Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2151,1,Mod(238,2151)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2151, 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("2151.238");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2151 = 3^{2} \cdot 239 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 2151.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: | \(1.07348884217\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{45})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{24} - x^{21} + x^{15} - x^{12} + x^{9} - x^{3} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{45}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{45} - \cdots)\) |
Embedding invariants
Embedding label | 238.8 | ||
Root | \(-0.241922 - 0.970296i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2151.238 |
Dual form | 2151.1.f.b.1672.8 |
$q$-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 \(\left(\mathbb{Z}/2151\mathbb{Z}\right)^\times\).
\(n\) | \(479\) | \(1441\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.374607 | + | 0.648838i | 0.374607 | + | 0.648838i | 0.990268 | − | 0.139173i | \(-0.0444444\pi\) |
−0.615661 | + | 0.788011i | \(0.711111\pi\) | |||||||
\(3\) | 0.669131 | + | 0.743145i | 0.669131 | + | 0.743145i | ||||
\(4\) | 0.219340 | − | 0.379908i | 0.219340 | − | 0.379908i | ||||
\(5\) | −0.0348995 | + | 0.0604477i | −0.0348995 | + | 0.0604477i | −0.882948 | − | 0.469472i | \(-0.844444\pi\) |
0.848048 | + | 0.529919i | \(0.177778\pi\) | |||||||
\(6\) | −0.231520 | + | 0.712544i | −0.231520 | + | 0.712544i | ||||
\(7\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(8\) | 1.07788 | 1.07788 | ||||||||
\(9\) | −0.104528 | + | 0.994522i | −0.104528 | + | 0.994522i | ||||
\(10\) | −0.0522943 | −0.0522943 | ||||||||
\(11\) | −0.559193 | − | 0.968551i | −0.559193 | − | 0.968551i | −0.997564 | − | 0.0697565i | \(-0.977778\pi\) |
0.438371 | − | 0.898794i | \(-0.355556\pi\) | |||||||
\(12\) | 0.429093 | − | 0.0912066i | 0.429093 | − | 0.0912066i | ||||
\(13\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.0682737 | + | 0.0145120i | −0.0682737 | + | 0.0145120i | ||||
\(16\) | 0.184440 | + | 0.319460i | 0.184440 | + | 0.319460i | ||||
\(17\) | 1.53209 | 1.53209 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(18\) | −0.684440 | + | 0.304732i | −0.684440 | + | 0.304732i | ||||
\(19\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(20\) | 0.0153097 | + | 0.0265172i | 0.0153097 | + | 0.0265172i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.418955 | − | 0.725651i | 0.418955 | − | 0.725651i | ||||
\(23\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(24\) | 0.721241 | + | 0.801019i | 0.721241 | + | 0.801019i | ||||
\(25\) | 0.497564 | + | 0.861806i | 0.497564 | + | 0.861806i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.961262 | − | 1.66495i | −0.961262 | − | 1.66495i | −0.719340 | − | 0.694658i | \(-0.755556\pi\) |
−0.241922 | − | 0.970296i | \(-0.577778\pi\) | |||||||
\(30\) | −0.0349917 | − | 0.0388623i | −0.0349917 | − | 0.0388623i | ||||
\(31\) | −0.990268 | + | 1.71519i | −0.990268 | + | 1.71519i | −0.374607 | + | 0.927184i | \(0.622222\pi\) |
−0.615661 | + | 0.788011i | \(0.711111\pi\) | |||||||
\(32\) | 0.400754 | − | 0.694126i | 0.400754 | − | 0.694126i | ||||
\(33\) | 0.345600 | − | 1.06365i | 0.345600 | − | 1.06365i | ||||
\(34\) | 0.573931 | + | 0.994077i | 0.573931 | + | 0.994077i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.354899 | + | 0.257849i | 0.354899 | + | 0.257849i | ||||
\(37\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.0376174 | + | 0.0651552i | −0.0376174 | + | 0.0651552i | ||||
\(41\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(44\) | −0.490613 | −0.490613 | ||||||||
\(45\) | −0.0564686 | − | 0.0410268i | −0.0564686 | − | 0.0410268i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(48\) | −0.113990 | + | 0.350826i | −0.113990 | + | 0.350826i | ||||
\(49\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(50\) | −0.372782 | + | 0.645677i | −0.372782 | + | 0.645677i | ||||
\(51\) | 1.02517 | + | 1.13856i | 1.02517 | + | 1.13856i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(54\) | −0.684440 | − | 0.304732i | −0.684440 | − | 0.304732i | ||||
\(55\) | 0.0780622 | 0.0780622 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.720190 | − | 1.24741i | 0.720190 | − | 1.24741i | ||||
\(59\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(60\) | −0.00946191 | + | 0.0291208i | −0.00946191 | + | 0.0291208i | ||||
\(61\) | −0.766044 | − | 1.32683i | −0.766044 | − | 1.32683i | −0.939693 | − | 0.342020i | \(-0.888889\pi\) |
0.173648 | − | 0.984808i | \(-0.444444\pi\) | |||||||
\(62\) | −1.48384 | −1.48384 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.969381 | 0.969381 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.819599 | − | 0.174211i | 0.819599 | − | 0.174211i | ||||
\(67\) | −0.173648 | + | 0.300767i | −0.173648 | + | 0.300767i | −0.939693 | − | 0.342020i | \(-0.888889\pi\) |
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(68\) | 0.336048 | − | 0.582052i | 0.336048 | − | 0.582052i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.61803 | −1.61803 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(72\) | −0.112669 | + | 1.07197i | −0.112669 | + | 1.07197i | ||||
\(73\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.307511 | + | 0.946423i | −0.307511 | + | 0.946423i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(80\) | −0.0257475 | −0.0257475 | ||||||||
\(81\) | −0.978148 | − | 0.207912i | −0.978148 | − | 0.207912i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.241922 | + | 0.419021i | 0.241922 | + | 0.419021i | 0.961262 | − | 0.275637i | \(-0.0888889\pi\) |
