0581448 | + | 0.998308i | \(0.481481\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.707900 | − | 0.355521i | 0.707900 | − | 0.355521i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.04944 | + | 1.34794i | −2.04944 | + | 1.34794i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.396080 | − | 0.918216i | 0.396080 | − | 0.918216i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −1.33549 | − | 0.316516i | −1.33549 | − | 0.316516i | ||||
\(631\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.997837 | + | 0.656288i | 0.997837 | + | 0.656288i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.173648 | − | 0.984808i | −0.173648 | − | 0.984808i | ||||
\(641\) | −0.227194 | − | 0.526695i | −0.227194 | − | 0.526695i | 0.766044 | − | 0.642788i | \(-0.222222\pi\) |
−0.993238 | + | 0.116093i | \(0.962963\pi\) | |||||||
\(642\) | 0.0996057 | − | 0.564892i | 0.0996057 | − | 0.564892i | ||||
\(643\) | −0.569728 | − | 1.90302i | −0.569728 | − | 1.90302i | −0.396080 | − | 0.918216i | \(-0.629630\pi\) |
−0.173648 | − | 0.984808i | \(-0.555556\pi\) | |||||||
\(644\) | −0.649246 | − | 0.872089i | −0.649246 | − | 0.872089i | ||||
\(645\) | −0.238329 | + | 0.252614i | −0.238329 | + | 0.252614i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.19432 | −1.19432 | −0.597159 | − | 0.802123i | \(-0.703704\pi\) | ||||
−0.597159 | + | 0.802123i | \(0.703704\pi\) | |||||||
\(648\) | 0.686242 | − | 0.727374i | 0.686242 | − | 0.727374i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.914900 | − | 1.22892i | −0.914900 | − | 1.22892i | ||||
\(653\) | 0 | 0 | −0.286803 | − | 0.957990i | \(-0.592593\pi\) | ||||
0.286803 | + | 0.957990i | \(0.407407\pi\) | |||||||
\(654\) | −1.12229 | + | 0.408481i | −1.12229 | + | 0.408481i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −0.290162 | − | 1.64559i | −0.290162 | − | 1.64559i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.425958 | − | 2.41573i | 0.425958 | − | 2.41573i | ||||
\(659\) | 0 | 0 | 0.973045 | − | 0.230616i | \(-0.0740741\pi\) | ||||
−0.973045 | + | 0.230616i | \(0.925926\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.57020 | + | 1.03274i | 1.57020 | + | 1.03274i | 0.973045 | + | 0.230616i | \(0.0740741\pi\) |
0.597159 | + | 0.802123i | \(0.296296\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.479241 | − | 1.60078i | 0.479241 | − | 1.60078i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.47871 | − | 0.538205i | −1.47871 | − | 0.538205i | ||||
\(668\) | 1.18624 | − | 1.59340i | 1.18624 | − | 1.59340i | ||||
\(669\) | 1.36912 | − | 1.14883i | 1.36912 | − | 1.14883i | ||||
\(670\) | −0.113155 | − | 0.0268182i | −0.113155 | − | 0.0268182i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −1.14669 | − | 0.754192i | −1.14669 | − | 0.754192i | ||||
\(673\) | 0 | 0 | 0.835488 | − | 0.549509i | \(-0.185185\pi\) | ||||
−0.835488 | + | 0.549509i | \(0.814815\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.993238 | + | 0.116093i | 0.993238 | + | 0.116093i | ||||
\(676\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(677\) | 0 | 0 | −0.0581448 | − | 0.998308i | \(-0.518519\pi\) | ||||
0.0581448 | + | 0.998308i | \(0.481481\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.939693 | − | 1.62760i | 0.939693 | − | 1.62760i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.266044 | + | 0.223238i | −0.266044 | + | 0.223238i | −0.766044 | − | 0.642788i | \(-0.777778\pi\) |
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −0.109528 | − | 0.116093i | −0.109528 | − | 0.116093i | ||||
\(687\) | −0.569728 | + | 1.90302i | −0.569728 | + | 1.90302i | ||||
\(688\) | −0.310355 | + | 0.155866i | −0.310355 | + | 0.155866i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0.543613 | + | 0.576196i | 0.543613 | + | 0.576196i | ||||
\(691\) | 0 | 0 | −0.686242 | − | 0.727374i | \(-0.740741\pi\) | ||||
