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 | 166.7 | ||
Root | \(0.580057 + 0.814576i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1503.166 |
Dual form | 1503.1.f.b.1168.7 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.327068 | + | 0.566498i | 0.327068 | + | 0.566498i | 0.981929 | − | 0.189251i | \(-0.0606061\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(3\) | 0.723734 | + | 0.690079i | 0.723734 | + | 0.690079i | ||||
\(4\) | 0.286053 | − | 0.495458i | 0.286053 | − | 0.495458i | ||||
\(5\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(6\) | −0.154218 | + | 0.635697i | −0.154218 | + | 0.635697i | ||||
\(7\) | 0.995472 | + | 1.72421i | 0.995472 | + | 1.72421i | 0.580057 | + | 0.814576i | \(0.303030\pi\) |
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(8\) | 1.02837 | 1.02837 | ||||||||
\(9\) | 0.0475819 | + | 0.998867i | 0.0475819 | + | 0.998867i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.928368 | − | 1.60798i | −0.928368 | − | 1.60798i | −0.786053 | − | 0.618159i | \(-0.787879\pi\) |
−0.142315 | − | 0.989821i | \(-0.545455\pi\) | |||||||
\(12\) | 0.548932 | − | 0.161181i | 0.548932 | − | 0.161181i | ||||
\(13\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(14\) | −0.651174 | + | 1.12787i | −0.651174 | + | 1.12787i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.0502942 | + | 0.0871120i | 0.0502942 | + | 0.0871120i | ||||
\(17\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(18\) | −0.550294 | + | 0.353653i | −0.550294 | + | 0.353653i | ||||
\(19\) | −1.77767 | −1.77767 | −0.888835 | − | 0.458227i | \(-0.848485\pi\) | ||||
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.469383 | + | 1.93482i | −0.469383 | + | 1.93482i | ||||
\(22\) | 0.607279 | − | 1.05184i | 0.607279 | − | 1.05184i | ||||
\(23\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(24\) | 0.744267 | + | 0.709657i | 0.744267 | + | 0.709657i | ||||
\(25\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.654861 | + | 0.755750i | −0.654861 | + | 0.755750i | ||||
\(28\) | 1.13903 | 1.13903 | ||||||||
\(29\) | −0.580057 | − | 1.00469i | −0.580057 | − | 1.00469i | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) |
0.415415 | − | 0.909632i | \(-0.363636\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.327068 | − | 0.566498i | 0.327068 | − | 0.566498i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
0.981929 | + | 0.189251i | \(0.0606061\pi\) | |||||||
\(32\) | 0.481286 | − | 0.833612i | 0.481286 | − | 0.833612i | ||||
\(33\) | 0.437742 | − | 1.80440i | 0.437742 | − | 1.80440i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.508508 | + | 0.262154i | 0.508508 | + | 0.262154i | ||||
\(37\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(38\) | −0.581419 | − | 1.00705i | −0.581419 | − | 1.00705i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(42\) | −1.24959 | + | 0.366914i | −1.24959 | + | 0.366914i | ||||
\(43\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(44\) | −1.06225 | −1.06225 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.0475819 | − | 0.0824143i | −0.0475819 | − | 0.0824143i | 0.841254 | − | 0.540641i | \(-0.181818\pi\) |
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(48\) | −0.0237146 | + | 0.0977529i | −0.0237146 | + | 0.0977529i | ||||
\(49\) | −1.48193 | + | 2.56678i | −1.48193 | + | 2.56678i | ||||
\(50\) | 0.327068 | − | 0.566498i | 0.327068 | − | 0.566498i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(54\) | −0.642315 | − | 0.123796i | −0.642315 | − | 0.123796i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.02371 | + | 1.77313i | 1.02371 | + | 1.77313i | ||||
\(57\) | −1.28656 | − | 1.22673i | −1.28656 | − | 1.22673i | ||||
\(58\) | 0.379436 | − | 0.657203i | 0.379436 | − | 0.657203i | ||||
\(59\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.959493 | + | 1.66189i | 0.959493 | + | 1.66189i | 0.723734 | + | 0.690079i | \(0.242424\pi\) |
0.235759 | + | 0.971812i | \(0.424242\pi\) | |||||||
\(62\) | 0.427894 | 0.427894 | ||||||||
\(63\) | −1.67489 | + | 1.07639i | −1.67489 | + | 1.07639i | ||||
\(64\) | 0.730242 | 0.730242 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.16536 | − | 0.342180i | 1.16536 | − | 0.342180i | ||||
\(67\) | 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 | \(\pi\) | |||||||||
\(72\) | 0.0489319 | + | 1.02721i | 0.0489319 | + | 1.02721i | ||||
\(73\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.235759 | − | 0.971812i | 0.235759 | − | 0.971812i | ||||
\(76\) | −0.508508 | + | 0.880762i | −0.508508 | + | 0.880762i | ||||
\(77\) | 1.84833 | − | 3.20140i | 1.84833 | − | 3.20140i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.995472 | + | 0.0950560i | −0.995472 | + | 0.0950560i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(84\) | 0.824356 | + | 0.786022i | 0.824356 | + | 0.786022i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.273507 | − | 1.12741i | 0.273507 | − | 1.12741i | ||||
\(88\) | −0.954707 | − | 1.65360i | −0.954707 | − | 1.65360i | ||||
\(89\) | 1.44747 | 1.44747 | 0.723734 | − | 0.690079i | \(-0.242424\pi\) | ||||
0.723734 | + | 0.690079i | \(0.242424\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.627639 | − | 0.184291i | 0.627639 | − | 0.184291i | ||||