−0.719340 | + | 0.694658i | \(0.755556\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.0534691 | + | 0.0926113i | −0.0534691 | + | 0.0926113i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.594092 | − | 1.82843i | 0.594092 | − | 1.82843i | ||||
\(88\) | −0.602742 | − | 1.04398i | −0.602742 | − | 1.04398i | ||||
\(89\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(90\) | 0.00546625 | − | 0.0520079i | 0.00546625 | − | 0.0520079i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.93726 | + | 0.411777i | −1.93726 | + | 0.411777i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.783993 | − | 0.166643i | 0.783993 | − | 0.166643i | ||||
\(97\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(98\) | −0.749213 | −0.749213 | ||||||||
\(99\) | 1.02170 | − | 0.454888i | 1.02170 | − | 0.454888i | ||||
\(100\) | 0.436542 | 0.436542 | ||||||||
\(101\) | −0.309017 | − | 0.535233i | −0.309017 | − | 0.535233i | 0.669131 | − | 0.743145i | \(-0.266667\pi\) |
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(102\) | −0.354709 | + | 1.09168i | −0.354709 | + | 1.09168i | ||||
\(103\) | 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 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(108\) | 0.0458545 | + | 0.436276i | 0.0458545 | + | 0.436276i | ||||
\(109\) | −0.209057 | −0.209057 | −0.104528 | − | 0.994522i | \(-0.533333\pi\) | ||||
−0.104528 | + | 0.994522i | \(0.533333\pi\) | |||||||
\(110\) | 0.0292426 | + | 0.0506497i | 0.0292426 | + | 0.0506497i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.978148 | − | 1.69420i | 0.978148 | − | 1.69420i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
0.669131 | − | 0.743145i | \(-0.266667\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.843372 | −0.843372 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −0.0735907 | + | 0.0156422i | −0.0735907 | + | 0.0156422i | ||||
\(121\) | −0.125393 | + | 0.217188i | −0.125393 | + | 0.217188i | ||||
\(122\) | 0.573931 | − | 0.994077i | 0.573931 | − | 0.994077i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.434410 | + | 0.752421i | 0.434410 | + | 0.752421i | ||||
\(125\) | −0.139258 | −0.139258 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.876742 | 0.876742 | 0.438371 | − | 0.898794i | \(-0.355556\pi\) | ||||
0.438371 | + | 0.898794i | \(0.355556\pi\) | |||||||
\(128\) | −0.0376174 | − | 0.0651552i | −0.0376174 | − | 0.0651552i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(132\) | −0.328284 | − | 0.364597i | −0.328284 | − | 0.364597i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −0.260199 | −0.260199 | ||||||||
\(135\) | −0.00729598 | − | 0.0694166i | −0.00729598 | − | 0.0694166i | ||||
\(136\) | 1.65140 | 1.65140 | ||||||||
\(137\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.606126 | − | 1.04984i | −0.606126 | − | 1.04984i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.336989 | + | 0.150037i | −0.336989 | + | 0.150037i | ||||
\(145\) | 0.134190 | 0.134190 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.978148 | + | 0.207912i | −0.978148 | + | 0.207912i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(150\) | −0.729271 | + | 0.155011i | −0.729271 | + | 0.155011i | ||||
\(151\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.160147 | + | 1.52370i | −0.160147 | + | 1.52370i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.0691197 | − | 0.119719i | −0.0691197 | − | 0.119719i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.961262 | + | 1.66495i | −0.961262 | + | 1.66495i | −0.241922 | + | 0.970296i | \(0.577778\pi\) |
−0.719340 | + | 0.694658i | \(0.755556\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.0279722 | + | 0.0484493i | 0.0279722 | + | 0.0484493i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.231520 | − | 0.712544i | −0.231520 | − | 0.712544i | ||||
\(163\) | −1.76590 | −1.76590 | −0.882948 | − | 0.469472i | \(-0.844444\pi\) | ||||
−0.882948 | + | 0.469472i | \(0.844444\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.0522338 | + | 0.0580115i | 0.0522338 | + | 0.0580115i | ||||
\(166\) | −0.181251 | + | 0.313936i | −0.181251 | + | 0.313936i | ||||
\(167\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(170\) | −0.0801196 | −0.0801196 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(174\) | 1.40890 | − | 0.299472i | 1.40890 | − | 0.299472i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.206275 | − | 0.357280i | 0.206275 | − | 0.357280i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(180\) | −0.0279722 | + | 0.0124540i | −0.0279722 | + | 0.0124540i | ||||
\(181\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.473442 | − | 1.45710i | 0.473442 | − | 1.45710i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.992885 | − | 1.10271i | −0.992885 | − | 1.10271i | ||||
\(187\) | −0.856733 | − | 1.48391i | −0.856733 | − | 1.48391i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(192\) | 0.648642 | + | 0.720390i | 0.648642 | + | 0.720390i | ||||
\(193\) | 0.882948 | − | 1.52931i | 0.882948 | − | 1.52931i | 0.0348995 | − | 0.999391i | \(-0.488889\pi\) |
0.848048 | − | 0.529919i | \(-0.177778\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.219340 | + | 0.379908i | 0.219340 | + | 0.379908i | ||||
\(197\) | −1.99513 | −1.99513 | −0.997564 | − | 0.0697565i | \(-0.977778\pi\) | ||||
−0.997564 | + | 0.0697565i | \(0.977778\pi\) | |||||||
\(198\) | 0.677883 | + | 0.492511i | 0.677883 | + | 0.492511i | ||||
\(199\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(200\) | 0.536313 | + | 0.928922i | 0.536313 | + | 0.928922i | ||||
