Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1503,1,Mod(166,1503)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1503, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 3]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1503.166");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1503 = 3^{2} \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1503.f (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.750094713987\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{33})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - x^{19} + x^{17} - x^{16} + x^{14} - x^{13} + x^{11} - x^{10} + x^{9} - x^{7} + x^{6} - x^{4} + x^{3} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{33}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{33} + \cdots)\) |
Embedding invariants
Embedding label | 1168.3 | ||
Root | \(0.928368 - 0.371662i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1503.1168 |
Dual form | 1503.1.f.b.166.3 |
$q$-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 \(\left(\mathbb{Z}/1503\mathbb{Z}\right)^\times\).
\(n\) | \(172\) | \(335\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.723734 | + | 1.25354i | −0.723734 | + | 1.25354i | 0.235759 | + | 0.971812i | \(0.424242\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(3\) | 0.580057 | + | 0.814576i | 0.580057 | + | 0.814576i | ||||
\(4\) | −0.547582 | − | 0.948440i | −0.547582 | − | 0.948440i | ||||
\(5\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(6\) | −1.44091 | + | 0.137591i | −1.44091 | + | 0.137591i | ||||
\(7\) | 0.786053 | − | 1.36148i | 0.786053 | − | 1.36148i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) |
0.928368 | − | 0.371662i | \(-0.121212\pi\) | |||||||
\(8\) | 0.137747 | 0.137747 | ||||||||
\(9\) | −0.327068 | + | 0.945001i | −0.327068 | + | 0.945001i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.888835 | − | 1.53951i | 0.888835 | − | 1.53951i | 0.0475819 | − | 0.998867i | \(-0.484848\pi\) |
0.841254 | − | 0.540641i | \(-0.181818\pi\) | |||||||
\(12\) | 0.454947 | − | 0.996196i | 0.454947 | − | 0.996196i | ||||
\(13\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(14\) | 1.13779 | + | 1.97070i | 1.13779 | + | 1.97070i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.447890 | − | 0.775768i | 0.447890 | − | 0.775768i | ||||
\(17\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(18\) | −0.947890 | − | 1.09392i | −0.947890 | − | 1.09392i | ||||
\(19\) | 1.96386 | 1.96386 | 0.981929 | − | 0.189251i | \(-0.0606061\pi\) | ||||
0.981929 | + | 0.189251i | \(0.0606061\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.56499 | − | 0.149438i | 1.56499 | − | 0.149438i | ||||
\(22\) | 1.28656 | + | 2.22839i | 1.28656 | + | 2.22839i | ||||
\(23\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(24\) | 0.0799009 | + | 0.112205i | 0.0799009 | + | 0.112205i | ||||
\(25\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.959493 | + | 0.281733i | −0.959493 | + | 0.281733i | ||||
\(28\) | −1.72171 | −1.72171 | ||||||||
\(29\) | −0.928368 | + | 1.60798i | −0.928368 | + | 1.60798i | −0.142315 | + | 0.989821i | \(0.545455\pi\) |
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.723734 | − | 1.25354i | −0.723734 | − | 1.25354i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
0.235759 | − | 0.971812i | \(-0.424242\pi\) | |||||||
\(32\) | 0.717180 | + | 1.24219i | 0.717180 | + | 1.24219i | ||||
\(33\) | 1.76962 | − | 0.168978i | 1.76962 | − | 0.168978i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.07537 | − | 0.207261i | 1.07537 | − | 0.207261i | ||||
\(37\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(38\) | −1.42131 | + | 2.46178i | −1.42131 | + | 2.46178i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(42\) | −0.945307 | + | 2.06993i | −0.945307 | + | 2.06993i | ||||
\(43\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(44\) | −1.94684 | −1.94684 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.327068 | − | 0.566498i | 0.327068 | − | 0.566498i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
0.981929 | + | 0.189251i | \(0.0606061\pi\) | |||||||
\(48\) | 0.891724 | − | 0.0851493i | 0.891724 | − | 0.0851493i | ||||
\(49\) | −0.735759 | − | 1.27437i | −0.735759 | − | 1.27437i | ||||
\(50\) | −0.723734 | − | 1.25354i | −0.723734 | − | 1.25354i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(54\) | 0.341254 | − | 1.40667i | 0.341254 | − | 1.40667i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.108276 | − | 0.187540i | 0.108276 | − | 0.187540i | ||||
\(57\) | 1.13915 | + | 1.59971i | 1.13915 | + | 1.59971i | ||||
\(58\) | −1.34378 | − | 2.32750i | −1.34378 | − | 2.32750i | ||||
\(59\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.415415 | + | 0.719520i | −0.415415 | + | 0.719520i | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) |
0.580057 | + | 0.814576i | \(0.303030\pi\) | |||||||
\(62\) | 2.09516 | 2.09516 | ||||||||
\(63\) | 1.02951 | + | 1.18812i | 1.02951 | + | 1.18812i | ||||
\(64\) | −1.18041 | −1.18041 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.06891 | + | 2.34059i | −1.06891 | + | 2.34059i | ||||
\(67\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | −0.0450525 | + | 0.130171i | −0.0450525 | + | 0.130171i | ||||
