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 | 166.6 | ||
Root | \(0.723734 - 0.690079i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1503.166 |
Dual form | 1503.1.f.b.1168.6 |
$q$-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 \(\left(\mathbb{Z}/1503\mathbb{Z}\right)^\times\).
\(n\) | \(172\) | \(335\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.0475819 | − | 0.0824143i | −0.0475819 | − | 0.0824143i | 0.841254 | − | 0.540641i | \(-0.181818\pi\) |
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(3\) | −0.327068 | + | 0.945001i | −0.327068 | + | 0.945001i | ||||
\(4\) | 0.495472 | − | 0.858183i | 0.495472 | − | 0.858183i | ||||
\(5\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(6\) | 0.0934441 | − | 0.0180099i | 0.0934441 | − | 0.0180099i | ||||
\(7\) | −0.235759 | − | 0.408346i | −0.235759 | − | 0.408346i | 0.723734 | − | 0.690079i | \(-0.242424\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(8\) | −0.189466 | −0.189466 | ||||||||
\(9\) | −0.786053 | − | 0.618159i | −0.786053 | − | 0.618159i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.580057 | − | 1.00469i | −0.580057 | − | 1.00469i | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) |
0.415415 | − | 0.909632i | \(-0.363636\pi\) | |||||||
\(12\) | 0.648930 | + | 0.748905i | 0.648930 | + | 0.748905i | ||||
\(13\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(14\) | −0.0224357 | + | 0.0388598i | −0.0224357 | + | 0.0388598i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.486457 | − | 0.842568i | −0.486457 | − | 0.842568i | ||||
\(17\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(18\) | −0.0135432 | + | 0.0941952i | −0.0135432 | + | 0.0941952i | ||||
\(19\) | 1.85674 | 1.85674 | 0.928368 | − | 0.371662i | \(-0.121212\pi\) | ||||
0.928368 | + | 0.371662i | \(0.121212\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.462997 | − | 0.0892353i | 0.462997 | − | 0.0892353i | ||||
\(22\) | −0.0552004 | + | 0.0956100i | −0.0552004 | + | 0.0956100i | ||||
\(23\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(24\) | 0.0619682 | − | 0.179045i | 0.0619682 | − | 0.179045i | ||||
\(25\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.841254 | − | 0.540641i | 0.841254 | − | 0.540641i | ||||
\(28\) | −0.467248 | −0.467248 | ||||||||
\(29\) | −0.723734 | − | 1.25354i | −0.723734 | − | 1.25354i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
0.235759 | − | 0.971812i | \(-0.424242\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.0475819 | + | 0.0824143i | −0.0475819 | + | 0.0824143i | −0.888835 | − | 0.458227i | \(-0.848485\pi\) |
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(32\) | −0.141026 | + | 0.244264i | −0.141026 | + | 0.244264i | ||||
\(33\) | 1.13915 | − | 0.219553i | 1.13915 | − | 0.219553i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.919960 | + | 0.368297i | −0.919960 | + | 0.368297i | ||||
\(37\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(38\) | −0.0883470 | − | 0.153022i | −0.0883470 | − | 0.153022i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(42\) | −0.0293845 | − | 0.0339116i | −0.0293845 | − | 0.0339116i | ||||
\(43\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(44\) | −1.14961 | −1.14961 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.786053 | + | 1.36148i | 0.786053 | + | 1.36148i | 0.928368 | + | 0.371662i | \(0.121212\pi\) |
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(48\) | 0.955332 | − | 0.184125i | 0.955332 | − | 0.184125i | ||||
\(49\) | 0.388835 | − | 0.673483i | 0.388835 | − | 0.673483i | ||||
\(50\) | −0.0475819 | + | 0.0824143i | −0.0475819 | + | 0.0824143i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(54\) | −0.0845850 | − | 0.0436066i | −0.0845850 | − | 0.0436066i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.0446683 | + | 0.0773677i | 0.0446683 | + | 0.0773677i | ||||
\(57\) | −0.607279 | + | 1.75462i | −0.607279 | + | 1.75462i | ||||
\(58\) | −0.0688733 | + | 0.119292i | −0.0688733 | + | 0.119292i | ||||
\(59\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.654861 | + | 1.13425i | 0.654861 | + | 1.13425i | 0.981929 | + | 0.189251i | \(0.0606061\pi\) |
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(62\) | 0.00905615 | 0.00905615 | ||||||||
\(63\) | −0.0671040 | + | 0.466718i | −0.0671040 | + | 0.466718i | ||||
\(64\) | −0.946072 | −0.946072 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.0722972 | − | 0.0834354i | −0.0722972 | − | 0.0834354i | ||||
\(67\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 0.148930 | + | 0.117120i | 0.148930 | + | 0.117120i | ||||
\(73\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.981929 | − | 0.189251i | 0.981929 | − | 0.189251i | ||||
\(76\) | 0.919960 | − | 1.59342i | 0.919960 | − | 1.59342i | ||||
\(77\) | −0.273507 | + | 0.473728i | −0.273507 | + | 0.473728i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.235759 | + | 0.971812i | 0.235759 | + | 0.971812i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(84\) | 0.152822 | − | 0.441549i | 0.152822 | − | 0.441549i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.42131 | − | 0.273935i | 1.42131 | − | 0.273935i | ||||
