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 | 2144.4 | ||
Root | \(0.0348995 + 0.999391i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2717.2144 |
Dual form | 2717.1.db.c.2001.4 |
$q$-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 \(\left(\mathbb{Z}/2717\mathbb{Z}\right)^\times\).
\(n\) | \(210\) | \(287\) | \(2224\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{9}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.35275 | + | 1.13510i | 1.35275 | + | 1.13510i | 0.978148 | + | 0.207912i | \(0.0666667\pi\) |
0.374607 | + | 0.927184i | \(0.377778\pi\) | |||||||
\(3\) | −1.86110 | + | 0.677383i | −1.86110 | + | 0.677383i | −0.882948 | + | 0.469472i | \(0.844444\pi\) |
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(4\) | 0.367854 | + | 2.08620i | 0.367854 | + | 2.08620i | ||||
\(5\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(6\) | −3.28650 | − | 1.19619i | −3.28650 | − | 1.19619i | ||||
\(7\) | −0.719340 | − | 1.24593i | −0.719340 | − | 1.24593i | −0.961262 | − | 0.275637i | \(-0.911111\pi\) |
0.241922 | − | 0.970296i | \(-0.422222\pi\) | |||||||
\(8\) | −0.987476 | + | 1.71036i | −0.987476 | + | 1.71036i | ||||
\(9\) | 2.23878 | − | 1.87856i | 2.23878 | − | 1.87856i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(12\) | −2.09777 | − | 3.63344i | −2.09777 | − | 3.63344i | ||||
\(13\) | 0.939693 | + | 0.342020i | 0.939693 | + | 0.342020i | ||||
\(14\) | 0.441163 | − | 2.50196i | 0.441163 | − | 2.50196i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.28660 | + | 0.468285i | −1.28660 | + | 0.468285i | ||||
\(17\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(18\) | 5.16087 | 5.16087 | ||||||||
\(19\) | 0.615661 | − | 0.788011i | 0.615661 | − | 0.788011i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.18273 | + | 1.83153i | 2.18273 | + | 1.83153i | ||||
\(22\) | 1.65940 | − | 0.603972i | 1.65940 | − | 0.603972i | ||||
\(23\) | −0.346450 | − | 1.96482i | −0.346450 | − | 1.96482i | −0.241922 | − | 0.970296i | \(-0.577778\pi\) |
−0.104528 | − | 0.994522i | \(-0.533333\pi\) | |||||||
\(24\) | 0.679219 | − | 3.85204i | 0.679219 | − | 3.85204i | ||||
\(25\) | −0.939693 | − | 0.342020i | −0.939693 | − | 0.342020i | ||||
\(26\) | 0.882948 | + | 1.52931i | 0.882948 | + | 1.52931i | ||||
\(27\) | −1.90381 | + | 3.29750i | −1.90381 | + | 3.29750i | ||||
\(28\) | 2.33466 | − | 1.95901i | 2.33466 | − | 1.95901i | ||||
\(29\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(32\) | −0.416155 | − | 0.151468i | −0.416155 | − | 0.151468i | ||||
\(33\) | −0.343916 | + | 1.95045i | −0.343916 | + | 1.95045i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.74261 | + | 3.97952i | 4.74261 | + | 3.97952i | ||||
\(37\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(38\) | 1.72731 | − | 0.367150i | 1.72731 | − | 0.367150i | ||||
\(39\) | −1.98054 | −1.98054 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.454664 | + | 0.165484i | −0.454664 | + | 0.165484i | −0.559193 | − | 0.829038i | \(-0.688889\pi\) |
0.104528 | + | 0.994522i | \(0.466667\pi\) | |||||||
\(42\) | 0.873740 | + | 4.95522i | 0.873740 | + | 4.95522i | ||||
\(43\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(44\) | 1.99063 | + | 0.724531i | 1.99063 | + | 0.724531i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.76159 | − | 3.05117i | 1.76159 | − | 3.05117i | ||||
\(47\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(48\) | 2.07728 | − | 1.74304i | 2.07728 | − | 1.74304i | ||||
\(49\) | −0.534899 | + | 0.926473i | −0.534899 | + | 0.926473i | ||||
\(50\) | −0.882948 | − | 1.52931i | −0.882948 | − | 1.52931i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.367854 | + | 2.08620i | −0.367854 | + | 2.08620i | ||||
\(53\) | −0.130100 | − | 0.737831i | −0.130100 | − | 0.737831i | −0.978148 | − | 0.207912i | \(-0.933333\pi\) |
0.848048 | − | 0.529919i | \(-0.177778\pi\) | |||||||
\(54\) | −6.31837 | + | 2.29970i | −6.31837 | + | 2.29970i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.84132 | 2.84132 | ||||||||
\(57\) | −0.612019 | + | 1.88360i | −0.612019 | + | 1.88360i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.95101 | − | 1.43805i | −3.95101 | − | 1.43805i | ||||
\(64\) | 0.293561 | + | 0.508463i | 0.293561 | + | 0.508463i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.67918 | + | 2.24810i | −2.67918 | + | 2.24810i | ||||
\(67\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.97571 | + | 3.42203i | 1.97571 | + | 3.42203i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(72\) | 1.00227 | + | 5.68416i | 1.00227 | + | 5.68416i | ||||
\(73\) | 0.580762 | − | 0.211380i | 0.580762 | − | 0.211380i | −0.0348995 | − | 0.999391i | \(-0.511111\pi\) |
0.615661 | + | 0.788011i | \(0.288889\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.98054 | 1.98054 | ||||||||
\(76\) | 1.87042 | + | 0.994522i | 1.87042 | + | 0.994522i | ||||
\(77\) | −1.43868 | −1.43868 | ||||||||
\(78\) | −2.67918 | − | 2.24810i | −2.67918 | − | 2.24810i | ||||
\(79\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.802015 | − | 4.54845i | 0.802015 | − | 4.54845i | ||||
\(82\) | −0.802890 | − | 0.292228i | −0.802890 | − | 0.292228i | ||||
\(83\) | 0.438371 | + | 0.759281i | 0.438371 | + | 0.759281i | 0.997564 | − | 0.0697565i | \(-0.0222222\pi\) |
−0.559193 | + | 0.829038i | \(0.688889\pi\) | |||||||
\(84\) | −3.01802 | + | 5.22736i | −3.01802 | + | 5.22736i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.987476 | + | 1.71036i | 0.987476 | + | 1.71036i | ||||
\(89\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.249824 | − | 1.41682i | −0.249824 | − | 1.41682i | ||||
\(92\) | 3.97156 | − | 1.44553i | 3.97156 | − | 1.44553i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.877107 | 0.877107 | ||||||||
\(97\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(98\) | −1.77522 | + | 0.646128i | −1.77522 | + | 0.646128i | ||||
\(99\) | −0.507491 | − | 2.87812i | −0.507491 | − | 2.87812i | ||||
