Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [776,1,Mod(43,776)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(776, base_ring=CyclotomicField(24))
chi = DirichletCharacter(H, H._module([12, 12, 1]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("776.43");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 776.bh (of order , degree , 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: | |
Analytic rank: | |
Dimension: | |
Coefficient field: | |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
|
Coefficient ring: | |
Coefficient ring index: | |
Twist minimal: | yes |
Projective image: | |
Projective field: | Galois closure of |
Embedding invariants
Embedding label | 539.1 | ||
Root | of defining polynomial | ||
Character | 776.539 | ||
Dual form | 776.1.bh.a.203.1 |
-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 on generators for .
Coefficient data
For each we display the coefficients of the -expansion , the Satake parameters , and the Satake angles .
0.258819 | + | 0.965926i | 0.258819 | + | 0.965926i | |||||
−0.500000 | + | 0.133975i | −0.500000 | + | 0.133975i | −0.500000 | − | 0.866025i | ||
1.00000i | ||||||||||
−0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | |||||
0 | 0 | 0.130526 | − | 0.991445i | ||||||
−0.130526 | + | 0.991445i | ||||||||
−0.258819 | − | 0.448288i | −0.258819 | − | 0.448288i | |||||
0 | 0 | 0.793353 | − | 0.608761i | ||||||
−0.793353 | + | 0.608761i | ||||||||
−0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | |||||
−0.633975 | + | 0.366025i | −0.633975 | + | 0.366025i | |||||
0 | 0 | |||||||||
−0.448288 | + | 1.67303i | −0.448288 | + | 1.67303i | 0.258819 | + | 0.965926i | ||
−0.707107 | + | 0.707107i | ||||||||
0.366025 | − | 0.366025i | 0.366025 | − | 0.366025i | |||||
0 | 0 | 0.130526 | − | 0.991445i | ||||||
−0.130526 | + | 0.991445i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | |||||
0.607206 | + | 0.465926i | 0.607206 | + | 0.465926i | 0.866025 | − | 0.500000i | ||
−0.258819 | + | 0.965926i | ||||||||
−0.517638 | − | 0.517638i | −0.517638 | − | 0.517638i | |||||
−1.70711 | + | 0.707107i | −1.70711 | + | 0.707107i | −0.707107 | + | 0.707107i | ||
−1.00000 | ||||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.73205 | −1.73205 | |||||||||
0 | 0 | 0.608761 | − | 0.793353i | ||||||
−0.608761 | + | 0.793353i | ||||||||
0.448288 | + | 0.258819i | 0.448288 | + | 0.258819i | |||||
−0.965926 | − | 0.258819i | −0.965926 | − | 0.258819i | |||||
0 | 0 | |||||||||
0.633975 | − | 0.633975i | 0.633975 | − | 0.633975i | |||||
0 | 0 | |||||||||
0 | 0 | −0.991445 | − | 0.130526i | ||||||
0.991445 | + | 0.130526i | ||||||||
0 | 0 | |||||||||
0 | 0 | 0.965926 | − | 0.258819i | ||||||
−0.965926 | + | 0.258819i | ||||||||
0.965926 | + | 0.258819i | 0.965926 | + | 0.258819i | |||||
− | 0.896575i | − | 0.896575i | |||||||
−0.292893 | + | 0.707107i | −0.292893 | + | 0.707107i | |||||
0 | 0 | |||||||||
0.366025 | − | 0.633975i | 0.366025 | − | 0.633975i | |||||
0 | 0 | −0.608761 | − | 0.793353i | ||||||
0.608761 | + | 0.793353i | ||||||||
−1.12484 | − | 1.46593i | −1.12484 | − | 1.46593i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.83195 | + | 0.241181i | 1.83195 | + | 0.241181i | 0.965926 | − | 0.258819i | ||
0.866025 | + | 0.500000i | ||||||||
0 | 0 | |||||||||
1.67303 | + | 0.965926i | 1.67303 | + | 0.965926i | 0.965926 | + | 0.258819i | ||
0.707107 | + | 0.707107i | ||||||||
−0.448288 | − | 1.67303i | −0.448288 | − | 1.67303i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | − | 1.00000i | |||||||
1.00000i | ||||||||||
−0.133975 | + | 0.500000i | −0.133975 | + | 0.500000i | |||||
0.258819 | − | 0.965926i | 0.258819 | − | 0.965926i | |||||
− | 1.00000i | − | 1.00000i | |||||||
−0.366025 | − | 0.151613i | −0.366025 | − | 0.151613i | |||||
0 | 0 | |||||||||
0 | 0 | −0.258819 | − | 0.965926i | ||||||
0.258819 | + | 0.965926i | ||||||||
0.776457 | + | 0.448288i | 0.776457 | + | 0.448288i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.758819 | − | 0.582262i | 0.758819 | − | 0.582262i | |||||
0 | 0 | |||||||||
−0.465926 | − | 0.607206i | −0.465926 | − | 0.607206i | 0.500000 | − | 0.866025i | ||
−0.965926 | + | 0.258819i | ||||||||
0 | 0 | |||||||||
0 | 0 | 0.500000 | − | 0.866025i | ||||||
−0.500000 | + | 0.866025i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.00000i | 1.00000i | |||||||||
0 | 0 | |||||||||
0.866025 | − | 0.232051i | 0.866025 | − | 0.232051i | |||||
−1.83195 | + | 0.758819i | −1.83195 | + | 0.758819i | −0.866025 | + | 0.500000i | ||
−0.965926 | + | 0.258819i | ||||||||
−0.758819 | − | 0.0999004i | −0.758819 | − | 0.0999004i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.991445 | − | 0.130526i | ||||||
−0.991445 | + | 0.130526i | ||||||||
0.707107 | + | 0.189469i | 0.707107 | + | 0.189469i | |||||
0 | 0 | 0.500000 | − | 0.866025i | ||||||
−0.500000 | + | 0.866025i | ||||||||
0 | 0 | |||||||||
0.517638 | 0.517638 | |||||||||
1.12484 | − | 1.46593i | 1.12484 | − | 1.46593i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.707107 | − | 0.707107i | ||||||
0.707107 | + | 0.707107i | ||||||||
