Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [693,1,Mod(62,693)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(693, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 5, 7]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("693.62");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 693 = 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 693.bp (of order \(10\), degree \(4\), 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: | \(0.345852053755\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{10})\) |
Coefficient field: | \(\Q(\zeta_{40})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{12} + x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{20}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
Embedding invariants
Embedding label | 629.3 | ||
Root | \(-0.891007 - 0.453990i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 693.629 |
Dual form | 693.1.bp.a.314.3 |
$q$-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 \(\left(\mathbb{Z}/693\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(442\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{10}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.0966818 | − | 0.297556i | 0.0966818 | − | 0.297556i | −0.891007 | − | 0.453990i | \(-0.850000\pi\) |
0.987688 | + | 0.156434i | \(0.0500000\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.729825 | + | 0.530249i | 0.729825 | + | 0.530249i | ||||
\(5\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.587785 | + | 0.809017i | −0.587785 | + | 0.809017i | ||||
\(8\) | 0.481456 | − | 0.349798i | 0.481456 | − | 0.349798i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.453990 | − | 0.891007i | 0.453990 | − | 0.891007i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(14\) | 0.183900 | + | 0.253116i | 0.183900 | + | 0.253116i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.221232 | + | 0.680881i | 0.221232 | + | 0.680881i | ||||
\(17\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.221232 | − | 0.221232i | −0.221232 | − | 0.221232i | ||||
\(23\) | 1.97538i | 1.97538i | 0.156434 | + | 0.987688i | \(0.450000\pi\) | ||||
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.809017 | − | 0.587785i | 0.809017 | − | 0.587785i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.857960 | + | 0.278768i | −0.857960 | + | 0.278768i | ||||
\(29\) | −1.44168 | − | 1.04744i | −1.44168 | − | 1.04744i | −0.987688 | − | 0.156434i | \(-0.950000\pi\) |
−0.453990 | − | 0.891007i | \(-0.650000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(32\) | 0.819101 | 0.819101 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.951057 | − | 0.690983i | −0.951057 | − | 0.690983i | − | 1.00000i | \(-0.5\pi\) | |
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 0.618034i | − | 0.618034i | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||
0.951057 | − | 0.309017i | \(-0.100000\pi\) | |||||||
\(44\) | 0.803789 | − | 0.409551i | 0.803789 | − | 0.409551i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.587785 | + | 0.190983i | 0.587785 | + | 0.190983i | ||||
\(47\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.309017 | − | 0.951057i | −0.309017 | − | 0.951057i | ||||
\(50\) | −0.0966818 | − | 0.297556i | −0.0966818 | − | 0.297556i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.69480 | − | 0.550672i | −1.69480 | − | 0.550672i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.595112i | 0.595112i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.451057 | + | 0.327712i | −0.451057 | + | 0.327712i | ||||
\(59\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.142040 | + | 0.437153i | −0.142040 | + | 0.437153i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.618034 | 0.618034 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.863541 | − | 0.280582i | 0.863541 | − | 0.280582i | 0.156434 | − | 0.987688i | \(-0.450000\pi\) |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(74\) | −0.297556 | + | 0.216187i | −0.297556 | + | 0.216187i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.453990 | + | 0.891007i | 0.453990 | + | 0.891007i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.80902 | − | 0.587785i | −1.80902 | − | 0.587785i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.183900 | − | 0.0597526i | −0.183900 | − | 0.0597526i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.0930960 | − | 0.587785i | −0.0930960 | − | 0.587785i | ||||
\(89\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.04744 | + | 1.44168i | −1.04744 | + | 1.44168i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(98\) | −0.312869 | −0.312869 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.902113 | 0.902113 | ||||||||
\(101\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.327712 | + | 0.451057i | −0.327712 | + | 0.451057i | ||||
\(107\) | −1.59811 | + | 1.16110i | −1.59811 | + | 1.16110i | −0.707107 | + | 0.707107i | \(0.750000\pi\) |