\(201\) | −0.339707 | + | 0.0722070i | −0.339707 | + | 0.0722070i | ||||
\(202\) | 0.231520 | − | 0.401004i | 0.231520 | − | 0.401004i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.657409 | − | 0.139737i | 0.657409 | − | 0.139737i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.241922 | − | 0.419021i | 0.241922 | − | 0.419021i | −0.719340 | − | 0.694658i | \(-0.755556\pi\) |
0.961262 | + | 0.275637i | \(0.0888889\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.08268 | − | 1.20243i | −1.08268 | − | 1.20243i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.872021 | + | 0.633561i | −0.872021 | + | 0.633561i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −0.0783141 | − | 0.135644i | −0.0783141 | − | 0.135644i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.0171221 | − | 0.0296564i | 0.0171221 | − | 0.0296564i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.909095 | + | 0.404755i | −0.909095 | + | 0.404755i | ||||
\(226\) | 1.46568 | 1.46568 | ||||||||
\(227\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.03612 | − | 1.79462i | −1.03612 | − | 1.79462i | ||||
\(233\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(240\) | −0.0172284 | − | 0.0191341i | −0.0172284 | − | 0.0191341i | ||||
\(241\) | 0.978148 | + | 1.69420i | 0.978148 | + | 1.69420i | 0.669131 | + | 0.743145i | \(0.266667\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(242\) | −0.187893 | −0.187893 | ||||||||
\(243\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(244\) | −0.672096 | −0.672096 | ||||||||
\(245\) | −0.0348995 | − | 0.0604477i | −0.0348995 | − | 0.0604477i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −1.06739 | + | 1.84877i | −1.06739 | + | 1.84877i | ||||
\(249\) | −0.149516 | + | 0.460163i | −0.149516 | + | 0.460163i | ||||
\(250\) | −0.0521669 | − | 0.0903558i | −0.0521669 | − | 0.0903558i | ||||
\(251\) | −1.87939 | −1.87939 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0.328433 | + | 0.568863i | 0.328433 | + | 0.568863i | ||||
\(255\) | −0.104601 | + | 0.0222337i | −0.104601 | + | 0.0222337i | ||||
\(256\) | 0.512874 | − | 0.888323i | 0.512874 | − | 0.888323i | ||||
\(257\) | −0.438371 | + | 0.759281i | −0.438371 | + | 0.759281i | −0.997564 | − | 0.0697565i | \(-0.977778\pi\) |
0.559193 | + | 0.829038i | \(0.311111\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.75631 | − | 0.781961i | 1.75631 | − | 0.781961i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.719340 | + | 1.24593i | 0.719340 | + | 1.24593i | 0.961262 | + | 0.275637i | \(0.0888889\pi\) |
−0.241922 | + | 0.970296i | \(0.577778\pi\) | |||||||
\(264\) | 0.372515 | − | 1.14648i | 0.372515 | − | 1.14648i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.0761759 | + | 0.131941i | 0.0761759 | + | 0.131941i | ||||
\(269\) | 1.98054 | 1.98054 | 0.990268 | − | 0.139173i | \(-0.0444444\pi\) | ||||
0.990268 | + | 0.139173i | \(0.0444444\pi\) | |||||||
\(270\) | 0.0423070 | − | 0.0307378i | 0.0423070 | − | 0.0307378i | ||||
\(271\) | 1.11839 | 1.11839 | 0.559193 | − | 0.829038i | \(-0.311111\pi\) | ||||
0.559193 | + | 0.829038i | \(0.311111\pi\) | |||||||
\(272\) | 0.282579 | + | 0.489441i | 0.282579 | + | 0.489441i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.556469 | − | 0.963832i | 0.556469 | − | 0.963832i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.60229 | − | 1.16413i | −1.60229 | − | 1.16413i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.374607 | − | 0.648838i | 0.374607 | − | 0.648838i | −0.615661 | − | 0.788011i | \(-0.711111\pi\) |
0.990268 | + | 0.139173i | \(0.0444444\pi\) | |||||||
\(284\) | −0.354899 | + | 0.614704i | −0.354899 | + | 0.614704i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.648433 | + | 0.471114i | 0.648433 | + | 0.471114i | ||||
\(289\) | 1.34730 | 1.34730 | ||||||||
\(290\) | 0.0502685 | + | 0.0870677i | 0.0502685 | + | 0.0870677i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.809017 | − | 1.40126i | 0.809017 | − | 1.40126i | −0.104528 | − | 0.994522i | \(-0.533333\pi\) |
0.913545 | − | 0.406737i | \(-0.133333\pi\) | |||||||
\(294\) | −0.501321 | − | 0.556774i | −0.501321 | − | 0.556774i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.02170 | + | 0.454888i | 1.02170 | + | 0.454888i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0.292104 | + | 0.324414i | 0.292104 | + | 0.324414i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.190983 | − | 0.587785i | 0.190983 | − | 0.587785i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.106938 | 0.106938 | ||||||||
\(306\) | −1.04862 | + | 0.466877i | −1.04862 | + | 0.466877i | ||||
\(307\) | 0.0697990 | 0.0697990 | 0.0348995 | − | 0.999391i | \(-0.488889\pi\) | ||||
0.0348995 | + | 0.999391i | \(0.488889\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.0517854 | − | 0.0896949i | 0.0517854 | − | 0.0896949i | ||||
\(311\) | 0.939693 | − | 1.62760i | 0.939693 | − | 1.62760i | 0.173648 | − | 0.984808i | \(-0.444444\pi\) |
0.766044 | − | 0.642788i | \(-0.222222\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(314\) | −1.44038 | −1.44038 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.07506 | + | 1.86206i | −1.07506 | + | 1.86206i | ||||
\(320\) | −0.0338309 | + | 0.0585968i | −0.0338309 | + | 0.0585968i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −0.293534 | + | 0.326002i | −0.293534 | + | 0.326002i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.661516 | − | 1.14578i | −0.661516 | − | 1.14578i | ||||
\(327\) | −0.139886 | − | 0.155360i | −0.139886 | − | 0.155360i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −0.0180729 | + | 0.0556228i | −0.0180729 | + | 0.0556228i | ||||
