Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [961,1,Mod(115,961)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(961, base_ring=CyclotomicField(30))
chi = DirichletCharacter(H, H._module([17]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("961.115");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 961 = 31^{2} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 961.h (of order \(30\), degree \(8\), not 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: | \(0.479601477140\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 31) |
Projective image: | \(D_{3}\) |
Projective field: | Galois closure of 3.1.31.1 |
Artin image: | $S_3\times C_{15}$ |
Artin field: | Galois closure of \(\mathbb{Q}[x]/(x^{45} - \cdots)\) |
Embedding invariants
Embedding label | 145.1 | ||
Root | \(0.669131 - 0.743145i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 961.145 |
Dual form | 961.1.h.a.623.1 |
$q$-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 \(\left(\mathbb{Z}/961\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{29}{30}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.809017 | + | 0.587785i | 0.809017 | + | 0.587785i | 0.913545 | − | 0.406737i | \(-0.133333\pi\) |
−0.104528 | + | 0.994522i | \(0.533333\pi\) | |||||||
\(3\) | 0 | 0 | −0.104528 | − | 0.994522i | \(-0.533333\pi\) | ||||
0.104528 | + | 0.994522i | \(0.466667\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.978148 | + | 0.207912i | 0.978148 | + | 0.207912i | 0.669131 | − | 0.743145i | \(-0.266667\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(8\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(9\) | −0.978148 | + | 0.207912i | −0.978148 | + | 0.207912i | ||||
\(10\) | −0.104528 | + | 0.994522i | −0.104528 | + | 0.994522i | ||||
\(11\) | 0 | 0 | 0.669131 | − | 0.743145i | \(-0.266667\pi\) | ||||
−0.669131 | + | 0.743145i | \(0.733333\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | −0.913545 | − | 0.406737i | \(-0.866667\pi\) | ||||
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(14\) | 0.669131 | + | 0.743145i | 0.669131 | + | 0.743145i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.809017 | − | 0.587785i | 0.809017 | − | 0.587785i | ||||
\(17\) | 0 | 0 | −0.669131 | − | 0.743145i | \(-0.733333\pi\) | ||||
0.669131 | + | 0.743145i | \(0.266667\pi\) | |||||||
\(18\) | −0.913545 | − | 0.406737i | −0.913545 | − | 0.406737i | ||||
\(19\) | −0.913545 | + | 0.406737i | −0.913545 | + | 0.406737i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
−0.104528 | + | 0.994522i | \(0.533333\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | ||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.309017 | + | 0.951057i | 0.309017 | + | 0.951057i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(38\) | −0.978148 | − | 0.207912i | −0.978148 | − | 0.207912i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.978148 | − | 0.207912i | 0.978148 | − | 0.207912i | ||||
\(41\) | 0.104528 | − | 0.994522i | 0.104528 | − | 0.994522i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.913545 | − | 0.406737i | \(-0.133333\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 0.913545 | − | 0.406737i | \(-0.133333\pi\) | ||||
−0.913545 | + | 0.406737i | \(0.866667\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.669131 | − | 0.743145i | −0.669131 | − | 0.743145i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.61803 | + | 1.17557i | −1.61803 | + | 1.17557i | −0.809017 | + | 0.587785i | \(0.800000\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 0.978148 | − | 0.207912i | \(-0.0666667\pi\) | ||||
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.104528 | + | 0.994522i | 0.104528 | + | 0.994522i | 0.913545 | + | 0.406737i | \(0.133333\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.00000 | −1.00000 | ||||||||
\(64\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
−0.500000 | − | 0.866025i | \(-0.666667\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.309017 | + | 0.951057i | −0.309017 | + | 0.951057i | ||||
\(71\) | 0.978148 | − | 0.207912i | 0.978148 | − | 0.207912i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
0.669131 | + | 0.743145i | \(0.266667\pi\) | |||||||
\(72\) | −0.104528 | + | 0.994522i | −0.104528 | + | 0.994522i | ||||