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 1.61803i | − | 1.61803i | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||
0.587785 | − | 0.809017i | \(-0.300000\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.680881 | − | 0.221232i | −0.680881 | − | 0.221232i | ||||
\(113\) | 0.533698 | + | 0.734572i | 0.533698 | + | 0.734572i | 0.987688 | − | 0.156434i | \(-0.0500000\pi\) |
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.496769 | − | 1.52890i | −0.496769 | − | 1.52890i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.587785 | − | 0.809017i | −0.587785 | − | 0.809017i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.11803 | + | 0.363271i | −1.11803 | + | 0.363271i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(128\) | 0.779012 | + | 0.565985i | 0.779012 | + | 0.565985i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.0597526 | − | 0.183900i | 0.0597526 | − | 0.183900i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.297556 | − | 0.0966818i | 0.297556 | − | 0.0966818i | −0.156434 | − | 0.987688i | \(-0.550000\pi\) |
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 0.284079i | − | 0.284079i | ||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.327712 | − | 1.00859i | −0.327712 | − | 1.00859i | ||||
\(149\) | 0.437016 | + | 1.34500i | 0.437016 | + | 1.34500i | 0.891007 | + | 0.453990i | \(0.150000\pi\) |
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.951057 | + | 1.30902i | 0.951057 | + | 1.30902i | 0.951057 | + | 0.309017i | \(0.100000\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.309017 | − | 0.0489435i | 0.309017 | − | 0.0489435i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(158\) | −0.349798 | + | 0.481456i | −0.349798 | + | 0.481456i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.59811 | − | 1.16110i | −1.59811 | − | 1.16110i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.500000 | + | 1.53884i | −0.500000 | + | 1.53884i | 0.309017 | + | 0.951057i | \(0.400000\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.809017 | + | 0.587785i | 0.809017 | + | 0.587785i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.327712 | − | 0.451057i | 0.327712 | − | 0.451057i | ||||
\(173\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.00000i | 1.00000i | ||||||||
\(176\) | 0.707107 | + | 0.111995i | 0.707107 | + | 0.111995i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.183900 | − | 0.253116i | −0.183900 | − | 0.253116i | 0.707107 | − | 0.707107i | \(-0.250000\pi\) |
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.690983 | + | 0.951057i | 0.690983 | + | 0.951057i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.04744 | − | 1.44168i | 1.04744 | − | 1.44168i | 0.156434 | − | 0.987688i | \(-0.450000\pi\) |
0.891007 | − | 0.453990i | \(-0.150000\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.587785 | − | 0.190983i | 0.587785 | − | 0.190983i | − | 1.00000i | \(-0.5\pi\) | |
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.278768 | − | 0.857960i | 0.278768 | − | 0.857960i | ||||
\(197\) | 1.97538 | 1.97538 | 0.987688 | − | 0.156434i | \(-0.0500000\pi\) | ||||
0.987688 | + | 0.156434i | \(0.0500000\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(200\) | 0.183900 | − | 0.565985i | 0.183900 | − | 0.565985i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.69480 | − | 0.550672i | 1.69480 | − | 0.550672i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.53884 | + | 0.500000i | 1.53884 | + | 0.500000i | 0.951057 | − | 0.309017i | \(-0.100000\pi\) |
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(212\) | −0.944910 | − | 1.30056i | −0.944910 | − | 1.30056i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.190983 | + | 0.587785i | 0.190983 | + | 0.587785i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −0.481456 | − | 0.156434i | −0.481456 | − | 0.156434i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(224\) | −0.481456 | + | 0.662667i | −0.481456 | + | 0.662667i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.270175 | − | 0.0877853i | 0.270175 | − | 0.0877853i | ||||
\(227\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.06050 | −1.06050 | ||||||||
\(233\) | 0.437016 | − | 1.34500i | 0.437016 | − | 1.34500i | −0.453990 | − | 0.891007i | \(-0.650000\pi\) |
0.891007 | − | 0.453990i | \(-0.150000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.734572 | + | 0.533698i | −0.734572 | + | 0.533698i | −0.891007 | − | 0.453990i | \(-0.850000\pi\) |
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(242\) | −0.297556 | + | 0.0966818i | −0.297556 | + | 0.0966818i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.76007 | + | 0.896802i | 1.76007 | + | 0.896802i | ||||
\(254\) | 0.367799i | 0.367799i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.128136 | + | 0.0930960i | −0.128136 | + | 0.0930960i | ||||
\(257\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.11803 | − | 0.363271i | 1.11803 | − | 0.363271i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.78201 | 1.78201 | 0.891007 | − | 0.453990i | \(-0.150000\pi\) | ||||