\(100\) | 0.367854 | − | 2.08620i | 0.367854 | − | 2.08620i | ||||
\(101\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.559193 | + | 0.968551i | −0.559193 | + | 0.968551i | 0.438371 | + | 0.898794i | \(0.355556\pi\) |
−0.997564 | + | 0.0697565i | \(0.977778\pi\) | |||||||
\(104\) | −1.51290 | + | 1.26947i | −1.51290 | + | 1.26947i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.661516 | − | 1.14578i | 0.661516 | − | 1.14578i | ||||
\(107\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(108\) | −7.57958 | − | 2.75874i | −7.57958 | − | 2.75874i | ||||
\(109\) | −0.232387 | + | 1.31793i | −0.232387 | + | 1.31793i | 0.615661 | + | 0.788011i | \(0.288889\pi\) |
−0.848048 | + | 0.529919i | \(0.822222\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.50895 | + | 1.26616i | 1.50895 | + | 1.26616i | ||||
\(113\) | 0.0697990 | 0.0697990 | 0.0348995 | − | 0.999391i | \(-0.488889\pi\) | ||||
0.0348995 | + | 0.999391i | \(0.488889\pi\) | |||||||
\(114\) | −2.96598 | + | 1.85335i | −2.96598 | + | 1.85335i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.74627 | − | 0.999562i | 2.74627 | − | 0.999562i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.734077 | − | 0.615964i | 0.734077 | − | 0.615964i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −3.71242 | − | 6.43010i | −3.71242 | − | 6.43010i | ||||
\(127\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(128\) | −0.256940 | + | 1.45718i | −0.256940 | + | 1.45718i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(132\) | −4.19554 | −4.19554 | ||||||||
\(133\) | −1.42468 | − | 0.200226i | −1.42468 | − | 0.200226i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(138\) | −1.21168 | + | 6.87179i | −1.21168 | + | 6.87179i | ||||
\(139\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.766044 | − | 0.642788i | 0.766044 | − | 0.642788i | ||||
\(144\) | −2.00072 | + | 3.46535i | −2.00072 | + | 3.46535i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.02556 | + | 0.373275i | 1.02556 | + | 0.373275i | ||||
\(147\) | 0.367922 | − | 2.08659i | 0.367922 | − | 2.08659i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.71690 | − | 0.624902i | 1.71690 | − | 0.624902i | 0.719340 | − | 0.694658i | \(-0.244444\pi\) |
0.997564 | + | 0.0697565i | \(0.0222222\pi\) | |||||||
\(150\) | 2.67918 | + | 2.24810i | 2.67918 | + | 2.24810i | ||||
\(151\) | 1.00000 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(152\) | 0.739830 | + | 1.83114i | 0.739830 | + | 1.83114i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.94618 | − | 1.63304i | −1.94618 | − | 1.63304i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.728548 | − | 4.13180i | −0.728548 | − | 4.13180i | ||||
\(157\) | −0.0363024 | + | 0.205881i | −0.0363024 | + | 0.205881i | −0.997564 | − | 0.0697565i | \(-0.977778\pi\) |
0.961262 | + | 0.275637i | \(0.0888889\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.741922 | + | 1.28505i | 0.741922 | + | 1.28505i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.19882 | + | 1.84503i | −2.19882 | + | 1.84503i | ||||
\(162\) | 6.24786 | − | 5.24257i | 6.24786 | − | 5.24257i | ||||
\(163\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(164\) | −0.512484 | − | 0.887648i | −0.512484 | − | 0.887648i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.268848 | + | 1.52471i | −0.268848 | + | 1.52471i | ||||
\(167\) | −0.0121205 | − | 0.0687386i | −0.0121205 | − | 0.0687386i | 0.978148 | − | 0.207912i | \(-0.0666667\pi\) |
−0.990268 | + | 0.139173i | \(0.955556\pi\) | |||||||
\(168\) | −5.28797 | + | 1.92466i | −5.28797 | + | 1.92466i | ||||
\(169\) | 0.766044 | + | 0.642788i | 0.766044 | + | 0.642788i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.101995 | − | 2.92074i | −0.101995 | − | 2.92074i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.249824 | + | 1.41682i | 0.249824 | + | 1.41682i | ||||
\(176\) | −0.237754 | + | 1.34837i | −0.237754 | + | 1.34837i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.939693 | − | 1.62760i | 0.939693 | − | 1.62760i | 0.173648 | − | 0.984808i | \(-0.444444\pi\) |
0.766044 | − | 0.642788i | \(-0.222222\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.29929 | − | 1.09023i | 1.29929 | − | 1.09023i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
0.990268 | − | 0.139173i | \(-0.0444444\pi\) | |||||||
\(182\) | 1.27028 | − | 2.20019i | 1.27028 | − | 2.20019i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.70265 | + | 1.34766i | 3.70265 | + | 1.34766i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.47796 | 5.47796 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.33826 | 1.33826 | 0.669131 | − | 0.743145i | \(-0.266667\pi\) | ||||
0.669131 | + | 0.743145i | \(0.266667\pi\) | |||||||
\(192\) | −0.890770 | − | 0.747445i | −0.890770 | − | 0.747445i | ||||
\(193\) | −1.87481 | + | 0.682374i | −1.87481 | + | 0.682374i | −0.913545 | + | 0.406737i | \(0.866667\pi\) |
−0.961262 | + | 0.275637i | \(0.911111\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.12958 | − | 0.775102i | −2.12958 | − | 0.775102i | ||||
\(197\) | 0.848048 | + | 1.46886i | 0.848048 | + | 1.46886i | 0.882948 | + | 0.469472i | \(0.155556\pi\) |
−0.0348995 | + | 0.999391i | \(0.511111\pi\) | |||||||
\(198\) | 2.58043 | − | 4.46944i | 2.58043 | − | 4.46944i | ||||
\(199\) | −0.943248 | + | 0.791479i | −0.943248 | + | 0.791479i | −0.978148 | − | 0.207912i | \(-0.933333\pi\) |
0.0348995 | + | 0.999391i | \(0.488889\pi\) | |||||||
\(200\) | 1.51290 | − | 1.26947i | 1.51290 | − | 1.26947i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.85585 | + | 0.675473i | −1.85585 | + | 0.675473i | ||||
\(207\) | −4.46666 | − | 3.74797i | −4.46666 | − | 3.74797i | ||||
\(208\) | −1.36917 | −1.36917 | ||||||||
\(209\) | −0.374607 | − | 0.927184i | −0.374607 | − | 0.927184i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(212\) | 1.49141 | − | 0.542828i | 1.49141 | − | 0.542828i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −3.75994 | − | 6.51241i | −3.75994 | − | 6.51241i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1.81034 | + | 1.51905i | −1.81034 | + | 1.51905i | ||||