0.686242 | + | 0.727374i | \(0.259259\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.17365 | − | 0.984808i | 1.17365 | − | 0.984808i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.98648 | −1.98648 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 1.77518 | − | 0.207489i | 1.77518 | − | 0.207489i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.0798028 | − | 1.37016i | −0.0798028 | − | 1.37016i | ||||
\(701\) | −0.893633 | + | 1.54782i | −0.893633 | + | 1.54782i | −0.0581448 | + | 0.998308i | \(0.518519\pi\) |
−0.835488 | + | 0.549509i | \(0.814815\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.103920 | + | 1.78424i | −0.103920 | + | 1.78424i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.04609 | + | 0.484931i | 2.04609 | + | 0.484931i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.0694434 | + | 0.0932786i | −0.0694434 | + | 0.0932786i | −0.835488 | − | 0.549509i | \(-0.814815\pi\) |
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.67948 | − | 0.611281i | 1.67948 | − | 0.611281i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(720\) | 0.893633 | + | 0.448799i | 0.893633 | + | 0.448799i | ||||
\(721\) | 0.447912 | + | 2.54024i | 0.447912 | + | 2.54024i | ||||
\(722\) | −0.396080 | − | 0.918216i | −0.396080 | − | 0.918216i | ||||
\(723\) | 0.439408 | + | 0.368707i | 0.439408 | + | 0.368707i | ||||
\(724\) | 0.164512 | + | 0.549509i | 0.164512 | + | 0.549509i | ||||
\(725\) | −1.18624 | − | 1.59340i | −1.18624 | − | 1.59340i | ||||
\(726\) | 0.973045 | + | 0.230616i | 0.973045 | + | 0.230616i | ||||
\(727\) | −1.73909 | − | 0.873403i | −1.73909 | − | 0.873403i | −0.973045 | − | 0.230616i | \(-0.925926\pi\) |
−0.766044 | − | 0.642788i | \(-0.777778\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.173648 | + | 0.984808i | 0.173648 | + | 0.984808i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −1.89363 | − | 0.448799i | −1.89363 | − | 0.448799i | ||||
\(733\) | 0 | 0 | −0.597159 | − | 0.802123i | \(-0.703704\pi\) | ||||
0.597159 | + | 0.802123i | \(0.296296\pi\) | |||||||
\(734\) | 0.286803 | + | 0.957990i | 0.286803 | + | 0.957990i | ||||
\(735\) | −0.676961 | − | 0.568038i | −0.676961 | − | 0.568038i | ||||
\(736\) | 0.313758 | + | 0.727374i | 0.313758 | + | 0.727374i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 1.49324 | + | 0.749932i | 1.49324 | + | 0.749932i | ||||
\(739\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0.103920 | − | 1.78424i | 0.103920 | − | 1.78424i | −0.396080 | − | 0.918216i | \(-0.629630\pi\) |
0.500000 | − | 0.866025i | \(-0.333333\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.342534 | + | 1.14414i | −0.342534 | + | 1.14414i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.997837 | + | 1.34033i | 0.997837 | + | 1.34033i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.470122 | − | 0.631484i | 0.470122 | − | 0.631484i | ||||
\(750\) | 0.173648 | + | 0.984808i | 0.173648 | + | 0.984808i | ||||
\(751\) | 0 | 0 | −0.973045 | − | 0.230616i | \(-0.925926\pi\) | ||||
0.973045 | + | 0.230616i | \(0.0740741\pi\) | |||||||
\(752\) | −0.707900 | + | 1.64110i | −0.707900 | + | 1.64110i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.28971 | − | 0.469417i | 1.28971 | − | 0.469417i | ||||
\(757\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.0798028 | − | 0.0845860i | 0.0798028 | − | 0.0845860i | −0.686242 | − | 0.727374i | \(-0.740741\pi\) |
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(762\) | −1.19432 | −1.19432 | ||||||||
\(763\) | −1.62810 | − | 0.190297i | −1.62810 | − | 0.190297i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.17365 | + | 0.984808i | 1.17365 | + | 0.984808i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0.686242 | + | 0.727374i | 0.686242 | + | 0.727374i | ||||
\(769\) | −1.22650 | + | 0.615969i | −1.22650 | + | 0.615969i | −0.939693 | − | 0.342020i | \(-0.888889\pi\) |
