Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2289,1,Mod(158,2289)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2289, base_ring=CyclotomicField(54))
chi = DirichletCharacter(H, H._module([27, 36, 40]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2289.158");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2289 = 3 \cdot 7 \cdot 109 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 2289.en (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: | \(1.14235981392\) |
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: | \(\Z[a_1, a_2, a_3]\) |
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 | 2195.1 | ||
Root | \(0.286803 + 0.957990i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2289.2195 |
Dual form | 2289.1.en.a.1388.1 |
$q$-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 \(\left(\mathbb{Z}/2289\mathbb{Z}\right)^\times\).
\(n\) | \(442\) | \(764\) | \(1963\) |
\(\chi(n)\) | \(e\left(\frac{5}{27}\right)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
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 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(3\) | 0.597159 | + | 0.802123i | 0.597159 | + | 0.802123i | ||||
\(4\) | 0.766044 | − | 0.642788i | 0.766044 | − | 0.642788i | ||||
\(5\) | 0 | 0 | −0.286803 | − | 0.957990i | \(-0.592593\pi\) | ||||
0.286803 | + | 0.957990i | \(0.407407\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.766044 | − | 0.642788i | 0.766044 | − | 0.642788i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.286803 | + | 0.957990i | −0.286803 | + | 0.957990i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | −0.993238 | − | 0.116093i | \(-0.962963\pi\) | ||||
0.993238 | + | 0.116093i | \(0.0370370\pi\) | |||||||
\(12\) | 0.973045 | + | 0.230616i | 0.973045 | + | 0.230616i | ||||
\(13\) | −0.439408 | − | 1.46773i | −0.439408 | − | 1.46773i | −0.835488 | − | 0.549509i | \(-0.814815\pi\) |
0.396080 | − | 0.918216i | \(-0.370370\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.173648 | − | 0.984808i | 0.173648 | − | 0.984808i | ||||
\(17\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.914900 | + | 0.767692i | 0.914900 | + | 0.767692i | 0.973045 | − | 0.230616i | \(-0.0740741\pi\) |
−0.0581448 | + | 0.998308i | \(0.518519\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.973045 | + | 0.230616i | 0.973045 | + | 0.230616i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.835488 | + | 0.549509i | −0.835488 | + | 0.549509i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.939693 | + | 0.342020i | −0.939693 | + | 0.342020i | ||||
\(28\) | 0.173648 | − | 0.984808i | 0.173648 | − | 0.984808i | ||||
\(29\) | 0 | 0 | −0.597159 | − | 0.802123i | \(-0.703704\pi\) | ||||
0.597159 | + | 0.802123i | \(0.296296\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.05138 | − | 1.11440i | −1.05138 | − | 1.11440i | −0.993238 | − | 0.116093i | \(-0.962963\pi\) |
−0.0581448 | − | 0.998308i | \(-0.518519\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.396080 | + | 0.918216i | 0.396080 | + | 0.918216i | ||||
\(37\) | 0.393633 | + | 0.417226i | 0.393633 | + | 0.417226i | 0.893633 | − | 0.448799i | \(-0.148148\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.914900 | − | 1.22892i | 0.914900 | − | 1.22892i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.290162 | + | 1.64559i | −0.290162 | + | 1.64559i | 0.396080 | + | 0.918216i | \(0.370370\pi\) |
−0.686242 | + | 0.727374i | \(0.740741\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.0581448 | − | 0.998308i | \(-0.518519\pi\) | ||||
0.0581448 | + | 0.998308i | \(0.481481\pi\) | |||||||
\(48\) | 0.893633 | − | 0.448799i | 0.893633 | − | 0.448799i | ||||
\(49\) | 0.173648 | − | 0.984808i | 0.173648 | − | 0.984808i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.28004 | − | 0.841897i | −1.28004 | − | 0.841897i | ||||
\(53\) | 0 | 0 | 0.686242 | − | 0.727374i | \(-0.259259\pi\) | ||||
−0.686242 | + | 0.727374i | \(0.740741\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.0694434 | + | 1.19230i | −0.0694434 | + | 1.19230i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | −0.396080 | − | 0.918216i | \(-0.629630\pi\) | ||||
0.396080 | + | 0.918216i | \(0.370370\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.14669 | + | 0.754192i | 1.14669 | + | 0.754192i | 0.973045 | − | 0.230616i | \(-0.0740741\pi\) |
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.396080 | + | 0.918216i | 0.396080 | + | 0.918216i | ||||
\(64\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.686242 | + | 0.727374i | 0.686242 | + | 0.727374i | 0.973045 | − | 0.230616i | \(-0.0740741\pi\) |
−0.286803 | + | 0.957990i | \(0.592593\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.77518 | − | 0.207489i | −1.77518 | − | 0.207489i | −0.835488 | − | 0.549509i | \(-0.814815\pi\) |
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.939693 | − | 0.342020i | −0.939693 | − | 0.342020i | ||||
\(76\) | 1.19432 | 1.19432 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.512593 | + | 1.71218i | −0.512593 | + | 1.71218i | 0.173648 | + | 0.984808i | \(0.444444\pi\) |
−0.686242 | + | 0.727374i | \(0.740741\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.835488 | − | 0.549509i | −0.835488 | − | 0.549509i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 0.993238 | − | 0.116093i | \(-0.0370370\pi\) | ||||
