(* ::Package:: *)

(* ::Section:: *)
(*Wigner 6j coefficients for up to 4 quark-antiquark pairs or gluons, for leading order QCD*)


(* ::Text:: *)
(*This package contains all Wigner 6j coefficients required to evaluate any QCD color structure with up to 4 quark-antiquark pairs or gluons with any number of colors, Nc, for leading order QCD. (The coefficients from arXiv:1507.03814 have been included for convenience.) It also contains a function, Wigner6jCoefficient, that takes as input an arbitrary Wigner coefficient that can occur for up to 4 quark-antiquark pairs or gluons for leading order QCD and gives its value. (See the notebook UsingWignerCoefficients.nb.)*)


(* ::Subsection::Closed:: *)
(*All Wigner 6j Coefficients required for up to 4 quark-antiquark pairs or gluons, for leading order QCD*)


Wig6j[{{"0", "0", "0", "8", "8", "8"}, {1, 1, 1, 1}}] = 
    1/(Sqrt[2]*Sqrt[(-3 + Nc)*Nc]*(-1 + Nc^2))
 
Wig6j[{{"0", "0", "0", "8", "8", "8"}, {1, 1, 1, 2}}] = 0
 
Wig6j[{{"0", "0", "0", "8", "8", "8"}, {1, 2, 1, 1}}] = 0
 
Wig6j[{{"0", "0", "0", "8", "8", "8"}, {1, 2, 1, 2}}] = 
    Sqrt[(-4 + Nc)/(-3 + Nc)]/(Sqrt[2]*Nc*(-1 + Nc^2))
 
Wig6j[{{"0", "0", "0", "8", "8", "8"}, {2, 2, 1, 1}}] = 
    1/(Sqrt[2]*Sqrt[(-3 + Nc)*Nc]*(-1 + Nc^2))
 
Wig6j[{{"0", "0", "0", "8", "8", "8"}, {2, 2, 1, 2}}] = 0
 
Wig6j[{{"0", "0", "0", "8", "8", "8"}, {2, 2, 2, 1}}] = 0
 
Wig6j[{{"0", "0", "0", "8", "8", "8"}, {2, 2, 2, 2}}] = 
    (Sqrt[(-4 + Nc)/(-3 + Nc)]*(32 - 20*Nc - 4*Nc^2 + Nc^3))/
     (Sqrt[2]*(-2 + Nc)*Nc*(1 + Nc)*(8 - 6*Nc - 3*Nc^2 + Nc^3))
 
Wig6j[{{"0", "0", "10", "8", "8", "8"}, {1, 1, 1, 1}}] = 
    (-2 + Nc)/(Sqrt[2]*Sqrt[-3 + Nc]*Nc^(3/2)*(-1 + Nc^2))
 
Wig6j[{{"0", "0", "10", "8", "8", "8"}, {1, 1, 1, 2}}] = 
    Sqrt[(6*Nc + Nc^2 - Nc^3)/(4 - 2*Nc)]/(6 + Nc - 7*Nc^2 - Nc^3 + Nc^4)
 
Wig6j[{{"0", "0", "8", "0", "0", "8"}, {1, 1, 1, 1}}] = 
    (-4 + 3*Nc)/((-3 + Nc)*(-1 + Nc)*Nc^2*(1 + Nc))
 
Wig6j[{{"0", "0", "8", "0", "0", "8"}, {1, 2, 1, 1}}] = 0
 
Wig6j[{{"0", "0", "8", "0", "0", "8"}, {1, 2, 1, 2}}] = 
    -(1/(Nc*(3 - Nc - 3*Nc^2 + Nc^3)))
 
Wig6j[{{"0", "0", "8", "0", "0", "8"}, {2, 2, 1, 1}}] = 
    (-4 + 3*Nc)/((-3 + Nc)*(-1 + Nc)*Nc^2*(1 + Nc))
 
Wig6j[{{"0", "0", "8", "0", "0", "8"}, {2, 2, 1, 2}}] = 0
 
Wig6j[{{"0", "0", "8", "0", "0", "8"}, {2, 2, 2, 2}}] = 
    (-64 + 80*Nc - 12*Nc^2 - 16*Nc^3 + 3*Nc^4)/((-3 + Nc)*(-2 + Nc)*Nc^2*
      (1 + Nc)*(8 - 6*Nc - 3*Nc^2 + Nc^3))
 
Wig6j[{{"0", "0", "8", "0", "10", "8"}, {1, 1, 1, 1}}] = 
    (2 - Nc)/(Nc^2*(3 - Nc - 3*Nc^2 + Nc^3))
 
Wig6j[{{"0", "0", "8", "0", "8", "8"}, {1, 1, 1, 1}}] = 
    -2/((-3 + Nc)*Nc^2*(1 + Nc))
 
Wig6j[{{"0", "0", "8", "10", "0", "8"}, {1, 2, 1, 1}}] = 
    -(Sqrt[(-4 + Nc)/(Nc*(-4 + Nc^2))]/(3 - Nc - 3*Nc^2 + Nc^3))
 
Wig6j[{{"0", "0", "8", "10", "10", "8"}, {1, 1, 1, 1}}] = 
    ((-2 + 3*Nc)*Sqrt[(-6 - Nc + Nc^2)/(-2 + Nc)])/((-3 + Nc)*(-1 + Nc)*
      Nc^(3/2)*(1 + Nc)*(2 + Nc))
 
Wig6j[{{"0", "0", "8", "10", "10", "8"}, {1, 1, 1, 2}}] = 
    -(Sqrt[(-6 + Nc + Nc^2)/(Nc^3*(2 + Nc))]/(3 - Nc - 3*Nc^2 + Nc^3))
 
Wig6j[{{"0", "0", "8", "10", "8", "8"}, {1, 1, 1, 1}}] = 
    -((Sqrt[2]*Sqrt[(3 - 4*Nc + Nc^2)/((-2 + Nc)*Nc^3)])/
      (3 - Nc - 3*Nc^2 + Nc^3))
 
Wig6j[{{"0", "0", "8", "8", "0", "8"}, {1, 2, 1, 1}}] = 0
 
Wig6j[{{"0", "0", "8", "8", "8", "8"}, {1, 1, 1, 1}}] = 
    Sqrt[2]/(Sqrt[-3 + Nc]*Nc^(3/2)*(1 + Nc))
 
Wig6j[{{"0", "0", "8", "8", "8", "8"}, {1, 1, 1, 2}}] = 0
 
Wig6j[{{"0", "10", "0", "8", "8", "8"}, {1, 2, 1, 1}}] = 
    Sqrt[(8 - 6*Nc + Nc^2)*(-6 - Nc + Nc^2)]/(Sqrt[2]*(-3 + Nc)*(-2 + Nc)*
      (-1 + Nc)*(1 + Nc)*(2 + Nc))
 
Wig6j[{{"0", "10", "0", "8", "8", "8"}, {1, 2, 1, 2}}] = 
    (Sqrt[(-4 + Nc)/(-3 + Nc)]*(-4 + 2*Nc + Nc^2))/
     (Sqrt[2]*Nc*(4 - 5*Nc^2 + Nc^4))
 
Wig6j[{{"0", "10", "10", "8", "8", "8"}, {1, 1, 1, 1}}] = 
    Sqrt[-4 + Nc^2]/(Sqrt[2]*Nc*(2 - Nc - 2*Nc^2 + Nc^3))
 
Wig6j[{{"0", "10", "10", "8", "8", "8"}, {1, 1, 1, 2}}] = 
    Nc/(Sqrt[2]*(4 - 5*Nc^2 + Nc^4))
 
Wig6j[{{"0", "10", "10", "8", "8", "8"}, {2, 1, 1, 1}}] = 
    Sqrt[((3 + Nc)*(-4 + Nc^2))/(-3 + Nc)]/(Sqrt[2]*(-1 + Nc)*Nc*(1 + Nc)*
      (2 + Nc))
 
Wig6j[{{"0", "10", "10", "8", "8", "8"}, {2, 1, 1, 2}}] = 
    ((-4 + Nc)*Sqrt[(3 + Nc)/(-3 + Nc)])/(Sqrt[2]*(4 - 5*Nc^2 + Nc^4))
 
Wig6j[{{"0", "10", "8", "0", "0", "8"}, {1, 2, 1, 2}}] = 
    (4 - 2*Nc + Nc^2)/(12*Nc - 4*Nc^2 - 15*Nc^3 + 5*Nc^4 + 3*Nc^5 - Nc^6)
 
Wig6j[{{"0", "10", "8", "0", "10", "8"}, {1, 1, 1, 1}}] = 
    (2*(2 - 2*Nc - 2*Nc^2 + Nc^3))/((-3 + Nc)*Nc^2*(4 - 5*Nc^2 + Nc^4))
 
Wig6j[{{"0", "10", "8", "0", "10bar", "8"}, {1, 1, 1, 1}}] = 
    -4/(Nc^2*(12 + 8*Nc - 7*Nc^2 - 2*Nc^3 + Nc^4))
 
Wig6j[{{"0", "10", "8", "0", "8", "8"}, {1, 1, 1, 1}}] = 
    -2/(Nc^2*(6 + Nc - 4*Nc^2 + Nc^3))
 
Wig6j[{{"0", "10", "8", "10", "0", "8"}, {1, 2, 1, 1}}] = 
    -(Sqrt[(-4 + Nc)/(-3 + Nc)]/(4 - 5*Nc^2 + Nc^4))
 
Wig6j[{{"0", "10", "8", "10", "0", "8"}, {2, 2, 1, 1}}] = 
    ((-4 + 3*Nc)*Sqrt[-12 - Nc + Nc^2])/((-3 + Nc)*(-2 + Nc)*Nc*(1 + Nc)*
      (-2 + Nc + Nc^2))
 
Wig6j[{{"0", "10", "8", "10", "10", "8"}, {1, 1, 1, 1}}] = 
    -(1/(Nc*(2 - Nc - 2*Nc^2 + Nc^3)))
 
Wig6j[{{"0", "10", "8", "10", "10", "8"}, {1, 1, 1, 2}}] = 
    Sqrt[(3 + Nc)/(-3 + Nc)]/(Nc*(2 + Nc - 2*Nc^2 - Nc^3))
 
Wig6j[{{"0", "10", "8", "10", "10", "8"}, {2, 1, 1, 2}}] = 
    (6 - 3*Nc + Nc^2)/(12*Nc - 4*Nc^2 - 15*Nc^3 + 5*Nc^4 + 3*Nc^5 - Nc^6)
 
Wig6j[{{"0", "10", "8", "10", "8", "8"}, {1, 1, 1, 1}}] = 
    Sqrt[2]/(Nc*(2 + Nc - Nc^2)*Sqrt[-2 + Nc + Nc^2])
 
Wig6j[{{"0", "10", "8", "10", "8", "8"}, {2, 1, 1, 1}}] = 
    (Sqrt[2]*Sqrt[3 + Nc])/((-2 + Nc)*Nc*(1 + Nc)*
      Sqrt[(-3 + Nc)*(-1 + Nc)*(2 + Nc)])
 
Wig6j[{{"0", "10", "8", "27", "10", "8"}, {1, 1, 1, 1}}] = 
    -4/(4*Nc^2 - 5*Nc^4 + Nc^6)
 
Wig6j[{{"0", "10", "8", "27", "10bar", "8"}, {1, 1, 1, 1}}] = 
    4/(Nc^2*(-4 + Nc^2))
 
Wig6j[{{"0", "10", "8", "27", "8", "8"}, {1, 1, 1, 1}}] = 
    -2/(Nc^2*Sqrt[4 - 5*Nc^2 + Nc^4])
 
Wig6j[{{"0", "10", "8", "8", "0", "8"}, {1, 2, 1, 1}}] = 
    (Sqrt[2]*Sqrt[(24 - 2*Nc - 5*Nc^2 + Nc^3)/(-1 + Nc)])/
     (12*Nc + 8*Nc^2 - 7*Nc^3 - 2*Nc^4 + Nc^5)
 
Wig6j[{{"0", "10", "8", "8", "10", "8"}, {1, 1, 1, 1}}] = 
    2/(4*Nc - 5*Nc^3 + Nc^5)
 
Wig6j[{{"0", "10", "8", "8", "10bar", "8"}, {1, 1, 1, 1}}] = 
    -2/(Nc*(1 + Nc)*(-4 + Nc^2))
 
Wig6j[{{"0", "10", "8", "8", "8", "8"}, {1, 1, 1, 1}}] = 
    1/(Sqrt[2 - 3*Nc + Nc^2]*(Nc + Nc^2))
 
Wig6j[{{"0", "10", "8", "8", "8", "8"}, {1, 1, 1, 2}}] = 
    1/((-2 + Nc)*(1 + Nc)*Sqrt[-2 + Nc + Nc^2])
 
Wig6j[{{"0", "8", "0", "8", "8", "8"}, {1, 2, 1, 1}}] = 0
 
Wig6j[{{"0", "8", "0", "8", "8", "8"}, {1, 2, 1, 2}}] = 
    (Sqrt[2]*Sqrt[(-4 + Nc)/(-3 + Nc)])/((-2 + Nc)*Nc*(1 + Nc))
 
Wig6j[{{"0", "8", "8", "0", "0", "8"}, {1, 2, 1, 2}}] = 
    2/(Nc*(6 + Nc - 4*Nc^2 + Nc^3))
 
Wig6j[{{"0", "8", "8", "0", "8", "8"}, {1, 1, 1, 1}}] = 
    (2 - Nc + Nc^2)/((-3 + Nc)*(-2 + Nc)*Nc^2*(-1 + Nc^2))
 
Wig6j[{{"0", "8", "8", "1", "8", "8"}, {1, 1, 1, 1}}] = (-1 + Nc^2)^(-1)
 
Wig6j[{{"0", "8", "8", "10", "8", "8"}, {1, 1, 1, 1}}] = 
    (2*Nc - Nc^2 - 2*Nc^3 + Nc^4)^(-1)
 
Wig6j[{{"0", "8", "8", "27", "8", "8"}, {1, 1, 1, 1}}] = 1/(Nc^2*(-1 + Nc^2))
 
Wig6j[{{"0", "8", "8", "8", "8", "8"}, {1, 1, 1, 1}}] = -(Nc - Nc^3)^(-1)
 
Wig6j[{{"0", "8", "8", "8", "8", "8"}, {2, 1, 1, 1}}] = 0
 
Wig6j[{{"0", "8", "8", "8", "8", "8"}, {2, 1, 1, 2}}] = 
    (-2 + Nc + 2*Nc^2 - Nc^3)^(-1)
 
Wig6j[{{"0", "c2c1", "3", "0", "c1c2", "3"}, {1, 1, 1, 1}}] = 
    -4/(Nc^2*(6 + Nc - 4*Nc^2 + Nc^3))
 
Wig6j[{{"0", "c2c1", "3", "8", "c1c2", "3"}, {1, 1, 1, 1}}] = 
    -2/(2*Nc + Nc^2 - Nc^3)
 
Wig6j[{{"0", "c2c1", "8", "15", "8", "3"}, {1, 1, 1, 1}}] = 
    -((Sqrt[2]*Sqrt[(2 - 3*Nc + Nc^2)/Nc^3])/(2 - Nc - 2*Nc^2 + Nc^3))
 
Wig6j[{{"0", "c2c1", "8", "3", "8", "3"}, {1, 1, 1, 1}}] = 
    -(Sqrt[2]/((1 + Nc)*Sqrt[Nc*(2 - 3*Nc + Nc^2)]))
 
Wig6j[{{"0", "c2c1", "8", "c2c1", "8", "3"}, {1, 1, 1, 1}}] = 
    -2/((-2 - Nc + Nc^2)*Sqrt[Nc*(-1 - 2*Nc + 3*Nc^2)])
 
Wig6j[{{"0", "c2c1", "8", "c2c1", "8", "3"}, {2, 1, 1, 1}}] = 
    (Sqrt[2]*Sqrt[(6 - 5*Nc - 2*Nc^2 + Nc^3)/(Nc^3 + 3*Nc^4)])/
     (-6 + 11*Nc - 6*Nc^2 + Nc^3)
 
Wig6j[{{"1", "3", "3", "1", "3bar", "3"}, {1, 1, 1, 1}}] = Nc^(-1)
 
Wig6j[{{"1", "3", "8", "3", "8", "3"}, {1, 1, 1, 1}}] = 1/Sqrt[Nc*(-1 + Nc^2)]
 
Wig6j[{{"1", "8", "8", "1", "8", "8"}, {1, 1, 1, 1}}] = (-1 + Nc^2)^(-1)
 
Wig6j[{{"1", "8", "8", "8", "8", "8"}, {1, 1, 1, 1}}] = (-1 + Nc^2)^(-1)
 
Wig6j[{{"1", "8", "8", "8", "8", "8"}, {2, 1, 1, 1}}] = 0
 
Wig6j[{{"1", "8", "8", "8", "8", "8"}, {2, 1, 1, 2}}] = (-1 + Nc^2)^(-1)
 
Wig6j[{{"10", "10", "10", "8", "8", "8"}, {1, 1, 1, 1}}] = 
    1/(Sqrt[2]*Sqrt[-4 + Nc^2]*(-1 + Nc^2))
 
Wig6j[{{"10", "10", "10", "8", "8", "8"}, {1, 1, 1, 2}}] = 
    3/(Sqrt[2]*(4 - 5*Nc^2 + Nc^4))
 
Wig6j[{{"10", "10", "10", "8", "8", "8"}, {1, 2, 1, 1}}] = 0
 
Wig6j[{{"10", "10", "10", "8", "8", "8"}, {1, 2, 1, 2}}] = 
    Sqrt[-9 + Nc^2]/(Sqrt[2]*(4 - 5*Nc^2 + Nc^4))
 
Wig6j[{{"10", "10", "10", "8", "8", "8"}, {2, 2, 1, 1}}] = 
    1/(Sqrt[2]*Sqrt[-4 + Nc^2]*(-1 + Nc^2))
 
Wig6j[{{"10", "10", "10", "8", "8", "8"}, {2, 2, 1, 2}}] = 
    1/(Sqrt[2]*(4 - 5*Nc^2 + Nc^4))
 
Wig6j[{{"10", "10", "10", "8", "8", "8"}, {2, 2, 2, 1}}] = 
    Sqrt[2]/((1 - Nc^2)*Sqrt[36 - 13*Nc^2 + Nc^4])
 
Wig6j[{{"10", "10", "10", "8", "8", "8"}, {2, 2, 2, 2}}] = 
    (-27 + Nc^2)/(Sqrt[2]*Sqrt[-9 + Nc^2]*(4 - 5*Nc^2 + Nc^4))
 
Wig6j[{{"10", "10", "27", "8", "8", "8"}, {1, 1, 1, 1}}] = 
    Sqrt[(-2 + Nc)/(2 + Nc)]/(Sqrt[2]*Nc*(-1 + Nc^2))
 
Wig6j[{{"10", "10", "27", "8", "8", "8"}, {1, 1, 1, 2}}] = 
    -(Nc/(Sqrt[2]*(4 - 5*Nc^2 + Nc^4)))
 
Wig6j[{{"10", "10", "8", "10", "10", "8"}, {1, 1, 1, 1}}] = 
    3/(4 - 5*Nc^2 + Nc^4)
 
Wig6j[{{"10", "10", "8", "10", "10", "8"}, {1, 2, 1, 1}}] = 0
 
Wig6j[{{"10", "10", "8", "10", "10", "8"}, {1, 2, 1, 2}}] = 
    -(4 - 5*Nc^2 + Nc^4)^(-1)
 
Wig6j[{{"10", "10", "8", "10", "10", "8"}, {2, 2, 1, 1}}] = 
    3/(4 - 5*Nc^2 + Nc^4)
 
Wig6j[{{"10", "10", "8", "10", "10", "8"}, {2, 2, 1, 2}}] = 
    (2*Sqrt[-36 + 49*Nc^2 - 14*Nc^4 + Nc^6])/((-9 + Nc^2)*
      (4 - 5*Nc^2 + Nc^4)^(3/2))
 
Wig6j[{{"10", "10", "8", "10", "10", "8"}, {2, 2, 2, 2}}] = 
    (-47 + 3*Nc^2)/((-9 + Nc^2)*(4 - 5*Nc^2 + Nc^4))
 
Wig6j[{{"10", "10", "8", "10", "27", "8"}, {1, 1, 1, 1}}] = 
    (2*Nc + Nc^2 - 2*Nc^3 - Nc^4)^(-1)
 
