Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [799,1,Mod(93,799)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(799, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([5, 4]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("799.93");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 799 = 17 \cdot 47 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 799.h (of order \(8\), 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: | \(0.398752945094\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{8})\) |
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: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{40}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{40} + \cdots)\) |
Embedding invariants
Embedding label | 610.1 | ||
Root | \(-0.453990 + 0.891007i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 799.610 |
Dual form | 799.1.h.b.93.1 |
$q$-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 \(\left(\mathbb{Z}/799\mathbb{Z}\right)^\times\).
\(n\) | \(52\) | \(377\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{8}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.34500 | − | 1.34500i | −1.34500 | − | 1.34500i | −0.891007 | − | 0.453990i | \(-0.850000\pi\) |
−0.453990 | − | 0.891007i | \(-0.650000\pi\) | |||||||
\(3\) | −0.652583 | − | 1.57547i | −0.652583 | − | 1.57547i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.156434 | − | 0.987688i | \(-0.450000\pi\) | |||||||
\(4\) | 2.61803i | 2.61803i | ||||||||
\(5\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(6\) | −1.24129 | + | 2.99673i | −1.24129 | + | 2.99673i | ||||
\(7\) | 1.84206 | + | 0.763007i | 1.84206 | + | 0.763007i | 0.951057 | + | 0.309017i | \(0.100000\pi\) |
0.891007 | + | 0.453990i | \(0.150000\pi\) | |||||||
\(8\) | 2.17625 | − | 2.17625i | 2.17625 | − | 2.17625i | ||||
\(9\) | −1.34915 | + | 1.34915i | −1.34915 | + | 1.34915i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(12\) | 4.12464 | − | 1.70848i | 4.12464 | − | 1.70848i | ||||
\(13\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(14\) | −1.45133 | − | 3.50381i | −1.45133 | − | 3.50381i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.23607 | −3.23607 | ||||||||
\(17\) | 0.809017 | − | 0.587785i | 0.809017 | − | 0.587785i | ||||
\(18\) | 3.62920 | 3.62920 | ||||||||
\(19\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 3.40005i | − | 3.40005i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(24\) | −4.84881 | − | 2.00844i | −4.84881 | − | 2.00844i | ||||
\(25\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.43050 | + | 0.592533i | 1.43050 | + | 0.592533i | ||||
\(28\) | −1.99758 | + | 4.82258i | −1.99758 | + | 4.82258i | ||||
\(29\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(32\) | 2.17625 | + | 2.17625i | 2.17625 | + | 2.17625i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.87869 | − | 0.297556i | −1.87869 | − | 0.297556i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3.53211 | − | 3.53211i | −3.53211 | − | 3.53211i | ||||
\(37\) | −0.399903 | − | 0.965451i | −0.399903 | − | 0.965451i | −0.987688 | − | 0.156434i | \(-0.950000\pi\) |
0.587785 | − | 0.809017i | \(-0.300000\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(42\) | −4.57305 | + | 4.57305i | −4.57305 | + | 4.57305i | ||||
\(43\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.00000i | 1.00000i | ||||||||
\(48\) | 2.11180 | + | 5.09834i | 2.11180 | + | 5.09834i | ||||
\(49\) | 2.10391 | + | 2.10391i | 2.10391 | + | 2.10391i | ||||
\(50\) | −1.90211 | −1.90211 | ||||||||
\(51\) | −1.45399 | − | 0.891007i | −1.45399 | − | 0.891007i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.642040 | + | 0.642040i | 0.642040 | + | 0.642040i | 0.951057 | − | 0.309017i | \(-0.100000\pi\) |
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(54\) | −1.12706 | − | 2.72097i | −1.12706 | − | 2.72097i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 5.66929 | − | 2.34830i | 5.66929 | − | 2.34830i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.437016 | + | 0.437016i | −0.437016 | + | 0.437016i | −0.891007 | − | 0.453990i | \(-0.850000\pi\) |
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.20002 | − | 0.497066i | −1.20002 | − | 0.497066i | −0.309017 | − | 0.951057i | \(-0.600000\pi\) |
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.51462 | + | 1.45580i | −3.51462 | + | 1.45580i | ||||
\(64\) | − | 2.61803i | − | 2.61803i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(68\) | 1.53884 | + | 2.11803i | 1.53884 | + | 2.11803i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.178671 | + | 0.431351i | 0.178671 | + | 0.431351i | 0.987688 | − | 0.156434i | \(-0.0500000\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(72\) | 5.87216i | 5.87216i | ||||||||
\(73\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(74\) | −0.760661 | + | 1.83640i | −0.760661 | + | 1.83640i | ||||