\(331\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(332\) | 0.212252 | 0.212252 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.0121205 | − | 0.0209933i | −0.0121205 | − | 0.0209933i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.0348995 | + | 0.0604477i | −0.0348995 | + | 0.0604477i | −0.882948 | − | 0.469472i | \(-0.844444\pi\) |
0.848048 | + | 0.529919i | \(0.177778\pi\) | |||||||
\(338\) | 0.374607 | − | 0.648838i | 0.374607 | − | 0.648838i | ||||
\(339\) | 1.91355 | − | 0.406737i | 1.91355 | − | 0.406737i | ||||
\(340\) | 0.0234558 | + | 0.0406267i | 0.0234558 | + | 0.0406267i | ||||
\(341\) | 2.21500 | 2.21500 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.990268 | + | 1.71519i | −0.990268 | + | 1.71519i | −0.374607 | + | 0.927184i | \(0.622222\pi\) |
−0.615661 | + | 0.788011i | \(0.711111\pi\) | |||||||
\(348\) | −0.564326 | − | 0.626747i | −0.564326 | − | 0.626747i | ||||
\(349\) | −0.438371 | − | 0.759281i | −0.438371 | − | 0.759281i | 0.559193 | − | 0.829038i | \(-0.311111\pi\) |
−0.997564 | + | 0.0697565i | \(0.977778\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.896395 | −0.896395 | ||||||||
\(353\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.0564686 | − | 0.0978064i | 0.0564686 | − | 0.0978064i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.618034 | 0.618034 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(360\) | −0.0608662 | − | 0.0442219i | −0.0608662 | − | 0.0442219i | ||||
\(361\) | 1.00000 | 1.00000 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.245307 | + | 0.0521415i | −0.245307 | + | 0.0521415i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.12278 | − | 0.238654i | 1.12278 | − | 0.238654i | ||||
\(367\) | 0.241922 | + | 0.419021i | 0.241922 | + | 0.419021i | 0.961262 | − | 0.275637i | \(-0.0888889\pi\) |
−0.719340 | + | 0.694658i | \(0.755556\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −0.268480 | + | 0.826298i | −0.268480 | + | 0.826298i | ||||
\(373\) | 0.809017 | − | 1.40126i | 0.809017 | − | 1.40126i | −0.104528 | − | 0.994522i | \(-0.533333\pi\) |
0.913545 | − | 0.406737i | \(-0.133333\pi\) | |||||||
\(374\) | 0.641876 | − | 1.11176i | 0.641876 | − | 1.11176i | ||||
\(375\) | −0.0931817 | − | 0.103489i | −0.0931817 | − | 0.103489i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.586655 | + | 0.651546i | 0.586655 | + | 0.651546i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(384\) | 0.0232488 | − | 0.0715525i | 0.0232488 | − | 0.0715525i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.32303 | 1.32303 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.615661 | + | 1.06636i | 0.615661 | + | 1.06636i | 0.990268 | + | 0.139173i | \(0.0444444\pi\) |
−0.374607 | + | 0.927184i | \(0.622222\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −0.538939 | + | 0.933469i | −0.538939 | + | 0.933469i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −0.747388 | − | 1.29451i | −0.747388 | − | 1.29451i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.0512830 | − | 0.487925i | 0.0512830 | − | 0.487925i | ||||
\(397\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.183542 | + | 0.317904i | −0.183542 | + | 0.317904i | ||||
\(401\) | 0.241922 | − | 0.419021i | 0.241922 | − | 0.419021i | −0.719340 | − | 0.694658i | \(-0.755556\pi\) |
0.961262 | + | 0.275637i | \(0.0888889\pi\) | |||||||
\(402\) | −0.174107 | − | 0.193366i | −0.174107 | − | 0.193366i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −0.271119 | −0.271119 | ||||||||
\(405\) | 0.0467046 | − | 0.0518708i | 0.0467046 | − | 0.0518708i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 1.10501 | + | 1.22723i | 1.10501 | + | 1.22723i | ||||
\(409\) | −0.848048 | + | 1.46886i | −0.848048 | + | 1.46886i | 0.0348995 | + | 0.999391i | \(0.488889\pi\) |
−0.882948 | + | 0.469472i | \(0.844444\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.0337718 | −0.0337718 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.719340 | − | 1.24593i | 0.719340 | − | 1.24593i | −0.241922 | − | 0.970296i | \(-0.577778\pi\) |
0.961262 | − | 0.275637i | \(-0.0888889\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.978148 | + | 1.69420i | 0.978148 | + | 1.69420i | 0.669131 | + | 0.743145i | \(0.266667\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(422\) | 0.362502 | 0.362502 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.762312 | + | 1.32036i | 0.762312 | + | 1.32036i | ||||
\(426\) | 0.374607 | − | 1.15292i | 0.374607 | − | 1.15292i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.76590 | −1.76590 | −0.882948 | − | 0.469472i | \(-0.844444\pi\) | ||||
−0.882948 | + | 0.469472i | \(0.844444\pi\) | |||||||
\(432\) | −0.336989 | − | 0.150037i | −0.336989 | − | 0.150037i | ||||
\(433\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.0897908 | + | 0.0997228i | 0.0897908 | + | 0.0997228i | ||||
\(436\) | −0.0458545 | + | 0.0794223i | −0.0458545 | + | 0.0794223i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.669131 | − | 1.15897i | −0.669131 | − | 1.15897i | −0.978148 | − | 0.207912i | \(-0.933333\pi\) |
0.309017 | − | 0.951057i | \(-0.400000\pi\) | |||||||
\(440\) | 0.0841415 | 0.0841415 | ||||||||
\(441\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.848048 | − | 1.46886i | −0.848048 | − | 1.46886i | −0.882948 | − | 0.469472i | \(-0.844444\pi\) |
0.0348995 | − | 0.999391i | \(-0.488889\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(450\) | −0.603173 | − | 0.438231i | −0.603173 | − | 0.438231i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −0.429093 | − | 0.743212i | −0.429093 | − | 0.743212i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.809017 | + | 1.40126i | 0.809017 | + | 1.40126i | 0.913545 | + | 0.406737i | \(0.133333\pi\) |