0 | 0 | |||||||||
0.133975 | − | 0.232051i | 0.133975 | − | 0.232051i | |||||
0.241181 | + | 1.83195i | 0.241181 | + | 1.83195i | |||||
0.965926 | + | 0.741181i | 0.965926 | + | 0.741181i | 0.965926 | − | 0.258819i | ||
1.00000i | ||||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.500000 | + | 1.86603i | −0.500000 | + | 1.86603i | |||||
0 | 0 | |||||||||
1.50000 | − | 0.866025i | 1.50000 | − | 0.866025i | |||||
1.36603 | + | 1.36603i | 1.36603 | + | 1.36603i | 0.866025 | + | 0.500000i | ||
0.500000 | + | 0.866025i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.517638 | −0.517638 | |||||||||
0.965926 | − | 0.258819i | 0.965926 | − | 0.258819i | |||||
1.00000 | 1.00000 | |||||||||
−0.328169 | − | 1.22474i | −0.328169 | − | 1.22474i | |||||
0.965926 | − | 0.258819i | 0.965926 | − | 0.258819i | |||||
0 | 0 | 0.866025 | − | 0.500000i | ||||||
−0.866025 | + | 0.500000i | ||||||||
0.0517123 | − | 0.392794i | 0.0517123 | − | 0.392794i | |||||
0 | 0 | −0.500000 | − | 0.866025i | ||||||
0.500000 | + | 0.866025i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.57313 | − | 0.207107i | 1.57313 | − | 0.207107i | 0.707107 | − | 0.707107i | ||
0.866025 | + | 0.500000i | ||||||||
−0.232051 | + | 0.866025i | −0.232051 | + | 0.866025i | |||||
0 | 0 | 0.707107 | − | 0.707107i | ||||||
−0.707107 | + | 0.707107i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.965926 | + | 1.67303i | −0.965926 | + | 1.67303i | −0.258819 | + | 0.965926i | ||
−0.707107 | + | 0.707107i | ||||||||
0.758819 | + | 0.582262i | 0.758819 | + | 0.582262i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.465926 | − | 0.607206i | 0.465926 | − | 0.607206i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.73205 | − | 1.00000i | −1.73205 | − | 1.00000i | |||||
0 | 0 | |||||||||
−0.948288 | + | 0.124844i | −0.948288 | + | 0.124844i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.923880 | − | 0.382683i | ||||||
−0.923880 | + | 0.382683i | ||||||||
−0.965926 | + | 0.258819i | −0.965926 | + | 0.258819i | |||||
−0.965926 | − | 0.258819i | −0.965926 | − | 0.258819i | |||||
0 | 0 | |||||||||
0.607206 | − | 1.46593i | 0.607206 | − | 1.46593i | −0.258819 | − | 0.965926i | ||
0.866025 | − | 0.500000i | ||||||||
0.448288 | + | 0.776457i | 0.448288 | + | 0.776457i | |||||
0 | 0 | |||||||||
−1.20711 | − | 1.57313i | −1.20711 | − | 1.57313i | |||||
0 | 0 | |||||||||
−0.0999004 | − | 0.758819i | −0.0999004 | − | 0.758819i | |||||
0.207107 | − | 0.158919i | 0.207107 | − | 0.158919i | −0.500000 | − | 0.866025i | ||
0.707107 | + | 0.707107i | ||||||||
0 | 0 | |||||||||
−0.241181 | − | 0.0999004i | −0.241181 | − | 0.0999004i | 0.258819 | − | 0.965926i | ||
−0.500000 | + | 0.866025i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.732051i | 0.732051i | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.517638i | 0.517638i | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.382683 | − | 0.923880i | ||||||
0.382683 | + | 0.923880i | ||||||||
0.133975 | + | 0.500000i | 0.133975 | + | 0.500000i | |||||
0 | 0 | −0.866025 | − | 0.500000i | ||||||
0.866025 | + | 0.500000i | ||||||||
1.70711 | + | 0.707107i | 1.70711 | + | 0.707107i | |||||
−0.555494 | − | 0.0731322i | −0.555494 | − | 0.0731322i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.608761 | − | 0.793353i | ||||||
0.608761 | + | 0.793353i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.258819 | + | 0.0693504i | 0.258819 | + | 0.0693504i | |||||
0.965926 | − | 0.258819i | 0.965926 | − | 0.258819i | 0.258819 | − | 0.965926i | ||
0.707107 | + | 0.707107i | ||||||||
−1.70711 | + | 0.707107i | −1.70711 | + | 0.707107i | |||||
0 | 0 | |||||||||
−0.465926 | + | 1.12484i | −0.465926 | + | 1.12484i | |||||
0 | 0 | 0.707107 | − | 0.707107i | ||||||
−0.707107 | + | 0.707107i | ||||||||
0 | 0 | |||||||||
−0.965926 | − | 0.258819i | −0.965926 | − | 0.258819i | |||||
0 | 0 | |||||||||
0.823443 | − | 1.07313i | 0.823443 | − | 1.07313i | |||||
−1.93185 | −1.93185 | |||||||||
0 | 0 | 0.608761 | − | 0.793353i | ||||||
−0.608761 | + | 0.793353i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.22474 | + | 1.22474i | 1.22474 | + | 1.22474i | |||||
0.314313 | + | 0.241181i | 0.314313 | + | 0.241181i | |||||
−0.965926 | + | 1.67303i | −0.965926 | + | 1.67303i | |||||
−0.0999004 | − | 0.758819i | −0.0999004 | − | 0.758819i | −0.965926 | − | 0.258819i | ||
0.866025 | − | 0.500000i | ||||||||
0 | 0 | |||||||||
0 | 0 | 0.130526 | − | 0.991445i | ||||||
−0.130526 | + | 0.991445i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.05171 | + | 0.807007i | −1.05171 | + | 0.807007i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.965926 | − | 0.258819i | ||||||
−0.965926 | + | 0.258819i | ||||||||
−0.133975 | − | 0.500000i | −0.133975 | − | 0.500000i | |||||
−1.00000 | −1.00000 | −0.500000 | − | 0.866025i | ||||||
−0.500000 | + | 0.866025i | ||||||||
0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | |||||
0 | 0 | |||||||||
0.258819 | + | 0.965926i | 0.258819 | + | 0.965926i | |||||
0 | 0 | 0.965926 | − | 0.258819i | ||||||
−0.965926 | + | 0.258819i | ||||||||