0.891007 | + | 0.453990i | \(0.150000\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.451057 | + | 0.327712i | 0.451057 | + | 0.327712i | ||||
\(269\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 0.0978870i | − | 0.0978870i | ||||||
\(275\) | −0.156434 | − | 0.987688i | −0.156434 | − | 0.987688i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.11803 | − | 0.363271i | −1.11803 | − | 0.363271i | −0.309017 | − | 0.951057i | \(-0.600000\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.280582 | − | 0.863541i | −0.280582 | − | 0.863541i | −0.987688 | − | 0.156434i | \(-0.950000\pi\) |
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(284\) | 0.779012 | + | 0.253116i | 0.779012 | + | 0.253116i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.699596 | −0.699596 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.442463 | 0.442463 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.500000 | + | 0.363271i | 0.500000 | + | 0.363271i | ||||
\(302\) | 0.481456 | − | 0.156434i | 0.481456 | − | 0.156434i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(308\) | −0.141122 | + | 0.891007i | −0.141122 | + | 0.891007i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.00859 | − | 1.38821i | −1.00859 | − | 1.38821i | ||||
\(317\) | −0.863541 | − | 0.280582i | −0.863541 | − | 0.280582i | −0.156434 | − | 0.987688i | \(-0.550000\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.58779 | + | 0.809017i | −1.58779 | + | 0.809017i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.500000 | + | 0.363271i | −0.500000 | + | 0.363271i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0.409551 | + | 0.297556i | 0.409551 | + | 0.297556i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.17557 | 1.17557 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.951057 | + | 1.30902i | −0.951057 | + | 1.30902i | 1.00000i | \(0.5\pi\) | ||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(338\) | 0.253116 | − | 0.183900i | 0.253116 | − | 0.183900i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.951057 | + | 0.309017i | 0.951057 | + | 0.309017i | ||||
\(344\) | −0.216187 | − | 0.297556i | −0.216187 | − | 0.297556i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.280582 | + | 0.863541i | 0.280582 | + | 0.863541i | 0.987688 | + | 0.156434i | \(0.0500000\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(350\) | 0.297556 | + | 0.0966818i | 0.297556 | + | 0.0966818i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.371864 | − | 0.729825i | 0.371864 | − | 0.729825i | ||||
\(353\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.0930960 | + | 0.0302487i | −0.0930960 | + | 0.0302487i | ||||
\(359\) | 1.59811 | + | 1.16110i | 1.59811 | + | 1.16110i | 0.891007 | + | 0.453990i | \(0.150000\pi\) |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.309017 | + | 0.951057i | −0.309017 | + | 0.951057i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(368\) | −1.34500 | + | 0.437016i | −1.34500 | + | 0.437016i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.44168 | − | 1.04744i | 1.44168 | − | 1.04744i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.363271 | − | 1.11803i | −0.363271 | − | 1.11803i | −0.951057 | − | 0.309017i | \(-0.900000\pi\) |
0.587785 | − | 0.809017i | \(-0.300000\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −0.327712 | − | 0.451057i | −0.327712 | − | 0.451057i | ||||
\(383\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 0.193364i | − | 0.193364i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.183900 | + | 0.253116i | −0.183900 | + | 0.253116i | −0.891007 | − | 0.453990i | \(-0.850000\pi\) |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −0.481456 | − | 0.349798i | −0.481456 | − | 0.349798i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.190983 | − | 0.587785i | 0.190983 | − | 0.587785i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.579192 | + | 0.420808i | 0.579192 | + | 0.420808i | ||||
\(401\) | −1.87869 | + | 0.610425i | −1.87869 | + | 0.610425i | −0.891007 | + | 0.453990i | \(0.850000\pi\) |
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | − | 0.557537i | − | 0.557537i | ||||||
\(407\) | −1.04744 | + | 0.533698i | −1.04744 | + | 0.533698i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.30902 | − | 0.951057i | 1.30902 | − | 0.951057i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
1.00000 | \(0\) | |||||||||
\(422\) | 0.297556 | − | 0.409551i | 0.297556 | − | 0.409551i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.00859 | + | 0.327712i | −1.00859 | + | 0.327712i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −1.78201 | −1.78201 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.610425 | + | 1.87869i | −0.610425 | + | 1.87869i | −0.156434 | + | 0.987688i | \(0.550000\pi\) |
