Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2717,1,Mod(142,2717)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2717, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([9, 9, 8]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2717.142");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2717 = 11 \cdot 13 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 2717.db (of order \(18\), degree \(6\), 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: | \(1.35595963932\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{18})\) |
Coefficient field: | \(\Q(\zeta_{45})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{24} - x^{21} + x^{15} - x^{12} + x^{9} - x^{3} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{45}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{45} - \cdots)\) |
Embedding invariants
Embedding label | 1715.4 | ||
Root | \(-0.882948 - 0.469472i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2717.1715 |
Dual form | 2717.1.db.c.1429.4 |
$q$-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 \(\left(\mathbb{Z}/2717\mathbb{Z}\right)^\times\).
\(n\) | \(210\) | \(287\) | \(2224\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{8}{9}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.59381 | − | 0.580099i | 1.59381 | − | 0.580099i | 0.615661 | − | 0.788011i | \(-0.288889\pi\) |
0.978148 | + | 0.207912i | \(0.0666667\pi\) | |||||||
\(3\) | −0.130100 | + | 0.737831i | −0.130100 | + | 0.737831i | 0.848048 | + | 0.529919i | \(0.177778\pi\) |
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(4\) | 1.43767 | − | 1.20635i | 1.43767 | − | 1.20635i | ||||
\(5\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(6\) | 0.220661 | + | 1.25143i | 0.220661 | + | 1.25143i | ||||
\(7\) | −0.241922 | − | 0.419021i | −0.241922 | − | 0.419021i | 0.719340 | − | 0.694658i | \(-0.244444\pi\) |
−0.961262 | + | 0.275637i | \(0.911111\pi\) | |||||||
\(8\) | 0.743520 | − | 1.28781i | 0.743520 | − | 1.28781i | ||||
\(9\) | 0.412224 | + | 0.150037i | 0.412224 | + | 0.150037i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(12\) | 0.703040 | + | 1.21770i | 0.703040 | + | 1.21770i | ||||
\(13\) | −0.173648 | − | 0.984808i | −0.173648 | − | 0.984808i | ||||
\(14\) | −0.628651 | − | 0.527501i | −0.628651 | − | 0.527501i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.112076 | − | 0.635614i | 0.112076 | − | 0.635614i | ||||
\(17\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(18\) | 0.744043 | 0.744043 | ||||||||
\(19\) | −0.990268 | − | 0.139173i | −0.990268 | − | 0.139173i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.340641 | − | 0.123983i | 0.340641 | − | 0.123983i | ||||
\(22\) | 0.294524 | − | 1.67033i | 0.294524 | − | 1.67033i | ||||
\(23\) | 0.856733 | − | 0.718885i | 0.856733 | − | 0.718885i | −0.104528 | − | 0.994522i | \(-0.533333\pi\) |
0.961262 | + | 0.275637i | \(0.0888889\pi\) | |||||||
\(24\) | 0.853457 | + | 0.716136i | 0.853457 | + | 0.716136i | ||||
\(25\) | 0.173648 | + | 0.984808i | 0.173648 | + | 0.984808i | ||||
\(26\) | −0.848048 | − | 1.46886i | −0.848048 | − | 1.46886i | ||||
\(27\) | −0.538939 | + | 0.933469i | −0.538939 | + | 0.933469i | ||||
\(28\) | −0.853288 | − | 0.310571i | −0.853288 | − | 0.310571i | ||||
\(29\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(32\) | 0.0681302 | + | 0.386385i | 0.0681302 | + | 0.386385i | ||||
\(33\) | 0.573931 | + | 0.481585i | 0.573931 | + | 0.481585i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.773638 | − | 0.281581i | 0.773638 | − | 0.281581i | ||||
\(37\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(38\) | −1.65903 | + | 0.352638i | −1.65903 | + | 0.352638i | ||||
\(39\) | 0.749213 | 0.749213 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.333843 | + | 1.89332i | −0.333843 | + | 1.89332i | 0.104528 | + | 0.994522i | \(0.466667\pi\) |
−0.438371 | + | 0.898794i | \(0.644444\pi\) | |||||||
\(42\) | 0.470994 | − | 0.395211i | 0.470994 | − | 0.395211i | ||||
\(43\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(44\) | −0.325893 | − | 1.84823i | −0.325893 | − | 1.84823i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.948445 | − | 1.64275i | 0.948445 | − | 1.64275i | ||||
\(47\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(48\) | 0.454395 | + | 0.165386i | 0.454395 | + | 0.165386i | ||||
\(49\) | 0.382948 | − | 0.663285i | 0.382948 | − | 0.663285i | ||||
\(50\) | 0.848048 | + | 1.46886i | 0.848048 | + | 1.46886i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.43767 | − | 1.20635i | −1.43767 | − | 1.20635i | ||||
\(53\) | −0.943248 | + | 0.791479i | −0.943248 | + | 0.791479i | −0.978148 | − | 0.207912i | \(-0.933333\pi\) |
0.0348995 | + | 0.999391i | \(0.488889\pi\) | |||||||
\(54\) | −0.317461 | + | 1.80041i | −0.317461 | + | 1.80041i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.719495 | −0.719495 | ||||||||
\(57\) | 0.231520 | − | 0.712544i | 0.231520 | − | 0.712544i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.0368572 | − | 0.209028i | −0.0368572 | − | 0.209028i | ||||
\(64\) | 0.655438 | + | 1.13525i | 0.655438 | + | 1.13525i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.19410 | + | 0.434618i | 1.19410 | + | 0.434618i | ||||
\(67\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.418955 | + | 0.725651i | 0.418955 | + | 0.725651i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(72\) | 0.499717 | − | 0.419312i | 0.499717 | − | 0.419312i | ||||
\(73\) | −0.107320 | + | 0.608645i | −0.107320 | + | 0.608645i | 0.882948 | + | 0.469472i | \(0.155556\pi\) |
−0.990268 | + | 0.139173i | \(0.955556\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.749213 | −0.749213 | ||||||||
\(76\) | −1.59157 | + | 0.994522i | −1.59157 | + | 0.994522i | ||||
\(77\) | −0.483844 | −0.483844 | ||||||||
\(78\) | 1.19410 | − | 0.434618i | 1.19410 | − | 0.434618i | ||||
\(79\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.282579 | − | 0.237112i | −0.282579 | − | 0.237112i | ||||
\(82\) | 0.566229 | + | 3.21125i | 0.566229 | + | 3.21125i | ||||