−0.286803 | + | 0.957990i | \(0.592593\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(774\) | 0.0603074 | − | 0.342020i | 0.0603074 | − | 0.342020i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −0.0798028 | + | 0.0845860i | −0.0798028 | + | 0.0845860i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.18624 | − | 1.59340i | 1.18624 | − | 1.59340i | ||||
\(784\) | −0.441855 | − | 0.765316i | −0.441855 | − | 0.765316i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.396080 | − | 0.918216i | 0.396080 | − | 0.918216i | −0.597159 | − | 0.802123i | \(-0.703704\pi\) |
0.993238 | − | 0.116093i | \(-0.0370370\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.43969 | + | 1.20805i | −1.43969 | + | 1.20805i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | −0.835488 | − | 0.549509i | \(-0.814815\pi\) | ||||
0.835488 | + | 0.549509i | \(0.185185\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −0.173648 | + | 0.984808i | −0.173648 | + | 0.984808i | ||||
\(801\) | −0.512593 | + | 1.71218i | −0.512593 | + | 1.71218i | ||||
\(802\) | −0.0603074 | − | 0.342020i | −0.0603074 | − | 0.342020i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0.109277 | − | 0.0397734i | 0.109277 | − | 0.0397734i | ||||
\(805\) | 0.311820 | + | 1.04155i | 0.311820 | + | 1.04155i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.164512 | − | 0.549509i | −0.164512 | − | 0.549509i | ||||
\(808\) | −1.36912 | − | 0.687600i | −1.36912 | − | 0.687600i | ||||
\(809\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(810\) | −0.893633 | + | 0.448799i | −0.893633 | + | 0.448799i | ||||
\(811\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(812\) | −2.43641 | − | 1.22361i | −2.43641 | − | 1.22361i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.439408 | + | 1.46773i | 0.439408 | + | 1.46773i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0.326352 | + | 1.85083i | 0.326352 | + | 1.85083i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.290162 | + | 1.64559i | −0.290162 | + | 1.64559i | ||||
\(821\) | 0.770807 | − | 0.182685i | 0.770807 | − | 0.182685i | 0.173648 | − | 0.984808i | \(-0.444444\pi\) |
0.597159 | + | 0.802123i | \(0.296296\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.62593 | + | 1.06939i | 1.62593 | + | 1.06939i | 0.939693 | + | 0.342020i | \(0.111111\pi\) |
0.686242 | + | 0.727374i | \(0.259259\pi\) | |||||||
\(824\) | 0.109277 | − | 1.87621i | 0.109277 | − | 1.87621i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.86668 | + | 0.679415i | −1.86668 | + | 0.679415i | −0.893633 | + | 0.448799i | \(0.851852\pi\) |
−0.973045 | + | 0.230616i | \(0.925926\pi\) | |||||||
\(828\) | −0.770807 | − | 0.182685i | −0.770807 | − | 0.182685i | ||||
\(829\) | −0.744386 | − | 0.270935i | −0.744386 | − | 0.270935i | −0.0581448 | − | 0.998308i | \(-0.518519\pi\) |
−0.686242 | + | 0.727374i | \(0.740741\pi\) | |||||||
\(830\) | −0.997837 | + | 1.34033i | −0.997837 | + | 1.34033i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.65968 | + | 1.09159i | −1.65968 | + | 1.09159i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.0581448 | − | 0.998308i | \(-0.518519\pi\) | ||||
0.0581448 | + | 0.998308i | \(0.481481\pi\) | |||||||
\(840\) | 0.819590 | + | 1.10090i | 0.819590 | + | 1.10090i | ||||
\(841\) | −2.92617 | + | 0.342020i | −2.92617 | + | 0.342020i | ||||
\(842\) | 0.238329 | − | 0.252614i | 0.238329 | − | 0.252614i | ||||
\(843\) | 0.973045 | + | 1.68536i | 0.973045 | + | 1.68536i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.766044 | − | 0.642788i | 0.766044 | − | 0.642788i | ||||
\(846\) | −0.893633 | − | 1.54782i | −0.893633 | − | 1.54782i | ||||
\(847\) | 1.05138 | + | 0.882215i | 1.05138 | + | 0.882215i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.16212 | − | 0.275428i | 1.16212 | − | 0.275428i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | −0.686242 | − | 0.727374i | \(-0.740741\pi\) | ||||
0.686242 | + | 0.727374i | \(0.259259\pi\) | |||||||
\(854\) | −2.04609 | − | 1.71687i | −2.04609 | − | 1.71687i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.439408 | + | 0.368707i | −0.439408 | + | 0.368707i | ||||