\(94\) | 0.0311250 | − | 0.0539102i | 0.0311250 | − | 0.0539102i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.923582 | − | 0.271188i | 0.923582 | − | 0.271188i | ||||
\(97\) | 0.142315 | + | 0.246497i | 0.142315 | + | 0.246497i | 0.928368 | − | 0.371662i | \(-0.121212\pi\) |
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(98\) | −1.93877 | −1.93877 | ||||||||
\(99\) | 1.56199 | − | 1.00383i | 1.56199 | − | 1.00383i | ||||
\(100\) | −0.572106 | −0.572106 | ||||||||
\(101\) | 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 | ||||||||
\(107\) | −1.99094 | −1.99094 | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) | ||||
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(108\) | 0.187118 | + | 0.540641i | 0.187118 | + | 0.540641i | ||||
\(109\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.100133 | + | 0.173435i | −0.100133 | + | 0.173435i | ||||
\(113\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(114\) | 0.274150 | − | 1.13006i | 0.274150 | − | 1.13006i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.663708 | −0.663708 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.22373 | + | 2.11957i | −1.22373 | + | 2.11957i | ||||
\(122\) | −0.627639 | + | 1.08710i | −0.627639 | + | 1.08710i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.187118 | − | 0.324097i | −0.187118 | − | 0.324097i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.15757 | − | 0.596770i | −1.15757 | − | 0.596770i | ||||
\(127\) | 1.85674 | 1.85674 | 0.928368 | − | 0.371662i | \(-0.121212\pi\) | ||||
0.928368 | + | 0.371662i | \(0.121212\pi\) | |||||||
\(128\) | −0.242448 | − | 0.419932i | −0.242448 | − | 0.419932i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(132\) | −0.768787 | − | 0.733036i | −0.768787 | − | 0.733036i | ||||
\(133\) | −1.76962 | − | 3.06507i | −1.76962 | − | 3.06507i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.786053 | + | 1.36148i | 0.786053 | + | 1.36148i | 0.928368 | + | 0.371662i | \(0.121212\pi\) |
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.0224357 | − | 0.0924813i | 0.0224357 | − | 0.0924813i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.0846203 | + | 0.0543822i | −0.0846203 | + | 0.0543822i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.84380 | + | 0.835015i | −2.84380 | + | 0.835015i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(150\) | 0.627639 | − | 0.184291i | 0.627639 | − | 0.184291i | ||||
\(151\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(152\) | −1.82811 | −1.82811 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.41812 | 2.41812 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.654861 | − | 1.13425i | 0.654861 | − | 1.13425i | −0.327068 | − | 0.945001i | \(-0.606061\pi\) |
0.981929 | − | 0.189251i | \(-0.0606061\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.379436 | − | 0.532843i | −0.379436 | − | 0.532843i | ||||
\(163\) | 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 | ||||
\(168\) | −0.482700 | + | 1.98972i | −0.482700 | + | 1.98972i | ||||
\(169\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.0845850 | − | 1.77566i | −0.0845850 | − | 1.77566i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.142315 | + | 0.246497i | 0.142315 | + | 0.246497i | 0.928368 | − | 0.371662i | \(-0.121212\pi\) |
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(174\) | 0.728132 | − | 0.213799i | 0.728132 | − | 0.213799i | ||||
\(175\) | 0.995472 | − | 1.72421i | 0.995472 | − | 1.72421i | ||||
\(176\) | 0.0933830 | − | 0.161744i | 0.0933830 | − | 0.161744i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.473420 | + | 0.819988i | 0.473420 | + | 0.819988i | ||||
\(179\) | −1.77767 | −1.77767 | −0.888835 | − | 0.458227i | \(-0.848485\pi\) | ||||
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.0951638 | 0.0951638 | 0.0475819 | − | 0.998867i | \(-0.484848\pi\) | ||||
0.0475819 | + | 0.998867i | \(0.484848\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.452418 | + | 1.86489i | −0.452418 | + | 1.86489i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.309681 | + | 0.295281i | 0.309681 | + | 0.295281i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −0.0544438 | −0.0544438 | ||||||||
\(189\) | −1.95496 | − | 0.376789i | −1.95496 | − | 0.376789i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.981929 | − | 1.70075i | −0.981929 | − | 1.70075i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
−0.327068 | − | 0.945001i | \(-0.606061\pi\) | |||||||
\(192\) | 0.528501 | + | 0.503924i | 0.528501 | + | 0.503924i | ||||
\(193\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(194\) | −0.0930932 | + | 0.161242i | −0.0930932 | + | 0.161242i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.847821 | + | 1.46847i | 0.847821 | + | 1.46847i | ||||
\(197\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(198\) | 1.07954 | + | 0.556543i | 1.07954 | + | 0.556543i | ||||
\(199\) | −0.284630 | −0.284630 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(200\) | −0.514186 | − | 0.890596i | −0.514186 | − | 0.890596i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.15486 | − | 2.00028i | 1.15486 | − | 2.00028i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.65033 | + | 2.85846i | 1.65033 | + | 2.85846i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.654861 | − | 1.13425i | 0.654861 | − | 1.13425i | −0.327068 | − | 0.945001i | \(-0.606061\pi\) |