\(219\) | −0.937668 | + | 0.786797i | −0.937668 | + | 0.786797i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(224\) | 0.110638 | + | 0.627459i | 0.110638 | + | 0.627459i | ||||
\(225\) | −2.74627 | + | 0.999562i | −2.74627 | + | 0.999562i | ||||
\(226\) | 0.0944209 | + | 0.0792285i | 0.0944209 | + | 0.0792285i | ||||
\(227\) | −0.618034 | −0.618034 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(228\) | −4.15471 | − | 0.583906i | −4.15471 | − | 0.583906i | ||||
\(229\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.67752 | − | 0.974537i | 2.67752 | − | 0.974537i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(234\) | 4.84963 | + | 1.76512i | 4.84963 | + | 1.76512i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.615661 | + | 1.06636i | −0.615661 | + | 1.06636i | 0.374607 | + | 0.927184i | \(0.377778\pi\) |
−0.990268 | + | 0.139173i | \(0.955556\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.823868 | + | 0.299864i | 0.823868 | + | 0.299864i | 0.719340 | − | 0.694658i | \(-0.244444\pi\) |
0.104528 | + | 0.994522i | \(0.466667\pi\) | |||||||
\(242\) | 0.306644 | − | 1.73907i | 0.306644 | − | 1.73907i | ||||
\(243\) | 0.927232 | + | 5.25859i | 0.927232 | + | 5.25859i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.69220 | 1.69220 | ||||||||
\(247\) | 0.848048 | − | 0.529919i | 0.848048 | − | 0.529919i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.33017 | − | 1.11615i | −1.33017 | − | 1.11615i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.280969 | − | 1.59345i | −0.280969 | − | 1.59345i | −0.719340 | − | 0.694658i | \(-0.755556\pi\) |
0.438371 | − | 0.898794i | \(-0.355556\pi\) | |||||||
\(252\) | 1.54667 | − | 8.77160i | 1.54667 | − | 8.77160i | ||||
\(253\) | −1.87481 | − | 0.682374i | −1.87481 | − | 0.682374i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.55185 | + | 1.30216i | −1.55185 | + | 1.30216i | ||||
\(257\) | −1.23949 | + | 1.04005i | −1.23949 | + | 1.04005i | −0.241922 | + | 0.970296i | \(0.577778\pi\) |
−0.997564 | + | 0.0697565i | \(0.977778\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(264\) | −2.99636 | − | 2.51424i | −2.99636 | − | 2.51424i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.69996 | − | 1.88800i | −1.69996 | − | 1.88800i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.454664 | − | 0.165484i | 0.454664 | − | 0.165484i | −0.104528 | − | 0.994522i | \(-0.533333\pi\) |
0.559193 | + | 0.829038i | \(0.311111\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.294524 | + | 1.67033i | −0.294524 | + | 1.67033i | 0.374607 | + | 0.927184i | \(0.377778\pi\) |
−0.669131 | + | 0.743145i | \(0.733333\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.42468 | + | 2.46762i | 1.42468 | + | 2.46762i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.766044 | + | 0.642788i | −0.766044 | + | 0.642788i | ||||
\(276\) | −6.41228 | + | 5.38054i | −6.41228 | + | 5.38054i | ||||
\(277\) | 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 | ||||||||
\(281\) | −0.294524 | − | 1.67033i | −0.294524 | − | 1.67033i | −0.669131 | − | 0.743145i | \(-0.733333\pi\) |
0.374607 | − | 0.927184i | \(-0.377778\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.76590 | 1.76590 | ||||||||
\(287\) | 0.533241 | + | 0.447442i | 0.533241 | + | 0.447442i | ||||
\(288\) | −1.21622 | + | 0.442669i | −1.21622 | + | 0.442669i | ||||
\(289\) | 0.173648 | + | 0.984808i | 0.173648 | + | 0.984808i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.654617 | + | 1.13383i | 0.654617 | + | 1.13383i | ||||
\(293\) | 0.173648 | − | 0.300767i | 0.173648 | − | 0.300767i | −0.766044 | − | 0.642788i | \(-0.777778\pi\) |
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(294\) | 2.86618 | − | 2.40501i | 2.86618 | − | 2.40501i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.90381 | + | 3.29750i | 1.90381 | + | 3.29750i | ||||
\(298\) | 3.03187 | + | 1.10351i | 3.03187 | + | 1.10351i | ||||
\(299\) | 0.346450 | − | 1.96482i | 0.346450 | − | 1.96482i | ||||
\(300\) | 0.728548 | + | 4.13180i | 0.728548 | + | 4.13180i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1.35275 | + | 1.13510i | 1.35275 | + | 1.13510i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.423098 | + | 1.30216i | −0.423098 | + | 1.30216i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.76604 | + | 0.642788i | −1.76604 | + | 0.642788i | −0.766044 | + | 0.642788i | \(0.777778\pi\) |
−1.00000 | \(1.00000\pi\) | |||||||||
\(308\) | −0.529224 | − | 3.00138i | −0.529224 | − | 3.00138i | ||||
\(309\) | 0.384631 | − | 2.18135i | 0.384631 | − | 2.18135i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.990268 | − | 1.71519i | −0.990268 | − | 1.71519i | −0.615661 | − | 0.788011i | \(-0.711111\pi\) |
−0.374607 | − | 0.927184i | \(-0.622222\pi\) | |||||||
\(312\) | 1.95573 | − | 3.38743i | 1.95573 | − | 3.38743i | ||||
\(313\) | 1.39963 | − | 1.17443i | 1.39963 | − | 1.17443i | 0.438371 | − | 0.898794i | \(-0.355556\pi\) |
0.961262 | − | 0.275637i | \(-0.0888889\pi\) | |||||||
\(314\) | −0.282803 | + | 0.237300i | −0.282803 | + | 0.237300i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(318\) | −0.455013 | + | 2.58050i | −0.455013 | + | 2.58050i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −5.06874 | −5.06874 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 9.78402 | 9.78402 | ||||||||
\(325\) | −0.766044 | − | 0.642788i | −0.766044 | − | 0.642788i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.460250 | − | 2.61021i | −0.460250 | − | 2.61021i | ||||
\(328\) | 0.165933 | − | 0.941051i | 0.165933 | − | 0.941051i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(332\) | −1.42276 | + | 1.19384i | −1.42276 | + | 1.19384i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0.0616289 | − | 0.106744i | 0.0616289 | − | 0.106744i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −3.66599 | − | 1.33431i | −3.66599 | − | 1.33431i | ||||