Wig6j[{{"10", "10", "8", "10", "8", "8"}, {1, 1, 1, 1}}] = 
    -2/(4 - 5*Nc^2 + Nc^4)
 
Wig6j[{{"10", "10", "8", "27", "10", "8"}, {1, 2, 1, 1}}] = 
    Sqrt[(-3 + Nc)/(3 + Nc)]/(Nc*(2 - Nc - 2*Nc^2 + Nc^3))
 
Wig6j[{{"10", "10", "8", "27", "27", "8"}, {1, 1, 1, 1}}] = 
    ((2 + 3*Nc)*Sqrt[(-6 + Nc + Nc^2)/(2 + Nc)])/((-2 + Nc)*(-1 + Nc)*
      Nc^(3/2)*(1 + Nc)*(3 + Nc))
 
Wig6j[{{"10", "10", "8", "27", "27", "8"}, {1, 1, 1, 2}}] = 
    Sqrt[(4 + Nc)/(3 + Nc)]/(4 - 5*Nc^2 + Nc^4)
 
Wig6j[{{"10", "10", "8", "27", "8", "8"}, {1, 1, 1, 1}}] = 
    -(Sqrt[2]/((-1 + Nc)*Nc*Sqrt[(-2 + Nc)*(1 + Nc)]*(2 + Nc)))
 
Wig6j[{{"10", "10", "8", "8", "10", "8"}, {1, 2, 1, 1}}] = 0
 
Wig6j[{{"10", "10", "8", "8", "8", "8"}, {1, 1, 1, 1}}] = 
    Sqrt[2]/(Sqrt[-4 + Nc^2]*(-1 + Nc^2))
 
Wig6j[{{"10", "10", "8", "8", "8", "8"}, {1, 1, 1, 2}}] = 
    Sqrt[2]/(4 - 5*Nc^2 + Nc^4)
 
Wig6j[{{"10", "15", "3", "10", "c1c2", "3"}, {1, 1, 1, 1}}] = 
    -4/(4*Nc - 5*Nc^3 + Nc^5)
 
Wig6j[{{"10", "15", "3", "8", "c1c2", "3"}, {1, 1, 1, 1}}] = 
    2/(Nc*Sqrt[4 - 5*Nc^2 + Nc^4])
 
Wig6j[{{"10", "15", "8", "15", "8", "3"}, {1, 1, 1, 1}}] = 
    2/(Sqrt[Nc*(1 + Nc)*(-1 + 3*Nc)]*(-2 + Nc + Nc^2))
 
Wig6j[{{"10", "15", "8", "15", "8", "3"}, {2, 1, 1, 1}}] = 
    -((Sqrt[2]*Sqrt[((3 + Nc)*(4 - 5*Nc^2 + Nc^4))/(Nc*(-1 + 3*Nc))])/
      ((-2 + Nc)*(1 + Nc)*(-2 + Nc + Nc^2)^(3/2)))
 
Wig6j[{{"10", "15", "8", "3", "8", "3"}, {1, 1, 1, 1}}] = 
    -(Sqrt[2]/((-1 + Nc)*Sqrt[Nc*(2 + 3*Nc + Nc^2)]))
 
Wig6j[{{"10", "15", "8", "c2c1", "8", "3"}, {1, 1, 1, 1}}] = 
    (Sqrt[2]*Sqrt[-4 - 4/Nc + Nc + Nc^2])/((-2 + Nc)^(3/2)*(-1 + Nc)*(1 + Nc)*
      (2 + Nc))
 
Wig6j[{{"10", "27", "10", "8", "8", "8"}, {1, 2, 1, 1}}] = 
    -(Sqrt[((-3 + Nc)*(6 + 5*Nc + Nc^2))/(-2 + Nc)]/(Sqrt[2]*(-1 + Nc)*Nc*
       (1 + Nc)*(3 + Nc)))
 
Wig6j[{{"10", "27", "10", "8", "8", "8"}, {1, 2, 1, 2}}] = 
    (Sqrt[(-3 + Nc)/(3 + Nc)]*(4 + Nc))/(Sqrt[2]*(4 - 5*Nc^2 + Nc^4))
 
Wig6j[{{"10", "27", "27", "8", "8", "8"}, {1, 1, 1, 1}}] = 
    (2 + Nc)/(Sqrt[2]*Nc^(3/2)*Sqrt[3 + Nc]*(-1 + Nc^2))
 
Wig6j[{{"10", "27", "27", "8", "8", "8"}, {1, 1, 1, 2}}] = 
    -(1/((-1 + Nc^2)*Sqrt[-8 - 24/Nc + 6*Nc + 2*Nc^2]))
 
Wig6j[{{"10", "27", "27", "8", "8", "8"}, {2, 1, 1, 1}}] = 
    -(1/(Sqrt[2]*Sqrt[((-2 + Nc)*(2 + Nc)*(3 + Nc))/(4 + Nc)]*(-1 + Nc^2)))
 
Wig6j[{{"10", "27", "27", "8", "8", "8"}, {2, 1, 1, 2}}] = 
    (Sqrt[(4 + Nc)/(3 + Nc)]*(-4 - 2*Nc + Nc^2))/
     (Sqrt[2]*Nc*(4 - 5*Nc^2 + Nc^4))
 
Wig6j[{{"10", "27", "8", "10", "10", "8"}, {1, 2, 1, 2}}] = 
    -((6 + 3*Nc + Nc^2)/(12*Nc + 4*Nc^2 - 15*Nc^3 - 5*Nc^4 + 3*Nc^5 + Nc^6))
 
Wig6j[{{"10", "27", "8", "10", "27", "8"}, {1, 1, 1, 1}}] = 
    (2*(-2 - 2*Nc + 2*Nc^2 + Nc^3))/((-2 + Nc)*(-1 + Nc)*Nc^2*(1 + Nc)*
      (2 + Nc)*(3 + Nc))
 
Wig6j[{{"10", "27", "8", "10", "8", "8"}, {1, 1, 1, 1}}] = 
    -2/(4*Nc - 5*Nc^3 + Nc^5)
 
Wig6j[{{"10", "27", "8", "10bar", "27", "8"}, {1, 1, 1, 1}}] = 
    -4/((-1 + Nc)*Nc^2*(3 + Nc)*(-4 + Nc^2))
 
Wig6j[{{"10", "27", "8", "10bar", "8", "8"}, {1, 1, 1, 1}}] = 
    -2/(Nc*(4 - 4*Nc - Nc^2 + Nc^3))
 
Wig6j[{{"10", "27", "8", "27", "10", "8"}, {1, 2, 1, 1}}] = 
    Sqrt[((-3 + Nc)*(2 + Nc))/(-2 + Nc)]/((-1 + Nc)*Nc^(3/2)*(1 + Nc)*
      (3 + Nc))
 
Wig6j[{{"10", "27", "8", "27", "10", "8"}, {2, 2, 1, 1}}] = 
    ((4 + 3*Nc)*Sqrt[-12 + Nc + Nc^2])/((-2 + Nc)*(-1 + Nc)*Nc*(1 + Nc)*
      (2 + Nc)*(3 + Nc))
 
Wig6j[{{"10", "27", "8", "27", "27", "8"}, {1, 1, 1, 1}}] = 
    (2 + Nc)/(Nc^2*(3 + Nc - 3*Nc^2 - Nc^3))
 
Wig6j[{{"10", "27", "8", "27", "27", "8"}, {1, 1, 1, 2}}] = 
    1/((-1 + Nc)*(1 + Nc)*(3 + Nc)*Sqrt[(Nc*(-4 + Nc^2))/(4 + Nc)])
 
Wig6j[{{"10", "27", "8", "27", "27", "8"}, {2, 1, 1, 2}}] = 
    -((4 + 2*Nc + Nc^2)/(12*Nc + 4*Nc^2 - 15*Nc^3 - 5*Nc^4 + 3*Nc^5 + Nc^6))
 
Wig6j[{{"10", "27", "8", "27", "8", "8"}, {1, 1, 1, 1}}] = 
    (Sqrt[2]*Sqrt[(3 + 4*Nc + Nc^2)/(Nc^3*(2 + Nc))])/(3 + Nc - 3*Nc^2 - Nc^3)
 
Wig6j[{{"10", "27", "8", "27", "8", "8"}, {2, 1, 1, 1}}] = 
    -((Sqrt[2]*Sqrt[((4 + Nc)*(3 + 4*Nc + Nc^2))/(-2 + Nc)])/
      ((-1 + Nc)*Nc*(1 + Nc)*(2 + Nc)*(3 + Nc)))
 
Wig6j[{{"10", "27", "8", "8", "10", "8"}, {1, 2, 1, 1}}] = 
    -((Sqrt[2]*Sqrt[-9 + Nc^2])/((-1 + Nc)*Nc*Sqrt[(-2 + Nc)*(1 + Nc)]*
       (2 + Nc)*(3 + Nc)))
 
Wig6j[{{"10", "27", "8", "8", "27", "8"}, {1, 1, 1, 1}}] = 
    2/((-1 + Nc)*Nc^2*(2 + Nc)*(3 + Nc))
 
Wig6j[{{"10", "27", "8", "8", "8", "8"}, {1, 1, 1, 1}}] = 
    1/((-1 + Nc)*Nc*Sqrt[(1 + Nc)*(2 + Nc)])
 
Wig6j[{{"10", "27", "8", "8", "8", "8"}, {1, 1, 1, 2}}] = 
    -(1/(Sqrt[(-2 + Nc)*(1 + Nc)]*(-2 + Nc + Nc^2)))
 
Wig6j[{{"10", "8", "10", "8", "8", "8"}, {1, 2, 1, 1}}] = 0
 
Wig6j[{{"10", "8", "10", "8", "8", "8"}, {1, 2, 1, 2}}] = 
    (Sqrt[2]*Sqrt[-9 + Nc^2])/(4 - 5*Nc^2 + Nc^4)
 
Wig6j[{{"10", "8", "8", "1", "8", "8"}, {1, 1, 1, 1}}] = (1 - Nc^2)^(-1)
 
Wig6j[{{"10", "8", "8", "10", "10", "8"}, {1, 2, 1, 2}}] = 
    2/(4 - 5*Nc^2 + Nc^4)
 
Wig6j[{{"10", "8", "8", "10", "8", "8"}, {1, 1, 1, 1}}] = 
    (4 - 5*Nc^2 + Nc^4)^(-1)
 
Wig6j[{{"10", "8", "8", "10bar", "8", "8"}, {1, 1, 1, 1}}] = 
    (4 - 5*Nc^2 + Nc^4)^(-1)
 
Wig6j[{{"10", "8", "8", "27", "8", "8"}, {1, 1, 1, 1}}] = 
    1/((-1 + Nc)*Nc*(1 + Nc)*(2 + Nc))
 
Wig6j[{{"10", "8", "8", "8", "8", "8"}, {1, 1, 1, 1}}] = 0
 
Wig6j[{{"10", "8", "8", "8", "8", "8"}, {2, 1, 1, 1}}] = 
    1/((1 - Nc^2)*Sqrt[-4 + Nc^2])
 
Wig6j[{{"10", "8", "8", "8", "8", "8"}, {2, 1, 1, 2}}] = 
    -2/(4 - 5*Nc^2 + Nc^4)
 
Wig6j[{{"10bar", "c2c1", "8", "15", "8", "3"}, {1, 1, 1, 1}}] = 
    (Sqrt[2]*Sqrt[-3 + 2/Nc + Nc])/(4 - 5*Nc^2 + Nc^4)
 
Wig6j[{{"10bar", "c2c1", "8", "3", "8", "3"}, {1, 1, 1, 1}}] = 
    Sqrt[2]/((1 + Nc)*Sqrt[Nc*(2 - 3*Nc + Nc^2)])
 
Wig6j[{{"10bar", "c2c1", "8", "c2c1", "8", "3"}, {1, 1, 1, 1}}] = 
    2/((-2 + Nc)*(1 + Nc)*Sqrt[(-1 + Nc)*Nc*(1 + 3*Nc)])
 
Wig6j[{{"10bar", "c2c1", "8", "c2c1", "8", "3"}, {2, 1, 1, 1}}] = 
    -((Sqrt[2]*Sqrt[(3 - 4*Nc + Nc^2)/(2*Nc + 7*Nc^2 + 3*Nc^3)])/
      (2 - Nc - 2*Nc^2 + Nc^3))
 
Wig6j[{{"15", "15", "3", "8", "8", "8"}, {1, 1, 1, 1}}] = 
    (-1 - 2*Nc)/((-1 + Nc)^(3/2)*(1 + Nc)*(2 + Nc)*
      Sqrt[(Nc*(-1 + 3*Nc))/(-2 + Nc + Nc^2)])
 
Wig6j[{{"15", "15", "3", "8", "8", "8"}, {1, 1, 1, 2}}] = 
    (2 - Nc)/((-1 + Nc)*(1 + Nc)*(2 + Nc)*Sqrt[Nc*(2 - 7*Nc + 3*Nc^2)])
 
Wig6j[{{"15", "15", "8", "15", "3", "8"}, {1, 1, 1, 1}}] = 
    -((2 + 4*Nc)/(2 - 5*Nc - 5*Nc^2 + 5*Nc^3 + 3*Nc^4))
 
Wig6j[{{"15", "15", "8", "3", "15", "8"}, {1, 2, 1, 1}}] = 
    -((Sqrt[2]*Sqrt[12 + 4*Nc - 15*Nc^2 - 5*Nc^3 + 3*Nc^4 + Nc^5])/
      ((-1 + 3*Nc)*(-2 - Nc + 2*Nc^2 + Nc^3)^(3/2)))
 
Wig6j[{{"15", "24", "15", "3", "8", "3"}, {1, 1, 1, 1}}] = 
    ((-1 + 2*Nc)*Sqrt[-4 + 10*Nc + 6*Nc^2])/(Nc*(2 + Nc)*(-1 + 3*Nc)*
      (-1 + Nc^2))
 
Wig6j[{{"15", "24", "15", "3", "8", "3"}, {1, 2, 1, 1}}] = 
    (2*(-2 + Nc))/((-1 + Nc^2)*Sqrt[12 - 32*Nc - 15*Nc^2 + 8*Nc^3 + 3*Nc^4])
 
Wig6j[{{"15", "24", "3", "15", "10", "3"}, {1, 1, 1, 1}}] = 
    2/(Nc*(-2 - Nc + 2*Nc^2 + Nc^3))
 
Wig6j[{{"15", "24", "3", "15", "27", "3"}, {1, 1, 1, 1}}] = 
    2/((-1 + Nc)*Nc*(2 + Nc)*(3 + Nc))
 
Wig6j[{{"15", "24", "3", "15", "8", "3"}, {1, 1, 1, 1}}] = 
    2/((-1 + Nc)*Nc*(2 + Nc))
 
Wig6j[{{"15", "3", "15", "8", "8", "8"}, {1, 2, 1, 1}}] = 
    -(1/(Sqrt[2]*(2 + 3*Nc + Nc^2)*Sqrt[((-1 + Nc)^2*Nc*(-1 + 3*Nc))/
         (-12 - 4*Nc + 3*Nc^2 + Nc^3)]))
 
Wig6j[{{"15", "3", "15", "8", "8", "8"}, {1, 2, 1, 2}}] = 
    (3*Sqrt[(Nc*(3 + Nc))/(-2 + 6*Nc)])/(-2 - Nc + 2*Nc^2 + Nc^3)
 
Wig6j[{{"15", "3", "3", "8", "8", "8"}, {1, 1, 1, 1}}] = 
    -(1/(Sqrt[2]*Sqrt[Nc]*(-1 + Nc^2)))
 
Wig6j[{{"15", "3", "3", "8", "8", "8"}, {1, 1, 1, 2}}] = 
    Sqrt[-4/Nc + Nc]/(Sqrt[2]*(2 + Nc)*(-1 + Nc^2))
 
Wig6j[{{"15", "3", "8", "15", "15", "8"}, {1, 2, 1, 2}}] = 
    (1 - Nc + 4*Nc^2)/(2*Nc - 5*Nc^2 - 5*Nc^3 + 5*Nc^4 + 3*Nc^5)
 
Wig6j[{{"15", "3", "8", "15", "3", "8"}, {1, 1, 1, 1}}] = 
    1/((1 + Nc)*(-2 + Nc + Nc^2))
 
Wig6j[{{"15", "6", "15", "3", "8", "3"}, {1, 1, 1, 1}}] = 
    -(((1 + Nc^2)*Sqrt[-4 + 10*Nc + 6*Nc^2])/(Nc*(2 + Nc)*(-1 + 3*Nc)*
       (-1 + Nc^2)))
 
Wig6j[{{"15", "6", "15", "3", "8", "3"}, {1, 2, 1, 1}}] = 
    (-2*(-6 + Nc + Nc^2))/((-1 + Nc^2)*Sqrt[12 - 32*Nc - 15*Nc^2 + 8*Nc^3 + 
        3*Nc^4])
 
Wig6j[{{"15", "6", "3", "15", "10", "3"}, {1, 1, 1, 1}}] = 
    -2/(Nc*(-2 + Nc + Nc^2))
 
Wig6j[{{"15", "6", "3", "15", "27", "3"}, {1, 1, 1, 1}}] = 
    2/((-1 + Nc)*Nc*(2 + Nc))
 
Wig6j[{{"15", "6", "3", "15", "8", "3"}, {1, 1, 1, 1}}] = 
    2/(Nc*(2 + Nc - 2*Nc^2 - Nc^3))
 
Wig6j[{{"15", "6", "3", "3", "8", "3"}, {1, 1, 1, 1}}] = 
    -(Sqrt[2]/(Sqrt[(-1 + Nc)*Nc]*(1 + Nc)))
 
Wig6j[{{"15", "6", "8", "6", "15", "3"}, {1, 1, 1, 1}}] = 
    (-2*Sqrt[2]*(-1 + Nc + Nc^2))/(Nc*(1 + Nc)*Sqrt[-1 + 3*Nc]*
      (-2 + Nc + Nc^2))
 
Wig6j[{{"15", "6", "8", "6", "15", "3"}, {1, 2, 1, 1}}] = 
    (2*Sqrt[(-6 + Nc + Nc^2)/(-1 + 3*Nc)])/((1 + Nc)*(-2 + Nc + Nc^2))
 
Wig6j[{{"15", "6", "8", "6", "3", "3"}, {1, 1, 1, 1}}] = 
    Sqrt[2]/((1 + Nc)*Sqrt[Nc*(-2 + Nc + Nc^2)])
 
Wig6j[{{"15", "6", "8", "c2c0", "3", "3"}, {1, 1, 1, 1}}] = 
    Sqrt[2]/((-1 + Nc)*Nc*Sqrt[1 + Nc])
 
Wig6j[{{"15", "c21c1", "15", "3", "8", "3"}, {1, 1, 1, 1}}] = 
    Sqrt[2]/((Nc - Nc^2)*Sqrt[-2 + 5*Nc + 3*Nc^2])
 
Wig6j[{{"15", "c21c1", "15", "3", "8", "3"}, {1, 2, 1, 1}}] = 
    (-3 - Nc)/((-1 + Nc)*Nc*Sqrt[12 - 32*Nc - 15*Nc^2 + 8*Nc^3 + 3*Nc^4])
 
Wig6j[{{"15", "c21c1", "3", "15", "10", "3"}, {1, 1, 1, 1}}] = 
    2/(Nc*(4 - 4*Nc - Nc^2 + Nc^3))
 
Wig6j[{{"15", "c21c1", "3", "15", "27", "3"}, {1, 1, 1, 1}}] = 
    2/(Nc^2*(-2 + Nc + Nc^2))
 
Wig6j[{{"15", "c21c1", "3", "15", "8", "3"}, {1, 1, 1, 1}}] = 
    -(1/(Nc*(-2 + Nc + Nc^2)))
 
Wig6j[{{"15bar", "10bar", "15bar", "3", "8", "3"}, {1, 1, 1, 1}}] = 
    Sqrt[2]/((Nc + Nc^2)*Sqrt[-2 + 5*Nc + 3*Nc^2])
 
Wig6j[{{"15bar", "10bar", "15bar", "3", "8", "3"}, {1, 2, 1, 1}}] = 
    (-2*(3 + Nc))/((-1 + Nc^2)*Sqrt[(2 + Nc)*(6 - 19*Nc + 2*Nc^2 + 3*Nc^3)])
 
Wig6j[{{"15bar", "27", "15bar", "3", "8", "3"}, {1, 1, 1, 1}}] = 
    -(Sqrt[-4 + 10*Nc + 6*Nc^2]/((-1 + Nc)*Nc*(2 + Nc)*(-1 + 3*Nc)))
 