\(73\) | 0 | 0 | 0.669131 | − | 0.743145i | \(-0.266667\pi\) | ||||
−0.669131 | + | 0.743145i | \(0.733333\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | −0.669131 | − | 0.743145i | \(-0.733333\pi\) | ||||
0.669131 | + | 0.743145i | \(0.266667\pi\) | |||||||
\(80\) | 0.913545 | + | 0.406737i | 0.913545 | + | 0.406737i | ||||
\(81\) | 0.913545 | − | 0.406737i | 0.913545 | − | 0.406737i | ||||
\(82\) | 0.669131 | − | 0.743145i | 0.669131 | − | 0.743145i | ||||
\(83\) | 0 | 0 | 0.104528 | − | 0.994522i | \(-0.466667\pi\) | ||||
−0.104528 | + | 0.994522i | \(0.533333\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(90\) | −0.104528 | − | 0.994522i | −0.104528 | − | 0.994522i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.00000 | −2.00000 | ||||||||
\(95\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.309017 | − | 0.951057i | −0.309017 | − | 0.951057i | −0.978148 | − | 0.207912i | \(-0.933333\pi\) |
0.669131 | − | 0.743145i | \(-0.266667\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.309017 | + | 0.951057i | −0.309017 | + | 0.951057i | 0.669131 | + | 0.743145i | \(0.266667\pi\) |
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.104528 | − | 0.994522i | 0.104528 | − | 0.994522i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.913545 | − | 0.406737i | \(-0.133333\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.669131 | − | 0.743145i | −0.669131 | − | 0.743145i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.809017 | − | 0.587785i | 0.809017 | − | 0.587785i | −0.104528 | − | 0.994522i | \(-0.533333\pi\) |
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.913545 | − | 0.406737i | 0.913545 | − | 0.406737i | ||||
\(113\) | −0.669131 | + | 0.743145i | −0.669131 | + | 0.743145i | −0.978148 | − | 0.207912i | \(-0.933333\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.104528 | − | 0.994522i | −0.104528 | − | 0.994522i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 1.00000 | ||||||||
\(126\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(127\) | 0 | 0 | −0.104528 | − | 0.994522i | \(-0.533333\pi\) | ||||
0.104528 | + | 0.994522i | \(0.466667\pi\) | |||||||
\(128\) | −0.309017 | − | 0.951057i | −0.309017 | − | 0.951057i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.95630 | − | 0.415823i | −1.95630 | − | 0.415823i | −0.978148 | − | 0.207912i | \(-0.933333\pi\) |
−0.978148 | − | 0.207912i | \(-0.933333\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.978148 | + | 0.207912i | −0.978148 | + | 0.207912i | ||||
\(134\) | 0.209057 | − | 1.98904i | 0.209057 | − | 1.98904i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.913545 | − | 0.406737i | \(-0.866667\pi\) | ||||
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.913545 | + | 0.406737i | 0.913545 | + | 0.406737i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.669131 | + | 0.743145i | −0.669131 | + | 0.743145i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | −0.500000 | + | 0.866025i | \(0.666667\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(152\) | 0.104528 | + | 0.994522i | 0.104528 | + | 0.994522i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.809017 | + | 0.587785i | 0.809017 | + | 0.587785i | 0.913545 | − | 0.406737i | \(-0.133333\pi\) |
−0.104528 | + | 0.994522i | \(0.533333\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.978148 | + | 0.207912i | 0.978148 | + | 0.207912i | ||||
\(163\) | −0.309017 | + | 0.951057i | −0.309017 | + | 0.951057i | 0.669131 | + | 0.743145i | \(0.266667\pi\) |
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 0.913545 | − | 0.406737i | \(-0.133333\pi\) | ||||
−0.913545 | + | 0.406737i | \(0.866667\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.669131 | + | 0.743145i | 0.669131 | + | 0.743145i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.809017 | − | 0.587785i | 0.809017 | − | 0.587785i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.82709 | + | 0.813473i | 1.82709 | + | 0.813473i | 0.913545 | + | 0.406737i | \(0.133333\pi\) |
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | −0.978148 | − | 0.207912i | \(-0.933333\pi\) | ||||
0.978148 | + | 0.207912i | \(0.0666667\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.309017 | − | 0.951057i | −0.309017 | − | 0.951057i | ||||