\(337\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(338\) | 0.306644 | + | 1.73907i | 0.306644 | + | 1.73907i | ||||
\(339\) | −0.129903 | + | 0.0472807i | −0.129903 | + | 0.0472807i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 3.17735 | − | 4.06682i | 3.17735 | − | 4.06682i | ||||
\(343\) | 0.100418 | 0.100418 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.559193 | + | 0.968551i | 0.559193 | + | 0.968551i | 0.997564 | + | 0.0697565i | \(0.0222222\pi\) |
−0.438371 | + | 0.898794i | \(0.644444\pi\) | |||||||
\(350\) | −1.27028 | + | 2.20019i | −1.27028 | + | 2.20019i | ||||
\(351\) | −2.91681 | + | 2.44750i | −2.91681 | + | 2.44750i | ||||
\(352\) | −0.339253 | + | 0.284667i | −0.339253 | + | 0.284667i | ||||
\(353\) | 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 | ||||||||
\(358\) | 3.11865 | − | 1.13510i | 3.11865 | − | 1.13510i | ||||
\(359\) | 1.52836 | + | 1.28244i | 1.52836 | + | 1.28244i | 0.809017 | + | 0.587785i | \(0.200000\pi\) |
0.719340 | + | 0.694658i | \(0.244444\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.241922 | − | 0.970296i | −0.241922 | − | 0.970296i | ||||
\(362\) | 2.99513 | 2.99513 | ||||||||
\(363\) | 1.51718 | + | 1.27306i | 1.51718 | + | 1.27306i | ||||
\(364\) | 2.86388 | − | 1.04237i | 2.86388 | − | 1.04237i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.580762 | − | 0.211380i | −0.580762 | − | 0.211380i | 0.0348995 | − | 0.999391i | \(-0.488889\pi\) |
−0.615661 | + | 0.788011i | \(0.711111\pi\) | |||||||
\(368\) | 1.36584 | + | 2.36570i | 1.36584 | + | 2.36570i | ||||
\(369\) | −0.707022 | + | 1.22460i | −0.707022 | + | 1.22460i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.825702 | + | 0.692846i | −0.825702 | + | 0.692846i | ||||
\(372\) | 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 | ||||||||
\(378\) | 7.41033 | + | 6.21800i | 7.41033 | + | 6.21800i | ||||
\(379\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.81034 | + | 1.51905i | 1.81034 | + | 1.51905i | ||||
\(383\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(384\) | −0.508880 | − | 2.88600i | −0.508880 | − | 2.88600i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3.31071 | − | 1.20500i | −3.31071 | − | 1.20500i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.49861 | + | 1.25748i | −1.49861 | + | 1.25748i | −0.615661 | + | 0.788011i | \(0.711111\pi\) |
−0.882948 | + | 0.469472i | \(0.844444\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −1.05640 | − | 1.82974i | −1.05640 | − | 1.82974i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −0.520099 | + | 2.94963i | −0.520099 | + | 2.94963i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 5.81767 | − | 2.11746i | 5.81767 | − | 2.11746i | ||||
\(397\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(398\) | −2.17439 | −2.17439 | ||||||||
\(399\) | 2.78709 | − | 0.592415i | 2.78709 | − | 0.592415i | ||||
\(400\) | 1.36917 | 1.36917 | ||||||||
\(401\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.17365 | + | 0.984808i | −1.17365 | + | 0.984808i | −0.173648 | + | 0.984808i | \(0.555556\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.22629 | − | 0.810305i | −2.22629 | − | 0.810305i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1.78799 | − | 10.1402i | −1.78799 | − | 10.1402i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.339253 | − | 0.284667i | −0.339253 | − | 0.284667i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.545692 | − | 1.67947i | 0.545692 | − | 1.67947i | ||||
\(419\) | 1.82709 | 1.82709 | 0.913545 | − | 0.406737i | \(-0.133333\pi\) | ||||
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.39043 | + | 0.506074i | 1.39043 | + | 0.506074i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.990268 | + | 1.71519i | −0.990268 | + | 1.71519i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.05094 | + | 0.382510i | 1.05094 | + | 0.382510i | 0.809017 | − | 0.587785i | \(-0.200000\pi\) |
0.241922 | + | 0.970296i | \(0.422222\pi\) | |||||||
\(432\) | 0.905280 | − | 5.13410i | 0.905280 | − | 5.13410i | ||||
\(433\) | −0.213817 | − | 1.21262i | −0.213817 | − | 1.21262i | −0.882948 | − | 0.469472i | \(-0.844444\pi\) |
0.669131 | − | 0.743145i | \(-0.266667\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.83495 | −2.83495 | ||||||||
\(437\) | −1.76159 | − | 0.936656i | −1.76159 | − | 0.936656i | ||||
\(438\) | −2.16152 | −2.16152 | ||||||||
\(439\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.542913 | + | 3.07901i | 0.542913 | + | 3.07901i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.823868 | − | 0.299864i | −0.823868 | − | 0.299864i | −0.104528 | − | 0.994522i | \(-0.533333\pi\) |
−0.719340 | + | 0.694658i | \(0.755556\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.77202 | + | 2.32600i | −2.77202 | + | 2.32600i | ||||
\(448\) | 0.422341 | − | 0.731515i | 0.422341 | − | 0.731515i | ||||
\(449\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(450\) | −4.84963 | − | 1.76512i | −4.84963 | − | 1.76512i | ||||
\(451\) | −0.0840186 | + | 0.476493i | −0.0840186 | + | 0.476493i | ||||
\(452\) | 0.0256758 | + | 0.145615i | 0.0256758 | + | 0.145615i | ||||
\(453\) | −1.86110 | + | 0.677383i | −1.86110 | + | 0.677383i | ||||
\(454\) | −0.836048 | − | 0.701528i | −0.836048 | − | 0.701528i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.61728 | − | 2.90678i | −2.61728 | − | 2.90678i | ||||
\(457\) | 1.23132 | 1.23132 | 0.615661 | − | 0.788011i | \(-0.288889\pi\) | ||||
0.615661 | + | 0.788011i | \(0.288889\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.339707 | − | 1.92657i | 0.339707 | − | 1.92657i | −0.0348995 | − | 0.999391i | \(-0.511111\pi\) |
0.374607 | − | 0.927184i | \(-0.377778\pi\) | |||||||
\(462\) | 4.72822 | + | 1.72093i | 4.72822 | + | 1.72093i | ||||
