diff --git a/src/basisselectors.jl b/src/basisselectors.jl
index b8ad3dab..05740634 100644
--- a/src/basisselectors.jl
+++ b/src/basisselectors.jl
@@ -128,7 +128,7 @@ maxorder(Bsel::SimpleSparseBasis, args...) =
 """
 `AbstractSparseBasis`: Super-type for sparse basis selection as sub-levelsets of
 the levelset function `level` and corresponding (possibly order-dependent)
-levels provided in the dictionary `maxdegs::Dict{Any, Float64}`. In the default
+levels provided in the dictionary `maxlevels::Dict{Any, Float64}`. In the default
 implementation the levelset function and the degree function are identical.
 
 Basis functions are selected in two steps. First, "admissible" basis 
@@ -183,15 +183,15 @@ function SparseBasis(;  maxorder::Integer = nothing,
                         p = 1, 
                         weight = Dict(:l => 1.0, :n => 1.0), 
                         default_maxdeg = nothing, 
-                        maxdegs = nothing ) 
-   if (default_maxdeg != nothing) && (maxdegs == nothing )
+                        maxlevels = nothing ) 
+   if (default_maxdeg != nothing) && (maxlevels == nothing )
       return SparseBasis(maxorder, weight, 
                          Dict{Any, Float64}("default" => default_maxdeg), 
                          p)
-   elseif (default_maxdeg == nothing) && (maxdegs != nothing)
-      SparseBasis(maxorder, weight, maxdegs, p)
+   elseif (default_maxdeg == nothing) && (maxlevels != nothing)
+      SparseBasis(maxorder, weight, maxlevels, p)
    else
-      error("""Either both or neither optional arguments `maxdegs` and 
+      error("""Either both or neither optional arguments `maxlevels` and 
                `default_maxdeg` were provided. To avoid ambiguity ensure that 
                exactly one of these arguments is provided.""")
    end
@@ -282,10 +282,87 @@ cat_weighted_degree(bb::Prodb, Bsel::CategorySparseBasis, basis::OneParticleBasi
       )
 
 
-# --------------------------- 
+      # --------------------------- 
 # Some useful filters 
 
 struct NoConstant 
 end
 
 (::NoConstant)(bb) = (length(bb) > 0)
+
+
+"""
+`EvenL`: selects all basis functions where the sum `L = sum_i l_i` of the degrees `l_i` of the spherical harmonics is even.   
+"""
+struct EvenL
+      isym::Symbol
+      categories
+end
+  
+function (f::ACE.EvenL)(bb) 
+      if isempty(bb)
+            return true
+      else
+            suml(s) = sum( [getl(O3(), b) for b in bb if getproperty(b, f.isym) == s])
+            return all(iseven(suml(s)) for s in f.categories)
+      end
+end
+
+
+
+"""
+`DownsetIntersection`: Basis selector whose set of admissible specifications is the intersection 
+of the sets of admissible specifications of the sparse basis selectors contained in the lists `DBsels` and `ABsels`.
+"""
+struct DownsetIntersection <: DownsetBasisSelector
+   DBsels::Vector{DownsetBasisSelector}
+   ABsels::Vector{AbstractBasisSelector}
+   maxorder::Int
+end
+
+maxlevel(Bsel::DownsetIntersection, basis::OneParticleBasis) = 1.0 
+
+maxlevel(bb::Prodb, Bsel::DownsetIntersection, basis::OneParticleBasis) = 1.0
+
+
+maxorder(Bsel::DownsetIntersection) = Bsel.maxorder
+
+const MAXORDER = 10000
+function Base.intersect(Bsel1::DownsetIntersection,Bsel2::DownsetBasisSelector)
+      return DownsetIntersection(vcat(Bsel1.DBsels,[Bsel2]), Bsel1.ABsels, minimum([maxorder(Bsel1),maxorder(Bsel2)]))
+end
+
+function Base.intersect(Bsel1::DownsetIntersection,Bsel2::AbstractBasisSelector)
+      return DownsetIntersection(Bsel1.DBsels, vcat(Bsel1.ABsels,[Bsel2]), minimum([maxorder(Bsel1),maxorder(Bsel2)]))
+end
+
+function Base.intersect(Bsel1::DownsetBasisSelector, Bsel2::AbstractBasisSelector) 
+      Bsel = DownsetIntersection(Vector{DownsetBasisSelector}([]), Vector{AbstractBasisSelector}([]), MAXORDER)
+      return intersect(intersect(Bsel, Bsel1), Bsel2)
+end
+
+function Base.intersect(Bsel1::DownsetBasisSelector, Bsel2::DownsetBasisSelector) 
+      Bsel = DownsetIntersection(Vector{DownsetBasisSelector}([]), Vector{AbstractBasisSelector}([]), MAXORDER)
+      return intersect(intersect(Bsel, Bsel1), Bsel2)
+end
+
+Base.intersect(Bsel1::AbstractBasisSelector, Bsel2::DownsetBasisSelector)  = intersect(Bsel2,Bsel1)
+Base.intersect(Bsel1::AbstractBasisSelector, Bsel2::DownsetIntersection) = intersect(Bsel2,Bsel1)
+
+function Base.intersect(Bsel1::DownsetIntersection, Bsel2::DownsetIntersection)
+      Bsel = deepcopy(Bsel1)
+      for b in Bsel2
+            Bsel = intersect(Bsel, b)
+      end
+      return Bsel
+end
+
+function level(bb, Bsel::DownsetIntersection, basis::OneParticleBasis) 
+   return maximum([ level(bb, bsel, basis)/maxlevel(bsel,basis) for bsel in Bsel.DBsels])
+   #return maximum([ level(bb, bsel, basis)/maxlevel(length(bb),bsel,basis) for bsel in Bsel.DBsels])
+end
+
+function filter(bb, Bsel::DownsetIntersection, basis::OneParticleBasis) 
+   return all([filter(bb, bsel, basis) for bsel in Bsel.DBsels]) && all([filter(bb, bsel, basis) for bsel in Bsel.ABsels])
+end
+
diff --git a/src/bonds.jl b/src/bonds.jl
index 005cb9e1..5ce1f5a5 100644
--- a/src/bonds.jl
+++ b/src/bonds.jl
@@ -42,7 +42,7 @@ cutoff_env(env::CylindricalBondEnvelope) = sqrt(env.rcut^2 + (env.r0cut + env.zc
 cutoff_radialbasis(env::CylindricalBondEnvelope) = sqrt(env.rcut^2 + (env.zcut + env.floppy * env.λ * env.r0cut)^2)
 