Wig6j[{{"15bar", "27", "15bar", "3", "8", "3"}, {1, 2, 1, 1}}] = 
    (2*(-2 + Nc)*Sqrt[(3 + Nc)/(4 - 12*Nc - Nc^2 + 3*Nc^3)])/
     (Nc*(-3 + 2*Nc + Nc^2))
 
Wig6j[{{"15bar", "8", "15bar", "3", "8", "3"}, {1, 1, 1, 1}}] = 
    (Sqrt[2]*(-1 + Nc + Nc^2)*Sqrt[2 - 5*Nc - 5*Nc^2 + 5*Nc^3 + 3*Nc^4])/
     (Nc*(2 + Nc)*(-1 + 3*Nc)*(-1 + Nc^2)^(3/2))
 
Wig6j[{{"15bar", "8", "15bar", "3", "8", "3"}, {1, 2, 1, 1}}] = 
    -((-6 + Nc + Nc^2)/((-1 + Nc^2)*Sqrt[12 - 32*Nc - 15*Nc^2 + 8*Nc^3 + 
         3*Nc^4]))
 
Wig6j[{{"15bar", "8", "3bar", "3", "8", "3"}, {1, 1, 1, 1}}] = 
    (-1 + Nc^2)^(-1)
 
Wig6j[{{"15bar", "8", "8", "1", "3bar", "3"}, {1, 1, 1, 1}}] = 
    1/Sqrt[Nc*(-1 + Nc^2)]
 
Wig6j[{{"24", "6", "6", "8", "8", "8"}, {1, 1, 1, 1}}] = 
    -(Sqrt[2]/(Sqrt[Nc*(2 + Nc)]*(-1 + Nc^2)))
 
Wig6j[{{"24", "6", "6", "8", "8", "8"}, {1, 1, 1, 2}}] = 
    Sqrt[2 - 4/Nc]/((-1 + Nc)*(1 + Nc)*(2 + Nc))
 
Wig6j[{{"24", "6", "8", "24", "6", "8"}, {1, 1, 1, 1}}] = 
    2/((1 + Nc)*(-6 + Nc + 4*Nc^2 + Nc^3))
 
Wig6j[{{"24", "6", "8", "6", "6", "8"}, {1, 1, 1, 1}}] = 
    2/((1 + Nc)*(-2 + Nc + Nc^2))
 
Wig6j[{{"24", "6", "8", "c2c0", "6", "8"}, {1, 1, 1, 1}}] = -2/(Nc - Nc^3)
 
Wig6j[{{"24", "c111c0", "3", "24", "15", "3"}, {1, 1, 1, 1}}] = 
    -6/(Nc*(-6 - 5*Nc + 5*Nc^2 + 5*Nc^3 + Nc^4))
 
Wig6j[{{"24", "c111c0", "3", "6", "15", "3"}, {1, 1, 1, 1}}] = 
    (2*Sqrt[3])/(Sqrt[-1 + Nc^2]*(2*Nc + Nc^2))
 
Wig6j[{{"24", "c111c0", "6", "3", "8", "3"}, {1, 1, 1, 1}}] = 
    Sqrt[6]/((1 + Nc)*Sqrt[Nc*(-2 + Nc + Nc^2)])
 
Wig6j[{{"24", "c111c0", "8", "c111c0", "6", "3"}, {1, 1, 1, 1}}] = 
    (2*Sqrt[3])/((1 + Nc)*(2 + Nc)*Sqrt[Nc*(-3 + 2*Nc + Nc^2)])
 
Wig6j[{{"24", "c111c0", "8", "c21c0", "6", "3"}, {1, 1, 1, 1}}] = 
    (2*Sqrt[3])/(Sqrt[2 + Nc]*(Nc - Nc^3))
 
Wig6j[{{"24bar", "15bar", "6bar", "3", "8", "3"}, {1, 1, 1, 1}}] = 
    Sqrt[6 + 4/Nc + 2*Nc]/((-1 + Nc)*(1 + Nc)*(2 + Nc))
 
Wig6j[{{"24bar", "15bar", "8", "15bar", "6bar", "3"}, {1, 1, 1, 1}}] = 
    2/(Sqrt[Nc*(1 + Nc)*(-1 + 3*Nc)]*(-2 + Nc + Nc^2))
 
Wig6j[{{"24bar", "15bar", "8", "15bar", "6bar", "3"}, {2, 1, 1, 1}}] = 
    (2*Sqrt[2]*Sqrt[(-6 - 5*Nc + 2*Nc^2 + Nc^3)/((-1 + Nc)^2*Nc*
         (-1 + 3*Nc))])/(6 + 11*Nc + 6*Nc^2 + Nc^3)
 
Wig6j[{{"24bar", "15bar", "8", "3bar", "6bar", "3"}, {1, 1, 1, 1}}] = 
    2/(Nc*Sqrt[(2 + Nc)*(-1 + Nc^2)])
 
Wig6j[{{"27", "15", "3", "27", "15bar", "3"}, {1, 1, 1, 1}}] = 
    -4/(Nc^2*(3 + Nc)*(-2 + Nc + Nc^2))
 
Wig6j[{{"27", "15", "3", "8", "15bar", "3"}, {1, 1, 1, 1}}] = 
    2/((-1 + Nc)*Nc*(2 + Nc))
 
Wig6j[{{"27", "15", "8", "15", "8", "3"}, {1, 1, 1, 1}}] = 
    -2/((-2 + Nc + Nc^2)*Sqrt[Nc*(-1 + 2*Nc + 3*Nc^2)])
 
Wig6j[{{"27", "15", "8", "15", "8", "3"}, {2, 1, 1, 1}}] = 
    (Sqrt[2]*Sqrt[(-2 - Nc + Nc^2)/(Nc^3*(-3 + 8*Nc + 3*Nc^2))])/
     (2 + 3*Nc + Nc^2)
 
Wig6j[{{"27", "15", "8", "3", "8", "3"}, {1, 1, 1, 1}}] = 
    Sqrt[2]/((-1 + Nc)*Sqrt[Nc*(2 + 3*Nc + Nc^2)])
 
Wig6j[{{"27", "15", "8", "c2c1", "8", "3"}, {1, 1, 1, 1}}] = 
    (Sqrt[2]*Sqrt[(2 + 3*Nc + Nc^2)/Nc^3])/(2 + Nc - 2*Nc^2 - Nc^3)
 
Wig6j[{{"27", "27", "27", "8", "8", "8"}, {1, 1, 1, 1}}] = 
    1/(Sqrt[2]*Sqrt[Nc*(3 + Nc)]*(-1 + Nc^2))
 
Wig6j[{{"27", "27", "27", "8", "8", "8"}, {1, 1, 1, 2}}] = 0
 
Wig6j[{{"27", "27", "27", "8", "8", "8"}, {1, 2, 1, 1}}] = 0
 
Wig6j[{{"27", "27", "27", "8", "8", "8"}, {1, 2, 1, 2}}] = 
    Sqrt[(4 + Nc)/(3 + Nc)]/(Sqrt[2]*Nc*(-1 + Nc^2))
 
Wig6j[{{"27", "27", "27", "8", "8", "8"}, {2, 2, 1, 1}}] = 
    1/(Sqrt[2]*Sqrt[Nc*(3 + Nc)]*(-1 + Nc^2))
 
Wig6j[{{"27", "27", "27", "8", "8", "8"}, {2, 2, 1, 2}}] = 0
 
Wig6j[{{"27", "27", "27", "8", "8", "8"}, {2, 2, 2, 1}}] = 0
 
Wig6j[{{"27", "27", "27", "8", "8", "8"}, {2, 2, 2, 2}}] = 
    (-32 - 20*Nc + 4*Nc^2 + Nc^3)/(Sqrt[2]*Nc*Sqrt[(3 + Nc)*(4 + Nc)]*
      (4 - 5*Nc^2 + Nc^4))
 
Wig6j[{{"27", "27", "8", "27", "27", "8"}, {1, 1, 1, 1}}] = 
    (4 + 3*Nc)/((-1 + Nc)*Nc^2*(1 + Nc)*(3 + Nc))
 
Wig6j[{{"27", "27", "8", "27", "27", "8"}, {1, 2, 1, 1}}] = 0
 
Wig6j[{{"27", "27", "8", "27", "27", "8"}, {1, 2, 1, 2}}] = 
    (3*Nc + Nc^2 - 3*Nc^3 - Nc^4)^(-1)
 
Wig6j[{{"27", "27", "8", "27", "27", "8"}, {2, 2, 1, 1}}] = 
    (4 + 3*Nc)/((-1 + Nc)*Nc^2*(1 + Nc)*(3 + Nc))
 
Wig6j[{{"27", "27", "8", "27", "27", "8"}, {2, 2, 1, 2}}] = 0
 
Wig6j[{{"27", "27", "8", "27", "27", "8"}, {2, 2, 2, 2}}] = 
    (-64 - 80*Nc - 12*Nc^2 + 16*Nc^3 + 3*Nc^4)/((-2 + Nc)*(-1 + Nc)*Nc^2*
      (1 + Nc)*(2 + Nc)*(3 + Nc)*(4 + Nc))
 
Wig6j[{{"27", "27", "8", "27", "8", "8"}, {1, 1, 1, 1}}] = 
    -2/((-1 + Nc)*Nc^2*(3 + Nc))
 
Wig6j[{{"27", "27", "8", "8", "27", "8"}, {1, 2, 1, 1}}] = 0
 
Wig6j[{{"27", "27", "8", "8", "8", "8"}, {1, 1, 1, 1}}] = 
    Sqrt[2]/((-1 + Nc)*Nc^(3/2)*Sqrt[3 + Nc])
 
Wig6j[{{"27", "27", "8", "8", "8", "8"}, {1, 1, 1, 2}}] = 0
 
Wig6j[{{"27", "8", "27", "8", "8", "8"}, {1, 2, 1, 1}}] = 0
 
Wig6j[{{"27", "8", "27", "8", "8", "8"}, {1, 2, 1, 2}}] = 
    (Sqrt[2]*Sqrt[(4 + Nc)/(3 + Nc)])/((-1 + Nc)*Nc*(2 + Nc))
 
Wig6j[{{"27", "8", "8", "1", "8", "8"}, {1, 1, 1, 1}}] = (-1 + Nc^2)^(-1)
 
Wig6j[{{"27", "8", "8", "27", "27", "8"}, {1, 2, 1, 2}}] = 
    2/((-1 + Nc)*Nc*(2 + Nc)*(3 + Nc))
 
Wig6j[{{"27", "8", "8", "27", "8", "8"}, {1, 1, 1, 1}}] = 
    (2 + Nc + Nc^2)/(Nc^2*(2 + Nc)*(3 + Nc)*(-1 + Nc^2))
 
Wig6j[{{"27", "8", "8", "8", "8", "8"}, {1, 1, 1, 1}}] = (Nc - Nc^3)^(-1)
 
Wig6j[{{"27", "8", "8", "8", "8", "8"}, {2, 1, 1, 1}}] = 0
 
Wig6j[{{"27", "8", "8", "8", "8", "8"}, {2, 1, 1, 2}}] = 
    1/((-1 + Nc)*(1 + Nc)*(2 + Nc))
 
Wig6j[{{"3", "3", "3", "8", "8", "8"}, {1, 1, 1, 1}}] = 
    Sqrt[Nc]/(Sqrt[2]*(-1 + Nc^2))
 
Wig6j[{{"3", "3", "3", "8", "8", "8"}, {1, 1, 1, 2}}] = 
    Sqrt[-4/Nc + Nc]/(Sqrt[2]*(-1 + Nc^2))
 
Wig6j[{{"3", "6", "3", "3", "1", "3"}, {1, 1, 1, 1}}] = Nc^(-1)
 
Wig6j[{{"3", "6", "3", "3", "8", "3"}, {1, 1, 1, 1}}] = (Nc + Nc^2)^(-1)
 
Wig6j[{{"3", "c2c0", "3", "3", "1", "3"}, {1, 1, 1, 1}}] = -Nc^(-1)
 
Wig6j[{{"3", "c2c0", "3", "3", "8", "3"}, {1, 1, 1, 1}}] = (Nc - Nc^2)^(-1)
 
Wig6j[{{"35", "10", "10", "8", "8", "8"}, {1, 1, 1, 1}}] = 
    3/(Sqrt[2]*Sqrt[-4 + Nc^2]*(Nc - Nc^3))
 
Wig6j[{{"35", "10", "10", "8", "8", "8"}, {1, 1, 1, 2}}] = 
    1/(Sqrt[2]*(4 - 5*Nc^2 + Nc^4))
 
Wig6j[{{"35", "10", "10", "8", "8", "8"}, {2, 1, 1, 1}}] = 
    Sqrt[(-9 + Nc^2)/(-4 + Nc^2)]/(Sqrt[2]*(3*Nc + Nc^2 - 3*Nc^3 - Nc^4))
 
Wig6j[{{"35", "10", "10", "8", "8", "8"}, {2, 1, 1, 2}}] = 
    (3*Sqrt[-9 + Nc^2])/(Sqrt[2]*(12 + 4*Nc - 15*Nc^2 - 5*Nc^3 + 3*Nc^4 + 
       Nc^5))
 
Wig6j[{{"35", "10", "27", "8", "8", "8"}, {1, 1, 1, 1}}] = 
    Sqrt[3]/(Sqrt[-6 + Nc + Nc^2]*(Nc - Nc^3))
 
Wig6j[{{"35", "10", "27", "8", "8", "8"}, {1, 1, 1, 2}}] = 
    -(Sqrt[3]/(Sqrt[6 + 5*Nc + Nc^2]*(2 - Nc - 2*Nc^2 + Nc^3)))
 
Wig6j[{{"35", "10", "35", "8", "8", "8"}, {1, 2, 1, 1}}] = 
    -((Sqrt[3]*(3 + 5*Nc + Nc^2))/((-1 + Nc)*Nc*(3 + Nc)*(4 + Nc)*
       Sqrt[((-4 + Nc^2)*(-81 - 66*Nc + 16*Nc^2 + 20*Nc^3 + 3*Nc^4))/
         (12 + 7*Nc + Nc^2)]))
 
Wig6j[{{"35", "10", "35", "8", "8", "8"}, {1, 2, 1, 2}}] = 
    (3*Sqrt[3]*(-9 + 3*Nc + Nc^2))/(Nc*(2 - 3*Nc + Nc^2)*
      Sqrt[(12 + 7*Nc + Nc^2)*(-81 - 66*Nc + 16*Nc^2 + 20*Nc^3 + 3*Nc^4)])
 
Wig6j[{{"35", "10", "35", "8", "8", "8"}, {1, 3, 1, 1}}] = 
    (Sqrt[3/2]*(9 + 9*Nc + 2*Nc^2))/(Nc^(3/2)*(1 + Nc)*
      Sqrt[((-2 + Nc)*(4 + Nc)*(-2 + Nc + Nc^2)*(-243 - 279*Nc - 18*Nc^2 + 
          76*Nc^3 + 29*Nc^4 + 3*Nc^5))/(-15 + 2*Nc + Nc^2)])
 
Wig6j[{{"35", "10", "35", "8", "8", "8"}, {1, 3, 1, 2}}] = 
    (Sqrt[3/2]*(3 + Nc))/((1 + Nc)*(2 + Nc)*
      Sqrt[((-2 + Nc)^2*(-1 + Nc)*Nc*(4 + Nc)*(-243 - 279*Nc - 18*Nc^2 + 
          76*Nc^3 + 29*Nc^4 + 3*Nc^5))/(-15 + 2*Nc + Nc^2)])
 
Wig6j[{{"35", "10", "8", "0", "10", "8"}, {1, 1, 1, 1}}] = 
    4/(4*Nc - 5*Nc^3 + Nc^5)
 
Wig6j[{{"35", "10", "8", "10", "10", "8"}, {1, 1, 1, 1}}] = 
    3/(4*Nc - 5*Nc^3 + Nc^5)
 
Wig6j[{{"35", "10", "8", "10", "10", "8"}, {1, 1, 1, 2}}] = 
    Sqrt[-9 + Nc^2]/(12*Nc + 4*Nc^2 - 15*Nc^3 - 5*Nc^4 + 3*Nc^5 + Nc^6)
 
Wig6j[{{"35", "10", "8", "10", "10", "8"}, {2, 1, 1, 2}}] = 
    (-1 + 3*Nc)/(Nc*(1 + Nc)*(3 + Nc)*(4 - 4*Nc - Nc^2 + Nc^3))
 
Wig6j[{{"35", "10", "8", "10", "27", "8"}, {1, 1, 1, 1}}] = 
    Sqrt[6]/(Nc*Sqrt[6 + 5*Nc + Nc^2]*(2 - Nc - 2*Nc^2 + Nc^3))
 
Wig6j[{{"35", "10", "8", "10", "27", "8"}, {2, 1, 1, 1}}] = 
    -((Sqrt[6]*Sqrt[(-3 + Nc)/(2 + Nc)])/(Nc*(6 - Nc - 7*Nc^2 + Nc^3 + Nc^4)))
 
Wig6j[{{"35", "10", "8", "27", "10", "8"}, {1, 1, 1, 1}}] = 
    2/(12 + 4*Nc - 15*Nc^2 - 5*Nc^3 + 3*Nc^4 + Nc^5)
 
Wig6j[{{"35", "10", "8", "27", "27", "8"}, {1, 1, 1, 1}}] = 
    Sqrt[6]/(Sqrt[-2 + Nc]*(-1 + Nc)*Nc^(3/2)*(1 + Nc)*(3 + Nc))
 
Wig6j[{{"35", "10", "8", "27", "27", "8"}, {1, 1, 1, 2}}] = 
    Sqrt[6]/(Nc*Sqrt[8 + 6*Nc + Nc^2]*(3 + Nc - 3*Nc^2 - Nc^3))
 
Wig6j[{{"35", "10", "8", "35", "10", "8"}, {1, 1, 1, 1}}] = 
    (6 + 4*Nc + 4*Nc^2)/(Nc^2*(3 + Nc)*(4 + Nc)*(4 - 5*Nc^2 + Nc^4))
 
Wig6j[{{"35", "10", "8", "35", "27", "8"}, {1, 1, 1, 1}}] = 
    18/((-1 + Nc)*Nc^2*(1 + Nc)*(3 + Nc)*(4 + Nc)*(-4 + Nc^2))
 
Wig6j[{{"35", "10", "8", "8", "10", "8"}, {1, 1, 1, 1}}] = 
    2/(4 - 5*Nc^2 + Nc^4)
 
Wig6j[{{"35", "10", "8", "8", "27", "8"}, {1, 1, 1, 1}}] = 
    (2*Sqrt[3]*Sqrt[(-4 - 4*Nc + Nc^2 + Nc^3)/(3 + Nc)])/
     (4*Nc - 5*Nc^3 + Nc^5)
 
Wig6j[{{"35", "27", "27", "8", "8", "8"}, {1, 1, 1, 1}}] = 
    -(1/(Sqrt[2]*Nc^(3/2)*Sqrt[3 + Nc]*(-1 + Nc^2)))
 
Wig6j[{{"35", "27", "27", "8", "8", "8"}, {1, 1, 1, 2}}] = 
    3/(Sqrt[2]*Sqrt[Nc*(3 + Nc)*(-4 + Nc^2)]*(-1 + Nc^2))
 
Wig6j[{{"35", "27", "27", "8", "8", "8"}, {2, 1, 1, 1}}] = 
    (-3*(2 + Nc))/(Sqrt[2]*Nc*(-1 + Nc^2)*Sqrt[-48 - 28*Nc + 8*Nc^2 + 
        7*Nc^3 + Nc^4])
 
Wig6j[{{"35", "27", "27", "8", "8", "8"}, {2, 1, 1, 2}}] = 
    (-8 + Nc)/(Sqrt[2]*(-2 + Nc)*(-1 + Nc)*Nc*(1 + Nc)*
      Sqrt[(3 + Nc)*(4 + Nc)])
 
Wig6j[{{"35", "27", "35", "8", "8", "8"}, {1, 2, 1, 1}}] = 
    (Sqrt[3]*(3 + 5*Nc + Nc^2))/((-1 + Nc)*Nc*
      Sqrt[(-4 + Nc^2)*(12 + 7*Nc + Nc^2)*(-81 - 66*Nc + 16*Nc^2 + 20*Nc^3 + 
         3*Nc^4)])
 