\(191\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.978148 | + | 0.207912i | 0.978148 | + | 0.207912i | 0.669131 | − | 0.743145i | \(-0.266667\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(194\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0 | 0 | 0.669131 | − | 0.743145i | \(-0.266667\pi\) | ||||
−0.669131 | + | 0.743145i | \(0.733333\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | −0.913545 | − | 0.406737i | \(-0.866667\pi\) | ||||
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.913545 | − | 0.406737i | 0.913545 | − | 0.406737i | ||||
\(206\) | 0.669131 | − | 0.743145i | 0.669131 | − | 0.743145i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.104528 | − | 0.994522i | −0.104528 | − | 0.994522i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1.00000 | 1.00000 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.978148 | + | 0.207912i | −0.978148 | + | 0.207912i | ||||
\(227\) | −0.209057 | + | 1.98904i | −0.209057 | + | 1.98904i | −0.104528 | + | 0.994522i | \(0.533333\pi\) |
−0.104528 | + | 0.994522i | \(0.533333\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | 0.913545 | − | 0.406737i | \(-0.133333\pi\) | ||||
−0.913545 | + | 0.406737i | \(0.866667\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.809017 | − | 0.587785i | 0.809017 | − | 0.587785i | −0.104528 | − | 0.994522i | \(-0.533333\pi\) |
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.82709 | − | 0.813473i | −1.82709 | − | 0.813473i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.978148 | − | 0.207912i | \(-0.0666667\pi\) | ||||
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | −0.978148 | − | 0.207912i | \(-0.933333\pi\) | ||||
0.978148 | + | 0.207912i | \(0.0666667\pi\) | |||||||
\(242\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.809017 | + | 0.587785i | 0.809017 | + | 0.587785i | ||||
\(251\) | 0 | 0 | −0.104528 | − | 0.994522i | \(-0.533333\pi\) | ||||
0.104528 | + | 0.994522i | \(0.466667\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.978148 | − | 0.207912i | 0.978148 | − | 0.207912i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
0.669131 | + | 0.743145i | \(0.266667\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.33826 | − | 1.48629i | −1.33826 | − | 1.48629i | ||||
\(263\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.913545 | − | 0.406737i | −0.913545 | − | 0.406737i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | 0.104528 | − | 0.994522i | \(-0.466667\pi\) | ||||
−0.104528 | + | 0.994522i | \(0.533333\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.00000 | 1.00000 | ||||||||
\(281\) | 0.809017 | + | 0.587785i | 0.809017 | + | 0.587785i | 0.913545 | − | 0.406737i | \(-0.133333\pi\) |
−0.104528 | + | 0.994522i | \(0.533333\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.618034 | + | 1.90211i | 0.618034 | + | 1.90211i | 0.309017 | + | 0.951057i | \(0.400000\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.104528 | + | 0.994522i | −0.104528 | + | 0.994522i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.33826 | + | 1.48629i | 1.33826 | + | 1.48629i | 0.669131 | + | 0.743145i | \(0.266667\pi\) |
0.669131 | + | 0.743145i | \(0.266667\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.82709 | + | 0.813473i | −1.82709 | + | 0.813473i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.104528 | + | 0.994522i | 0.104528 | + | 0.994522i | 0.913545 | + | 0.406737i | \(0.133333\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | −0.104528 | − | 0.994522i | \(-0.533333\pi\) | ||||
0.104528 | + | 0.994522i | \(0.466667\pi\) | |||||||
\(314\) | 0.309017 | + | 0.951057i | 0.309017 | + | 0.951057i | ||||
\(315\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.978148 | + | 0.207912i | 0.978148 | + | 0.207912i | 0.669131 | − | 0.743145i | \(-0.266667\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0.104528 | − | 0.994522i | 0.104528 | − | 0.994522i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −0.913545 | − | 0.406737i | −0.913545 | − | 0.406737i | ||||
\(329\) | −1.82709 | + | 0.813473i | −1.82709 | + | 0.813473i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | 0.104528 | − | 0.994522i | \(-0.466667\pi\) | ||||