\(73\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.995472 | + | 0.0950560i | −0.995472 | + | 0.0950560i | ||||
\(76\) | −1.07537 | − | 1.86260i | −1.07537 | − | 1.86260i | ||||
\(77\) | −1.39734 | − | 2.42027i | −1.39734 | − | 2.42027i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.786053 | − | 0.618159i | −0.786053 | − | 0.618159i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(84\) | −0.998692 | − | 1.40247i | −0.998692 | − | 1.40247i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.84833 | + | 0.176494i | −1.84833 | + | 0.176494i | ||||
\(88\) | 0.122434 | − | 0.212062i | 0.122434 | − | 0.212062i | ||||
\(89\) | 1.16011 | 1.16011 | 0.580057 | − | 0.814576i | \(-0.303030\pi\) | ||||
0.580057 | + | 0.814576i | \(0.303030\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.601300 | − | 1.31666i | 0.601300 | − | 1.31666i | ||||
\(94\) | 0.473420 | + | 0.819988i | 0.473420 | + | 0.819988i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.595855 | + | 1.30474i | −0.595855 | + | 1.30474i | ||||
\(97\) | −0.841254 | + | 1.45709i | −0.841254 | + | 1.45709i | 0.0475819 | + | 0.998867i | \(0.484848\pi\) |
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(98\) | 2.12998 | 2.12998 | ||||||||
\(99\) | 1.16413 | + | 1.34347i | 1.16413 | + | 1.34347i | ||||
\(100\) | 1.09516 | 1.09516 | ||||||||
\(101\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.57211 | −1.57211 | −0.786053 | − | 0.618159i | \(-0.787879\pi\) | ||||
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(108\) | 0.792607 | + | 0.755750i | 0.792607 | + | 0.755750i | ||||
\(109\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.704131 | − | 1.21959i | −0.704131 | − | 1.21959i | ||||
\(113\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(114\) | −2.82975 | + | 0.270208i | −2.82975 | + | 0.270208i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.03343 | 2.03343 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.08006 | − | 1.87071i | −1.08006 | − | 1.87071i | ||||
\(122\) | −0.601300 | − | 1.04148i | −0.601300 | − | 1.04148i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.792607 | + | 1.37284i | −0.792607 | + | 1.37284i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.23445 | + | 0.430655i | −2.23445 | + | 0.430655i | ||||
\(127\) | −1.77767 | −1.77767 | −0.888835 | − | 0.458227i | \(-0.848485\pi\) | ||||
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(128\) | 0.137123 | − | 0.237504i | 0.137123 | − | 0.237504i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(132\) | −1.12928 | − | 1.58585i | −1.12928 | − | 1.58585i | ||||
\(133\) | 1.54370 | − | 2.67376i | 1.54370 | − | 2.67376i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.0475819 | + | 0.0824143i | −0.0475819 | + | 0.0824143i | −0.888835 | − | 0.458227i | \(-0.848485\pi\) |
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.651174 | − | 0.0621796i | 0.651174 | − | 0.0621796i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.586611 | + | 0.676985i | 0.586611 | + | 0.676985i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.611291 | − | 1.33854i | 0.611291 | − | 1.33854i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(150\) | 0.601300 | − | 1.31666i | 0.601300 | − | 1.31666i | ||||
\(151\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(152\) | 0.270515 | 0.270515 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 4.04522 | 4.04522 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.959493 | + | 1.66189i | 0.959493 | + | 1.66189i | 0.723734 | + | 0.690079i | \(0.242424\pi\) |
0.235759 | + | 0.971812i | \(0.424242\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.34378 | − | 0.537970i | 1.34378 | − | 0.537970i | ||||
\(163\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(168\) | 0.215572 | − | 0.0205846i | 0.215572 | − | 0.0205846i | ||||
\(169\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.642315 | + | 1.85585i | −0.642315 | + | 1.85585i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.841254 | + | 1.45709i | −0.841254 | + | 1.45709i | 0.0475819 | + | 0.998867i | \(0.484848\pi\) |
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(174\) | 1.11646 | − | 2.44470i | 1.11646 | − | 2.44470i | ||||
\(175\) | 0.786053 | + | 1.36148i | 0.786053 | + | 1.36148i | ||||
\(176\) | −0.796201 | − | 1.37906i | −0.796201 | − | 1.37906i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.839614 | + | 1.45425i | −0.839614 | + | 1.45425i | ||||
\(179\) | 1.96386 | 1.96386 | 0.981929 | − | 0.189251i | \(-0.0606061\pi\) | ||||
0.981929 | + | 0.189251i | \(0.0606061\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.654136 | −0.654136 | −0.327068 | − | 0.945001i | \(-0.606061\pi\) | ||||
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.827068 | + | 0.0789754i | −0.827068 | + | 0.0789754i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.21531 | + | 1.70667i | 1.21531 | + | 1.70667i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −0.716386 | −0.716386 | ||||||||
\(189\) | −0.370638 | + | 1.52779i | −0.370638 | + | 1.52779i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.235759 | + | 0.408346i | −0.235759 | + | 0.408346i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