 struct EllipsoidBondEnvelope{T} <: BondEnvelope{T}
-   r0cut::T
+   r0cut::T # bond-length cutoff
    rcut::T
    zcut::T  # must satisfy zcut >= r0cut/2
    p0::Int
diff --git a/src/cov_coeffs_dict.jl b/src/cov_coeffs_dict.jl
new file mode 100644
index 00000000..36b637b5
--- /dev/null
+++ b/src/cov_coeffs_dict.jl
@@ -0,0 +1,29 @@
+crmatrices=Dict(
+(l=1, m=-1, mu=-1, i=1) => SVector{3,ComplexF64}(0.1666666666666667+0.0im, 0.0+0.1666666666666667im, 0.0+0.0im),
+(l=1, m=-1, mu=0, i=1) => SVector{3,ComplexF64}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=-1, mu=1, i=1) => SVector{3,ComplexF64}(-0.1666666666666667+0.0im, 0.0+-0.1666666666666667im, 0.0+0.0im),
+(l=1, m=0, mu=-1, i=1) => SVector{3,ComplexF64}(0.0+0.0im, 0.0+0.0im, -0.2357022603955158+0.0im),
+(l=1, m=0, mu=0, i=1) => SVector{3,ComplexF64}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=0, mu=1, i=1) => SVector{3,ComplexF64}(0.0+0.0im, 0.0+0.0im, 0.2357022603955158+0.0im),
+(l=1, m=1, mu=-1, i=1) => SVector{3,ComplexF64}(-0.1666666666666667+0.0im, 0.0+0.1666666666666667im, 0.0+0.0im),
+(l=1, m=1, mu=0, i=1) => SVector{3,ComplexF64}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=1, mu=1, i=1) => SVector{3,ComplexF64}(0.1666666666666667+0.0im, 0.0+-0.1666666666666667im, 0.0+0.0im),
+(l=1, m=-1, mu=-1, i=2) => SVector{3,ComplexF64}(0.0+-0.1666666666666667im, 0.1666666666666667+0.0im, 0.0+0.0im),
+(l=1, m=-1, mu=0, i=2) => SVector{3,ComplexF64}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=-1, mu=1, i=2) => SVector{3,ComplexF64}(0.0+-0.1666666666666667im, 0.1666666666666667+0.0im, 0.0+0.0im),
+(l=1, m=0, mu=-1, i=2) => SVector{3,ComplexF64}(0.0+0.0im, 0.0+0.0im, 0.0+0.2357022603955158im),
+(l=1, m=0, mu=0, i=2) => SVector{3,ComplexF64}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=0, mu=1, i=2) => SVector{3,ComplexF64}(0.0+0.0im, 0.0+0.0im, 0.0+0.2357022603955158im),
+(l=1, m=1, mu=-1, i=2) => SVector{3,ComplexF64}(0.0+0.1666666666666667im, 0.1666666666666667+0.0im, 0.0+0.0im),
+(l=1, m=1, mu=0, i=2) => SVector{3,ComplexF64}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=1, mu=1, i=2) => SVector{3,ComplexF64}(0.0+0.1666666666666667im, 0.1666666666666667+0.0im, 0.0+0.0im),
+(l=1, m=-1, mu=-1, i=3) => SVector{3,ComplexF64}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=-1, mu=0, i=3) => SVector{3,ComplexF64}(-0.2357022603955158+0.0im, 0.0+-0.2357022603955158im, 0.0+0.0im),
+(l=1, m=-1, mu=1, i=3) => SVector{3,ComplexF64}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=0, mu=-1, i=3) => SVector{3,ComplexF64}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=0, mu=0, i=3) => SVector{3,ComplexF64}(0.0+0.0im, 0.0+0.0im, 0.3333333333333333+0.0im),
+(l=1, m=0, mu=1, i=3) => SVector{3,ComplexF64}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=1, mu=-1, i=3) => SVector{3,ComplexF64}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=1, mu=0, i=3) => SVector{3,ComplexF64}(0.2357022603955158+0.0im, 0.0+-0.2357022603955158im, 0.0+0.0im),
+(l=1, m=1, mu=1, i=3) => SVector{3,ComplexF64}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im)
+)
diff --git a/src/equi_coeffs_dict.jl b/src/equi_coeffs_dict.jl
new file mode 100644
index 00000000..167f08ff
--- /dev/null
+++ b/src/equi_coeffs_dict.jl
@@ -0,0 +1,317 @@
+mrmatrices=Dict(
+(l=0, m=0, mu=0, i=1, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.3333333333333333+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.3333333333333333+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.3333333333333333+0.0im),
+(l=0, m=0, mu=0, i=1, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=0, m=0, mu=0, i=1, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=0, m=0, mu=0, i=2, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=0, m=0, mu=0, i=2, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.3333333333333333+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.3333333333333333+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.3333333333333333+0.0im),
+(l=0, m=0, mu=0, i=2, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=0, m=0, mu=0, i=3, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=0, m=0, mu=0, i=3, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=0, m=0, mu=0, i=3, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.3333333333333333+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.3333333333333333+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.3333333333333333+0.0im),
+(l=1, m=-1, mu=-1, i=1, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=-1, mu=0, i=1, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=-1, mu=1, i=1, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=0, mu=-1, i=1, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=0, mu=0, i=1, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=0, mu=1, i=1, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=1, mu=-1, i=1, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=1, mu=0, i=1, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=1, mu=1, i=1, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=-1, mu=-1, i=1, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=-1, mu=0, i=1, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+-0.1178511301977579im, 0.0+0.0im, 0.0+0.0im, 0.1178511301977579+0.0im, 0.0+0.1178511301977579im, -0.1178511301977579+0.0im, 0.0+0.0im),
+(l=1, m=-1, mu=1, i=1, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=0, mu=-1, i=1, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=0, mu=0, i=1, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, -0.1666666666666667+0.0im, 0.0+0.0im, 0.1666666666666667+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=0, mu=1, i=1, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=1, mu=-1, i=1, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=1, mu=0, i=1, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+-0.1178511301977579im, 0.0+0.0im, 0.0+0.0im, -0.1178511301977579+0.0im, 0.0+0.1178511301977579im, 0.1178511301977579+0.0im, 0.0+0.0im),
+(l=1, m=1, mu=1, i=1, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=-1, mu=-1, i=1, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, -0.0833333333333333+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+-0.0833333333333333im, 0.0833333333333333+0.0im, 0.0+0.0833333333333333im, 0.0+0.0im),
+(l=1, m=-1, mu=0, i=1, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=-1, mu=1, i=1, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, -0.0833333333333333+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+-0.0833333333333333im, 0.0833333333333333+0.0im, 0.0+0.0833333333333333im, 0.0+0.0im),
+(l=1, m=0, mu=-1, i=1, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.1178511301977579im, 0.0+0.0im, 0.0+-0.1178511301977579im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=0, mu=0, i=1, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=0, mu=1, i=1, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.1178511301977579im, 0.0+0.0im, 0.0+-0.1178511301977579im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=1, mu=-1, i=1, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, -0.0833333333333333+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0833333333333333im, 0.0833333333333333+0.0im, 0.0+-0.0833333333333333im, 0.0+0.0im),
+(l=1, m=1, mu=0, i=1, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=1, mu=1, i=1, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, -0.0833333333333333+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0833333333333333im, 0.0833333333333333+0.0im, 0.0+-0.0833333333333333im, 0.0+0.0im),
+(l=1, m=-1, mu=-1, i=2, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=-1, mu=0, i=2, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.1178511301977579im, 0.0+0.0im, 0.0+0.0im, -0.1178511301977579+0.0im, 0.0+-0.1178511301977579im, 0.1178511301977579+0.0im, 0.0+0.0im),
+(l=1, m=-1, mu=1, i=2, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=0, mu=-1, i=2, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=0, mu=0, i=2, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.1666666666666667+0.0im, 0.0+0.0im, -0.1666666666666667+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=0, mu=1, i=2, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=1, mu=-1, i=2, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=1, mu=0, i=2, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.1178511301977579im, 0.0+0.0im, 0.0+0.0im, 0.1178511301977579+0.0im, 0.0+-0.1178511301977579im, -0.1178511301977579+0.0im, 0.0+0.0im),
+(l=1, m=1, mu=1, i=2, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=-1, mu=-1, i=2, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=-1, mu=0, i=2, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=-1, mu=1, i=2, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=0, mu=-1, i=2, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=0, mu=0, i=2, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=0, mu=1, i=2, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=1, mu=-1, i=2, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=1, mu=0, i=2, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=1, mu=1, i=2, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=-1, mu=-1, i=2, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0833333333333333im, 0.0+0.0im, 0.0+0.0im, -0.0833333333333333+0.0im, 0.0+-0.0833333333333333im, 0.0833333333333333+0.0im, 0.0+0.0im),
+(l=1, m=-1, mu=0, i=2, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=-1, mu=1, i=2, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+-0.0833333333333333im, 0.0+0.0im, 0.0+0.0im, 0.0833333333333333+0.0im, 0.0+0.0833333333333333im, -0.0833333333333333+0.0im, 0.0+0.0im),
+(l=1, m=0, mu=-1, i=2, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.1178511301977579+0.0im, 0.0+0.0im, -0.1178511301977579+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=0, mu=0, i=2, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=0, mu=1, i=2, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, -0.1178511301977579+0.0im, 0.0+0.0im, 0.1178511301977579+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=1, mu=-1, i=2, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0833333333333333im, 0.0+0.0im, 0.0+0.0im, 0.0833333333333333+0.0im, 0.0+-0.0833333333333333im, -0.0833333333333333+0.0im, 0.0+0.0im),
+(l=1, m=1, mu=0, i=2, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=1, mu=1, i=2, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+-0.0833333333333333im, 0.0+0.0im, 0.0+0.0im, -0.0833333333333333+0.0im, 0.0+0.0833333333333333im, 0.0833333333333333+0.0im, 0.0+0.0im),
+(l=1, m=-1, mu=-1, i=3, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0833333333333333+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0833333333333333im, -0.0833333333333333+0.0im, 0.0+-0.0833333333333333im, 0.0+0.0im),
+(l=1, m=-1, mu=0, i=3, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=-1, mu=1, i=3, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0833333333333333+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0833333333333333im, -0.0833333333333333+0.0im, 0.0+-0.0833333333333333im, 0.0+0.0im),
+(l=1, m=0, mu=-1, i=3, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+-0.1178511301977579im, 0.0+0.0im, 0.0+0.1178511301977579im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=0, mu=0, i=3, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=0, mu=1, i=3, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+-0.1178511301977579im, 0.0+0.0im, 0.0+0.1178511301977579im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=1, mu=-1, i=3, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0833333333333333+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+-0.0833333333333333im, -0.0833333333333333+0.0im, 0.0+0.0833333333333333im, 0.0+0.0im),
+(l=1, m=1, mu=0, i=3, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=1, mu=1, i=3, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0833333333333333+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+-0.0833333333333333im, -0.0833333333333333+0.0im, 0.0+0.0833333333333333im, 0.0+0.0im),
+(l=1, m=-1, mu=-1, i=3, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+-0.0833333333333333im, 0.0+0.0im, 0.0+0.0im, 0.0833333333333333+0.0im, 0.0+0.0833333333333333im, -0.0833333333333333+0.0im, 0.0+0.0im),
+(l=1, m=-1, mu=0, i=3, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=-1, mu=1, i=3, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0833333333333333im, 0.0+0.0im, 0.0+0.0im, -0.0833333333333333+0.0im, 0.0+-0.0833333333333333im, 0.0833333333333333+0.0im, 0.0+0.0im),
+(l=1, m=0, mu=-1, i=3, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, -0.1178511301977579+0.0im, 0.0+0.0im, 0.1178511301977579+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=0, mu=0, i=3, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=0, mu=1, i=3, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.1178511301977579+0.0im, 0.0+0.0im, -0.1178511301977579+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=1, mu=-1, i=3, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+-0.0833333333333333im, 0.0+0.0im, 0.0+0.0im, -0.0833333333333333+0.0im, 0.0+0.0833333333333333im, 0.0833333333333333+0.0im, 0.0+0.0im),
+(l=1, m=1, mu=0, i=3, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=1, mu=1, i=3, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0833333333333333im, 0.0+0.0im, 0.0+0.0im, 0.0833333333333333+0.0im, 0.0+-0.0833333333333333im, -0.0833333333333333+0.0im, 0.0+0.0im),