\(857\) | 0 | 0 | −0.993238 | − | 0.116093i | \(-0.962963\pi\) | ||||
0.993238 | + | 0.116093i | \(0.0370370\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | 0.686242 | − | 0.727374i | \(-0.259259\pi\) | ||||
−0.686242 | + | 0.727374i | \(0.740741\pi\) | |||||||
\(860\) | 0.344948 | − | 0.0403186i | 0.344948 | − | 0.0403186i | ||||
\(861\) | 1.36952 | + | 1.83958i | 1.36952 | + | 1.83958i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −0.286803 | + | 0.496758i | −0.286803 | + | 0.496758i | −0.973045 | − | 0.230616i | \(-0.925926\pi\) |
0.686242 | + | 0.727374i | \(0.259259\pi\) | |||||||
\(864\) | −0.993238 | + | 0.116093i | −0.993238 | + | 0.116093i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.893633 | + | 0.448799i | −0.893633 | + | 0.448799i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 1.86668 | + | 0.679415i | 1.86668 | + | 0.679415i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 1.12229 | + | 0.408481i | 1.12229 | + | 0.408481i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.393633 | + | 1.31482i | −0.393633 | + | 1.31482i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | 0.0581448 | − | 0.998308i | \(-0.481481\pi\) | ||||
−0.0581448 | + | 0.998308i | \(0.518519\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.207391 | − | 1.17617i | 0.207391 | − | 1.17617i | −0.686242 | − | 0.727374i | \(-0.740741\pi\) |
0.893633 | − | 0.448799i | \(-0.148148\pi\) | |||||||
\(882\) | 0.877735 | + | 0.102593i | 0.877735 | + | 0.102593i | ||||
\(883\) | 0.290162 | + | 1.64559i | 0.290162 | + | 1.64559i | 0.686242 | + | 0.727374i | \(0.259259\pi\) |
−0.396080 | + | 0.918216i | \(0.629630\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.0333522 | + | 0.111404i | 0.0333522 | + | 0.111404i | ||||
\(887\) | −0.914900 | − | 1.22892i | −0.914900 | − | 1.22892i | −0.973045 | − | 0.230616i | \(-0.925926\pi\) |
0.0581448 | − | 0.998308i | \(-0.481481\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.46483 | − | 0.735663i | −1.46483 | − | 0.735663i | ||||
\(890\) | −1.78727 | −1.78727 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.78727 | −1.78727 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −0.342534 | − | 1.14414i | −0.342534 | − | 1.14414i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.393633 | + | 1.31482i | 0.393633 | + | 1.31482i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −0.606829 | − | 1.40679i | −0.606829 | − | 1.40679i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −0.686242 | − | 0.727374i | −0.686242 | − | 0.727374i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.284641 | − | 0.382339i | 0.284641 | − | 0.382339i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.0333522 | − | 0.572636i | 0.0333522 | − | 0.572636i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.164512 | + | 0.549509i | −0.164512 | + | 0.549509i | 0.835488 | + | 0.549509i | \(0.185185\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(908\) | −1.76604 | + | 0.642788i | −1.76604 | + | 0.642788i | ||||
\(909\) | 1.36912 | − | 0.687600i | 1.36912 | − | 0.687600i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 0.597159 | − | 0.802123i | \(-0.296296\pi\) | ||||
−0.597159 | + | 0.802123i | \(0.703704\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.62593 | + | 1.06939i | 1.62593 | + | 1.06939i | ||||
\(916\) | 1.65968 | − | 1.09159i | 1.65968 | − | 1.09159i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(920\) | −0.0460600 | − | 0.790819i | −0.0460600 | − | 0.790819i | ||||
\(921\) | −0.786803 | + | 0.0919641i | −0.786803 | + | 0.0919641i | ||||
\(922\) | −0.569728 | + | 0.0665916i | −0.569728 | + | 0.0665916i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −1.43969 | + | 1.20805i | −1.43969 | + | 1.20805i | ||||
\(927\) | 1.43969 | + | 1.20805i | 1.43969 | + | 1.20805i | ||||
\(928\) | 1.52173 | + | 1.27688i | 1.52173 | + | 1.27688i | ||||