0.981929 | − | 0.189251i | \(-0.0606061\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.651174 | − | 1.12787i | −0.651174 | − | 1.12787i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.673440 | + | 0.777191i | −0.673440 | + | 0.777191i | ||||
\(217\) | 1.30235 | 1.30235 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.723734 | − | 1.25354i | −0.723734 | − | 1.25354i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
0.235759 | − | 0.971812i | \(-0.424242\pi\) | |||||||
\(224\) | 1.91643 | 1.91643 | ||||||||
\(225\) | 0.841254 | − | 0.540641i | 0.841254 | − | 0.540641i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(228\) | −0.975820 | + | 0.286527i | −0.975820 | + | 0.286527i | ||||
\(229\) | −0.580057 | + | 1.00469i | −0.580057 | + | 1.00469i | 0.415415 | + | 0.909632i | \(0.363636\pi\) |
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.54692 | − | 1.04147i | 3.54692 | − | 1.04147i | ||||
\(232\) | −0.596514 | − | 1.03319i | −0.596514 | − | 1.03319i | ||||
\(233\) | 1.96386 | 1.96386 | 0.981929 | − | 0.189251i | \(-0.0606061\pi\) | ||||
0.981929 | + | 0.189251i | \(0.0606061\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.723734 | + | 1.25354i | −0.723734 | + | 1.25354i | 0.235759 | + | 0.971812i | \(0.424242\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(242\) | −1.60098 | −1.60098 | ||||||||
\(243\) | −0.786053 | − | 0.618159i | −0.786053 | − | 0.618159i | ||||
\(244\) | 1.09786 | 1.09786 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0.336347 | − | 0.582571i | 0.336347 | − | 0.582571i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.830830 | 0.830830 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(252\) | 0.0541973 | + | 1.13774i | 0.0541973 | + | 1.13774i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0.607279 | + | 1.05184i | 0.607279 | + | 1.05184i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.523715 | − | 0.907100i | 0.523715 | − | 0.907100i | ||||
\(257\) | 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 | ||||||||
\(261\) | 0.975950 | − | 0.627205i | 0.975950 | − | 0.627205i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.959493 | + | 1.66189i | 0.959493 | + | 1.66189i | 0.723734 | + | 0.690079i | \(0.242424\pi\) |
0.235759 | + | 0.971812i | \(0.424242\pi\) | |||||||
\(264\) | 0.450161 | − | 1.85559i | 0.450161 | − | 1.85559i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.15757 | − | 2.00498i | 1.15757 | − | 2.00498i | ||||
\(267\) | 1.04758 | + | 0.998867i | 1.04758 | + | 0.998867i | ||||
\(268\) | 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 | ||||||||
\(274\) | −0.514186 | + | 0.890596i | −0.514186 | + | 0.890596i | ||||
\(275\) | −0.928368 | + | 1.60798i | −0.928368 | + | 1.60798i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.581419 | + | 0.299742i | 0.581419 | + | 0.299742i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.235759 | − | 0.408346i | −0.235759 | − | 0.408346i | 0.723734 | − | 0.690079i | \(-0.242424\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(282\) | 0.0597285 | − | 0.0175379i | 0.0597285 | − | 0.0175379i | ||||
\(283\) | 0.142315 | − | 0.246497i | 0.142315 | − | 0.246497i | −0.786053 | − | 0.618159i | \(-0.787879\pi\) |
0.928368 | + | 0.371662i | \(0.121212\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.855569 | + | 0.441076i | 0.855569 | + | 0.441076i | ||||
\(289\) | 1.00000 | 1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.0671040 | + | 0.276606i | −0.0671040 | + | 0.276606i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.981929 | + | 1.70075i | −0.981929 | + | 1.70075i | −0.327068 | + | 0.945001i | \(0.606061\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(294\) | −1.40315 | − | 1.33790i | −1.40315 | − | 1.33790i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.82318 | + | 0.351390i | 1.82318 | + | 0.351390i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −0.414053 | − | 0.394798i | −0.414053 | − | 0.394798i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.0894065 | − | 0.154857i | −0.0894065 | − | 0.154857i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(308\) | −1.05744 | − | 1.83154i | −1.05744 | − | 1.83154i | ||||
\(309\) | 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 | \(0.333333\pi\) | |||||||
\(314\) | 0.856736 | 0.856736 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.235759 | − | 0.408346i | −0.235759 | − | 0.408346i | 0.723734 | − | 0.690079i | \(-0.242424\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.07701 | + | 1.86544i | −1.07701 | + | 1.86544i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.44091 | − | 1.37391i | −1.44091 | − | 1.37391i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −0.237662 | + | 0.520406i | −0.237662 | + | 0.520406i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.0947329 | − | 0.164082i | 0.0947329 | − | 0.164082i | ||||
\(330\) | 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 | ||||||||
\(334\) | −0.654136 | −0.654136 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.192154 | + | 0.0564214i | −0.192154 | + | 0.0564214i | ||||