+(l=1, m=-1, mu=-1, i=3, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=-1, mu=0, i=3, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=-1, mu=1, i=3, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=0, mu=-1, i=3, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=0, mu=0, i=3, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=0, mu=1, i=3, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=1, mu=-1, i=3, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=1, mu=0, i=3, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=1, m=1, mu=1, i=3, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-2, mu=-2, i=1, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.05+0.0im, 0.0+0.05im, 0.0+0.0im, 0.0+0.05im, -0.05+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-2, mu=-1, i=1, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-2, mu=0, i=1, j=1) => SMatrix{3, 3, ComplexF64, 9}(-0.04082482904638631+0.0im, 0.0+-0.04082482904638631im, 0.0+0.0im, 0.0+-0.04082482904638631im, 0.04082482904638631+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-2, mu=1, i=1, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-2, mu=2, i=1, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.05+0.0im, 0.0+0.05im, 0.0+0.0im, 0.0+0.05im, -0.05+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-1, mu=-2, i=1, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, -0.05+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+-0.05im, -0.05+0.0im, 0.0+-0.05im, 0.0+0.0im),
+(l=2, m=-1, mu=-1, i=1, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-1, mu=0, i=1, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.04082482904638631+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.04082482904638631im, 0.04082482904638631+0.0im, 0.0+0.04082482904638631im, 0.0+0.0im),
+(l=2, m=-1, mu=1, i=1, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-1, mu=2, i=1, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, -0.05+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+-0.05im, -0.05+0.0im, 0.0+-0.05im, 0.0+0.0im),
+(l=2, m=0, mu=-2, i=1, j=1) => SMatrix{3, 3, ComplexF64, 9}(-0.04082482904638631+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, -0.04082482904638631+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0816496580927726+0.0im),
+(l=2, m=0, mu=-1, i=1, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=0, mu=0, i=1, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.03333333333333333+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.03333333333333333+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, -0.06666666666666666+0.0im),
+(l=2, m=0, mu=1, i=1, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=0, mu=2, i=1, j=1) => SMatrix{3, 3, ComplexF64, 9}(-0.04082482904638631+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, -0.04082482904638631+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0816496580927726+0.0im),
+(l=2, m=1, mu=-2, i=1, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.05+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+-0.05im, 0.05+0.0im, 0.0+-0.05im, 0.0+0.0im),
+(l=2, m=1, mu=-1, i=1, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=1, mu=0, i=1, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, -0.04082482904638631+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.04082482904638631im, -0.04082482904638631+0.0im, 0.0+0.04082482904638631im, 0.0+0.0im),
+(l=2, m=1, mu=1, i=1, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=1, mu=2, i=1, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.05+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+-0.05im, 0.05+0.0im, 0.0+-0.05im, 0.0+0.0im),
+(l=2, m=2, mu=-2, i=1, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.05+0.0im, 0.0+-0.05im, 0.0+0.0im, 0.0+-0.05im, -0.05+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=2, mu=-1, i=1, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=2, mu=0, i=1, j=1) => SMatrix{3, 3, ComplexF64, 9}(-0.04082482904638631+0.0im, 0.0+0.04082482904638631im, 0.0+0.0im, 0.0+0.04082482904638631im, 0.04082482904638631+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=2, mu=1, i=1, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=2, mu=2, i=1, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.05+0.0im, 0.0+-0.05im, 0.0+0.0im, 0.0+-0.05im, -0.05+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-2, mu=-2, i=1, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+-0.05im, 0.05+0.0im, 0.0+0.0im, 0.05+0.0im, 0.0+0.05im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-2, mu=-1, i=1, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-2, mu=0, i=1, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-2, mu=1, i=1, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-2, mu=2, i=1, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.05im, -0.05+0.0im, 0.0+0.0im, -0.05+0.0im, 0.0+-0.05im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-1, mu=-2, i=1, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.05im, 0.0+0.0im, 0.0+0.0im, -0.05+0.0im, 0.0+0.05im, -0.05+0.0im, 0.0+0.0im),
+(l=2, m=-1, mu=-1, i=1, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-1, mu=0, i=1, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-1, mu=1, i=1, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-1, mu=2, i=1, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+-0.05im, 0.0+0.0im, 0.0+0.0im, 0.05+0.0im, 0.0+-0.05im, 0.05+0.0im, 0.0+0.0im),
+(l=2, m=0, mu=-2, i=1, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.04082482904638631im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.04082482904638631im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+-0.0816496580927726im),
+(l=2, m=0, mu=-1, i=1, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=0, mu=0, i=1, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=0, mu=1, i=1, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=0, mu=2, i=1, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+-0.04082482904638631im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+-0.04082482904638631im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0816496580927726im),
+(l=2, m=1, mu=-2, i=1, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+-0.05im, 0.0+0.0im, 0.0+0.0im, -0.05+0.0im, 0.0+-0.05im, -0.05+0.0im, 0.0+0.0im),
+(l=2, m=1, mu=-1, i=1, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=1, mu=0, i=1, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=1, mu=1, i=1, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=1, mu=2, i=1, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.05im, 0.0+0.0im, 0.0+0.0im, 0.05+0.0im, 0.0+0.05im, 0.05+0.0im, 0.0+0.0im),
+(l=2, m=2, mu=-2, i=1, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+-0.05im, -0.05+0.0im, 0.0+0.0im, -0.05+0.0im, 0.0+0.05im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=2, mu=-1, i=1, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=2, mu=0, i=1, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=2, mu=1, i=1, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=2, mu=2, i=1, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.05im, 0.05+0.0im, 0.0+0.0im, 0.05+0.0im, 0.0+-0.05im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-2, mu=-2, i=1, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-2, mu=-1, i=1, j=3) => SMatrix{3, 3, ComplexF64, 9}(-0.05+0.0im, 0.0+-0.05im, 0.0+0.0im, 0.0+-0.05im, 0.05+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-2, mu=0, i=1, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-2, mu=1, i=1, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.05+0.0im, 0.0+0.05im, 0.0+0.0im, 0.0+0.05im, -0.05+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-2, mu=2, i=1, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-1, mu=-2, i=1, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-1, mu=-1, i=1, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.05+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.05im, 0.05+0.0im, 0.0+0.05im, 0.0+0.0im),
+(l=2, m=-1, mu=0, i=1, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-1, mu=1, i=1, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, -0.05+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+-0.05im, -0.05+0.0im, 0.0+-0.05im, 0.0+0.0im),
+(l=2, m=-1, mu=2, i=1, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=0, mu=-2, i=1, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=0, mu=-1, i=1, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.04082482904638631+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.04082482904638631+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, -0.0816496580927726+0.0im),
+(l=2, m=0, mu=0, i=1, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=0, mu=1, i=1, j=3) => SMatrix{3, 3, ComplexF64, 9}(-0.04082482904638631+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, -0.04082482904638631+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0816496580927726+0.0im),
+(l=2, m=0, mu=2, i=1, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=1, mu=-2, i=1, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=1, mu=-1, i=1, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, -0.05+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.05im, -0.05+0.0im, 0.0+0.05im, 0.0+0.0im),
+(l=2, m=1, mu=0, i=1, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=1, mu=1, i=1, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.05+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+-0.05im, 0.05+0.0im, 0.0+-0.05im, 0.0+0.0im),
+(l=2, m=1, mu=2, i=1, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=2, mu=-2, i=1, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=2, mu=-1, i=1, j=3) => SMatrix{3, 3, ComplexF64, 9}(-0.05+0.0im, 0.0+0.05im, 0.0+0.0im, 0.0+0.05im, 0.05+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=2, mu=0, i=1, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=2, mu=1, i=1, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.05+0.0im, 0.0+-0.05im, 0.0+0.0im, 0.0+-0.05im, -0.05+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=2, mu=2, i=1, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-2, mu=-2, i=2, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+-0.05im, 0.05+0.0im, 0.0+0.0im, 0.05+0.0im, 0.0+0.05im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-2, mu=-1, i=2, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-2, mu=0, i=2, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-2, mu=1, i=2, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-2, mu=2, i=2, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.05im, -0.05+0.0im, 0.0+0.0im, -0.05+0.0im, 0.0+-0.05im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-1, mu=-2, i=2, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.05im, 0.0+0.0im, 0.0+0.0im, -0.05+0.0im, 0.0+0.05im, -0.05+0.0im, 0.0+0.0im),
+(l=2, m=-1, mu=-1, i=2, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-1, mu=0, i=2, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-1, mu=1, i=2, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-1, mu=2, i=2, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+-0.05im, 0.0+0.0im, 0.0+0.0im, 0.05+0.0im, 0.0+-0.05im, 0.05+0.0im, 0.0+0.0im),
+(l=2, m=0, mu=-2, i=2, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.04082482904638631im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.04082482904638631im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+-0.0816496580927726im),
+(l=2, m=0, mu=-1, i=2, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=0, mu=0, i=2, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=0, mu=1, i=2, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=0, mu=2, i=2, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+-0.04082482904638631im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+-0.04082482904638631im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0816496580927726im),
+(l=2, m=1, mu=-2, i=2, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+-0.05im, 0.0+0.0im, 0.0+0.0im, -0.05+0.0im, 0.0+-0.05im, -0.05+0.0im, 0.0+0.0im),
+(l=2, m=1, mu=-1, i=2, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=1, mu=0, i=2, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=1, mu=1, i=2, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=1, mu=2, i=2, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.05im, 0.0+0.0im, 0.0+0.0im, 0.05+0.0im, 0.0+0.05im, 0.05+0.0im, 0.0+0.0im),
+(l=2, m=2, mu=-2, i=2, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+-0.05im, -0.05+0.0im, 0.0+0.0im, -0.05+0.0im, 0.0+0.05im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=2, mu=-1, i=2, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=2, mu=0, i=2, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=2, mu=1, i=2, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=2, mu=2, i=2, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.05im, 0.05+0.0im, 0.0+0.0im, 0.05+0.0im, 0.0+-0.05im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-2, mu=-2, i=2, j=2) => SMatrix{3, 3, ComplexF64, 9}(-0.05+0.0im, 0.0+-0.05im, 0.0+0.0im, 0.0+-0.05im, 0.05+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-2, mu=-1, i=2, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-2, mu=0, i=2, j=2) => SMatrix{3, 3, ComplexF64, 9}(-0.04082482904638631+0.0im, 0.0+-0.04082482904638631im, 0.0+0.0im, 0.0+-0.04082482904638631im, 0.04082482904638631+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-2, mu=1, i=2, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-2, mu=2, i=2, j=2) => SMatrix{3, 3, ComplexF64, 9}(-0.05+0.0im, 0.0+-0.05im, 0.0+0.0im, 0.0+-0.05im, 0.05+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-1, mu=-2, i=2, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.05+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.05im, 0.05+0.0im, 0.0+0.05im, 0.0+0.0im),
+(l=2, m=-1, mu=-1, i=2, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-1, mu=0, i=2, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.04082482904638631+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.04082482904638631im, 0.04082482904638631+0.0im, 0.0+0.04082482904638631im, 0.0+0.0im),