\(88\) | 0.109901 | + | 0.190354i | 0.109901 | + | 0.190354i | ||||
\(89\) | −0.654136 | −0.654136 | −0.327068 | − | 0.945001i | \(-0.606061\pi\) | ||||
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.0623191 | − | 0.0719200i | −0.0623191 | − | 0.0719200i | ||||
\(94\) | 0.0748038 | − | 0.129564i | 0.0748038 | − | 0.129564i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.184705 | − | 0.213161i | −0.184705 | − | 0.213161i | ||||
\(97\) | −0.415415 | − | 0.719520i | −0.415415 | − | 0.719520i | 0.580057 | − | 0.814576i | \(-0.303030\pi\) |
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(98\) | −0.0740061 | −0.0740061 | ||||||||
\(99\) | −0.165101 | + | 1.14831i | −0.165101 | + | 1.14831i | ||||
\(100\) | −0.990944 | −0.990944 | ||||||||
\(101\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.471518 | 0.471518 | 0.235759 | − | 0.971812i | \(-0.424242\pi\) | ||||
0.235759 | + | 0.971812i | \(0.424242\pi\) | |||||||
\(108\) | −0.0471510 | − | 0.989821i | −0.0471510 | − | 0.989821i | ||||
\(109\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.229373 | + | 0.397286i | −0.229373 | + | 0.397286i | ||||
\(113\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(114\) | 0.173501 | − | 0.0334396i | 0.173501 | − | 0.0334396i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.43436 | −1.43436 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.172932 | + | 0.299527i | −0.172932 | + | 0.299527i | ||||
\(122\) | 0.0623191 | − | 0.107940i | 0.0623191 | − | 0.107940i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.0471510 | + | 0.0816679i | 0.0471510 | + | 0.0816679i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.0416572 | − | 0.0166770i | 0.0416572 | − | 0.0166770i | ||||
\(127\) | 1.16011 | 1.16011 | 0.580057 | − | 0.814576i | \(-0.303030\pi\) | ||||
0.580057 | + | 0.814576i | \(0.303030\pi\) | |||||||
\(128\) | 0.186042 | + | 0.322234i | 0.186042 | + | 0.322234i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(132\) | 0.376000 | − | 1.08638i | 0.376000 | − | 1.08638i | ||||
\(133\) | −0.437742 | − | 0.758192i | −0.437742 | − | 0.758192i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.995472 | + | 1.72421i | 0.995472 | + | 1.72421i | 0.580057 | + | 0.814576i | \(0.303030\pi\) |
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.54370 | + | 0.297523i | −1.54370 | + | 0.297523i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.138460 | + | 0.963011i | −0.138460 | + | 0.963011i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.509266 | + | 0.587724i | 0.509266 | + | 0.587724i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(150\) | −0.0623191 | − | 0.0719200i | −0.0623191 | − | 0.0719200i | ||||
\(151\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(152\) | −0.351788 | −0.351788 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.0520560 | 0.0520560 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.841254 | + | 1.45709i | −0.841254 | + | 1.45709i | 0.0475819 | + | 0.998867i | \(0.484848\pi\) |
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.0688733 | − | 0.0656706i | 0.0688733 | − | 0.0656706i | ||||
\(163\) | 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 | ||||
\(168\) | −0.0877221 | + | 0.0169070i | −0.0877221 | + | 0.0169070i | ||||
\(169\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.45949 | − | 1.14776i | −1.45949 | − | 1.14776i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.415415 | − | 0.719520i | −0.415415 | − | 0.719520i | 0.580057 | − | 0.814576i | \(-0.303030\pi\) |
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(174\) | −0.0902048 | − | 0.104102i | −0.0902048 | − | 0.104102i | ||||
\(175\) | −0.235759 | + | 0.408346i | −0.235759 | + | 0.408346i | ||||
\(176\) | −0.564345 | + | 0.977475i | −0.564345 | + | 0.977475i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.0311250 | + | 0.0539102i | 0.0311250 | + | 0.0539102i | ||||
\(179\) | 1.85674 | 1.85674 | 0.928368 | − | 0.371662i | \(-0.121212\pi\) | ||||
0.928368 | + | 0.371662i | \(0.121212\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.57211 | −1.57211 | −0.786053 | − | 0.618159i | \(-0.787879\pi\) | ||||
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.28605 | + | 0.247866i | −1.28605 | + | 0.247866i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.00296198 | + | 0.00855807i | −0.00296198 | + | 0.00855807i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 1.55787 | 1.55787 | ||||||||
\(189\) | −0.419102 | − | 0.216062i | −0.419102 | − | 0.216062i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.888835 | + | 1.53951i | 0.888835 | + | 1.53951i | 0.841254 | + | 0.540641i | \(0.181818\pi\) |
0.0475819 | + | 0.998867i | \(0.484848\pi\) | |||||||
\(192\) | 0.309430 | − | 0.894039i | 0.309430 | − | 0.894039i | ||||
\(193\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(194\) | −0.0395325 | + | 0.0684723i | −0.0395325 | + | 0.0684723i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.385314 | − | 0.667384i | −0.385314 | − | 0.667384i | ||||
\(197\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(198\) | 0.102493 | − | 0.0410319i | 0.102493 | − | 0.0410319i | ||||