\(337\) | −0.0475819 | + | 0.0824143i | −0.0475819 | + | 0.0824143i | −0.888835 | − | 0.458227i | \(-0.848485\pi\) |
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(338\) | 0.327068 | − | 0.566498i | 0.327068 | − | 0.566498i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.21456 | −1.21456 | ||||||||
\(342\) | 0.978242 | − | 0.628678i | 0.978242 | − | 0.628678i | ||||
\(343\) | −3.90993 | −3.90993 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.0930932 | + | 0.161242i | −0.0930932 | + | 0.161242i | ||||
\(347\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(348\) | −0.480348 | − | 0.458011i | −0.480348 | − | 0.458011i | ||||
\(349\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(350\) | 1.30235 | 1.30235 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.78724 | −1.78724 | ||||||||
\(353\) | −0.415415 | − | 0.719520i | −0.415415 | − | 0.719520i | 0.580057 | − | 0.814576i | \(-0.303030\pi\) |
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0.414053 | − | 0.717160i | 0.414053 | − | 0.717160i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.581419 | − | 1.00705i | −0.581419 | − | 1.00705i | ||||
\(359\) | −1.30972 | −1.30972 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.16011 | 2.16011 | ||||||||
\(362\) | 0.0311250 | + | 0.0539102i | 0.0311250 | + | 0.0539102i | ||||
\(363\) | −2.34833 | + | 0.689531i | −2.34833 | + | 0.689531i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.20443 | + | 0.353653i | −1.20443 | + | 0.353653i | ||||
\(367\) | −0.0475819 | − | 0.0824143i | −0.0475819 | − | 0.0824143i | 0.841254 | − | 0.540641i | \(-0.181818\pi\) |
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0.0882293 | − | 0.363686i | 0.0882293 | − | 0.363686i | ||||
\(373\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.0489319 | − | 0.0847525i | −0.0489319 | − | 0.0847525i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −0.425956 | − | 1.23072i | −0.425956 | − | 1.23072i | ||||
\(379\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.34378 | + | 1.28129i | 1.34378 | + | 1.28129i | ||||
\(382\) | 0.642315 | − | 1.11252i | 0.642315 | − | 1.11252i | ||||
\(383\) | −0.415415 | + | 0.719520i | −0.415415 | + | 0.719520i | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) |
0.580057 | + | 0.814576i | \(0.303030\pi\) | |||||||
\(384\) | 0.114318 | − | 0.471227i | 0.114318 | − | 0.471227i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0.162838 | 0.162838 | ||||||||
\(389\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −1.52397 | + | 2.63960i | −1.52397 | + | 2.63960i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.0505439 | − | 1.06105i | −0.0505439 | − | 1.06105i | ||||
\(397\) | 0.471518 | 0.471518 | 0.235759 | − | 0.971812i | \(-0.424242\pi\) | ||||
0.235759 | + | 0.971812i | \(0.424242\pi\) | |||||||
\(398\) | −0.0930932 | − | 0.161242i | −0.0930932 | − | 0.161242i | ||||
\(399\) | 0.834408 | − | 3.43948i | 0.834408 | − | 3.43948i | ||||
\(400\) | 0.0502942 | − | 0.0871120i | 0.0502942 | − | 0.0871120i | ||||
\(401\) | 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 | ||||||||
\(406\) | 1.51087 | 1.51087 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.928368 | + | 1.60798i | −0.928368 | + | 1.60798i | −0.142315 | + | 0.989821i | \(0.545455\pi\) |
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.370638 | + | 1.52779i | −0.370638 | + | 1.52779i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.07954 | + | 1.86982i | −1.07954 | + | 1.86982i | ||||
\(419\) | −0.981929 | + | 1.70075i | −0.981929 | + | 1.70075i | −0.327068 | + | 0.945001i | \(0.606061\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.415415 | − | 0.719520i | −0.415415 | − | 0.719520i | 0.580057 | − | 0.814576i | \(-0.303030\pi\) |
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(422\) | 0.856736 | 0.856736 | ||||||||
\(423\) | 0.0800569 | − | 0.0514495i | 0.0800569 | − | 0.0514495i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.91030 | + | 3.30873i | −1.91030 | + | 3.30873i | ||||
\(428\) | −0.569516 | + | 0.986430i | −0.569516 | + | 0.986430i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.471518 | 0.471518 | 0.235759 | − | 0.971812i | \(-0.424242\pi\) | ||||
0.235759 | + | 0.971812i | \(0.424242\pi\) | |||||||
\(432\) | −0.0987706 | − | 0.0190365i | −0.0987706 | − | 0.0190365i | ||||
\(433\) | 1.68251 | 1.68251 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(434\) | 0.425956 | + | 0.737778i | 0.425956 | + | 0.737778i | ||||
\(435\) | 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 | ||||||||
\(441\) | −2.63438 | − | 1.35812i | −2.63438 | − | 1.35812i | ||||
\(442\) | 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 | ||||||||
\(446\) | 0.473420 | − | 0.819988i | 0.473420 | − | 0.819988i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.726935 | + | 1.25909i | 0.726935 | + | 1.25909i | ||||
\(449\) | 1.68251 | 1.68251 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(450\) | 0.581419 | + | 0.299742i | 0.581419 | + | 0.299742i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.32306 | − | 1.26154i | −1.32306 | − | 1.26154i | ||||
