Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1287,1,Mod(142,1287)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1287, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 3, 3]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1287.142");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1287 = 3^{2} \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1287.ba (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: | \(0.642296671259\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{15})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{15}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{15} + \cdots)\) |
Embedding invariants
Embedding label | 571.1 | ||
Root | \(-0.978148 - 0.207912i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1287.571 |
Dual form | 1287.1.ba.d.142.1 |
$q$-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 \(\left(\mathbb{Z}/1287\mathbb{Z}\right)^\times\).
\(n\) | \(496\) | \(937\) | \(1145\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.978148 | − | 1.69420i | −0.978148 | − | 1.69420i | −0.669131 | − | 0.743145i | \(-0.733333\pi\) |
−0.309017 | − | 0.951057i | \(-0.600000\pi\) | |||||||
\(3\) | 0.669131 | − | 0.743145i | 0.669131 | − | 0.743145i | ||||
\(4\) | −1.41355 | + | 2.44833i | −1.41355 | + | 2.44833i | ||||
\(5\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(6\) | −1.91355 | − | 0.406737i | −1.91355 | − | 0.406737i | ||||
\(7\) | −0.809017 | − | 1.40126i | −0.809017 | − | 1.40126i | −0.913545 | − | 0.406737i | \(-0.866667\pi\) |
0.104528 | − | 0.994522i | \(-0.466667\pi\) | |||||||
\(8\) | 3.57433 | 3.57433 | ||||||||
\(9\) | −0.104528 | − | 0.994522i | −0.104528 | − | 0.994522i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(12\) | 0.873619 | + | 2.68872i | 0.873619 | + | 2.68872i | ||||
\(13\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(14\) | −1.58268 | + | 2.74128i | −1.58268 | + | 2.74128i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.08268 | − | 3.60730i | −2.08268 | − | 3.60730i | ||||
\(17\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(18\) | −1.58268 | + | 1.14988i | −1.58268 | + | 1.14988i | ||||
\(19\) | −1.33826 | −1.33826 | −0.669131 | − | 0.743145i | \(-0.733333\pi\) | ||||
−0.669131 | + | 0.743145i | \(0.733333\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.58268 | − | 0.336408i | −1.58268 | − | 0.336408i | ||||
\(22\) | 0.978148 | − | 1.69420i | 0.978148 | − | 1.69420i | ||||
\(23\) | 0.104528 | − | 0.181049i | 0.104528 | − | 0.181049i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(24\) | 2.39169 | − | 2.65624i | 2.39169 | − | 2.65624i | ||||
\(25\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(26\) | −1.95630 | −1.95630 | ||||||||
\(27\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(28\) | 4.57433 | 4.57433 | ||||||||
\(29\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(32\) | −2.28716 | + | 3.96149i | −2.28716 | + | 3.96149i | ||||
\(33\) | 0.978148 | + | 0.207912i | 0.978148 | + | 0.207912i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.58268 | + | 1.14988i | 2.58268 | + | 1.14988i | ||||
\(37\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(38\) | 1.30902 | + | 2.26728i | 1.30902 | + | 2.26728i | ||||
\(39\) | −0.309017 | − | 0.951057i | −0.309017 | − | 0.951057i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.104528 | + | 0.181049i | −0.104528 | + | 0.181049i | −0.913545 | − | 0.406737i | \(-0.866667\pi\) |
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(42\) | 0.978148 | + | 3.01043i | 0.978148 | + | 3.01043i | ||||
\(43\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(44\) | −2.82709 | −2.82709 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.408977 | −0.408977 | ||||||||
\(47\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(48\) | −4.07433 | − | 0.866025i | −4.07433 | − | 0.866025i | ||||
\(49\) | −0.809017 | + | 1.40126i | −0.809017 | + | 1.40126i | ||||
\(50\) | −0.978148 | + | 1.69420i | −0.978148 | + | 1.69420i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.41355 | + | 2.44833i | 1.41355 | + | 2.44833i | ||||
\(53\) | 0.618034 | 0.618034 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(54\) | −0.204489 | + | 1.94558i | −0.204489 | + | 1.94558i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.89169 | − | 5.00856i | −2.89169 | − | 5.00856i | ||||
\(57\) | −0.895472 | + | 0.994522i | −0.895472 | + | 0.994522i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.30902 | + | 0.951057i | −1.30902 | + | 0.951057i | ||||
\(64\) | 4.78339 | 4.78339 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.604528 | − | 1.86055i | −0.604528 | − | 1.86055i | ||||
\(67\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.0646021 | − | 0.198825i | −0.0646021 | − | 0.198825i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | −0.373619 | − | 3.55475i | −0.373619 | − | 3.55475i | ||||
\(73\) | −0.618034 | −0.618034 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.978148 | − | 0.207912i | −0.978148 | − | 0.207912i | ||||
\(76\) | 1.89169 | − | 3.27651i | 1.89169 | − | 3.27651i | ||||
\(77\) | 0.809017 | − | 1.40126i | 0.809017 | − | 1.40126i | ||||
\(78\) | −1.30902 | + | 1.45381i | −1.30902 | + | 1.45381i | ||||
\(79\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.978148 | + | 0.207912i | −0.978148 | + | 0.207912i | ||||
\(82\) | 0.408977 | 0.408977 | ||||||||
\(83\) | 0.913545 | + | 1.58231i | 0.913545 | + | 1.58231i | 0.809017 | + | 0.587785i | \(0.200000\pi\) |
0.104528 | + | 0.994522i | \(0.466667\pi\) | |||||||
\(84\) | 3.06082 | − | 3.39939i | 3.06082 | − | 3.39939i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.78716 | + | 3.09546i | 1.78716 | + | 3.09546i | ||||