\(463\) | 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 | ||||||||
\(467\) | −0.766044 | + | 1.32683i | −0.766044 | + | 1.32683i | 0.173648 | + | 0.984808i | \(0.444444\pi\) |
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(468\) | 3.09552 | + | 5.36159i | 3.09552 | + | 5.36159i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.0718981 | − | 0.407755i | −0.0718981 | − | 0.407755i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.848048 | + | 0.529919i | −0.848048 | + | 0.529919i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.67733 | − | 1.40744i | −1.67733 | − | 1.40744i | ||||
\(478\) | −2.04326 | + | 0.743684i | −2.04326 | + | 0.743684i | ||||
\(479\) | −0.0603074 | − | 0.342020i | −0.0603074 | − | 0.342020i | 0.939693 | − | 0.342020i | \(-0.111111\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0.774117 | + | 1.34081i | 0.774117 | + | 1.34081i | ||||
\(483\) | 2.84242 | − | 4.92321i | 2.84242 | − | 4.92321i | ||||
\(484\) | 1.62278 | − | 1.36167i | 1.62278 | − | 1.36167i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −4.71469 | + | 8.16608i | −4.71469 | + | 8.16608i | ||||
\(487\) | 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 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(492\) | 1.55506 | + | 1.30485i | 1.55506 | + | 1.30485i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 1.74871 | + | 0.245765i | 1.74871 | + | 0.245765i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −0.532464 | − | 3.01975i | −0.532464 | − | 3.01975i | ||||
\(499\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.0691197 | + | 0.119719i | 0.0691197 | + | 0.119719i | ||||
\(502\) | 1.42864 | − | 2.47448i | 1.42864 | − | 2.47448i | ||||
\(503\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(504\) | 6.36111 | − | 5.33760i | 6.36111 | − | 5.33760i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.76159 | − | 3.05117i | −1.76159 | − | 3.05117i | ||||
\(507\) | −1.86110 | − | 0.677383i | −1.86110 | − | 0.677383i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.681131 | − | 0.571536i | −0.681131 | − | 0.571536i | ||||
\(512\) | −2.09769 | −2.09769 | ||||||||
\(513\) | 1.42636 | + | 3.53037i | 1.42636 | + | 3.53037i | ||||
\(514\) | −2.85728 | −2.85728 | ||||||||
\(515\) | 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 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.42468 | − | 2.46762i | −1.42468 | − | 2.46762i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −0.470881 | − | 2.67050i | −0.470881 | − | 2.67050i | ||||
\(529\) | −2.80079 | + | 1.01940i | −2.80079 | + | 1.01940i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.106362 | − | 3.04582i | −0.106362 | − | 3.04582i | ||||
\(533\) | −0.483844 | −0.483844 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.646352 | + | 3.66564i | −0.646352 | + | 3.66564i | ||||
\(538\) | 0.802890 | + | 0.292228i | 0.802890 | + | 0.292228i | ||||
\(539\) | 0.534899 | + | 0.926473i | 0.534899 | + | 0.926473i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.47274 | + | 1.23577i | −1.47274 | + | 1.23577i | −0.559193 | + | 0.829038i | \(0.688889\pi\) |
−0.913545 | + | 0.406737i | \(0.866667\pi\) | |||||||
\(542\) | −2.29440 | + | 1.92523i | −2.29440 | + | 1.92523i | ||||
\(543\) | −1.67959 | + | 2.90914i | −1.67959 | + | 2.90914i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −0.873740 | + | 4.95522i | −0.873740 | + | 4.95522i | ||||
\(547\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.76590 | −1.76590 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −7.80387 | −7.80387 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −0.454664 | − | 0.165484i | −0.454664 | − | 0.165484i | 0.104528 | − | 0.994522i | \(-0.466667\pi\) |
−0.559193 | + | 0.829038i | \(0.688889\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.49756 | − | 2.59386i | 1.49756 | − | 2.59386i | ||||
\(563\) | 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 | ||||||||
\(567\) | −6.24399 | + | 2.27263i | −6.24399 | + | 2.27263i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(572\) | 1.62278 | + | 1.36167i | 1.62278 | + | 1.36167i | ||||
\(573\) | −2.49063 | + | 0.906516i | −2.49063 | + | 0.906516i | ||||
\(574\) | 0.213454 | + | 1.21056i | 0.213454 | + | 1.21056i | ||||
\(575\) | −0.346450 | + | 1.96482i | −0.346450 | + | 1.96482i | ||||
\(576\) | 1.61240 | + | 0.586865i | 1.61240 | + | 0.586865i | ||||
\(577\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(578\) | −0.882948 | + | 1.52931i | −0.882948 | + | 1.52931i | ||||
\(579\) | 3.02697 | − | 2.53993i | 3.02697 | − | 2.53993i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.630676 | − | 1.09236i | 0.630676 | − | 1.09236i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.704030 | − | 0.256246i | −0.704030 | − | 0.256246i | ||||
\(584\) | −0.211953 | + | 1.20204i | −0.211953 | + | 1.20204i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.576303 | − | 0.209757i | 0.576303 | − | 0.209757i | ||||
\(587\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(588\) | 4.48838 | 4.48838 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.57328 | − | 2.15924i | −2.57328 | − | 2.15924i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.0363024 | + | 0.205881i | 0.0363024 | + | 0.205881i | 0.997564 | − | 0.0697565i | \(-0.0222222\pi\) |
−0.961262 | + | 0.275637i | \(0.911111\pi\) | |||||||
\(594\) | −1.16759 | + | 6.62172i | −1.16759 | + | 6.62172i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.93524 | + | 3.35194i | 1.93524 | + | 3.35194i | ||||
\(597\) | 1.21934 | − | 2.11196i | 1.21934 | − | 2.11196i | ||||
\(598\) | 2.69892 | − | 2.26466i | 2.69892 | − | 2.26466i | ||||
\(599\) | −1.35275 | + | 1.13510i | −1.35275 | + | 1.13510i | −0.374607 | + | 0.927184i | \(0.622222\pi\) |
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(600\) | −1.95573 | + | 3.38743i | −1.95573 | + | 3.38743i | ||||