\(457\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(458\) | −0.758872 | −0.758872 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.841254 | − | 1.45709i | −0.841254 | − | 1.45709i | −0.888835 | − | 0.458227i | \(-0.848485\pi\) |
0.0475819 | − | 0.998867i | \(-0.484848\pi\) | |||||||
\(462\) | 1.75007 | + | 1.66869i | 1.75007 | + | 1.66869i | ||||
\(463\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(464\) | 0.0583469 | − | 0.101060i | 0.0583469 | − | 0.101060i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.642315 | + | 1.11252i | 0.642315 | + | 1.11252i | ||||
\(467\) | 1.16011 | 1.16011 | 0.580057 | − | 0.814576i | \(-0.303030\pi\) | ||||
0.580057 | + | 0.814576i | \(0.303030\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.25667 | − | 0.368991i | 1.25667 | − | 0.368991i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.888835 | + | 1.53951i | 0.888835 | + | 1.53951i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −0.946841 | −0.946841 | ||||||||
\(479\) | 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 | ||||||||
\(484\) | 0.700106 | + | 1.21262i | 0.700106 | + | 1.21262i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.0930932 | − | 0.647478i | 0.0930932 | − | 0.647478i | ||||
\(487\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(488\) | 0.986715 | + | 1.70904i | 0.986715 | + | 1.70904i | ||||
\(489\) | 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 | ||||||||
\(496\) | 0.0657984 | 0.0657984 | ||||||||
\(497\) | 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 | ||||||||
\(501\) | −0.959493 | + | 0.281733i | −0.959493 | + | 0.281733i | ||||
\(502\) | 0.271738 | + | 0.470664i | 0.271738 | + | 0.470664i | ||||
\(503\) | 0.471518 | 0.471518 | 0.235759 | − | 0.971812i | \(-0.424242\pi\) | ||||
0.235759 | + | 0.971812i | \(0.424242\pi\) | |||||||
\(504\) | −1.72241 | + | 1.10692i | −1.72241 | + | 1.10692i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.235759 | − | 0.971812i | 0.235759 | − | 0.971812i | ||||
\(508\) | 0.531125 | − | 0.919936i | 0.531125 | − | 0.919936i | ||||
\(509\) | 0.786053 | − | 1.36148i | 0.786053 | − | 1.36148i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) |
0.928368 | − | 0.371662i | \(-0.121212\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0.200266 | 0.200266 | ||||||||
\(513\) | 1.16413 | − | 1.34347i | 1.16413 | − | 1.34347i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.0883470 | + | 0.153022i | −0.0883470 | + | 0.153022i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.0671040 | + | 0.276606i | −0.0671040 | + | 0.276606i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(522\) | 0.674512 | + | 0.347735i | 0.674512 | + | 0.347735i | ||||
\(523\) | 1.96386 | 1.96386 | 0.981929 | − | 0.189251i | \(-0.0606061\pi\) | ||||
0.981929 | + | 0.189251i | \(0.0606061\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.91030 | − | 0.560914i | 1.91030 | − | 0.560914i | ||||
\(526\) | −0.627639 | + | 1.08710i | −0.627639 | + | 1.08710i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0.179201 | − | 0.0526180i | 0.179201 | − | 0.0526180i | ||||
\(529\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.02482 | −2.02482 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −0.223226 | + | 0.920151i | −0.223226 | + | 0.920151i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.28656 | − | 1.22673i | −1.28656 | − | 1.22673i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.50310 | 5.50310 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.0688733 | + | 0.0656706i | 0.0688733 | + | 0.0656706i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(548\) | 0.899412 | 0.899412 | ||||||||
\(549\) | −1.61435 | + | 1.03748i | −1.61435 | + | 1.03748i | ||||
\(550\) | −1.21456 | −1.21456 | ||||||||
\(551\) | 1.03115 | + | 1.78600i | 1.03115 | + | 1.78600i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.57211 | −1.57211 | −0.786053 | − | 0.618159i | \(-0.787879\pi\) | ||||
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(558\) | 0.0203600 | + | 0.427409i | 0.0203600 | + | 0.427409i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.154218 | − | 0.267114i | 0.154218 | − | 0.267114i | ||||
\(563\) | −0.841254 | + | 1.45709i | −0.841254 | + | 1.45709i | 0.0475819 | + | 0.998867i | \(0.484848\pi\) |
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(564\) | −0.0394028 | − | 0.0375705i | −0.0394028 | − | 0.0375705i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0.186186 | 0.186186 | ||||||||
\(567\) | −1.15486 | − | 1.62177i | −1.15486 | − | 1.62177i | ||||
\(568\) | 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 | ||||||||
\(573\) | 0.462997 | − | 1.90850i | 0.462997 | − | 1.90850i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.0347463 | + | 0.729415i | 0.0347463 | + | 0.729415i | ||||
\(577\) | −1.30972 | −1.30972 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(578\) | 0.327068 | + | 0.566498i | 0.327068 | + | 0.566498i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −0.178645 | + | 0.0524548i | −0.178645 | + | 0.0524548i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.28463 | −1.28463 | ||||||||
\(587\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(588\) | −0.399763 | + | 1.64784i | −0.399763 | + | 1.64784i | ||||