\(83\) | −0.997564 | − | 1.72783i | −0.997564 | − | 1.72783i | −0.559193 | − | 0.829038i | \(-0.688889\pi\) |
−0.438371 | − | 0.898794i | \(-0.644444\pi\) | |||||||
\(84\) | 0.340162 | − | 0.589177i | 0.340162 | − | 0.589177i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.743520 | − | 1.28781i | −0.743520 | − | 1.28781i | ||||
\(89\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.370646 | + | 0.311009i | −0.370646 | + | 0.311009i | ||||
\(92\) | 0.364474 | − | 2.06703i | 0.364474 | − | 2.06703i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.293951 | −0.293951 | ||||||||
\(97\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(98\) | 0.225575 | − | 1.27930i | 0.225575 | − | 1.27930i | ||||
\(99\) | 0.336048 | − | 0.281978i | 0.336048 | − | 0.281978i | ||||
\(100\) | 1.43767 | + | 1.20635i | 1.43767 | + | 1.20635i | ||||
\(101\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.438371 | + | 0.759281i | −0.438371 | + | 0.759281i | −0.997564 | − | 0.0697565i | \(-0.977778\pi\) |
0.559193 | + | 0.829038i | \(0.311111\pi\) | |||||||
\(104\) | −1.39736 | − | 0.508597i | −1.39736 | − | 0.508597i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.04422 | + | 1.80864i | −1.04422 | + | 1.80864i | ||||
\(107\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(108\) | 0.351273 | + | 1.99217i | 0.351273 | + | 1.99217i | ||||
\(109\) | −1.02517 | − | 0.860218i | −1.02517 | − | 0.860218i | −0.0348995 | − | 0.999391i | \(-0.511111\pi\) |
−0.990268 | + | 0.139173i | \(0.955556\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.293449 | + | 0.106807i | −0.293449 | + | 0.106807i | ||||
\(113\) | −1.76590 | −1.76590 | −0.882948 | − | 0.469472i | \(-0.844444\pi\) | ||||
−0.882948 | + | 0.469472i | \(0.844444\pi\) | |||||||
\(114\) | −0.0443481 | − | 1.26996i | −0.0443481 | − | 1.26996i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.0761759 | − | 0.432015i | 0.0761759 | − | 0.432015i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.35351 | − | 0.492639i | −1.35351 | − | 0.492639i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.180000 | − | 0.311770i | −0.180000 | − | 0.311770i | ||||
\(127\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(128\) | 1.40265 | + | 1.17696i | 1.40265 | + | 1.17696i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(132\) | 1.40608 | 1.40608 | ||||||||
\(133\) | 0.181251 | + | 0.448612i | 0.181251 | + | 0.448612i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(138\) | 1.08868 | + | 0.913514i | 1.08868 | + | 0.913514i | ||||
\(139\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.939693 | − | 0.342020i | −0.939693 | − | 0.342020i | ||||
\(144\) | 0.141566 | − | 0.245200i | 0.141566 | − | 0.245200i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.182026 | + | 1.03232i | 0.182026 | + | 1.03232i | ||||
\(147\) | 0.439571 | + | 0.368844i | 0.439571 | + | 0.368844i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.317271 | + | 1.79933i | −0.317271 | + | 1.79933i | 0.241922 | + | 0.970296i | \(0.422222\pi\) |
−0.559193 | + | 0.829038i | \(0.688889\pi\) | |||||||
\(150\) | −1.19410 | + | 0.434618i | −1.19410 | + | 0.434618i | ||||
\(151\) | 1.00000 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(152\) | −0.915513 | + | 1.17180i | −0.915513 | + | 1.17180i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.771155 | + | 0.280677i | −0.771155 | + | 0.280677i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.07712 | − | 0.903811i | 1.07712 | − | 0.903811i | ||||
\(157\) | −0.160147 | − | 0.134379i | −0.160147 | − | 0.134379i | 0.559193 | − | 0.829038i | \(-0.311111\pi\) |
−0.719340 | + | 0.694658i | \(0.755556\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.461262 | − | 0.798929i | −0.461262 | − | 0.798929i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.508490 | − | 0.185075i | −0.508490 | − | 0.185075i | ||||
\(162\) | −0.587925 | − | 0.213987i | −0.587925 | − | 0.213987i | ||||
\(163\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(164\) | 1.80404 | + | 3.12469i | 1.80404 | + | 3.12469i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.59224 | − | 2.17515i | −2.59224 | − | 2.17515i | ||||
\(167\) | 1.35275 | − | 1.13510i | 1.35275 | − | 1.13510i | 0.374607 | − | 0.927184i | \(-0.377778\pi\) |
0.978148 | − | 0.207912i | \(-0.0666667\pi\) | |||||||
\(168\) | 0.0936059 | − | 0.530865i | 0.0936059 | − | 0.530865i | ||||
\(169\) | −0.939693 | + | 0.342020i | −0.939693 | + | 0.342020i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.387331 | − | 0.205948i | −0.387331 | − | 0.205948i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.370646 | − | 0.311009i | 0.370646 | − | 0.311009i | ||||
\(176\) | −0.494420 | − | 0.414868i | −0.494420 | − | 0.414868i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.173648 | + | 0.300767i | −0.173648 | + | 0.300767i | −0.939693 | − | 0.342020i | \(-0.888889\pi\) |
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.0655896 | − | 0.0238727i | −0.0655896 | − | 0.0238727i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
−0.374607 | + | 0.927184i | \(0.622222\pi\) | |||||||
\(182\) | −0.410323 | + | 0.710700i | −0.410323 | + | 0.710700i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.288791 | − | 1.63782i | −0.288791 | − | 1.63782i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.521524 | 0.521524 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.33826 | 1.33826 | 0.669131 | − | 0.743145i | \(-0.266667\pi\) | ||||
0.669131 | + | 0.743145i | \(0.266667\pi\) | |||||||
\(192\) | −0.922896 | + | 0.335907i | −0.922896 | + | 0.335907i | ||||
\(193\) | −0.194206 | + | 1.10140i | −0.194206 | + | 1.10140i | 0.719340 | + | 0.694658i | \(0.244444\pi\) |
−0.913545 | + | 0.406737i | \(0.866667\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.249600 | − | 1.41555i | −0.249600 | − | 1.41555i | ||||
\(197\) | 0.0348995 | + | 0.0604477i | 0.0348995 | + | 0.0604477i | 0.882948 | − | 0.469472i | \(-0.155556\pi\) |
−0.848048 | + | 0.529919i | \(0.822222\pi\) | |||||||
\(198\) | 0.372021 | − | 0.644360i | 0.372021 | − | 0.644360i | ||||
\(199\) | −1.86110 | − | 0.677383i | −1.86110 | − | 0.677383i | −0.978148 | − | 0.207912i | \(-0.933333\pi\) |