−0.993238 | + | 0.116093i | \(0.962963\pi\) | |||||||
\(84\) | 0.893633 | − | 0.448799i | 0.893633 | − | 0.448799i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 0.0581448 | − | 0.998308i | \(-0.481481\pi\) | ||||
−0.0581448 | + | 0.998308i | \(0.518519\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.28004 | − | 0.841897i | −1.28004 | − | 0.841897i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.266044 | − | 1.50881i | 0.266044 | − | 1.50881i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.05138 | + | 1.11440i | −1.05138 | + | 1.11440i | −0.0581448 | + | 0.998308i | \(0.518519\pi\) |
−0.993238 | + | 0.116093i | \(0.962963\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.286803 | + | 0.957990i | −0.286803 | + | 0.957990i | ||||
\(101\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.00676164 | − | 0.116093i | 0.00676164 | − | 0.116093i | −0.993238 | − | 0.116093i | \(-0.962963\pi\) |
1.00000 | \(0\) | |||||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(108\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(109\) | −0.939693 | − | 0.342020i | −0.939693 | − | 0.342020i | ||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.0996057 | + | 0.564892i | −0.0996057 | + | 0.564892i | ||||
\(112\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(113\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.53209 | 1.53209 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.973045 | + | 0.230616i | 0.973045 | + | 0.230616i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.52173 | − | 0.177865i | −1.52173 | − | 0.177865i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.39608 | − | 0.918216i | 1.39608 | − | 0.918216i | 0.396080 | − | 0.918216i | \(-0.370370\pi\) |
1.00000 | \(0\) | |||||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.49324 | + | 0.749932i | −1.49324 | + | 0.749932i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.686242 | − | 0.727374i | \(-0.740741\pi\) | ||||
0.686242 | + | 0.727374i | \(0.259259\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.19432 | 1.19432 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.835488 | − | 0.549509i | \(-0.814815\pi\) | ||||
0.835488 | + | 0.549509i | \(0.185185\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.22650 | − | 1.30001i | −1.22650 | − | 1.30001i | −0.939693 | − | 0.342020i | \(-0.888889\pi\) |
−0.286803 | − | 0.957990i | \(-0.592593\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.893633 | + | 0.448799i | 0.893633 | + | 0.448799i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.893633 | − | 0.448799i | 0.893633 | − | 0.448799i | ||||
\(148\) | 0.569728 | + | 0.0665916i | 0.569728 | + | 0.0665916i | ||||
\(149\) | 0 | 0 | −0.973045 | − | 0.230616i | \(-0.925926\pi\) | ||||
0.973045 | + | 0.230616i | \(0.0740741\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.14669 | + | 1.21542i | 1.14669 | + | 1.21542i | 0.973045 | + | 0.230616i | \(0.0740741\pi\) |
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.0890830 | − | 1.52950i | −0.0890830 | − | 1.52950i | ||||
\(157\) | 0.00676164 | − | 0.116093i | 0.00676164 | − | 0.116093i | −0.993238 | − | 0.116093i | \(-0.962963\pi\) |
1.00000 | \(0\) | |||||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.606829 | − | 0.509190i | 0.606829 | − | 0.509190i | −0.286803 | − | 0.957990i | \(-0.592593\pi\) |
0.893633 | + | 0.448799i | \(0.148148\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 0.893633 | − | 0.448799i | \(-0.148148\pi\) | ||||
−0.893633 | + | 0.448799i | \(0.851852\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.12565 | + | 0.740351i | −1.12565 | + | 0.740351i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.997837 | + | 0.656288i | −0.997837 | + | 0.656288i | ||||
\(172\) | 0.835488 | + | 1.44711i | 0.835488 | + | 1.44711i | ||||
\(173\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.286803 | + | 0.957990i | −0.286803 | + | 0.957990i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | 0.597159 | − | 0.802123i | \(-0.296296\pi\) | ||||
−0.597159 | + | 0.802123i | \(0.703704\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.770807 | − | 0.182685i | 0.770807 | − | 0.182685i | 0.173648 | − | 0.984808i | \(-0.444444\pi\) |
0.597159 | + | 0.802123i | \(0.296296\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.0798028 | + | 1.37016i | 0.0798028 | + | 1.37016i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(192\) | 0.396080 | − | 0.918216i | 0.396080 | − | 0.918216i | ||||
\(193\) | −1.62593 | + | 1.06939i | −1.62593 | + | 1.06939i | −0.686242 | + | 0.727374i | \(0.740741\pi\) |
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(197\) | 0 | 0 | −0.993238 | − | 0.116093i | \(-0.962963\pi\) | ||||
0.993238 | + | 0.116093i | \(0.0370370\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.173648 | + | 0.984808i | −0.173648 | + | 0.984808i | 0.766044 | + | 0.642788i | \(0.222222\pi\) |
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.173648 | + | 0.984808i | −0.173648 | + | 0.984808i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.52173 | + | 0.177865i | −1.52173 | + | 0.177865i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.539014 | + | 1.80043i | 0.539014 | + | 1.80043i | 0.597159 | + | 0.802123i | \(0.296296\pi\) |