\(75\) | −1.57547 | − | 0.652583i | −1.57547 | − | 0.652583i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.178671 | − | 0.431351i | 0.178671 | − | 0.431351i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.987688 | + | 0.156434i | \(0.0500000\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | − | 0.732410i | − | 0.732410i | ||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | − | 1.00000i | \(-0.5\pi\) | |
−1.00000 | \(\pi\) | |||||||||
\(84\) | 8.90144 | 8.90144 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 1.90211i | − | 1.90211i | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||
0.309017 | − | 0.951057i | \(-0.400000\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.34500 | − | 1.34500i | 1.34500 | − | 1.34500i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.00844 | − | 4.84881i | 2.00844 | − | 4.84881i | ||||
\(97\) | 1.40505 | − | 0.581990i | 1.40505 | − | 0.581990i | 0.453990 | − | 0.891007i | \(-0.350000\pi\) |
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(98\) | − | 5.65950i | − | 5.65950i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.85123 | + | 1.85123i | 1.85123 | + | 1.85123i | ||||
\(101\) | 0.312869 | 0.312869 | 0.156434 | − | 0.987688i | \(-0.450000\pi\) | ||||
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(102\) | 0.757212 | + | 3.15401i | 0.757212 | + | 3.15401i | ||||
\(103\) | −1.97538 | −1.97538 | −0.987688 | − | 0.156434i | \(-0.950000\pi\) | ||||
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 1.72708i | − | 1.72708i | ||||||
\(107\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(108\) | −1.55127 | + | 3.74510i | −1.55127 | + | 3.74510i | ||||
\(109\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.26007 | + | 1.26007i | −1.26007 | + | 1.26007i | ||||
\(112\) | −5.96104 | − | 2.46914i | −5.96104 | − | 2.46914i | ||||
\(113\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.17557 | 1.17557 | ||||||||
\(119\) | 1.93874 | − | 0.465451i | 1.93874 | − | 0.465451i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(122\) | 0.945476 | + | 2.28258i | 0.945476 | + | 2.28258i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 6.68521 | + | 2.76910i | 6.68521 | + | 2.76910i | ||||
\(127\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(128\) | −1.34500 | + | 1.34500i | −1.34500 | + | 1.34500i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.40505 | + | 0.581990i | −1.40505 | + | 0.581990i | −0.951057 | − | 0.309017i | \(-0.900000\pi\) |
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.481456 | − | 3.03979i | 0.481456 | − | 3.03979i | ||||
\(137\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.57547 | − | 0.652583i | 1.57547 | − | 0.652583i | ||||
\(142\) | 0.339853 | − | 0.820478i | 0.339853 | − | 0.820478i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 4.36593 | − | 4.36593i | 4.36593 | − | 4.36593i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.94168 | − | 4.68763i | 1.94168 | − | 4.68763i | ||||
\(148\) | 2.52758 | − | 1.04696i | 2.52758 | − | 1.04696i | ||||
\(149\) | 1.97538i | 1.97538i | 0.156434 | + | 0.987688i | \(0.450000\pi\) | ||||
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(150\) | 1.24129 | + | 2.99673i | 1.24129 | + | 2.99673i | ||||
\(151\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.298474 | + | 1.88449i | −0.298474 | + | 1.88449i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.78201i | 1.78201i | 0.453990 | + | 0.891007i | \(0.350000\pi\) | ||||
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(158\) | −0.820478 | + | 0.339853i | −0.820478 | + | 0.339853i | ||||
\(159\) | 0.592533 | − | 1.43050i | 0.592533 | − | 1.43050i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.985090 | + | 0.985090i | −0.985090 | + | 0.985090i | ||||
\(163\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.68999i | 2.68999i | ||||||||
\(167\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(168\) | −7.39936 | − | 7.39936i | −7.39936 | − | 7.39936i | ||||
\(169\) | −1.00000 | −1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.0600500 | − | 0.144974i | −0.0600500 | − | 0.144974i | 0.891007 | − | 0.453990i | \(-0.150000\pi\) |
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.84206 | − | 0.763007i | 1.84206 | − | 0.763007i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.973696 | + | 0.403318i | 0.973696 | + | 0.403318i | ||||
\(178\) | −2.55834 | + | 2.55834i | −2.55834 | + | 2.55834i | ||||
\(179\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.21498i | 2.21498i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −2.61803 | −2.61803 | ||||||||
\(189\) | 2.18296 | + | 2.18296i | 2.18296 | + | 2.18296i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.41421i | 1.41421i | 0.707107 | + | 0.707107i | \(0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(192\) | −4.12464 | + | 1.70848i | −4.12464 | + | 1.70848i | ||||