1.09808 | − | 0.633975i | 1.09808 | − | 0.633975i | |||||
0 | 0 | 0.130526 | − | 0.991445i | ||||||
−0.130526 | + | 0.991445i | ||||||||
0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | |||||
0.814313 | − | 0.624844i | 0.814313 | − | 0.624844i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.392794 | − | 0.0517123i | 0.392794 | − | 0.0517123i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.417738 | − | 3.17303i | −0.417738 | − | 3.17303i | |||||
0 | 0 | |||||||||
−1.57313 | − | 1.20711i | −1.57313 | − | 1.20711i | −0.866025 | − | 0.500000i | ||
−0.707107 | − | 0.707107i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.607206 | + | 1.46593i | 0.607206 | + | 1.46593i | |||||
0 | 0 | |||||||||
−0.896575 | −0.896575 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.991445 | − | 0.130526i | ||||||
0.991445 | + | 0.130526i | ||||||||
0 | 0 | |||||||||
0.707107 | − | 0.189469i | 0.707107 | − | 0.189469i | |||||
−1.86603 | − | 0.500000i | −1.86603 | − | 0.500000i | |||||
1.00000i | 1.00000i | 0.866025 | + | 0.500000i | ||||||
−0.866025 | + | 0.500000i | ||||||||
−0.366025 | + | 0.883663i | −0.366025 | + | 0.883663i | |||||
0 | 0 | −0.500000 | − | 0.866025i | ||||||
0.500000 | + | 0.866025i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.158919 | − | 1.20711i | −0.158919 | − | 1.20711i | −0.866025 | − | 0.500000i | ||
0.707107 | − | 0.707107i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.707107 | + | 0.292893i | 0.707107 | + | 0.292893i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.382683 | − | 0.923880i | ||||||
0.382683 | + | 0.923880i | ||||||||
0 | 0 | |||||||||
2.00000i | 2.00000i | 1.00000i | ||||||||
1.00000i | ||||||||||
0.517638 | − | 1.93185i | 0.517638 | − | 1.93185i | |||||
−0.267949 | + | 1.00000i | −0.267949 | + | 1.00000i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.366025 | − | 0.883663i | −0.366025 | − | 0.883663i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.582262 | − | 0.241181i | −0.582262 | − | 0.241181i | |||||
0 | 0 | |||||||||
1.46593 | − | 1.12484i | 1.46593 | − | 1.12484i | 0.500000 | − | 0.866025i | ||
0.965926 | − | 0.258819i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | |||||
−0.607206 | + | 1.46593i | −0.607206 | + | 1.46593i | 0.258819 | + | 0.965926i | ||
−0.866025 | + | 0.500000i | ||||||||
− | 1.00000i | − | 1.00000i | |||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.57313 | + | 0.207107i | 1.57313 | + | 0.207107i | |||||
0 | 0 | 0.382683 | − | 0.923880i | ||||||
−0.382683 | + | 0.923880i | ||||||||
−0.633975 | + | 0.633975i | −0.633975 | + | 0.633975i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | |||||
1.20711 | − | 1.57313i | 1.20711 | − | 1.57313i | |||||
0 | 0 | 1.00000 | ||||||||
−1.00000 | ||||||||||
0 | 0 | |||||||||
0 | 0 | −0.382683 | − | 0.923880i | ||||||
0.382683 | + | 0.923880i | ||||||||
0.707107 | − | 0.292893i | 0.707107 | − | 0.292893i | |||||
0 | 0 | |||||||||
0.207107 | + | 0.158919i | 0.207107 | + | 0.158919i | |||||
0.866025 | − | 1.50000i | 0.866025 | − | 1.50000i | |||||
0 | 0 | |||||||||
0 | 0 | −0.793353 | − | 0.608761i | ||||||
0.793353 | + | 0.608761i | ||||||||
0.0340742 | − | 0.258819i | 0.0340742 | − | 0.258819i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.96593 | + | 0.258819i | −1.96593 | + | 0.258819i | −0.965926 | + | 0.258819i | ||
−1.00000 | ||||||||||
0 | 0 | |||||||||
0 | 0 | 0.707107 | − | 0.707107i | ||||||
−0.707107 | + | 0.707107i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.707107 | + | 0.189469i | −0.707107 | + | 0.189469i | |||||
−0.107206 | − | 0.400100i | −0.107206 | − | 0.400100i | |||||
0 | 0 | |||||||||
−0.448288 | + | 0.258819i | −0.448288 | + | 0.258819i | |||||
0 | 0 | |||||||||
0 | 0 | −0.258819 | − | 0.965926i | ||||||
0.258819 | + | 0.965926i | ||||||||
−0.500000 | + | 0.133975i | −0.500000 | + | 0.133975i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.776457 | + | 1.34486i | 0.776457 | + | 1.34486i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.448288 | + | 0.258819i | −0.448288 | + | 0.258819i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.241181 | + | 1.83195i | −0.241181 | + | 1.83195i | |||||
0 | 0 | |||||||||
−0.0731322 | − | 0.555494i | −0.0731322 | − | 0.555494i | |||||
0.258819 | − | 0.448288i | 0.258819 | − | 0.448288i | −0.707107 | − | 0.707107i | ||
0.965926 | + | 0.258819i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.382683 | − | 0.923880i | ||||||
0.382683 | + | 0.923880i | ||||||||
0 | 0 | |||||||||
−1.93185 | −1.93185 | −0.965926 | − | 0.258819i | ||||||
−0.965926 | + | 0.258819i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.991445 | − | 0.130526i | ||||||
−0.991445 | + | 0.130526i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.758819 | + | 0.314313i | −0.758819 | + | 0.314313i | |||||
0 | 0 | |||||||||
−1.36603 | − | 0.366025i | −1.36603 | − | 0.366025i | |||||
0.267949i | 0.267949i | |||||||||
0 | 0 | |||||||||
0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | |||||
0 | 0 | |||||||||
−1.12484 | − | 1.46593i | −1.12484 | − | 1.46593i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.207107 | + | 0.158919i | −0.207107 | + | 0.158919i | −0.707107 | − | 0.707107i | ||