\(601\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0.367854 | + | 2.08620i | 0.367854 | + | 2.08620i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(608\) | −0.375569 | + | 0.234682i | −0.375569 | + | 0.234682i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.0121205 | + | 0.0687386i | −0.0121205 | + | 0.0687386i | −0.990268 | − | 0.139173i | \(-0.955556\pi\) |
0.978148 | + | 0.207912i | \(0.0666667\pi\) | |||||||
\(614\) | −3.11865 | − | 1.13510i | −3.11865 | − | 1.13510i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.42066 | − | 2.46066i | 1.42066 | − | 2.46066i | ||||
\(617\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(618\) | 2.99636 | − | 2.51424i | 2.99636 | − | 2.51424i | ||||
\(619\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.13857 | + | 2.59823i | 7.13857 | + | 2.59823i | ||||
\(622\) | 0.607320 | − | 3.44429i | 0.607320 | − | 3.44429i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 2.54816 | − | 0.927455i | 2.54816 | − | 0.927455i | ||||
\(625\) | 0.766044 | + | 0.642788i | 0.766044 | + | 0.642788i | ||||
\(626\) | 3.22645 | 3.22645 | ||||||||
\(627\) | 1.32524 | + | 1.47183i | 1.32524 | + | 1.47183i | ||||
\(628\) | −0.442863 | −0.442863 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −2.40795 | + | 2.02051i | −2.40795 | + | 2.02051i | ||||
\(637\) | −0.819514 | + | 0.687654i | −0.819514 | + | 0.687654i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.194206 | − | 1.10140i | 0.194206 | − | 1.10140i | −0.719340 | − | 0.694658i | \(-0.755556\pi\) |
0.913545 | − | 0.406737i | \(-0.133333\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(644\) | −4.65794 | − | 3.90848i | −4.65794 | − | 3.90848i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.69610 | 1.69610 | 0.848048 | − | 0.529919i | \(-0.177778\pi\) | ||||
0.848048 | + | 0.529919i | \(0.177778\pi\) | |||||||
\(648\) | 6.98751 | + | 5.86322i | 6.98751 | + | 5.86322i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −0.306644 | − | 1.73907i | −0.306644 | − | 1.73907i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.173648 | − | 0.300767i | −0.173648 | − | 0.300767i | 0.766044 | − | 0.642788i | \(-0.222222\pi\) |
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(654\) | 2.34023 | − | 4.05340i | 2.34023 | − | 4.05340i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0.507478 | − | 0.425825i | 0.507478 | − | 0.425825i | ||||
\(657\) | 0.903109 | − | 1.56423i | 0.903109 | − | 1.56423i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.73152 | −1.73152 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0.138944 | − | 0.0505715i | 0.138944 | − | 0.0505715i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −0.630938 | − | 1.09282i | −0.630938 | − | 1.09282i | ||||
\(673\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.91681 | − | 2.44750i | 2.91681 | − | 2.44750i | ||||
\(676\) | −1.05919 | + | 1.83458i | −1.05919 | + | 1.83458i | ||||
\(677\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(678\) | −0.229394 | − | 0.0834927i | −0.229394 | − | 0.0834927i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.15022 | − | 0.418646i | 1.15022 | − | 0.418646i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(684\) | 6.05574 | − | 1.28719i | 6.05574 | − | 1.28719i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0.135841 | + | 0.113984i | 0.135841 | + | 0.113984i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.130100 | − | 0.737831i | 0.130100 | − | 0.737831i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.22089 | + | 2.70265i | −3.22089 | + | 2.70265i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −0.342947 | + | 1.94495i | −0.342947 | + | 1.94495i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.86388 | + | 1.04237i | −2.86388 | + | 1.04237i | ||||
\(701\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(702\) | −6.72387 | −6.72387 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0.587123 | 0.587123 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.74116 | + | 1.36167i | 3.74116 | + | 1.36167i | ||||
\(717\) | 0.423472 | − | 2.40163i | 0.423472 | − | 2.40163i | ||||
\(718\) | 0.611795 | + | 3.46966i | 0.611795 | + | 3.46966i | ||||
\(719\) | −0.326352 | + | 0.118782i | −0.326352 | + | 0.118782i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.60900 | 1.60900 | ||||||||
\(722\) | 0.774117 | − | 1.58718i | 0.774117 | − | 1.58718i | ||||
\(723\) | −1.73642 | −1.73642 | ||||||||
\(724\) | 2.75239 | + | 2.30953i | 2.75239 | + | 2.30953i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0.607320 | + | 3.44429i | 0.607320 | + | 3.44429i | ||||
\(727\) | −0.249824 | + | 1.41682i | −0.249824 | + | 1.41682i | 0.559193 | + | 0.829038i | \(0.311111\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(728\) | 2.66997 | + | 0.971790i | 2.66997 | + | 0.971790i | ||||
\(729\) | −2.97844 | − | 5.15881i | −2.97844 | − | 5.15881i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.438371 | − | 0.759281i | 0.438371 | − | 0.759281i | −0.559193 | − | 0.829038i | \(-0.688889\pi\) |
0.997564 | + | 0.0697565i | \(0.0222222\pi\) | |||||||
\(734\) | −0.545692 | − | 0.945166i | −0.545692 | − | 0.945166i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.153430 | + | 0.870145i | −0.153430 | + | 0.870145i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −2.34646 | + | 0.854043i | −2.34646 | + | 0.854043i | ||||
\(739\) | 0.370646 | + | 0.311009i | 0.370646 | + | 0.311009i | 0.809017 | − | 0.587785i | \(-0.200000\pi\) |
−0.438371 | + | 0.898794i | \(0.644444\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.21934 | + | 1.56068i | −1.21934 | + | 1.56068i | ||||
\(742\) | −1.90342 | −1.90342 | ||||||||
\(743\) | 1.43969 | + | 1.20805i | 1.43969 | + | 1.20805i | 0.939693 | + | 0.342020i | \(0.111111\pi\) |
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.40777 | + | 0.876358i | 2.40777 | + | 0.876358i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.49861 | + | 1.25748i | −1.49861 | + | 1.25748i | −0.615661 | + | 0.788011i | \(0.711111\pi\) |