\(193\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(194\) | −2.67256 | − | 1.10701i | −2.67256 | − | 1.10701i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.50811 | + | 5.50811i | −5.50811 | + | 5.50811i | ||||
\(197\) | 1.70711 | + | 0.707107i | 1.70711 | + | 0.707107i | 1.00000 | \(0\) | ||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(200\) | − | 3.07768i | − | 3.07768i | ||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.420808 | − | 0.420808i | −0.420808 | − | 0.420808i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 2.33269 | − | 3.80660i | 2.33269 | − | 3.80660i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2.65688 | + | 2.65688i | 2.65688 | + | 2.65688i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(212\) | −1.68088 | + | 1.68088i | −1.68088 | + | 1.68088i | ||||
\(213\) | 0.562984 | − | 0.562984i | 0.562984 | − | 0.562984i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 4.40263 | − | 1.82363i | 4.40263 | − | 1.82363i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 3.38959 | 3.38959 | ||||||||
\(223\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(224\) | 2.34830 | + | 5.66929i | 2.34830 | + | 5.66929i | ||||
\(225\) | 1.90798i | 1.90798i | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.14412 | − | 1.14412i | −1.14412 | − | 1.14412i | ||||
\(237\) | −0.796180 | −0.796180 | ||||||||
\(238\) | −3.23364 | − | 1.98158i | −3.23364 | − | 1.98158i | ||||
\(239\) | −1.17557 | −1.17557 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.399903 | + | 0.965451i | 0.399903 | + | 0.965451i | 0.987688 | + | 0.156434i | \(0.0500000\pi\) |
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(242\) | 1.90211i | 1.90211i | ||||||||
\(243\) | 0.276607 | − | 0.114574i | 0.276607 | − | 0.114574i | ||||
\(244\) | 1.30134 | − | 3.14170i | 1.30134 | − | 3.14170i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.922891 | + | 2.22806i | −0.922891 | + | 2.22806i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 0.312869i | − | 0.312869i | −0.987688 | − | 0.156434i | \(-0.950000\pi\) | ||
0.987688 | − | 0.156434i | \(-0.0500000\pi\) | |||||||
\(252\) | −3.81134 | − | 9.20140i | −3.81134 | − | 9.20140i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 1.00000 | ||||||||
\(257\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 2.08355i | − | 2.08355i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.67256 | + | 1.10701i | 2.67256 | + | 1.10701i | ||||
\(263\) | 0.437016 | − | 0.437016i | 0.437016 | − | 0.437016i | −0.453990 | − | 0.891007i | \(-0.650000\pi\) |
0.891007 | + | 0.453990i | \(0.150000\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.99673 | + | 1.24129i | −2.99673 | + | 1.24129i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.292893 | − | 0.707107i | −0.292893 | − | 0.707107i | 0.707107 | − | 0.707107i | \(-0.250000\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.312869 | −0.312869 | −0.156434 | − | 0.987688i | \(-0.550000\pi\) | ||||
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(272\) | −2.61803 | + | 1.90211i | −2.61803 | + | 1.90211i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.431351 | − | 0.178671i | 0.431351 | − | 0.178671i | −0.156434 | − | 0.987688i | \(-0.550000\pi\) |
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(282\) | −2.99673 | − | 1.24129i | −2.99673 | − | 1.24129i | ||||
\(283\) | 0.763007 | − | 1.84206i | 0.763007 | − | 1.84206i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
0.453990 | − | 0.891007i | \(-0.350000\pi\) | |||||||
\(284\) | −1.12929 | + | 0.467768i | −1.12929 | + | 0.467768i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −5.87216 | −5.87216 | ||||||||
\(289\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.83382 | − | 1.83382i | −1.83382 | − | 1.83382i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(294\) | −8.91640 | + | 3.69329i | −8.91640 | + | 3.69329i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2.97135 | − | 1.23078i | −2.97135 | − | 1.23078i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.65688 | − | 2.65688i | 2.65688 | − | 2.65688i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 1.70848 | − | 4.12464i | 1.70848 | − | 4.12464i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.204173 | − | 0.492917i | −0.204173 | − | 0.492917i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 2.93608 | − | 2.13319i | 2.93608 | − | 2.13319i | ||||
\(307\) | −0.312869 | −0.312869 | −0.156434 | − | 0.987688i | \(-0.550000\pi\) | ||||
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.28910 | + | 3.11215i | 1.28910 | + | 3.11215i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(314\) | 2.39680 | − | 2.39680i | 2.39680 | − | 2.39680i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.12929 | + | 0.467768i | 1.12929 | + | 0.467768i | ||||