\(89\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.61803 | −1.61803 | ||||||||
\(92\) | 0.295511 | + | 0.511841i | 0.295511 | + | 0.511841i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.41355 | + | 4.35045i | 1.41355 | + | 4.35045i | ||||
\(97\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(98\) | 3.16535 | 3.16535 | ||||||||
\(99\) | 0.809017 | − | 0.587785i | 0.809017 | − | 0.587785i | ||||
\(100\) | 2.82709 | 2.82709 | ||||||||
\(101\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.104528 | − | 0.181049i | 0.104528 | − | 0.181049i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(104\) | 1.78716 | − | 3.09546i | 1.78716 | − | 3.09546i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.604528 | − | 1.04707i | −0.604528 | − | 1.04707i | ||||
\(107\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(108\) | 2.58268 | − | 1.14988i | 2.58268 | − | 1.14988i | ||||
\(109\) | 1.95630 | 1.95630 | 0.978148 | − | 0.207912i | \(-0.0666667\pi\) | ||||
0.978148 | + | 0.207912i | \(0.0666667\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.36984 | + | 5.83674i | −3.36984 | + | 5.83674i | ||||
\(113\) | 0.978148 | − | 1.69420i | 0.978148 | − | 1.69420i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
0.669131 | − | 0.743145i | \(-0.266667\pi\) | |||||||
\(114\) | 2.56082 | + | 0.544320i | 2.56082 | + | 0.544320i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.913545 | − | 0.406737i | −0.913545 | − | 0.406737i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.0646021 | + | 0.198825i | 0.0646021 | + | 0.198825i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.89169 | + | 1.28746i | 2.89169 | + | 1.28746i | ||||
\(127\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(128\) | −2.39169 | − | 4.14253i | −2.39169 | − | 4.14253i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(132\) | −1.89169 | + | 2.10094i | −1.89169 | + | 2.10094i | ||||
\(133\) | 1.08268 | + | 1.87525i | 1.08268 | + | 1.87525i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(138\) | −0.273659 | + | 0.303929i | −0.273659 | + | 0.303929i | ||||
\(139\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.00000 | 1.00000 | ||||||||
\(144\) | −3.36984 | + | 2.44833i | −3.36984 | + | 2.44833i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.604528 | + | 1.04707i | 0.604528 | + | 1.04707i | ||||
\(147\) | 0.500000 | + | 1.53884i | 0.500000 | + | 1.53884i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.913545 | − | 1.58231i | 0.913545 | − | 1.58231i | 0.104528 | − | 0.994522i | \(-0.466667\pi\) |
0.809017 | − | 0.587785i | \(-0.200000\pi\) | |||||||
\(150\) | 0.604528 | + | 1.86055i | 0.604528 | + | 1.86055i | ||||
\(151\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(152\) | −4.78339 | −4.78339 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.16535 | −3.16535 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.76531 | + | 0.587785i | 2.76531 | + | 0.587785i | ||||
\(157\) | 0.809017 | − | 1.40126i | 0.809017 | − | 1.40126i | −0.104528 | − | 0.994522i | \(-0.533333\pi\) |
0.913545 | − | 0.406737i | \(-0.133333\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.413545 | − | 0.459289i | 0.413545 | − | 0.459289i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.338261 | −0.338261 | ||||||||
\(162\) | 1.30902 | + | 1.45381i | 1.30902 | + | 1.45381i | ||||
\(163\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(164\) | −0.295511 | − | 0.511841i | −0.295511 | − | 0.511841i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.78716 | − | 3.09546i | 1.78716 | − | 3.09546i | ||||
\(167\) | 0.309017 | − | 0.535233i | 0.309017 | − | 0.535233i | −0.669131 | − | 0.743145i | \(-0.733333\pi\) |
0.978148 | + | 0.207912i | \(0.0666667\pi\) | |||||||
\(168\) | −5.65701 | − | 1.20243i | −5.65701 | − | 1.20243i | ||||
\(169\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.139886 | + | 1.33093i | 0.139886 | + | 1.33093i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.809017 | + | 1.40126i | −0.809017 | + | 1.40126i | ||||
\(176\) | 2.08268 | − | 3.60730i | 2.08268 | − | 3.60730i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.33826 | 1.33826 | 0.669131 | − | 0.743145i | \(-0.266667\pi\) | ||||
0.669131 | + | 0.743145i | \(0.266667\pi\) | |||||||
\(182\) | 1.58268 | + | 2.74128i | 1.58268 | + | 2.74128i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.373619 | − | 0.647127i | 0.373619 | − | 0.647127i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.169131 | + | 1.60917i | −0.169131 | + | 1.60917i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.978148 | + | 1.69420i | 0.978148 | + | 1.69420i | 0.669131 | + | 0.743145i | \(0.266667\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(192\) | 3.20071 | − | 3.55475i | 3.20071 | − | 3.55475i | ||||
\(193\) | 0.913545 | − | 1.58231i | 0.913545 | − | 1.58231i | 0.104528 | − | 0.994522i | \(-0.466667\pi\) |
0.809017 | − | 0.587785i | \(-0.200000\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.28716 | − | 3.96149i | −2.28716 | − | 3.96149i | ||||
\(197\) | −0.618034 | −0.618034 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(198\) | −1.78716 | − | 0.795697i | −1.78716 | − | 0.795697i | ||||
\(199\) | −1.95630 | −1.95630 | −0.978148 | − | 0.207912i | \(-0.933333\pi\) | ||||
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(200\) | −1.78716 | − | 3.09546i | −1.78716 | − | 3.09546i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −0.408977 | −0.408977 | ||||||||
\(207\) | −0.190983 | − | 0.0850311i | −0.190983 | − | 0.0850311i | ||||
\(208\) | −4.16535 | −4.16535 | ||||||||