0.723734 | + | 0.690079i | \(0.242424\pi\) | |||||||
\(192\) | −0.684705 | − | 0.961533i | −0.684705 | − | 0.961533i | ||||
\(193\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(194\) | −1.21769 | − | 2.10910i | −1.21769 | − | 2.10910i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.805777 | + | 1.39565i | −0.805777 | + | 1.39565i | ||||
\(197\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(198\) | −2.52662 | + | 0.486967i | −2.52662 | + | 0.486967i | ||||
\(199\) | 1.68251 | 1.68251 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(200\) | −0.0688733 | + | 0.119292i | −0.0688733 | + | 0.119292i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.45949 | + | 2.52792i | 1.45949 | + | 2.52792i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.74555 | − | 3.02337i | 1.74555 | − | 3.02337i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.959493 | + | 1.66189i | 0.959493 | + | 1.66189i | 0.723734 | + | 0.690079i | \(0.242424\pi\) |
0.235759 | + | 0.971812i | \(0.424242\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.13779 | − | 1.97070i | 1.13779 | − | 1.97070i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.132167 | + | 0.0388077i | −0.132167 | + | 0.0388077i | ||||
\(217\) | −2.27557 | −2.27557 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.580057 | + | 1.00469i | −0.580057 | + | 1.00469i | 0.415415 | + | 0.909632i | \(0.363636\pi\) |
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(224\) | 2.25497 | 2.25497 | ||||||||
\(225\) | −0.654861 | − | 0.755750i | −0.654861 | − | 0.755750i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(228\) | 0.893452 | − | 1.95639i | 0.893452 | − | 1.95639i | ||||
\(229\) | −0.928368 | − | 1.60798i | −0.928368 | − | 1.60798i | −0.786053 | − | 0.618159i | \(-0.787879\pi\) |
−0.142315 | − | 0.989821i | \(-0.545455\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.16096 | − | 2.54214i | 1.16096 | − | 2.54214i | ||||
\(232\) | −0.127880 | + | 0.221494i | −0.127880 | + | 0.221494i | ||||
\(233\) | 0.471518 | 0.471518 | 0.235759 | − | 0.971812i | \(-0.424242\pi\) | ||||
0.235759 | + | 0.971812i | \(0.424242\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.580057 | − | 1.00469i | −0.580057 | − | 1.00469i | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) |
0.415415 | − | 0.909632i | \(-0.363636\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(242\) | 3.12670 | 3.12670 | ||||||||
\(243\) | 0.0475819 | − | 0.998867i | 0.0475819 | − | 0.998867i | ||||
\(244\) | 0.909895 | 0.909895 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −0.0996919 | − | 0.172671i | −0.0996919 | − | 0.172671i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.284630 | −0.284630 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(252\) | 0.563117 | − | 1.62702i | 0.563117 | − | 1.62702i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 1.28656 | − | 2.22839i | 1.28656 | − | 2.22839i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.391724 | − | 0.678486i | −0.391724 | − | 0.678486i | ||||
\(257\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.21590 | − | 1.40323i | −1.21590 | − | 1.40323i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.415415 | + | 0.719520i | −0.415415 | + | 0.719520i | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) |
0.580057 | + | 0.814576i | \(0.303030\pi\) | |||||||
\(264\) | 0.243759 | − | 0.0232762i | 0.243759 | − | 0.0232762i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.23445 | + | 3.87018i | 2.23445 | + | 3.87018i | ||||
\(267\) | 0.672932 | + | 0.945001i | 0.672932 | + | 0.945001i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.0688733 | − | 0.119292i | −0.0688733 | − | 0.119292i | ||||
\(275\) | 0.888835 | + | 1.53951i | 0.888835 | + | 1.53951i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.42131 | − | 0.273935i | 1.42131 | − | 0.273935i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.995472 | − | 1.72421i | 0.995472 | − | 1.72421i | 0.415415 | − | 0.909632i | \(-0.363636\pi\) |
0.580057 | − | 0.814576i | \(-0.303030\pi\) | |||||||
\(282\) | −0.393332 | + | 0.861277i | −0.393332 | + | 0.861277i | ||||
\(283\) | −0.841254 | − | 1.45709i | −0.841254 | − | 1.45709i | −0.888835 | − | 0.458227i | \(-0.848485\pi\) |
0.0475819 | − | 0.998867i | \(-0.484848\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.40844 | + | 0.271454i | −1.40844 | + | 0.271454i | ||||
\(289\) | 1.00000 | 1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.67489 | + | 0.159932i | −1.67489 | + | 0.159932i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.235759 | − | 0.408346i | −0.235759 | − | 0.408346i | 0.723734 | − | 0.690079i | \(-0.242424\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(294\) | 1.23551 | + | 1.73503i | 1.23551 | + | 1.73503i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.419102 | + | 1.72756i | −0.419102 | + | 1.72756i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0.635257 | + | 0.892094i | 0.635257 | + | 0.892094i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.879592 | − | 1.52350i | 0.879592 | − | 1.52350i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(308\) | −1.53032 | + | 2.65059i | −1.53032 | + | 2.65059i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(314\) | −2.77767 | −2.77767 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.995472 | − | 1.72421i | 0.995472 | − | 1.72421i | 0.415415 | − | 0.909632i | \(-0.363636\pi\) |