−0.0581448 | + | 0.998308i | \(0.518519\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.52173 | − | 0.177865i | −1.52173 | − | 0.177865i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.893633 | − | 1.54782i | −0.893633 | − | 1.54782i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.558145 | − | 0.132283i | −0.558145 | − | 0.132283i | −0.0581448 | − | 0.998308i | \(-0.518519\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.286803 | − | 0.957990i | −0.286803 | − | 0.957990i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.973045 | − | 0.230616i | \(-0.0740741\pi\) | ||||
−0.973045 | + | 0.230616i | \(0.925926\pi\) | |||||||
\(228\) | 0.713197 | + | 0.957990i | 0.713197 | + | 0.957990i | ||||
\(229\) | 0.207391 | − | 0.278574i | 0.207391 | − | 0.278574i | −0.686242 | − | 0.727374i | \(-0.740741\pi\) |
0.893633 | + | 0.448799i | \(0.148148\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | −0.993238 | − | 0.116093i | \(-0.962963\pi\) | ||||
0.993238 | + | 0.116093i | \(0.0370370\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.67948 | + | 0.611281i | −1.67948 | + | 0.611281i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.993238 | − | 0.116093i | \(-0.962963\pi\) | ||||
0.993238 | + | 0.116093i | \(0.0370370\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.49079 | − | 1.25092i | 1.49079 | − | 1.25092i | 0.597159 | − | 0.802123i | \(-0.296296\pi\) |
0.893633 | − | 0.448799i | \(-0.148148\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.0581448 | − | 0.998308i | −0.0581448 | − | 0.998308i | ||||
\(244\) | 1.36320 | − | 0.159336i | 1.36320 | − | 0.159336i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.724747 | − | 1.68015i | 0.724747 | − | 1.68015i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(252\) | 0.893633 | + | 0.448799i | 0.893633 | + | 0.448799i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.939693 | − | 0.342020i | −0.939693 | − | 0.342020i | ||||
\(257\) | 0 | 0 | −0.396080 | − | 0.918216i | \(-0.629630\pi\) | ||||
0.396080 | + | 0.918216i | \(0.370370\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.569728 | + | 0.0665916i | 0.569728 | + | 0.0665916i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.993238 | + | 0.116093i | 0.993238 | + | 0.116093i | ||||
\(269\) | 0 | 0 | 0.0581448 | − | 0.998308i | \(-0.481481\pi\) | ||||
−0.0581448 | + | 0.998308i | \(0.518519\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.558145 | − | 1.86433i | −0.558145 | − | 1.86433i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
−0.0581448 | − | 0.998308i | \(-0.518519\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.0890830 | − | 1.52950i | −0.0890830 | − | 1.52950i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.744386 | − | 1.72568i | −0.744386 | − | 1.72568i | −0.686242 | − | 0.727374i | \(-0.740741\pi\) |
−0.0581448 | − | 0.998308i | \(-0.518519\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.36912 | − | 0.687600i | 1.36912 | − | 0.687600i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.22650 | − | 0.615969i | −1.22650 | − | 0.615969i | −0.286803 | − | 0.957990i | \(-0.592593\pi\) |
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.766044 | − | 0.642788i | 0.766044 | − | 0.642788i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.52173 | − | 0.177865i | −1.52173 | − | 0.177865i | ||||
\(292\) | −1.49324 | + | 0.982118i | −1.49324 | + | 0.982118i | ||||
\(293\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −0.939693 | + | 0.342020i | −0.939693 | + | 0.342020i | ||||
\(301\) | 0.835488 | + | 1.44711i | 0.835488 | + | 1.44711i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.914900 | − | 0.767692i | 0.914900 | − | 0.767692i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.49324 | − | 0.982118i | −1.49324 | − | 0.982118i | −0.993238 | − | 0.116093i | \(-0.962963\pi\) |
−0.500000 | − | 0.866025i | \(-0.666667\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.0971586 | − | 0.0639022i | 0.0971586 | − | 0.0639022i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.713197 | + | 0.957990i | 0.713197 | + | 0.957990i | 1.00000 | \(0\) | ||
−0.286803 | + | 0.957990i | \(0.592593\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.707900 | + | 1.64110i | 0.707900 | + | 1.64110i | ||||
\(317\) | 0 | 0 | 0.993238 | − | 0.116093i | \(-0.0370370\pi\) | ||||
−0.993238 | + | 0.116093i | \(0.962963\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −0.993238 | + | 0.116093i | −0.993238 | + | 0.116093i | ||||
\(325\) | 1.17365 | + | 0.984808i | 1.17365 | + | 0.984808i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.286803 | − | 0.957990i | −0.286803 | − | 0.957990i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.290162 | − | 1.64559i | −0.290162 | − | 1.64559i | −0.686242 | − | 0.727374i | \(-0.740741\pi\) |
0.396080 | − | 0.918216i | \(-0.370370\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.512593 | + | 0.257434i | −0.512593 | + | 0.257434i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.396080 | − | 0.918216i | 0.396080 | − | 0.918216i | ||||