\(929\) | −0.238329 | − | 0.252614i | −0.238329 | − | 0.252614i | 0.597159 | − | 0.802123i | \(-0.296296\pi\) |
−0.835488 | + | 0.549509i | \(0.814815\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −0.238329 | − | 0.252614i | −0.238329 | − | 0.252614i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(938\) | 0.158526 | + | 0.0185291i | 0.158526 | + | 0.0185291i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.22650 | − | 1.30001i | 1.22650 | − | 1.30001i | ||||
\(941\) | 1.65968 | − | 0.193988i | 1.65968 | − | 0.193988i | 0.766044 | − | 0.642788i | \(-0.222222\pi\) |
0.893633 | + | 0.448799i | \(0.148148\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.0769651 | − | 1.32144i | −0.0769651 | − | 1.32144i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.37248 | −1.37248 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.39608 | + | 0.918216i | −1.39608 | + | 0.918216i | −0.396080 | + | 0.918216i | \(0.629630\pi\) |
−1.00000 | \(1.00000\pi\) | |||||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −0.396080 | − | 0.918216i | −0.396080 | − | 0.918216i | ||||
\(961\) | 0.973045 | − | 0.230616i | 0.973045 | − | 0.230616i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.0333522 | − | 0.572636i | −0.0333522 | − | 0.572636i | ||||
\(964\) | −0.0996057 | − | 0.564892i | −0.0996057 | − | 0.564892i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −0.832863 | − | 0.698855i | −0.832863 | − | 0.698855i | ||||
\(967\) | 0.227194 | + | 0.758881i | 0.227194 | + | 0.758881i | 0.993238 | + | 0.116093i | \(0.0370370\pi\) |
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(968\) | −0.597159 | − | 0.802123i | −0.597159 | − | 0.802123i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(972\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −0.893633 | − | 0.448799i | −0.893633 | − | 0.448799i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.16212 | + | 1.56100i | 1.16212 | + | 1.56100i | ||||
\(977\) | 0 | 0 | −0.286803 | − | 0.957990i | \(-0.592593\pi\) | ||||
0.286803 | + | 0.957990i | \(0.407407\pi\) | |||||||
\(978\) | −1.17365 | − | 0.984808i | −1.17365 | − | 0.984808i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0.153455 | + | 0.870285i | 0.153455 | + | 0.870285i | ||||
\(981\) | −0.997837 | + | 0.656288i | −0.997837 | + | 0.656288i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.33549 | − | 0.316516i | 1.33549 | − | 0.316516i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
0.835488 | + | 0.549509i | \(0.185185\pi\) | |||||||
\(984\) | −0.661840 | − | 1.53432i | −0.661840 | − | 1.53432i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.142629 | − | 2.44884i | −0.142629 | − | 2.44884i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.258523 | + | 0.0940946i | −0.258523 | + | 0.0940946i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0.0971586 | − | 1.66815i | 0.0971586 | − | 1.66815i | ||||
\(997\) | 0 | 0 | 0.835488 | − | 0.549509i | \(-0.185185\pi\) | ||||
−0.835488 | + | 0.549509i | \(0.814815\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1620.1.bp.a.499.1 | ✓ | 18 | |
4.3 | odd | 2 | 1620.1.bp.b.499.1 | yes | 18 | ||
5.4 | even | 2 | 1620.1.bp.b.499.1 | yes | 18 | ||
20.19 | odd | 2 | CM | 1620.1.bp.a.499.1 | ✓ | 18 | |
81.25 | even | 27 | inner | 1620.1.bp.a.1159.1 | yes | 18 | |
324.187 | odd | 54 | 1620.1.bp.b.1159.1 | yes | 18 | ||
405.349 | even | 54 | 1620.1.bp.b.1159.1 | yes | 18 | ||
1620.1159 | odd | 54 | inner | 1620.1.bp.a.1159.1 | yes | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1620.1.bp.a.499.1 | ✓ | 18 | 1.1 | even | 1 | trivial | |
1620.1.bp.a.499.1 | ✓ | 18 | 20.19 | odd | 2 | CM | |
1620.1.bp.a.1159.1 | yes | 18 | 81.25 | even | 27 | inner | |
1620.1.bp.a.1159.1 | yes | 18 | 1620.1159 | odd | 54 | inner | |
1620.1.bp.b.499.1 | yes | 18 | 4.3 | odd | 2 | ||
1620.1.bp.b.499.1 | yes | 18 | 5.4 | even | 2 | ||
1620.1.bp.b.1159.1 | yes | 18 | 324.187 | odd | 54 | ||
1620.1.bp.b.1159.1 | yes | 18 | 405.349 | even | 54 |