\(317\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(318\) | −2.72097 | + | 1.12706i | −2.72097 | + | 1.12706i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 1.91748 | 1.91748 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.763007 | + | 1.84206i | −0.763007 | + | 1.84206i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.34500 | + | 1.34500i | −1.34500 | + | 1.34500i | −0.453990 | + | 0.891007i | \(0.650000\pi\) |
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(332\) | 2.61803 | − | 2.61803i | 2.61803 | − | 2.61803i | ||||
\(333\) | 1.84206 | + | 0.763007i | 1.84206 | + | 0.763007i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 11.0028i | 11.0028i | ||||||||
\(337\) | 0.0600500 | + | 0.144974i | 0.0600500 | + | 0.144974i | 0.951057 | − | 0.309017i | \(-0.100000\pi\) |
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(338\) | 1.34500 | + | 1.34500i | 1.34500 | + | 1.34500i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.50723 | + | 3.63877i | 1.50723 | + | 3.63877i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.114222 | + | 0.275756i | −0.114222 | + | 0.275756i | ||||
\(347\) | 1.57547 | + | 0.652583i | 1.57547 | + | 0.652583i | 0.987688 | − | 0.156434i | \(-0.0500000\pi\) |
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(350\) | −3.50381 | − | 1.45133i | −3.50381 | − | 1.45133i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 1.78201i | − | 1.78201i | −0.453990 | − | 0.891007i | \(-0.650000\pi\) | ||
0.453990 | − | 0.891007i | \(-0.350000\pi\) | |||||||
\(354\) | −0.767157 | − | 1.85208i | −0.767157 | − | 1.85208i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 4.97980 | 4.97980 | ||||||||
\(357\) | −1.99850 | − | 2.75070i | −1.99850 | − | 2.75070i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000i | 1.00000i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.652583 | + | 1.57547i | −0.652583 | + | 1.57547i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2.97914 | − | 2.97914i | 2.97914 | − | 2.97914i | ||||
\(367\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.692796 | + | 1.67256i | 0.692796 | + | 1.67256i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.17625 | + | 2.17625i | 2.17625 | + | 2.17625i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | − | 5.87216i | − | 5.87216i | ||||||
\(379\) | −0.144974 | + | 0.0600500i | −0.144974 | + | 0.0600500i | −0.453990 | − | 0.891007i | \(-0.650000\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.90211 | − | 1.90211i | 1.90211 | − | 1.90211i | ||||
\(383\) | −1.39680 | + | 1.39680i | −1.39680 | + | 1.39680i | −0.587785 | + | 0.809017i | \(0.700000\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(384\) | 2.99673 | + | 1.24129i | 2.99673 | + | 1.24129i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.52367 | + | 3.67846i | 1.52367 | + | 3.67846i | ||||
\(389\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 9.15727 | 9.15727 | ||||||||
\(393\) | 1.83382 | + | 1.83382i | 1.83382 | + | 1.83382i | ||||
\(394\) | −1.34500 | − | 3.24711i | −1.34500 | − | 3.24711i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.744220 | − | 1.79671i | 0.744220 | − | 1.79671i | 0.156434 | − | 0.987688i | \(-0.450000\pi\) |
0.587785 | − | 0.809017i | \(-0.300000\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.28825 | + | 2.28825i | −2.28825 | + | 2.28825i | ||||
\(401\) | −1.57547 | − | 0.652583i | −1.57547 | − | 0.652583i | −0.587785 | − | 0.809017i | \(-0.700000\pi\) |
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0.819101i | 0.819101i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −5.10330 | + | 1.22519i | −5.10330 | + | 1.22519i | ||||
\(409\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 5.17160i | − | 5.17160i | ||||||
\(413\) | −1.13846 | + | 0.471565i | −1.13846 | + | 0.471565i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.34915 | − | 1.34915i | −1.34915 | − | 1.34915i | ||||
\(424\) | 2.79448 | 2.79448 | ||||||||
\(425\) | 0.156434 | − | 0.987688i | 0.156434 | − | 0.987688i | ||||
\(426\) | −1.51442 | −1.51442 | ||||||||
\(427\) | −1.83125 | − | 1.83125i | −1.83125 | − | 1.83125i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.581990 | + | 1.40505i | −0.581990 | + | 1.40505i | 0.309017 | + | 0.951057i | \(0.400000\pi\) |
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(432\) | −4.62920 | − | 1.91748i | −4.62920 | − | 1.91748i | ||||
\(433\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.707107 | + | 1.70711i | 0.707107 | + | 1.70711i | 0.707107 | + | 0.707107i | \(0.250000\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.67696 | −5.67696 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(444\) | −3.29892 | − | 3.29892i | −3.29892 | − | 3.29892i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.11215 | − | 1.28910i | 3.11215 | − | 1.28910i | ||||
\(448\) | 1.99758 | − | 4.82258i | 1.99758 | − | 4.82258i | ||||