−0.882948 | + | 0.469472i | \(0.844444\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.60229 | + | 2.77524i | 1.60229 | + | 2.77524i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.01509 | + | 11.4281i | 2.01509 | + | 11.4281i | ||||
\(757\) | 1.52045 | − | 0.553400i | 1.52045 | − | 0.553400i | 0.559193 | − | 0.829038i | \(-0.311111\pi\) |
0.961262 | + | 0.275637i | \(0.0888889\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.95142 | 3.95142 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.92252 | −1.92252 | −0.961262 | − | 0.275637i | \(-0.911111\pi\) | ||||
−0.961262 | + | 0.275637i | \(0.911111\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.80922 | − | 0.658501i | 1.80922 | − | 0.658501i | ||||
\(764\) | 0.492285 | + | 2.79188i | 0.492285 | + | 2.79188i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 2.00609 | − | 3.47464i | 2.00609 | − | 3.47464i | ||||
\(769\) | 0.370646 | − | 0.311009i | 0.370646 | − | 0.311009i | −0.438371 | − | 0.898794i | \(-0.644444\pi\) |
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.60229 | − | 2.77524i | 1.60229 | − | 2.77524i | ||||
\(772\) | −2.11323 | − | 3.66021i | −2.11323 | − | 3.66021i | ||||
\(773\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −3.45461 | −3.45461 | ||||||||
\(779\) | −0.149516 | + | 0.460163i | −0.149516 | + | 0.460163i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.254349 | − | 1.44249i | 0.254349 | − | 1.44249i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.719340 | + | 1.24593i | −0.719340 | + | 1.24593i | 0.241922 | + | 0.970296i | \(0.422222\pi\) |
−0.961262 | + | 0.275637i | \(0.911111\pi\) | |||||||
\(788\) | −2.75239 | + | 2.30953i | −2.75239 | + | 2.30953i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.0502092 | − | 0.0869649i | −0.0502092 | − | 0.0869649i | ||||
\(792\) | 5.42376 | + | 1.97409i | 5.42376 | + | 1.97409i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.99816 | − | 1.67666i | −1.99816 | − | 1.67666i | ||||
\(797\) | 0.347296 | 0.347296 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(798\) | 4.44270 | + | 2.36222i | 4.44270 | + | 2.36222i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0.339253 | + | 0.284667i | 0.339253 | + | 0.284667i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.107320 | − | 0.608645i | 0.107320 | − | 0.608645i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.734077 | + | 0.615964i | −0.734077 | + | 0.615964i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.80658 | + | 0.657542i | 1.80658 | + | 0.657542i | 0.997564 | + | 0.0697565i | \(0.0222222\pi\) |
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.583315 | − | 3.30815i | −0.583315 | − | 3.30815i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −2.70551 | −2.70551 | ||||||||
\(819\) | −3.22089 | − | 2.70265i | −3.22089 | − | 2.70265i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.173648 | + | 0.984808i | 0.173648 | + | 0.984808i | 0.939693 | + | 0.342020i | \(0.111111\pi\) |
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.52045 | + | 0.553400i | 1.52045 | + | 0.553400i | 0.961262 | − | 0.275637i | \(-0.0888889\pi\) |
0.559193 | + | 0.829038i | \(0.311111\pi\) | |||||||
\(824\) | −1.10438 | − | 1.91284i | −1.10438 | − | 1.91284i | ||||
\(825\) | 0.990268 | − | 1.71519i | 0.990268 | − | 1.71519i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.49861 | − | 1.25748i | 1.49861 | − | 1.25748i | 0.615661 | − | 0.788011i | \(-0.288889\pi\) |
0.882948 | − | 0.469472i | \(-0.155556\pi\) | |||||||
\(828\) | 6.17595 | − | 10.6971i | 6.17595 | − | 10.6971i | ||||
\(829\) | 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 | ||||||||
\(832\) | 0.101953 | + | 0.578203i | 0.101953 | + | 0.578203i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.79649 | − | 1.12257i | 1.79649 | − | 1.12257i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.47160 | + | 2.07392i | 2.47160 | + | 2.07392i | ||||
\(839\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.173648 | − | 0.984808i | 0.173648 | − | 0.984808i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.67959 | + | 2.90914i | 1.67959 | + | 2.90914i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.719340 | + | 1.24593i | −0.719340 | + | 1.24593i | ||||
\(848\) | 0.512901 | + | 0.888371i | 0.512901 | + | 0.888371i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.35275 | + | 1.13510i | 1.35275 | + | 1.13510i | 0.978148 | + | 0.207912i | \(0.0666667\pi\) |
0.374607 | + | 0.927184i | \(0.377778\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(858\) | −3.28650 | + | 1.19619i | −3.28650 | + | 1.19619i | ||||
\(859\) | 0.294524 | + | 1.67033i | 0.294524 | + | 1.67033i | 0.669131 | + | 0.743145i | \(0.266667\pi\) |
−0.374607 | + | 0.927184i | \(0.622222\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.29550 | − | 0.471524i | −1.29550 | − | 0.471524i | ||||
\(862\) | 0.987476 | + | 1.71036i | 0.987476 | + | 1.71036i | ||||
\(863\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(864\) | 1.29175 | − | 1.08391i | 1.29175 | − | 1.08391i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.08719 | − | 1.88307i | 1.08719 | − | 1.88307i | ||||
\(867\) | −0.990268 | − | 1.71519i | −0.990268 | − | 1.71519i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −2.02466 | − | 1.69889i | −2.02466 | − | 1.69889i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.31981 | − | 3.26664i | −1.31981 | − | 3.26664i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.98634 | − | 1.66674i | −1.98634 | − | 1.66674i | ||||
\(877\) | 0.580762 | − | 0.211380i | 0.580762 | − | 0.211380i | −0.0348995 | − | 0.999391i | \(-0.511111\pi\) |
0.615661 | + | 0.788011i | \(0.288889\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.119441 | + | 0.677383i | −0.119441 | + | 0.677383i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.374607 | + | 0.648838i | 0.374607 | + | 0.648838i | 0.990268 | − | 0.139173i | \(-0.0444444\pi\) |