\(589\) | −0.581419 | + | 1.00705i | −0.581419 | + | 1.00705i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(594\) | 0.397243 | + | 1.14776i | 0.397243 | + | 1.14776i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.205996 | − | 0.196417i | −0.205996 | − | 0.196417i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.580057 | + | 1.00469i | −0.580057 | + | 1.00469i | 0.415415 | + | 0.909632i | \(0.363636\pi\) |
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(600\) | 0.242448 | − | 0.999383i | 0.242448 | − | 0.999383i | ||||
\(601\) | −0.580057 | − | 1.00469i | −0.580057 | − | 1.00469i | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) |
0.415415 | − | 0.909632i | \(-0.363636\pi\) | |||||||
\(602\) | 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 | \(0.666667\pi\) | |||||||
\(608\) | −0.855569 | + | 1.48189i | −0.855569 | + | 1.48189i | ||||
\(609\) | 2.21616 | − | 0.650724i | 2.21616 | − | 0.650724i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.654136 | −0.654136 | −0.327068 | − | 0.945001i | \(-0.606061\pi\) | ||||
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.90077 | − | 3.29223i | 1.90077 | − | 3.29223i | ||||
\(617\) | −0.415415 | + | 0.719520i | −0.415415 | + | 0.719520i | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) |
0.580057 | + | 0.814576i | \(0.303030\pi\) | |||||||
\(618\) | 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 | ||||||||
\(622\) | 0.654136 | 0.654136 | ||||||||
\(623\) | 1.44091 | + | 2.49574i | 1.44091 | + | 2.49574i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.778161 | + | 3.20762i | −0.778161 | + | 3.20762i | ||||
\(628\) | −0.374650 | − | 0.648913i | −0.374650 | − | 0.648913i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.91899 | −1.91899 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.25667 | − | 0.368991i | 1.25667 | − | 0.368991i | ||||
\(634\) | 0.154218 | − | 0.267114i | 0.154218 | − | 0.267114i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.40903 | −1.40903 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(642\) | 0.307040 | − | 1.26564i | 0.307040 | − | 1.26564i | ||||
\(643\) | 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 | \(\pi\) | |||||||||
\(648\) | −1.02371 | + | 0.0977529i | −1.02371 | + | 0.0977529i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.942554 | + | 0.898723i | 0.942554 | + | 0.898723i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0.654861 | − | 1.13425i | 0.654861 | − | 1.13425i | −0.327068 | − | 0.945001i | \(-0.606061\pi\) |
0.981929 | − | 0.189251i | \(-0.0606061\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.123936 | 0.123936 | ||||||||
\(659\) | 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 | ||||||||
\(668\) | 0.286053 | + | 0.495458i | 0.286053 | + | 0.495458i | ||||
\(669\) | 0.341254 | − | 1.40667i | 0.341254 | − | 1.40667i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.78153 | − | 3.08569i | 1.78153 | − | 3.08569i | ||||
\(672\) | 1.38698 | + | 1.32249i | 1.38698 | + | 1.32249i | ||||
\(673\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(674\) | −0.0622501 | −0.0622501 | ||||||||
\(675\) | 0.981929 | + | 0.189251i | 0.981929 | + | 0.189251i | ||||
\(676\) | −0.572106 | −0.572106 | ||||||||
\(677\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.283341 | + | 0.490761i | −0.283341 | + | 0.490761i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.397243 | − | 0.688045i | −0.397243 | − | 0.688045i | ||||
\(683\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(684\) | −0.903960 | − | 0.466024i | −0.903960 | − | 0.466024i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.27881 | − | 2.21497i | −1.27881 | − | 2.21497i | ||||
\(687\) | −1.11312 | + | 0.326842i | −1.11312 | + | 0.326842i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(692\) | 0.162838 | 0.162838 | ||||||||
\(693\) | 3.28572 | + | 1.69391i | 3.28572 | + | 1.69391i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0.281267 | − | 1.15940i | 0.281267 | − | 1.15940i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.42131 | + | 1.35522i | 1.42131 | + | 1.35522i | ||||
\(700\) | −0.569516 | − | 0.986430i | −0.569516 | − | 0.986430i | ||||
\(701\) | 1.44747 | 1.44747 | 0.723734 | − | 0.690079i | \(-0.242424\pi\) | ||||
0.723734 | + | 0.690079i | \(0.242424\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −0.677933 | − | 1.17421i | −0.677933 | − | 1.17421i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.271738 | − | 0.470664i | 0.271738 | − | 0.470664i | ||||
\(707\) | 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 | ||||||||
\(712\) | 1.48853 | 1.48853 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −0.508508 | + | 0.880762i | −0.508508 | + | 0.880762i | ||||
\(717\) | −1.38884 | + | 0.407799i | −1.38884 | + | 0.407799i | ||||
\(718\) | −0.428368 | − | 0.741955i | −0.428368 | − | 0.741955i | ||||
\(719\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0.706504 | + | 1.22370i | 0.706504 | + | 1.22370i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0.0272219 | − | 0.0471497i | 0.0272219 | − | 0.0471497i | ||||
\(725\) | −0.580057 | + | 1.00469i | −0.580057 | + | 1.00469i | ||||
\(726\) | −1.15868 | − | 1.10480i | −1.15868 | − | 1.10480i | ||||