\(449\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(450\) | 2.56623 | − | 2.56623i | 2.56623 | − | 2.56623i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.221232 | + | 0.221232i | 0.221232 | + | 0.221232i | 0.809017 | − | 0.587785i | \(-0.200000\pi\) |
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.50558 | − | 0.361458i | 1.50558 | − | 0.361458i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.80751 | − | 1.16291i | 2.80751 | − | 1.16291i | ||||
\(472\) | 1.90211i | 1.90211i | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 1.07086 | + | 1.07086i | 1.07086 | + | 1.07086i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.21857 | + | 5.07570i | 1.21857 | + | 5.07570i | ||||
\(477\) | −1.73241 | −1.73241 | ||||||||
\(478\) | 1.58114 | + | 1.58114i | 1.58114 | + | 1.58114i | ||||
\(479\) | −0.763007 | − | 1.84206i | −0.763007 | − | 1.84206i | −0.453990 | − | 0.891007i | \(-0.650000\pi\) |
−0.309017 | − | 0.951057i | \(-0.600000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0.760661 | − | 1.83640i | 0.760661 | − | 1.83640i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.85123 | − | 1.85123i | 1.85123 | − | 1.85123i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.526137 | − | 0.217933i | −0.526137 | − | 0.217933i | ||||
\(487\) | −0.707107 | + | 1.70711i | −0.707107 | + | 1.70711i | 1.00000i | \(0.5\pi\) | ||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(488\) | −3.69329 | + | 1.52981i | −3.69329 | + | 1.52981i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.26007 | + | 1.26007i | 1.26007 | + | 1.26007i | 0.951057 | + | 0.309017i | \(0.100000\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.930903i | 0.930903i | ||||||||
\(498\) | 4.23801 | − | 1.75544i | 4.23801 | − | 1.75544i | ||||
\(499\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −0.420808 | + | 0.420808i | −0.420808 | + | 0.420808i | ||||
\(503\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(504\) | −4.48050 | + | 10.8169i | −4.48050 | + | 10.8169i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.652583 | + | 1.57547i | 0.652583 | + | 1.57547i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −2.80237 | + | 2.80237i | −2.80237 | + | 2.80237i | ||||
\(519\) | −0.189214 | + | 0.189214i | −0.189214 | + | 0.189214i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.0600500 | + | 0.144974i | −0.0600500 | + | 0.144974i | −0.951057 | − | 0.309017i | \(-0.900000\pi\) |
0.891007 | + | 0.453990i | \(0.150000\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(524\) | −1.52367 | − | 3.67846i | −1.52367 | − | 3.67846i | ||||
\(525\) | −2.40420 | − | 2.40420i | −2.40420 | − | 2.40420i | ||||
\(526\) | −1.17557 | −1.17557 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 1.17920i | − | 1.17920i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 5.70012 | + | 2.36107i | 5.70012 | + | 2.36107i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −0.557116 | + | 1.34500i | −0.557116 | + | 1.34500i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.0600500 | − | 0.144974i | −0.0600500 | − | 0.144974i | 0.891007 | − | 0.453990i | \(-0.150000\pi\) |
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(542\) | 0.420808 | + | 0.420808i | 0.420808 | + | 0.420808i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.03979 | + | 0.481456i | 3.03979 | + | 0.481456i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.28962 | − | 0.948393i | 2.28962 | − | 0.948393i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.658248 | − | 0.658248i | 0.658248 | − | 0.658248i | ||||
\(554\) | −0.820478 | − | 0.339853i | −0.820478 | − | 0.339853i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(564\) | 1.70848 | + | 4.12464i | 1.70848 | + | 4.12464i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −3.50381 | + | 1.45133i | −3.50381 | + | 1.45133i | ||||
\(567\) | 0.558835 | − | 1.34915i | 0.558835 | − | 1.34915i | ||||
\(568\) | 1.32756 | + | 0.549894i | 1.32756 | + | 0.549894i | ||||
\(569\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.79671 | + | 0.744220i | 1.79671 | + | 0.744220i | 0.987688 | + | 0.156434i | \(0.0500000\pi\) |
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.22806 | − | 0.922891i | 2.22806 | − | 0.922891i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 3.53211 | + | 3.53211i | 3.53211 | + | 3.53211i | ||||
\(577\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(578\) | −1.69480 | + | 0.863541i | −1.69480 | + | 0.863541i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.07906 | − | 2.60507i | −1.07906 | − | 2.60507i | ||||
\(582\) | 4.93296i | 4.93296i | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(588\) | 12.2724 | + | 5.08338i | 12.2724 | + | 5.08338i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 3.15095i | − | 3.15095i | ||||||
\(592\) | 1.29411 | + | 3.12427i | 1.29411 | + | 3.12427i | ||||