0.580057 | − | 0.814576i | \(-0.303030\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.65033 | + | 2.85846i | 1.65033 | + | 2.85846i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.911911 | − | 1.28060i | −0.911911 | − | 1.28060i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −0.155858 | + | 1.08402i | −0.155858 | + | 1.08402i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.514186 | − | 0.890596i | −0.514186 | − | 0.890596i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.44747 | 1.44747 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.585013 | − | 1.28100i | 0.585013 | − | 1.28100i | ||||
\(337\) | 0.327068 | + | 0.566498i | 0.327068 | + | 0.566498i | 0.981929 | − | 0.189251i | \(-0.0606061\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(338\) | −0.723734 | − | 1.25354i | −0.723734 | − | 1.25354i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.57312 | −2.57312 | ||||||||
\(342\) | −1.86152 | − | 2.14831i | −1.86152 | − | 2.14831i | ||||
\(343\) | −0.741276 | −0.741276 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.21769 | − | 2.10910i | −1.21769 | − | 2.10910i | ||||
\(347\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(348\) | 1.17951 | + | 1.65638i | 1.17951 | + | 1.65638i | ||||
\(349\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(350\) | −2.27557 | −2.27557 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.54982 | 2.54982 | ||||||||
\(353\) | 0.142315 | − | 0.246497i | 0.142315 | − | 0.246497i | −0.786053 | − | 0.618159i | \(-0.787879\pi\) |
0.928368 | + | 0.371662i | \(0.121212\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −0.635257 | − | 1.10030i | −0.635257 | − | 1.10030i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.42131 | + | 2.46178i | −1.42131 | + | 2.46178i | ||||
\(359\) | −1.91899 | −1.91899 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.85674 | 2.85674 | ||||||||
\(362\) | 0.473420 | − | 0.819988i | 0.473420 | − | 0.819988i | ||||
\(363\) | 0.897344 | − | 1.96491i | 0.897344 | − | 1.96491i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.499578 | − | 1.09392i | 0.499578 | − | 1.09392i | ||||
\(367\) | 0.327068 | − | 0.566498i | 0.327068 | − | 0.566498i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
0.981929 | + | 0.189251i | \(0.0606061\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −1.57804 | + | 0.150684i | −1.57804 | + | 0.150684i | ||||
\(373\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.0450525 | − | 0.0780332i | 0.0450525 | − | 0.0780332i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −1.64691 | − | 1.57033i | −1.64691 | − | 1.57033i | ||||
\(379\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.03115 | − | 1.44805i | −1.03115 | − | 1.44805i | ||||
\(382\) | −0.341254 | − | 0.591068i | −0.341254 | − | 0.591068i | ||||
\(383\) | 0.142315 | + | 0.246497i | 0.142315 | + | 0.246497i | 0.928368 | − | 0.371662i | \(-0.121212\pi\) |
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(384\) | 0.273004 | − | 0.0260687i | 0.273004 | − | 0.0260687i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.84262 | 1.84262 | ||||||||
\(389\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −0.101348 | − | 0.175540i | −0.101348 | − | 0.175540i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.636749 | − | 1.83977i | 0.636749 | − | 1.83977i | ||||
\(397\) | −1.99094 | −1.99094 | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) | ||||
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(398\) | −1.21769 | + | 2.10910i | −1.21769 | + | 2.10910i | ||||
\(399\) | 3.07341 | − | 0.293475i | 3.07341 | − | 0.293475i | ||||
\(400\) | 0.447890 | + | 0.775768i | 0.447890 | + | 0.775768i | ||||
\(401\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.22514 | −4.22514 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.888835 | + | 1.53951i | 0.888835 | + | 1.53951i | 0.841254 | + | 0.540641i | \(0.181818\pi\) |
0.0475819 | + | 0.998867i | \(0.484848\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.0947329 | + | 0.00904590i | −0.0947329 | + | 0.00904590i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.52662 | + | 4.37624i | 2.52662 | + | 4.37624i | ||||
\(419\) | −0.235759 | − | 0.408346i | −0.235759 | − | 0.408346i | 0.723734 | − | 0.690079i | \(-0.242424\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.142315 | − | 0.246497i | 0.142315 | − | 0.246497i | −0.786053 | − | 0.618159i | \(-0.787879\pi\) |
0.928368 | + | 0.371662i | \(0.121212\pi\) | |||||||
\(422\) | −2.77767 | −2.77767 | ||||||||
\(423\) | 0.428368 | + | 0.494363i | 0.428368 | + | 0.494363i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.653077 | + | 1.13116i | 0.653077 | + | 1.13116i | ||||
\(428\) | 0.860857 | + | 1.49105i | 0.860857 | + | 1.49105i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.99094 | −1.99094 | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) | ||||
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(432\) | −0.211188 | + | 0.870529i | −0.211188 | + | 0.870529i | ||||