−0.882948 | − | 0.469472i | \(-0.844444\pi\) | |||||||
\(200\) | 1.39736 | + | 0.508597i | 1.39736 | + | 0.508597i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −0.258222 | + | 1.46445i | −0.258222 | + | 1.46445i | ||||
\(207\) | 0.461025 | − | 0.167800i | 0.461025 | − | 0.167800i | ||||
\(208\) | −0.645419 | −0.645419 | ||||||||
\(209\) | −0.615661 | + | 0.788011i | −0.615661 | + | 0.788011i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(212\) | −0.401279 | + | 2.27577i | −0.401279 | + | 2.27577i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0.801423 | + | 1.38811i | 0.801423 | + | 1.38811i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −2.13293 | − | 0.776324i | −2.13293 | − | 0.776324i | ||||
\(219\) | −0.435115 | − | 0.158369i | −0.435115 | − | 0.158369i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(224\) | 0.145421 | − | 0.122023i | 0.145421 | − | 0.122023i | ||||
\(225\) | −0.0761759 | + | 0.432015i | −0.0761759 | + | 0.432015i | ||||
\(226\) | −2.81450 | + | 1.02439i | −2.81450 | + | 1.02439i | ||||
\(227\) | −0.618034 | −0.618034 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(228\) | −0.526727 | − | 1.30369i | −0.526727 | − | 1.30369i | ||||
\(229\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.0629478 | − | 0.356995i | 0.0629478 | − | 0.356995i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(234\) | −0.129202 | − | 0.732739i | −0.129202 | − | 0.732739i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.990268 | − | 1.71519i | 0.990268 | − | 1.71519i | 0.374607 | − | 0.927184i | \(-0.377778\pi\) |
0.615661 | − | 0.788011i | \(-0.288889\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.346450 | + | 1.96482i | 0.346450 | + | 1.96482i | 0.241922 | + | 0.970296i | \(0.422222\pi\) |
0.104528 | + | 0.994522i | \(0.466667\pi\) | |||||||
\(242\) | −1.29929 | − | 1.09023i | −1.29929 | − | 1.09023i | ||||
\(243\) | −0.613990 | + | 0.515199i | −0.613990 | + | 0.515199i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.44302 | −2.44302 | ||||||||
\(247\) | 0.0348995 | + | 0.999391i | 0.0348995 | + | 0.999391i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.40463 | − | 0.511244i | 1.40463 | − | 0.511244i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.23949 | + | 1.04005i | −1.23949 | + | 1.04005i | −0.241922 | + | 0.970296i | \(0.577778\pi\) |
−0.997564 | + | 0.0697565i | \(0.977778\pi\) | |||||||
\(252\) | −0.305148 | − | 0.256050i | −0.305148 | − | 0.256050i | ||||
\(253\) | −0.194206 | − | 1.10140i | −0.194206 | − | 1.10140i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.68648 | + | 0.613830i | 1.68648 | + | 0.613830i | ||||
\(257\) | 1.52045 | + | 0.553400i | 1.52045 | + | 0.553400i | 0.961262 | − | 0.275637i | \(-0.0888889\pi\) |
0.559193 | + | 0.829038i | \(0.311111\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(264\) | 1.04692 | − | 0.381048i | 1.04692 | − | 0.381048i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.549119 | + | 0.609859i | 0.549119 | + | 0.609859i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.333843 | − | 1.89332i | 0.333843 | − | 1.89332i | −0.104528 | − | 0.994522i | \(-0.533333\pi\) |
0.438371 | − | 0.898794i | \(-0.355556\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.0534691 | − | 0.0448659i | −0.0534691 | − | 0.0448659i | 0.615661 | − | 0.788011i | \(-0.288889\pi\) |
−0.669131 | + | 0.743145i | \(0.733333\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.181251 | − | 0.313936i | −0.181251 | − | 0.313936i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.939693 | + | 0.342020i | 0.939693 | + | 0.342020i | ||||
\(276\) | 1.47770 | + | 0.537840i | 1.47770 | + | 0.537840i | ||||
\(277\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.0534691 | + | 0.0448659i | −0.0534691 | + | 0.0448659i | −0.669131 | − | 0.743145i | \(-0.733333\pi\) |
0.615661 | + | 0.788011i | \(0.288889\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.69610 | −1.69610 | ||||||||
\(287\) | 0.874103 | − | 0.318147i | 0.874103 | − | 0.318147i | ||||
\(288\) | −0.0298873 | + | 0.169499i | −0.0298873 | + | 0.169499i | ||||
\(289\) | 0.766044 | − | 0.642788i | 0.766044 | − | 0.642788i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.579945 | + | 1.00449i | 0.579945 | + | 1.00449i | ||||
\(293\) | 0.766044 | − | 1.32683i | 0.766044 | − | 1.32683i | −0.173648 | − | 0.984808i | \(-0.555556\pi\) |
0.939693 | − | 0.342020i | \(-0.111111\pi\) | |||||||
\(294\) | 0.914558 | + | 0.332872i | 0.914558 | + | 0.332872i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.538939 | + | 0.933469i | 0.538939 | + | 0.933469i | ||||
\(298\) | 0.538122 | + | 3.05184i | 0.538122 | + | 3.05184i | ||||
\(299\) | −0.856733 | − | 0.718885i | −0.856733 | − | 0.718885i | ||||
\(300\) | −1.07712 | + | 0.903811i | −1.07712 | + | 0.903811i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1.59381 | − | 0.580099i | 1.59381 | − | 0.580099i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.199446 | + | 0.613830i | −0.199446 | + | 0.613830i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.0603074 | + | 0.342020i | −0.0603074 | + | 0.342020i | 0.939693 | + | 0.342020i | \(0.111111\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(308\) | −0.695607 | + | 0.583683i | −0.695607 | + | 0.583683i | ||||
\(309\) | −0.503189 | − | 0.422226i | −0.503189 | − | 0.422226i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.374607 | + | 0.648838i | 0.374607 | + | 0.648838i | 0.990268 | − | 0.139173i | \(-0.0444444\pi\) |
−0.615661 | + | 0.788011i | \(0.711111\pi\) | |||||||
\(312\) | 0.557055 | − | 0.964847i | 0.557055 | − | 0.964847i | ||||
\(313\) | −1.71690 | − | 0.624902i | −1.71690 | − | 0.624902i | −0.719340 | − | 0.694658i | \(-0.755556\pi\) |
−0.997564 | + | 0.0697565i | \(0.977778\pi\) | |||||||
\(314\) | −0.333197 | − | 0.121274i | −0.333197 | − | 0.121274i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(318\) | −1.19862 | − | 1.00576i | −1.19862 | − | 1.00576i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.917798 | −0.917798 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −0.692294 | −0.692294 | ||||||||