+(l=2, m=-1, mu=1, i=2, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-1, mu=2, i=2, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.05+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.05im, 0.05+0.0im, 0.0+0.05im, 0.0+0.0im),
+(l=2, m=0, mu=-2, i=2, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.04082482904638631+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.04082482904638631+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, -0.0816496580927726+0.0im),
+(l=2, m=0, mu=-1, i=2, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=0, mu=0, i=2, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.03333333333333333+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.03333333333333333+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, -0.06666666666666666+0.0im),
+(l=2, m=0, mu=1, i=2, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=0, mu=2, i=2, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.04082482904638631+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.04082482904638631+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, -0.0816496580927726+0.0im),
+(l=2, m=1, mu=-2, i=2, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, -0.05+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.05im, -0.05+0.0im, 0.0+0.05im, 0.0+0.0im),
+(l=2, m=1, mu=-1, i=2, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=1, mu=0, i=2, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, -0.04082482904638631+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.04082482904638631im, -0.04082482904638631+0.0im, 0.0+0.04082482904638631im, 0.0+0.0im),
+(l=2, m=1, mu=1, i=2, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=1, mu=2, i=2, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, -0.05+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.05im, -0.05+0.0im, 0.0+0.05im, 0.0+0.0im),
+(l=2, m=2, mu=-2, i=2, j=2) => SMatrix{3, 3, ComplexF64, 9}(-0.05+0.0im, 0.0+0.05im, 0.0+0.0im, 0.0+0.05im, 0.05+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=2, mu=-1, i=2, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=2, mu=0, i=2, j=2) => SMatrix{3, 3, ComplexF64, 9}(-0.04082482904638631+0.0im, 0.0+0.04082482904638631im, 0.0+0.0im, 0.0+0.04082482904638631im, 0.04082482904638631+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=2, mu=1, i=2, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=2, mu=2, i=2, j=2) => SMatrix{3, 3, ComplexF64, 9}(-0.05+0.0im, 0.0+0.05im, 0.0+0.0im, 0.0+0.05im, 0.05+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-2, mu=-2, i=2, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-2, mu=-1, i=2, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.05im, -0.05+0.0im, 0.0+0.0im, -0.05+0.0im, 0.0+-0.05im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-2, mu=0, i=2, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-2, mu=1, i=2, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.05im, -0.05+0.0im, 0.0+0.0im, -0.05+0.0im, 0.0+-0.05im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-2, mu=2, i=2, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-1, mu=-2, i=2, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-1, mu=-1, i=2, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+-0.05im, 0.0+0.0im, 0.0+0.0im, 0.05+0.0im, 0.0+-0.05im, 0.05+0.0im, 0.0+0.0im),
+(l=2, m=-1, mu=0, i=2, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-1, mu=1, i=2, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+-0.05im, 0.0+0.0im, 0.0+0.0im, 0.05+0.0im, 0.0+-0.05im, 0.05+0.0im, 0.0+0.0im),
+(l=2, m=-1, mu=2, i=2, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=0, mu=-2, i=2, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=0, mu=-1, i=2, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+-0.04082482904638631im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+-0.04082482904638631im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0816496580927726im),
+(l=2, m=0, mu=0, i=2, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=0, mu=1, i=2, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+-0.04082482904638631im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+-0.04082482904638631im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0816496580927726im),
+(l=2, m=0, mu=2, i=2, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=1, mu=-2, i=2, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=1, mu=-1, i=2, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.05im, 0.0+0.0im, 0.0+0.0im, 0.05+0.0im, 0.0+0.05im, 0.05+0.0im, 0.0+0.0im),
+(l=2, m=1, mu=0, i=2, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=1, mu=1, i=2, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.05im, 0.0+0.0im, 0.0+0.0im, 0.05+0.0im, 0.0+0.05im, 0.05+0.0im, 0.0+0.0im),
+(l=2, m=1, mu=2, i=2, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=2, mu=-2, i=2, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=2, mu=-1, i=2, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.05im, 0.05+0.0im, 0.0+0.0im, 0.05+0.0im, 0.0+-0.05im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=2, mu=0, i=2, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=2, mu=1, i=2, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.05im, 0.05+0.0im, 0.0+0.0im, 0.05+0.0im, 0.0+-0.05im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=2, mu=2, i=2, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-2, mu=-2, i=3, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-2, mu=-1, i=3, j=1) => SMatrix{3, 3, ComplexF64, 9}(-0.05+0.0im, 0.0+-0.05im, 0.0+0.0im, 0.0+-0.05im, 0.05+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-2, mu=0, i=3, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-2, mu=1, i=3, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.05+0.0im, 0.0+0.05im, 0.0+0.0im, 0.0+0.05im, -0.05+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-2, mu=2, i=3, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-1, mu=-2, i=3, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-1, mu=-1, i=3, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.05+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.05im, 0.05+0.0im, 0.0+0.05im, 0.0+0.0im),
+(l=2, m=-1, mu=0, i=3, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-1, mu=1, i=3, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, -0.05+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+-0.05im, -0.05+0.0im, 0.0+-0.05im, 0.0+0.0im),
+(l=2, m=-1, mu=2, i=3, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=0, mu=-2, i=3, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=0, mu=-1, i=3, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.04082482904638631+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.04082482904638631+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, -0.0816496580927726+0.0im),
+(l=2, m=0, mu=0, i=3, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=0, mu=1, i=3, j=1) => SMatrix{3, 3, ComplexF64, 9}(-0.04082482904638631+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, -0.04082482904638631+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0816496580927726+0.0im),
+(l=2, m=0, mu=2, i=3, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=1, mu=-2, i=3, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=1, mu=-1, i=3, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, -0.05+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.05im, -0.05+0.0im, 0.0+0.05im, 0.0+0.0im),
+(l=2, m=1, mu=0, i=3, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=1, mu=1, i=3, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.05+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+-0.05im, 0.05+0.0im, 0.0+-0.05im, 0.0+0.0im),
+(l=2, m=1, mu=2, i=3, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=2, mu=-2, i=3, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=2, mu=-1, i=3, j=1) => SMatrix{3, 3, ComplexF64, 9}(-0.05+0.0im, 0.0+0.05im, 0.0+0.0im, 0.0+0.05im, 0.05+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=2, mu=0, i=3, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=2, mu=1, i=3, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.05+0.0im, 0.0+-0.05im, 0.0+0.0im, 0.0+-0.05im, -0.05+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=2, mu=2, i=3, j=1) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-2, mu=-2, i=3, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-2, mu=-1, i=3, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.05im, -0.05+0.0im, 0.0+0.0im, -0.05+0.0im, 0.0+-0.05im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-2, mu=0, i=3, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-2, mu=1, i=3, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.05im, -0.05+0.0im, 0.0+0.0im, -0.05+0.0im, 0.0+-0.05im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-2, mu=2, i=3, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-1, mu=-2, i=3, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-1, mu=-1, i=3, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+-0.05im, 0.0+0.0im, 0.0+0.0im, 0.05+0.0im, 0.0+-0.05im, 0.05+0.0im, 0.0+0.0im),
+(l=2, m=-1, mu=0, i=3, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-1, mu=1, i=3, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+-0.05im, 0.0+0.0im, 0.0+0.0im, 0.05+0.0im, 0.0+-0.05im, 0.05+0.0im, 0.0+0.0im),
+(l=2, m=-1, mu=2, i=3, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=0, mu=-2, i=3, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=0, mu=-1, i=3, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+-0.04082482904638631im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+-0.04082482904638631im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0816496580927726im),
+(l=2, m=0, mu=0, i=3, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=0, mu=1, i=3, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+-0.04082482904638631im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+-0.04082482904638631im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0816496580927726im),
+(l=2, m=0, mu=2, i=3, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=1, mu=-2, i=3, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=1, mu=-1, i=3, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.05im, 0.0+0.0im, 0.0+0.0im, 0.05+0.0im, 0.0+0.05im, 0.05+0.0im, 0.0+0.0im),
+(l=2, m=1, mu=0, i=3, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=1, mu=1, i=3, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.05im, 0.0+0.0im, 0.0+0.0im, 0.05+0.0im, 0.0+0.05im, 0.05+0.0im, 0.0+0.0im),
+(l=2, m=1, mu=2, i=3, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=2, mu=-2, i=3, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=2, mu=-1, i=3, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.05im, 0.05+0.0im, 0.0+0.0im, 0.05+0.0im, 0.0+-0.05im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=2, mu=0, i=3, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=2, mu=1, i=3, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.05im, 0.05+0.0im, 0.0+0.0im, 0.05+0.0im, 0.0+-0.05im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=2, mu=2, i=3, j=2) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-2, mu=-2, i=3, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-2, mu=-1, i=3, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-2, mu=0, i=3, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0816496580927726+0.0im, 0.0+0.0816496580927726im, 0.0+0.0im, 0.0+0.0816496580927726im, -0.0816496580927726+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-2, mu=1, i=3, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-2, mu=2, i=3, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-1, mu=-2, i=3, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-1, mu=-1, i=3, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-1, mu=0, i=3, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, -0.0816496580927726+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+-0.0816496580927726im, -0.0816496580927726+0.0im, 0.0+-0.0816496580927726im, 0.0+0.0im),
+(l=2, m=-1, mu=1, i=3, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=-1, mu=2, i=3, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=0, mu=-2, i=3, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=0, mu=-1, i=3, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=0, mu=0, i=3, j=3) => SMatrix{3, 3, ComplexF64, 9}(-0.06666666666666666+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, -0.06666666666666666+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.1333333333333333+0.0im),
+(l=2, m=0, mu=1, i=3, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=0, mu=2, i=3, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=1, mu=-2, i=3, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=1, mu=-1, i=3, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=1, mu=0, i=3, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0816496580927726+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+-0.0816496580927726im, 0.0816496580927726+0.0im, 0.0+-0.0816496580927726im, 0.0+0.0im),
+(l=2, m=1, mu=1, i=3, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=1, mu=2, i=3, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=2, mu=-2, i=3, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=2, mu=-1, i=3, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=2, mu=0, i=3, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0816496580927726+0.0im, 0.0+-0.0816496580927726im, 0.0+0.0im, 0.0+-0.0816496580927726im, -0.0816496580927726+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=2, mu=1, i=3, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im),
+(l=2, m=2, mu=2, i=3, j=3) => SMatrix{3, 3, ComplexF64, 9}(0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im, 0.0+0.0im)
+)
diff --git a/src/properties.jl b/src/properties.jl
index acc7a69a..a0be4270 100644
--- a/src/properties.jl
+++ b/src/properties.jl
@@ -214,9 +214,14 @@ end
 