\(593\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5.17160 | −5.17160 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(600\) | −4.84881 | + | 2.00844i | −4.84881 | + | 2.00844i | ||||
\(601\) | −0.497066 | + | 1.20002i | −0.497066 | + | 1.20002i | 0.453990 | + | 0.891007i | \(0.350000\pi\) |
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −0.388360 | + | 0.937583i | −0.388360 | + | 0.937583i | ||||
\(607\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −4.93366 | − | 0.781415i | −4.93366 | − | 0.781415i | ||||
\(613\) | −1.90211 | −1.90211 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(614\) | 0.420808 | + | 0.420808i | 0.420808 | + | 0.420808i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.79671 | + | 0.744220i | −1.79671 | + | 0.744220i | −0.809017 | + | 0.587785i | \(0.800000\pi\) |
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(618\) | 2.45201 | − | 5.91967i | 2.45201 | − | 5.91967i | ||||
\(619\) | −0.707107 | − | 0.292893i | −0.707107 | − | 0.292893i | − | 1.00000i | \(-0.5\pi\) | |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.45133 | − | 3.50381i | 1.45133 | − | 3.50381i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | − | 1.00000i | − | 1.00000i | ||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −4.66537 | −4.66537 | ||||||||
\(629\) | −0.891007 | − | 0.546010i | −0.891007 | − | 0.546010i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(632\) | −0.549894 | − | 1.32756i | −0.549894 | − | 1.32756i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 3.74510 | + | 1.55127i | 3.74510 | + | 1.55127i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.823009 | − | 0.340902i | −0.823009 | − | 0.340902i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.497066 | + | 1.20002i | 0.497066 | + | 1.20002i | 0.951057 | + | 0.309017i | \(0.100000\pi\) |
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.78201 | −1.78201 | −0.891007 | − | 0.453990i | \(-0.850000\pi\) | ||||
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(648\) | −1.59391 | − | 1.59391i | −1.59391 | − | 1.59391i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0.965451 | + | 0.399903i | 0.965451 | + | 0.399903i | 0.809017 | − | 0.587785i | \(-0.200000\pi\) |
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3.50381 | − | 1.45133i | 3.50381 | − | 1.45133i | ||||
\(659\) | 1.61803i | 1.61803i | 0.587785 | + | 0.809017i | \(0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.831254 | + | 0.831254i | 0.831254 | + | 0.831254i | 0.987688 | − | 0.156434i | \(-0.0500000\pi\) |
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(662\) | 3.61803 | 3.61803 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.35250 | −4.35250 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.45133 | − | 3.50381i | −1.45133 | − | 3.50381i | ||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 7.39936 | − | 7.39936i | 7.39936 | − | 7.39936i | ||||
\(673\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(674\) | 0.114222 | − | 0.275756i | 0.114222 | − | 0.275756i | ||||
\(675\) | 1.43050 | − | 0.592533i | 1.43050 | − | 0.592533i | ||||
\(676\) | − | 2.61803i | − | 2.61803i | ||||||
\(677\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.03225 | 3.03225 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.497066 | − | 1.20002i | −0.497066 | − | 1.20002i | −0.951057 | − | 0.309017i | \(-0.900000\pi\) |
0.453990 | − | 0.891007i | \(-0.350000\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 2.86692 | − | 6.92135i | 2.86692 | − | 6.92135i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(692\) | 0.379546 | − | 0.157213i | 0.379546 | − | 0.157213i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.24129 | − | 2.99673i | −1.24129 | − | 2.99673i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.99758 | + | 4.82258i | 1.99758 | + | 4.82258i | ||||
\(701\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.39680 | + | 2.39680i | −2.39680 | + | 2.39680i | ||||
\(707\) | 0.576324 | + | 0.238721i | 0.576324 | + | 0.238721i | ||||
\(708\) | −1.05590 | + | 2.54917i | −1.05590 | + | 2.54917i | ||||
\(709\) | 1.84206 | − | 0.763007i | 1.84206 | − | 0.763007i | 0.891007 | − | 0.453990i | \(-0.150000\pi\) |
0.951057 | − | 0.309017i | \(-0.100000\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.340902 | + | 0.823009i | 0.340902 | + | 0.823009i | ||||
\(712\) | −4.13948 | − | 4.13948i | −4.13948 | − | 4.13948i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | −1.01170 | + | 6.38765i | −1.01170 | + | 6.38765i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.767157 | + | 1.85208i | 0.767157 | + | 1.85208i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.20002 | − | 0.497066i | 1.20002 | − | 0.497066i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
0.891007 | + | 0.453990i | \(0.150000\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.63877 | − | 1.50723i | −3.63877 | − | 1.50723i | ||||