\(337\) | −0.227194 | + | 0.526695i | −0.227194 | + | 0.526695i | −0.993238 | − | 0.116093i | \(-0.962963\pi\) |
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 0.893633 | − | 0.448799i | \(-0.148148\pi\) | ||||
−0.893633 | + | 0.448799i | \(0.851852\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.33549 | + | 0.316516i | −1.33549 | + | 0.316516i | −0.835488 | − | 0.549509i | \(-0.814815\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.914900 | + | 1.22892i | 0.914900 | + | 1.22892i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 0.396080 | − | 0.918216i | \(-0.370370\pi\) | ||||
−0.396080 | + | 0.918216i | \(0.629630\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.0740425 | + | 0.419916i | 0.0740425 | + | 0.419916i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.396080 | + | 0.918216i | 0.396080 | + | 0.918216i | ||||
\(364\) | −1.52173 | + | 0.177865i | −1.52173 | + | 0.177865i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.439408 | − | 1.46773i | −0.439408 | − | 1.46773i | −0.835488 | − | 0.549509i | \(-0.814815\pi\) |
0.396080 | − | 0.918216i | \(-0.370370\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −0.766044 | − | 1.32683i | −0.766044 | − | 1.32683i | ||||
\(373\) | −1.87939 | −1.87939 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.0798028 | − | 1.37016i | 0.0798028 | − | 1.37016i | −0.686242 | − | 0.727374i | \(-0.740741\pi\) |
0.766044 | − | 0.642788i | \(-0.222222\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.57020 | + | 0.571507i | 1.57020 | + | 0.571507i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.286803 | − | 0.957990i | \(-0.592593\pi\) | ||||
0.286803 | + | 0.957990i | \(0.407407\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.49324 | − | 0.749932i | −1.49324 | − | 0.749932i | ||||
\(388\) | −0.0890830 | + | 1.52950i | −0.0890830 | + | 1.52950i | ||||
\(389\) | 0 | 0 | 0.835488 | − | 0.549509i | \(-0.185185\pi\) | ||||
−0.835488 | + | 0.549509i | \(0.814815\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.543613 | − | 1.26024i | −0.543613 | − | 1.26024i | −0.939693 | − | 0.342020i | \(-0.888889\pi\) |
0.396080 | − | 0.918216i | \(-0.370370\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.713197 | + | 0.957990i | 0.713197 | + | 0.957990i | ||||
\(400\) | 0.396080 | + | 0.918216i | 0.396080 | + | 0.918216i | ||||
\(401\) | 0 | 0 | 0.835488 | − | 0.549509i | \(-0.185185\pi\) | ||||
−0.835488 | + | 0.549509i | \(0.814815\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.17365 | + | 2.03282i | −1.17365 | + | 2.03282i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.0996057 | + | 0.564892i | −0.0996057 | + | 0.564892i | 0.893633 | + | 0.448799i | \(0.148148\pi\) |
−0.993238 | + | 0.116093i | \(0.962963\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.0694434 | − | 0.0932786i | −0.0694434 | − | 0.0932786i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.310355 | − | 1.76011i | 0.310355 | − | 1.76011i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.819590 | + | 1.10090i | −0.819590 | + | 1.10090i | 0.173648 | + | 0.984808i | \(0.444444\pi\) |
−0.993238 | + | 0.116093i | \(0.962963\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.36320 | − | 0.159336i | 1.36320 | − | 0.159336i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.686242 | − | 0.727374i | \(-0.259259\pi\) | ||||
−0.686242 | + | 0.727374i | \(0.740741\pi\) | |||||||
\(432\) | 0.173648 | + | 0.984808i | 0.173648 | + | 0.984808i | ||||
\(433\) | −0.786803 | + | 1.82401i | −0.786803 | + | 1.82401i | −0.286803 | + | 0.957990i | \(0.592593\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.939693 | + | 0.342020i | −0.939693 | + | 0.342020i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.344948 | + | 0.0403186i | −0.344948 | + | 0.0403186i | −0.286803 | − | 0.957990i | \(-0.592593\pi\) |
−0.0581448 | + | 0.998308i | \(0.518519\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.893633 | + | 0.448799i | 0.893633 | + | 0.448799i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 0.686242 | − | 0.727374i | \(-0.259259\pi\) | ||||
−0.686242 | + | 0.727374i | \(0.740741\pi\) | |||||||
\(444\) | 0.286803 | + | 0.496758i | 0.286803 | + | 0.496758i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.939693 | − | 0.342020i | −0.939693 | − | 0.342020i | ||||
\(449\) | 0 | 0 | −0.286803 | − | 0.957990i | \(-0.592593\pi\) | ||||
0.286803 | + | 0.957990i | \(0.407407\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.290162 | + | 1.64559i | −0.290162 | + | 1.64559i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.137557 | + | 0.318893i | 0.137557 | + | 0.318893i | 0.973045 | − | 0.230616i | \(-0.0740741\pi\) |
−0.835488 | + | 0.549509i | \(0.814815\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.893633 | − | 0.448799i | \(-0.851852\pi\) | ||||
0.893633 | + | 0.448799i | \(0.148148\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.86668 | − | 0.679415i | 1.86668 | − | 0.679415i | 0.893633 | − | 0.448799i | \(-0.148148\pi\) |
0.973045 | − | 0.230616i | \(-0.0740741\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | 0.973045 | − | 0.230616i | \(-0.0740741\pi\) | ||||
−0.973045 | + | 0.230616i | \(0.925926\pi\) | |||||||
\(468\) | 1.17365 | − | 0.984808i | 1.17365 | − | 0.984808i | ||||