−0.104528 | + | 0.994522i | \(0.533333\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.23949 | + | 0.900539i | −1.23949 | + | 0.900539i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(464\) | 0.354591 | − | 0.614169i | 0.354591 | − | 0.614169i | ||||
\(465\) | 0.0427183 | − | 0.131474i | 0.0427183 | − | 0.131474i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.88051 | + | 0.399715i | −1.88051 | + | 0.399715i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −0.749213 | −0.749213 | ||||||||
\(479\) | 0.615661 | + | 1.06636i | 0.615661 | + | 1.06636i | 0.990268 | + | 0.139173i | \(0.0444444\pi\) |
−0.374607 | + | 0.927184i | \(0.622222\pi\) | |||||||
\(480\) | −0.0172878 | + | 0.0532063i | −0.0172878 | + | 0.0532063i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −0.732841 | + | 1.26932i | −0.732841 | + | 1.26932i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.0550075 | + | 0.0952758i | 0.0550075 | + | 0.0952758i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.374607 | − | 0.648838i | 0.374607 | − | 0.648838i | ||||
\(487\) | −1.87939 | −1.87939 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(488\) | −0.825702 | − | 1.43016i | −0.825702 | − | 1.43016i | ||||
\(489\) | −1.18161 | − | 1.31232i | −1.18161 | − | 1.31232i | ||||
\(490\) | 0.0261472 | − | 0.0452882i | 0.0261472 | − | 0.0452882i | ||||
\(491\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.47274 | − | 2.55086i | −1.47274 | − | 2.55086i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.00815972 | + | 0.0776346i | −0.00815972 | + | 0.0776346i | ||||
\(496\) | −0.730581 | −0.730581 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −0.354581 | + | 0.0753684i | −0.354581 | + | 0.0753684i | ||||
\(499\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(500\) | −0.0305448 | + | 0.0529052i | −0.0305448 | + | 0.0529052i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −0.704030 | − | 1.21942i | −0.704030 | − | 1.21942i | ||||
\(503\) | 0.347296 | 0.347296 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.0431382 | 0.0431382 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(508\) | 0.192304 | − | 0.333081i | 0.192304 | − | 0.333081i | ||||
\(509\) | −0.173648 | + | 0.300767i | −0.173648 | + | 0.300767i | −0.939693 | − | 0.342020i | \(-0.888889\pi\) |
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(510\) | −0.0536104 | − | 0.0595404i | −0.0536104 | − | 0.0595404i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0.693269 | 0.693269 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −0.656867 | −0.656867 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(522\) | 1.16529 | + | 0.846634i | 1.16529 | + | 0.846634i | ||||
\(523\) | 1.53209 | 1.53209 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.538939 | + | 0.933469i | −0.538939 | + | 0.933469i | ||||
\(527\) | −1.51718 | + | 2.62783i | −1.51718 | + | 2.62783i | ||||
\(528\) | 0.403536 | − | 0.0857741i | 0.403536 | − | 0.0857741i | ||||
\(529\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −0.187172 | + | 0.324191i | −0.187172 | + | 0.324191i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0.741922 | + | 1.28505i | 0.741922 | + | 1.28505i | ||||
\(539\) | 1.11839 | 1.11839 | ||||||||
\(540\) | −0.0279722 | − | 0.0124540i | −0.0279722 | − | 0.0124540i | ||||
\(541\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(542\) | 0.418955 | + | 0.725651i | 0.418955 | + | 0.725651i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.613990 | − | 1.06346i | 0.613990 | − | 1.06346i | ||||
\(545\) | 0.00729598 | − | 0.0126370i | 0.00729598 | − | 0.0126370i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.39963 | − | 0.623157i | 1.39963 | − | 0.623157i | ||||
\(550\) | 0.833827 | 0.833827 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(558\) | 0.155104 | − | 1.47572i | 0.155104 | − | 1.47572i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.529490 | − | 1.62960i | 0.529490 | − | 1.62960i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | −0.500000 | + | 0.866025i | \(0.666667\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.0682737 | + | 0.118254i | 0.0682737 | + | 0.118254i | ||||
\(566\) | 0.561320 | 0.561320 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.74404 | −1.74404 | ||||||||
\(569\) | −0.990268 | − | 1.71519i | −0.990268 | − | 1.71519i | −0.615661 | − | 0.788011i | \(-0.711111\pi\) |
−0.374607 | − | 0.927184i | \(-0.622222\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.913545 | + | 1.58231i | −0.913545 | + | 1.58231i | −0.104528 | + | 0.994522i | \(0.533333\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.101328 | + | 0.964070i | −0.101328 | + | 0.964070i | ||||
\(577\) | 1.82709 | 1.82709 | 0.913545 | − | 0.406737i | \(-0.133333\pi\) | ||||
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(578\) | 0.504706 | + | 0.874177i | 0.504706 | + | 0.874177i | ||||
\(579\) | 1.72731 | − | 0.367150i | 1.72731 | − | 0.367150i | ||||
\(580\) | 0.0294333 | − | 0.0509799i | 0.0294333 | − | 0.0509799i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.21225 | 1.21225 | ||||||||
\(587\) | 0.882948 | + | 1.52931i | 0.882948 | + | 1.52931i | 0.848048 | + | 0.529919i | \(0.177778\pi\) |
0.0348995 | + | 0.999391i | \(0.488889\pi\) | |||||||
\(588\) | −0.135559 | + | 0.417209i | −0.135559 | + | 0.417209i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.33500 | − | 1.48267i | −1.33500 | − | 1.48267i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(594\) | 0.0875854 | + | 0.833319i | 0.0875854 | + | 0.833319i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.669131 | + | 1.15897i | −0.669131 | + | 1.15897i | 0.309017 | + | 0.951057i | \(0.400000\pi\) |