\(722\) | 1.34500 | − | 1.34500i | 1.34500 | − | 1.34500i | ||||
\(723\) | 1.26007 | − | 1.26007i | 1.26007 | − | 1.26007i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 2.99673 | − | 1.24129i | 2.99673 | − | 1.24129i | ||||
\(727\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.878910 | − | 0.878910i | −0.878910 | − | 0.878910i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −5.79890 | −5.79890 | ||||||||
\(733\) | 0.831254 | + | 0.831254i | 0.831254 | + | 0.831254i | 0.987688 | − | 0.156434i | \(-0.0500000\pi\) |
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.26007 | + | 1.26007i | −1.26007 | + | 1.26007i | −0.309017 | + | 0.951057i | \(0.600000\pi\) |
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.31778 | − | 3.18139i | 1.31778 | − | 3.18139i | ||||
\(743\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.69829 | 2.69829 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(752\) | − | 3.23607i | − | 3.23607i | ||||||
\(753\) | −0.492917 | + | 0.204173i | −0.492917 | + | 0.204173i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −5.71508 | + | 5.71508i | −5.71508 | + | 5.71508i | ||||
\(757\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(758\) | 0.275756 | + | 0.114222i | 0.275756 | + | 0.114222i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 1.41421i | − | 1.41421i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −3.70246 | −3.70246 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.75739 | 3.75739 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −0.652583 | − | 1.57547i | −0.652583 | − | 1.57547i | ||||
\(769\) | 1.17557i | 1.17557i | 0.809017 | + | 0.587785i | \(0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −0.831254 | + | 0.831254i | −0.831254 | + | 0.831254i | −0.987688 | − | 0.156434i | \(-0.950000\pi\) |
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.79118 | − | 4.32429i | 1.79118 | − | 4.32429i | ||||
\(777\) | −3.28258 | + | 1.35969i | −3.28258 | + | 1.35969i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.80839 | − | 6.80839i | −6.80839 | − | 6.80839i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | − | 4.93296i | − | 4.93296i | ||||||
\(787\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(788\) | −1.85123 | + | 4.46926i | −1.85123 | + | 4.46926i | ||||
\(789\) | −0.973696 | − | 0.403318i | −0.973696 | − | 0.403318i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −3.41754 | + | 1.41559i | −3.41754 | + | 1.41559i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.587785 | + | 0.809017i | 0.587785 | + | 0.809017i | ||||
\(800\) | 3.07768 | 3.07768 | ||||||||
\(801\) | 2.56623 | + | 2.56623i | 2.56623 | + | 2.56623i | ||||
\(802\) | 1.24129 | + | 2.99673i | 1.24129 | + | 2.99673i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.922891 | + | 0.922891i | −0.922891 | + | 0.922891i | ||||
\(808\) | 0.680881 | − | 0.680881i | 0.680881 | − | 0.680881i | ||||
\(809\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.431351 | + | 0.178671i | −0.431351 | + | 0.178671i | −0.587785 | − | 0.809017i | \(-0.700000\pi\) |
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.204173 | + | 0.492917i | 0.204173 | + | 0.492917i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 4.70521 | + | 2.88336i | 4.70521 | + | 2.88336i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.707107 | − | 0.292893i | −0.707107 | − | 0.292893i | − | 1.00000i | \(-0.5\pi\) | |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(824\) | −4.29892 | + | 4.29892i | −4.29892 | + | 4.29892i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.16547 | + | 0.896969i | 2.16547 | + | 0.896969i | ||||
\(827\) | −0.497066 | + | 1.20002i | −0.497066 | + | 1.20002i | 0.453990 | + | 0.891007i | \(0.350000\pi\) |
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.562984 | − | 0.562984i | −0.562984 | − | 0.562984i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.93874 | + | 0.465451i | 2.93874 | + | 0.465451i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 3.62920i | 3.62920i | ||||||||
\(847\) | −0.763007 | − | 1.84206i | −0.763007 | − | 1.84206i | ||||
\(848\) | −2.07768 | − | 2.07768i | −2.07768 | − | 2.07768i | ||||
\(849\) | −3.40005 | −3.40005 | ||||||||
\(850\) | −1.53884 | + | 1.11803i | −1.53884 | + | 1.11803i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 1.47391 | + | 1.47391i | 1.47391 | + | 1.47391i | ||||
\(853\) | −0.744220 | − | 1.79671i | −0.744220 | − | 1.79671i | −0.587785 | − | 0.809017i | \(-0.700000\pi\) |
−0.156434 | − | 0.987688i | \(-0.550000\pi\) | |||||||
\(854\) | 4.92606i | 4.92606i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.67256 | − | 1.10701i | 2.67256 | − | 1.10701i | ||||
\(863\) | − | 1.61803i | − | 1.61803i | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||
0.587785 | − | 0.809017i | \(-0.300000\pi\) | |||||||