\(325\) | 0.939693 | − | 0.342020i | 0.939693 | − | 0.342020i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.768069 | − | 0.644486i | 0.768069 | − | 0.644486i | ||||
\(328\) | 2.19002 | + | 1.83764i | 2.19002 | + | 1.83764i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(332\) | −3.51853 | − | 1.28064i | −3.51853 | − | 1.28064i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.49756 | − | 2.59386i | 1.49756 | − | 2.59386i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.0406278 | − | 0.230411i | −0.0406278 | − | 0.230411i | ||||
\(337\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(338\) | −1.29929 | + | 1.09023i | −1.29929 | + | 1.09023i | ||||
\(339\) | 0.229742 | − | 1.30293i | 0.229742 | − | 1.30293i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −0.736802 | − | 0.103551i | −0.736802 | − | 0.103551i | ||||
\(343\) | −0.854417 | −0.854417 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.438371 | + | 0.759281i | 0.438371 | + | 0.759281i | 0.997564 | − | 0.0697565i | \(-0.0222222\pi\) |
−0.559193 | + | 0.829038i | \(0.688889\pi\) | |||||||
\(350\) | 0.410323 | − | 0.710700i | 0.410323 | − | 0.710700i | ||||
\(351\) | 1.01287 | + | 0.368656i | 1.01287 | + | 0.368656i | ||||
\(352\) | 0.368685 | + | 0.134190i | 0.368685 | + | 0.134190i | ||||
\(353\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.102287 | + | 0.580099i | −0.102287 | + | 0.580099i | ||||
\(359\) | 1.05094 | − | 0.382510i | 1.05094 | − | 0.382510i | 0.241922 | − | 0.970296i | \(-0.422222\pi\) |
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.961262 | + | 0.275637i | 0.961262 | + | 0.275637i | ||||
\(362\) | −0.118386 | −0.118386 | ||||||||
\(363\) | 0.704030 | − | 0.256246i | 0.704030 | − | 0.256246i | ||||
\(364\) | −0.157681 | + | 0.894255i | −0.157681 | + | 0.894255i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.107320 | + | 0.608645i | 0.107320 | + | 0.608645i | 0.990268 | + | 0.139173i | \(0.0444444\pi\) |
−0.882948 | + | 0.469472i | \(0.844444\pi\) | |||||||
\(368\) | −0.360914 | − | 0.625121i | −0.360914 | − | 0.625121i | ||||
\(369\) | −0.421686 | + | 0.730381i | −0.421686 | + | 0.730381i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.559839 | + | 0.203765i | 0.559839 | + | 0.203765i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0.831210 | − | 0.302536i | 0.831210 | − | 0.302536i | ||||
\(379\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.13293 | − | 0.776324i | 2.13293 | − | 0.776324i | ||||
\(383\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(384\) | −1.05088 | + | 0.881794i | −1.05088 | + | 0.881794i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.329391 | + | 1.86807i | 0.329391 | + | 1.86807i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.83832 | + | 0.669092i | 1.83832 | + | 0.669092i | 0.990268 | + | 0.139173i | \(0.0444444\pi\) |
0.848048 | + | 0.529919i | \(0.177778\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −0.569458 | − | 0.986330i | −0.569458 | − | 0.986330i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.0906888 | + | 0.0760969i | 0.0906888 | + | 0.0760969i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.142963 | − | 0.810781i | 0.142963 | − | 0.810781i | ||||
\(397\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(398\) | −3.35918 | −3.35918 | ||||||||
\(399\) | −0.354581 | + | 0.0753684i | −0.354581 | + | 0.0753684i | ||||
\(400\) | 0.645419 | 0.645419 | ||||||||
\(401\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.76604 | − | 0.642788i | −1.76604 | − | 0.642788i | −0.766044 | − | 0.642788i | \(-0.777778\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.285724 | + | 1.62042i | 0.285724 | + | 1.62042i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0.637446 | − | 0.534881i | 0.637446 | − | 0.534881i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.368685 | − | 0.134190i | 0.368685 | − | 0.134190i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.524123 | + | 1.61308i | −0.524123 | + | 1.61308i | ||||
\(419\) | 1.82709 | 1.82709 | 0.913545 | − | 0.406737i | \(-0.133333\pi\) | ||||
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.317954 | + | 1.80321i | 0.317954 | + | 1.80321i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.374607 | − | 0.648838i | 0.374607 | − | 0.648838i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.152245 | − | 0.863423i | −0.152245 | − | 0.863423i | −0.961262 | − | 0.275637i | \(-0.911111\pi\) |
0.809017 | − | 0.587785i | \(-0.200000\pi\) | |||||||
\(432\) | 0.532924 | + | 0.447176i | 0.532924 | + | 0.447176i | ||||
\(433\) | 1.51718 | − | 1.27306i | 1.51718 | − | 1.27306i | 0.669131 | − | 0.743145i | \(-0.266667\pi\) |
0.848048 | − | 0.529919i | \(-0.177778\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.51157 | −2.51157 | ||||||||
\(437\) | −0.948445 | + | 0.592654i | −0.948445 | + | 0.592654i | ||||
\(438\) | −0.785359 | −0.785359 | ||||||||
\(439\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.257378 | − | 0.215965i | 0.257378 | − | 0.215965i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.346450 | − | 1.96482i | −0.346450 | − | 1.96482i | −0.241922 | − | 0.970296i | \(-0.577778\pi\) |
−0.104528 | − | 0.994522i | \(-0.533333\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.28633 | − | 0.468185i | −1.28633 | − | 0.468185i | ||||
\(448\) | 0.317130 | − | 0.549285i | 0.317130 | − | 0.549285i | ||||
\(449\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(450\) | 0.129202 | + | 0.732739i | 0.129202 | + | 0.732739i | ||||
\(451\) | 1.47274 | + | 1.23577i | 1.47274 | + | 1.23577i | ||||
\(452\) | −2.53877 | + | 2.13028i | −2.53877 | + | 2.13028i | ||||
\(453\) | −0.130100 | + | 0.737831i | −0.130100 | + | 0.737831i | ||||
\(454\) | −0.985028 | + | 0.358521i | −0.985028 | + | 0.358521i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.745485 | − | 0.827945i | −0.745485 | − | 0.827945i | ||||
\(457\) | −1.98054 | −1.98054 | −0.990268 | − | 0.139173i | \(-0.955556\pi\) | ||||