Wig6j[{{"35", "27", "35", "8", "8", "8"}, {1, 2, 1, 2}}] = 
    (Sqrt[3]*(-54 - 15*Nc + 5*Nc^2 + Nc^3))/((-1 + Nc)*Nc*(-4 + Nc^2)*
      Sqrt[(12 + 7*Nc + Nc^2)*(-81 - 66*Nc + 16*Nc^2 + 20*Nc^3 + 3*Nc^4)])
 
Wig6j[{{"35", "27", "35", "8", "8", "8"}, {1, 3, 1, 1}}] = 
    -((Sqrt[3/2]*(3 + Nc)*(3 + 2*Nc)*Sqrt[(-15 + 2*Nc + Nc^2)/
         ((-1 + Nc)*(-48 - 28*Nc + 8*Nc^2 + 7*Nc^3 + Nc^4)*
          (-81 - 66*Nc + 16*Nc^2 + 20*Nc^3 + 3*Nc^4))])/(Nc^(3/2)*(1 + Nc)))
 
Wig6j[{{"35", "27", "35", "8", "8", "8"}, {1, 3, 1, 2}}] = 
    (Sqrt[3/2]*(3 + Nc)*(7 + 4*Nc)*Sqrt[(-15 + 2*Nc + Nc^2)/
        ((-1 + Nc)*Nc*(12 + 7*Nc + Nc^2)*(-81 - 66*Nc + 16*Nc^2 + 20*Nc^3 + 
          3*Nc^4))])/((1 + Nc)*(-4 + Nc^2))
 
Wig6j[{{"35", "27", "8", "10", "27", "8"}, {1, 1, 1, 1}}] = 
    -2/(Nc^2*(-3 - Nc + 3*Nc^2 + Nc^3))
 
Wig6j[{{"35", "27", "8", "10bar", "27", "8"}, {1, 1, 1, 1}}] = 
    4/(Nc^2*(6 - 7*Nc + Nc^3))
 
Wig6j[{{"35", "27", "8", "27", "27", "8"}, {1, 1, 1, 1}}] = 
    1/((-1 + Nc)*Nc^2*(1 + Nc)*(3 + Nc))
 
Wig6j[{{"35", "27", "8", "27", "27", "8"}, {1, 1, 1, 2}}] = 
    (3*(2 + Nc))/((-1 + Nc)*Nc^(3/2)*(1 + Nc)*(3 + Nc)*
      Sqrt[-16 - 4*Nc + 4*Nc^2 + Nc^3])
 
Wig6j[{{"35", "27", "8", "27", "27", "8"}, {2, 1, 1, 2}}] = 
    (10 + Nc)/(24*Nc + 2*Nc^2 - 29*Nc^3 - 3*Nc^4 + 5*Nc^5 + Nc^6)
 
Wig6j[{{"35", "27", "8", "35", "27", "8"}, {1, 1, 1, 1}}] = 
    (2*(-5 + 6*Nc + 2*Nc^2))/((-1 + Nc)*Nc^2*(3 + Nc)*
      (-16 - 20*Nc + 5*Nc^3 + Nc^4))
 
Wig6j[{{"35", "27", "8", "35bar", "27", "8"}, {1, 1, 1, 1}}] = 
    4/((-1 + Nc)*Nc^2*(3 + Nc)*(-8 + 2*Nc + Nc^2))
 
Wig6j[{{"35", "27", "8", "64", "27", "8"}, {1, 1, 1, 1}}] = 
    4/((-1 + Nc)*Nc^2*(1 + Nc)*(3 + Nc)*(4 + Nc))
 
Wig6j[{{"35", "27", "8", "8", "27", "8"}, {1, 1, 1, 1}}] = 
    -2/((-1 + Nc)*Nc^2*(3 + Nc))
 
Wig6j[{{"35", "35", "10", "8", "8", "8"}, {1, 1, 1, 1}}] = 
    (Sqrt[3/2]*(3 + 2*Nc))/(Nc^(3/2)*Sqrt[(4 + Nc)*(-4 + Nc^2)]*(-1 + Nc^2))
 
Wig6j[{{"35", "35", "10", "8", "8", "8"}, {1, 1, 1, 2}}] = 
    Sqrt[3/2]/(Sqrt[Nc*(4 + Nc)]*(4 - 5*Nc^2 + Nc^4))
 
Wig6j[{{"35", "35", "27", "8", "8", "8"}, {1, 1, 1, 1}}] = 
    (Sqrt[3/2]*(1 + 2*Nc))/(Nc^(3/2)*(-1 + Nc^2)*
      Sqrt[-16 - 4*Nc + 4*Nc^2 + Nc^3])
 
Wig6j[{{"35", "35", "27", "8", "8", "8"}, {1, 1, 1, 2}}] = 
    (3*Sqrt[3/2])/(Sqrt[Nc*(4 + Nc)]*(4 - 5*Nc^2 + Nc^4))
 
Wig6j[{{"35", "64", "27", "8", "8", "8"}, {1, 1, 1, 1}}] = 
    Sqrt[6]/(Sqrt[Nc^3*(4 + Nc)]*(-1 + Nc^2))
 
Wig6j[{{"35", "64", "27", "8", "8", "8"}, {1, 1, 1, 2}}] = 
    -(Sqrt[6]/(Sqrt[Nc*(4 + Nc)*(-4 + Nc^2)]*(-1 + Nc^2)))
 
Wig6j[{{"3bar", "1", "3bar", "3", "8", "3"}, {1, 1, 1, 1}}] = Nc^(-1)
 
Wig6j[{{"3bar", "8", "3bar", "3", "8", "3"}, {1, 1, 1, 1}}] = (Nc - Nc^3)^(-1)
 
Wig6j[{{"6", "6", "6", "8", "8", "8"}, {1, 1, 1, 1}}] = 
    Nc/(Sqrt[2]*Sqrt[Nc*(2 + Nc)]*(-1 + Nc^2))
 
Wig6j[{{"6", "6", "6", "8", "8", "8"}, {1, 1, 1, 2}}] = 
    (Sqrt[(-2 + Nc)/Nc]*(4 + Nc))/(Sqrt[2]*(1 + Nc)*(-2 + Nc + Nc^2))
 
Wig6j[{{"6", "6", "8", "6", "6", "8"}, {1, 1, 1, 1}}] = 
    (-4 + 2*Nc + Nc^2)/(Nc*(1 + Nc)*(-2 + Nc + Nc^2))
 
Wig6j[{{"6", "c111c0", "3", "6", "15", "3"}, {1, 1, 1, 1}}] = 
    2/(2*Nc + 3*Nc^2 + Nc^3)
 
Wig6j[{{"6", "c111c0", "3", "6", "3", "3"}, {1, 1, 1, 1}}] = 2/(Nc + Nc^2)
 
Wig6j[{{"6", "c111c0", "6", "3", "8", "3"}, {1, 1, 1, 1}}] = 
    2/(Sqrt[2 + Nc]*(Nc + Nc^2))
 
Wig6j[{{"6", "c21c0", "3", "6", "15", "3"}, {1, 1, 1, 1}}] = -2/(Nc - Nc^3)
 
Wig6j[{{"6", "c21c0", "3", "6", "3", "3"}, {1, 1, 1, 1}}] = -(Nc + Nc^2)^(-1)
 
Wig6j[{{"6", "c21c0", "6", "3", "8", "3"}, {1, 1, 1, 1}}] = 
    Sqrt[2 + Nc]/(Nc - Nc^3)
 
Wig6j[{{"64", "27", "27", "8", "8", "8"}, {1, 1, 1, 1}}] = 
    (-2*Sqrt[2])/(Nc^(3/2)*Sqrt[3 + Nc]*(-1 + Nc^2))
 
Wig6j[{{"64", "27", "27", "8", "8", "8"}, {1, 1, 1, 2}}] = 0
 
Wig6j[{{"64", "27", "27", "8", "8", "8"}, {2, 1, 1, 1}}] = 0
 
Wig6j[{{"64", "27", "27", "8", "8", "8"}, {2, 1, 1, 2}}] = 
    (-2*Sqrt[2])/(Sqrt[12 + 7*Nc + Nc^2]*(Nc - Nc^3))
 
Wig6j[{{"64", "27", "64", "8", "8", "8"}, {1, 2, 1, 1}}] = 0
 
Wig6j[{{"64", "27", "64", "8", "8", "8"}, {1, 2, 1, 2}}] = 
    (2*Sqrt[3])/(Nc*(1 + Nc)*Sqrt[((-1 + Nc)^2*(1 + Nc)*(4 + Nc)*(5 + Nc))/
        (6 + Nc)])
 
Wig6j[{{"64", "27", "8", "10", "27", "8"}, {1, 1, 1, 1}}] = 
    4/((-1 + Nc)*Nc^2*(1 + Nc)*(3 + Nc))
 
Wig6j[{{"64", "27", "8", "27", "27", "8"}, {1, 1, 1, 1}}] = 
    4/((-1 + Nc)*Nc^2*(1 + Nc)*(3 + Nc))
 
Wig6j[{{"64", "27", "8", "27", "27", "8"}, {1, 1, 1, 2}}] = 0
 
Wig6j[{{"64", "27", "8", "27", "27", "8"}, {2, 1, 1, 2}}] = 
    4/((-1 + Nc)*Nc*(1 + Nc)*(3 + Nc)*(4 + Nc))
 
Wig6j[{{"64", "27", "8", "64", "27", "8"}, {1, 1, 1, 1}}] = 
    (4*(8 + 3*Nc + Nc^2))/((-1 + Nc)*Nc^2*(1 + Nc)^2*(3 + Nc)*(4 + Nc)*
      (5 + Nc))
 
Wig6j[{{"64", "27", "8", "8", "27", "8"}, {1, 1, 1, 1}}] = 
    4/((-1 + Nc)*Nc^2*(3 + Nc))
 
Wig6j[{{"64", "64", "27", "8", "8", "8"}, {1, 1, 1, 1}}] = 
    (2*Sqrt[3]*Sqrt[(2 + Nc)/(5 + Nc)])/((-1 + Nc)*(Nc*(1 + Nc))^(3/2))
 
Wig6j[{{"64", "64", "27", "8", "8", "8"}, {1, 1, 1, 2}}] = 0
 
Wig6j[{{"6bar", "15bar", "6bar", "3", "8", "3"}, {1, 1, 1, 1}}] = 
    2/(Sqrt[2 + Nc]*(Nc - Nc^3))
 
Wig6j[{{"6bar", "3bar", "6bar", "3", "8", "3"}, {1, 1, 1, 1}}] = 
    -(Sqrt[2 + Nc]/(Nc + Nc^2))
 
Wig6j[{{"8", "8", "8", "8", "8", "8"}, {1, 1, 1, 1}}] = 1/(2*(-1 + Nc^2))
 
Wig6j[{{"8", "8", "8", "8", "8", "8"}, {1, 2, 1, 1}}] = 0
 
Wig6j[{{"8", "8", "8", "8", "8", "8"}, {2, 2, 1, 1}}] = 1/(2*(-1 + Nc^2))
 
Wig6j[{{"8", "8", "8", "8", "8", "8"}, {2, 2, 2, 1}}] = 0
 
Wig6j[{{"8", "8", "8", "8", "8", "8"}, {2, 2, 2, 2}}] = 
    (-12 + Nc^2)/(2*(4 - 5*Nc^2 + Nc^4))
 
Wig6j[{{"c0c111", "24bar", "c0c111", "3", "8", "3"}, {1, 1, 1, 1}}] = 
    (3*Sqrt[2]*Sqrt[(3 + Nc)/(2 + Nc)])/(Nc*(3 + Nc - 3*Nc^2 - Nc^3))
 
Wig6j[{{"c0c111", "6bar", "8", "6bar", "c0c111", "3"}, {1, 1, 1, 1}}] = 
    (2*Sqrt[2]*Sqrt[3 + Nc])/(Nc*(2 + 3*Nc + Nc^2))
 
Wig6j[{{"c0c111", "6bar", "c0c111", "3", "8", "3"}, {1, 1, 1, 1}}] = 
    (Sqrt[2]*Sqrt[6 + 5*Nc + Nc^2])/(Nc*(2 + 3*Nc + Nc^2))
 
Wig6j[{{"c0c2", "3bar", "6bar", "3", "8", "3"}, {1, 1, 1, 1}}] = 
    1/Sqrt[Nc*(-1 + Nc^2)]
 
Wig6j[{{"c0c2", "3bar", "c0c2", "3", "8", "3"}, {1, 1, 1, 1}}] = 
    Sqrt[-2 + Nc]/(Nc - Nc^2)
 
Wig6j[{{"c0c2", "c1c2", "c0c2", "3", "8", "3"}, {1, 1, 1, 1}}] = 
    2/(Sqrt[-2 + Nc]*(Nc - Nc^3))
 
Wig6j[{{"c0c21", "6bar", "8", "6bar", "c0c111", "3"}, {1, 1, 1, 1}}] = 
    Sqrt[2]/((1 + Nc)*Sqrt[Nc*(-2 + Nc + Nc^2)])
 
Wig6j[{{"c0c21", "6bar", "8", "6bar", "c0c21", "3"}, {1, 1, 1, 1}}] = 
    ((-3 + 2*Nc)*Sqrt[-6 - 3*Nc + 2*Nc^2 + Nc^3])/(Nc*(3 - 4*Nc^2 + Nc^4))
 
Wig6j[{{"c0c21", "6bar", "8", "6bar", "c0c21", "3"}, {1, 2, 1, 1}}] = 
    (2 - Nc)/(Sqrt[(-2 + Nc)*(-3 + Nc^2)]*(-1 + Nc^2))
 
Wig6j[{{"c0c21", "6bar", "c0c111", "3", "8", "3"}, {1, 1, 1, 1}}] = 
    Sqrt[-2/Nc + 2*Nc]/((-1 + Nc)*(1 + Nc)^(3/2))
 
Wig6j[{{"c0c21", "6bar", "c0c21", "3", "8", "3"}, {1, 1, 1, 1}}] = 
    (-3 - Nc + Nc^2)/(Nc*Sqrt[-3 + Nc^2]*(-1 + Nc^2))
 
Wig6j[{{"c0c21", "6bar", "c0c21", "3", "8", "3"}, {1, 2, 1, 1}}] = 
    Sqrt[(-4 + Nc^2)/(-3 + Nc^2)]/(-1 + Nc^2)
 
Wig6j[{{"c0c21", "c0c2", "8", "6bar", "c0c111", "3"}, {1, 1, 1, 1}}] = 
    -((Sqrt[6]*Sqrt[-1 + Nc])/(Nc - Nc^3))
 
Wig6j[{{"c0c21", "c0c2", "8", "6bar", "c0c21", "3"}, {1, 1, 1, 1}}] = 
    (Sqrt[3]*Sqrt[-3/Nc + Nc])/(3 - 4*Nc^2 + Nc^4)
 
Wig6j[{{"c0c21", "c0c2", "8", "6bar", "c0c21", "3"}, {1, 2, 1, 1}}] = 
    -(Sqrt[3]/(Sqrt[(Nc*(-3 + Nc^2))/(-4 + Nc^2)]*(-1 + Nc^2)))
 
Wig6j[{{"c0c21", "c0c2", "8", "c0c2", "c0c21", "3"}, {1, 1, 1, 1}}] = 
    ((3 + 2*Nc)*Sqrt[6 - 3*Nc - 2*Nc^2 + Nc^3])/(Nc*(3 - 4*Nc^2 + Nc^4))
 
Wig6j[{{"c0c21", "c0c2", "8", "c0c2", "c0c21", "3"}, {1, 2, 1, 1}}] = 
    -((-2 - Nc)/(Sqrt[(2 + Nc)*(-3 + Nc^2)]*(-1 + Nc^2)))
 
Wig6j[{{"c0c21", "c0c2", "c0c21", "3", "8", "3"}, {1, 1, 1, 1}}] = 
    (-3 + Nc + Nc^2)/(Nc*Sqrt[-3 + Nc^2]*(-1 + Nc^2))
 
Wig6j[{{"c0c21", "c0c2", "c0c21", "3", "8", "3"}, {1, 2, 1, 1}}] = 
    (4 - Nc^2)/((-1 + Nc^2)*Sqrt[12 - 7*Nc^2 + Nc^4])
 
Wig6j[{{"c0c21", "c1c21", "c0c21", "3", "8", "3"}, {1, 1, 1, 1}}] = 
    3/(Sqrt[-3 + Nc^2]*(Nc - Nc^3))
 
Wig6j[{{"c0c21", "c1c21", "c0c21", "3", "8", "3"}, {1, 2, 1, 1}}] = 
    3/((Nc - Nc^3)*Sqrt[12 - 7*Nc^2 + Nc^4])
 
Wig6j[{{"c0c3", "c0c2", "8", "6bar", "c0c21", "3"}, {1, 1, 1, 1}}] = 
    -((Sqrt[6]*Sqrt[1 + Nc])/(Nc - Nc^3))
 
Wig6j[{{"c0c3", "c0c2", "8", "c0c2", "c0c21", "3"}, {1, 1, 1, 1}}] = 
    Sqrt[-2 - 4/Nc + 2*Nc]/((-2 + Nc)*(-1 + Nc)*(1 + Nc))
 
Wig6j[{{"c0c3", "c0c2", "8", "c0c2", "c0c3", "3"}, {1, 1, 1, 1}}] = 
    (2*Sqrt[2]*Sqrt[-3 + Nc])/(Nc*(2 - 3*Nc + Nc^2))
 
Wig6j[{{"c0c3", "c0c2", "c0c21", "3", "8", "3"}, {1, 1, 1, 1}}] = 
    Sqrt[-2/Nc + 2*Nc]/((-1 + Nc)^(3/2)*(1 + Nc))
 
Wig6j[{{"c0c3", "c0c2", "c0c3", "3", "8", "3"}, {1, 1, 1, 1}}] = 
    (Sqrt[2]*Sqrt[6 - 5*Nc + Nc^2])/(Nc*(2 - 3*Nc + Nc^2))
 
Wig6j[{{"c0c3", "c1c3", "c0c3", "3", "8", "3"}, {1, 1, 1, 1}}] = 
    (-3*Sqrt[2]*Sqrt[(-3 + Nc)/(-2 + Nc)])/(Nc*(3 - Nc - 3*Nc^2 + Nc^3))
 
Wig6j[{{"c111c0", "c1111c0", "3", "c111c0", "24", "3"}, {1, 1, 1, 1}}] = 
    6/(6*Nc + 11*Nc^2 + 6*Nc^3 + Nc^4)
 
Wig6j[{{"c111c0", "c1111c0", "3", "c111c0", "6", "3"}, {1, 1, 1, 1}}] = 
    6/(Nc*(2 + 3*Nc + Nc^2))
 
Wig6j[{{"c111c0", "c1111c0", "c111c0", "3", "8", "3"}, {1, 1, 1, 1}}] = 
    (3*Sqrt[2])/((Nc + Nc^2)*Sqrt[6 + 5*Nc + Nc^2])
 
Wig6j[{{"c111c0", "c211c0", "3", "c111c0", "24", "3"}, {1, 1, 1, 1}}] = 
    6/(Nc*(1 + Nc)*(-2 + Nc + Nc^2))
 
Wig6j[{{"c111c0", "c211c0", "3", "c111c0", "6", "3"}, {1, 1, 1, 1}}] = 
    -2/(Nc*(2 + 3*Nc + Nc^2))
 
Wig6j[{{"c111c0", "c211c0", "c111c0", "3", "8", "3"}, {1, 1, 1, 1}}] = 
    (Sqrt[2]*Sqrt[(3 + Nc)/(2 + Nc)])/(Nc - Nc^3)
 
Wig6j[{{"c111c3", "10", "10", "8", "8", "8"}, {1, 1, 1, 1}}] = 0
 
Wig6j[{{"c111c3", "10", "10", "8", "8", "8"}, {1, 1, 1, 2}}] = 
    (2*Sqrt[2])/(4 - 5*Nc^2 + Nc^4)
 
Wig6j[{{"c111c3", "10", "10", "8", "8", "8"}, {2, 1, 1, 1}}] = 
    (-2*Sqrt[2])/((-1 + Nc^2)*Sqrt[36 - 13*Nc^2 + Nc^4])
 
Wig6j[{{"c111c3", "10", "10", "8", "8", "8"}, {2, 1, 1, 2}}] = 
    (-6*Sqrt[2])/(Sqrt[-9 + Nc^2]*(4 - 5*Nc^2 + Nc^4))
 
Wig6j[{{"c111c3", "10", "8", "0", "10", "8"}, {1, 1, 1, 1}}] = 
    4/((-3 + Nc)*(-2 + Nc)*(-1 + Nc)*(1 + Nc)*(2 + Nc))
 