\(469\) | 0.993238 | + | 0.116093i | 0.993238 | + | 0.116093i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.0971586 | − | 0.0639022i | 0.0971586 | − | 0.0639022i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.18624 | − | 0.138652i | −1.18624 | − | 0.138652i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.439408 | − | 0.761077i | 0.439408 | − | 0.761077i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.893633 | − | 0.448799i | 0.893633 | − | 0.448799i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.115503 | − | 1.98312i | 0.115503 | − | 1.98312i | −0.0581448 | − | 0.998308i | \(-0.518519\pi\) |
0.173648 | − | 0.984808i | \(-0.444444\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.770807 | + | 0.182685i | 0.770807 | + | 0.182685i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.28004 | + | 0.841897i | −1.28004 | + | 0.841897i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.78727 | 1.78727 | 0.893633 | − | 0.448799i | \(-0.148148\pi\) | ||||
0.893633 | + | 0.448799i | \(0.148148\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.286803 | − | 0.957990i | \(-0.407407\pi\) | ||||
−0.286803 | + | 0.957990i | \(0.592593\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.26604 | − | 0.460802i | −1.26604 | − | 0.460802i | ||||
\(508\) | 0.479241 | − | 1.60078i | 0.479241 | − | 1.60078i | ||||
\(509\) | 0 | 0 | 0.597159 | − | 0.802123i | \(-0.296296\pi\) | ||||
−0.597159 | + | 0.802123i | \(0.703704\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.49324 | + | 0.982118i | −1.49324 | + | 0.982118i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.12229 | − | 0.408481i | −1.12229 | − | 0.408481i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.661840 | + | 1.53432i | −0.661840 | + | 1.53432i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.993238 | − | 0.116093i | \(-0.0370370\pi\) | ||||
−0.993238 | + | 0.116093i | \(0.962963\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.28971 | + | 1.36702i | 1.28971 | + | 1.36702i | 0.893633 | + | 0.448799i | \(0.148148\pi\) |
0.396080 | + | 0.918216i | \(0.370370\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.939693 | + | 0.342020i | −0.939693 | + | 0.342020i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.939693 | + | 0.342020i | −0.939693 | + | 0.342020i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.914900 | − | 0.767692i | 0.914900 | − | 0.767692i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.137557 | + | 0.780125i | 0.137557 | + | 0.780125i | 0.973045 | + | 0.230616i | \(0.0740741\pi\) |
−0.835488 | + | 0.549509i | \(0.814815\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.606829 | + | 0.509190i | 0.606829 | + | 0.509190i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.207391 | − | 1.17617i | 0.207391 | − | 1.17617i | −0.686242 | − | 0.727374i | \(-0.740741\pi\) |
0.893633 | − | 0.448799i | \(-0.148148\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.05138 | + | 0.882215i | −1.05138 | + | 0.882215i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.707900 | + | 1.64110i | 0.707900 | + | 1.64110i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.77518 | − | 0.207489i | −1.77518 | − | 0.207489i | ||||
\(557\) | 0 | 0 | −0.286803 | − | 0.957990i | \(-0.592593\pi\) | ||||
0.286803 | + | 0.957990i | \(0.407407\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.54277 | − | 0.297208i | 2.54277 | − | 0.297208i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | −0.0581448 | − | 0.998308i | \(-0.518519\pi\) | ||||
0.0581448 | + | 0.998308i | \(0.481481\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.993238 | + | 0.116093i | −0.993238 | + | 0.116093i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 0.396080 | − | 0.918216i | \(-0.370370\pi\) | ||||
−0.396080 | + | 0.918216i | \(0.629630\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.473045 | − | 1.09664i | 0.473045 | − | 1.09664i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
0.973045 | − | 0.230616i | \(-0.0740741\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.973045 | − | 0.230616i | 0.973045 | − | 0.230616i | ||||
\(577\) | −0.0201935 | − | 0.114523i | −0.0201935 | − | 0.114523i | 0.973045 | − | 0.230616i | \(-0.0740741\pi\) |
−0.993238 | + | 0.116093i | \(0.962963\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.82873 | − | 0.665602i | −1.82873 | − | 0.665602i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 0.286803 | − | 0.957990i | \(-0.407407\pi\) | ||||
−0.286803 | + | 0.957990i | \(0.592593\pi\) | |||||||
\(588\) | 0.396080 | − | 0.918216i | 0.396080 | − | 0.918216i | ||||
\(589\) | −0.106393 | − | 1.82670i | −0.106393 | − | 1.82670i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.479241 | − | 0.315202i | 0.479241 | − | 0.315202i | ||||
\(593\) | 0 | 0 | −0.835488 | − | 0.549509i | \(-0.814815\pi\) | ||||
0.835488 | + | 0.549509i | \(0.185185\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.893633 | + | 0.448799i | −0.893633 | + | 0.448799i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.94609 | + | 0.461232i | 1.94609 | + | 0.461232i | 0.973045 | + | 0.230616i | \(0.0740741\pi\) |
0.973045 | + | 0.230616i | \(0.0740741\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.893633 | + | 0.448799i | −0.893633 | + | 0.448799i | ||||