\(209\) | −0.669131 | − | 1.15897i | −0.669131 | − | 1.15897i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(212\) | −0.873619 | + | 1.51315i | −0.873619 | + | 1.51315i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.89169 | − | 2.10094i | −2.89169 | − | 2.10094i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1.91355 | − | 3.31436i | −1.91355 | − | 3.31436i | ||||
\(219\) | −0.413545 | + | 0.459289i | −0.413545 | + | 0.459289i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(224\) | 7.40142 | 7.40142 | ||||||||
\(225\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(226\) | −3.82709 | −3.82709 | ||||||||
\(227\) | 0.669131 | + | 1.15897i | 0.669131 | + | 1.15897i | 0.978148 | + | 0.207912i | \(0.0666667\pi\) |
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(228\) | −1.16913 | − | 3.59821i | −1.16913 | − | 3.59821i | ||||
\(229\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.500000 | − | 1.53884i | −0.500000 | − | 1.53884i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(234\) | 0.204489 | + | 1.94558i | 0.204489 | + | 1.94558i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.669131 | − | 1.15897i | 0.669131 | − | 1.15897i | −0.309017 | − | 0.951057i | \(-0.600000\pi\) |
0.978148 | − | 0.207912i | \(-0.0666667\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.104528 | − | 0.181049i | −0.104528 | − | 0.181049i | 0.809017 | − | 0.587785i | \(-0.200000\pi\) |
−0.913545 | + | 0.406737i | \(0.866667\pi\) | |||||||
\(242\) | 1.95630 | 1.95630 | ||||||||
\(243\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.273659 | − | 0.303929i | 0.273659 | − | 0.303929i | ||||
\(247\) | −0.669131 | + | 1.15897i | −0.669131 | + | 1.15897i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.78716 | + | 0.379874i | 1.78716 | + | 0.379874i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.61803 | −1.61803 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(252\) | −0.478148 | − | 4.54927i | −0.478148 | − | 4.54927i | ||||
\(253\) | 0.209057 | 0.209057 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.28716 | + | 3.96149i | −2.28716 | + | 3.96149i | ||||
\(257\) | −0.913545 | + | 1.58231i | −0.913545 | + | 1.58231i | −0.104528 | + | 0.994522i | \(0.533333\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(264\) | 3.49622 | + | 0.743145i | 3.49622 | + | 0.743145i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.11803 | − | 3.66854i | 2.11803 | − | 3.66854i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.82709 | 1.82709 | 0.913545 | − | 0.406737i | \(-0.133333\pi\) | ||||
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.95630 | 1.95630 | 0.978148 | − | 0.207912i | \(-0.0666667\pi\) | ||||
0.978148 | + | 0.207912i | \(0.0666667\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.08268 | + | 1.20243i | −1.08268 | + | 1.20243i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(276\) | 0.578108 | + | 0.122881i | 0.578108 | + | 0.122881i | ||||
\(277\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.309017 | + | 0.535233i | 0.309017 | + | 0.535233i | 0.978148 | − | 0.207912i | \(-0.0666667\pi\) |
−0.669131 | + | 0.743145i | \(0.733333\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.978148 | − | 1.69420i | −0.978148 | − | 1.69420i | ||||
\(287\) | 0.338261 | 0.338261 | ||||||||
\(288\) | 4.17886 | + | 1.86055i | 4.17886 | + | 1.86055i | ||||
\(289\) | 1.00000 | 1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.873619 | − | 1.51315i | 0.873619 | − | 1.51315i | ||||
\(293\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(294\) | 2.11803 | − | 2.35232i | 2.11803 | − | 2.35232i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.104528 | − | 0.994522i | 0.104528 | − | 0.994522i | ||||
\(298\) | −3.57433 | −3.57433 | ||||||||
\(299\) | −0.104528 | − | 0.181049i | −0.104528 | − | 0.181049i | ||||
\(300\) | 1.89169 | − | 2.10094i | 1.89169 | − | 2.10094i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −0.978148 | + | 1.69420i | −0.978148 | + | 1.69420i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.78716 | + | 4.82751i | 2.78716 | + | 4.82751i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.00000 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(308\) | 2.28716 | + | 3.96149i | 2.28716 | + | 3.96149i | ||||
\(309\) | −0.0646021 | − | 0.198825i | −0.0646021 | − | 0.198825i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.309017 | + | 0.535233i | −0.309017 | + | 0.535233i | −0.978148 | − | 0.207912i | \(-0.933333\pi\) |
0.669131 | + | 0.743145i | \(0.266667\pi\) | |||||||
\(312\) | −1.10453 | − | 3.39939i | −1.10453 | − | 3.39939i | ||||
\(313\) | 0.809017 | + | 1.40126i | 0.809017 | + | 1.40126i | 0.913545 | + | 0.406737i | \(0.133333\pi\) |
−0.104528 | + | 0.994522i | \(0.533333\pi\) | |||||||
\(314\) | −3.16535 | −3.16535 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(318\) | −1.18264 | − | 0.251377i | −1.18264 | − | 0.251377i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.330869 | + | 0.573083i | 0.330869 | + | 0.573083i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0.873619 | − | 2.68872i | 0.873619 | − | 2.68872i | ||||
\(325\) | −1.00000 | −1.00000 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.30902 | − | 1.45381i | 1.30902 | − | 1.45381i | ||||
\(328\) | −0.373619 | + | 0.647127i | −0.373619 | + | 0.647127i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(332\) | −5.16535 | −5.16535 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.20906 | −1.20906 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.08268 | + | 6.40982i | 2.08268 | + | 6.40982i | ||||
\(337\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(338\) | −0.978148 | + | 1.69420i | −0.978148 | + | 1.69420i | ||||