−0.615661 | + | 0.788011i | \(0.711111\pi\) | |||||||
\(882\) | −2.76055 | + | 4.78141i | −2.76055 | + | 4.78141i | ||||
\(883\) | 1.51718 | − | 1.27306i | 1.51718 | − | 1.27306i | 0.669131 | − | 0.743145i | \(-0.266667\pi\) |
0.848048 | − | 0.529919i | \(-0.177778\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.774117 | − | 1.34081i | −0.774117 | − | 1.34081i | ||||
\(887\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.53807 | − | 2.96879i | −3.53807 | − | 2.96879i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −6.39010 | −6.39010 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.00038 | − | 0.728078i | 2.00038 | − | 0.728078i | ||||
\(897\) | 0.686157 | + | 3.89139i | 0.686157 | + | 3.89139i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −3.09552 | − | 5.36159i | −3.09552 | − | 5.36159i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −0.654522 | + | 0.549209i | −0.654522 | + | 0.549209i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.0689248 | + | 0.119381i | −0.0689248 | + | 0.119381i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −3.28650 | − | 1.19619i | −3.28650 | − | 1.19619i | ||||
\(907\) | −0.280969 | + | 1.59345i | −0.280969 | + | 1.59345i | 0.438371 | + | 0.898794i | \(0.355556\pi\) |
−0.719340 | + | 0.694658i | \(0.755556\pi\) | |||||||
\(908\) | −0.227346 | − | 1.28934i | −0.227346 | − | 1.28934i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.99513 | −1.99513 | −0.997564 | − | 0.0697565i | \(-0.977778\pi\) | ||||
−0.997564 | + | 0.0697565i | \(0.977778\pi\) | |||||||
\(912\) | −0.0946368 | − | 2.71004i | −0.0946368 | − | 2.71004i | ||||
\(913\) | 0.876742 | 0.876742 | ||||||||
\(914\) | 1.66568 | + | 1.39767i | 1.66568 | + | 1.39767i | ||||
\(915\) | 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 | ||||||||
\(921\) | 2.85136 | − | 2.39258i | 2.85136 | − | 2.39258i | ||||
\(922\) | 2.64639 | − | 2.22058i | 2.64639 | − | 2.22058i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 3.01802 | + | 5.22736i | 3.01802 | + | 5.22736i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.567571 | + | 3.21885i | 0.567571 | + | 3.21885i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.400754 | + | 0.991900i | 0.400754 | + | 0.991900i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.00483 | + | 2.52135i | 3.00483 | + | 2.52135i | ||||
\(934\) | −2.54235 | + | 0.925338i | −2.54235 | + | 0.925338i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.00227 | + | 5.68416i | −1.00227 | + | 5.68416i | ||||
\(937\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.80931 | + | 3.13382i | −1.80931 | + | 3.13382i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.49861 | − | 1.25748i | 1.49861 | − | 1.25748i | 0.615661 | − | 0.788011i | \(-0.288889\pi\) |
0.882948 | − | 0.469472i | \(-0.155556\pi\) | |||||||
\(942\) | 0.365580 | − | 0.633203i | 0.365580 | − | 0.633203i | ||||
\(943\) | 0.482665 | + | 0.836001i | 0.482665 | + | 0.836001i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.618034 | 0.618034 | ||||||||
\(950\) | −1.74871 | − | 0.245765i | −1.74871 | − | 0.245765i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(954\) | −0.671427 | − | 3.80785i | −0.671427 | − | 3.80785i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −2.45111 | − | 0.892131i | −2.45111 | − | 0.892131i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0.306644 | − | 0.531124i | 0.306644 | − | 0.531124i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −0.322513 | + | 1.82906i | −0.322513 | + | 1.82906i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 9.43340 | − | 3.43348i | 9.43340 | − | 3.43348i | ||||
\(967\) | −0.0534691 | − | 0.0448659i | −0.0534691 | − | 0.0448659i | 0.615661 | − | 0.788011i | \(-0.288889\pi\) |
−0.669131 | + | 0.743145i | \(0.733333\pi\) | |||||||
\(968\) | 1.97495 | 1.97495 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.49861 | − | 1.25748i | −1.49861 | − | 1.25748i | −0.882948 | − | 0.469472i | \(-0.844444\pi\) |
−0.615661 | − | 0.788011i | \(-0.711111\pi\) | |||||||
\(972\) | −10.6294 | + | 3.86879i | −10.6294 | + | 3.86879i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.86110 | + | 0.677383i | 1.86110 | + | 0.677383i | ||||
\(976\) | 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 | ||||||||
\(981\) | 1.95555 | + | 3.38711i | 1.95555 | + | 3.38711i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(984\) | 0.328636 | + | 1.86379i | 0.328636 | + | 1.86379i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.41748 | + | 1.57427i | 1.41748 | + | 1.57427i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.704030 | − | 0.256246i | 0.704030 | − | 0.256246i | 0.0348995 | − | 0.999391i | \(-0.488889\pi\) |
0.669131 | + | 0.743145i | \(0.266667\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.83920 | − | 3.18559i | 1.83920 | − | 3.18559i | ||||
\(997\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(998\) | 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.2144.4 | yes | 24 | |
11.10 | odd | 2 | 2717.1.db.d.2144.1 | yes | 24 | ||
13.12 | even | 2 | 2717.1.db.d.2144.1 | yes | 24 | ||
19.6 | even | 9 | inner | 2717.1.db.c.2001.4 | ✓ | 24 | |
143.142 | odd | 2 | CM | 2717.1.db.c.2144.4 | yes | 24 | |
209.120 | odd | 18 | 2717.1.db.d.2001.1 | yes | 24 | ||
247.25 | even | 18 | 2717.1.db.d.2001.1 | yes | 24 | ||
2717.2001 | odd | 18 | inner | 2717.1.db.c.2001.4 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2717.1.db.c.2001.4 | ✓ | 24 | 19.6 | even | 9 | inner | |
2717.1.db.c.2001.4 | ✓ | 24 | 2717.2001 | odd | 18 | inner | |
2717.1.db.c.2144.4 | yes | 24 | 1.1 | even | 1 | trivial | |
2717.1.db.c.2144.4 | yes | 24 | 143.142 | odd | 2 | CM | |
2717.1.db.d.2001.1 | yes | 24 | 209.120 | odd | 18 | ||
2717.1.db.d.2001.1 | yes | 24 | 247.25 | even | 18 | ||
2717.1.db.d.2144.1 | yes | 24 | 11.10 | odd | 2 | ||
2717.1.db.d.2144.1 | yes | 24 | 13.12 | even | 2 |