\(433\) | −1.30972 | −1.30972 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(434\) | 1.64691 | − | 2.85253i | 1.64691 | − | 2.85253i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.44493 | − | 0.278487i | 1.44493 | − | 0.278487i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −0.839614 | − | 1.45425i | −0.839614 | − | 1.45425i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.927865 | + | 1.60711i | −0.927865 | + | 1.60711i | ||||
\(449\) | −1.30972 | −1.30972 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(450\) | 1.42131 | − | 0.273935i | 1.42131 | − | 0.273935i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.156914 | + | 0.220355i | 0.156914 | + | 0.220355i | ||||
\(457\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(458\) | 2.68757 | 2.68757 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.654861 | − | 1.13425i | 0.654861 | − | 1.13425i | −0.327068 | − | 0.945001i | \(-0.606061\pi\) |
0.981929 | − | 0.189251i | \(-0.0606061\pi\) | |||||||
\(462\) | 2.34646 | + | 3.29514i | 2.34646 | + | 3.29514i | ||||
\(463\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(464\) | 0.831613 | + | 1.44040i | 0.831613 | + | 1.44040i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.341254 | + | 0.591068i | −0.341254 | + | 0.591068i | ||||
\(467\) | 1.85674 | 1.85674 | 0.928368 | − | 0.371662i | \(-0.121212\pi\) | ||||
0.928368 | + | 0.371662i | \(0.121212\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.797176 | + | 1.74557i | −0.797176 | + | 1.74557i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.981929 | + | 1.70075i | −0.981929 | + | 1.70075i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.67923 | 1.67923 | ||||||||
\(479\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.18284 | + | 2.04874i | −1.18284 | + | 2.04874i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.21769 | + | 0.782560i | 1.21769 | + | 0.782560i | ||||
\(487\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(488\) | −0.0572220 | + | 0.0991114i | −0.0572220 | + | 0.0991114i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
−0.500000 | − | 0.866025i | \(-0.666667\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.29661 | −1.29661 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.415415 | − | 0.909632i | 0.415415 | − | 0.909632i | ||||
\(502\) | 0.205996 | − | 0.356796i | 0.205996 | − | 0.356796i | ||||
\(503\) | −1.99094 | −1.99094 | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) | ||||
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(504\) | 0.141812 | + | 0.163659i | 0.141812 | + | 0.163659i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.995472 | + | 0.0950560i | −0.995472 | + | 0.0950560i | ||||
\(508\) | 0.973420 | + | 1.68601i | 0.973420 | + | 1.68601i | ||||
\(509\) | −0.0475819 | − | 0.0824143i | −0.0475819 | − | 0.0824143i | 0.841254 | − | 0.540641i | \(-0.181818\pi\) |
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.40826 | 1.40826 | ||||||||
\(513\) | −1.88431 | + | 0.553283i | −1.88431 | + | 0.553283i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.581419 | − | 1.00705i | −0.581419 | − | 1.00705i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.67489 | + | 0.159932i | −1.67489 | + | 0.159932i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(522\) | 2.63900 | − | 0.508625i | 2.63900 | − | 0.508625i | ||||
\(523\) | 0.471518 | 0.471518 | 0.235759 | − | 0.971812i | \(-0.424242\pi\) | ||||
0.235759 | + | 0.971812i | \(0.424242\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.653077 | + | 1.43004i | −0.653077 | + | 1.43004i | ||||
\(526\) | −0.601300 | − | 1.04148i | −0.601300 | − | 1.04148i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0.661508 | − | 1.44850i | 0.661508 | − | 1.44850i | ||||
\(529\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3.38120 | −3.38120 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −1.67162 | + | 0.159621i | −1.67162 | + | 0.159621i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.13915 | + | 1.59971i | 1.13915 | + | 1.59971i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.61587 | −2.61587 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.379436 | − | 0.532843i | −0.379436 | − | 0.532843i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(548\) | 0.104220 | 0.104220 | ||||||||
\(549\) | −0.544078 | − | 0.627899i | −0.544078 | − | 0.627899i | ||||
\(550\) | −2.57312 | −2.57312 | ||||||||
\(551\) | −1.82318 | + | 3.15784i | −1.82318 | + | 3.15784i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0.0951638 | 0.0951638 | 0.0475819 | − | 0.998867i | \(-0.484848\pi\) | ||||
0.0475819 | + | 0.998867i | \(0.484848\pi\) | |||||||
\(558\) | −0.685261 | + | 1.97993i | −0.685261 | + | 1.97993i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.44091 | + | 2.49574i | 1.44091 | + | 2.49574i | ||||
\(563\) | 0.654861 | + | 1.13425i | 0.654861 | + | 1.13425i | 0.981929 | + | 0.189251i | \(0.0606061\pi\) |
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(564\) | −0.415545 | − | 0.583551i | −0.415545 | − | 0.583551i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 2.43538 | 2.43538 | ||||||||