 coco_init(phi::EuclideanVector{CT}, l, m, μ, T, A) where {CT<:Real} = (
       (l == 1 && abs(m) <= 1 && abs(μ) <= 1)
-         ? [EuclideanVector(rmatrices[m,μ][:,k]) for k=1:3]
+         ? [EuclideanVector(conj(crmatrices[(l=l,m=-m,mu=-μ,i=i)])) for i=1:3]
          : coco_zeros(phi, l, m, μ, T, A)  )
 
+#coco_init(phi::EuclideanVector{CT}, l, m, μ, T, A) where {CT<:Real} = (
+#      (l == 1 && abs(m) <= 1 && abs(μ) <= 1)
+#         ? [EuclideanVector(rmatrices[m,μ][:,k]) for k=1:3]
+#         : coco_zeros(phi, l, m, μ, T, A)  )
+
 # coco_init(phi::EuclideanVector{CT}
 #   this is not needed, since the EuclideanVector should never give us 
 #   a constant basis anyhow. Still ... this could become a problem if we 
@@ -238,18 +243,100 @@ coco_filter(::EuclideanVector, ll, mm, kk) =
 
 coco_dot(u1::EuclideanVector, u2::EuclideanVector) = dot(u1.val, u2.val)
 
-rmatrices = Dict(
-  (-1,-1) => SMatrix{3, 3, ComplexF64, 9}(1/6, 1im/6, 0, -1im/6, 1/6, 0, 0, 0, 0),
-  (-1,0) => SMatrix{3, 3, ComplexF64, 9}(0, 0, 0, 0, 0, 0, 1/(3*sqrt(2)), 1im/(3*sqrt(2)), 0),
-  (-1,1) => SMatrix{3, 3, ComplexF64, 9}(-1/6, -1im/6, 0, -1im/6, 1/6, 0, 0, 0, 0),
-  (0,-1) => SMatrix{3, 3, ComplexF64, 9}(0, 0, 1/(3*sqrt(2)), 0, 0, -1im/(3*sqrt(2)), 0, 0, 0),
-  (0,0) => SMatrix{3, 3, ComplexF64, 9}(0, 0, 0, 0, 0, 0, 0, 0, 1/3),
-  (0,1) => SMatrix{3, 3, ComplexF64, 9}(0, 0, -1/(3*sqrt(2)), 0, 0, -1im/(3*sqrt(2)), 0, 0, 0),
-  (1,-1) => SMatrix{3, 3, ComplexF64, 9}(-1/6, 1im/6, 0, 1im/6, 1/6, 0, 0, 0, 0),
-  (1,0) => SMatrix{3, 3, ComplexF64, 9}(0, 0, 0, 0, 0, 0, -1/(3*sqrt(2)), 1im/(3*sqrt(2)), 0),
-  (1,1) => SMatrix{3, 3, ComplexF64, 9}(1/6, -1im/6, 0, 1im/6, 1/6, 0, 0, 0, 0)
-  )
+include("cov_coeffs_dict.jl")
+
+#---------------------- Equivariant matrices
+
+struct EuclideanMatrix{T} <: AbstractProperty
+   val::SMatrix{3, 3, T, 9}
+end
+
+function Base.show(io::IO, φ::EuclideanMatrix)
+   # println(io, "3x3 $(typeof(φ)):")
+   println(io, "e[ $(φ.val[1,1]), $(φ.val[1,2]), $(φ.val[1,3]);")
+   println(io, "   $(φ.val[2,1]), $(φ.val[2,2]), $(φ.val[2,3]);")
+   print(io,   "   $(φ.val[3,1]), $(φ.val[3,2]), $(φ.val[3,3]) ]")
+end
+
+real(φ::EuclideanMatrix) = EuclideanMatrix(real.(φ.val))
+complex(φ::EuclideanMatrix) = EuclideanMatrix(complex(φ.val))
+complex(::Type{EuclideanMatrix{T}}) where {T} = EuclideanMatrix{complex(T)}
+
++(x::SMatrix{3}, y::EuclideanMatrix) = EuclideanMatrix(x + y.val)
+Base.convert(::Type{SMatrix{3, 3, T, 9}}, φ::EuclideanMatrix) where {T} =  convert(SMatrix{3, 3, T, 9}, φ.val)
+
+isrealB(::EuclideanMatrix{T}) where {T} = (T == real(T))
+isrealAA(::EuclideanMatrix) = false
+
+
+#fltype(::EuclideanMatrix{T}) where {T} = T
+
+EuclideanMatrix{T}() where {T <: Number} = EuclideanMatrix{T}(zero(SMatrix{3, 3, T, 9}))
+EuclideanMatrix(T::DataType=Float64) = EuclideanMatrix{T}()
+
+
+function filter(φ::EuclideanMatrix, grp::O3, bb::Array)
+   if length(bb) == 0  # no zero-correlations allowed 
+      return false 
+   end
+   if length(bb) == 1 #MS: Not sure if this should be here
+      return true
+   end
+   suml = sum( getl(grp, bi) for bi in bb )
+   if haskey(bb[1], msym(grp))  # depends on context whether m come along?
+      summ = sum( getm(grp, bi) for bi in bb )
+      return iseven(suml) && abs(summ) <= 2
+   end
+   return iseven(suml)
+end
+
+rot3Dcoeffs(::EuclideanMatrix,T=Float64) = Rot3DCoeffsEquiv{T,1}(Dict[], ClebschGordan(T))
+
+write_dict(φ::EuclideanMatrix{T}) where {T} =
+      Dict("__id__" => "ACE_EuclideanMatrix",
+              "valr" => write_dict(real.(Matrix(φ.val))),
+              "vali" => write_dict(imag.(Matrix(φ.val))),
+                "T" => write_dict(T) )
+
+function read_dict(::Val{:ACE_EuclideanMatrix}, D::Dict)
+   T = read_dict(D["T"])
+   valr = SMatrix{3, 3, T, 9}(read_dict(D["valr"]))
+   vali = SMatrix{3, 3, T, 9}(read_dict(D["vali"]))
+   return EuclideanMatrix{T}(valr + im * vali)
+end
+
+# differentiation - cf #27
+# *(φ::EuclideanMatrix, dAA::SVector) = φ.val * dAA'
+
+#coco_init(phi::EuclideanMatrix{CT}, l, m, μ, T, A) where {CT<:Real} = (
+#      (l <= 2 && abs(m) <= l && abs(μ) <= l)
+#         ? vec([EuclideanMatrix(conj.(transpose(mrmatrices[(m,μ,i,j)]))) for i=1:3 for j=1:3])
+#         : coco_zeros(phi, l, m, μ, T, A)  )
+coco_init(phi::EuclideanMatrix{CT}, l, m, μ, T, A) where {CT<:Real} = (
+   (l <= 2 && abs(m) <= l && abs(μ) <= l)
+      ? vec([EuclideanMatrix(conj.(mrmatrices[(l=l,m=-m,mu=-μ,i=i,j=j)])) for i=1:3 for j=1:3])
+      : coco_zeros(phi, l, m, μ, T, A)  )
+
+#coco_init(::EuclideanMatrix{CT}) where {CT<:Real} = [EuclideanMatrix(SMatrix{3,3,Complex{CT},9}([1.0,0,0,0,1.0,0,0,0,1.0]))]       
+coco_type(φ::EuclideanMatrix) = typeof(complex(φ))
+coco_type(::Type{EuclideanMatrix{T}}) where {T} = EuclideanMatrix{complex(T)}
+
+# This is slightly different from implementation in EuclideanVector!
+coco_zeros(φ::EuclideanMatrix, ll, mm, kk, T, A) =  zeros(typeof(complex(φ)), 9)
+#EuclideanMatrix.(zeros(SMatrix{3, 3, Complex{T}, 9},9))
+
+coco_filter(::EuclideanMatrix, ll, mm) =
+            iseven(sum(ll)) && (abs(sum(mm)) <= 2)
+
+coco_filter(::EuclideanMatrix, ll, mm, kk) =
+      abs(sum(mm)) <= 2 &&
+      abs(sum(kk)) <= 2 &&
+      iseven(sum(ll))
+
+coco_dot(u1::EuclideanMatrix, u2::EuclideanMatrix) = sum(transpose(conj.( u1.val)) * u2.val)
+#dot(u1.val, u2.val)
 