0.500000 | + | 0.866025i | ||||||||
−1.20711 | − | 0.158919i | −1.20711 | − | 0.158919i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.12484 | + | 0.465926i | 1.12484 | + | 0.465926i | 0.866025 | − | 0.500000i | ||
0.258819 | + | 0.965926i | ||||||||
− | 1.00000i | − | 1.00000i | |||||||
0.258819 | − | 0.965926i | 0.258819 | − | 0.965926i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.24969 | + | 0.517638i | 1.24969 | + | 0.517638i | |||||
0 | 0 | |||||||||
−0.500000 | − | 1.86603i | −0.500000 | − | 1.86603i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.20711 | + | 0.158919i | 1.20711 | + | 0.158919i | 0.707107 | − | 0.707107i | ||
0.500000 | + | 0.866025i | ||||||||
0 | 0 | |||||||||
0 | 0 | −0.130526 | − | 0.991445i | ||||||
0.130526 | + | 0.991445i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.866025 | + | 1.50000i | −0.866025 | + | 1.50000i | |||||
1.00000 | + | 1.73205i | 1.00000 | + | 1.73205i | 0.500000 | + | 0.866025i | ||
0.500000 | + | 0.866025i | ||||||||
−0.151613 | + | 0.366025i | −0.151613 | + | 0.366025i | |||||
0 | 0 | |||||||||
−1.86603 | − | 0.500000i | −1.86603 | − | 0.500000i | |||||
0 | 0 | |||||||||
0.707107 | − | 0.292893i | 0.707107 | − | 0.292893i | |||||
0 | 0 | −0.991445 | − | 0.130526i | ||||||
0.991445 | + | 0.130526i | ||||||||
0 | 0 | |||||||||
1.70711 | − | 1.70711i | 1.70711 | − | 1.70711i | |||||
0 | 0 | |||||||||
1.00000 | + | 0.267949i | 1.00000 | + | 0.267949i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.608761 | − | 0.793353i | ||||||
−0.608761 | + | 0.793353i | ||||||||
0 | 0 | |||||||||
−1.24969 | + | 0.517638i | −1.24969 | + | 0.517638i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.130526 | − | 0.991445i | ||||||
0.130526 | + | 0.991445i | ||||||||
−1.05171 | − | 0.807007i | −1.05171 | − | 0.807007i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | − | 1.00000i | |||
0.866025 | + | 0.500000i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.130526 | − | 0.991445i | ||||||
−0.130526 | + | 0.991445i | ||||||||
0.448288 | − | 0.258819i | 0.448288 | − | 0.258819i | |||||
0 | 0 | |||||||||
−0.258819 | − | 0.965926i | −0.258819 | − | 0.965926i | |||||
−1.41421 | −1.41421 | |||||||||
−0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | |||||
0 | 0 | 1.00000 | ||||||||
−1.00000 | ||||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | |||||
−0.107206 | + | 0.814313i | −0.107206 | + | 0.814313i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.896575 | + | 0.896575i | 0.896575 | + | 0.896575i | |||||
0 | 0 | 0.866025 | − | 0.500000i | ||||||
−0.866025 | + | 0.500000i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | |||||
−0.0340742 | + | 0.258819i | −0.0340742 | + | 0.258819i | 0.965926 | + | 0.258819i | ||
−1.00000 | ||||||||||
0.814313 | + | 0.624844i | 0.814313 | + | 0.624844i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.151613 | + | 0.366025i | 0.151613 | + | 0.366025i | |||||
0.741181 | − | 0.965926i | 0.741181 | − | 0.965926i | −0.258819 | − | 0.965926i | ||
1.00000 | ||||||||||
0 | 0 | |||||||||
−0.0822623 | + | 0.107206i | −0.0822623 | + | 0.107206i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.133975 | + | 0.0176381i | 0.133975 | + | 0.0176381i | |||||
2.95680 | − | 1.22474i | 2.95680 | − | 1.22474i | |||||
−0.500000 | + | 0.133975i | −0.500000 | + | 0.133975i | −0.500000 | − | 0.866025i | ||
1.00000i | ||||||||||
0 | 0 | |||||||||
0 | 0 | − | 1.00000i | |||||||
1.00000i | ||||||||||
0.758819 | − | 1.83195i | 0.758819 | − | 1.83195i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.465926 | − | 0.607206i | −0.465926 | − | 0.607206i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.25882 | + | 0.965926i | −1.25882 | + | 0.965926i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.866025 | − | 0.500000i | ||||||
0.866025 | + | 0.500000i | ||||||||
−0.232051 | − | 0.866025i | −0.232051 | − | 0.866025i | |||||
0.758819 | + | 1.83195i | 0.758819 | + | 1.83195i | 0.500000 | + | 0.866025i | ||
0.258819 | + | 0.965926i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.923880 | − | 0.382683i | ||||||
0.923880 | + | 0.382683i | ||||||||
0 | 0 | |||||||||
0.189469 | + | 0.707107i | 0.189469 | + | 0.707107i | |||||
0 | 0 | |||||||||
0.241181 | + | 0.0999004i | 0.241181 | + | 0.0999004i | 0.500000 | − | 0.866025i | ||
−0.258819 | + | 0.965926i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.258819 | + | 0.448288i | −0.258819 | + | 0.448288i | −0.965926 | − | 0.258819i | ||
0.707107 | + | 0.707107i | ||||||||
0.366025 | + | 0.633975i | 0.366025 | + | 0.633975i | |||||
−1.22474 | + | 2.95680i | −1.22474 | + | 2.95680i | |||||
− | 1.93185i | − | 1.93185i | |||||||
0 | 0 | |||||||||
−0.965926 | + | 0.258819i | −0.965926 | + | 0.258819i | |||||
0 | 0 | |||||||||
−0.948288 | − | 0.124844i | −0.948288 | − | 0.124844i | |||||
0.607206 | − | 1.46593i | 0.607206 | − | 1.46593i | −0.258819 | − | 0.965926i | ||
0.866025 | − | 0.500000i | ||||||||
0 | 0 | |||||||||
0.680339 | − | 0.0895683i | 0.680339 | − | 0.0895683i | |||||