\(567\) | −1.45949 | + | 0.584293i | −1.45949 | + | 0.584293i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.469383 | + | 0.0448206i | −0.469383 | + | 0.0448206i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.386074 | − | 1.11549i | 0.386074 | − | 1.11549i | ||||
\(577\) | −1.91899 | −1.91899 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(578\) | −0.723734 | + | 1.25354i | −0.723734 | + | 1.25354i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 1.01169 | − | 2.21530i | 1.01169 | − | 2.21530i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.682507 | 0.682507 | ||||||||
\(587\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(588\) | −1.60426 | + | 0.153188i | −1.60426 | + | 0.153188i | ||||
\(589\) | −1.42131 | − | 2.46178i | −1.42131 | − | 2.46178i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(594\) | −1.86226 | − | 1.77566i | −1.86226 | − | 1.77566i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.975950 | + | 1.37053i | 0.975950 | + | 1.37053i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.928368 | − | 1.60798i | −0.928368 | − | 1.60798i | −0.786053 | − | 0.618159i | \(-0.787879\pi\) |
−0.142315 | − | 0.989821i | \(-0.545455\pi\) | |||||||
\(600\) | −0.137123 | + | 0.0130936i | −0.137123 | + | 0.0130936i | ||||
\(601\) | −0.928368 | + | 1.60798i | −0.928368 | + | 1.60798i | −0.142315 | + | 0.989821i | \(0.545455\pi\) |
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(608\) | 1.40844 | + | 2.43949i | 1.40844 | + | 2.43949i | ||||
\(609\) | −1.21259 | + | 2.65520i | −1.21259 | + | 2.65520i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.44747 | 1.44747 | 0.723734 | − | 0.690079i | \(-0.242424\pi\) | ||||
0.723734 | + | 0.690079i | \(0.242424\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.192479 | − | 0.333384i | −0.192479 | − | 0.333384i | ||||
\(617\) | 0.142315 | + | 0.246497i | 0.142315 | + | 0.246497i | 0.928368 | − | 0.371662i | \(-0.121212\pi\) |
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.44747 | −1.44747 | ||||||||
\(623\) | 0.911911 | − | 1.57948i | 0.911911 | − | 1.57948i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.47528 | − | 0.331849i | 3.47528 | − | 0.331849i | ||||
\(628\) | 1.05080 | − | 1.82004i | 1.05080 | − | 1.82004i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.830830 | 0.830830 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.797176 | + | 1.74557i | −0.797176 | + | 1.74557i | ||||
\(634\) | 1.44091 | + | 2.49574i | 1.44091 | + | 2.49574i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −4.77761 | −4.77761 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(642\) | 2.26527 | − | 0.216307i | 2.26527 | − | 0.216307i | ||||
\(643\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(648\) | −0.108276 | − | 0.0851493i | −0.108276 | − | 0.0851493i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.31996 | − | 1.85363i | −1.31996 | − | 1.85363i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0.959493 | + | 1.66189i | 0.959493 | + | 1.66189i | 0.723734 | + | 0.690079i | \(0.242424\pi\) |
0.235759 | + | 0.971812i | \(0.424242\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.48853 | 1.48853 | ||||||||
\(659\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −0.547582 | + | 0.948440i | −0.547582 | + | 0.948440i | ||||
\(669\) | −1.15486 | + | 0.110276i | −1.15486 | + | 0.110276i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.738471 | + | 1.27907i | 0.738471 | + | 1.27907i | ||||
\(672\) | 1.30801 | + | 1.83684i | 1.30801 | + | 1.83684i | ||||
\(673\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(674\) | −0.946841 | −0.946841 | ||||||||
\(675\) | 0.235759 | − | 0.971812i | 0.235759 | − | 0.971812i | ||||
\(676\) | 1.09516 | 1.09516 | ||||||||
\(677\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.32254 | + | 2.29071i | 1.32254 | + | 2.29071i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.86226 | − | 3.22552i | 1.86226 | − | 3.22552i | ||||
\(683\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(684\) | 2.11188 | − | 0.407031i | 2.11188 | − | 0.407031i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0.536487 | − | 0.929222i | 0.536487 | − | 0.929222i | ||||
\(687\) | 0.771316 | − | 1.68895i | 0.771316 | − | 1.68895i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(692\) | 1.84262 | 1.84262 | ||||||||
\(693\) | 2.74418 | − | 0.528898i | 2.74418 | − | 0.528898i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −0.254601 | + | 0.0243114i | −0.254601 | + | 0.0243114i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.273507 | + | 0.384087i | 0.273507 | + | 0.384087i | ||||
\(700\) | 0.860857 | − | 1.49105i | 0.860857 | − | 1.49105i | ||||
\(701\) | 1.16011 | 1.16011 | 0.580057 | − | 0.814576i | \(-0.303030\pi\) | ||||
0.580057 | + | 0.814576i | \(0.303030\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −1.04919 | + | 1.81725i | −1.04919 | + | 1.81725i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.205996 | + | 0.356796i | 0.205996 | + | 0.356796i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0.159802 | 0.159802 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.07537 | − | 1.86260i | −1.07537 | − | 1.86260i | ||||
\(717\) | 0.481929 | − | 1.05528i | 0.481929 | − | 1.05528i | ||||
\(718\) | 1.38884 | − | 2.40553i | 1.38884 | − | 2.40553i | ||||