\(339\) | −0.604528 | − | 1.86055i | −0.604528 | − | 1.86055i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 2.11803 | − | 1.53884i | 2.11803 | − | 1.53884i | ||||
\(343\) | 1.00000 | 1.00000 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.913545 | + | 1.58231i | 0.913545 | + | 1.58231i | 0.809017 | + | 0.587785i | \(0.200000\pi\) |
0.104528 | + | 0.994522i | \(0.466667\pi\) | |||||||
\(350\) | 3.16535 | 3.16535 | ||||||||
\(351\) | −0.913545 | + | 0.406737i | −0.913545 | + | 0.406737i | ||||
\(352\) | −4.57433 | −4.57433 | ||||||||
\(353\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.978148 | + | 1.69420i | 0.978148 | + | 1.69420i | ||||
\(359\) | 0.209057 | 0.209057 | 0.104528 | − | 0.994522i | \(-0.466667\pi\) | ||||
0.104528 | + | 0.994522i | \(0.466667\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.790943 | 0.790943 | ||||||||
\(362\) | −1.30902 | − | 2.26728i | −1.30902 | − | 2.26728i | ||||
\(363\) | 0.309017 | + | 0.951057i | 0.309017 | + | 0.951057i | ||||
\(364\) | 2.28716 | − | 3.96149i | 2.28716 | − | 3.96149i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.309017 | − | 0.535233i | −0.309017 | − | 0.535233i | 0.669131 | − | 0.743145i | \(-0.266667\pi\) |
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(368\) | −0.870796 | −0.870796 | ||||||||
\(369\) | 0.190983 | + | 0.0850311i | 0.190983 | + | 0.0850311i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 2.89169 | − | 1.28746i | 2.89169 | − | 1.28746i | ||||
\(379\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.91355 | − | 3.31436i | 1.91355 | − | 3.31436i | ||||
\(383\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(384\) | −4.67886 | − | 0.994522i | −4.67886 | − | 0.994522i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3.57433 | −3.57433 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.669131 | − | 1.15897i | −0.669131 | − | 1.15897i | −0.978148 | − | 0.207912i | \(-0.933333\pi\) |
0.309017 | − | 0.951057i | \(-0.400000\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −2.89169 | + | 5.00856i | −2.89169 | + | 5.00856i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.604528 | + | 1.04707i | 0.604528 | + | 1.04707i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.295511 | + | 2.81160i | 0.295511 | + | 2.81160i | ||||
\(397\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(398\) | 1.91355 | + | 3.31436i | 1.91355 | + | 3.31436i | ||||
\(399\) | 2.11803 | + | 0.450202i | 2.11803 | + | 0.450202i | ||||
\(400\) | −2.08268 | + | 3.60730i | −2.08268 | + | 3.60730i | ||||
\(401\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.295511 | + | 0.511841i | 0.295511 | + | 0.511841i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0.0427497 | + | 0.406737i | 0.0427497 | + | 0.406737i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.28716 | + | 3.96149i | 2.28716 | + | 3.96149i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.30902 | + | 2.26728i | −1.30902 | + | 2.26728i | ||||
\(419\) | −0.913545 | + | 1.58231i | −0.913545 | + | 1.58231i | −0.104528 | + | 0.994522i | \(0.533333\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.20906 | 2.20906 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.669131 | − | 0.743145i | 0.669131 | − | 0.743145i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.61803 | 1.61803 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(432\) | −0.435398 | + | 4.14253i | −0.435398 | + | 4.14253i | ||||
\(433\) | 1.33826 | 1.33826 | 0.669131 | − | 0.743145i | \(-0.266667\pi\) | ||||
0.669131 | + | 0.743145i | \(0.266667\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.76531 | + | 4.78966i | −2.76531 | + | 4.78966i | ||||
\(437\) | −0.139886 | + | 0.242290i | −0.139886 | + | 0.242290i | ||||
\(438\) | 1.18264 | + | 0.251377i | 1.18264 | + | 0.251377i | ||||
\(439\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.47815 | + | 0.658114i | 1.47815 | + | 0.658114i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.913545 | − | 1.58231i | −0.913545 | − | 1.58231i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
−0.104528 | − | 0.994522i | \(-0.533333\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.564602 | − | 1.73767i | −0.564602 | − | 1.73767i | ||||
\(448\) | −3.86984 | − | 6.70276i | −3.86984 | − | 6.70276i | ||||
\(449\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(450\) | 1.78716 | + | 0.795697i | 1.78716 | + | 0.795697i | ||||
\(451\) | −0.209057 | −0.209057 | ||||||||
\(452\) | 2.76531 | + | 4.78966i | 2.76531 | + | 4.78966i | ||||
\(453\) | −0.978148 | − | 0.207912i | −0.978148 | − | 0.207912i | ||||
\(454\) | 1.30902 | − | 2.26728i | 1.30902 | − | 2.26728i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.20071 | + | 3.55475i | −3.20071 | + | 3.55475i | ||||
\(457\) | −0.978148 | − | 1.69420i | −0.978148 | − | 1.69420i | −0.669131 | − | 0.743145i | \(-0.733333\pi\) |
−0.309017 | − | 0.951057i | \(-0.600000\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.669131 | + | 1.15897i | 0.669131 | + | 1.15897i | 0.978148 | + | 0.207912i | \(0.0666667\pi\) |
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(462\) | −2.11803 | + | 2.35232i | −2.11803 | + | 2.35232i | ||||
\(463\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.00000 | 2.00000 | 1.00000 | \(0\) | ||||||
1.00000 | \(0\) | |||||||||
\(468\) | 2.28716 | − | 1.66172i | 2.28716 | − | 1.66172i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.500000 | − | 1.53884i | −0.500000 | − | 1.53884i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.669131 | + | 1.15897i | 0.669131 | + | 1.15897i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.0646021 | − | 0.614648i | −0.0646021 | − | 0.614648i | ||||