−0.104528 | + | 0.994522i | \(0.533333\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.00000 | − | 1.73205i | 1.00000 | − | 1.73205i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(338\) | 0.104528 | + | 0.994522i | 0.104528 | + | 0.994522i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 1.00000 | 1.00000 | ||||||||
\(343\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.00000 | + | 1.73205i | 1.00000 | + | 1.73205i | ||||
\(347\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.618034 | − | 1.90211i | 0.618034 | − | 1.90211i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
0.309017 | − | 0.951057i | \(-0.400000\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 0.913545 | − | 0.406737i | \(-0.133333\pi\) | ||||
−0.913545 | + | 0.406737i | \(0.866667\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.669131 | + | 0.743145i | 0.669131 | + | 0.743145i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −0.913545 | − | 0.406737i | −0.913545 | − | 0.406737i | −0.104528 | − | 0.994522i | \(-0.533333\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(360\) | −0.913545 | + | 0.406737i | −0.913545 | + | 0.406737i | ||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.104528 | + | 0.994522i | 0.104528 | + | 0.994522i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.618034 | + | 1.90211i | 0.618034 | + | 1.90211i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.95630 | − | 0.415823i | −1.95630 | − | 0.415823i | −0.978148 | − | 0.207912i | \(-0.933333\pi\) |
−0.978148 | − | 0.207912i | \(-0.933333\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −0.104528 | + | 0.994522i | −0.104528 | + | 0.994522i | ||||
\(383\) | 0 | 0 | 0.669131 | − | 0.743145i | \(-0.266667\pi\) | ||||
−0.669131 | + | 0.743145i | \(0.733333\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.669131 | + | 0.743145i | 0.669131 | + | 0.743145i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | −0.669131 | − | 0.743145i | \(-0.733333\pi\) | ||||
0.669131 | + | 0.743145i | \(0.266667\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.809017 | + | 0.587785i | 0.809017 | + | 0.587785i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(410\) | 0.978148 | + | 0.207912i | 0.978148 | + | 0.207912i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.104528 | + | 0.994522i | −0.104528 | + | 0.994522i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.809017 | − | 0.587785i | 0.809017 | − | 0.587785i | −0.104528 | − | 0.994522i | \(-0.533333\pi\) |
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.913545 | − | 0.406737i | −0.913545 | − | 0.406737i | −0.104528 | − | 0.994522i | \(-0.533333\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(422\) | 0.913545 | − | 0.406737i | 0.913545 | − | 0.406737i | ||||
\(423\) | 1.33826 | − | 1.48629i | 1.33826 | − | 1.48629i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.209057 | − | 1.98904i | −0.209057 | − | 1.98904i | −0.104528 | − | 0.994522i | \(-0.533333\pi\) |
−0.104528 | − | 0.994522i | \(-0.533333\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.978148 | − | 0.207912i | 0.978148 | − | 0.207912i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
0.669131 | + | 0.743145i | \(0.266667\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.669131 | − | 0.743145i | −0.669131 | − | 0.743145i | ||||
\(449\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.33826 | + | 1.48629i | −1.33826 | + | 1.48629i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.00000 | 1.00000 | ||||||||
\(467\) | 0.809017 | + | 0.587785i | 0.809017 | + | 0.587785i | 0.913545 | − | 0.406737i | \(-0.133333\pi\) |
−0.104528 | + | 0.994522i | \(0.533333\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.618034 | − | 1.90211i | −0.618034 | − | 1.90211i | ||||
\(470\) | −1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0.978148 | + | 0.207912i | 0.978148 | + | 0.207912i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.669131 | − | 0.743145i | −0.669131 | − | 0.743145i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.669131 | − | 0.743145i | 0.669131 | − | 0.743145i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0 | 0 | 0.978148 | − | 0.207912i | \(-0.0666667\pi\) | ||||
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.00000 | 1.00000 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0 | 0 | −0.104528 | − | 0.994522i | \(-0.533333\pi\) | ||||