\(604\) | 1.65968 | + | 0.193988i | 1.65968 | + | 0.193988i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.109277 | + | 1.87621i | 0.109277 | + | 1.87621i | 0.396080 | + | 0.918216i | \(0.370370\pi\) |
−0.286803 | + | 0.957990i | \(0.592593\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.37248 | −1.37248 | −0.686242 | − | 0.727374i | \(-0.740741\pi\) | ||||
−0.686242 | + | 0.727374i | \(0.740741\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 0.973045 | − | 0.230616i | \(-0.0740741\pi\) | ||||
−0.973045 | + | 0.230616i | \(0.925926\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.73909 | + | 0.873403i | 1.73909 | + | 0.873403i | 0.973045 | + | 0.230616i | \(0.0740741\pi\) |
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −1.05138 | − | 1.11440i | −1.05138 | − | 1.11440i | ||||
\(625\) | 0.396080 | − | 0.918216i | 0.396080 | − | 0.918216i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.0694434 | − | 0.0932786i | −0.0694434 | − | 0.0932786i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.86668 | + | 0.679415i | 1.86668 | + | 0.679415i | 0.973045 | + | 0.230616i | \(0.0740741\pi\) |
0.893633 | + | 0.448799i | \(0.148148\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.12229 | + | 1.50750i | −1.12229 | + | 1.50750i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.52173 | + | 0.177865i | −1.52173 | + | 0.177865i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | −0.973045 | − | 0.230616i | \(-0.925926\pi\) | ||||
0.973045 | + | 0.230616i | \(0.0740741\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.786803 | − | 1.82401i | −0.786803 | − | 1.82401i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
−0.286803 | − | 0.957990i | \(-0.592593\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.973045 | − | 0.230616i | \(-0.925926\pi\) | ||||
0.973045 | + | 0.230616i | \(0.0740741\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.766044 | − | 1.32683i | −0.766044 | − | 1.32683i | ||||
\(652\) | 0.137557 | − | 0.780125i | 0.137557 | − | 0.780125i | ||||
\(653\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.707900 | − | 1.64110i | 0.707900 | − | 1.64110i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | −0.973045 | − | 0.230616i | \(-0.925926\pi\) | ||||
0.973045 | + | 0.230616i | \(0.0740741\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.16212 | + | 0.275428i | 1.16212 | + | 0.275428i | 0.766044 | − | 0.642788i | \(-0.222222\pi\) |
0.396080 | + | 0.918216i | \(0.370370\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.227194 | − | 0.526695i | −0.227194 | − | 0.526695i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.82873 | + | 0.665602i | −1.82873 | + | 0.665602i | −0.835488 | + | 0.549509i | \(0.814815\pi\) |
−0.993238 | + | 0.116093i | \(0.962963\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.597159 | − | 0.802123i | 0.597159 | − | 0.802123i | ||||
\(676\) | −0.386409 | + | 1.29070i | −0.386409 | + | 1.29070i | ||||
\(677\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.0890830 | + | 1.52950i | −0.0890830 | + | 1.52950i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 0.993238 | − | 0.116093i | \(-0.0370370\pi\) | ||||
−0.993238 | + | 0.116093i | \(0.962963\pi\) | |||||||
\(684\) | −0.342534 | + | 1.14414i | −0.342534 | + | 1.14414i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.347296 | 0.347296 | ||||||||
\(688\) | 1.57020 | + | 0.571507i | 1.57020 | + | 0.571507i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.238329 | − | 0.252614i | −0.238329 | − | 0.252614i | 0.597159 | − | 0.802123i | \(-0.296296\pi\) |
−0.835488 | + | 0.549509i | \(0.814815\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.396080 | + | 0.918216i | 0.396080 | + | 0.918216i | ||||
\(701\) | 0 | 0 | −0.893633 | − | 0.448799i | \(-0.851852\pi\) | ||||
0.893633 | + | 0.448799i | \(0.148148\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.0398332 | + | 0.683909i | 0.0398332 | + | 0.683909i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.17365 | − | 0.984808i | 1.17365 | − | 0.984808i | 0.173648 | − | 0.984808i | \(-0.444444\pi\) |
1.00000 | \(0\) | |||||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.49324 | − | 0.982118i | −1.49324 | − | 0.982118i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.835488 | − | 0.549509i | \(-0.185185\pi\) | ||||
−0.835488 | + | 0.549509i | \(0.814815\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.0694434 | − | 0.0932786i | −0.0694434 | − | 0.0932786i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.89363 | + | 0.448799i | 1.89363 | + | 0.448799i | ||||
\(724\) | 0.473045 | − | 0.635410i | 0.473045 | − | 0.635410i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.0460600 | − | 0.106779i | −0.0460600 | − | 0.106779i | 0.893633 | − | 0.448799i | \(-0.148148\pi\) |
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.766044 | − | 0.642788i | 0.766044 | − | 0.642788i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0.941855 | + | 0.998308i | 0.941855 | + | 0.998308i | ||||
\(733\) | −0.573606 | + | 1.91598i | −0.573606 | + | 1.91598i | −0.286803 | + | 0.957990i | \(0.592593\pi\) |