\(478\) | −2.61803 | −2.61803 | ||||||||
\(479\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −0.204489 | + | 0.354185i | −0.204489 | + | 0.354185i | ||||
\(483\) | −0.226341 | + | 0.251377i | −0.226341 | + | 0.251377i | ||||
\(484\) | −1.41355 | − | 2.44833i | −1.41355 | − | 2.44833i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.95630 | 1.95630 | ||||||||
\(487\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(492\) | −0.578108 | − | 0.122881i | −0.578108 | − | 0.122881i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 2.61803 | 2.61803 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −1.10453 | − | 3.39939i | −1.10453 | − | 3.39939i | ||||
\(499\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.190983 | − | 0.587785i | −0.190983 | − | 0.587785i | ||||
\(502\) | 1.58268 | + | 2.74128i | 1.58268 | + | 2.74128i | ||||
\(503\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(504\) | −4.67886 | + | 3.39939i | −4.67886 | + | 3.39939i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −0.204489 | − | 0.354185i | −0.204489 | − | 0.354185i | ||||
\(507\) | −0.978148 | − | 0.207912i | −0.978148 | − | 0.207912i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(512\) | 4.16535 | 4.16535 | ||||||||
\(513\) | 1.08268 | + | 0.786610i | 1.08268 | + | 0.786610i | ||||
\(514\) | 3.57433 | 3.57433 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.209057 | −0.209057 | −0.104528 | − | 0.994522i | \(-0.533333\pi\) | ||||
−0.104528 | + | 0.994522i | \(0.533333\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.500000 | + | 1.53884i | 0.500000 | + | 1.53884i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −1.28716 | − | 3.96149i | −1.28716 | − | 3.96149i | ||||
\(529\) | 0.478148 | + | 0.828176i | 0.478148 | + | 0.828176i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −6.12165 | −6.12165 | ||||||||
\(533\) | 0.104528 | + | 0.181049i | 0.104528 | + | 0.181049i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.669131 | + | 0.743145i | −0.669131 | + | 0.743145i | ||||
\(538\) | −1.78716 | − | 3.09546i | −1.78716 | − | 3.09546i | ||||
\(539\) | −1.61803 | −1.61803 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.82709 | −1.82709 | −0.913545 | − | 0.406737i | \(-0.866667\pi\) | ||||
−0.913545 | + | 0.406737i | \(0.866667\pi\) | |||||||
\(542\) | −1.91355 | − | 3.31436i | −1.91355 | − | 3.31436i | ||||
\(543\) | 0.895472 | − | 0.994522i | 0.895472 | − | 0.994522i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 3.09618 | + | 0.658114i | 3.09618 | + | 0.658114i | ||||
\(547\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.95630 | −1.95630 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −0.230909 | − | 0.710666i | −0.230909 | − | 0.710666i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.61803 | 1.61803 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.604528 | − | 1.04707i | 0.604528 | − | 1.04707i | ||||
\(563\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.08268 | + | 1.20243i | 1.08268 | + | 1.20243i | ||||
\(568\) | 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 | \(0.666667\pi\) | |||||||
\(572\) | −1.41355 | + | 2.44833i | −1.41355 | + | 2.44833i | ||||
\(573\) | 1.91355 | + | 0.406737i | 1.91355 | + | 0.406737i | ||||
\(574\) | −0.330869 | − | 0.573083i | −0.330869 | − | 0.573083i | ||||
\(575\) | −0.209057 | −0.209057 | ||||||||
\(576\) | −0.500000 | − | 4.75718i | −0.500000 | − | 4.75718i | ||||
\(577\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(578\) | −0.978148 | − | 1.69420i | −0.978148 | − | 1.69420i | ||||
\(579\) | −0.564602 | − | 1.73767i | −0.564602 | − | 1.73767i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.47815 | − | 2.56023i | 1.47815 | − | 2.56023i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.309017 | + | 0.535233i | 0.309017 | + | 0.535233i | ||||
\(584\) | −2.20906 | −2.20906 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.95630 | 1.95630 | ||||||||
\(587\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(588\) | −4.47437 | − | 0.951057i | −4.47437 | − | 0.951057i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.413545 | + | 0.459289i | −0.413545 | + | 0.459289i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.82709 | −1.82709 | −0.913545 | − | 0.406737i | \(-0.866667\pi\) | ||||
−0.913545 | + | 0.406737i | \(0.866667\pi\) | |||||||
\(594\) | −1.78716 | + | 0.795697i | −1.78716 | + | 0.795697i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.58268 | + | 4.47333i | 2.58268 | + | 4.47333i | ||||
\(597\) | −1.30902 | + | 1.45381i | −1.30902 | + | 1.45381i | ||||
\(598\) | −0.204489 | + | 0.354185i | −0.204489 | + | 0.354185i | ||||
\(599\) | −0.309017 | + | 0.535233i | −0.309017 | + | 0.535233i | −0.978148 | − | 0.207912i | \(-0.933333\pi\) |
0.669131 | + | 0.743145i | \(0.266667\pi\) | |||||||
\(600\) | −3.49622 | − | 0.743145i | −3.49622 | − | 0.743145i | ||||
\(601\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.82709 | 2.82709 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(608\) | 3.06082 | − | 5.30150i | 3.06082 | − | 5.30150i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.33826 | −1.33826 | −0.669131 | − | 0.743145i | \(-0.733333\pi\) | ||||
−0.669131 | + | 0.743145i | \(0.733333\pi\) | |||||||
\(614\) | −0.978148 | − | 1.69420i | −0.978148 | − | 1.69420i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.89169 | − | 5.00856i | 2.89169 | − | 5.00856i | ||||
\(617\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(618\) | −0.273659 | + | 0.303929i | −0.273659 | + | 0.303929i | ||||