−0.990268 | + | 0.139173i | \(0.955556\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.49861 | + | 1.25748i | 1.49861 | + | 1.25748i | 0.882948 | + | 0.469472i | \(0.155556\pi\) |
0.615661 | + | 0.788011i | \(0.288889\pi\) | |||||||
\(462\) | −0.106766 | − | 0.605498i | −0.106766 | − | 0.605498i | ||||
\(463\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.939693 | − | 1.62760i | 0.939693 | − | 1.62760i | 0.173648 | − | 0.984808i | \(-0.444444\pi\) |
0.766044 | − | 0.642788i | \(-0.222222\pi\) | |||||||
\(468\) | −0.411644 | − | 0.712989i | −0.411644 | − | 0.712989i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.119984 | − | 0.100679i | 0.119984 | − | 0.100679i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.0348995 | − | 0.999391i | −0.0348995 | − | 0.999391i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.507581 | + | 0.184744i | −0.507581 | + | 0.184744i | ||||
\(478\) | 0.583315 | − | 3.30815i | 0.583315 | − | 3.30815i | ||||
\(479\) | −1.17365 | + | 0.984808i | −1.17365 | + | 0.984808i | −0.173648 | + | 0.984808i | \(0.555556\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 1.69196 | + | 2.93057i | 1.69196 | + | 2.93057i | ||||
\(483\) | 0.202709 | − | 0.351102i | 0.202709 | − | 0.351102i | ||||
\(484\) | −1.76356 | − | 0.641884i | −1.76356 | − | 0.641884i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.679717 | + | 1.17730i | −0.679717 | + | 1.17730i | ||||
\(487\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(492\) | −2.54020 | + | 0.924556i | −2.54020 | + | 0.924556i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0.635369 | + | 1.57259i | 0.635369 | + | 1.57259i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 1.94214 | − | 1.62965i | 1.94214 | − | 1.62965i | ||||
\(499\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.661516 | + | 1.14578i | 0.661516 | + | 1.14578i | ||||
\(502\) | −1.37217 | + | 2.37667i | −1.37217 | + | 2.37667i | ||||
\(503\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(504\) | −0.296593 | − | 0.107951i | −0.296593 | − | 0.107951i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −0.948445 | − | 1.64275i | −0.948445 | − | 1.64275i | ||||
\(507\) | −0.130100 | − | 0.737831i | −0.130100 | − | 0.737831i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.280998 | − | 0.102275i | 0.280998 | − | 0.102275i | ||||
\(512\) | 1.21299 | 1.21299 | ||||||||
\(513\) | 0.663608 | − | 0.849379i | 0.663608 | − | 0.849379i | ||||
\(514\) | 2.74434 | 2.74434 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.104528 | − | 0.181049i | 0.104528 | − | 0.181049i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.181251 | + | 0.313936i | 0.181251 | + | 0.313936i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0.370426 | − | 0.310824i | 0.370426 | − | 0.310824i | ||||
\(529\) | 0.0435487 | − | 0.246977i | 0.0435487 | − | 0.246977i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.801761 | + | 0.426304i | 0.801761 | + | 0.426304i | ||||
\(533\) | 1.92252 | 1.92252 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.199324 | − | 0.167253i | −0.199324 | − | 0.167253i | ||||
\(538\) | −0.566229 | − | 3.21125i | −0.566229 | − | 3.21125i | ||||
\(539\) | −0.382948 | − | 0.663285i | −0.382948 | − | 0.663285i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.35192 | − | 0.492057i | −1.35192 | − | 0.492057i | −0.438371 | − | 0.898794i | \(-0.644444\pi\) |
−0.913545 | + | 0.406737i | \(0.866667\pi\) | |||||||
\(542\) | −0.111246 | − | 0.0404903i | −0.111246 | − | 0.0404903i | ||||
\(543\) | 0.0261472 | − | 0.0452882i | 0.0261472 | − | 0.0452882i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −0.470994 | − | 0.395211i | −0.470994 | − | 0.395211i | ||||
\(547\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.69610 | 1.69610 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 1.24600 | 1.24600 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −0.333843 | − | 1.89332i | −0.333843 | − | 1.89332i | −0.438371 | − | 0.898794i | \(-0.644444\pi\) |
0.104528 | − | 0.994522i | \(-0.466667\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −0.0591929 | + | 0.102525i | −0.0591929 | + | 0.102525i | ||||
\(563\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.0309928 | + | 0.175769i | −0.0309928 | + | 0.175769i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(572\) | −1.76356 | + | 0.641884i | −1.76356 | + | 0.641884i | ||||
\(573\) | −0.174107 | + | 0.987411i | −0.174107 | + | 0.987411i | ||||
\(574\) | 1.20860 | − | 1.01413i | 1.20860 | − | 1.01413i | ||||
\(575\) | 0.856733 | + | 0.718885i | 0.856733 | + | 0.718885i | ||||
\(576\) | 0.0998572 | + | 0.566318i | 0.0998572 | + | 0.566318i | ||||
\(577\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(578\) | 0.848048 | − | 1.46886i | 0.848048 | − | 1.46886i | ||||
\(579\) | −0.787377 | − | 0.286582i | −0.787377 | − | 0.286582i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.482665 | + | 0.836001i | −0.482665 | + | 0.836001i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.213817 | + | 1.21262i | 0.213817 | + | 1.21262i | ||||
\(584\) | 0.704026 | + | 0.590748i | 0.704026 | + | 0.590748i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.451237 | − | 2.55909i | 0.451237 | − | 2.55909i | ||||
\(587\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(588\) | 1.07691 | 1.07691 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.0491406 | + | 0.0178857i | −0.0491406 | + | 0.0178857i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.160147 | − | 0.134379i | 0.160147 | − | 0.134379i | −0.559193 | − | 0.829038i | \(-0.688889\pi\) |
0.719340 | + | 0.694658i | \(0.244444\pi\) | |||||||
\(594\) | 1.40047 | + | 1.17513i | 1.40047 | + | 1.17513i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.71449 | + | 2.96958i | 1.71449 | + | 2.96958i | ||||
\(597\) | 0.741922 | − | 1.28505i | 0.741922 | − | 1.28505i | ||||
\(598\) | −1.78249 | − | 0.648775i | −1.78249 | − | 0.648775i | ||||
\(599\) | −1.59381 | − | 0.580099i | −1.59381 | − | 0.580099i | −0.615661 | − | 0.788011i | \(-0.711111\pi\) |