0 | 0 | |||||||||
0 | 0 | −0.866025 | − | 0.500000i | ||||||
0.866025 | + | 0.500000i | ||||||||
0 | 0 | |||||||||
0 | 0 | 1.00000 | ||||||||
−1.00000 | ||||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.12484 | − | 0.465926i | 1.12484 | − | 0.465926i | |||||
1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | 1.00000 | ||||
1.00000i | ||||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.0999004 | + | 0.758819i | −0.0999004 | + | 0.758819i | |||||
−2.36603 | + | 2.36603i | −2.36603 | + | 2.36603i | |||||
0 | 0 | |||||||||
1.83195 | − | 0.241181i | 1.83195 | − | 0.241181i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.500000 | − | 0.866025i | ||||||
0.500000 | + | 0.866025i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.93185 | + | 0.517638i | −1.93185 | + | 0.517638i | |||||
0 | 0 | |||||||||
2.00000 | 2.00000 | |||||||||
0 | 0 | |||||||||
−1.03528 | −1.03528 | |||||||||
0 | 0 | −0.258819 | − | 0.965926i | ||||||
0.258819 | + | 0.965926i | ||||||||
0 | 0 | |||||||||
−0.448288 | + | 0.258819i | −0.448288 | + | 0.258819i | |||||
0 | 0 | |||||||||
−0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||
−1.00000 | ||||||||||
0.758819 | − | 0.582262i | 0.758819 | − | 0.582262i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.0822623 | − | 0.624844i | 0.0822623 | − | 0.624844i | |||||
1.46593 | + | 1.12484i | 1.46593 | + | 1.12484i | 0.965926 | + | 0.258819i | ||
0.500000 | + | 0.866025i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.46593 | + | 1.12484i | 1.46593 | + | 1.12484i | |||||
0 | 0 | −0.707107 | − | 0.707107i | ||||||
0.707107 | + | 0.707107i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.517638 | 0.517638 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.866025 | − | 0.500000i | ||||||
0.866025 | + | 0.500000i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | |||||
−0.633975 | + | 1.53055i | −0.633975 | + | 1.53055i | |||||
−1.57313 | − | 0.207107i | −1.57313 | − | 0.207107i | |||||
0 | 0 | |||||||||
0.965926 | − | 0.258819i | 0.965926 | − | 0.258819i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||
1.00000 | ||||||||||
0 | 0 | |||||||||
0.741181 | + | 0.965926i | 0.741181 | + | 0.965926i | 1.00000 | ||||
−0.258819 | + | 0.965926i | ||||||||
0.207107 | + | 1.57313i | 0.207107 | + | 1.57313i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.776457 | − | 0.448288i | −0.776457 | − | 0.448288i | |||||
−0.258819 | − | 0.965926i | −0.258819 | − | 0.965926i | |||||
0 | 0 | |||||||||
0.517638 | + | 0.214413i | 0.517638 | + | 0.214413i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.258819 | − | 0.965926i | 0.258819 | − | 0.965926i | |||||
0 | 0 | |||||||||
1.83195 | + | 0.758819i | 1.83195 | + | 0.758819i | |||||
0.151613 | + | 0.366025i | 0.151613 | + | 0.366025i | |||||
0 | 0 | |||||||||
1.50000 | + | 0.866025i | 1.50000 | + | 0.866025i | |||||
0 | 0 | |||||||||
0 | 0 | −0.991445 | − | 0.130526i | ||||||
0.991445 | + | 0.130526i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.465926 | + | 0.607206i | 0.465926 | + | 0.607206i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.965926 | − | 1.67303i | −0.965926 | − | 1.67303i | −0.707107 | − | 0.707107i | ||
−0.258819 | − | 0.965926i | ||||||||
−0.0999004 | + | 0.241181i | −0.0999004 | + | 0.241181i | |||||
0 | 0 | |||||||||
1.67303 | + | 0.448288i | 1.67303 | + | 0.448288i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.258819 | − | 0.0340742i | 0.258819 | − | 0.0340742i | |||||
0 | 0 | −0.965926 | − | 0.258819i | ||||||
0.965926 | + | 0.258819i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.417738 | − | 0.544406i | 0.417738 | − | 0.544406i | |||||
−0.758819 | − | 1.83195i | −0.758819 | − | 1.83195i | |||||
0.707107 | − | 0.292893i | 0.707107 | − | 0.292893i | − | 1.00000i | |||
0.707107 | + | 0.707107i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.258819 | + | 1.96593i | −0.258819 | + | 1.96593i | 1.00000i | ||||
−0.258819 | + | 0.965926i | ||||||||
0 | 0 | |||||||||
−0.133975 | + | 0.500000i | −0.133975 | + | 0.500000i | 0.866025 | + | 0.500000i | ||
−1.00000 | ||||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.366025 | − | 0.633975i | −0.366025 | − | 0.633975i | |||||
0.258819 | − | 1.96593i | 0.258819 | − | 1.96593i | − | 1.00000i | |||
0.258819 | − | 0.965926i | ||||||||
0.358719 | − | 0.207107i | 0.358719 | − | 0.207107i | |||||
0.500000 | − | 0.133975i | 0.500000 | − | 0.133975i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.366025 | − | 0.366025i | −0.366025 | − | 0.366025i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.0340742 | − | 0.258819i | 0.0340742 | − | 0.258819i | −0.965926 | − | 0.258819i | ||
1.00000 | ||||||||||
−0.258819 | − | 0.448288i | −0.258819 | − | 0.448288i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.258819 | − | 0.965926i | 0.258819 | − | 0.965926i | −0.707107 | − | 0.707107i | ||
0.965926 | − | 0.258819i | ||||||||
−1.09808 | + | 1.09808i | −1.09808 | + | 1.09808i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.793353 | − | 0.608761i | ||||||
0.793353 | + | 0.608761i | ||||||||