\(619\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.190983 | + | 0.0850311i | −0.190983 | + | 0.0850311i | ||||
\(622\) | 1.20906 | 1.20906 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −2.78716 | + | 3.09546i | −2.78716 | + | 3.09546i | ||||
\(625\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(626\) | 1.58268 | − | 2.74128i | 1.58268 | − | 2.74128i | ||||
\(627\) | −1.30902 | − | 0.278240i | −1.30902 | − | 0.278240i | ||||
\(628\) | 2.28716 | + | 3.96149i | 2.28716 | + | 3.96149i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.539926 | + | 1.66172i | 0.539926 | + | 1.66172i | ||||
\(637\) | 0.809017 | + | 1.40126i | 0.809017 | + | 1.40126i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.809017 | + | 1.40126i | 0.809017 | + | 1.40126i | 0.913545 | + | 0.406737i | \(0.133333\pi\) |
−0.104528 | + | 0.994522i | \(0.533333\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(644\) | 0.478148 | − | 0.828176i | 0.478148 | − | 0.828176i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.33826 | 1.33826 | 0.669131 | − | 0.743145i | \(-0.266667\pi\) | ||||
0.669131 | + | 0.743145i | \(0.266667\pi\) | |||||||
\(648\) | −3.49622 | + | 0.743145i | −3.49622 | + | 0.743145i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0.978148 | + | 1.69420i | 0.978148 | + | 1.69420i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | −0.500000 | + | 0.866025i | \(0.666667\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(654\) | −3.74346 | − | 0.795697i | −3.74346 | − | 0.795697i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0.870796 | 0.870796 | ||||||||
\(657\) | 0.0646021 | + | 0.614648i | 0.0646021 | + | 0.614648i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 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 | ||||||||
\(664\) | 3.26531 | + | 5.65569i | 3.26531 | + | 5.65569i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0.873619 | + | 1.51315i | 0.873619 | + | 1.51315i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 4.95252 | − | 5.50033i | 4.95252 | − | 5.50033i | ||||
\(673\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.104528 | + | 0.994522i | −0.104528 | + | 0.994522i | ||||
\(676\) | 2.82709 | 2.82709 | ||||||||
\(677\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(678\) | −2.56082 | + | 2.84408i | −2.56082 | + | 2.84408i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.30902 | + | 0.278240i | 1.30902 | + | 0.278240i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(684\) | −3.45630 | − | 1.53884i | −3.45630 | − | 1.53884i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −0.978148 | − | 1.69420i | −0.978148 | − | 1.69420i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.309017 | − | 0.535233i | 0.309017 | − | 0.535233i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.47815 | − | 0.658114i | −1.47815 | − | 0.658114i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 1.78716 | − | 3.09546i | 1.78716 | − | 3.09546i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.28716 | − | 3.96149i | −2.28716 | − | 3.96149i | ||||
\(701\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(702\) | 1.58268 | + | 1.14988i | 1.58268 | + | 1.14988i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 2.39169 | + | 4.14253i | 2.39169 | + | 4.14253i | ||||
\(705\) | 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 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.41355 | − | 2.44833i | 1.41355 | − | 2.44833i | ||||
\(717\) | −0.413545 | − | 1.27276i | −0.413545 | − | 1.27276i | ||||
\(718\) | −0.204489 | − | 0.354185i | −0.204489 | − | 0.354185i | ||||
\(719\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.338261 | −0.338261 | ||||||||
\(722\) | −0.773659 | − | 1.34002i | −0.773659 | − | 1.34002i | ||||
\(723\) | −0.204489 | − | 0.0434654i | −0.204489 | − | 0.0434654i | ||||
\(724\) | −1.89169 | + | 3.27651i | −1.89169 | + | 3.27651i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.30902 | − | 1.45381i | 1.30902 | − | 1.45381i | ||||
\(727\) | −0.913545 | − | 1.58231i | −0.913545 | − | 1.58231i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
−0.104528 | − | 0.994522i | \(-0.533333\pi\) | |||||||
\(728\) | −5.78339 | −5.78339 | ||||||||
\(729\) | 0.309017 | + | 0.951057i | 0.309017 | + | 0.951057i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.104528 | + | 0.181049i | −0.104528 | + | 0.181049i | −0.913545 | − | 0.406737i | \(-0.866667\pi\) |
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(734\) | −0.604528 | + | 1.04707i | −0.604528 | + | 1.04707i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.478148 | + | 0.828176i | 0.478148 | + | 0.828176i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −0.0427497 | − | 0.406737i | −0.0427497 | − | 0.406737i | ||||
\(739\) | −1.82709 | −1.82709 | −0.913545 | − | 0.406737i | \(-0.866667\pi\) | ||||
−0.913545 | + | 0.406737i | \(0.866667\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.413545 | + | 1.27276i | 0.413545 | + | 1.27276i | ||||
\(742\) | −0.978148 | + | 1.69420i | −0.978148 | + | 1.69420i | ||||
\(743\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.47815 | − | 1.07394i | 1.47815 | − | 1.07394i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.669131 | + | 1.15897i | −0.669131 | + | 1.15897i | 0.309017 | + | 0.951057i | \(0.400000\pi\) |
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.08268 | + | 1.20243i | −1.08268 | + | 1.20243i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −3.70071 | − | 2.68872i | −3.70071 | − | 2.68872i | ||||
\(757\) | 1.82709 | 1.82709 | 0.913545 | − | 0.406737i | \(-0.133333\pi\) | ||||