0.104528 | + | 0.994522i | \(0.466667\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0.978148 | + | 0.207912i | 0.978148 | + | 0.207912i | 0.669131 | − | 0.743145i | \(-0.266667\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(504\) | −0.309017 | + | 0.951057i | −0.309017 | + | 0.951057i | ||||
\(505\) | −0.978148 | + | 0.207912i | −0.978148 | + | 0.207912i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | −0.913545 | − | 0.406737i | \(-0.866667\pi\) | ||||
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0.913545 | + | 0.406737i | 0.913545 | + | 0.406737i | ||||
\(515\) | 0.913545 | − | 0.406737i | 0.913545 | − | 0.406737i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | −0.500000 | + | 0.866025i | \(0.666667\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.309017 | − | 0.951057i | −0.309017 | − | 0.951057i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(536\) | −1.95630 | + | 0.415823i | −1.95630 | + | 0.415823i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.669131 | − | 0.743145i | −0.669131 | − | 0.743145i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.913545 | + | 0.406737i | 0.913545 | + | 0.406737i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.669131 | + | 0.743145i | −0.669131 | + | 0.743145i | −0.978148 | − | 0.207912i | \(-0.933333\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 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 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0.809017 | + | 0.587785i | 0.809017 | + | 0.587785i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.309017 | + | 0.951057i | 0.309017 | + | 0.951057i | ||||
\(563\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.978148 | − | 0.207912i | −0.978148 | − | 0.207912i | ||||
\(566\) | −0.618034 | + | 1.90211i | −0.618034 | + | 1.90211i | ||||
\(567\) | 0.978148 | − | 0.207912i | 0.978148 | − | 0.207912i | ||||
\(568\) | 0.104528 | − | 0.994522i | 0.104528 | − | 0.994522i | ||||
\(569\) | 0 | 0 | 0.669131 | − | 0.743145i | \(-0.266667\pi\) | ||||
−0.669131 | + | 0.743145i | \(0.733333\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | −0.913545 | − | 0.406737i | \(-0.866667\pi\) | ||||
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.809017 | − | 0.587785i | 0.809017 | − | 0.587785i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.913545 | + | 0.406737i | 0.913545 | + | 0.406737i | ||||
\(577\) | 1.82709 | − | 0.813473i | 1.82709 | − | 0.813473i | 0.913545 | − | 0.406737i | \(-0.133333\pi\) |
0.913545 | − | 0.406737i | \(-0.133333\pi\) | |||||||
\(578\) | −0.669131 | + | 0.743145i | −0.669131 | + | 0.743145i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.209057 | + | 1.98904i | 0.209057 | + | 1.98904i | ||||
\(587\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −1.00000 | −1.00000 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −0.309017 | − | 0.951057i | −0.309017 | − | 0.951057i | −0.978148 | − | 0.207912i | \(-0.933333\pi\) |
0.669131 | − | 0.743145i | \(-0.266667\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0.104528 | − | 0.994522i | 0.104528 | − | 0.994522i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.913545 | − | 0.406737i | \(-0.133333\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | 0.913545 | − | 0.406737i | \(-0.133333\pi\) | ||||
−0.913545 | + | 0.406737i | \(0.866667\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.33826 | + | 1.48629i | 1.33826 | + | 1.48629i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.809017 | − | 0.587785i | 0.809017 | − | 0.587785i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.82709 | + | 0.813473i | 1.82709 | + | 0.813473i | 0.913545 | + | 0.406737i | \(0.133333\pi\) |
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | −0.978148 | − | 0.207912i | \(-0.933333\pi\) | ||||
0.978148 | + | 0.207912i | \(0.0666667\pi\) | |||||||
\(614\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.209057 | − | 1.98904i | −0.209057 | − | 1.98904i | −0.104528 | − | 0.994522i | \(-0.533333\pi\) |
−0.104528 | − | 0.994522i | \(-0.533333\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0.104528 | − | 0.994522i | 0.104528 | − | 0.994522i | ||||
\(631\) | 0 | 0 | 0.669131 | − | 0.743145i | \(-0.266667\pi\) | ||||