\(727\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.142315 | − | 0.989821i | −0.142315 | − | 0.989821i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0.794561 | + | 0.757613i | 0.794561 | + | 0.757613i | ||||
\(733\) | 0.888835 | − | 1.53951i | 0.888835 | − | 1.53951i | 0.0475819 | − | 0.998867i | \(-0.484848\pi\) |
0.841254 | − | 0.540641i | \(-0.181818\pi\) | |||||||
\(734\) | 0.0311250 | − | 0.0539102i | 0.0311250 | − | 0.0539102i | ||||
\(735\) | 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 | \(0\) | |||||||||
\(744\) | 0.645446 | − | 0.189520i | 0.645446 | − | 0.189520i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.98193 | − | 3.43280i | −1.98193 | − | 3.43280i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(752\) | 0.00478618 | − | 0.00828992i | 0.00478618 | − | 0.00828992i | ||||
\(753\) | 0.601300 | + | 0.573338i | 0.601300 | + | 0.573338i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.745907 | + | 0.860822i | −0.745907 | + | 0.860822i | ||||
\(757\) | −0.284630 | −0.284630 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.959493 | − | 1.66189i | 0.959493 | − | 1.66189i | 0.235759 | − | 0.971812i | \(-0.424242\pi\) |
0.723734 | − | 0.690079i | \(-0.242424\pi\) | |||||||
\(762\) | −0.286343 | + | 1.18032i | −0.286343 | + | 1.18032i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −1.12353 | −1.12353 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −0.543476 | −0.543476 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.00500 | − | 0.295095i | 1.00500 | − | 0.295095i | ||||
\(769\) | 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 | ||||||||
\(775\) | −0.654136 | −0.654136 | ||||||||
\(776\) | 0.146352 | + | 0.253490i | 0.146352 | + | 0.253490i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.13915 | + | 0.219553i | 1.13915 | + | 0.219553i | ||||
\(784\) | −0.298129 | −0.298129 | ||||||||
\(785\) | 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 | ||||||||
\(789\) | −0.452418 | + | 1.86489i | −0.452418 | + | 1.86489i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.60630 | − | 1.03231i | 1.60630 | − | 1.03231i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0.154218 | + | 0.267114i | 0.154218 | + | 0.267114i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.0814192 | + | 0.141022i | −0.0814192 | + | 0.141022i | ||||
\(797\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(798\) | 2.22137 | − | 0.652252i | 2.22137 | − | 0.652252i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −0.962573 | −0.962573 | ||||||||
\(801\) | 0.0688733 | + | 1.44583i | 0.0688733 | + | 1.44583i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −0.284630 | −0.284630 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(812\) | −0.660703 | − | 1.14437i | −0.660703 | − | 1.14437i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −1.21456 | −1.21456 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(822\) | −0.986715 | + | 0.289726i | −0.986715 | + | 0.289726i | ||||
\(823\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.78153 | + | 0.523103i | −1.78153 | + | 0.523103i | ||||
\(826\) | 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 | ||||||||
\(836\) | 1.88833 | 1.88833 | ||||||||
\(837\) | 0.213947 | + | 0.618159i | 0.213947 | + | 0.618159i | ||||
\(838\) | −1.28463 | −1.28463 | ||||||||
\(839\) | 0.959493 | + | 1.66189i | 0.959493 | + | 1.66189i | 0.723734 | + | 0.690079i | \(0.242424\pi\) |
0.235759 | + | 0.971812i | \(0.424242\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.172932 | + | 0.299527i | −0.172932 | + | 0.299527i | ||||
\(842\) | 0.271738 | − | 0.470664i | 0.271738 | − | 0.470664i | ||||
\(843\) | 0.111165 | − | 0.458227i | 0.111165 | − | 0.458227i | ||||
\(844\) | −0.374650 | − | 0.648913i | −0.374650 | − | 0.648913i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.0553301 | + | 0.0285246i | 0.0553301 | + | 0.0285246i | ||||
\(847\) | −4.87277 | −4.87277 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.273100 | − | 0.0801894i | 0.273100 | − | 0.0801894i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.786053 | + | 1.36148i | 0.786053 | + | 1.36148i | 0.928368 | + | 0.371662i | \(0.121212\pi\) |
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(854\) | −2.49919 | −2.49919 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.04743 | −2.04743 | ||||||||
\(857\) | 0.888835 | + | 1.53951i | 0.888835 | + | 1.53951i | 0.841254 | + | 0.540641i | \(0.181818\pi\) |
0.0475819 | + | 0.998867i | \(0.484848\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.580057 | + | 1.00469i | −0.580057 | + | 1.00469i | 0.415415 | + | 0.909632i | \(0.363636\pi\) |
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.154218 | + | 0.267114i | 0.154218 | + | 0.267114i | ||||
\(863\) | −0.284630 | −0.284630 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(864\) | 0.314827 | + | 0.909632i | 0.314827 | + | 0.909632i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0.550294 | + | 0.953137i | 0.550294 | + | 0.953137i | ||||
\(867\) | 0.723734 | + | 0.690079i | 0.723734 | + | 0.690079i | ||||