\(864\) | 1.82363 | + | 4.40263i | 1.82363 | + | 4.40263i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.70002 | + | 0.133795i | −1.70002 | + | 0.133795i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.11042 | + | 2.68080i | −1.11042 | + | 2.68080i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(878\) | 1.34500 | − | 3.24711i | 1.34500 | − | 3.24711i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(882\) | 7.63550 | + | 7.63550i | 7.63550 | + | 7.63550i | ||||
\(883\) | −1.78201 | −1.78201 | −0.891007 | − | 0.453990i | \(-0.850000\pi\) | ||||
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(888\) | 5.48447i | 5.48447i | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −5.91967 | − | 2.45201i | −5.91967 | − | 2.45201i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3.50381 | + | 1.45133i | −3.50381 | + | 1.45133i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −4.99516 | −4.99516 | ||||||||
\(901\) | 0.896802 | + | 0.142040i | 0.896802 | + | 0.142040i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.292893 | − | 0.707107i | 0.292893 | − | 0.707107i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
1.00000 | \(0\) | |||||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.422106 | + | 0.422106i | −0.422106 | + | 0.422106i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.20002 | + | 0.497066i | 1.20002 | + | 0.497066i | 0.891007 | − | 0.453990i | \(-0.150000\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | − | 0.595112i | − | 0.595112i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.03225 | −3.03225 | ||||||||
\(918\) | −2.51116 | − | 1.53884i | −2.51116 | − | 1.53884i | ||||
\(919\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.204173 | + | 0.492917i | 0.204173 | + | 0.492917i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.965451 | − | 0.399903i | −0.965451 | − | 0.399903i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.66507 | − | 2.66507i | 2.66507 | − | 2.66507i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −0.399903 | + | 0.965451i | −0.399903 | + | 0.965451i | 0.587785 | + | 0.809017i | \(0.300000\pi\) |
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.581990 | − | 1.40505i | 0.581990 | − | 1.40505i | −0.309017 | − | 0.951057i | \(-0.600000\pi\) |
0.891007 | − | 0.453990i | \(-0.150000\pi\) | |||||||
\(942\) | −5.34021 | − | 2.21199i | −5.34021 | − | 2.21199i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 1.41421 | − | 1.41421i | 1.41421 | − | 1.41421i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −0.707107 | + | 0.292893i | −0.707107 | + | 0.292893i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(948\) | − | 2.08443i | − | 2.08443i | ||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 3.20626 | − | 5.23213i | 3.20626 | − | 5.23213i | ||||
\(953\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(954\) | 2.33009 | + | 2.33009i | 2.33009 | + | 2.33009i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 3.07768i | − | 3.07768i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.45133 | + | 3.50381i | −1.45133 | + | 3.50381i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.52758 | + | 1.04696i | −2.52758 | + | 1.04696i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.26007 | − | 1.26007i | −1.26007 | − | 1.26007i | −0.951057 | − | 0.309017i | \(-0.900000\pi\) |
−0.309017 | − | 0.951057i | \(-0.600000\pi\) | |||||||
\(968\) | −3.07768 | −3.07768 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(972\) | 0.299959 | + | 0.724166i | 0.299959 | + | 0.724166i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 3.24711 | − | 1.34500i | 3.24711 | − | 1.34500i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.88336 | + | 1.60854i | 3.88336 | + | 1.60854i | ||||
\(977\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 3.38959i | − | 3.38959i | ||||||
\(983\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.40005 | 3.40005 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.20002 | + | 0.497066i | −1.20002 | + | 0.497066i | −0.891007 | − | 0.453990i | \(-0.850000\pi\) |
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.99673 | + | 1.24129i | 2.99673 | + | 1.24129i | ||||
\(994\) | 1.25206 | − | 1.25206i | 1.25206 | − | 1.25206i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −5.83313 | − | 2.41616i | −5.83313 | − | 2.41616i | ||||
\(997\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 1.61803i | − | 1.61803i |
(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 | 799.1.h.b.610.1 | yes | 16 | |
17.8 | even | 8 | inner | 799.1.h.b.93.1 | ✓ | 16 | |
47.46 | odd | 2 | CM | 799.1.h.b.610.1 | yes | 16 | |
799.93 | odd | 8 | inner | 799.1.h.b.93.1 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
799.1.h.b.93.1 | ✓ | 16 | 17.8 | even | 8 | inner | |
799.1.h.b.93.1 | ✓ | 16 | 799.93 | odd | 8 | inner | |
799.1.h.b.610.1 | yes | 16 | 1.1 | even | 1 | trivial | |
799.1.h.b.610.1 | yes | 16 | 47.46 | odd | 2 | CM |