\(719\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −2.06752 | + | 3.58104i | −2.06752 | + | 3.58104i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0.358193 | + | 0.620408i | 0.358193 | + | 0.620408i | ||||
\(725\) | −0.928368 | − | 1.60798i | −0.928368 | − | 1.60798i | ||||
\(726\) | 1.81366 | + | 2.54693i | 1.81366 | + | 2.54693i | ||||
\(727\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.841254 | − | 0.540641i | 0.841254 | − | 0.540641i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0.527791 | + | 0.741179i | 0.527791 | + | 0.741179i | ||||
\(733\) | −0.981929 | − | 1.70075i | −0.981929 | − | 1.70075i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
−0.327068 | − | 0.945001i | \(-0.606061\pi\) | |||||||
\(734\) | 0.473420 | + | 0.819988i | 0.473420 | + | 0.819988i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(744\) | 0.0828270 | − | 0.181366i | 0.0828270 | − | 0.181366i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.23576 | + | 2.14040i | −1.23576 | + | 2.14040i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(752\) | −0.292981 | − | 0.507458i | −0.292981 | − | 0.507458i | ||||
\(753\) | −0.165101 | − | 0.231852i | −0.165101 | − | 0.231852i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.65197 | − | 0.485063i | 1.65197 | − | 0.485063i | ||||
\(757\) | 1.68251 | 1.68251 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −0.415415 | − | 0.719520i | −0.415415 | − | 0.719520i | 0.580057 | − | 0.814576i | \(-0.303030\pi\) |
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(762\) | 2.56147 | − | 0.244591i | 2.56147 | − | 0.244591i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0.516389 | 0.516389 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −0.411992 | −0.411992 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0.325456 | − | 0.712649i | 0.325456 | − | 0.712649i | ||||
\(769\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.44747 | 1.44747 | ||||||||
\(776\) | −0.115880 | + | 0.200710i | −0.115880 | + | 0.200710i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.437742 | − | 1.80440i | 0.437742 | − | 1.80440i | ||||
\(784\) | −1.31816 | −1.31816 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.827068 | + | 0.0789754i | −0.827068 | + | 0.0789754i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0.160355 | + | 0.185059i | 0.160355 | + | 0.185059i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 1.44091 | − | 2.49574i | 1.44091 | − | 2.49574i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.921310 | − | 1.59576i | −0.921310 | − | 1.59576i | ||||
\(797\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(798\) | −1.85645 | + | 4.06506i | −1.85645 | + | 4.06506i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −1.43436 | −1.43436 | ||||||||
\(801\) | −0.379436 | + | 1.09631i | −0.379436 | + | 1.09631i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.68251 | 1.68251 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(812\) | 1.59838 | − | 2.76848i | 1.59838 | − | 2.76848i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −2.57312 | −2.57312 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(822\) | 0.0572220 | − | 0.125299i | 0.0572220 | − | 0.125299i | ||||
\(823\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.738471 | + | 1.61703i | −0.738471 | + | 1.61703i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3.82332 | −3.82332 | ||||||||
\(837\) | 1.04758 | + | 0.998867i | 1.04758 | + | 0.998867i | ||||
\(838\) | 0.682507 | 0.682507 | ||||||||
\(839\) | −0.415415 | + | 0.719520i | −0.415415 | + | 0.719520i | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) |
0.580057 | + | 0.814576i | \(0.303030\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.22373 | − | 2.11957i | −1.22373 | − | 2.11957i | ||||
\(842\) | 0.205996 | + | 0.356796i | 0.205996 | + | 0.356796i | ||||
\(843\) | 1.98193 | − | 0.189251i | 1.98193 | − | 0.189251i | ||||
\(844\) | 1.05080 | − | 1.82004i | 1.05080 | − | 1.82004i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −0.929730 | + | 0.179191i | −0.929730 | + | 0.179191i | ||||
\(847\) | −3.39593 | −3.39593 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.698939 | − | 1.53046i | 0.698939 | − | 1.53046i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −0.0475819 | + | 0.0824143i | −0.0475819 | + | 0.0824143i | −0.888835 | − | 0.458227i | \(-0.848485\pi\) |
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(854\) | −1.89061 | −1.89061 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.216552 | −0.216552 | ||||||||
\(857\) | −0.981929 | + | 1.70075i | −0.981929 | + | 1.70075i | −0.327068 | + | 0.945001i | \(0.606061\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.928368 | − | 1.60798i | −0.928368 | − | 1.60798i | −0.786053 | − | 0.618159i | \(-0.787879\pi\) |
−0.142315 | − | 0.989821i | \(-0.545455\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.44091 | − | 2.49574i | 1.44091 | − | 2.49574i | ||||
\(863\) | 1.68251 | 1.68251 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(864\) | −1.03809 | − | 0.989821i | −1.03809 | − | 0.989821i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0.947890 | − | 1.64179i | 0.947890 | − | 1.64179i | ||||