−0.366025 | − | 0.366025i | −0.366025 | − | 0.366025i | |||||
−0.707107 | + | 0.292893i | −0.707107 | + | 0.292893i | −0.707107 | − | 0.707107i | ||
1.00000i | ||||||||||
0 | 0 | |||||||||
0.883663 | − | 1.15161i | 0.883663 | − | 1.15161i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.965926 | − | 0.258819i | ||||||
0.965926 | + | 0.258819i | ||||||||
−1.83195 | + | 0.241181i | −1.83195 | + | 0.241181i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.517638 | − | 0.214413i | 0.517638 | − | 0.214413i | |||||
0 | 0 | 0.965926 | − | 0.258819i | ||||||
−0.965926 | + | 0.258819i | ||||||||
0.500000 | + | 0.133975i | 0.500000 | + | 0.133975i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.707107 | + | 1.22474i | 0.707107 | + | 1.22474i | 0.965926 | + | 0.258819i | ||
−0.258819 | + | 0.965926i | ||||||||
0 | 0 | |||||||||
−1.12484 | − | 1.46593i | −1.12484 | − | 1.46593i | −0.866025 | − | 0.500000i | ||
−0.258819 | − | 0.965926i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | |||||
−0.500000 | − | 1.86603i | −0.500000 | − | 1.86603i | |||||
0.633975 | + | 1.53055i | 0.633975 | + | 1.53055i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.258819 | − | 0.965926i | ||||||
−0.258819 | + | 0.965926i | ||||||||
0 | 0 | |||||||||
0.948288 | + | 0.392794i | 0.948288 | + | 0.392794i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.158919 | + | 0.207107i | 0.158919 | + | 0.207107i | 0.866025 | − | 0.500000i | ||
−0.707107 | + | 0.707107i | ||||||||
−0.500000 | − | 0.651613i | −0.500000 | − | 0.651613i | |||||
0.707107 | − | 1.22474i | 0.707107 | − | 1.22474i | −0.258819 | − | 0.965926i | ||
0.965926 | − | 0.258819i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
− | 1.41421i | − | 1.41421i | |||||||
0 | 0 | −0.965926 | − | 0.258819i | ||||||
0.965926 | + | 0.258819i | ||||||||
−0.258819 | + | 0.0693504i | −0.258819 | + | 0.0693504i | |||||
1.22474 | − | 0.507306i | 1.22474 | − | 0.507306i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | |||||
0 | 0 | 0.991445 | − | 0.130526i | ||||||
−0.991445 | + | 0.130526i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.12484 | − | 1.46593i | 1.12484 | − | 1.46593i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.607206 | − | 1.46593i | −0.607206 | − | 1.46593i | −0.866025 | − | 0.500000i | ||
0.258819 | − | 0.965926i | ||||||||
0 | 0 | |||||||||
0 | 0 | −0.707107 | − | 0.707107i | ||||||
0.707107 | + | 0.707107i | ||||||||
−0.207107 | − | 0.158919i | −0.207107 | − | 0.158919i | |||||
0 | 0 | |||||||||
−0.158919 | − | 1.20711i | −0.158919 | − | 1.20711i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.258819 | + | 0.448288i | 0.258819 | + | 0.448288i | 0.965926 | − | 0.258819i | ||
−0.707107 | + | 0.707107i | ||||||||
−0.158919 | + | 1.20711i | −0.158919 | + | 1.20711i | |||||
−0.776457 | + | 0.448288i | −0.776457 | + | 0.448288i | |||||
0.965926 | − | 0.258819i | 0.965926 | − | 0.258819i | |||||
0 | 0 | −0.258819 | − | 0.965926i | ||||||
0.258819 | + | 0.965926i | ||||||||
1.00000 | 1.00000 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.133975 | − | 0.500000i | −0.133975 | − | 0.500000i | |||||
0 | 0 | |||||||||
−0.448288 | + | 0.258819i | −0.448288 | + | 0.258819i | −0.707107 | − | 0.707107i | ||
0.258819 | + | 0.965926i | ||||||||
−0.176557 | + | 1.34108i | −0.176557 | + | 1.34108i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.67303 | − | 0.965926i | 1.67303 | − | 0.965926i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | 1.00000i | ||||
−1.00000 | ||||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.158919 | + | 1.20711i | 0.158919 | + | 1.20711i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | |||||
0 | 0 | |||||||||
0.241181 | + | 0.582262i | 0.241181 | + | 0.582262i | |||||
0 | 0 | |||||||||
0 | 0 | 1.00000 | ||||||||
−1.00000 | ||||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.67303 | − | 0.448288i | −1.67303 | − | 0.448288i | |||||
0 | 0 | |||||||||
−1.41421 | + | 1.41421i | −1.41421 | + | 1.41421i | |||||
0 | 0 | |||||||||
−0.392794 | − | 0.0517123i | −0.392794 | − | 0.0517123i | |||||
0 | 0 | 0.923880 | − | 0.382683i | ||||||
−0.923880 | + | 0.382683i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
− | 1.93185i | − | 1.93185i | |||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.465926 | + | 0.607206i | 0.465926 | + | 0.607206i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.793353 | − | 0.608761i | ||||||
−0.793353 | + | 0.608761i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
2.09077 | + | 1.20711i | 2.09077 | + | 1.20711i | |||||
−0.267949 | − | 1.00000i | −0.267949 | − | 1.00000i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.03528i | 1.03528i | |||||||||
0 | 0 | 0.258819 | − | 0.965926i | ||||||
−0.258819 | + | 0.965926i | ||||||||
0 | 0 | |||||||||
− | 0.267949i | − | 0.267949i | |||||||
0 | 0 | |||||||||
0.565826 | + | 1.36603i | 0.565826 | + | 1.36603i | |||||
0 | 0 | |||||||||
0 | 0 | −0.866025 | − | 0.500000i | ||||||
0.866025 | + | 0.500000i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.448288 | − | 3.40508i | −0.448288 | − | 3.40508i | |||||