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.139886 | − | 0.155360i | 0.139886 | − | 0.155360i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −0.809017 | + | 1.40126i | −0.809017 | + | 1.40126i | 0.104528 | + | 0.994522i | \(0.466667\pi\) |
−0.913545 | + | 0.406737i | \(0.866667\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.58268 | − | 2.74128i | −1.58268 | − | 2.74128i | ||||
\(764\) | −5.53062 | −5.53062 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.41355 | + | 4.35045i | 1.41355 | + | 4.35045i | ||||
\(769\) | −0.104528 | + | 0.181049i | −0.104528 | + | 0.181049i | −0.913545 | − | 0.406737i | \(-0.866667\pi\) |
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.564602 | + | 1.73767i | 0.564602 | + | 1.73767i | ||||
\(772\) | 2.58268 | + | 4.47333i | 2.58268 | + | 4.47333i | ||||
\(773\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.30902 | + | 2.26728i | −1.30902 | + | 2.26728i | ||||
\(779\) | 0.139886 | − | 0.242290i | 0.139886 | − | 0.242290i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 6.73968 | 6.73968 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.104528 | + | 0.181049i | −0.104528 | + | 0.181049i | −0.913545 | − | 0.406737i | \(-0.866667\pi\) |
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(788\) | 0.873619 | − | 1.51315i | 0.873619 | − | 1.51315i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.16535 | −3.16535 | ||||||||
\(792\) | 2.89169 | − | 2.10094i | 2.89169 | − | 2.10094i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.76531 | − | 4.78966i | 2.76531 | − | 4.78966i | ||||
\(797\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(798\) | −1.30902 | − | 4.02874i | −1.30902 | − | 4.02874i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 4.57433 | 4.57433 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.309017 | − | 0.535233i | −0.309017 | − | 0.535233i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.22256 | − | 1.35779i | 1.22256 | − | 1.35779i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.209057 | 0.209057 | 0.104528 | − | 0.994522i | \(-0.466667\pi\) | ||||
0.104528 | + | 0.994522i | \(0.466667\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.30902 | − | 1.45381i | 1.30902 | − | 1.45381i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 1.95630 | 1.95630 | ||||||||
\(819\) | 0.169131 | + | 1.60917i | 0.169131 | + | 1.60917i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.809017 | − | 1.40126i | 0.809017 | − | 1.40126i | −0.104528 | − | 0.994522i | \(-0.533333\pi\) |
0.913545 | − | 0.406737i | \(-0.133333\pi\) | |||||||
\(824\) | 0.373619 | − | 0.647127i | 0.373619 | − | 0.647127i | ||||
\(825\) | −0.309017 | − | 0.951057i | −0.309017 | − | 0.951057i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.33826 | −1.33826 | −0.669131 | − | 0.743145i | \(-0.733333\pi\) | ||||
−0.669131 | + | 0.743145i | \(0.733333\pi\) | |||||||
\(828\) | 0.478148 | − | 0.347395i | 0.478148 | − | 0.347395i | ||||
\(829\) | 1.82709 | 1.82709 | 0.913545 | − | 0.406737i | \(-0.133333\pi\) | ||||
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.39169 | − | 4.14253i | 2.39169 | − | 4.14253i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 3.78339 | 3.78339 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.57433 | 3.57433 | ||||||||
\(839\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.604528 | + | 0.128496i | 0.604528 | + | 0.128496i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.61803 | 1.61803 | ||||||||
\(848\) | −1.28716 | − | 2.22943i | −1.28716 | − | 2.22943i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.669131 | + | 1.15897i | 0.669131 | + | 1.15897i | 0.978148 | + | 0.207912i | \(0.0666667\pi\) |
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(858\) | −1.91355 | − | 0.406737i | −1.91355 | − | 0.406737i | ||||
\(859\) | 0.978148 | − | 1.69420i | 0.978148 | − | 1.69420i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
0.669131 | − | 0.743145i | \(-0.266667\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.226341 | − | 0.251377i | 0.226341 | − | 0.251377i | ||||
\(862\) | −1.58268 | − | 2.74128i | −1.58268 | − | 2.74128i | ||||
\(863\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(864\) | 4.17886 | − | 1.86055i | 4.17886 | − | 1.86055i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.30902 | − | 2.26728i | −1.30902 | − | 2.26728i | ||||
\(867\) | 0.669131 | − | 0.743145i | 0.669131 | − | 0.743145i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 6.99244 | 6.99244 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.547318 | 0.547318 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −0.539926 | − | 1.66172i | −0.539926 | − | 1.66172i | ||||
\(877\) | 0.309017 | − | 0.535233i | 0.309017 | − | 0.535233i | −0.669131 | − | 0.743145i | \(-0.733333\pi\) |
0.978148 | + | 0.207912i | \(0.0666667\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.309017 | + | 0.951057i | 0.309017 | + | 0.951057i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.618034 | 0.618034 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(882\) | −0.330869 | − | 3.14801i | −0.330869 | − | 3.14801i | ||||
\(883\) | 0.618034 | 0.618034 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.78716 | + | 3.09546i | −1.78716 | + | 3.09546i | ||||
\(887\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.669131 | − | 0.743145i | −0.669131 | − | 0.743145i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −2.39169 | + | 2.65624i | −2.39169 | + | 2.65624i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3.86984 | + | 6.70276i | −3.86984 | + | 6.70276i | ||||