\(867\) | 0.580057 | + | 0.814576i | 0.580057 | + | 0.814576i | ||||
\(868\) | 1.24606 | + | 2.15824i | 1.24606 | + | 2.15824i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.10181 | − | 1.27155i | −1.10181 | − | 1.27155i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.981929 | − | 1.70075i | −0.981929 | − | 1.70075i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
−0.327068 | − | 0.945001i | \(-0.606061\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.195876 | − | 0.428908i | 0.195876 | − | 0.428908i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | −0.696647 | + | 2.01283i | −0.696647 | + | 2.01283i | ||||
\(883\) | −0.284630 | −0.284630 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.39734 | + | 2.42027i | −1.39734 | + | 2.42027i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.65033 | + | 0.660694i | −1.65033 | + | 0.660694i | ||||
\(892\) | 1.27051 | 1.27051 | ||||||||
\(893\) | 0.642315 | − | 1.11252i | 0.642315 | − | 1.11252i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.215572 | − | 0.373381i | −0.215572 | − | 0.373381i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0.947890 | − | 1.64179i | 0.947890 | − | 1.64179i | ||||
\(899\) | 2.68757 | 2.68757 | ||||||||
\(900\) | −0.358193 | + | 1.03493i | −0.358193 | + | 1.03493i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.995472 | − | 1.72421i | 0.995472 | − | 1.72421i | 0.415415 | − | 0.909632i | \(-0.363636\pi\) |
0.580057 | − | 0.814576i | \(-0.303030\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.654861 | − | 1.13425i | 0.654861 | − | 1.13425i | −0.327068 | − | 0.945001i | \(-0.606061\pi\) |
0.981929 | − | 0.189251i | \(-0.0606061\pi\) | |||||||
\(912\) | 1.75122 | − | 0.167221i | 1.75122 | − | 0.167221i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.01671 | + | 1.76100i | −1.01671 | + | 1.76100i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.30972 | −1.30972 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0.947890 | + | 1.64179i | 0.947890 | + | 1.64179i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −3.04678 | + | 0.290932i | −3.04678 | + | 0.290932i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.66323 | −2.66323 | ||||||||
\(929\) | −0.235759 | + | 0.408346i | −0.235759 | + | 0.408346i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
0.723734 | + | 0.690079i | \(0.242424\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.44493 | − | 2.50268i | −1.44493 | − | 2.50268i | ||||
\(932\) | −0.258195 | − | 0.447206i | −0.258195 | − | 0.447206i | ||||
\(933\) | −0.415415 | + | 0.909632i | −0.415415 | + | 0.909632i | ||||
\(934\) | −1.34378 | + | 2.32750i | −1.34378 | + | 2.32750i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(942\) | −1.61121 | − | 2.26262i | −1.61121 | − | 2.26262i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −0.580057 | + | 1.00469i | −0.580057 | + | 1.00469i | 0.415415 | + | 0.909632i | \(0.363636\pi\) |
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −1.42131 | − | 2.46178i | −1.42131 | − | 2.46178i | ||||
\(951\) | 1.98193 | − | 0.189251i | 1.98193 | − | 0.189251i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −0.635257 | + | 1.10030i | −0.635257 | + | 1.10030i | ||||
\(957\) | −1.37115 | + | 3.00239i | −1.37115 | + | 3.00239i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.0748038 | + | 0.129564i | 0.0748038 | + | 0.129564i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.547582 | + | 0.948440i | −0.547582 | + | 0.948440i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.514186 | − | 1.48564i | 0.514186 | − | 1.48564i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.235759 | − | 0.408346i | −0.235759 | − | 0.408346i | 0.723734 | − | 0.690079i | \(-0.242424\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(968\) | −0.148774 | − | 0.257684i | −0.148774 | − | 0.257684i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(972\) | −0.973420 | + | 0.501833i | −0.973420 | + | 0.501833i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.372120 | + | 0.644532i | 0.372120 | + | 0.644532i | ||||
\(977\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.03115 | − | 1.78600i | 1.03115 | − | 1.78600i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2.89494 | 2.89494 | ||||||||
\(983\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.427201 | − | 0.935439i | 0.427201 | − | 0.935439i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(992\) | 1.03809 | − | 1.79803i | 1.03809 | − | 1.79803i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.928368 | + | 1.60798i | −0.928368 | + | 1.60798i | −0.142315 | + | 0.989821i | \(0.545455\pi\) |
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(998\) | 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 | 1503.1.f.b.1168.3 | yes | 20 | |
9.4 | even | 3 | inner | 1503.1.f.b.166.3 | ✓ | 20 | |
167.166 | odd | 2 | CM | 1503.1.f.b.1168.3 | yes | 20 | |
1503.166 | odd | 6 | inner | 1503.1.f.b.166.3 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1503.1.f.b.166.3 | ✓ | 20 | 9.4 | even | 3 | inner | |
1503.1.f.b.166.3 | ✓ | 20 | 1503.166 | odd | 6 | inner | |
1503.1.f.b.1168.3 | yes | 20 | 1.1 | even | 1 | trivial | |
1503.1.f.b.1168.3 | yes | 20 | 167.166 | odd | 2 | CM |