Wig6j[{{"c111c3", "10", "8", "10", "10", "8"}, {1, 1, 1, 1}}] = 0
 
Wig6j[{{"c111c3", "10", "8", "10", "10", "8"}, {1, 1, 1, 2}}] = 
    (4*Sqrt[-36 + 49*Nc^2 - 14*Nc^4 + Nc^6])/((-9 + Nc^2)*
      (4 - 5*Nc^2 + Nc^4)^(3/2))
 
Wig6j[{{"c111c3", "10", "8", "10", "10", "8"}, {2, 1, 1, 2}}] = 
    8/((-9 + Nc^2)*(4 - 5*Nc^2 + Nc^4))
 
Wig6j[{{"c111c3", "10", "8", "27", "10", "8"}, {1, 1, 1, 1}}] = 
    -4/(12 + 4*Nc - 15*Nc^2 - 5*Nc^3 + 3*Nc^4 + Nc^5)
 
Wig6j[{{"c111c3", "10", "8", "35", "10", "8"}, {1, 1, 1, 1}}] = 
    4/(12*Nc + 4*Nc^2 - 15*Nc^3 - 5*Nc^4 + 3*Nc^5 + Nc^6)
 
Wig6j[{{"c111c3", "10", "8", "8", "10", "8"}, {1, 1, 1, 1}}] = 
    -4/(4 - 5*Nc^2 + Nc^4)
 
Wig6j[{{"c111c3", "10", "8", "c111c3", "10", "8"}, {1, 1, 1, 1}}] = 
    4/((-9 + Nc^2)*(4 - 5*Nc^2 + Nc^4))
 
Wig6j[{{"c111c3", "10", "c111c3", "8", "8", "8"}, {1, 2, 1, 1}}] = 0
 
Wig6j[{{"c111c3", "10", "c111c3", "8", "8", "8"}, {1, 2, 1, 2}}] = 
    (2*Sqrt[3]*Sqrt[(-16 + Nc^2)/(-9 + Nc^2)])/(4 - 5*Nc^2 + Nc^4)
 
Wig6j[{{"c111c3", "35", "10", "8", "8", "8"}, {1, 1, 1, 1}}] = 
    Sqrt[6]/((-1 + Nc)*Nc*Sqrt[(-2 + Nc)*(1 + Nc)*(2 + Nc)*(3 + Nc)])
 
Wig6j[{{"c111c3", "35", "10", "8", "8", "8"}, {1, 1, 1, 2}}] = 
    -(Sqrt[6]/(Sqrt[3 + 4*Nc + Nc^2]*(4 - 4*Nc - Nc^2 + Nc^3)))
 
Wig6j[{{"c111c3", "c111c3", "10", "8", "8", "8"}, {1, 1, 1, 1}}] = 
    (2*Sqrt[3])/((-1 + Nc^2)*Sqrt[36 - 13*Nc^2 + Nc^4])
 
Wig6j[{{"c111c3", "c111c3", "10", "8", "8", "8"}, {1, 1, 1, 2}}] = 
    (4*Sqrt[3]*Sqrt[-36 + 49*Nc^2 - 14*Nc^4 + Nc^6])/
     ((-9 + Nc^2)*(4 - 5*Nc^2 + Nc^4)^(3/2))
 
Wig6j[{{"c1c2", "0", "c1c2", "3", "8", "3"}, {1, 1, 1, 1}}] = 
    Sqrt[-4 - 10*Nc + 6*Nc^2]/((-2 + Nc)*Nc*(1 + Nc)*(1 + 3*Nc))
 
Wig6j[{{"c1c2", "0", "c1c2", "3", "8", "3"}, {1, 2, 1, 1}}] = 
    (-2*Sqrt[(-4 + Nc^2)/(-3 - 8*Nc + 3*Nc^2)])/(2*Nc + Nc^2 - Nc^3)
 
Wig6j[{{"c1c2", "10", "c1c2", "3", "8", "3"}, {1, 1, 1, 1}}] = 
    Sqrt[(2 + 6*Nc)/(-2 + Nc)]/(Nc + 2*Nc^2 - 3*Nc^3)
 
Wig6j[{{"c1c2", "10", "c1c2", "3", "8", "3"}, {1, 2, 1, 1}}] = 
    (-2*Sqrt[(6 + Nc - Nc^2)/(2 + 5*Nc - 3*Nc^2)])/(-2 - Nc + 2*Nc^2 + Nc^3)
 
Wig6j[{{"c1c2", "8", "15bar", "3", "8", "3"}, {1, 1, 1, 1}}] = 
    (-1 + Nc^2)^(-1)
 
Wig6j[{{"c1c2", "8", "3bar", "3", "8", "3"}, {1, 1, 1, 1}}] = (1 - Nc^2)^(-1)
 
Wig6j[{{"c1c2", "8", "8", "1", "3bar", "3"}, {1, 1, 1, 1}}] = 
    1/Sqrt[Nc*(-1 + Nc^2)]
 
Wig6j[{{"c1c2", "8", "c1c2", "3", "8", "3"}, {1, 1, 1, 1}}] = 
    (Sqrt[2]*(-1 - Nc + Nc^2)*Sqrt[2 + 5*Nc - 5*Nc^2 - 5*Nc^3 + 3*Nc^4])/
     ((-2 + Nc)*Nc*(1 + 3*Nc)*(-1 + Nc^2)^(3/2))
 
Wig6j[{{"c1c2", "8", "c1c2", "3", "8", "3"}, {1, 2, 1, 1}}] = 
    -(Sqrt[(12 - 4*Nc - 3*Nc^2 + Nc^3)/(1 + 3*Nc)]/(2 - Nc - 2*Nc^2 + Nc^3))
 
Wig6j[{{"c1c21", "15bar", "6bar", "3", "8", "3"}, {1, 1, 1, 1}}] = 
    -(Sqrt[6 + 4/Nc + 2*Nc]/((-1 + Nc)*(1 + Nc)*(2 + Nc)))
 
Wig6j[{{"c1c21", "15bar", "8", "15bar", "6bar", "3"}, {1, 1, 1, 1}}] = 
    -2/((-2 + Nc + Nc^2)*Sqrt[Nc*(-1 + 2*Nc + 3*Nc^2)])
 
Wig6j[{{"c1c21", "15bar", "8", "15bar", "6bar", "3"}, {2, 1, 1, 1}}] = 
    (Sqrt[2]*(1 - 2*Nc)*Sqrt[((3 + Nc)*(4 - 4*Nc - Nc^2 + Nc^3))/
        ((1 + Nc)*(-1 + 3*Nc))])/((-2 + Nc)*(Nc*(-2 + Nc + Nc^2))^(3/2))
 
Wig6j[{{"c1c21", "15bar", "8", "3bar", "6bar", "3"}, {1, 1, 1, 1}}] = 
    Sqrt[-2 - Nc + 2*Nc^2 + Nc^3]/((-1 + Nc)*Nc*(1 + Nc)*(2 + Nc))
 
Wig6j[{{"c1c21", "15bar", "8", "3bar", "c0c2", "3"}, {1, 1, 1, 1}}] = 
    Sqrt[3]/(Sqrt[2 + Nc]*(Nc - Nc^2))
 
Wig6j[{{"c1c21", "15bar", "8", "c1c2", "c0c2", "3"}, {1, 1, 1, 1}}] = 
    -(Sqrt[6]/(Nc^(3/2)*(2 - 3*Nc + Nc^2)*Sqrt[2 + 3*Nc + Nc^2]))
 
Wig6j[{{"c1c21", "c1c2", "8", "15bar", "6bar", "3"}, {1, 1, 1, 1}}] = 
    -(Sqrt[6]/(Nc^(3/2)*Sqrt[2 - 3*Nc + Nc^2]*(2 + 3*Nc + Nc^2)))
 
Wig6j[{{"c1c21", "c1c2", "8", "3bar", "6bar", "3"}, {1, 1, 1, 1}}] = 
    -(Sqrt[3]/(Sqrt[-2 + Nc]*(Nc + Nc^2)))
 
Wig6j[{{"c1c21", "c1c2", "8", "3bar", "c0c2", "3"}, {1, 1, 1, 1}}] = 
    1/(Nc*Sqrt[2 - Nc - 2*Nc^2 + Nc^3])
 
Wig6j[{{"c1c21", "c1c2", "8", "c1c2", "c0c2", "3"}, {1, 1, 1, 1}}] = 
    2/((-2 - Nc + Nc^2)*Sqrt[Nc*(-1 - 2*Nc + 3*Nc^2)])
 
Wig6j[{{"c1c21", "c1c2", "8", "c1c2", "c0c2", "3"}, {2, 1, 1, 1}}] = 
    (Sqrt[2]*(1 + 2*Nc)*Sqrt[(-12 + 16*Nc - Nc^2 - 4*Nc^3 + Nc^4)/
        (1 + 3*Nc)])/((-1 + Nc)*((-2 + Nc)*Nc)^(3/2)*(1 + Nc)*(2 + Nc))
 
Wig6j[{{"c1c21", "c1c2", "c0c2", "3", "8", "3"}, {1, 1, 1, 1}}] = 
    -(Sqrt[-2 + 4/Nc - 4*Nc + 2*Nc^2]/((-2 + Nc)*(-1 + Nc)*(1 + Nc)^(3/2)))
 
Wig6j[{{"c1c3", "c1c2", "8", "3bar", "c0c2", "3"}, {1, 1, 1, 1}}] = 
    2/(Nc*Sqrt[2 - Nc - 2*Nc^2 + Nc^3])
 
Wig6j[{{"c1c3", "c1c2", "8", "c1c2", "c0c2", "3"}, {1, 1, 1, 1}}] = 
    -2/(Sqrt[(-1 + Nc)*Nc*(1 + 3*Nc)]*(-2 - Nc + Nc^2))
 
Wig6j[{{"c1c3", "c1c2", "8", "c1c2", "c0c2", "3"}, {2, 1, 1, 1}}] = 
    (-2*Sqrt[2]*Sqrt[(6 - 5*Nc - 2*Nc^2 + Nc^3)/(Nc + 3*Nc^2)])/
     ((1 + Nc)*(-6 + 11*Nc - 6*Nc^2 + Nc^3))
 
Wig6j[{{"c1c3", "c1c2", "c0c2", "3", "8", "3"}, {1, 1, 1, 1}}] = 
    -(Sqrt[-6 + 4/Nc + 2*Nc]/((-2 + Nc)*(-1 + Nc)*(1 + Nc)))
 
Wig6j[{{"c21c0", "c211c0", "3", "c111c0", "6", "3"}, {1, 1, 1, 1}}] = 
    4/(Sqrt[-2 + Nc + Nc^2]*(Nc + Nc^2))
 
Wig6j[{{"c21c0", "c211c0", "3", "c21c0", "6", "3"}, {1, 1, 1, 1}}] = 
    -(Nc - Nc^3)^(-1)
 
Wig6j[{{"c21c0", "c211c0", "3", "c21c0", "c21c1", "3"}, {1, 1, 1, 1}}] = 
    3/(Nc*(-2 - Nc + 2*Nc^2 + Nc^3))
 
Wig6j[{{"c21c0", "c211c0", "3", "c21c0", "c2c0", "3"}, {1, 1, 1, 1}}] = 
    -3/(Nc - Nc^3)
 
Wig6j[{{"c21c0", "c211c0", "c111c0", "3", "8", "3"}, {1, 1, 1, 1}}] = 
    (2*Sqrt[6 + 4/Nc + 2*Nc])/((1 + Nc)^(3/2)*(-2 + Nc + Nc^2))
 
Wig6j[{{"c21c0", "c211c0", "c21c0", "3", "8", "3"}, {1, 1, 1, 1}}] = 
    ((-3 + 2*Nc)*Sqrt[-3 + Nc^2])/(Nc*(3 - 4*Nc^2 + Nc^4))
 
Wig6j[{{"c21c0", "c211c0", "c21c0", "3", "8", "3"}, {1, 2, 1, 1}}] = 
    -(1/((-1 + Nc^2)^(3/2)*Sqrt[((2 + Nc)*(-3 + Nc^2))/(2 - Nc - 2*Nc^2 + 
          Nc^3)]))
 
Wig6j[{{"c21c0", "c22c0", "3", "c21c0", "6", "3"}, {1, 1, 1, 1}}] = 
    -3/(Nc - Nc^3)
 
Wig6j[{{"c21c0", "c22c0", "3", "c21c0", "c21c1", "3"}, {1, 1, 1, 1}}] = 
    3/(Nc^2*(-1 + Nc^2))
 
Wig6j[{{"c21c0", "c22c0", "3", "c21c0", "c2c0", "3"}, {1, 1, 1, 1}}] = 
    3/(Nc - Nc^3)
 
Wig6j[{{"c21c0", "c22c0", "c21c0", "3", "8", "3"}, {1, 1, 1, 1}}] = 
    3/(Sqrt[-3 + Nc^2]*(Nc - Nc^3))
 
Wig6j[{{"c21c0", "c22c0", "c21c0", "3", "8", "3"}, {1, 2, 1, 1}}] = 
    (-3*Sqrt[(-4 + Nc^2)/(-3 + Nc^2)])/(Nc - Nc^3)
 
Wig6j[{{"c21c0", "c31c0", "3", "c21c0", "6", "3"}, {1, 1, 1, 1}}] = 
    3/(Nc - Nc^3)
 
Wig6j[{{"c21c0", "c31c0", "3", "c21c0", "c21c1", "3"}, {1, 1, 1, 1}}] = 
    3/(Nc*(2 - Nc - 2*Nc^2 + Nc^3))
 
Wig6j[{{"c21c0", "c31c0", "3", "c21c0", "c2c0", "3"}, {1, 1, 1, 1}}] = 
    (Nc - Nc^3)^(-1)
 
Wig6j[{{"c21c0", "c31c0", "c21c0", "3", "8", "3"}, {1, 1, 1, 1}}] = 
    -(((3 + 2*Nc)*Sqrt[-3 + Nc^2])/(Nc*(3 - 4*Nc^2 + Nc^4)))
 
Wig6j[{{"c21c0", "c31c0", "c21c0", "3", "8", "3"}, {1, 2, 1, 1}}] = 
    -(1/(Sqrt[((-2 + Nc)*(-3 + Nc^2))/(2 + Nc)]*(-1 + Nc^2)))
 
Wig6j[{{"c21c1", "6", "6", "8", "8", "8"}, {1, 1, 1, 1}}] = 
    1/(Sqrt[2]*Sqrt[Nc*(2 + Nc)]*(-1 + Nc^2))
 
Wig6j[{{"c21c1", "6", "6", "8", "8", "8"}, {1, 1, 1, 2}}] = 
    -((4 + Nc)/(Sqrt[2]*(-1 + Nc)*Sqrt[(-2 + Nc)*Nc]*(1 + Nc)*(2 + Nc)))
 
Wig6j[{{"c21c1", "6", "8", "24", "6", "8"}, {1, 1, 1, 1}}] = 
    2/(Nc*(1 + Nc)*(-2 + Nc + Nc^2))
 
Wig6j[{{"c21c1", "6", "8", "6", "6", "8"}, {1, 1, 1, 1}}] = 
    (2 + Nc - 2*Nc^2 - Nc^3)^(-1)
 
Wig6j[{{"c21c1", "6", "8", "c21c1", "6", "8"}, {1, 1, 1, 1}}] = 
    (-3 + 2*Nc + 2*Nc^2)/(Nc^2*(4 - 5*Nc^2 + Nc^4))
 
Wig6j[{{"c21c1", "6", "8", "c2c0", "6", "8"}, {1, 1, 1, 1}}] = 
    (Nc - Nc^3)^(-1)
 
Wig6j[{{"c21c1", "c21c0", "3", "6", "15", "3"}, {1, 1, 1, 1}}] = 
    Sqrt[6]/((-1 + Nc)*Nc*Sqrt[(1 + Nc)*(2 + Nc)])
 
Wig6j[{{"c21c1", "c21c0", "3", "c21c1", "15", "3"}, {1, 1, 1, 1}}] = 
    -3/(Nc^2*(4 - 4*Nc - Nc^2 + Nc^3))
 
Wig6j[{{"c21c1", "c21c0", "3", "c21c1", "c2c1", "3"}, {1, 1, 1, 1}}] = 
    -3/((-2 + Nc)*Nc^2*(1 + Nc)*(2 + Nc))
 
Wig6j[{{"c21c1", "c21c0", "3", "c2c0", "c2c1", "3"}, {1, 1, 1, 1}}] = 
    (Sqrt[6]*Sqrt[2 - 3*Nc + Nc^2])/(Nc*(2 - Nc - 2*Nc^2 + Nc^3))
 
Wig6j[{{"c21c1", "c21c0", "6", "3", "8", "3"}, {1, 1, 1, 1}}] = 
    Sqrt[3 + 3/Nc]/((-1 + Nc)*(1 + Nc)^(3/2))
 
Wig6j[{{"c21c1", "c21c0", "8", "c111c0", "6", "3"}, {1, 1, 1, 1}}] = 
    -(Sqrt[6]/(Sqrt[-1 + Nc]*Nc*(2 + 3*Nc + Nc^2)))
 
Wig6j[{{"c21c1", "c21c0", "8", "c21c0", "6", "3"}, {1, 1, 1, 1}}] = 
    (Sqrt[3]*Sqrt[-3 - 3/Nc + Nc + Nc^2])/((-1 + Nc)*(1 + Nc)^(3/2)*
      (-3 + Nc^2))
 
Wig6j[{{"c21c1", "c21c0", "8", "c21c0", "6", "3"}, {2, 1, 1, 1}}] = 
    (Sqrt[3]*(-3 + Nc + Nc^2))/(Nc^(3/2)*(-1 + Nc^2)*Sqrt[12 - 7*Nc^2 + Nc^4])
 
Wig6j[{{"c21c1", "c21c0", "8", "c21c0", "c2c0", "3"}, {1, 1, 1, 1}}] = 
    Sqrt[-9/Nc + 3*Nc]/(3 - 4*Nc^2 + Nc^4)
 
Wig6j[{{"c21c1", "c21c0", "8", "c21c0", "c2c0", "3"}, {2, 1, 1, 1}}] = 
    -((Sqrt[3]*(-1 + Nc)*(1 + Nc)*(-3 - Nc + Nc^2)*
       Sqrt[-12 + 19*Nc^2 - 8*Nc^4 + Nc^6])/(Nc^(3/2)*(-1 + Nc^2)^(5/2)*
       (12 - 7*Nc^2 + Nc^4)))
 
Wig6j[{{"c21c1", "c21c0", "8", "c3c0", "c2c0", "3"}, {1, 1, 1, 1}}] = 
    -(Sqrt[6]/(Sqrt[1 + Nc]*(2*Nc - 3*Nc^2 + Nc^3)))
 
Wig6j[{{"c21c1", "c21c0", "c2c0", "3", "8", "3"}, {1, 1, 1, 1}}] = 
    Sqrt[3]/(Sqrt[Nc]*(-1 + Nc^2))
 
Wig6j[{{"c21c1", "c2c0", "6", "8", "8", "8"}, {1, 1, 1, 1}}] = 
    Sqrt[3/2]/(Nc - Nc^3)
 
Wig6j[{{"c21c1", "c2c0", "6", "8", "8", "8"}, {1, 1, 1, 2}}] = 
    Sqrt[3/2]/(Sqrt[-4 + Nc^2]*(-1 + Nc^2))
 
Wig6j[{{"c21c1", "c2c0", "8", "6", "6", "8"}, {1, 1, 1, 1}}] = 
    Sqrt[3]/(Sqrt[Nc*(2 + Nc)]*(-1 + Nc^2))
 
Wig6j[{{"c21c1", "c2c0", "8", "6", "c2c0", "8"}, {1, 1, 1, 1}}] = 
    -(Nc - Nc^3)^(-1)
 
Wig6j[{{"c21c1", "c2c0", "8", "c21c1", "6", "8"}, {1, 1, 1, 1}}] = 
    3/(4*Nc^2 - 5*Nc^4 + Nc^6)
 
Wig6j[{{"c21c1", "c2c0", "8", "c21c1", "c2c0", "8"}, {1, 1, 1, 1}}] = 
    (-3 - 2*Nc + 2*Nc^2)/(Nc^2*(4 - 5*Nc^2 + Nc^4))
 