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.857960 | − | 1.18088i | 0.857960 | − | 1.18088i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.533698 | − | 0.734572i | −0.533698 | − | 0.734572i | 0.453990 | − | 0.891007i | \(-0.350000\pi\) |
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.270175 | − | 0.371864i | −0.270175 | − | 0.371864i | ||||
\(449\) | 1.87869 | + | 0.610425i | 1.87869 | + | 0.610425i | 0.987688 | + | 0.156434i | \(0.0500000\pi\) |
0.891007 | + | 0.453990i | \(0.150000\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0.819101i | 0.819101i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.53884 | − | 0.500000i | 1.53884 | − | 0.500000i | 0.587785 | − | 0.809017i | \(-0.300000\pi\) |
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.618034 | −0.618034 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(464\) | 0.394238 | − | 1.21334i | 0.394238 | − | 1.21334i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.357960 | − | 0.260074i | −0.357960 | − | 0.260074i | ||||
\(467\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.363271 | + | 0.500000i | −0.363271 | + | 0.500000i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.550672 | − | 0.280582i | −0.550672 | − | 0.280582i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0.0877853 | + | 0.270175i | 0.0877853 | + | 0.270175i | ||||
\(479\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 0.902113i | − | 0.902113i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.53884 | + | 1.11803i | −1.53884 | + | 1.11803i | −0.587785 | + | 0.809017i | \(0.700000\pi\) |
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.14412 | − | 0.831254i | −1.14412 | − | 0.831254i | −0.156434 | − | 0.987688i | \(-0.550000\pi\) |
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.280582 | + | 0.863541i | −0.280582 | + | 0.863541i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.53884 | − | 1.11803i | −1.53884 | − | 1.11803i | −0.951057 | − | 0.309017i | \(-0.900000\pi\) |
−0.587785 | − | 0.809017i | \(-0.700000\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.437016 | − | 0.437016i | 0.437016 | − | 0.437016i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.00859 | − | 0.327712i | −1.00859 | − | 0.327712i | ||||
\(509\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0.312869 | + | 0.962912i | 0.312869 | + | 0.962912i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | − | 0.367799i | − | 0.367799i | ||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.172288 | − | 0.530249i | 0.172288 | − | 0.530249i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.90211 | −2.90211 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0.297556 | − | 0.216187i | 0.297556 | − | 0.216187i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.987688 | − | 0.156434i | −0.987688 | − | 0.156434i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.11803 | + | 0.363271i | 1.11803 | + | 0.363271i | 0.809017 | − | 0.587785i | \(-0.200000\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(548\) | 0.268429 | + | 0.0872179i | 0.268429 | + | 0.0872179i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.309017 | − | 0.0489435i | −0.309017 | − | 0.0489435i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.53884 | − | 1.11803i | 1.53884 | − | 1.11803i | ||||
\(554\) | −0.216187 | + | 0.297556i | −0.216187 | + | 0.297556i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0.734572 | + | 0.533698i | 0.734572 | + | 0.533698i | 0.891007 | − | 0.453990i | \(-0.150000\pi\) |
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −0.284079 | −0.284079 | ||||||||
\(563\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0.317610 | − | 0.437153i | 0.317610 | − | 0.437153i | ||||
\(569\) | −1.14412 | + | 0.831254i | −1.14412 | + | 0.831254i | −0.987688 | − | 0.156434i | \(-0.950000\pi\) |
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.17557i | 1.17557i | 0.809017 | + | 0.587785i | \(0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.16110 | + | 1.59811i | 1.16110 | + | 1.59811i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(578\) | 0.0966818 | + | 0.297556i | 0.0966818 | + | 0.297556i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.26007 | + | 1.26007i | −1.26007 | + | 1.26007i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.260074 | − | 0.800424i | 0.260074 | − | 0.800424i | ||||
\(593\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.394238 | + | 1.21334i | −0.394238 | + | 1.21334i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.297556 | + | 0.0966818i | −0.297556 | + | 0.0966818i | −0.453990 | − | 0.891007i | \(-0.650000\pi\) |
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(602\) | 0.156434 | − | 0.113656i | 0.156434 | − | 0.113656i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.45965i | 1.45965i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.11803 | − | 1.53884i | −1.11803 | − | 1.53884i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