+include("equi_coeffs_dict.jl")
 
 # --------------------- 
 # some codes to help convert from svector, smatrix to spherical ... 
diff --git a/src/utils.jl b/src/utils.jl
index d2a5ee35..d9e7ba3d 100644
--- a/src/utils.jl
+++ b/src/utils.jl
@@ -74,7 +74,7 @@ BondBasisSelector(Bsel::ACE.SparseBasis;
             weight_cat = Dict(:bond => bond_weight, :env=> env_weight) 
          )
 
-function SymmetricBond_basis(ϕ::ACE.AbstractProperty, env::ACE.BondEnvelope, Bsel::ACE.SparseBasis; RnYlm = nothing, kwargs...)
+function SymmetricBond_basis(ϕ::ACE.AbstractProperty, env::ACE.BondEnvelope, Bsel::ACE.SparseBasis; RnYlm = nothing, bondsymmetry=nothing, kwargs...)
    BondSelector =  BondBasisSelector(Bsel; kwargs...)
    if RnYlm === nothing
        RnYlm = RnYlm_1pbasis(;   r0 = ACE.cutoff_radialbasis(env), 
@@ -85,9 +85,16 @@ function SymmetricBond_basis(ϕ::ACE.AbstractProperty, env::ACE.BondEnvelope, Bs
                                            kwargs...
                                        )
    end
+   filterfun = _->true
+   if bondsymmetry == "Invariant"
+      filterfun = ACE.EvenL(:be, [:bond])
+   end
+   if bondsymmetry == "Covariant"
+      filterfun = x -> !(ACE.EvenL(:be, [:bond])(x))
+   end
    Bc = ACE.Categorical1pBasis([:bond, :env]; varsym = :be, idxsym = :be )
    B1p =  Bc * RnYlm * env
-   return ACE.SymmetricBasis(ϕ, B1p, BondSelector)
+   return ACE.SymmetricBasis(ϕ, B1p, BondSelector; filterfun = filterfun)
 end
 
 # invariant_basis(; kwargs...) =
diff --git a/test/runtests.jl b/test/runtests.jl
index c1dc0d42..d4c119de 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -27,6 +27,7 @@ using ACE, Test, Printf, LinearAlgebra, StaticArrays, BenchmarkTools
     # @testset "Clebsch-Gordan" begin include("test_cg.jl") end
     @testset "SymmetricBasis" begin include("test_symmbasis.jl") end
     @testset "EuclideanVector" begin include("test_euclvec.jl") end
+    @testset "EuclideanMatrix" begin include("test_EuclideanMatrix.jl") end
     @testset "Multiple SH Bases" begin include("test_multish.jl") end
 
     # Model tests
@@ -35,11 +36,12 @@ using ACE, Test, Printf, LinearAlgebra, StaticArrays, BenchmarkTools
     @testset "AD-LinearACEModel"  begin include("test_admodel.jl") end 
 
     # Experimental material
+    @testset "Bonds" begin include("test_bonds.jl") end
+    @testset "Bond BasisSelectors" begin include("test_bondbasisselectors.jl") end
     @testset "Sparsification" begin include("test_sparsify.jl") end 
     @testset "XScal1pBasis" begin include("test_xscal1p.jl") end 
     # @testset "Multipliers" begin include("test_multiplier.jl") end
     # @testset "Bonds" begin include("test_bonds.jl") end
-    # @testset "BasisSelectors" begin include("test_basisselectors.jl") end
 end
 