\(199\) | 0.830830 | 0.830830 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(200\) | 0.0947329 | + | 0.164082i | 0.0947329 | + | 0.164082i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.341254 | + | 0.591068i | −0.341254 | + | 0.591068i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.07701 | − | 1.86544i | −1.07701 | − | 1.86544i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.841254 | + | 1.45709i | −0.841254 | + | 1.45709i | 0.0475819 | + | 0.998867i | \(0.484848\pi\) |
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.0224357 | − | 0.0388598i | −0.0224357 | − | 0.0388598i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.159389 | + | 0.102433i | −0.159389 | + | 0.102433i | ||||
\(217\) | 0.0448714 | 0.0448714 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.327068 | + | 0.566498i | 0.327068 | + | 0.566498i | 0.981929 | − | 0.189251i | \(-0.0606061\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(224\) | 0.132993 | 0.132993 | ||||||||
\(225\) | −0.142315 | + | 0.989821i | −0.142315 | + | 0.989821i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(228\) | 1.20489 | + | 1.39052i | 1.20489 | + | 1.39052i | ||||
\(229\) | −0.723734 | + | 1.25354i | −0.723734 | + | 1.25354i | 0.235759 | + | 0.971812i | \(0.424242\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.358218 | − | 0.413406i | −0.358218 | − | 0.413406i | ||||
\(232\) | 0.137123 | + | 0.237504i | 0.137123 | + | 0.237504i | ||||
\(233\) | −1.77767 | −1.77767 | −0.888835 | − | 0.458227i | \(-0.848485\pi\) | ||||
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.327068 | − | 0.566498i | 0.327068 | − | 0.566498i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
0.981929 | + | 0.189251i | \(0.0606061\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(242\) | 0.0329138 | 0.0329138 | ||||||||
\(243\) | −0.995472 | − | 0.0950560i | −0.995472 | − | 0.0950560i | ||||
\(244\) | 1.29786 | 1.29786 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0.00901515 | − | 0.0156147i | 0.00901515 | − | 0.0156147i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.91899 | −1.91899 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(252\) | 0.367282 | + | 0.288833i | 0.367282 | + | 0.288833i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −0.0552004 | − | 0.0956100i | −0.0552004 | − | 0.0956100i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.455332 | + | 0.788658i | −0.455332 | + | 0.788658i | ||||
\(257\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.205996 | + | 1.43273i | −0.205996 | + | 1.43273i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.654861 | + | 1.13425i | 0.654861 | + | 1.13425i | 0.981929 | + | 0.189251i | \(0.0606061\pi\) |
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(264\) | −0.215830 | + | 0.0415978i | −0.215830 | + | 0.0415978i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.0416572 | + | 0.0721524i | −0.0416572 | + | 0.0721524i | ||||
\(267\) | 0.213947 | − | 0.618159i | 0.213947 | − | 0.618159i | ||||
\(268\) | 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 | ||||||||
\(274\) | 0.0947329 | − | 0.164082i | 0.0947329 | − | 0.164082i | ||||
\(275\) | −0.580057 | + | 1.00469i | −0.580057 | + | 1.00469i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.0883470 | − | 0.0353688i | 0.0883470 | − | 0.0353688i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.981929 | − | 1.70075i | −0.981929 | − | 1.70075i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
−0.327068 | − | 0.945001i | \(-0.606061\pi\) | |||||||
\(282\) | 0.0979722 | + | 0.113066i | 0.0979722 | + | 0.113066i | ||||
\(283\) | −0.415415 | + | 0.719520i | −0.415415 | + | 0.719520i | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) |
0.580057 | + | 0.814576i | \(0.303030\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.261848 | − | 0.104828i | 0.261848 | − | 0.104828i | ||||
\(289\) | 1.00000 | 1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.815816 | − | 0.157236i | 0.815816 | − | 0.157236i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.888835 | − | 1.53951i | 0.888835 | − | 1.53951i | 0.0475819 | − | 0.998867i | \(-0.484848\pi\) |
0.841254 | − | 0.540641i | \(-0.181818\pi\) | |||||||
\(294\) | 0.0242050 | − | 0.0699359i | 0.0242050 | − | 0.0699359i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.03115 | − | 0.531595i | −1.03115 | − | 0.531595i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0.324106 | − | 0.936443i | 0.324106 | − | 0.936443i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.903222 | − | 1.56443i | −0.903222 | − | 1.56443i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(308\) | 0.271030 | + | 0.469438i | 0.271030 | + | 0.469438i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(314\) | 0.160114 | 0.160114 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.981929 | − | 1.70075i | −0.981929 | − | 1.70075i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
−0.327068 | − | 0.945001i | \(-0.606061\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.839614 | + | 1.45425i | −0.839614 | + | 1.45425i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.154218 | + | 0.445585i | −0.154218 | + | 0.445585i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0.950804 | + | 0.279181i | 0.950804 | + | 0.279181i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.370638 | − | 0.641964i | 0.370638 | − | 0.641964i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0.0951638 | 0.0951638 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.300415 | − | 0.346697i | −0.300415 | − | 0.346697i | ||||