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(600\) | −0.557055 | + | 0.964847i | −0.557055 | + | 0.964847i | ||||
\(601\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.43767 | − | 1.20635i | 1.43767 | − | 1.20635i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(608\) | −0.0136927 | − | 0.392107i | −0.0136927 | − | 0.392107i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.35275 | + | 1.13510i | 1.35275 | + | 1.13510i | 0.978148 | + | 0.207912i | \(0.0666667\pi\) |
0.374607 | + | 0.927184i | \(0.377778\pi\) | |||||||
\(614\) | 0.102287 | + | 0.580099i | 0.102287 | + | 0.580099i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.359747 | + | 0.623101i | −0.359747 | + | 0.623101i | ||||
\(617\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(618\) | −1.04692 | − | 0.381048i | −1.04692 | − | 0.381048i | ||||
\(619\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.209330 | + | 1.18717i | 0.209330 | + | 1.18717i | ||||
\(622\) | 0.973442 | + | 0.816814i | 0.973442 | + | 0.816814i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0.0839687 | − | 0.476210i | 0.0839687 | − | 0.476210i | ||||
\(625\) | −0.939693 | + | 0.342020i | −0.939693 | + | 0.342020i | ||||
\(626\) | −3.09892 | −3.09892 | ||||||||
\(627\) | −0.501321 | − | 0.556774i | −0.501321 | − | 0.556774i | ||||
\(628\) | −0.392346 | −0.392346 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.62693 | − | 0.592153i | −1.62693 | − | 0.592153i | ||||
\(637\) | −0.719706 | − | 0.261952i | −0.719706 | − | 0.261952i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.671624 | + | 0.563559i | 0.671624 | + | 0.563559i | 0.913545 | − | 0.406737i | \(-0.133333\pi\) |
−0.241922 | + | 0.970296i | \(0.577778\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(644\) | −0.954305 | + | 0.347339i | −0.954305 | + | 0.347339i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.0697990 | 0.0697990 | 0.0348995 | − | 0.999391i | \(-0.488889\pi\) | ||||
0.0348995 | + | 0.999391i | \(0.488889\pi\) | |||||||
\(648\) | −0.515459 | + | 0.187612i | −0.515459 | + | 0.187612i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 1.29929 | − | 1.09023i | 1.29929 | − | 1.09023i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.766044 | − | 1.32683i | −0.766044 | − | 1.32683i | −0.939693 | − | 0.342020i | \(-0.888889\pi\) |
0.173648 | − | 0.984808i | \(-0.444444\pi\) | |||||||
\(654\) | 0.850289 | − | 1.47274i | 0.850289 | − | 1.47274i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.16600 | + | 0.424390i | 1.16600 | + | 0.424390i | ||||
\(657\) | −0.135559 | + | 0.234796i | −0.135559 | + | 0.234796i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.96683 | −2.96683 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0.575493 | − | 3.26378i | 0.575493 | − | 3.26378i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0.0711131 | + | 0.123172i | 0.0711131 | + | 0.123172i | ||||
\(673\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.01287 | − | 0.368656i | −1.01287 | − | 0.368656i | ||||
\(676\) | −0.938371 | + | 1.62531i | −0.938371 | + | 1.62531i | ||||
\(677\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(678\) | −0.389665 | − | 2.20990i | −0.389665 | − | 2.20990i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.0804059 | − | 0.456005i | 0.0804059 | − | 0.456005i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(684\) | −0.805298 | + | 0.171171i | −0.805298 | + | 0.171171i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.36178 | + | 0.495647i | −1.36178 | + | 0.495647i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.943248 | + | 0.791479i | 0.943248 | + | 0.791479i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.199452 | − | 0.0725946i | −0.199452 | − | 0.0725946i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 1.13914 | + | 0.955850i | 1.13914 | + | 0.955850i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.157681 | − | 0.894255i | 0.157681 | − | 0.894255i | ||||
\(701\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(702\) | 1.82818 | 1.82818 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 1.31088 | 1.31088 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.113181 | + | 0.641884i | 0.113181 | + | 0.641884i | ||||
\(717\) | 1.13669 | + | 0.953796i | 1.13669 | + | 0.953796i | ||||
\(718\) | 1.45310 | − | 1.21930i | 1.45310 | − | 1.21930i | ||||
\(719\) | 0.266044 | − | 1.50881i | 0.266044 | − | 1.50881i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
0.766044 | − | 0.642788i | \(-0.222222\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.424206 | 0.424206 | ||||||||
\(722\) | 1.69196 | − | 0.118314i | 1.69196 | − | 0.118314i | ||||
\(723\) | −1.49478 | −1.49478 | ||||||||
\(724\) | −0.123095 | + | 0.0448028i | −0.123095 | + | 0.0448028i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0.973442 | − | 0.816814i | 0.973442 | − | 0.816814i | ||||
\(727\) | −0.370646 | − | 0.311009i | −0.370646 | − | 0.311009i | 0.438371 | − | 0.898794i | \(-0.355556\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(728\) | 0.124939 | + | 0.708564i | 0.124939 | + | 0.708564i | ||||
\(729\) | −0.484690 | − | 0.839508i | −0.484690 | − | 0.839508i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.997564 | + | 1.72783i | −0.997564 | + | 1.72783i | −0.438371 | + | 0.898794i | \(0.644444\pi\) |
−0.559193 | + | 0.829038i | \(0.688889\pi\) | |||||||
\(734\) | 0.524123 | + | 0.907807i | 0.524123 | + | 0.907807i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.336136 | + | 0.282051i | 0.336136 | + | 0.282051i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −0.248393 | + | 1.40871i | −0.248393 | + | 1.40871i | ||||
\(739\) | 1.80658 | − | 0.657542i | 1.80658 | − | 0.657542i | 0.809017 | − | 0.587785i | \(-0.200000\pi\) |
0.997564 | − | 0.0697565i | \(-0.0222222\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.741922 | − | 0.104270i | −0.741922 | − | 0.104270i | ||||
\(742\) | 1.01048 | 1.01048 | ||||||||
\(743\) | 0.326352 | − | 0.118782i | 0.326352 | − | 0.118782i | −0.173648 | − | 0.984808i | \(-0.555556\pi\) |