\(897\) | −0.204489 | − | 0.0434654i | −0.204489 | − | 0.0434654i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −0.295511 | − | 2.81160i | −0.295511 | − | 2.81160i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0.204489 | + | 0.354185i | 0.204489 | + | 0.354185i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.49622 | − | 6.05563i | 3.49622 | − | 6.05563i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0.604528 | + | 1.86055i | 0.604528 | + | 1.86055i | ||||
\(907\) | 0.104528 | + | 0.181049i | 0.104528 | + | 0.181049i | 0.913545 | − | 0.406737i | \(-0.133333\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(908\) | −3.78339 | −3.78339 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.809017 | + | 1.40126i | 0.809017 | + | 1.40126i | 0.913545 | + | 0.406737i | \(0.133333\pi\) |
−0.104528 | + | 0.994522i | \(0.533333\pi\) | |||||||
\(912\) | 5.45252 | + | 1.15897i | 5.45252 | + | 1.15897i | ||||
\(913\) | −0.913545 | + | 1.58231i | −0.913545 | + | 1.58231i | ||||
\(914\) | −1.91355 | + | 3.31436i | −1.91355 | + | 3.31436i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.669131 | − | 0.743145i | 0.669131 | − | 0.743145i | ||||
\(922\) | 1.30902 | − | 2.26728i | 1.30902 | − | 2.26728i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 4.47437 | + | 0.951057i | 4.47437 | + | 0.951057i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.190983 | − | 0.0850311i | −0.190983 | − | 0.0850311i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.08268 | − | 1.87525i | 1.08268 | − | 1.87525i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.190983 | + | 0.587785i | 0.190983 | + | 0.587785i | ||||
\(934\) | −1.95630 | − | 3.38840i | −1.95630 | − | 3.38840i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3.26531 | − | 1.45381i | −3.26531 | − | 1.45381i | ||||
\(937\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.58268 | + | 0.336408i | 1.58268 | + | 0.336408i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.309017 | − | 0.535233i | 0.309017 | − | 0.535233i | −0.669131 | − | 0.743145i | \(-0.733333\pi\) |
0.978148 | + | 0.207912i | \(0.0666667\pi\) | |||||||
\(942\) | −2.11803 | + | 2.35232i | −2.11803 | + | 2.35232i | ||||
\(943\) | 0.0218524 | + | 0.0378495i | 0.0218524 | + | 0.0378495i | ||||
\(944\) | 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 | ||||||||
\(949\) | −0.309017 | + | 0.535233i | −0.309017 | + | 0.535233i | ||||
\(950\) | 1.30902 | − | 2.26728i | 1.30902 | − | 2.26728i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(954\) | −0.978148 | + | 0.710666i | −0.978148 | + | 0.710666i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.89169 | + | 3.27651i | 1.89169 | + | 3.27651i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −0.978148 | + | 1.69420i | −0.978148 | + | 1.69420i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0.591023 | 0.591023 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.647278 | + | 0.137583i | 0.647278 | + | 0.137583i | ||||
\(967\) | −0.978148 | + | 1.69420i | −0.978148 | + | 1.69420i | −0.309017 | + | 0.951057i | \(0.600000\pi\) |
−0.669131 | + | 0.743145i | \(0.733333\pi\) | |||||||
\(968\) | −1.78716 | + | 3.09546i | −1.78716 | + | 3.09546i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.95630 | −1.95630 | −0.978148 | − | 0.207912i | \(-0.933333\pi\) | ||||
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(972\) | −1.41355 | − | 2.44833i | −1.41355 | − | 2.44833i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.669131 | + | 0.743145i | −0.669131 | + | 0.743145i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.204489 | − | 1.94558i | −0.204489 | − | 1.94558i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(984\) | 0.230909 | + | 0.710666i | 0.230909 | + | 0.710666i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.89169 | − | 3.27651i | −1.89169 | − | 3.27651i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.95630 | −1.95630 | −0.978148 | − | 0.207912i | \(-0.933333\pi\) | ||||
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −3.45630 | + | 3.83860i | −3.45630 | + | 3.83860i | ||||
\(997\) | 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 | 1287.1.ba.d.571.1 | yes | 8 | |
3.2 | odd | 2 | 3861.1.ba.c.3574.4 | 8 | |||
9.2 | odd | 6 | 3861.1.ba.c.2287.4 | 8 | |||
9.7 | even | 3 | inner | 1287.1.ba.d.142.1 | yes | 8 | |
11.10 | odd | 2 | 1287.1.ba.c.571.4 | yes | 8 | ||
13.12 | even | 2 | 1287.1.ba.c.571.4 | yes | 8 | ||
33.32 | even | 2 | 3861.1.ba.d.3574.1 | 8 | |||
39.38 | odd | 2 | 3861.1.ba.d.3574.1 | 8 | |||
99.43 | odd | 6 | 1287.1.ba.c.142.4 | ✓ | 8 | ||
99.65 | even | 6 | 3861.1.ba.d.2287.1 | 8 | |||
117.25 | even | 6 | 1287.1.ba.c.142.4 | ✓ | 8 | ||
117.38 | odd | 6 | 3861.1.ba.d.2287.1 | 8 | |||
143.142 | odd | 2 | CM | 1287.1.ba.d.571.1 | yes | 8 | |
429.428 | even | 2 | 3861.1.ba.c.3574.4 | 8 | |||
1287.142 | odd | 6 | inner | 1287.1.ba.d.142.1 | yes | 8 | |
1287.857 | even | 6 | 3861.1.ba.c.2287.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1287.1.ba.c.142.4 | ✓ | 8 | 99.43 | odd | 6 | ||
1287.1.ba.c.142.4 | ✓ | 8 | 117.25 | even | 6 | ||
1287.1.ba.c.571.4 | yes | 8 | 11.10 | odd | 2 | ||
1287.1.ba.c.571.4 | yes | 8 | 13.12 | even | 2 | ||
1287.1.ba.d.142.1 | yes | 8 | 9.7 | even | 3 | inner | |
1287.1.ba.d.142.1 | yes | 8 | 1287.142 | odd | 6 | inner | |
1287.1.ba.d.571.1 | yes | 8 | 1.1 | even | 1 | trivial | |
1287.1.ba.d.571.1 | yes | 8 | 143.142 | odd | 2 | CM | |
3861.1.ba.c.2287.4 | 8 | 9.2 | odd | 6 | |||
3861.1.ba.c.2287.4 | 8 | 1287.857 | even | 6 | |||
3861.1.ba.c.3574.4 | 8 | 3.2 | odd | 2 | |||
3861.1.ba.c.3574.4 | 8 | 429.428 | even | 2 | |||
3861.1.ba.d.2287.1 | 8 | 99.65 | even | 6 | |||
3861.1.ba.d.2287.1 | 8 | 117.38 | odd | 6 | |||
3861.1.ba.d.3574.1 | 8 | 33.32 | even | 2 | |||
3861.1.ba.d.3574.1 | 8 | 39.38 | odd | 2 |