\(337\) | 0.786053 | − | 1.36148i | 0.786053 | − | 1.36148i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) |
0.928368 | − | 0.371662i | \(-0.121212\pi\) | |||||||
\(338\) | −0.0475819 | + | 0.0824143i | −0.0475819 | + | 0.0824143i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.110401 | 0.110401 | ||||||||
\(342\) | −0.0251462 | + | 0.174896i | −0.0251462 | + | 0.174896i | ||||
\(343\) | −0.838204 | −0.838204 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.0395325 | + | 0.0684723i | −0.0395325 | + | 0.0684723i | ||||
\(347\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(348\) | 0.469133 | − | 1.35547i | 0.469133 | − | 1.35547i | ||||
\(349\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(350\) | 0.0448714 | 0.0448714 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.327212 | 0.327212 | ||||||||
\(353\) | 0.959493 | + | 1.66189i | 0.959493 | + | 1.66189i | 0.723734 | + | 0.690079i | \(0.242424\pi\) |
0.235759 | + | 0.971812i | \(0.424242\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −0.324106 | + | 0.561368i | −0.324106 | + | 0.561368i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.0883470 | − | 0.153022i | −0.0883470 | − | 0.153022i | ||||
\(359\) | 1.68251 | 1.68251 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.44747 | 2.44747 | ||||||||
\(362\) | 0.0748038 | + | 0.129564i | 0.0748038 | + | 0.129564i | ||||
\(363\) | −0.226493 | − | 0.261387i | −0.226493 | − | 0.261387i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.0816206 | + | 0.0941952i | 0.0816206 | + | 0.0941952i | ||||
\(367\) | 0.786053 | + | 1.36148i | 0.786053 | + | 1.36148i | 0.928368 | + | 0.371662i | \(0.121212\pi\) |
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −0.0925979 | + | 0.0178468i | −0.0925979 | + | 0.0178468i | ||||
\(373\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.148930 | − | 0.257955i | −0.148930 | − | 0.257955i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0.00213507 | + | 0.0448206i | 0.00213507 | + | 0.0448206i | ||||
\(379\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.379436 | + | 1.09631i | −0.379436 | + | 1.09631i | ||||
\(382\) | 0.0845850 | − | 0.146505i | 0.0845850 | − | 0.146505i | ||||
\(383\) | 0.959493 | − | 1.66189i | 0.959493 | − | 1.66189i | 0.235759 | − | 0.971812i | \(-0.424242\pi\) |
0.723734 | − | 0.690079i | \(-0.242424\pi\) | |||||||
\(384\) | −0.365360 | + | 0.0704173i | −0.365360 | + | 0.0704173i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.823306 | −0.823306 | ||||||||
\(389\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −0.0736710 | + | 0.127602i | −0.0736710 | + | 0.127602i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.903653 | + | 0.710640i | 0.903653 | + | 0.710640i | ||||
\(397\) | 1.96386 | 1.96386 | 0.981929 | − | 0.189251i | \(-0.0606061\pi\) | ||||
0.981929 | + | 0.189251i | \(0.0606061\pi\) | |||||||
\(398\) | −0.0395325 | − | 0.0684723i | −0.0395325 | − | 0.0684723i | ||||
\(399\) | 0.859663 | − | 0.165686i | 0.859663 | − | 0.165686i | ||||
\(400\) | −0.486457 | + | 0.842568i | −0.486457 | + | 0.842568i | ||||
\(401\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.0649500 | 0.0649500 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.580057 | + | 1.00469i | −0.580057 | + | 1.00469i | 0.415415 | + | 0.909632i | \(0.363636\pi\) |
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.95496 | + | 0.376789i | −1.95496 | + | 0.376789i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.102493 | + | 0.177522i | −0.102493 | + | 0.177522i | ||||
\(419\) | 0.888835 | − | 1.53951i | 0.888835 | − | 1.53951i | 0.0475819 | − | 0.998867i | \(-0.484848\pi\) |
0.841254 | − | 0.540641i | \(-0.181818\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.959493 | + | 1.66189i | 0.959493 | + | 1.66189i | 0.723734 | + | 0.690079i | \(0.242424\pi\) |
0.235759 | + | 0.971812i | \(0.424242\pi\) | |||||||
\(422\) | 0.160114 | 0.160114 | ||||||||
\(423\) | 0.223734 | − | 1.55610i | 0.223734 | − | 1.55610i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.308779 | − | 0.534820i | 0.308779 | − | 0.534820i | ||||
\(428\) | 0.233624 | − | 0.404648i | 0.233624 | − | 0.404648i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.96386 | 1.96386 | 0.981929 | − | 0.189251i | \(-0.0606061\pi\) | ||||
0.981929 | + | 0.189251i | \(0.0606061\pi\) | |||||||
\(432\) | −0.864760 | − | 0.445815i | −0.864760 | − | 0.445815i | ||||
\(433\) | −0.284630 | −0.284630 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(434\) | −0.00213507 | − | 0.00369805i | −0.00213507 | − | 0.00369805i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.721965 | + | 0.289031i | −0.721965 | + | 0.289031i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0.0311250 | − | 0.0539102i | 0.0311250 | − | 0.0539102i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.223045 | + | 0.386325i | 0.223045 | + | 0.386325i | ||||