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(600\) | −0.331460 | + | 1.02013i | −0.331460 | + | 1.02013i | ||||
\(601\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.280969 | − | 0.204136i | −0.280969 | − | 0.204136i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.00875233 | − | 0.0151595i | −0.00875233 | − | 0.0151595i | ||||
\(606\) | 0.452921 | − | 0.0962713i | 0.452921 | − | 0.0962713i | ||||
\(607\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.0400598 | + | 0.0693856i | 0.0400598 | + | 0.0693856i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0.543737 | + | 0.395048i | 0.543737 | + | 0.395048i | ||||
\(613\) | 0.618034 | 0.618034 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(614\) | 0.0261472 | + | 0.0452882i | 0.0261472 | + | 0.0452882i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(620\) | −0.0606428 | −0.0606428 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.40806 | 1.40806 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.492704 | + | 0.853388i | −0.492704 | + | 0.853388i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.421686 | + | 0.730381i | 0.421686 | + | 0.730381i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.0697990 | 0.0697990 | 0.0348995 | − | 0.999391i | \(-0.488889\pi\) | ||||
0.0348995 | + | 0.999391i | \(0.488889\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.473271 | − | 0.100597i | 0.473271 | − | 0.100597i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.0305979 | + | 0.0529971i | −0.0305979 | + | 0.0529971i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.61090 | −1.61090 | ||||||||
\(639\) | 0.169131 | − | 1.60917i | 0.169131 | − | 1.60917i | ||||
\(640\) | 0.00525131 | 0.00525131 | ||||||||
\(641\) | 0.997564 | + | 1.72783i | 0.997564 | + | 1.72783i | 0.559193 | + | 0.829038i | \(0.311111\pi\) |
0.438371 | + | 0.898794i | \(0.355556\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.438371 | + | 0.759281i | −0.438371 | + | 0.759281i | −0.997564 | − | 0.0697565i | \(-0.977778\pi\) |
0.559193 | + | 0.829038i | \(0.311111\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.23132 | −1.23132 | −0.615661 | − | 0.788011i | \(-0.711111\pi\) | ||||
−0.615661 | + | 0.788011i | \(0.711111\pi\) | |||||||
\(648\) | −1.05432 | − | 0.224103i | −1.05432 | − | 0.224103i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.387331 | + | 0.670877i | −0.387331 | + | 0.670877i | ||||
\(653\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(654\) | 0.0484008 | − | 0.148962i | 0.0484008 | − | 0.148962i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(660\) | 0.0334960 | − | 0.00711979i | 0.0334960 | − | 0.00711979i | ||||
\(661\) | −0.559193 | + | 0.968551i | −0.559193 | + | 0.968551i | 0.438371 | + | 0.898794i | \(0.355556\pi\) |
−0.997564 | + | 0.0697565i | \(0.977778\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.260762 | + | 0.451653i | 0.260762 | + | 0.451653i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0.00908081 | − | 0.0157284i | 0.00908081 | − | 0.0157284i | ||||
\(671\) | −0.856733 | + | 1.48391i | −0.856733 | + | 1.48391i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(674\) | −0.0522943 | −0.0522943 | ||||||||
\(675\) | −0.909095 | − | 0.404755i | −0.909095 | − | 0.404755i | ||||
\(676\) | −0.438680 | −0.438680 | ||||||||
\(677\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(678\) | 0.980733 | + | 1.08921i | 0.980733 | + | 1.08921i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −0.0576332 | + | 0.0998236i | −0.0576332 | + | 0.0998236i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.829755 | + | 1.43718i | 0.829755 | + | 1.43718i | ||||
\(683\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.939693 | + | 1.62760i | 0.939693 | + | 1.62760i | 0.766044 | + | 0.642788i | \(0.222222\pi\) |
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.48384 | −1.48384 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0.640359 | − | 1.97082i | 0.640359 | − | 1.97082i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0.328433 | − | 0.568863i | 0.328433 | − | 0.568863i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −0.542071 | − | 0.938894i | −0.542071 | − | 0.938894i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(710\) | 0.0846140 | 0.0846140 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −0.978148 | + | 0.207912i | −0.978148 | + | 0.207912i | ||||
\(718\) | 0.231520 | + | 0.401004i | 0.231520 | + | 0.401004i | ||||
\(719\) | 1.69610 | 1.69610 | 0.848048 | − | 0.529919i | \(-0.177778\pi\) | ||||
0.848048 | + | 0.529919i | \(0.177778\pi\) | |||||||
\(720\) | 0.00269135 | − | 0.0256064i | 0.00269135 | − | 0.0256064i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0.374607 | + | 0.648838i | 0.374607 | + | 0.648838i | ||||
\(723\) | −0.604528 | + | 1.86055i | −0.604528 | + | 1.86055i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.956579 | − | 1.65684i | 0.956579 | − | 1.65684i | ||||
\(726\) | −0.125725 | − | 0.139632i | −0.125725 | − | 0.139632i | ||||
\(727\) | −0.669131 | − | 1.15897i | −0.669131 | − | 1.15897i | −0.978148 | − | 0.207912i | \(-0.933333\pi\) |
0.309017 | − | 0.951057i | \(-0.400000\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −0.449720 | − | 0.499465i | −0.449720 | − | 0.499465i | ||||
\(733\) | −0.990268 | + | 1.71519i | −0.990268 | + | 1.71519i | −0.374607 | + | 0.927184i | \(0.622222\pi\) |
−0.615661 | + | 0.788011i | \(0.711111\pi\) | |||||||