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.151981 | − | 0.861925i | −0.151981 | − | 0.861925i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.83832 | + | 0.669092i | 1.83832 | + | 0.669092i | 0.990268 | + | 0.139173i | \(0.0444444\pi\) |
0.848048 | + | 0.529919i | \(0.177778\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.606126 | − | 1.04984i | −0.606126 | − | 1.04984i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.749779 | − | 0.629139i | 0.749779 | − | 0.629139i | ||||
\(757\) | −0.280969 | + | 1.59345i | −0.280969 | + | 1.59345i | 0.438371 | + | 0.898794i | \(0.355556\pi\) |
−0.719340 | + | 0.694658i | \(0.755556\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.837909 | 0.837909 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.43868 | 1.43868 | 0.719340 | − | 0.694658i | \(-0.244444\pi\) | ||||
0.719340 | + | 0.694658i | \(0.244444\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.112439 | + | 0.637672i | −0.112439 | + | 0.637672i | ||||
\(764\) | 1.92398 | − | 1.61441i | 1.92398 | − | 1.61441i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −0.672314 | + | 1.16448i | −0.672314 | + | 1.16448i | ||||
\(769\) | 1.80658 | + | 0.657542i | 1.80658 | + | 0.657542i | 0.997564 | + | 0.0697565i | \(0.0222222\pi\) |
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.606126 | + | 1.04984i | −0.606126 | + | 1.04984i | ||||
\(772\) | 1.04946 | + | 1.81772i | 1.04946 | + | 1.81772i | ||||
\(773\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.31806 | 3.31806 | ||||||||
\(779\) | 0.594092 | − | 1.82843i | 0.594092 | − | 1.82843i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.378674 | − | 0.317745i | −0.378674 | − | 0.317745i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.241922 | + | 0.419021i | −0.241922 | + | 0.419021i | −0.961262 | − | 0.275637i | \(-0.911111\pi\) |
0.719340 | + | 0.694658i | \(0.244444\pi\) | |||||||
\(788\) | 0.123095 | + | 0.0448028i | 0.123095 | + | 0.0448028i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.427209 | + | 0.739947i | 0.427209 | + | 0.739947i | ||||
\(792\) | −0.113277 | − | 0.642423i | −0.113277 | − | 0.642423i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.49280 | + | 1.27127i | −3.49280 | + | 1.27127i | ||||
\(797\) | 1.53209 | 1.53209 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(798\) | −0.521413 | + | 0.325815i | −0.521413 | + | 0.325815i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −0.368685 | + | 0.134190i | −0.368685 | + | 0.134190i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.473442 | + | 0.397265i | 0.473442 | + | 0.397265i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.35351 | + | 0.492639i | 1.35351 | + | 0.492639i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.249824 | + | 1.41682i | 0.249824 | + | 1.41682i | 0.809017 | + | 0.587785i | \(0.200000\pi\) |
−0.559193 | + | 0.829038i | \(0.688889\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.0400598 | − | 0.0336141i | 0.0400598 | − | 0.0336141i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −3.18762 | −3.18762 | ||||||||
\(819\) | −0.199452 | + | 0.0725946i | −0.199452 | + | 0.0725946i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.766044 | − | 0.642788i | 0.766044 | − | 0.642788i | −0.173648 | − | 0.984808i | \(-0.555556\pi\) |
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.280969 | − | 1.59345i | −0.280969 | − | 1.59345i | −0.719340 | − | 0.694658i | \(-0.755556\pi\) |
0.438371 | − | 0.898794i | \(-0.355556\pi\) | |||||||
\(824\) | 0.651875 | + | 1.12908i | 0.651875 | + | 1.12908i | ||||
\(825\) | −0.374607 | + | 0.648838i | −0.374607 | + | 0.648838i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.83832 | − | 0.669092i | −1.83832 | − | 0.669092i | −0.990268 | − | 0.139173i | \(-0.955556\pi\) |
−0.848048 | − | 0.529919i | \(-0.822222\pi\) | |||||||
\(828\) | 0.460377 | − | 0.797397i | 0.460377 | − | 0.797397i | ||||
\(829\) | 0.809017 | + | 1.40126i | 0.809017 | + | 1.40126i | 0.913545 | + | 0.406737i | \(0.133333\pi\) |
−0.104528 | + | 0.994522i | \(0.533333\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.00419 | − | 0.842615i | 1.00419 | − | 0.842615i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.0654974 | + | 1.87560i | 0.0654974 | + | 1.87560i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.91203 | − | 1.05989i | 2.91203 | − | 1.05989i | ||||
\(839\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.766044 | + | 0.642788i | 0.766044 | + | 0.642788i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.0261472 | − | 0.0452882i | −0.0261472 | − | 0.0452882i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.241922 | + | 0.419021i | −0.241922 | + | 0.419021i | ||||
\(848\) | 0.397360 | + | 0.688247i | 0.397360 | + | 0.688247i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.59381 | − | 0.580099i | 1.59381 | − | 0.580099i | 0.615661 | − | 0.788011i | \(-0.288889\pi\) |
0.978148 | + | 0.207912i | \(0.0666667\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(858\) | 0.220661 | − | 1.25143i | 0.220661 | − | 1.25143i | ||||
\(859\) | 0.0534691 | − | 0.0448659i | 0.0534691 | − | 0.0448659i | −0.615661 | − | 0.788011i | \(-0.711111\pi\) |
0.669131 | + | 0.743145i | \(0.266667\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.121019 | + | 0.686331i | 0.121019 | + | 0.686331i | ||||
\(862\) | −0.743520 | − | 1.28781i | −0.743520 | − | 1.28781i | ||||
\(863\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(864\) | −0.397397 | − | 0.144641i | −0.397397 | − | 0.144641i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.67959 | − | 2.90914i | 1.67959 | − | 2.90914i | ||||
\(867\) | 0.374607 | + | 0.648838i | 0.374607 | + | 0.648838i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −1.87003 | + | 0.680636i | −1.87003 | + | 0.680636i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.16784 | + | 1.49477i | −1.16784 | + | 1.49477i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −0.816598 | + | 0.297217i | −0.816598 | + | 0.297217i | ||||
\(877\) | −0.107320 | + | 0.608645i | −0.107320 | + | 0.608645i | 0.882948 | + | 0.469472i | \(0.155556\pi\) |