\(449\) | −0.284630 | −0.284630 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(450\) | 0.0883470 | − | 0.0353688i | 0.0883470 | − | 0.0353688i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.115059 | − | 0.332440i | 0.115059 | − | 0.332440i | ||||
\(457\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(458\) | 0.137747 | 0.137747 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.142315 | + | 0.246497i | 0.142315 | + | 0.246497i | 0.928368 | − | 0.371662i | \(-0.121212\pi\) |
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(462\) | −0.0170258 | + | 0.0491929i | −0.0170258 | + | 0.0491929i | ||||
\(463\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(464\) | −0.704131 | + | 1.21959i | −0.704131 | + | 1.21959i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.0845850 | + | 0.146505i | 0.0845850 | + | 0.146505i | ||||
\(467\) | 1.44747 | 1.44747 | 0.723734 | − | 0.690079i | \(-0.242424\pi\) | ||||
0.723734 | + | 0.690079i | \(0.242424\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.10181 | − | 1.27155i | −1.10181 | − | 1.27155i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.928368 | − | 1.60798i | −0.928368 | − | 1.60798i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −0.0622501 | −0.0622501 | ||||||||
\(479\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.171366 | + | 0.296815i | 0.171366 | + | 0.296815i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.0395325 | + | 0.0865641i | 0.0395325 | + | 0.0865641i | ||||
\(487\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(488\) | −0.124074 | − | 0.214902i | −0.124074 | − | 0.214902i | ||||
\(489\) | 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 | ||||||||
\(496\) | 0.0925862 | 0.0925862 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.654861 | − | 0.755750i | −0.654861 | − | 0.755750i | ||||
\(502\) | 0.0913090 | + | 0.158152i | 0.0913090 | + | 0.158152i | ||||
\(503\) | 1.96386 | 1.96386 | 0.981929 | − | 0.189251i | \(-0.0606061\pi\) | ||||
0.981929 | + | 0.189251i | \(0.0606061\pi\) | |||||||
\(504\) | 0.0127139 | − | 0.0884272i | 0.0127139 | − | 0.0884272i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.981929 | − | 0.189251i | 0.981929 | − | 0.189251i | ||||
\(508\) | 0.574804 | − | 0.995589i | 0.574804 | − | 0.995589i | ||||
\(509\) | 0.995472 | − | 1.72421i | 0.995472 | − | 1.72421i | 0.415415 | − | 0.909632i | \(-0.363636\pi\) |
0.580057 | − | 0.814576i | \(-0.303030\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0.458746 | 0.458746 | ||||||||
\(513\) | 1.56199 | − | 1.00383i | 1.56199 | − | 1.00383i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.911911 | − | 1.57948i | 0.911911 | − | 1.57948i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.815816 | − | 0.157236i | 0.815816 | − | 0.157236i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(522\) | 0.127880 | − | 0.0511952i | 0.127880 | − | 0.0511952i | ||||
\(523\) | −1.77767 | −1.77767 | −0.888835 | − | 0.458227i | \(-0.848485\pi\) | ||||
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.308779 | − | 0.356349i | −0.308779 | − | 0.356349i | ||||
\(526\) | 0.0623191 | − | 0.107940i | 0.0623191 | − | 0.107940i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −0.739135 | − | 0.853007i | −0.739135 | − | 0.853007i | ||||
\(529\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.867556 | −0.867556 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −0.0611251 | + | 0.0117809i | −0.0611251 | + | 0.0117809i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.607279 | + | 1.75462i | −0.607279 | + | 1.75462i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.902187 | −0.902187 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.514186 | − | 1.48564i | 0.514186 | − | 1.48564i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(548\) | 1.97291 | 1.97291 | ||||||||
\(549\) | 0.186393 | − | 1.29639i | 0.186393 | − | 1.29639i | ||||
\(550\) | 0.110401 | 0.110401 | ||||||||
\(551\) | −1.34378 | − | 2.32750i | −1.34378 | − | 2.32750i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.99094 | −1.99094 | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) | ||||
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(558\) | −0.00711862 | − | 0.00559814i | −0.00711862 | − | 0.00559814i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −0.0934441 | + | 0.161850i | −0.0934441 | + | 0.161850i | ||||
\(563\) | 0.142315 | − | 0.246497i | 0.142315 | − | 0.246497i | −0.786053 | − | 0.618159i | \(-0.787879\pi\) |
0.928368 | + | 0.371662i | \(0.121212\pi\) | |||||||
\(564\) | −0.509529 | + | 1.47219i | −0.509529 | + | 1.47219i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0.0790650 | 0.0790650 | ||||||||
\(567\) | 0.341254 | − | 0.325385i | 0.341254 | − | 0.325385i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.74555 | + | 0.336426i | −1.74555 | + | 0.336426i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.743663 | + | 0.584823i | 0.743663 | + | 0.584823i | ||||
\(577\) | 1.68251 | 1.68251 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(578\) | −0.0475819 | − | 0.0824143i | −0.0475819 | − | 0.0824143i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −0.0517765 | − | 0.0597533i | −0.0517765 | − | 0.0597533i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.169170 | −0.169170 | ||||||||