−0.309017 | − | 0.951057i | \(-0.600000\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.530249 | + | 0.270175i | 0.530249 | + | 0.270175i | ||||
\(617\) | − | 1.78201i | − | 1.78201i | −0.453990 | − | 0.891007i | \(-0.650000\pi\) | ||
0.453990 | − | 0.891007i | \(-0.350000\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.30902 | − | 0.951057i | −1.30902 | − | 0.951057i | −0.309017 | − | 0.951057i | \(-0.600000\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(632\) | −1.07657 | + | 0.349798i | −1.07657 | + | 0.349798i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −0.166977 | + | 0.229825i | −0.166977 | + | 0.229825i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0.0872179 | + | 0.550672i | 0.0872179 | + | 0.550672i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.04744 | + | 1.44168i | 1.04744 | + | 1.44168i | 0.891007 | + | 0.453990i | \(0.150000\pi\) |
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(644\) | −0.550672 | − | 1.69480i | −0.550672 | − | 1.69480i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.18088 | + | 0.857960i | −1.18088 | + | 0.857960i | ||||
\(653\) | 1.16110 | − | 1.59811i | 1.16110 | − | 1.59811i | 0.453990 | − | 0.891007i | \(-0.350000\pi\) |
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.41421 | −1.41421 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(662\) | 0.113656 | − | 0.349798i | 0.113656 | − | 0.349798i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.06909 | − | 2.84786i | 2.06909 | − | 2.84786i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.587785 | − | 0.190983i | −0.587785 | − | 0.190983i | − | 1.00000i | \(-0.5\pi\) | |
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(674\) | 0.297556 | + | 0.409551i | 0.297556 | + | 0.409551i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.278768 | + | 0.857960i | 0.278768 | + | 0.857960i | ||||
\(677\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 0.312869i | − | 0.312869i | −0.987688 | − | 0.156434i | \(-0.950000\pi\) | ||
0.987688 | − | 0.156434i | \(-0.0500000\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0.183900 | − | 0.253116i | 0.183900 | − | 0.253116i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.420808 | − | 0.136729i | 0.420808 | − | 0.136729i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0.284079 | 0.284079 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.530249 | + | 0.729825i | −0.530249 | + | 0.729825i | ||||
\(701\) | 1.59811 | − | 1.16110i | 1.59811 | − | 1.16110i | 0.707107 | − | 0.707107i | \(-0.250000\pi\) |
0.891007 | − | 0.453990i | \(-0.150000\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0.325021 | + | 0.325021i | 0.325021 | + | 0.325021i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.587785 | + | 1.80902i | 0.587785 | + | 1.80902i | 0.587785 | + | 0.809017i | \(0.300000\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 0.282243i | − | 0.282243i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0.500000 | − | 0.363271i | 0.500000 | − | 0.363271i | ||||
\(719\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0.253116 | + | 0.183900i | 0.253116 | + | 0.183900i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.78201 | −1.78201 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.61803i | 1.61803i | ||||||||
\(737\) | 0.280582 | − | 0.550672i | 0.280582 | − | 0.550672i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.80902 | + | 0.587785i | 1.80902 | + | 0.587785i | 1.00000 | \(0\) | ||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.172288 | − | 0.530249i | −0.172288 | − | 0.530249i | ||||
\(743\) | −0.550672 | − | 1.69480i | −0.550672 | − | 1.69480i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
0.156434 | − | 0.987688i | \(-0.450000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 1.97538i | − | 1.97538i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.951057 | − | 0.690983i | 0.951057 | − | 0.690983i | − | 1.00000i | \(-0.5\pi\) | |
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.587785 | + | 1.80902i | −0.587785 | + | 1.80902i | 1.00000i | \(0.5\pi\) | ||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(758\) | −0.367799 | −0.367799 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.30902 | + | 0.951057i | 1.30902 | + | 0.951057i | ||||
\(764\) | 1.52890 | − | 0.496769i | 1.52890 | − | 0.496769i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0.530249 | + | 0.172288i | 0.530249 | + | 0.172288i | ||||
\(773\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.0575365 | + | 0.0791922i | 0.0575365 | + | 0.0791922i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.142040 | − | 0.896802i | 0.142040 | − | 0.896802i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.579192 | − | 0.420808i | 0.579192 | − | 0.420808i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(788\) | 1.44168 | + | 1.04744i | 1.44168 | + | 1.04744i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.907981 | −0.907981 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 |