 
diff --git a/test/test_BasisSelectorIntersection.jl b/test/test_BasisSelectorIntersection.jl
new file mode 100644
index 00000000..b0af562a
--- /dev/null
+++ b/test/test_BasisSelectorIntersection.jl
@@ -0,0 +1,45 @@
+using ACE, Test, ACEbase, ACEbase.Testing, StaticArrays
+using ACE.Random: rand_rot, rand_refl
+using Random: shuffle
+
+
+r0cut = 2.0
+rcut = 1.0
+zcut = 2.0
+env = ACE.EllipsoidBondEnvelope(r0cut, rcut, zcut;floppy=false, λ= .5)
+
+
+@info( "Very basic test for intersection")
+for maxorder = [1,2,3,4]
+
+    Bsel = ACE.SparseBasis(; maxorder=maxorder, p = 2, default_maxdeg = 4) 
+
+
+    RnYlm = ACE.Utils.RnYlm_1pbasis(;   r0 = ACE.cutoff_radialbasis(env), 
+                                            rin = 0.0,
+                                            trans = PolyTransform(1, ACE.cutoff_radialbasis(env)), 
+                                            pcut = 0,
+                                            pin = 0, Bsel = Bsel
+                                        )
+
+    basis = ACE.Utils.SymmetricBond_basis(ACE.Invariant(), env, Bsel;RnYlm=RnYlm )
+
+    Bsel2 = ACE.CategorySparseBasis(:be, [:bond, :env]; maxorder = ACE.maxorder(Bsel), 
+                                        p = Bsel.p, 
+                                        weight = Bsel.weight, 
+                                        maxlevels = Bsel.maxlevels,
+                                        minorder_dict = Dict( :bond => 1),
+                                        maxorder_dict = Dict( :bond => 1),
+                                        weight_cat = Dict(:bond => 1.0, :env=> 1.0) 
+                                    )
+
+
+    BselIntersection = intersect(Bsel,Bsel2)
+
+    Bc = ACE.Categorical1pBasis([:bond, :env]; varsym = :be, idxsym = :be )
+    B1p =  Bc * RnYlm * env
+    basis2 = ACE.SymmetricBasis(ACE.Invariant(), B1p, BselIntersection;)
+    
+    print_tf(@test length(basis) == length(basis2))
+
+end
\ No newline at end of file
diff --git a/test/test_EuclideanMatrix.jl b/test/test_EuclideanMatrix.jl
new file mode 100644
index 00000000..d1c940e9
--- /dev/null
+++ b/test/test_EuclideanMatrix.jl
@@ -0,0 +1,147 @@
+using ACE, StaticArrays
+using Random, Printf, Test, LinearAlgebra, ACE.Testing
+using ACE: evaluate, evaluate_d, SymmetricBasis, PIBasis, EuclideanMatrix
+using ACE.Random: rand_rot, rand_refl
+using ACEbase.Testing: fdtest
+
+## construct the 1p-basis
+maxdeg = 6
+ord = 3
+Bsel = SimpleSparseBasis(ord, maxdeg)
+
+B1p = ACE.Utils.RnYlm_1pbasis(; maxdeg=maxdeg)
+
+# generate a configuration
+nX = 10
+Xs = rand(PositionState{Float64}, B1p.bases[1], nX)
+cfg = ACEConfig(Xs)
+
+##
+
+@info("SymmetricBasis construction and evaluation: EuclideanMatrix")
+
+
+φ = ACE.EuclideanMatrix(Float64)
+pibasis = PIBasis(B1p, Bsel; property = φ)
+basis = SymmetricBasis(φ, pibasis)
+@time SymmetricBasis(φ, pibasis)
+
+BB = evaluate(basis, cfg)
+
+Iz = findall(iszero, sum(norm, basis.A2Bmap, dims=1)[:])
+if !isempty(Iz)
+   @warn("The A2B map for EuclideanMatrix has $(length(Iz))/$(length(basis.pibasis)) zero-columns!!!!")
+end
+
+##
+
+@info("Test FIO")
+using ACEbase.Testing: test_fio
+
+println(@test(all(test_fio(basis; warntype = false))))
+
+##
+
+@info("Test equivariance properties for real version")
+
+tol = 1e-12
+
+##
+#                     for (b1, b2) in zip(BB_rot, BB)  
+#print_tf(@test all([ norm(Q' * b1 * Q - b2) < tol
+#                     for (b1, b2) in zip(BB_rot, BB)  ]))
+##                      
+@info("check for rotation, permutation and inversion equivariance")
+for ntest = 1:30
+   local Xs, BB
+   Xs = rand(PositionState{Float64}, B1p.bases[1], nX)
+   BB = evaluate(basis, ACEConfig(Xs))
+   Q = rand([-1,1]) * ACE.Random.rand_rot()
+   Xs_rot = Ref(Q) .* shuffle(Xs)
+   BB_rot = evaluate(basis, ACEConfig(Xs_rot))
+   print_tf(@test all([ norm(Q' * b1 * Q - b2) < tol
+                        for (b1, b2) in zip(BB_rot, BB)  ]))
+end
+println()
+
+@info("Check for some non-symmetric matrix functions")
+for ntest = 1:30
+   local Xs, BB
+   Xs = rand(PositionState{Float64}, B1p.bases[1], nX)
+   BB = evaluate(basis, ACEConfig(Xs))
+   print_tf(@test any([ b.val != transpose(b.val)
+                        for b in BB  ]))
+end
+println()
+
+##
+
+imtol = 5.0
+@info("Check magnitude of complex part")
+for ntest = 1:30
+   local Xs, BB
+   Xs = rand(PositionState{Float64}, B1p.bases[1], nX)
+   BB = evaluate(basis, ACEConfig(Xs))
+   for (i,b) in enumerate(BB)
+      if norm(imag(b.val)) > imtol
+         @warn( "Large imaginary part for $(ACE.get_spec(basis)[i]), $(norm(imag(b.val)))")
+      end
+   end
+   #println(maximum([ norm(imag(b.val))/ norm(real(b.val))  for b in BBs  ]))
+   #print_tf(@test all([ norm(imag(b.val)) < .1  for b in BB  ]))
+end
+println()
+print(ACE.get_spec(basis)[1])
+##
+
+@info("Test equivariance properties for complex version")
+
+basis = SymmetricBasis(φ, pibasis; isreal=false)
+# a stupid but necessary test
+BB = evaluate(basis, cfg)
+BB1 = basis.A2Bmap * evaluate(basis.pibasis, cfg)
+println(@test isapprox(BB, BB1, rtol=1e-10)) # MS: This test will fail for isreal=true
+
+
+@info("check for rotation, permutation and inversion equivariance")
+for ntest = 1:30
+   local Xs, BB
+   Xs = rand(PositionState{Float64}, B1p.bases[1], nX)
+   BB = evaluate(basis, ACEConfig(Xs))
+   Q = rand([-1,1]) * ACE.Random.rand_rot()
+   Xs_rot = Ref(Q) .* shuffle(Xs)
+   BB_rot = evaluate(basis, ACEConfig(Xs_rot))
+   print_tf(@test all([ norm(Q' * b1 * Q - b2) < tol
+                        for (b1, b2) in zip(BB_rot, BB)  ]))
+end
+println()
+
+# ## keep for further profiling
+#
+# φ = ACE.EuclideanVector(Complex{Float64})
+# pibasis = PIBasis(B1p, ord, maxdeg; property = φ, isreal = false)
+# basis = SymmetricBasis(pibasis, φ)
+# @time SymmetricBasis(pibasis, φ);
+#
+# Profile.clear(); # Profile.init(; delay = 0.0001)
+# @profile SymmetricBasis(pibasis, φ);
+# ProfileView.view()
+
+##
+
+#=
+@info(" ... derivatives")
+_rrval(x::ACE.XState) = x.rr
+for ntest = 1:30
+   Us = randn(SVector{3,Float64 }, length(Xs))
+   C = randn(typeof(φ.val), length(basis))
+   F = t -> sum( sum(c .* b.val)
+                 for (c, b) in zip(C, ACE.evaluate(basis, ACEConfig(Xs + t[1] * Us))) )
+   dF = t -> [ sum( sum(c .* db)
+                    for (c, db) in zip(C, _rrval.(ACE.evaluate_d(basis, ACEConfig(Xs + t[1] * Us))) * Us) ) ]
+   print_tf(@test fdtest(F, dF, [0.0], verbose=false))
+end
+println()
+=#
+
+##
diff --git a/test/test_basisselectors.jl b/test/test_basisselectors.jl
deleted file mode 100644
index ea74f095..00000000
--- a/test/test_basisselectors.jl
+++ /dev/null
@@ -1,72 +0,0 @@
-using ACE, Test, ACEbase, ACEbase.Testing, StaticArrays
-using ACE.Random: rand_rot, rand_refl
-using Random: shuffle
-
-##
-#=
-@info("Rudimentary tests for sparse basis selectors and intersections of such")
-r0cut = 2.0
-rcut = 1.0
-zcut = 2.0
-env = ACE.EllipsoidBondEnvelope(r0cut, rcut, zcut;floppy=false, λ= .5)
-
-maxorder = 3
-dmaxdeg = 4
-Bsel_p2 = ACE.SparseBasis(maxorder; p = 2, default_maxdeg = dmaxdeg) 
-Bsel_p1 = ACE.SparseBasis(maxorder; p = 1, default_maxdeg = dmaxdeg) 
-
-Bsel_intesect = ACE.intersect(Bsel_p1,Bsel_p2)
-B1p = ACE.Utils.RnYlm_1pbasis(; maxdeg=dmaxdeg)
-basis_intersect_inv = ACE.SymmetricBasis(ACE.Invariant(), B1p, Bsel_intesect)
-=#
-
-@info("Test bond basis selectors")
-
-r0cut = 2.0
-rcut = 1.0
-zcut = 2.0
-env = ACE.EllipsoidBondEnvelope(r0cut, rcut, zcut;floppy=false, λ= .5)
-
-maxorder = 3
-Bsel = ACE.SparseBasis(; maxorder=maxorder, p = 2, default_maxdeg = 4) 
-
-##
-
-@info("Test invariance")
-
-
-basis_inv = ACE.Utils.SymmetricBond_basis(ACE.Invariant(), env, Bsel; )
-@show length(basis_inv)
-
-rr0 = SVector{3}(rand(Float64,3))
-cfg = [ ACE.State(rr = SVector{3}(rand(Float64,3)), rr0 = rr0,
-                  be = rand([:bond,:env])) 
-        for _ = 1:10 ] |> ACEConfig