\(587\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(588\) | 0.756702 | − | 0.145842i | 0.756702 | − | 0.145842i | ||||
\(589\) | −0.0883470 | + | 0.153022i | −0.0883470 | + | 0.153022i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(594\) | 0.00525309 | + | 0.110276i | 0.00525309 | + | 0.110276i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.271738 | + | 0.785135i | −0.271738 | + | 0.785135i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.723734 | + | 1.25354i | −0.723734 | + | 1.25354i | 0.235759 | + | 0.971812i | \(0.424242\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(600\) | −0.186042 | + | 0.0358566i | −0.186042 | + | 0.0358566i | ||||
\(601\) | −0.723734 | − | 1.25354i | −0.723734 | − | 1.25354i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
0.235759 | − | 0.971812i | \(-0.424242\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(608\) | −0.261848 | + | 0.453534i | −0.261848 | + | 0.453534i | ||||
\(609\) | −0.446947 | − | 0.515804i | −0.446947 | − | 0.515804i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.0951638 | 0.0951638 | 0.0475819 | − | 0.998867i | \(-0.484848\pi\) | ||||
0.0475819 | + | 0.998867i | \(0.484848\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.0518203 | − | 0.0897553i | 0.0518203 | − | 0.0897553i | ||||
\(617\) | 0.959493 | − | 1.66189i | 0.959493 | − | 1.66189i | 0.235759 | − | 0.971812i | \(-0.424242\pi\) |
0.723734 | − | 0.690079i | \(-0.242424\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −0.0951638 | −0.0951638 | ||||||||
\(623\) | 0.154218 | + | 0.267114i | 0.154218 | + | 0.267114i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.11510 | − | 0.407652i | 2.11510 | − | 0.407652i | ||||
\(628\) | 0.833635 | + | 1.44390i | 0.833635 | + | 1.44390i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.30972 | −1.30972 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.10181 | − | 1.27155i | −1.10181 | − | 1.27155i | ||||
\(634\) | −0.0934441 | + | 0.161850i | −0.0934441 | + | 0.161850i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0.159802 | 0.159802 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(642\) | 0.0440606 | − | 0.00849198i | 0.0440606 | − | 0.00849198i | ||||
\(643\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(648\) | −0.0446683 | − | 0.184125i | −0.0446683 | − | 0.184125i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.0146760 | + | 0.0424036i | −0.0146760 | + | 0.0424036i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.841254 | + | 1.45709i | −0.841254 | + | 1.45709i | 0.0475819 | + | 0.998867i | \(0.484848\pi\) |
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.0705427 | −0.0705427 | ||||||||
\(659\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0.495472 | + | 0.858183i | 0.495472 | + | 0.858183i | ||||
\(669\) | −0.642315 | + | 0.123796i | −0.642315 | + | 0.123796i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.759713 | − | 1.31586i | 0.759713 | − | 1.31586i | ||||
\(672\) | −0.0434976 | + | 0.125678i | −0.0434976 | + | 0.125678i | ||||
\(673\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(674\) | −0.149608 | −0.149608 | ||||||||
\(675\) | −0.888835 | − | 0.458227i | −0.888835 | − | 0.458227i | ||||
\(676\) | −0.990944 | −0.990944 | ||||||||
\(677\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.195876 | + | 0.339266i | −0.195876 | + | 0.339266i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.00525309 | − | 0.00909861i | −0.00525309 | − | 0.00909861i | ||||
\(683\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(684\) | −1.70812 | + | 0.683830i | −1.70812 | + | 0.683830i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0.0398833 | + | 0.0690800i | 0.0398833 | + | 0.0690800i | ||||
\(687\) | −0.947890 | − | 1.09392i | −0.947890 | − | 1.09392i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(692\) | −0.823306 | −0.823306 | ||||||||
\(693\) | 0.507831 | − | 0.203305i | 0.507831 | − | 0.203305i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −0.269290 | + | 0.0519014i | −0.269290 | + | 0.0519014i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.581419 | − | 1.67990i | 0.581419 | − | 1.67990i | ||||
\(700\) | 0.233624 | + | 0.404648i | 0.233624 | + | 0.404648i | ||||
\(701\) | −0.654136 | −0.654136 | −0.327068 | − | 0.945001i | \(-0.606061\pi\) | ||||
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0.548776 | + | 0.950508i | 0.548776 | + | 0.950508i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.0913090 | − | 0.158152i | 0.0913090 | − | 0.158152i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0.123936 | 0.123936 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.919960 | − | 1.59342i | 0.919960 | − | 1.59342i | ||||
\(717\) | 0.428368 | + | 0.494363i | 0.428368 | + | 0.494363i | ||||
\(718\) | −0.0800569 | − | 0.138663i | −0.0800569 | − | 0.138663i | ||||
\(719\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −0.116455 | − | 0.201706i | −0.116455 | − | 0.201706i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −0.778934 | + | 1.34915i | −0.778934 | + | 1.34915i | ||||
\(725\) | −0.723734 | + | 1.25354i | −0.723734 | + | 1.25354i | ||||