−0.669131 | + | 0.743145i | \(0.733333\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0.669131 | + | 0.743145i | 0.669131 | + | 0.743145i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.913545 | + | 0.406737i | −0.913545 | + | 0.406737i | ||||
\(640\) | 0.669131 | − | 0.743145i | 0.669131 | − | 0.743145i | ||||
\(641\) | 0 | 0 | 0.104528 | − | 0.994522i | \(-0.466667\pi\) | ||||
−0.104528 | + | 0.994522i | \(0.533333\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(648\) | −0.104528 | − | 0.994522i | −0.104528 | − | 0.994522i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.61803 | − | 1.17557i | −1.61803 | − | 1.17557i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
−0.809017 | − | 0.587785i | \(-0.800000\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.618034 | − | 1.90211i | −0.618034 | − | 1.90211i | ||||
\(656\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1.95630 | − | 0.415823i | −1.95630 | − | 0.415823i | ||||
\(659\) | −0.309017 | + | 0.951057i | −0.309017 | + | 0.951057i | 0.669131 | + | 0.743145i | \(0.266667\pi\) |
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.104528 | − | 0.994522i | 0.104528 | − | 0.994522i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.913545 | − | 0.406737i | \(-0.133333\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.669131 | − | 0.743145i | −0.669131 | − | 0.743145i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.82709 | − | 0.813473i | 1.82709 | − | 0.813473i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | 0.978148 | − | 0.207912i | \(-0.0666667\pi\) | ||||
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.104528 | − | 0.994522i | −0.104528 | − | 0.994522i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −0.309017 | − | 0.951057i | −0.309017 | − | 0.951057i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.978148 | − | 0.207912i | 0.978148 | − | 0.207912i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
0.669131 | + | 0.743145i | \(0.266667\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 1.61803 | − | 1.17557i | 1.61803 | − | 1.17557i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.913545 | + | 0.406737i | −0.913545 | + | 0.406737i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
−0.104528 | + | 0.994522i | \(0.533333\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(710\) | 0.104528 | + | 0.994522i | 0.104528 | + | 0.994522i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(719\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(720\) | −0.978148 | − | 0.207912i | −0.978148 | − | 0.207912i | ||||
\(721\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.669131 | − | 0.743145i | −0.669131 | − | 0.743145i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.669131 | + | 0.743145i | −0.669131 | + | 0.743145i | −0.978148 | − | 0.207912i | \(-0.933333\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(739\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.00000 | −2.00000 | ||||||||
\(746\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.978148 | + | 0.207912i | 0.978148 | + | 0.207912i | 0.669131 | − | 0.743145i | \(-0.266667\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(752\) | −0.618034 | + | 1.90211i | −0.618034 | + | 1.90211i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | −0.913545 | − | 0.406737i | \(-0.866667\pi\) | ||||
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(758\) | −1.33826 | − | 1.48629i | −1.33826 | − | 1.48629i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(761\) | 0 | 0 | −0.669131 | − | 0.743145i | \(-0.733333\pi\) | ||||
0.669131 | + | 0.743145i | \(0.266667\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.913545 | − | 0.406737i | 0.913545 | − | 0.406737i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1.00000 | −1.00000 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.309017 | + | 0.951057i | 0.309017 | + | 0.951057i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.104528 | + | 0.994522i | −0.104528 | + | 0.994522i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | 0.913545 | − | 0.406737i | \(-0.133333\pi\) | ||||
−0.913545 | + | 0.406737i | \(0.866667\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0.913545 | − | 0.406737i | 0.913545 | − | 0.406737i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 0.978148 | − | 0.207912i | \(-0.0666667\pi\) | ||||
−0.978148 | + | 0.207912i | \(0.933333\pi\) |