−0.286803 | + | 0.957990i | \(0.592593\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.993238 | − | 0.116093i | 0.993238 | − | 0.116093i | 0.396080 | − | 0.918216i | \(-0.370370\pi\) |
0.597159 | + | 0.802123i | \(0.296296\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.78048 | − | 0.421981i | 1.78048 | − | 0.421981i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.835488 | − | 0.549509i | \(-0.814815\pi\) | ||||
0.835488 | + | 0.549509i | \(0.185185\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.558145 | − | 0.132283i | −0.558145 | − | 0.132283i | −0.0581448 | − | 0.998308i | \(-0.518519\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.173648 | + | 0.984808i | 0.173648 | + | 0.984808i | ||||
\(757\) | 1.57020 | + | 1.03274i | 1.57020 | + | 1.03274i | 0.973045 | + | 0.230616i | \(0.0740741\pi\) |
0.597159 | + | 0.802123i | \(0.296296\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.939693 | + | 0.342020i | −0.939693 | + | 0.342020i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −0.286803 | − | 0.957990i | −0.286803 | − | 0.957990i | ||||
\(769\) | 1.65968 | + | 1.09159i | 1.65968 | + | 1.09159i | 0.893633 | + | 0.448799i | \(0.148148\pi\) |
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −0.558145 | + | 1.86433i | −0.558145 | + | 1.86433i | ||||
\(773\) | 0 | 0 | −0.597159 | − | 0.802123i | \(-0.703704\pi\) | ||||
0.597159 | + | 0.802123i | \(0.296296\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.49079 | + | 0.353324i | 1.49079 | + | 0.353324i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.286803 | + | 0.496758i | 0.286803 | + | 0.496758i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.939693 | − | 0.342020i | −0.939693 | − | 0.342020i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.97304 | − | 0.230616i | 1.97304 | − | 0.230616i | 0.973045 | − | 0.230616i | \(-0.0740741\pi\) |
1.00000 | \(0\) | |||||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.603080 | − | 2.01443i | 0.603080 | − | 2.01443i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(797\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.73909 | − | 0.873403i | 1.73909 | − | 0.873403i | 0.766044 | − | 0.642788i | \(-0.222222\pi\) |
0.973045 | − | 0.230616i | \(-0.0740741\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.16212 | − | 1.56100i | 1.16212 | − | 1.56100i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.52878 | + | 1.28280i | −1.52878 | + | 1.28280i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.17365 | − | 0.984808i | 1.17365 | − | 0.984808i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.835488 | − | 0.549509i | \(-0.814815\pi\) | ||||
0.835488 | + | 0.549509i | \(0.185185\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.0694434 | − | 1.19230i | −0.0694434 | − | 1.19230i | −0.835488 | − | 0.549509i | \(-0.814815\pi\) |
0.766044 | − | 0.642788i | \(-0.222222\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.0890830 | − | 0.0747496i | −0.0890830 | − | 0.0747496i | 0.597159 | − | 0.802123i | \(-0.296296\pi\) |
−0.686242 | + | 0.727374i | \(0.740741\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.939693 | − | 1.62760i | 0.939693 | − | 1.62760i | ||||
\(832\) | −1.05138 | + | 1.11440i | −1.05138 | + | 1.11440i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.36912 | + | 0.687600i | 1.36912 | + | 0.687600i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.286803 | + | 0.957990i | −0.286803 | + | 0.957990i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.57020 | + | 1.03274i | 1.57020 | + | 1.03274i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.893633 | − | 0.448799i | 0.893633 | − | 0.448799i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.238329 | − | 1.35163i | −0.238329 | − | 1.35163i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.539014 | − | 0.196185i | 0.539014 | − | 0.196185i | −0.0581448 | − | 0.998308i | \(-0.518519\pi\) |
0.597159 | + | 0.802123i | \(0.296296\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | −0.396080 | − | 0.918216i | \(-0.629630\pi\) | ||||
0.396080 | + | 0.918216i | \(0.370370\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.28971 | − | 1.36702i | 1.28971 | − | 1.36702i | 0.396080 | − | 0.918216i | \(-0.370370\pi\) |
0.893633 | − | 0.448799i | \(-0.148148\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 0.286803 | − | 0.957990i | \(-0.407407\pi\) | ||||
−0.286803 | + | 0.957990i | \(0.592593\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.973045 | + | 0.230616i | 0.973045 | + | 0.230616i | ||||
\(868\) | −1.28004 | + | 0.841897i | −1.28004 | + | 0.841897i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.766044 | − | 1.32683i | 0.766044 | − | 1.32683i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.766044 | − | 1.32683i | −0.766044 | − | 1.32683i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.67948 | − | 0.611281i | −1.67948 | − | 0.611281i | ||||
\(877\) | −0.227194 | − | 0.758881i | −0.227194 | − | 0.758881i | −0.993238 | − | 0.116093i | \(-0.962963\pi\) |
0.766044 | − | 0.642788i | \(-0.222222\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | −0.686242 | − | 0.727374i | \(-0.740741\pi\) | ||||
0.686242 | + | 0.727374i | \(0.259259\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.543613 | − | 1.26024i | −0.543613 | − | 1.26024i | −0.939693 | − | 0.342020i | \(-0.888889\pi\) |