\(734\) | −0.181251 | + | 0.313936i | −0.181251 | + | 0.313936i | ||||
\(735\) | 0.0215691 | − | 0.0663828i | 0.0215691 | − | 0.0663828i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.388411 | 0.388411 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.82709 | 1.82709 | 0.913545 | − | 0.406737i | \(-0.133333\pi\) | ||||
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(744\) | −2.08813 | + | 0.443845i | −2.08813 | + | 0.443845i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1.21225 | 1.21225 | ||||||||
\(747\) | −0.442013 | + | 0.196797i | −0.442013 | + | 0.196797i | ||||
\(748\) | −0.751663 | −0.751663 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0.0322409 | − | 0.0992274i | 0.0322409 | − | 0.0992274i | ||||
\(751\) | 0.104528 | − | 0.181049i | 0.104528 | − | 0.181049i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.25755 | − | 1.39666i | −1.25755 | − | 1.39666i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.749213 | −0.749213 | −0.374607 | − | 0.927184i | \(-0.622222\pi\) | ||||
−0.374607 | + | 0.927184i | \(0.622222\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.104528 | − | 0.181049i | 0.104528 | − | 0.181049i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(762\) | −0.202983 | + | 0.624718i | −0.202983 | + | 0.624718i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.0865149 | − | 0.0628567i | −0.0865149 | − | 0.0628567i | ||||
\(766\) | 0.749213 | 0.749213 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.00333 | − | 0.213265i | 1.00333 | − | 0.213265i | ||||
\(769\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.857583 | + | 0.182285i | −0.857583 | + | 0.182285i | ||||
\(772\) | −0.387331 | − | 0.670877i | −0.387331 | − | 0.670877i | ||||
\(773\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.97089 | −1.97089 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −0.461262 | + | 0.798929i | −0.461262 | + | 0.798929i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.904793 | + | 1.56715i | 0.904793 | + | 1.56715i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.75631 | + | 0.781961i | 1.75631 | + | 0.781961i | ||||
\(784\) | −0.368881 | −0.368881 | ||||||||
\(785\) | −0.0670951 | − | 0.116212i | −0.0670951 | − | 0.116212i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(788\) | −0.437611 | + | 0.757964i | −0.437611 | + | 0.757964i | ||||
\(789\) | −0.444576 | + | 1.36827i | −0.444576 | + | 1.36827i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.10126 | − | 0.490314i | 1.10126 | − | 0.490314i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0.615661 | − | 1.06636i | 0.615661 | − | 1.06636i | −0.374607 | − | 0.927184i | \(-0.622222\pi\) |
0.990268 | − | 0.139173i | \(-0.0444444\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0.797603 | 0.797603 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0.362502 | 0.362502 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −0.0470793 | + | 0.144895i | −0.0470793 | + | 0.144895i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.32524 | + | 1.47183i | 1.32524 | + | 1.47183i | ||||
\(808\) | −0.333083 | − | 0.576916i | −0.333083 | − | 0.576916i | ||||
\(809\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(810\) | 0.0511516 | + | 0.0108726i | 0.0511516 | + | 0.0108726i | ||||
\(811\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.748346 | + | 0.831123i | 0.748346 | + | 0.831123i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.0616289 | − | 0.106744i | 0.0616289 | − | 0.106744i | ||||
\(816\) | −0.174643 | + | 0.537497i | −0.174643 | + | 0.537497i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −1.27074 | −1.27074 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.08862 | − | 0.231393i | 1.08862 | − | 0.231393i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.92252 | 1.92252 | 0.961262 | − | 0.275637i | \(-0.0888889\pi\) | ||||
0.961262 | + | 0.275637i | \(0.0888889\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(830\) | −0.0126511 | − | 0.0219124i | −0.0126511 | − | 0.0219124i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.766044 | + | 1.32683i | −0.766044 | + | 1.32683i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.207022 | − | 1.96969i | −0.207022 | − | 1.96969i | ||||
\(838\) | 1.07788 | 1.07788 | ||||||||
\(839\) | 0.997564 | + | 1.72783i | 0.997564 | + | 1.72783i | 0.559193 | + | 0.829038i | \(0.311111\pi\) |
0.438371 | + | 0.898794i | \(0.355556\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.34805 | + | 2.33489i | −1.34805 | + | 2.33489i | ||||
\(842\) | −0.732841 | + | 1.26932i | −0.732841 | + | 1.26932i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −0.106126 | − | 0.183816i | −0.106126 | − | 0.183816i | ||||
\(845\) | 0.0697990 | 0.0697990 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.732841 | − | 0.155770i | 0.732841 | − | 0.155770i | ||||
\(850\) | −0.571134 | + | 0.989234i | −0.571134 | + | 0.989234i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −0.694288 | + | 0.147575i | −0.694288 | + | 0.147575i | ||||
\(853\) | −0.848048 | − | 1.46886i | −0.848048 | − | 1.46886i | −0.882948 | − | 0.469472i | \(-0.844444\pi\) |
0.0348995 | − | 0.999391i | \(-0.488889\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.997564 | − | 1.72783i | 0.997564 | − | 1.72783i | 0.438371 | − | 0.898794i | \(-0.355556\pi\) |
0.559193 | − | 0.829038i | \(-0.311111\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −0.661516 | − | 1.14578i | −0.661516 | − | 1.14578i | ||||