-B1_inv = ACE.evaluate(basis_inv, cfg)
-
-for ntest = 1:30
-    Q = rand_refl() * rand_rot()
-    Xs2 = ACE.shuffle([ ACE.State(rr = Q * X.rr, rr0 = Q * X.rr0, be = X.be)  for X in cfg.Xs ])
-    B2_inv = ACE.evaluate(basis_inv, ACEConfig(Xs2))
-    print_tf(@test isapprox(B1_inv, B2_inv, rtol=1e-10))
-end
-println()
-@info("Test Euclidian covariance")
-
-basis_cov = ACE.Utils.SymmetricBond_basis(ACE.EuclideanVector(), env, Bsel; )
-@show length(basis_cov)
-
-rr0 = SVector{3}(rand(Float64,3))
-cfg = [ ACE.State(rr = SVector{3}(rand(Float64,3)), rr0 = rr0,
-                  be = rand([:bond,:env])) 
-        for _ = 1:10 ] |> ACEConfig
-B1_cov = ACE.evaluate(basis_cov, cfg)
-
-
-for ntest = 1:30
-    Q = rand_refl() * rand_rot()
-    Xs2 = ACE.shuffle([ ACE.State(rr = Q * X.rr, rr0 = Q * X.rr0, be = X.be)  for X in cfg.Xs ])
-    B2_cov = ACE.evaluate(basis_cov, ACEConfig(Xs2))
-    print_tf(@test isapprox( map(x->Q*x, B1_cov), B2_cov, rtol=1e-10))
-end
-println()
\ No newline at end of file
diff --git a/test/test_bondbasisselectors.jl b/test/test_bondbasisselectors.jl
new file mode 100644
index 00000000..22ca02b1
--- /dev/null
+++ b/test/test_bondbasisselectors.jl
@@ -0,0 +1,170 @@
+using ACE, Test, ACEbase, ACEbase.Testing, StaticArrays
+using ACE.Random: rand_rot, rand_refl
+using Random: shuffle
+##
+#=
+@info("Rudimentary tests for sparse basis selectors and intersections of such")
+r0cut = 2.0
+rcut = 1.0
+zcut = 2.0
+env = ACE.EllipsoidBondEnvelope(r0cut, rcut, zcut;floppy=false, λ= .5)
+
+maxorder = 3
+dmaxdeg = 4
+Bsel_p2 = ACE.SparseBasis(maxorder; p = 2, default_maxdeg = dmaxdeg) 
+Bsel_p1 = ACE.SparseBasis(maxorder; p = 1, default_maxdeg = dmaxdeg) 
+
+Bsel_intesect = ACE.intersect(Bsel_p1,Bsel_p2)
+B1p = ACE.Utils.RnYlm_1pbasis(; maxdeg=dmaxdeg)
+basis_intersect_inv = ACE.SymmetricBasis(ACE.Invariant(), B1p, Bsel_intesect)
+=#
+
+@info("Test bond basis selectors")
+
+r0cut = 2.0
+rcut = 1.0
+zcut = 2.0
+env = ACE.EllipsoidBondEnvelope(r0cut, rcut, zcut;floppy=false, λ= .5)
+
+maxorder = 3
+Bsel = ACE.SparseBasis(; maxorder=maxorder, p = 2, default_maxdeg = 4) 
+
+##
+@info("Test rotation-equivariance properties")
+
+tol = 10^-14
+for property in [ACE.Invariant(), ACE.EuclideanVector(), ACE.EuclideanMatrix()]
+
+    basis = ACE.Utils.SymmetricBond_basis(property, env, Bsel; )
+    @show length(basis)
+
+    rr0 = SVector{3}(rand(Float64,3))
+    cfg = [ ACE.State(rr = SVector{3}(rand(Float64,3)), rr0 = rr0,
+                    be = rand([:bond,:env])) 
+            for _ = 1:10 ] |> ACEConfig
+    B1 = ACE.evaluate(basis, cfg)
+
+    println("------------------------------------------------------------")
+    @info("Test rotation-equivariance for property $(typeof(property)) with tol = $tol")
+
+    for ntest = 1:30
+        Q = rand_refl() * rand_rot()
+        Xs2 = ACE.shuffle([ ACE.State(rr = Q * X.rr, rr0 = Q * X.rr0, be = X.be)  for X in cfg.Xs ])
+        B2 = ACE.evaluate(basis, ACEConfig(Xs2))
+        if property == ACE.Invariant()
+            print_tf(@test isapprox(B1, B2, rtol=tol))
+        elseif property == ACE.EuclideanVector()
+            print_tf(@test isapprox( map(x->Q*x, B1), B2, rtol=tol))
+        elseif property == ACE.EuclideanMatrix()
+            print_tf(@test isapprox( map(x->Q * x * Q', B1), B2, rtol=tol))
+        end
+    end
+    println()
+end
+
+
+env0 = ACE.EllipsoidBondEnvelope(r0cut, rcut, zcut; p0=1, pr=1, floppy=false, λ= 0.0)
+
+maxorder = 2
+Bsel = ACE.SparseBasis(;maxorder=maxorder, p = 2, default_maxdeg = 5) 
+
+RnYlm = ACE.Utils.RnYlm_1pbasis(;   r0 = ACE.cutoff_radialbasis(env), 
+                                           rin = 0.0,
+                                           trans = PolyTransform(1, ACE.cutoff_radialbasis(env)), 
+                                           pcut = 0,
+                                           pin = 0, Bsel = Bsel
+                                       )
+
+function get_config(X::Vector{SVector{3, Float64}}, k::Int, j::Int)
+    n = length(X)
+    Js = [i for i = 1:n if i != k]
+    Rs = [X[i] - X[k] for i = 1:n if i != k]
+    ba = (j=j,r= X[j] - X[k])
+    config = [ ACE.State(rr = (j==ba.j ? ba.r :  r-.5 * ba.r), rr0 = ba.r, be = (j==ba.j ? :bond : :env ))  for (j,r) in zip(Js, Rs)] |> ACEConfig
+    return config
+end
+
+n_particle = 11
+tol = 10^-14
+#env0 = ACE.EllipsoidBondEnvelope(r0cut, rcut, zcut;floppy=false, λ= 0.0)
+@info("Test equivariance properties under bond symmetry constraints");
+for bs in ["Invariant", "Covariant"]
+    for property in [ACE.Invariant(), ACE.EuclideanVector(), ACE.EuclideanMatrix()]
+
+        k= rand(1:n_particle)
+        j= rand([ i for i =1:n_particle if i != k])
+        basis = ACE.Utils.SymmetricBond_basis(property, env0, Bsel; bondsymmetry="Invariant" )
+        @show length(basis)
+
+        rr0 = SVector{3}(rand(Float64,3))
+        X = [ SVector{3}(rand(Float64,3)) for _ = 1:n_particle ]
+        cfg = get_config(X, k, j)
+        B1 = ACE.evaluate(basis, cfg)
+
+        println("------------------------------------------------------------")
+        @info( string("Test rotation-equivariance for property $(typeof(property)) and bond symmetry of type ", bs))
+
+        for ntest = 1:30
+            Q = rand_refl() * rand_rot()
+            X2 = [Q * x for x in X]
+            cfg2 = get_config(X2, k, j)
+            B2 = ACE.evaluate(basis, cfg2)
+            if property == ACE.Invariant()
+                print_tf(@test isapprox(B1, B2, rtol=tol))
+            elseif property == ACE.EuclideanVector()
+                print_tf(@test isapprox( map(x->Q*x, B1), B2, rtol=tol))
+            elseif property == ACE.EuclideanMatrix()
+                print_tf(@test isapprox( map(x->Q * x * Q', B1), B2, rtol=tol))
+            end
+        end
+        println()
+    end
+end
+
+@info("Test bond-symmetry conditions")
+
+tol = 10^-10
+for property in [ACE.Invariant(), ACE.EuclideanVector(), ACE.EuclideanMatrix()]
+
+    println("------------------------------------------------------------")
+    @info("Test bond-symmetry conditions for property $(typeof(property)) and tolerance tol = $tol")
+    println()
+    basis_bondinv = ACE.Utils.SymmetricBond_basis(property, env0, Bsel; bondsymmetry="Invariant");
+    #@show length(basis_bondinv );
+
+    @info("Test for invariance under bond inversion");
+    for ntest = 1:300
+        rr0 = SVector{3}(rand(Float64,3));
+        randX = [ SVector{3}(rand(Float64,3)) for _ =1:10];
+        cfg1 = vcat( [ ACE.State(rr = r-.5*rr0, rr0 =  rr0, be = :env) for r in randX ] , [ACE.State(rr =  rr0, rr0 =  rr0, be = :bond)]) |> ACEConfig;
+        cfg2 = vcat( [ ACE.State(rr = r-.5*rr0, rr0 = -rr0, be = :env) for r in randX ] , [ACE.State(rr = -rr0, rr0 = -rr0, be = :bond)]) |> ACEConfig;
+        B1 = ACE.evaluate(basis_bondinv , cfg1);
+        B2 = ACE.evaluate(basis_bondinv, cfg2);
+        print_tf(@test all([ isapprox(b1.val,b2.val, rtol = tol) for (b1,b2) in zip(B1,B2)]));
+    end
+    println()
+
+    
+    @info("Test for covariance under bond inversion");
+    basis_bondcov = ACE.Utils.SymmetricBond_basis(property, env0, Bsel; bondsymmetry="Covariant");
+    #@show length(basis_bondcov );
+    for ntest = 1:300
+        rr0 = SVector{3}(rand(Float64,3));
+        randX = [ SVector{3}(rand(Float64,3)) for _ =1:10];
+        cfg1 = vcat( [ ACE.State(rr = r-.5*rr0, rr0 =  rr0, be = :env) for r in randX ] , [ACE.State(rr =  rr0, rr0 =  rr0, be = :bond)]) |> ACEConfig;
+        cfg2 = vcat( [ ACE.State(rr = r-.5*rr0, rr0 = -rr0, be = :env) for r in randX ] , [ACE.State(rr = -rr0, rr0 = -rr0, be = :bond)]) |> ACEConfig;
+        B1 = ACE.evaluate(basis_bondcov, cfg1);
+        B2 = ACE.evaluate(basis_bondcov, cfg2);
+        print_tf(@test all([ isapprox(b1.val,-b2.val, rtol = tol) for (b1,b2) in zip(B1,B2)]));
+    end
+    println()
+    
+
+end
+
+
+
+
+
+
+