\(726\) | −0.0107650 | + | 0.0311035i | −0.0107650 | + | 0.0311035i | ||||
\(727\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.415415 | − | 0.909632i | 0.415415 | − | 0.909632i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −0.424489 | + | 1.22648i | −0.424489 | + | 1.22648i | ||||
\(733\) | −0.928368 | + | 1.60798i | −0.928368 | + | 1.60798i | −0.142315 | + | 0.989821i | \(0.545455\pi\) |
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(734\) | 0.0748038 | − | 0.129564i | 0.0748038 | − | 0.129564i | ||||
\(735\) | 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 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(744\) | 0.0118073 | + | 0.0136264i | 0.0118073 | + | 0.0136264i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.111165 | − | 0.192543i | −0.111165 | − | 0.192543i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(752\) | 0.764762 | − | 1.32461i | 0.764762 | − | 1.32461i | ||||
\(753\) | 0.627639 | − | 1.81344i | 0.627639 | − | 1.81344i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.393074 | + | 0.252613i | −0.393074 | + | 0.252613i | ||||
\(757\) | 0.830830 | 0.830830 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.654861 | − | 1.13425i | 0.654861 | − | 1.13425i | −0.327068 | − | 0.945001i | \(-0.606061\pi\) |
0.981929 | − | 0.189251i | \(-0.0606061\pi\) | |||||||
\(762\) | 0.108406 | − | 0.0208935i | 0.108406 | − | 0.0208935i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 1.76157 | 1.76157 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −0.182618 | −0.182618 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −0.596358 | − | 0.688234i | −0.596358 | − | 0.688234i | ||||
\(769\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.0951638 | 0.0951638 | ||||||||
\(776\) | 0.0787070 | + | 0.136324i | 0.0787070 | + | 0.136324i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.28656 | − | 0.663268i | −1.28656 | − | 0.663268i | ||||
\(784\) | −0.756607 | −0.756607 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.28605 | + | 0.247866i | −1.28605 | + | 0.247866i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0.0312811 | − | 0.217565i | 0.0312811 | − | 0.217565i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −0.0934441 | − | 0.161850i | −0.0934441 | − | 0.161850i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.411653 | − | 0.713004i | 0.411653 | − | 0.713004i | ||||
\(797\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(798\) | −0.0545593 | − | 0.0629648i | −0.0545593 | − | 0.0629648i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0.282052 | 0.282052 | ||||||||
\(801\) | 0.514186 | + | 0.404360i | 0.514186 | + | 0.404360i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0.830830 | 0.830830 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(812\) | 0.338163 | + | 0.585716i | 0.338163 | + | 0.585716i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0.110401 | 0.110401 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(822\) | 0.124074 | + | 0.143189i | 0.124074 | + | 0.143189i | ||||
\(823\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.759713 | − | 0.876756i | −0.759713 | − | 0.876756i | ||||
\(826\) | 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 | ||||||||
\(836\) | −2.13452 | −2.13452 | ||||||||
\(837\) | 0.00452808 | + | 0.0950560i | 0.00452808 | + | 0.0950560i | ||||
\(838\) | −0.169170 | −0.169170 | ||||||||
\(839\) | 0.654861 | + | 1.13425i | 0.654861 | + | 1.13425i | 0.981929 | + | 0.189251i | \(0.0606061\pi\) |
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.547582 | + | 0.948440i | −0.547582 | + | 0.948440i | ||||
\(842\) | 0.0913090 | − | 0.158152i | 0.0913090 | − | 0.158152i | ||||
\(843\) | 1.92837 | − | 0.371662i | 1.92837 | − | 0.371662i | ||||
\(844\) | 0.833635 | + | 1.44390i | 0.833635 | + | 1.44390i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −0.138891 | + | 0.0556035i | −0.138891 | + | 0.0556035i | ||||
\(847\) | 0.163081 | 0.163081 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.544078 | − | 0.627899i | −0.544078 | − | 0.627899i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.995472 | + | 1.72421i | 0.995472 | + | 1.72421i | 0.580057 | + | 0.814576i | \(0.303030\pi\) |
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(854\) | −0.0587691 | −0.0587691 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.0893365 | −0.0893365 | ||||||||
\(857\) | −0.928368 | − | 1.60798i | −0.928368 | − | 1.60798i | −0.786053 | − | 0.618159i | \(-0.787879\pi\) |
−0.142315 | − | 0.989821i | \(-0.545455\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.723734 | + | 1.25354i | −0.723734 | + | 1.25354i | 0.235759 | + | 0.971812i | \(0.424242\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −0.0934441 | − | 0.161850i | −0.0934441 | − | 0.161850i | ||||
\(863\) | 0.830830 | 0.830830 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(864\) | 0.0134206 | + | 0.281733i | 0.0134206 | + | 0.281733i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0.0135432 | + | 0.0234576i | 0.0135432 | + | 0.0234576i | ||||
\(867\) | −0.327068 | + | 0.945001i | −0.327068 | + | 0.945001i | ||||