Wig6j[{{"c21c1", "c2c0", "8", "c2c0", "6", "8"}, {1, 1, 1, 1}}] = 
    Sqrt[-9 + 6/Nc + 3*Nc]/((-2 + Nc)*(-1 + Nc)^(3/2)*(1 + Nc))
 
Wig6j[{{"c21c1", "c2c0", "8", "c2c0", "c2c0", "8"}, {1, 1, 1, 1}}] = 
    (2 - Nc - 2*Nc^2 + Nc^3)^(-1)
 
Wig6j[{{"c21c1", "c2c0", "c2c0", "8", "8", "8"}, {1, 1, 1, 1}}] = 
    -(1/(Sqrt[2]*Sqrt[(-2 + Nc)*Nc]*(-1 + Nc^2)))
 
Wig6j[{{"c21c1", "c2c0", "c2c0", "8", "8", "8"}, {1, 1, 1, 2}}] = 
    (-4 + Nc)/(Sqrt[2]*(-2 + Nc)*(-1 + Nc)*(1 + Nc)*Sqrt[Nc*(2 + Nc)])
 
Wig6j[{{"c21c21", "0", "0", "8", "8", "8"}, {1, 1, 1, 1}}] = 
    -(Sqrt[2]/(Sqrt[-3 + Nc]*Nc^(3/2)*(-1 + Nc^2)))
 
Wig6j[{{"c21c21", "0", "0", "8", "8", "8"}, {1, 1, 1, 2}}] = 0
 
Wig6j[{{"c21c21", "0", "0", "8", "8", "8"}, {2, 1, 1, 1}}] = 0
 
Wig6j[{{"c21c21", "0", "0", "8", "8", "8"}, {2, 1, 1, 2}}] = 
    (Sqrt[2]*Sqrt[(-4 + Nc)/(-3 + Nc)])/((-1 + Nc)*Nc*(1 + Nc)*(2 + Nc))
 
Wig6j[{{"c21c21", "0", "10", "8", "8", "8"}, {1, 1, 1, 1}}] = 
    -(Sqrt[3]/(Sqrt[-6 - Nc + Nc^2]*(Nc - Nc^3)))
 
Wig6j[{{"c21c21", "0", "10", "8", "8", "8"}, {1, 1, 1, 2}}] = 
    -((Sqrt[3]*Sqrt[6 - 5*Nc + Nc^2])/(-12 + 4*Nc + 15*Nc^2 - 5*Nc^3 - 
       3*Nc^4 + Nc^5))
 
Wig6j[{{"c21c21", "0", "8", "0", "0", "8"}, {1, 1, 1, 1}}] = 
    2/(Nc^2*(3 - Nc - 3*Nc^2 + Nc^3))
 
Wig6j[{{"c21c21", "0", "8", "0", "0", "8"}, {1, 1, 1, 2}}] = 0
 
Wig6j[{{"c21c21", "0", "8", "0", "0", "8"}, {2, 1, 1, 2}}] = 
    2/(Nc*(6 + Nc - 7*Nc^2 - Nc^3 + Nc^4))
 
Wig6j[{{"c21c21", "0", "8", "0", "10", "8"}, {1, 1, 1, 1}}] = 
    -(Sqrt[6]/(Nc^(3/2)*Sqrt[2 + Nc]*(3 - Nc - 3*Nc^2 + Nc^3)))
 
Wig6j[{{"c21c21", "0", "8", "0", "10", "8"}, {2, 1, 1, 1}}] = 
    -((Sqrt[6]*Sqrt[8 - 6*Nc + Nc^2])/(Nc*(-12 + 4*Nc + 15*Nc^2 - 5*Nc^3 - 
        3*Nc^4 + Nc^5)))
 
Wig6j[{{"c21c21", "0", "8", "10", "0", "8"}, {1, 1, 1, 1}}] = 
    2/(Nc^2*(-6 - 7*Nc + Nc^3))
 
Wig6j[{{"c21c21", "0", "8", "10", "10", "8"}, {1, 1, 1, 1}}] = 
    -((Sqrt[6]*Sqrt[6 - 5*Nc + Nc^2])/(Nc*(-12 + 4*Nc + 15*Nc^2 - 5*Nc^3 - 
        3*Nc^4 + Nc^5)))
 
Wig6j[{{"c21c21", "0", "8", "10", "10", "8"}, {1, 1, 1, 2}}] = 
    -((Sqrt[6]*Sqrt[(-2 + Nc)/(3 + Nc)])/(4*Nc - 5*Nc^3 + Nc^5))
 
Wig6j[{{"c21c21", "0", "8", "10", "27", "8"}, {1, 1, 1, 1}}] = 
    (6*Sqrt[(-4 + Nc^2)/(-9 + Nc^2)])/(Nc^2*(4 - 5*Nc^2 + Nc^4))
 
Wig6j[{{"c21c21", "0", "8", "8", "0", "8"}, {1, 1, 1, 1}}] = 
    1/((-3 + Nc)*Nc^2*(1 + Nc))
 
Wig6j[{{"c21c21", "0", "8", "8", "10", "8"}, {1, 1, 1, 1}}] = 
    -(Sqrt[3]/(Nc*(1 + Nc)*Sqrt[(-3 + Nc)*(-1 + Nc)*(-4 + Nc^2)]))
 
Wig6j[{{"c21c21", "0", "8", "8", "27", "8"}, {1, 1, 1, 1}}] = 
    3/(Nc^2*Sqrt[9 - 10*Nc^2 + Nc^4])
 
Wig6j[{{"c21c21", "0", "8", "c21c21", "0", "8"}, {1, 1, 1, 1}}] = 
    (6 - 7*Nc + 4*Nc^3)/((-3 + Nc)*Nc^2*(2 + Nc)*(3 + Nc)*(-1 + Nc^2)^2)
 
Wig6j[{{"c21c21", "0", "8", "c21c21", "10", "8"}, {1, 1, 1, 1}}] = 
    9/((-3 + Nc)*Nc*(2 + Nc)*(3 + Nc)*(-1 + Nc^2)^2)
 
Wig6j[{{"c21c21", "0", "8", "c21c21", "27", "8"}, {1, 1, 1, 1}}] = 
    9/(Nc^2*(-9 + Nc^2)*(-1 + Nc^2)^2)
 
Wig6j[{{"c21c21", "0", "c21c21", "8", "8", "8"}, {1, 2, 1, 1}}] = 
    -((Sqrt[3]*Sqrt[(-4 + Nc^2)/((-9 + Nc^2)*(-1 + Nc^2)^3)])/Nc)
 
Wig6j[{{"c21c21", "0", "c21c21", "8", "8", "8"}, {1, 2, 1, 2}}] = 0
 
Wig6j[{{"c21c21", "0", "c21c21", "8", "8", "8"}, {1, 3, 1, 1}}] = 0
 
Wig6j[{{"c21c21", "0", "c21c21", "8", "8", "8"}, {1, 3, 1, 2}}] = 
    Sqrt[(27 + 30*Nc + 6*Nc^2)/(-9 + Nc^2)]/((2 + Nc)*(-1 + Nc^2)^(3/2))
 
Wig6j[{{"c21c21", "0", "c21c21", "8", "8", "8"}, {1, 4, 1, 1}}] = 0
 
Wig6j[{{"c21c21", "0", "c21c21", "8", "8", "8"}, {1, 4, 1, 2}}] = 0
 
Wig6j[{{"c21c21", "10", "10", "8", "8", "8"}, {1, 1, 1, 1}}] = 0
 
Wig6j[{{"c21c21", "10", "10", "8", "8", "8"}, {1, 1, 1, 2}}] = 
    -(Sqrt[2]/(4 - 5*Nc^2 + Nc^4))
 
Wig6j[{{"c21c21", "10", "10", "8", "8", "8"}, {2, 1, 1, 1}}] = 
    Sqrt[2]/((-1 + Nc^2)*Sqrt[36 - 13*Nc^2 + Nc^4])
 
Wig6j[{{"c21c21", "10", "10", "8", "8", "8"}, {2, 1, 1, 2}}] = 
    (-3*Sqrt[2])/(Sqrt[-9 + Nc^2]*(4 - 5*Nc^2 + Nc^4))
 
Wig6j[{{"c21c21", "10", "27", "8", "8", "8"}, {1, 1, 1, 1}}] = 
    -(Sqrt[3]/(Sqrt[-6 + Nc + Nc^2]*(Nc - Nc^3)))
 
Wig6j[{{"c21c21", "10", "27", "8", "8", "8"}, {1, 1, 1, 2}}] = 
    Sqrt[3]/(Sqrt[6 + 5*Nc + Nc^2]*(2 - Nc - 2*Nc^2 + Nc^3))
 
Wig6j[{{"c21c21", "10", "8", "0", "10", "8"}, {1, 1, 1, 1}}] = 
    -2/(4*Nc - 5*Nc^3 + Nc^5)
 
Wig6j[{{"c21c21", "10", "8", "0", "10bar", "8"}, {1, 1, 1, 1}}] = 
    -6/((-3 + Nc)*(-1 + Nc)*Nc*(1 + Nc)*(-4 + Nc^2))
 
Wig6j[{{"c21c21", "10", "8", "10", "10", "8"}, {1, 1, 1, 1}}] = 0
 
Wig6j[{{"c21c21", "10", "8", "10", "10", "8"}, {1, 1, 1, 2}}] = 
    -2/(Sqrt[-9 + Nc^2]*(4 - 5*Nc^2 + Nc^4))
 
Wig6j[{{"c21c21", "10", "8", "10", "10", "8"}, {2, 1, 1, 2}}] = 
    8/(-36 + 49*Nc^2 - 14*Nc^4 + Nc^6)
 
Wig6j[{{"c21c21", "10", "8", "10", "27", "8"}, {1, 1, 1, 1}}] = 
    -(Sqrt[6]/(Nc*Sqrt[6 + 5*Nc + Nc^2]*(2 - Nc - 2*Nc^2 + Nc^3)))
 
Wig6j[{{"c21c21", "10", "8", "10", "27", "8"}, {2, 1, 1, 1}}] = 
    (Sqrt[6]*Sqrt[(2 + Nc)/(-3 + Nc)])/(4*Nc - 5*Nc^3 + Nc^5)
 
Wig6j[{{"c21c21", "10", "8", "27", "10", "8"}, {1, 1, 1, 1}}] = 
    2/(4*Nc - 5*Nc^3 + Nc^5)
 
Wig6j[{{"c21c21", "10", "8", "27", "10bar", "8"}, {1, 1, 1, 1}}] = 
    -6/((-1 + Nc)*Nc*(1 + Nc)*(3 + Nc)*(-4 + Nc^2))
 
Wig6j[{{"c21c21", "10", "8", "27", "27", "8"}, {1, 1, 1, 1}}] = 
    Sqrt[6]/(Sqrt[-2 + Nc]*Nc^(3/2)*(3 + Nc - 3*Nc^2 - Nc^3))
 
Wig6j[{{"c21c21", "10", "8", "27", "27", "8"}, {1, 1, 1, 2}}] = 
    (Sqrt[6]*Sqrt[8 + 6*Nc + Nc^2])/(Nc*(12 + 4*Nc - 15*Nc^2 - 5*Nc^3 + 
       3*Nc^4 + Nc^5))
 
Wig6j[{{"c21c21", "10", "8", "35", "10", "8"}, {1, 1, 1, 1}}] = 
    4/(Nc*(3 + Nc)*(-4 + Nc^2)*(-1 + Nc^2))
 
Wig6j[{{"c21c21", "10", "8", "35", "27", "8"}, {1, 1, 1, 1}}] = 0
 
Wig6j[{{"c21c21", "10", "8", "8", "10", "8"}, {1, 1, 1, 1}}] = 
    (-4 + 5*Nc^2 - Nc^4)^(-1)
 
Wig6j[{{"c21c21", "10", "8", "8", "10bar", "8"}, {1, 1, 1, 1}}] = 
    -3/(4 - 5*Nc^2 + Nc^4)
 
Wig6j[{{"c21c21", "10", "8", "8", "27", "8"}, {1, 1, 1, 1}}] = 
    Sqrt[3]/((-1 + Nc)*Nc*Sqrt[(1 + Nc)*(3 + Nc)*(-4 + Nc^2)])
 
Wig6j[{{"c21c21", "10", "8", "c111c3", "10", "8"}, {1, 1, 1, 1}}] = 
    4/(-36 + 49*Nc^2 - 14*Nc^4 + Nc^6)
 
Wig6j[{{"c21c21", "10", "8", "c21c21", "10", "8"}, {1, 1, 1, 1}}] = 
    (-31 + 4*Nc^2)/((-9 + Nc^2)*(-4 + Nc^2)*(-1 + Nc^2)^2)
 
Wig6j[{{"c21c21", "10", "8", "c21c21", "10bar", "8"}, {1, 1, 1, 1}}] = 
    9/((-9 + Nc^2)*(-4 + Nc^2)*(-1 + Nc^2)^2)
 
Wig6j[{{"c21c21", "10", "8", "c21c21", "27", "8"}, {1, 1, 1, 1}}] = 
    9/((-3 + Nc)*(-2 + Nc)*Nc*(3 + Nc)*(-1 + Nc^2)^2)
 
Wig6j[{{"c21c21", "10", "c21c21", "8", "8", "8"}, {1, 2, 1, 1}}] = 0
 
Wig6j[{{"c21c21", "10", "c21c21", "8", "8", "8"}, {1, 2, 1, 2}}] = 
    Sqrt[3]/(Sqrt[-9 + Nc^2]*(-1 + Nc^2)^(3/2))
 
Wig6j[{{"c21c21", "10", "c21c21", "8", "8", "8"}, {1, 3, 1, 1}}] = 
    -(((-1 + 3*Nc + Nc^2)*Sqrt[(27 + 30*Nc + 6*Nc^2)/(36 - 13*Nc^2 + Nc^4)])/
      ((-1 + Nc^2)^(3/2)*(9 + 10*Nc + 2*Nc^2)))
 
Wig6j[{{"c21c21", "10", "c21c21", "8", "8", "8"}, {1, 3, 1, 2}}] = 
    (Sqrt[3]*(-18 - 10*Nc + 3*Nc^2 + Nc^3))/((-4 + Nc^2)*(-1 + Nc^2)^(3/2)*
      Sqrt[(-9 + Nc^2)*(9 + 10*Nc + 2*Nc^2)])
 
Wig6j[{{"c21c21", "10", "c21c21", "8", "8", "8"}, {1, 4, 1, 1}}] = 
    (Sqrt[3]*(2 + Nc))/((-1 + Nc^2)^(3/2)*
      Sqrt[((12 - 4*Nc - 3*Nc^2 + Nc^3)*(27 + 39*Nc + 16*Nc^2 + 2*Nc^3))/
        (-16 + Nc^2)])
 
Wig6j[{{"c21c21", "10", "c21c21", "8", "8", "8"}, {1, 4, 1, 2}}] = 
    (Sqrt[3]*Nc)/((-2 + Nc)*(-1 + Nc)*(1 + Nc)*
      Sqrt[((-3 + Nc)*(-1 + Nc^2)*(27 + 39*Nc + 16*Nc^2 + 2*Nc^3))/
        (-16 + Nc^2)])
 
Wig6j[{{"c21c21", "27", "27", "8", "8", "8"}, {1, 1, 1, 1}}] = 
    Sqrt[2]/(Nc^(3/2)*Sqrt[3 + Nc]*(-1 + Nc^2))
 
Wig6j[{{"c21c21", "27", "27", "8", "8", "8"}, {1, 1, 1, 2}}] = 0
 
Wig6j[{{"c21c21", "27", "27", "8", "8", "8"}, {2, 1, 1, 1}}] = 0
 
Wig6j[{{"c21c21", "27", "27", "8", "8", "8"}, {2, 1, 1, 2}}] = 
    -((Sqrt[2]*Sqrt[(4 + Nc)/(3 + Nc)])/(Nc*(2 - Nc - 2*Nc^2 + Nc^3)))
 
Wig6j[{{"c21c21", "27", "8", "10", "27", "8"}, {1, 1, 1, 1}}] = 
    -2/(Nc^2*(6 - 7*Nc + Nc^3))
 
Wig6j[{{"c21c21", "27", "8", "27", "27", "8"}, {1, 1, 1, 1}}] = 
    -2/(Nc^2*(-3 - Nc + 3*Nc^2 + Nc^3))
 
Wig6j[{{"c21c21", "27", "8", "27", "27", "8"}, {1, 1, 1, 2}}] = 0
 
Wig6j[{{"c21c21", "27", "8", "27", "27", "8"}, {2, 1, 1, 2}}] = 
    -2/(Nc*(6 - Nc - 7*Nc^2 + Nc^3 + Nc^4))
 
Wig6j[{{"c21c21", "27", "8", "35", "27", "8"}, {1, 1, 1, 1}}] = 
    4/(Nc^2*(6 - Nc - 7*Nc^2 + Nc^3 + Nc^4))
 
Wig6j[{{"c21c21", "27", "8", "64", "27", "8"}, {1, 1, 1, 1}}] = 
    4/((-1 + Nc)*Nc^2*(1 + Nc)^2*(3 + Nc))
 
Wig6j[{{"c21c21", "27", "8", "8", "27", "8"}, {1, 1, 1, 1}}] = 
    1/((-1 + Nc)*Nc^2*(3 + Nc))
 
Wig6j[{{"c21c21", "27", "8", "c21c21", "27", "8"}, {1, 1, 1, 1}}] = 
    (-6 - 7*Nc + 4*Nc^3)/((-3 + Nc)*(-2 + Nc)*Nc^2*(3 + Nc)*(-1 + Nc^2)^2)
 
Wig6j[{{"c21c21", "27", "c21c21", "8", "8", "8"}, {1, 2, 1, 1}}] = 
    (Sqrt[3]*Sqrt[(-4 + Nc^2)/((-9 + Nc^2)*(-1 + Nc^2)^3)])/Nc
 
Wig6j[{{"c21c21", "27", "c21c21", "8", "8", "8"}, {1, 2, 1, 2}}] = 0
 
Wig6j[{{"c21c21", "27", "c21c21", "8", "8", "8"}, {1, 3, 1, 1}}] = 0
 
Wig6j[{{"c21c21", "27", "c21c21", "8", "8", "8"}, {1, 3, 1, 2}}] = 
    (-9*Sqrt[3])/((-2 + Nc)*(-1 + Nc)^(3/2)*(1 + Nc)*
      Sqrt[(9 + 10*Nc + 2*Nc^2)*(-9 - 9*Nc + Nc^2 + Nc^3)])
 
Wig6j[{{"c21c21", "27", "c21c21", "8", "8", "8"}, {1, 4, 1, 1}}] = 0
 
Wig6j[{{"c21c21", "27", "c21c21", "8", "8", "8"}, {1, 4, 1, 2}}] = 
    (2*Sqrt[3]*Nc)/((-2 + Nc)*(-1 + Nc^2)^(3/2)*
      Sqrt[((-3 + Nc)*(3 + Nc)*(9 + 10*Nc + 2*Nc^2))/(-16 + Nc^2)])
 
Wig6j[{{"c21c21", "35", "10", "8", "8", "8"}, {1, 1, 1, 1}}] = 
    -((Sqrt[3]*Sqrt[-6 + Nc + Nc^2])/((Nc + Nc^2)*(6 - 7*Nc + Nc^3)))
 
Wig6j[{{"c21c21", "35", "10", "8", "8", "8"}, {1, 1, 1, 2}}] = 
    -((Sqrt[3]*Sqrt[(3 + Nc)/(2 + Nc)])/((1 + Nc)*(6 - 7*Nc + Nc^3)))
 
Wig6j[{{"c21c21", "35", "27", "8", "8", "8"}, {1, 1, 1, 1}}] = 
    Sqrt[3]/(Sqrt[-6 + Nc + Nc^2]*(-Nc + Nc^3))
 
Wig6j[{{"c21c21", "35", "27", "8", "8", "8"}, {1, 1, 1, 2}}] = 
    Sqrt[3]/(Sqrt[6 + 5*Nc + Nc^2]*(2 - Nc - 2*Nc^2 + Nc^3))
 
Wig6j[{{"c21c21", "c21c21", "0", "8", "8", "8"}, {1, 1, 1, 1}}] = 
    Sqrt[3]/((-1 + Nc)^(3/2)*Nc*Sqrt[(-3 + Nc)*(1 + Nc)*(3 + Nc)])
 
Wig6j[{{"c21c21", "c21c21", "0", "8", "8", "8"}, {1, 1, 1, 2}}] = 0
 
Wig6j[{{"c21c21", "c21c21", "10", "8", "8", "8"}, {1, 1, 1, 1}}] = 
    Sqrt[3]/(Sqrt[-9 + Nc^2]*(-1 + Nc^2)^(3/2))
 