−0.990268 | + | 0.139173i | \(0.955556\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.879313 | + | 0.737831i | 0.879313 | + | 0.737831i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.615661 | + | 1.06636i | 0.615661 | + | 1.06636i | 0.990268 | + | 0.139173i | \(0.0444444\pi\) |
−0.374607 | + | 0.927184i | \(0.622222\pi\) | |||||||
\(882\) | 0.284929 | − | 0.493512i | 0.284929 | − | 0.493512i | ||||
\(883\) | 0.704030 | + | 0.256246i | 0.704030 | + | 0.256246i | 0.669131 | − | 0.743145i | \(-0.266667\pi\) |
0.0348995 | + | 0.999391i | \(0.488889\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.69196 | − | 2.93057i | −1.69196 | − | 2.93057i | ||||
\(887\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.346634 | + | 0.126165i | −0.346634 | + | 0.126165i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −2.32175 | −2.32175 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.153840 | − | 0.872471i | 0.153840 | − | 0.872471i | ||||
\(897\) | 0.641876 | − | 0.538598i | 0.641876 | − | 0.538598i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0.411644 | + | 0.712989i | 0.411644 | + | 0.712989i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 3.06414 | + | 1.11525i | 3.06414 | + | 1.11525i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.31298 | + | 2.27414i | −1.31298 | + | 2.27414i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0.220661 | + | 1.25143i | 0.220661 | + | 1.25143i | ||||
\(907\) | −1.23949 | − | 1.04005i | −1.23949 | − | 1.04005i | −0.997564 | − | 0.0697565i | \(-0.977778\pi\) |
−0.241922 | − | 0.970296i | \(-0.577778\pi\) | |||||||
\(908\) | −0.888528 | + | 0.745563i | −0.888528 | + | 0.745563i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.11839 | 1.11839 | 0.559193 | − | 0.829038i | \(-0.311111\pi\) | ||||
0.559193 | + | 0.829038i | \(0.311111\pi\) | |||||||
\(912\) | −0.426955 | − | 0.227016i | −0.426955 | − | 0.227016i | ||||
\(913\) | −1.99513 | −1.99513 | ||||||||
\(914\) | −3.15660 | + | 1.14891i | −3.15660 | + | 1.14891i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.244507 | − | 0.0889933i | −0.244507 | − | 0.0889933i | ||||
\(922\) | 3.11796 | + | 1.13485i | 3.11796 | + | 1.13485i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −0.340162 | − | 0.589177i | −0.340162 | − | 0.589177i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.294628 | + | 0.247222i | −0.294628 | + | 0.247222i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.471532 | + | 0.603534i | −0.471532 | + | 0.603534i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −0.527469 | + | 0.191983i | −0.527469 | + | 0.191983i | ||||
\(934\) | 0.553524 | − | 3.13919i | 0.553524 | − | 3.13919i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −0.499717 | − | 0.419312i | −0.499717 | − | 0.419312i | ||||
\(937\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.684440 | − | 1.18549i | 0.684440 | − | 1.18549i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.83832 | − | 0.669092i | −1.83832 | − | 0.669092i | −0.990268 | − | 0.139173i | \(-0.955556\pi\) |
−0.848048 | − | 0.529919i | \(-0.822222\pi\) | |||||||
\(942\) | 0.132828 | − | 0.230065i | 0.132828 | − | 0.230065i | ||||
\(943\) | 1.07506 | + | 1.86206i | 1.07506 | + | 1.86206i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.618034 | 0.618034 | ||||||||
\(950\) | −0.635369 | − | 1.57259i | −0.635369 | − | 1.57259i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(954\) | −0.701817 | + | 0.588894i | −0.701817 | + | 0.588894i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −0.645443 | − | 3.66049i | −0.645443 | − | 3.66049i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.29929 | + | 2.25043i | −1.29929 | + | 2.25043i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.86833 | + | 2.40682i | 2.86833 | + | 2.40682i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.119405 | − | 0.677180i | 0.119405 | − | 0.677180i | ||||
\(967\) | −1.65940 | + | 0.603972i | −1.65940 | + | 0.603972i | −0.990268 | − | 0.139173i | \(-0.955556\pi\) |
−0.669131 | + | 0.743145i | \(0.733333\pi\) | |||||||
\(968\) | −1.48704 | −1.48704 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.83832 | − | 0.669092i | 1.83832 | − | 0.669092i | 0.848048 | − | 0.529919i | \(-0.177778\pi\) |
0.990268 | − | 0.139173i | \(-0.0444444\pi\) | |||||||
\(972\) | −0.261206 | + | 1.48137i | −0.261206 | + | 1.48137i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.130100 | + | 0.737831i | 0.130100 | + | 0.737831i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.293534 | − | 0.508416i | −0.293534 | − | 0.508416i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(984\) | −1.64079 | + | 1.37679i | −1.64079 | + | 1.37679i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.25579 | + | 1.39469i | 1.25579 | + | 1.39469i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.213817 | + | 1.21262i | −0.213817 | + | 1.21262i | 0.669131 | + | 0.743145i | \(0.266667\pi\) |
−0.882948 | + | 0.469472i | \(0.844444\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.40265 | − | 2.42947i | 1.40265 | − | 2.42947i | ||||
\(997\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(998\) | 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 | 2717.1.db.c.1715.4 | yes | 24 | |
11.10 | odd | 2 | 2717.1.db.d.1715.1 | yes | 24 | ||
13.12 | even | 2 | 2717.1.db.d.1715.1 | yes | 24 | ||
19.4 | even | 9 | inner | 2717.1.db.c.1429.4 | ✓ | 24 | |
143.142 | odd | 2 | CM | 2717.1.db.c.1715.4 | yes | 24 | |
209.175 | odd | 18 | 2717.1.db.d.1429.1 | yes | 24 | ||
247.194 | even | 18 | 2717.1.db.d.1429.1 | yes | 24 | ||
2717.1429 | odd | 18 | inner | 2717.1.db.c.1429.4 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2717.1.db.c.1429.4 | ✓ | 24 | 19.4 | even | 9 | inner | |
2717.1.db.c.1429.4 | ✓ | 24 | 2717.1429 | odd | 18 | inner | |
2717.1.db.c.1715.4 | yes | 24 | 1.1 | even | 1 | trivial | |
2717.1.db.c.1715.4 | yes | 24 | 143.142 | odd | 2 | CM | |
2717.1.db.d.1429.1 | yes | 24 | 209.175 | odd | 18 | ||
2717.1.db.d.1429.1 | yes | 24 | 247.194 | even | 18 | ||
2717.1.db.d.1715.1 | yes | 24 | 11.10 | odd | 2 | ||
2717.1.db.d.1715.1 | yes | 24 | 13.12 | even | 2 |