\(868\) | 0.372541 | − | 0.645259i | 0.372541 | − | 0.645259i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.239446 | + | 0.153882i | −0.239446 | + | 0.153882i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.888835 | − | 1.53951i | 0.888835 | − | 1.53951i | 0.0475819 | − | 0.998867i | \(-0.484848\pi\) |
0.841254 | − | 0.540641i | \(-0.181818\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.88431 | + | 0.553283i | −1.88431 | + | 0.553283i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | −0.0922502 | − | 1.93657i | −0.0922502 | − | 1.93657i | ||||
\(883\) | 0.830830 | 0.830830 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(884\) | 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 | ||||||||
\(889\) | 1.84833 | + | 3.20140i | 1.84833 | + | 3.20140i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.07701 | + | 1.51245i | 1.07701 | + | 1.51245i | ||||
\(892\) | −0.828105 | −0.828105 | ||||||||
\(893\) | 0.0845850 | + | 0.146505i | 0.0845850 | + | 0.146505i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.482700 | − | 0.836060i | 0.482700 | − | 0.836060i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0.550294 | + | 0.953137i | 0.550294 | + | 0.953137i | ||||
\(899\) | −0.758872 | −0.758872 | ||||||||
\(900\) | −0.0272219 | − | 0.571458i | −0.0272219 | − | 0.571458i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.235759 | − | 0.408346i | −0.235759 | − | 0.408346i | 0.723734 | − | 0.690079i | \(-0.242424\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.841254 | − | 1.45709i | −0.841254 | − | 1.45709i | −0.888835 | − | 0.458227i | \(-0.848485\pi\) |
0.0475819 | − | 0.998867i | \(-0.484848\pi\) | |||||||
\(912\) | 0.0421567 | − | 0.173772i | 0.0421567 | − | 0.173772i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.331854 | + | 0.574788i | 0.331854 | + | 0.574788i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.68251 | 1.68251 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0.550294 | − | 0.953137i | 0.550294 | − | 0.953137i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0.498602 | − | 2.05527i | 0.498602 | − | 2.05527i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.11669 | −1.11669 | ||||||||
\(929\) | −0.981929 | − | 1.70075i | −0.981929 | − | 1.70075i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
−0.327068 | − | 0.945001i | \(-0.606061\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.63438 | − | 4.56288i | 2.63438 | − | 4.56288i | ||||
\(932\) | 0.561767 | − | 0.973010i | 0.561767 | − | 0.973010i | ||||
\(933\) | 0.959493 | − | 0.281733i | 0.959493 | − | 0.281733i | ||||
\(934\) | 0.379436 | + | 0.657203i | 0.379436 | + | 0.657203i | ||||
\(935\) | 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 | \(0.666667\pi\) | |||||||
\(942\) | 0.620049 | + | 0.591215i | 0.620049 | + | 0.591215i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −0.723734 | − | 1.25354i | −0.723734 | − | 1.25354i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
0.235759 | − | 0.971812i | \(-0.424242\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −0.581419 | + | 1.00705i | −0.581419 | + | 1.00705i | ||||
\(951\) | 0.111165 | − | 0.458227i | 0.111165 | − | 0.458227i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0.414053 | + | 0.717160i | 0.414053 | + | 0.717160i | ||||
\(957\) | −2.06677 | + | 0.606859i | −2.06677 | + | 0.606859i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.56499 | + | 2.71064i | −1.56499 | + | 2.71064i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.286053 | + | 0.495458i | 0.286053 | + | 0.495458i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.0947329 | − | 1.98869i | −0.0947329 | − | 1.98869i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.981929 | + | 1.70075i | −0.981929 | + | 1.70075i | −0.327068 | + | 0.945001i | \(0.606061\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(968\) | −1.25845 | + | 2.17970i | −1.25845 | + | 2.17970i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(972\) | −0.531125 | + | 0.212630i | −0.531125 | + | 0.212630i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.0965138 | + | 0.167167i | −0.0965138 | + | 0.167167i | ||||
\(977\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.34378 | − | 2.32750i | −1.34378 | − | 2.32750i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.30827 | −1.30827 | ||||||||
\(983\) | 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 | ||||||||
\(987\) | 0.181791 | − | 0.0533787i | 0.181791 | − | 0.0533787i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(992\) | −0.314827 | − | 0.545296i | −0.314827 | − | 0.545296i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.580057 | − | 1.00469i | −0.580057 | − | 1.00469i | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) |
0.415415 | − | 0.909632i | \(-0.363636\pi\) | |||||||
\(998\) | 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.166.7 | ✓ | 20 | |
9.7 | even | 3 | inner | 1503.1.f.b.1168.7 | yes | 20 | |
167.166 | odd | 2 | CM | 1503.1.f.b.166.7 | ✓ | 20 | |
1503.1168 | odd | 6 | inner | 1503.1.f.b.1168.7 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1503.1.f.b.166.7 | ✓ | 20 | 1.1 | even | 1 | trivial | |
1503.1.f.b.166.7 | ✓ | 20 | 167.166 | odd | 2 | CM | |
1503.1.f.b.1168.7 | yes | 20 | 9.7 | even | 3 | inner | |
1503.1.f.b.1168.7 | yes | 20 | 1503.1168 | odd | 6 | inner |