−0.823443 | − | 1.07313i | −0.823443 | − | 1.07313i | |||||
−0.158919 | − | 0.207107i | −0.158919 | − | 0.207107i | 0.707107 | − | 0.707107i | ||
−0.866025 | + | 0.500000i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | − | 1.00000i | |||||||
1.00000i | ||||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.883663 | − | 0.116337i | −0.883663 | − | 0.116337i | |||||
0.507306 | − | 1.22474i | 0.507306 | − | 1.22474i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.965926 | − | 0.258819i | ||||||
0.965926 | + | 0.258819i | ||||||||
0 | 0 | |||||||||
−0.582262 | + | 0.758819i | −0.582262 | + | 0.758819i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.923880 | − | 0.382683i | ||||||
−0.923880 | + | 0.382683i | ||||||||
0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.0999004 | + | 0.758819i | 0.0999004 | + | 0.758819i | 0.965926 | + | 0.258819i | ||
−0.866025 | + | 0.500000i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.366025 | + | 0.366025i | 0.366025 | + | 0.366025i | |||||
1.46593 | − | 1.12484i | 1.46593 | − | 1.12484i | 0.500000 | − | 0.866025i | ||
0.965926 | − | 0.258819i | ||||||||
0 | 0 | |||||||||
0.107206 | − | 0.814313i | 0.107206 | − | 0.814313i | |||||
0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | |||||
0 | 0 | 0.965926 | − | 0.258819i | ||||||
−0.965926 | + | 0.258819i | ||||||||
−0.366025 | − | 1.36603i | −0.366025 | − | 1.36603i | |||||
0 | 0 | |||||||||
−0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−3.29788 | + | 0.883663i | −3.29788 | + | 0.883663i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | |||||
0 | 0 | |||||||||
−0.814313 | + | 0.107206i | −0.814313 | + | 0.107206i | |||||
0.366025 | − | 1.36603i | 0.366025 | − | 1.36603i | −0.500000 | − | 0.866025i | ||
0.866025 | − | 0.500000i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.633975 | + | 1.09808i | −0.633975 | + | 1.09808i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.608761 | − | 0.793353i | ||||||
−0.608761 | + | 0.793353i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | |||||
−1.36603 | − | 0.366025i | −1.36603 | − | 0.366025i | |||||
−0.258819 | + | 0.0340742i | −0.258819 | + | 0.0340742i | |||||
0 | 0 | |||||||||
−0.392794 | + | 0.948288i | −0.392794 | + | 0.948288i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.41421i | 1.41421i | 0.707107 | + | 0.707107i | ||||||
−0.707107 | + | 0.707107i | ||||||||
0 | 0 | |||||||||
0.965926 | + | 1.67303i | 0.965926 | + | 1.67303i | 0.707107 | + | 0.707107i | ||
0.258819 | + | 0.965926i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.314313 | + | 0.241181i | −0.314313 | + | 0.241181i | |||||
−3.53906 | − | 0.465926i | −3.53906 | − | 0.465926i | |||||
1.12484 | + | 0.465926i | 1.12484 | + | 0.465926i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.382683 | − | 0.923880i | ||||||
0.382683 | + | 0.923880i | ||||||||
−0.124844 | − | 0.0517123i | −0.124844 | − | 0.0517123i | |||||
0 | 0 | − | 1.00000i | |||||||
1.00000i | ||||||||||
0 | 0 | |||||||||
−0.232051 | + | 0.866025i | −0.232051 | + | 0.866025i | |||||
0 | 0 | |||||||||
−1.83195 | − | 0.758819i | −1.83195 | − | 0.758819i | −0.965926 | − | 0.258819i | ||
−0.866025 | − | 0.500000i | ||||||||
0 | 0 | |||||||||
0 | 0 | −0.258819 | − | 0.965926i | ||||||
0.258819 | + | 0.965926i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.607206 | − | 0.465926i | 0.607206 | − | 0.465926i | |||||
0.0176381 | + | 0.133975i | 0.0176381 | + | 0.133975i | |||||
0 | 0 | |||||||||
1.94829 | + | 2.53906i | 1.94829 | + | 2.53906i | |||||
0 | 0 | |||||||||
−0.258819 | − | 0.448288i | −0.258819 | − | 0.448288i | |||||
0 | 0 | 0.382683 | − | 0.923880i | ||||||
−0.382683 | + | 0.923880i | ||||||||
0 | 0 | |||||||||
0.965926 | + | 0.258819i | 0.965926 | + | 0.258819i | |||||
0 | 0 | |||||||||
0.948288 | − | 0.392794i | 0.948288 | − | 0.392794i | |||||
1.96593 | + | 0.258819i | 1.96593 | + | 0.258819i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.465926 | − | 0.607206i | 0.465926 | − | 0.607206i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.382683 | − | 0.923880i | ||||||
0.382683 | + | 0.923880i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.25882 | − | 0.965926i | −1.25882 | − | 0.965926i | |||||
0.866025 | − | 1.50000i | 0.866025 | − | 1.50000i | − | 1.00000i | |||
0.866025 | − | 0.500000i | ||||||||
0 | 0 | |||||||||
1.25882 | + | 0.965926i | 1.25882 | + | 0.965926i | 1.00000 | ||||
0.258819 | + | 0.965926i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.991445 | − | 0.130526i | ||||||
−0.991445 | + | 0.130526i | ||||||||
0.776457 | − | 0.448288i | 0.776457 | − | 0.448288i | |||||
0 | 0 | |||||||||
−1.57313 | + | 1.20711i | −1.57313 | + | 1.20711i | |||||
0.107206 | + | 0.185687i | 0.107206 | + | 0.185687i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.517638 | + | 0.517638i | −0.517638 | + | 0.517638i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.866025 | − | 0.500000i | ||||||
−0.866025 | + | 0.500000i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | 0.258819 | − | 0.965926i | ||
−0.965926 | + | 0.258819i | ||||||||