\(863\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(864\) | 0.0837803 | + | 0.797117i | 0.0837803 | + | 0.797117i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.901517 | + | 1.00124i | 0.901517 | + | 1.00124i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −0.0310677 | + | 0.0956164i | −0.0310677 | + | 0.0956164i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −0.225338 | −0.225338 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.241922 | − | 0.419021i | 0.241922 | − | 0.419021i | −0.719340 | − | 0.694658i | \(-0.755556\pi\) |
0.961262 | + | 0.275637i | \(0.0888889\pi\) | |||||||
\(878\) | 0.501321 | − | 0.868314i | 0.501321 | − | 0.868314i | ||||
\(879\) | 1.58268 | − | 0.336408i | 1.58268 | − | 0.336408i | ||||
\(880\) | 0.0143978 | + | 0.0249377i | 0.0143978 | + | 0.0249377i | ||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | 0.0783141 | − | 0.745109i | 0.0783141 | − | 0.745109i | ||||
\(883\) | −1.23132 | −1.23132 | −0.615661 | − | 0.788011i | \(-0.711111\pi\) | ||||
−0.615661 | + | 0.788011i | \(0.711111\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.635369 | − | 1.10049i | 0.635369 | − | 1.10049i | ||||
\(887\) | −0.913545 | + | 1.58231i | −0.913545 | + | 1.58231i | −0.104528 | + | 0.994522i | \(0.533333\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.345600 | + | 1.06365i | 0.345600 | + | 1.06365i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.80763 | 3.80763 | ||||||||
\(900\) | −0.0456311 | + | 0.434151i | −0.0456311 | + | 0.434151i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.05432 | − | 1.82614i | 1.05432 | − | 1.82614i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.564602 | − | 0.251377i | 0.564602 | − | 0.251377i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.270562 | − | 0.468627i | 0.270562 | − | 0.468627i | ||||
\(914\) | −0.606126 | + | 1.04984i | −0.606126 | + | 1.04984i | ||||
\(915\) | 0.0715557 | + | 0.0794706i | 0.0715557 | + | 0.0794706i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −1.04862 | − | 0.466877i | −1.04862 | − | 0.466877i | ||||
\(919\) | −1.76590 | −1.76590 | −0.882948 | − | 0.469472i | \(-0.844444\pi\) | ||||
−0.882948 | + | 0.469472i | \(0.844444\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.0467046 | + | 0.0518708i | 0.0467046 | + | 0.0518708i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.54092 | −1.54092 | ||||||||
\(929\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(930\) | 0.101308 | − | 0.0215336i | 0.101308 | − | 0.0215336i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.83832 | − | 0.390746i | 1.83832 | − | 0.390746i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.119598 | 0.119598 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.23132 | −1.23132 | −0.615661 | − | 0.788011i | \(-0.711111\pi\) | ||||
−0.615661 | + | 0.788011i | \(0.711111\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(942\) | −0.963802 | − | 1.07041i | −0.963802 | − | 1.07041i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0.219340 | + | 0.379908i | 0.219340 | + | 0.379908i | ||||
\(957\) | −2.10314 | + | 0.447036i | −2.10314 | + | 0.447036i | ||||
\(958\) | −0.461262 | + | 0.798929i | −0.461262 | + | 0.798929i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −0.0661832 | + | 0.0140677i | −0.0661832 | + | 0.0140677i | ||||
\(961\) | −1.46126 | − | 2.53098i | −1.46126 | − | 2.53098i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0.858187 | 0.858187 | ||||||||
\(965\) | 0.0616289 | + | 0.106744i | 0.0616289 | + | 0.106744i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.913545 | + | 1.58231i | −0.913545 | + | 1.58231i | −0.104528 | + | 0.994522i | \(0.533333\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(968\) | −0.135159 | + | 0.234102i | −0.135159 | + | 0.234102i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.69610 | 1.69610 | 0.848048 | − | 0.529919i | \(-0.177778\pi\) | ||||
0.848048 | + | 0.529919i | \(0.177778\pi\) | |||||||
\(972\) | −0.438680 | −0.438680 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −0.704030 | − | 1.21942i | −0.704030 | − | 1.21942i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.282579 | − | 0.489441i | 0.282579 | − | 0.489441i | ||||
\(977\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(978\) | 0.408839 | − | 1.25828i | 0.408839 | − | 1.25828i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −0.0306194 | −0.0306194 | ||||||||
\(981\) | 0.0218524 | − | 0.207912i | 0.0218524 | − | 0.207912i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −0.438371 | − | 0.759281i | −0.438371 | − | 0.759281i | 0.559193 | − | 0.829038i | \(-0.311111\pi\) |
−0.997564 | + | 0.0697565i | \(0.977778\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.0696290 | − | 0.120601i | 0.0696290 | − | 0.120601i | ||||
\(986\) | 1.10340 | − | 1.91114i | 1.10340 | − | 1.91114i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −0.0534289 | + | 0.0237881i | −0.0534289 | + | 0.0237881i | ||||
\(991\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(992\) | 0.793707 | + | 1.37474i | 0.793707 | + | 1.37474i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0.142025 | + | 0.157734i | 0.142025 | + | 0.157734i | ||||
\(997\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(998\) | 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 | 2151.1.f.b.238.8 | ✓ | 24 | |
9.7 | even | 3 | inner | 2151.1.f.b.1672.8 | yes | 24 | |
239.238 | odd | 2 | CM | 2151.1.f.b.238.8 | ✓ | 24 | |
2151.1672 | odd | 6 | inner | 2151.1.f.b.1672.8 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2151.1.f.b.238.8 | ✓ | 24 | 1.1 | even | 1 | trivial | |
2151.1.f.b.238.8 | ✓ | 24 | 239.238 | odd | 2 | CM | |
2151.1.f.b.1672.8 | yes | 24 | 9.7 | even | 3 | inner | |
2151.1.f.b.1672.8 | yes | 24 | 2151.1672 | odd | 6 | inner |