0.396080 | − | 0.918216i | \(-0.370370\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.993238 | − | 0.116093i | \(-0.962963\pi\) | ||||
0.993238 | + | 0.116093i | \(0.0370370\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.479241 | − | 1.60078i | 0.479241 | − | 1.60078i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −0.512593 | + | 0.257434i | −0.512593 | + | 0.257434i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −0.835488 | − | 0.549509i | −0.835488 | − | 0.549509i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.661840 | + | 1.53432i | −0.661840 | + | 1.53432i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.512593 | − | 0.257434i | −0.512593 | − | 0.257434i | 0.173648 | − | 0.984808i | \(-0.444444\pi\) |
−0.686242 | + | 0.727374i | \(0.740741\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.993238 | − | 0.116093i | \(-0.962963\pi\) | ||||
0.993238 | + | 0.116093i | \(0.0370370\pi\) | |||||||
\(912\) | 1.16212 | + | 0.275428i | 1.16212 | + | 0.275428i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.0201935 | − | 0.346709i | −0.0201935 | − | 0.346709i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.115503 | + | 1.98312i | 0.115503 | + | 1.98312i | 0.173648 | + | 0.984808i | \(0.444444\pi\) |
−0.0581448 | + | 0.998308i | \(0.518519\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.103920 | − | 1.78424i | −0.103920 | − | 1.78424i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.558145 | − | 0.132283i | −0.558145 | − | 0.132283i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.109277 | + | 0.0397734i | 0.109277 | + | 0.0397734i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | 0.893633 | − | 0.448799i | \(-0.148148\pi\) | ||||
−0.893633 | + | 0.448799i | \(0.851852\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.914900 | − | 0.767692i | 0.914900 | − | 0.767692i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.109277 | + | 1.87621i | 0.109277 | + | 1.87621i | 0.396080 | + | 0.918216i | \(0.370370\pi\) |
−0.286803 | + | 0.957990i | \(0.592593\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.342534 | + | 1.14414i | −0.342534 | + | 1.14414i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.286803 | − | 0.957990i | \(-0.592593\pi\) | ||||
0.286803 | + | 0.957990i | \(0.407407\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(948\) | −0.893633 | + | 1.54782i | −0.893633 | + | 1.54782i | ||||
\(949\) | 0.475492 | + | 2.69665i | 0.475492 | + | 2.69665i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 0.0581448 | − | 0.998308i | \(-0.481481\pi\) | ||||
−0.0581448 | + | 0.998308i | \(0.518519\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.0783383 | + | 1.34502i | −0.0783383 | + | 1.34502i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0.337935 | − | 1.91652i | 0.337935 | − | 1.91652i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.86668 | − | 0.218183i | 1.86668 | − | 0.218183i | 0.893633 | − | 0.448799i | \(-0.148148\pi\) |
0.973045 | + | 0.230616i | \(0.0740741\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.993238 | − | 0.116093i | \(-0.0370370\pi\) | ||||
−0.993238 | + | 0.116093i | \(0.962963\pi\) | |||||||
\(972\) | −0.686242 | − | 0.727374i | −0.686242 | − | 0.727374i | ||||
\(973\) | −1.77518 | − | 0.207489i | −1.77518 | − | 0.207489i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.0890830 | + | 1.52950i | −0.0890830 | + | 1.52950i | ||||
\(976\) | 0.941855 | − | 0.998308i | 0.941855 | − | 0.998308i | ||||
\(977\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.597159 | − | 0.802123i | 0.597159 | − | 0.802123i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.524793 | − | 1.75293i | −0.524793 | − | 1.75293i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.16212 | + | 1.56100i | 1.16212 | + | 1.56100i | 0.766044 | + | 0.642788i | \(0.222222\pi\) |
0.396080 | + | 0.918216i | \(0.370370\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.14669 | − | 1.21542i | 1.14669 | − | 1.21542i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.326352 | + | 0.118782i | −0.326352 | + | 0.118782i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.512593 | − | 0.257434i | −0.512593 | − | 0.257434i |
(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 | 2289.1.en.a.2195.1 | yes | 18 | |
3.2 | odd | 2 | CM | 2289.1.en.a.2195.1 | yes | 18 | |
7.2 | even | 3 | 2289.1.ep.a.233.1 | yes | 18 | ||
21.2 | odd | 6 | 2289.1.ep.a.233.1 | yes | 18 | ||
109.80 | even | 27 | 2289.1.ep.a.1061.1 | yes | 18 | ||
327.80 | odd | 54 | 2289.1.ep.a.1061.1 | yes | 18 | ||
763.625 | even | 27 | inner | 2289.1.en.a.1388.1 | ✓ | 18 | |
2289.1388 | odd | 54 | inner | 2289.1.en.a.1388.1 | ✓ | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2289.1.en.a.1388.1 | ✓ | 18 | 763.625 | even | 27 | inner | |
2289.1.en.a.1388.1 | ✓ | 18 | 2289.1388 | odd | 54 | inner | |
2289.1.en.a.2195.1 | yes | 18 | 1.1 | even | 1 | trivial | |
2289.1.en.a.2195.1 | yes | 18 | 3.2 | odd | 2 | CM | |
2289.1.ep.a.233.1 | yes | 18 | 7.2 | even | 3 | ||
2289.1.ep.a.233.1 | yes | 18 | 21.2 | odd | 6 | ||
2289.1.ep.a.1061.1 | yes | 18 | 109.80 | even | 27 | ||
2289.1.ep.a.1061.1 | yes | 18 | 327.80 | odd | 54 |