Wig6j[{{"c21c21", "c21c21", "10", "8", "8", "8"}, {1, 1, 1, 2}}] = 
    -(Sqrt[3]/((-1 + Nc^2)^(3/2)*Sqrt[36 - 13*Nc^2 + Nc^4]))
 
Wig6j[{{"c21c21", "c21c21", "27", "8", "8", "8"}, {1, 1, 1, 1}}] = 
    Sqrt[3]/((Nc + Nc^2)*Sqrt[9 - 10*Nc^2 + Nc^4])
 
Wig6j[{{"c21c21", "c21c21", "27", "8", "8", "8"}, {1, 1, 1, 2}}] = 0
 
Wig6j[{{"c21c3", "0", "0", "8", "8", "8"}, {1, 1, 1, 1}}] = 
    1/(Sqrt[2]*Sqrt[-3 + Nc]*Nc^(3/2)*(-1 + Nc^2))
 
Wig6j[{{"c21c3", "0", "0", "8", "8", "8"}, {1, 1, 1, 2}}] = 
    3/(Sqrt[2]*Sqrt[(-3 + Nc)*Nc*(-4 + Nc^2)]*(-1 + Nc^2))
 
Wig6j[{{"c21c3", "0", "0", "8", "8", "8"}, {2, 1, 1, 1}}] = 
    (-3*(-2 + Nc))/(Sqrt[2]*Nc*(-1 + Nc^2)*
      Sqrt[-48 + 28*Nc + 8*Nc^2 - 7*Nc^3 + Nc^4])
 
Wig6j[{{"c21c3", "0", "0", "8", "8", "8"}, {2, 1, 1, 2}}] = 
    -((8 + Nc)/(Sqrt[2]*Nc*(1 + Nc)*Sqrt[12 - 7*Nc + Nc^2]*(-2 + Nc + Nc^2)))
 
Wig6j[{{"c21c3", "0", "10", "8", "8", "8"}, {1, 1, 1, 1}}] = 
    Sqrt[3]/(Nc*Sqrt[(-3 + Nc)*(2 + Nc)]*(-1 + Nc^2))
 
Wig6j[{{"c21c3", "0", "10", "8", "8", "8"}, {1, 1, 1, 2}}] = 
    -((Sqrt[3]*Sqrt[6 - 5*Nc + Nc^2])/((-3 + Nc)*(-2 + Nc)*(1 + Nc)*
       (-2 + Nc + Nc^2)))
 
Wig6j[{{"c21c3", "0", "8", "0", "0", "8"}, {1, 1, 1, 1}}] = 
    -(1/(Nc^2*(3 - Nc - 3*Nc^2 + Nc^3)))
 
Wig6j[{{"c21c3", "0", "8", "0", "0", "8"}, {1, 1, 1, 2}}] = 
    (3*(-2 + Nc))/((-3 + Nc)*(-1 + Nc)*Nc^(3/2)*(1 + Nc)*
      Sqrt[16 - 4*Nc - 4*Nc^2 + Nc^3])
 
Wig6j[{{"c21c3", "0", "8", "0", "0", "8"}, {2, 1, 1, 2}}] = 
    (10 - Nc)/((-3 + Nc)*Nc*(1 + Nc)*(8 - 6*Nc - 3*Nc^2 + Nc^3))
 
Wig6j[{{"c21c3", "0", "8", "0", "10", "8"}, {1, 1, 1, 1}}] = 
    -(Sqrt[6]/(Nc^(3/2)*Sqrt[2 + Nc]*(3 - Nc - 3*Nc^2 + Nc^3)))
 
Wig6j[{{"c21c3", "0", "8", "0", "10", "8"}, {2, 1, 1, 1}}] = 
    -(Sqrt[6]/(Nc*Sqrt[8 - 6*Nc + Nc^2]*(3 - Nc - 3*Nc^2 + Nc^3)))
 
Wig6j[{{"c21c3", "0", "8", "10", "0", "8"}, {1, 1, 1, 1}}] = 
    2/(Nc^2*(3 - Nc - 3*Nc^2 + Nc^3))
 
Wig6j[{{"c21c3", "0", "8", "10", "10", "8"}, {1, 1, 1, 1}}] = 
    -((Sqrt[6]*Sqrt[6 - 5*Nc + Nc^2])/((-3 + Nc)*(-2 + Nc)*Nc*(1 + Nc)*
       (-2 + Nc + Nc^2)))
 
Wig6j[{{"c21c3", "0", "8", "10", "10", "8"}, {1, 1, 1, 2}}] = 
    -((Sqrt[6]*Sqrt[(3 + Nc)/(-2 + Nc)])/(Nc*(6 + Nc - 7*Nc^2 - Nc^3 + Nc^4)))
 
Wig6j[{{"c21c3", "0", "8", "10bar", "0", "8"}, {1, 1, 1, 1}}] = 
    -4/(Nc^2*(-6 - 7*Nc + Nc^3))
 
Wig6j[{{"c21c3", "0", "8", "8", "0", "8"}, {1, 1, 1, 1}}] = 
    -2/((-3 + Nc)*Nc^2*(1 + Nc))
 
Wig6j[{{"c21c3", "0", "8", "8", "10", "8"}, {1, 1, 1, 1}}] = 
    (2*Sqrt[3]*Sqrt[(4 - 4*Nc - Nc^2 + Nc^3)/(-3 + Nc)])/
     (4*Nc - 5*Nc^3 + Nc^5)
 
Wig6j[{{"c21c3", "0", "8", "c21c21", "0", "8"}, {1, 1, 1, 1}}] = 
    4/(Nc^2*(6 + Nc - 7*Nc^2 - Nc^3 + Nc^4))
 
Wig6j[{{"c21c3", "0", "8", "c21c21", "10", "8"}, {1, 1, 1, 1}}] = 0
 
Wig6j[{{"c21c3", "0", "8", "c21c3", "0", "8"}, {1, 1, 1, 1}}] = 
    (2*(-5 - 6*Nc + 2*Nc^2))/((-3 + Nc)*(-1 + Nc)*Nc^2*(1 + Nc)*(2 + Nc)*
      (8 - 6*Nc + Nc^2))
 
Wig6j[{{"c21c3", "0", "8", "c21c3", "10", "8"}, {1, 1, 1, 1}}] = 
    18/(Nc^2*(48 - 28*Nc - 56*Nc^2 + 35*Nc^3 + 7*Nc^4 - 7*Nc^5 + Nc^6))
 
Wig6j[{{"c21c3", "0", "8", "c3c21", "0", "8"}, {1, 1, 1, 1}}] = 
    4/((-4 + Nc)*(-3 + Nc)*Nc^2*(1 + Nc)*(2 + Nc))
 
Wig6j[{{"c21c3", "0", "c21c3", "8", "8", "8"}, {1, 2, 1, 1}}] = 
    (21 - 2*Nc - 4*Nc^2 + Nc^3)/(Nc*(-1 + Nc^2)*
      Sqrt[(-48 + 28*Nc + 8*Nc^2 - 7*Nc^3 + Nc^4)*(-3 + 30*Nc - 8*Nc^2 - 
         4*Nc^3 + Nc^4)])
 
Wig6j[{{"c21c3", "0", "c21c3", "8", "8", "8"}, {1, 2, 1, 2}}] = 
    (3*(-6 + 33*Nc - 8*Nc^2 - 4*Nc^3 + Nc^4))/(Nc*(4 - 5*Nc^2 + Nc^4)*
      Sqrt[(12 - 7*Nc + Nc^2)*(-3 + 30*Nc - 8*Nc^2 - 4*Nc^3 + Nc^4)])
 
Wig6j[{{"c21c3", "0", "c21c3", "8", "8", "8"}, {1, 3, 1, 1}}] = 
    -((-1 + 2*Nc)/(Sqrt[2]*(-1 + Nc)*Nc^(3/2)*
       Sqrt[((1 + Nc)*(2 + Nc)*(8 - 6*Nc + Nc^2)*(-3 + 30*Nc - 8*Nc^2 - 
           4*Nc^3 + Nc^4))/((-3 + Nc)*(-15 - 2*Nc + Nc^2))]))
 
Wig6j[{{"c21c3", "0", "c21c3", "8", "8", "8"}, {1, 3, 1, 2}}] = 
    -3/(Sqrt[2]*(4 - 4*Nc - Nc^2 + Nc^3)*
      Sqrt[(Nc*(12 - 111*Nc - 61*Nc^2 + 70*Nc^3 - 7*Nc^5 + Nc^6))/
        (45 - 9*Nc - 5*Nc^2 + Nc^3)])
 
Wig6j[{{"c21c3", "10", "10", "8", "8", "8"}, {1, 1, 1, 1}}] = 
    -3/(Sqrt[2]*Sqrt[-4 + Nc^2]*(Nc - Nc^3))
 
Wig6j[{{"c21c3", "10", "10", "8", "8", "8"}, {1, 1, 1, 2}}] = 
    1/(Sqrt[2]*(4 - 5*Nc^2 + Nc^4))
 
Wig6j[{{"c21c3", "10", "10", "8", "8", "8"}, {2, 1, 1, 1}}] = 
    -(Sqrt[(-9 + Nc^2)/(-4 + Nc^2)]/(Sqrt[2]*Nc*(3 - Nc - 3*Nc^2 + Nc^3)))
 
Wig6j[{{"c21c3", "10", "10", "8", "8", "8"}, {2, 1, 1, 2}}] = 
    (-3*Sqrt[-9 + Nc^2])/(Sqrt[2]*(-3 + Nc)*(-1 + Nc)*
      (-4 - 4*Nc + Nc^2 + Nc^3))
 
Wig6j[{{"c21c3", "10", "8", "0", "10", "8"}, {1, 1, 1, 1}}] = 
    -2/(-12 + 4*Nc + 15*Nc^2 - 5*Nc^3 - 3*Nc^4 + Nc^5)
 
Wig6j[{{"c21c3", "10", "8", "10", "10", "8"}, {1, 1, 1, 1}}] = 
    -3/(4*Nc - 5*Nc^3 + Nc^5)
 
Wig6j[{{"c21c3", "10", "8", "10", "10", "8"}, {1, 1, 1, 2}}] = 
    Sqrt[-9 + Nc^2]/((-3 + Nc)*(-1 + Nc)*Nc*(-4 - 4*Nc + Nc^2 + Nc^3))
 
Wig6j[{{"c21c3", "10", "8", "10", "10", "8"}, {2, 1, 1, 2}}] = 
    (-1 - 3*Nc)/((-3 + Nc)*(-1 + Nc)*Nc*(-4 - 4*Nc + Nc^2 + Nc^3))
 
Wig6j[{{"c21c3", "10", "8", "27", "10", "8"}, {1, 1, 1, 1}}] = 
    -4/(4*Nc - 5*Nc^3 + Nc^5)
 
Wig6j[{{"c21c3", "10", "8", "35", "10", "8"}, {1, 1, 1, 1}}] = 
    4/(4*Nc^2 - 5*Nc^4 + Nc^6)
 
Wig6j[{{"c21c3", "10", "8", "8", "10", "8"}, {1, 1, 1, 1}}] = 
    2/(4 - 5*Nc^2 + Nc^4)
 
Wig6j[{{"c21c3", "10", "8", "c111c3", "10", "8"}, {1, 1, 1, 1}}] = 
    4/((-3 + Nc)*(-1 + Nc)*Nc*(-4 - 4*Nc + Nc^2 + Nc^3))
 
Wig6j[{{"c21c3", "10", "8", "c21c21", "10", "8"}, {1, 1, 1, 1}}] = 
    4/((-3 + Nc)*Nc*(-4 + Nc^2)*(-1 + Nc^2))
 
Wig6j[{{"c21c3", "10", "8", "c21c3", "10", "8"}, {1, 1, 1, 1}}] = 
    (6 - 4*Nc + 4*Nc^2)/((-4 + Nc)*(-3 + Nc)*Nc^2*(4 - 5*Nc^2 + Nc^4))
 
Wig6j[{{"c21c3", "10", "c21c3", "8", "8", "8"}, {1, 2, 1, 1}}] = 
    -(((21 - 2*Nc - 4*Nc^2 + Nc^3)*(Nc*(-4 - 4*Nc + Nc^2 + Nc^3))^(3/2))/
      ((-1 + Nc)*(Nc*(1 + Nc))^(5/2)*(-4 + Nc^2)^2*
       Sqrt[(-4 + Nc)*(9 - 93*Nc + 54*Nc^2 + 4*Nc^3 - 7*Nc^4 + Nc^5)]))
 
Wig6j[{{"c21c3", "10", "c21c3", "8", "8", "8"}, {1, 2, 1, 2}}] = 
    (9 - 24*Nc - 2*Nc^2 + Nc^3)/((-1 + Nc)*Nc*(1 + Nc)*(2 + Nc)*
      Sqrt[(-4 + Nc)*(9 - 93*Nc + 54*Nc^2 + 4*Nc^3 - 7*Nc^4 + Nc^5)])
 
Wig6j[{{"c21c3", "10", "c21c3", "8", "8", "8"}, {1, 3, 1, 1}}] = 
    (-1 + 2*Nc)/(Sqrt[2]*(-1 + Nc)*Nc*
      Sqrt[((-4 + Nc)*Nc*(1 + Nc)*(-4 + Nc^2)*(-3 + 30*Nc - 8*Nc^2 - 4*Nc^3 + 
          Nc^4))/(45 - 9*Nc - 5*Nc^2 + Nc^3)])
 
Wig6j[{{"c21c3", "10", "c21c3", "8", "8", "8"}, {1, 3, 1, 2}}] = 
    (-5 + 4*Nc)/(Sqrt[2]*(-1 + Nc)*(-4 + Nc^2)*
      Sqrt[(Nc*(12 - 111*Nc - 61*Nc^2 + 70*Nc^3 - 7*Nc^5 + Nc^6))/
        (45 - 9*Nc - 5*Nc^2 + Nc^3)])
 
Wig6j[{{"c21c3", "c111c3", "10", "8", "8", "8"}, {1, 1, 1, 1}}] = 
    Sqrt[6]/(Nc*(1 + Nc)*Sqrt[(-3 + Nc)*(-1 + Nc)*(-4 + Nc^2)])
 
Wig6j[{{"c21c3", "c111c3", "10", "8", "8", "8"}, {1, 1, 1, 2}}] = 
    Sqrt[6]/(Sqrt[3 - 4*Nc + Nc^2]*(-4 - 4*Nc + Nc^2 + Nc^3))
 
Wig6j[{{"c21c3", "c21c21", "0", "8", "8", "8"}, {1, 1, 1, 1}}] = 
    Sqrt[3]/(Nc*Sqrt[(-3 + Nc)*(2 + Nc)]*(-1 + Nc^2))
 
Wig6j[{{"c21c3", "c21c21", "0", "8", "8", "8"}, {1, 1, 1, 2}}] = 
    Sqrt[3]/(Sqrt[6 - 5*Nc + Nc^2]*(2 + Nc - 2*Nc^2 - Nc^3))
 
Wig6j[{{"c21c3", "c21c21", "10", "8", "8", "8"}, {1, 1, 1, 1}}] = 
    Sqrt[3]/(Nc*Sqrt[(-3 + Nc)*(2 + Nc)]*(-1 + Nc^2))
 
Wig6j[{{"c21c3", "c21c21", "10", "8", "8", "8"}, {1, 1, 1, 2}}] = 
    -((Sqrt[3]*Sqrt[(-2 + Nc)/(-3 + Nc)])/(4 - 5*Nc^2 + Nc^4))
 
Wig6j[{{"c21c3", "c21c3", "0", "8", "8", "8"}, {1, 1, 1, 1}}] = 
    (Sqrt[3/2]*(-1 + 2*Nc))/(Nc^(3/2)*(-1 + Nc^2)*
      Sqrt[16 - 4*Nc - 4*Nc^2 + Nc^3])
 
Wig6j[{{"c21c3", "c21c3", "0", "8", "8", "8"}, {1, 1, 1, 2}}] = 
    (3*Sqrt[3/2])/(Sqrt[(-4 + Nc)*Nc]*(4 - 5*Nc^2 + Nc^4))
 
Wig6j[{{"c21c3", "c21c3", "10", "8", "8", "8"}, {1, 1, 1, 1}}] = 
    (Sqrt[3/2]*(-3 + 2*Nc))/((-1 + Nc)*Nc^(3/2)*(1 + Nc)*
      Sqrt[(-4 + Nc)*(-4 + Nc^2)])
 
Wig6j[{{"c21c3", "c21c3", "10", "8", "8", "8"}, {1, 1, 1, 2}}] = 
    Sqrt[3/2]/(Sqrt[(-4 + Nc)*Nc]*(4 - 5*Nc^2 + Nc^4))
 
Wig6j[{{"c2c0", "6", "6", "8", "8", "8"}, {1, 1, 1, 1}}] = 
    Sqrt[(2 + Nc)/Nc]/(Sqrt[2]*(-1 + Nc^2))
 
Wig6j[{{"c2c0", "6", "6", "8", "8", "8"}, {1, 1, 1, 2}}] = 
    Sqrt[(-2 + Nc)/Nc]/(Sqrt[2]*(-1 + Nc^2))
 
Wig6j[{{"c2c0", "6", "8", "6", "6", "8"}, {1, 1, 1, 1}}] = (1 - Nc^2)^(-1)
 
Wig6j[{{"c2c0", "6", "8", "c2c0", "6", "8"}, {1, 1, 1, 1}}] = (-1 + Nc^2)^(-1)
 
Wig6j[{{"c2c0", "c21c0", "3", "6", "3", "3"}, {1, 1, 1, 1}}] = 
    Sqrt[3]/(Nc*Sqrt[-1 + Nc^2])
 
Wig6j[{{"c2c0", "c21c0", "3", "c2c0", "3", "3"}, {1, 1, 1, 1}}] = 
    1/((-1 + Nc)*Nc)
 
Wig6j[{{"c2c0", "c21c0", "3", "c2c0", "c2c1", "3"}, {1, 1, 1, 1}}] = 
    -2/(Nc - Nc^3)
 
Wig6j[{{"c2c0", "c21c0", "6", "3", "8", "3"}, {1, 1, 1, 1}}] = 
    Sqrt[3]/(Sqrt[Nc]*(-1 + Nc^2))
 
Wig6j[{{"c2c0", "c21c0", "c2c0", "3", "8", "3"}, {1, 1, 1, 1}}] = 
    -(Sqrt[-2 + Nc]/(Nc - Nc^3))
 
Wig6j[{{"c2c0", "c2c0", "6", "8", "8", "8"}, {1, 1, 1, 1}}] = 
    Sqrt[(-2 + Nc)/Nc]/(Sqrt[2]*(-1 + Nc^2))
 
Wig6j[{{"c2c0", "c2c0", "6", "8", "8", "8"}, {1, 1, 1, 2}}] = 
    Sqrt[3 + 2/Nc + Nc]/(Sqrt[2]*(-1 + Nc)*(1 + Nc)^(3/2))
 
Wig6j[{{"c2c0", "c2c0", "8", "6", "6", "8"}, {1, 1, 1, 1}}] = 
    Sqrt[-4 - 4*Nc + Nc^2 + Nc^3]/((-1 + Nc)*Nc*(1 + Nc)^(3/2))
 
Wig6j[{{"c2c0", "c2c0", "8", "c2c0", "6", "8"}, {1, 1, 1, 1}}] = 
    (1 - Nc^2)^(-1)
 
Wig6j[{{"c2c0", "c2c0", "8", "c2c0", "c2c0", "8"}, {1, 1, 1, 1}}] = 
    (-4 - 2*Nc + Nc^2)/((-2 + Nc)*(-1 + Nc)*Nc*(1 + Nc))
 
Wig6j[{{"c2c0", "c2c0", "c2c0", "8", "8", "8"}, {1, 1, 1, 1}}] = 
    Sqrt[Nc*(2 - Nc - 2*Nc^2 + Nc^3)]/(Sqrt[2]*(-2 + Nc)*(-1 + Nc^2)^(3/2))
 
Wig6j[{{"c2c0", "c2c0", "c2c0", "8", "8", "8"}, {1, 1, 1, 2}}] = 
    ((-4 + Nc)*Sqrt[(2 + Nc)/Nc])/(Sqrt[2]*(-2 + Nc)*(-1 + Nc)*(1 + Nc))
 