−0.633975 | + | 0.366025i | −0.633975 | + | 0.366025i | |||||
1.57313 | − | 0.207107i | 1.57313 | − | 0.207107i | 0.707107 | − | 0.707107i | ||
0.866025 | + | 0.500000i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.0340742 | + | 0.258819i | −0.0340742 | + | 0.258819i | |||||
0 | 0 | −0.793353 | − | 0.608761i | ||||||
0.793353 | + | 0.608761i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.328169 | + | 0.328169i | 0.328169 | + | 0.328169i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.500000 | − | 0.133975i | −0.500000 | − | 0.133975i | |||||
0 | 0 | |||||||||
−0.517638 | + | 0.517638i | −0.517638 | + | 0.517638i | |||||
0 | 0 | |||||||||
−3.17303 | − | 0.417738i | −3.17303 | − | 0.417738i | |||||
0 | 0 | |||||||||
1.86603 | − | 0.500000i | 1.86603 | − | 0.500000i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.465926 | − | 1.12484i | 0.465926 | − | 1.12484i | −0.500000 | − | 0.866025i | ||
0.965926 | − | 0.258819i | ||||||||
−0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.608761 | − | 0.793353i | ||||||
0.608761 | + | 0.793353i | ||||||||
−0.124844 | − | 0.948288i | −0.124844 | − | 0.948288i | |||||
−1.67303 | + | 1.28376i | −1.67303 | + | 1.28376i | |||||
1.57313 | + | 0.207107i | 1.57313 | + | 0.207107i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.262601 | + | 0.633975i | 0.262601 | + | 0.633975i | |||||
0 | 0 | −0.923880 | − | 0.382683i | ||||||
0.923880 | + | 0.382683i | ||||||||
0 | 0 | |||||||||
−0.0693504 | + | 0.258819i | −0.0693504 | + | 0.258819i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.57313 | + | 0.207107i | 1.57313 | + | 0.207107i | 0.866025 | − | 0.500000i | ||
0.707107 | + | 0.707107i | ||||||||
0 | 0 | |||||||||
0.241181 | + | 1.83195i | 0.241181 | + | 1.83195i | |||||
0.741181 | + | 0.965926i | 0.741181 | + | 0.965926i | |||||
0 | 0 | |||||||||
−0.707107 | + | 1.22474i | −0.707107 | + | 1.22474i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.00000i | 1.00000i | 0.866025 | + | 0.500000i | ||||||
−0.866025 | + | 0.500000i | ||||||||
0 | 0 | |||||||||
0.965926 | − | 0.258819i | 0.965926 | − | 0.258819i | |||||
0 | 0 | |||||||||
0 | 0 | −0.991445 | − | 0.130526i | ||||||
0.991445 | + | 0.130526i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.758819 | + | 0.0999004i | −0.758819 | + | 0.0999004i | |||||
0 | 0 | |||||||||
−2.89778 | − | 1.67303i | −2.89778 | − | 1.67303i | |||||
−0.741181 | + | 0.965926i | −0.741181 | + | 0.965926i | 0.258819 | + | 0.965926i | ||
−1.00000 | ||||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.707107 | + | 1.70711i | 0.707107 | + | 1.70711i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.607206 | − | 0.465926i | −0.607206 | − | 0.465926i | 0.258819 | − | 0.965926i | ||
−0.866025 | + | 0.500000i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | |||||
0 | 0 | |||||||||
−0.921519 | + | 0.707107i | −0.921519 | + | 0.707107i | |||||
−1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.965926 | − | 0.258819i | ||||||
−0.965926 | + | 0.258819i | ||||||||
0.517638 | + | 1.93185i | 0.517638 | + | 1.93185i | |||||
0.732051 | 0.732051 | |||||||||
0 | 0 | |||||||||
−1.41421 | −1.41421 | −0.707107 | − | 0.707107i | ||||||
−0.707107 | + | 0.707107i | ||||||||
−0.267949 | − | 1.00000i | −0.267949 | − | 1.00000i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.607206 | + | 0.465926i | −0.607206 | + | 0.465926i | −0.866025 | − | 0.500000i | ||
0.258819 | + | 0.965926i | ||||||||
−0.366025 | − | 0.366025i | −0.366025 | − | 0.366025i | |||||
−2.89778 | + | 1.67303i | −2.89778 | + | 1.67303i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | |||||
0 | 0 | 0.130526 | − | 0.991445i | ||||||
−0.130526 | + | 0.991445i | ||||||||
0.758819 | + | 0.582262i | 0.758819 | + | 0.582262i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.608761 | − | 0.793353i | ||||||
−0.608761 | + | 0.793353i | ||||||||
0 | 0 | |||||||||
0.0822623 | − | 0.107206i | 0.0822623 | − | 0.107206i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.624844 | − | 0.0822623i | 0.624844 | − | 0.0822623i | |||||
0 | 0 | 0.707107 | − | 0.707107i | ||||||
−0.707107 | + | 0.707107i | ||||||||
−0.707107 | + | 1.70711i | −0.707107 | + | 1.70711i | |||||
0 | 0 |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 776.1.bh.a.539.1 | yes | 8 | |
4.3 | odd | 2 | 3104.1.dr.a.2479.1 | 8 | |||
8.3 | odd | 2 | CM | 776.1.bh.a.539.1 | yes | 8 | |
8.5 | even | 2 | 3104.1.dr.a.2479.1 | 8 | |||
97.9 | even | 24 | inner | 776.1.bh.a.203.1 | ✓ | 8 | |
388.203 | odd | 24 | 3104.1.dr.a.591.1 | 8 | |||
776.203 | odd | 24 | inner | 776.1.bh.a.203.1 | ✓ | 8 | |
776.397 | even | 24 | 3104.1.dr.a.591.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
776.1.bh.a.203.1 | ✓ | 8 | 97.9 | even | 24 | inner | |
776.1.bh.a.203.1 | ✓ | 8 | 776.203 | odd | 24 | inner | |
776.1.bh.a.539.1 | yes | 8 | 1.1 | even | 1 | trivial | |
776.1.bh.a.539.1 | yes | 8 | 8.3 | odd | 2 | CM | |
3104.1.dr.a.591.1 | 8 | 388.203 | odd | 24 | |||
3104.1.dr.a.591.1 | 8 | 776.397 | even | 24 | |||
3104.1.dr.a.2479.1 | 8 | 4.3 | odd | 2 | |||
3104.1.dr.a.2479.1 | 8 | 8.5 | even | 2 |