\(868\) | 0.0222325 | − | 0.0385079i | 0.0222325 | − | 0.0385079i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.118239 | + | 0.822373i | −0.118239 | + | 0.822373i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.928368 | + | 1.60798i | −0.928368 | + | 1.60798i | −0.142315 | + | 0.989821i | \(0.545455\pi\) |
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.16413 | + | 1.34347i | 1.16413 | + | 1.34347i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | 0.0581728 | + | 0.0457476i | 0.0581728 | + | 0.0457476i | ||||
\(883\) | −1.91899 | −1.91899 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.273507 | − | 0.473728i | −0.273507 | − | 0.473728i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.839614 | − | 0.800570i | 0.839614 | − | 0.800570i | ||||
\(892\) | 0.648212 | 0.648212 | ||||||||
\(893\) | 1.45949 | + | 2.52792i | 1.45949 | + | 2.52792i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.0877221 | − | 0.151939i | 0.0877221 | − | 0.151939i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0.0135432 | + | 0.0234576i | 0.0135432 | + | 0.0234576i | ||||
\(899\) | 0.137747 | 0.137747 | ||||||||
\(900\) | 0.778934 | + | 0.612561i | 0.778934 | + | 0.612561i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.981929 | − | 1.70075i | −0.981929 | − | 1.70075i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
−0.327068 | − | 0.945001i | \(-0.606061\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.142315 | + | 0.246497i | 0.142315 | + | 0.246497i | 0.928368 | − | 0.371662i | \(-0.121212\pi\) |
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(912\) | 1.77380 | − | 0.341872i | 1.77380 | − | 0.341872i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.717180 | + | 1.24219i | 0.717180 | + | 1.24219i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.284630 | −0.284630 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0.0135432 | − | 0.0234576i | 0.0135432 | − | 0.0234576i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −0.532265 | + | 0.102586i | −0.532265 | + | 0.102586i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0.408261 | 0.408261 | ||||||||
\(929\) | 0.888835 | + | 1.53951i | 0.888835 | + | 1.53951i | 0.841254 | + | 0.540641i | \(0.181818\pi\) |
0.0475819 | + | 0.998867i | \(0.484848\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.721965 | − | 1.25048i | 0.721965 | − | 1.25048i | ||||
\(932\) | −0.880786 | + | 1.52557i | −0.880786 | + | 1.52557i | ||||
\(933\) | 0.654861 | + | 0.755750i | 0.654861 | + | 0.755750i | ||||
\(934\) | −0.0688733 | − | 0.119292i | −0.0688733 | − | 0.119292i | ||||
\(935\) | 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 | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(942\) | −0.0523681 | + | 0.151308i | −0.0523681 | + | 0.151308i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0.327068 | + | 0.566498i | 0.327068 | + | 0.566498i | 0.981929 | − | 0.189251i | \(-0.0606061\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −0.0883470 | + | 0.153022i | −0.0883470 | + | 0.153022i | ||||
\(951\) | 1.92837 | − | 0.371662i | 1.92837 | − | 0.371662i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −0.324106 | − | 0.561368i | −0.324106 | − | 0.561368i | ||||
\(957\) | −1.09966 | − | 1.26908i | −1.09966 | − | 1.26908i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.469383 | − | 0.812995i | 0.469383 | − | 0.812995i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.495472 | + | 0.858183i | 0.495472 | + | 0.858183i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.370638 | − | 0.291473i | −0.370638 | − | 0.291473i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.888835 | − | 1.53951i | 0.888835 | − | 1.53951i | 0.0475819 | − | 0.998867i | \(-0.484848\pi\) |
0.841254 | − | 0.540641i | \(-0.181818\pi\) | |||||||
\(968\) | 0.0327647 | − | 0.0567502i | 0.0327647 | − | 0.0567502i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(972\) | −0.574804 | + | 0.807199i | −0.574804 | + | 0.807199i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.637123 | − | 1.10353i | 0.637123 | − | 1.10353i | ||||
\(977\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.379436 | + | 0.657203i | 0.379436 | + | 0.657203i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0.190328 | 0.190328 | ||||||||
\(983\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.485433 | + | 0.560219i | 0.485433 | + | 0.560219i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(992\) | −0.0134206 | − | 0.0232451i | −0.0134206 | − | 0.0232451i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.723734 | − | 1.25354i | −0.723734 | − | 1.25354i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
0.235759 | − | 0.971812i | \(-0.424242\pi\) | |||||||
\(998\) | 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.166.6 | ✓ | 20 | |
9.7 | even | 3 | inner | 1503.1.f.b.1168.6 | yes | 20 | |
167.166 | odd | 2 | CM | 1503.1.f.b.166.6 | ✓ | 20 | |
1503.1168 | odd | 6 | inner | 1503.1.f.b.1168.6 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1503.1.f.b.166.6 | ✓ | 20 | 1.1 | even | 1 | trivial | |
1503.1.f.b.166.6 | ✓ | 20 | 167.166 | odd | 2 | CM | |
1503.1.f.b.1168.6 | yes | 20 | 9.7 | even | 3 | inner | |
1503.1.f.b.1168.6 | yes | 20 | 1503.1168 | odd | 6 | inner |