Wig6j[{{"c2c0", "c3c0", "3", "c2c0", "3", "3"}, {1, 1, 1, 1}}] = 2/(Nc - Nc^2)
 
Wig6j[{{"c2c0", "c3c0", "3", "c2c0", "c2c1", "3"}, {1, 1, 1, 1}}] = 
    2/(2*Nc - 3*Nc^2 + Nc^3)
 
Wig6j[{{"c2c0", "c3c0", "c2c0", "3", "8", "3"}, {1, 1, 1, 1}}] = 
    2/(Sqrt[-2 + Nc]*(Nc - Nc^2))
 
Wig6j[{{"c2c1", "15", "3", "8", "8", "8"}, {1, 1, 1, 1}}] = 
    1/(Sqrt[2]*Sqrt[Nc]*(-1 + Nc^2))
 
Wig6j[{{"c2c1", "15", "3", "8", "8", "8"}, {1, 1, 1, 2}}] = 
    Sqrt[Nc*(-4 + Nc^2)]/(Sqrt[2]*(4 - 5*Nc^2 + Nc^4))
 
Wig6j[{{"c2c1", "15", "8", "15", "3", "8"}, {1, 1, 1, 1}}] = 
    Sqrt[-4 + 10*Nc + 6*Nc^2]/((-1 + Nc)*(1 + Nc)*(2 + Nc)*(-1 + 3*Nc))
 
Wig6j[{{"c2c1", "15", "8", "15", "3", "8"}, {2, 1, 1, 1}}] = 
    -(((1 - 2*Nc)*Sqrt[(-3 + 5*Nc + 11*Nc^2 + 3*Nc^3)/(-4 + Nc^2)])/
      ((-1 + Nc)*Nc*(1 + Nc)^(3/2)*(-1 + 3*Nc)))
 
Wig6j[{{"c2c1", "15", "8", "3", "15", "8"}, {1, 1, 1, 1}}] = 
    1/((-1 + Nc)*Nc*(1 + Nc)*(2 + Nc))
 
Wig6j[{{"c2c1", "15", "8", "3", "c2c1", "8"}, {1, 2, 1, 1}}] = 
    -(((1 + 2*Nc)*Sqrt[(3 + 5*Nc - 11*Nc^2 + 3*Nc^3)/(-4 + Nc^2)])/
      ((-1 + Nc)^(3/2)*Nc*(1 + Nc)*(1 + 3*Nc)))
 
Wig6j[{{"c2c1", "15", "8", "c2c1", "3", "8"}, {1, 1, 1, 1}}] = 
    -(1/(Nc*(2 - Nc - 2*Nc^2 + Nc^3)))
 
Wig6j[{{"c2c1", "3", "3", "8", "8", "8"}, {1, 1, 1, 1}}] = 
    1/(Sqrt[2]*Sqrt[Nc]*(-1 + Nc^2))
 
Wig6j[{{"c2c1", "3", "3", "8", "8", "8"}, {1, 1, 1, 2}}] = 
    -(Sqrt[-4/Nc + Nc]/(Sqrt[2]*(1 + Nc)*(2 - 3*Nc + Nc^2)))
 
Wig6j[{{"c2c1", "3", "8", "15", "3", "8"}, {1, 1, 1, 1}}] = -(Nc - Nc^3)^(-1)
 
Wig6j[{{"c2c1", "3", "8", "c2c1", "3", "8"}, {1, 1, 1, 1}}] = 
    (2 - Nc - 2*Nc^2 + Nc^3)^(-1)
 
Wig6j[{{"c2c1", "3", "8", "c2c1", "c2c1", "8"}, {1, 2, 1, 2}}] = 
    (1 + Nc + 4*Nc^2)/(2*Nc + 5*Nc^2 - 5*Nc^3 - 5*Nc^4 + 3*Nc^5)
 
Wig6j[{{"c2c1", "3", "c2c1", "8", "8", "8"}, {1, 2, 1, 1}}] = 
    -(1/((-2 + Nc)*(-1 + Nc)^(3/2)*(1 + Nc)*
       Sqrt[(Nc*(2 + 6*Nc))/(-12 + 16*Nc - Nc^2 - 4*Nc^3 + Nc^4)]))
 
Wig6j[{{"c2c1", "3", "c2c1", "8", "8", "8"}, {1, 2, 1, 2}}] = 
    (3*Sqrt[((-3 + Nc)*Nc)/((1 + 3*Nc)*(-1 + Nc^2)^2)])/(Sqrt[2]*(-2 + Nc))
 
Wig6j[{{"c2c1", "c21c1", "15", "3", "8", "3"}, {1, 1, 1, 1}}] = 
    Sqrt[3]/(Nc*Sqrt[4 - 5*Nc^2 + Nc^4])
 
Wig6j[{{"c2c1", "c21c1", "3", "15", "8", "3"}, {1, 1, 1, 1}}] = 
    Sqrt[3]/(Nc*Sqrt[4 - 5*Nc^2 + Nc^4])
 
Wig6j[{{"c2c1", "c21c1", "3", "c2c1", "0", "3"}, {1, 1, 1, 1}}] = 
    2/((-2 + Nc)*Nc^2*(1 + Nc))
 
Wig6j[{{"c2c1", "c21c1", "3", "c2c1", "10bar", "3"}, {1, 1, 1, 1}}] = 
    2/((-2 + Nc)*Nc*(1 + Nc)*(2 + Nc))
 
Wig6j[{{"c2c1", "c21c1", "3", "c2c1", "8", "3"}, {1, 1, 1, 1}}] = 
    1/((-2 + Nc)*Nc*(1 + Nc))
 
Wig6j[{{"c2c1", "c21c1", "c2c1", "3", "8", "3"}, {1, 1, 1, 1}}] = 
    Sqrt[2]/((Nc + Nc^2)*Sqrt[-2 - 5*Nc + 3*Nc^2])
 
Wig6j[{{"c2c1", "c21c1", "c2c1", "3", "8", "3"}, {1, 2, 1, 1}}] = 
    -(Sqrt[(-3 + Nc)/(-4 - 12*Nc + Nc^2 + 3*Nc^3)]/(Nc + Nc^2))
 
Wig6j[{{"c2c1", "c2c0", "3", "3", "8", "3"}, {1, 1, 1, 1}}] = 
    -(Sqrt[2]/((-1 + Nc)*Sqrt[Nc*(1 + Nc)]))
 
Wig6j[{{"c2c1", "c2c0", "3", "c2c1", "0", "3"}, {1, 1, 1, 1}}] = 
    2/(Nc*(2 + Nc - Nc^2))
 
Wig6j[{{"c2c1", "c2c0", "3", "c2c1", "10bar", "3"}, {1, 1, 1, 1}}] = 
    -2/(2*Nc + Nc^2 - Nc^3)
 
Wig6j[{{"c2c1", "c2c0", "3", "c2c1", "8", "3"}, {1, 1, 1, 1}}] = 
    -2/(Nc*(2 - Nc - 2*Nc^2 + Nc^3))
 
Wig6j[{{"c2c1", "c2c0", "8", "6", "15", "3"}, {1, 1, 1, 1}}] = 
    2/(Sqrt[Nc]*(-1 + Nc^2))
 
Wig6j[{{"c2c1", "c2c0", "8", "6", "3", "3"}, {1, 1, 1, 1}}] = 
    -(Sqrt[2]/(Sqrt[-1 + Nc]*(Nc + Nc^2)))
 
Wig6j[{{"c2c1", "c2c0", "8", "c2c0", "3", "3"}, {1, 1, 1, 1}}] = 
    -(Sqrt[2]/((-1 + Nc)*Sqrt[(-2 + Nc)*Nc*(1 + Nc)]))
 
Wig6j[{{"c2c1", "c2c0", "8", "c2c0", "c2c1", "3"}, {1, 1, 1, 1}}] = 
    (-2*Sqrt[2]*(-1 - Nc + Nc^2))/((-2 + Nc)*(-1 + Nc)*Nc*(1 + Nc)*
      Sqrt[1 + 3*Nc])
 
Wig6j[{{"c2c1", "c2c0", "8", "c2c0", "c2c1", "3"}, {1, 2, 1, 1}}] = 
    (2*Sqrt[(-6 - Nc + Nc^2)/(1 + 3*Nc)])/(2 - Nc - 2*Nc^2 + Nc^3)
 
Wig6j[{{"c2c1", "c2c0", "c2c1", "3", "8", "3"}, {1, 1, 1, 1}}] = 
    ((1 + Nc^2)*Sqrt[-4 - 10*Nc + 6*Nc^2])/((-2 + Nc)*Nc*(1 + 3*Nc)*
      (-1 + Nc^2))
 
Wig6j[{{"c2c1", "c2c0", "c2c1", "3", "8", "3"}, {1, 2, 1, 1}}] = 
    (2*Sqrt[(12 - 4*Nc - 3*Nc^2 + Nc^3)/(1 + 3*Nc)])/(2 - Nc - 2*Nc^2 + Nc^3)
 
Wig6j[{{"c2c1", "c2c1", "3", "8", "8", "8"}, {1, 1, 1, 1}}] = 
    (1 - 2*Nc)/((-2 + Nc)*(-1 + Nc)*(1 + Nc)^(3/2)*
      Sqrt[(Nc*(1 + 3*Nc))/(-2 - Nc + Nc^2)])
 
Wig6j[{{"c2c1", "c2c1", "3", "8", "8", "8"}, {1, 1, 1, 2}}] = 
    (2 + Nc)/((-2 + Nc)*(-1 + Nc)*(1 + Nc)*Sqrt[Nc*(2 + 7*Nc + 3*Nc^2)])
 
Wig6j[{{"c2c1", "c2c1", "8", "15", "3", "8"}, {1, 1, 1, 1}}] = 
    -(Sqrt[2]/(Sqrt[(-2 + Nc)*(1 + 3*Nc)]*(-1 + Nc^2)))
 
Wig6j[{{"c2c1", "c2c1", "8", "3", "c2c1", "8"}, {1, 2, 1, 1}}] = 
    -((Sqrt[2]*Sqrt[-6 - Nc + Nc^2])/(2 + 5*Nc - 5*Nc^2 - 5*Nc^3 + 3*Nc^4))
 
Wig6j[{{"c2c1", "c2c1", "8", "c2c1", "3", "8"}, {1, 1, 1, 1}}] = 
    (2 - 4*Nc)/(2 + 5*Nc - 5*Nc^2 - 5*Nc^3 + 3*Nc^4)
 
Wig6j[{{"c2c1", "c3c1", "3", "c2c1", "0", "3"}, {1, 1, 1, 1}}] = 
    2/(Nc*(6 + Nc - 4*Nc^2 + Nc^3))
 
Wig6j[{{"c2c1", "c3c1", "3", "c2c1", "10bar", "3"}, {1, 1, 1, 1}}] = 
    2/(Nc*(2 - Nc - 2*Nc^2 + Nc^3))
 
Wig6j[{{"c2c1", "c3c1", "3", "c2c1", "8", "3"}, {1, 1, 1, 1}}] = 
    2/(Nc*(2 + Nc - Nc^2))
 
Wig6j[{{"c2c1", "c3c1", "c2c1", "3", "8", "3"}, {1, 1, 1, 1}}] = 
    -(((1 + 2*Nc)*Sqrt[-4 - 10*Nc + 6*Nc^2])/((-2 + Nc)*Nc*(1 + 3*Nc)*
       (-1 + Nc^2)))
 
Wig6j[{{"c2c1", "c3c1", "c2c1", "3", "8", "3"}, {1, 2, 1, 1}}] = 
    (2*Sqrt[(-4 + Nc^2)/(-3 - 8*Nc + 3*Nc^2)])/(2 - Nc - 2*Nc^2 + Nc^3)
 
Wig6j[{{"c3c0", "c31c0", "3", "c21c0", "c2c0", "3"}, {1, 1, 1, 1}}] = 
    4/((-1 + Nc)*Nc*Sqrt[(-2 + Nc)*(1 + Nc)])
 
Wig6j[{{"c3c0", "c31c0", "3", "c3c0", "c2c0", "3"}, {1, 1, 1, 1}}] = 
    2/(2*Nc - 3*Nc^2 + Nc^3)
 
Wig6j[{{"c3c0", "c31c0", "3", "c3c0", "c3c1", "3"}, {1, 1, 1, 1}}] = 
    6/(Nc*(2 - Nc - 2*Nc^2 + Nc^3))
 
Wig6j[{{"c3c0", "c31c0", "c21c0", "3", "8", "3"}, {1, 1, 1, 1}}] = 
    (2*Sqrt[2])/(Sqrt[(-2 + Nc)*Nc]*(-1 + Nc^2))
 
Wig6j[{{"c3c0", "c31c0", "c3c0", "3", "8", "3"}, {1, 1, 1, 1}}] = 
    -((Sqrt[2]*Sqrt[(-3 + Nc)/(-2 + Nc)])/(Nc - Nc^3))
 
Wig6j[{{"c3c0", "c4c0", "3", "c3c0", "c2c0", "3"}, {1, 1, 1, 1}}] = 
    -6/(Nc*(2 - 3*Nc + Nc^2))
 
Wig6j[{{"c3c0", "c4c0", "3", "c3c0", "c3c1", "3"}, {1, 1, 1, 1}}] = 
    6/((-1 + Nc)*Nc*(6 - 5*Nc + Nc^2))
 
Wig6j[{{"c3c0", "c4c0", "c3c0", "3", "8", "3"}, {1, 1, 1, 1}}] = 
    (3*Sqrt[2])/((Nc - Nc^2)*Sqrt[6 - 5*Nc + Nc^2])
 
Wig6j[{{"c3c1", "c2c0", "8", "6", "c2c0", "8"}, {1, 1, 1, 1}}] = 2/(Nc - Nc^3)
 
Wig6j[{{"c3c1", "c2c0", "8", "c21c1", "c2c0", "8"}, {1, 1, 1, 1}}] = 
    2/(Nc*(2 - Nc - 2*Nc^2 + Nc^3))
 
Wig6j[{{"c3c1", "c2c0", "8", "c2c0", "c2c0", "8"}, {1, 1, 1, 1}}] = 
    -2/(2 - Nc - 2*Nc^2 + Nc^3)
 
Wig6j[{{"c3c1", "c2c0", "8", "c3c1", "c2c0", "8"}, {1, 1, 1, 1}}] = 
    2/(-6 + 5*Nc + 5*Nc^2 - 5*Nc^3 + Nc^4)
 
Wig6j[{{"c3c1", "c2c0", "c2c0", "8", "8", "8"}, {1, 1, 1, 1}}] = 
    Sqrt[2]/(Sqrt[(-2 + Nc)*Nc]*(-1 + Nc^2))
 
Wig6j[{{"c3c1", "c2c0", "c2c0", "8", "8", "8"}, {1, 1, 1, 2}}] = 
    -(Sqrt[2 + 4/Nc]/((-2 + Nc)*(-1 + Nc)*(1 + Nc)))
 
Wig6j[{{"c3c1", "c3c0", "3", "c2c0", "c2c1", "3"}, {1, 1, 1, 1}}] = 
    (2*Sqrt[3])/((-2 + Nc)*Nc*Sqrt[-1 + Nc^2])
 
Wig6j[{{"c3c1", "c3c0", "3", "c3c1", "c2c1", "3"}, {1, 1, 1, 1}}] = 
    -6/(Nc*(-6 + 5*Nc + 5*Nc^2 - 5*Nc^3 + Nc^4))
 
Wig6j[{{"c3c1", "c3c0", "8", "c21c0", "c2c0", "3"}, {1, 1, 1, 1}}] = 
    (2*Sqrt[3])/(Sqrt[-2 + Nc]*(Nc - Nc^3))
 
Wig6j[{{"c3c1", "c3c0", "8", "c3c0", "c2c0", "3"}, {1, 1, 1, 1}}] = 
    (2*Sqrt[3])/((-2 + Nc)*(-1 + Nc)*Sqrt[Nc*(-3 - 2*Nc + Nc^2)])
 
Wig6j[{{"c3c1", "c3c0", "c2c0", "3", "8", "3"}, {1, 1, 1, 1}}] = 
    (Sqrt[6]*Sqrt[(2 - 3*Nc + Nc^2)/(Nc + Nc^2)])/((-2 + Nc)*(-1 + Nc)^(3/2))
 
Wig6j[{{"c3c3", "0", "0", "8", "8", "8"}, {1, 1, 1, 1}}] = 
    (2*Sqrt[2])/(Sqrt[-3 + Nc]*Nc^(3/2)*(-1 + Nc^2))
 
Wig6j[{{"c3c3", "0", "0", "8", "8", "8"}, {1, 1, 1, 2}}] = 0
 
Wig6j[{{"c3c3", "0", "0", "8", "8", "8"}, {2, 1, 1, 1}}] = 0
 
Wig6j[{{"c3c3", "0", "0", "8", "8", "8"}, {2, 1, 1, 2}}] = 
    (2*Sqrt[2])/(Sqrt[12 - 7*Nc + Nc^2]*(Nc - Nc^3))
 
Wig6j[{{"c3c3", "0", "8", "0", "0", "8"}, {1, 1, 1, 1}}] = 
    -4/(Nc^2*(3 - Nc - 3*Nc^2 + Nc^3))
 
Wig6j[{{"c3c3", "0", "8", "0", "0", "8"}, {1, 1, 1, 2}}] = 0
 
Wig6j[{{"c3c3", "0", "8", "0", "0", "8"}, {2, 1, 1, 2}}] = 
    -4/((-3 + Nc)*Nc*(1 + Nc)*(4 - 5*Nc + Nc^2))
 
Wig6j[{{"c3c3", "0", "8", "10", "0", "8"}, {1, 1, 1, 1}}] = 
    -4/(Nc^2*(3 - Nc - 3*Nc^2 + Nc^3))
 
Wig6j[{{"c3c3", "0", "8", "8", "0", "8"}, {1, 1, 1, 1}}] = 
    4/((-3 + Nc)*Nc^2*(1 + Nc))
 
Wig6j[{{"c3c3", "0", "8", "c21c21", "0", "8"}, {1, 1, 1, 1}}] = 
    4/((-3 + Nc)*(-1 + Nc)^2*Nc^2*(1 + Nc))
 
Wig6j[{{"c3c3", "0", "8", "c21c3", "0", "8"}, {1, 1, 1, 1}}] = 
    4/((-4 + Nc)*(-3 + Nc)*(-1 + Nc)*Nc^2*(1 + Nc))
 
Wig6j[{{"c3c3", "0", "8", "c3c3", "0", "8"}, {1, 1, 1, 1}}] = 
    (4*(8 - 3*Nc + Nc^2))/((-5 + Nc)*(-4 + Nc)*(-3 + Nc)*(-1 + Nc)^2*Nc^2*
      (1 + Nc))
 
Wig6j[{{"c3c3", "0", "c3c3", "8", "8", "8"}, {1, 2, 1, 1}}] = 0
 
Wig6j[{{"c3c3", "0", "c3c3", "8", "8", "8"}, {1, 2, 1, 2}}] = 
    (2*Sqrt[3])/((-1 + Nc)*Nc*Sqrt[((-5 + Nc)*(-4 + Nc)*(-1 + Nc)*(1 + Nc)^2)/
        (-6 + Nc)])
 
Wig6j[{{"c3c3", "c21c3", "0", "8", "8", "8"}, {1, 1, 1, 1}}] = 
    Sqrt[6]/(Sqrt[(-4 + Nc)*Nc^3]*(-1 + Nc^2))
 
Wig6j[{{"c3c3", "c21c3", "0", "8", "8", "8"}, {1, 1, 1, 2}}] = 
    (Sqrt[6]*Sqrt[(-4 + Nc^2)/((-4 + Nc)*Nc)])/(4 - 5*Nc^2 + Nc^4)
 
Wig6j[{{"c3c3", "c3c3", "0", "8", "8", "8"}, {1, 1, 1, 1}}] = 
    (2*Sqrt[3]*Sqrt[(-2 + Nc)/((-5 + Nc)*(-1 + Nc)^3*Nc^3)])/(1 + Nc)
 
Wig6j[{{"c3c3", "c3c3", "0", "8", "8", "8"}, {1, 1, 1, 2}}] = 0
 



(* ::Subsection::Closed:: *)
(*Functions to draw and evaluate Wigner coefficients*)


Dim[Representation_] := Representation /. RepresentationDimensionRules
 
RepresentationDimensionRules = {"1" -> 1, "3" -> Nc, "3bar" -> Nc, 
     "c2c0" -> ((-1 + Nc)*Nc)/2, "6" -> (Nc*(1 + Nc))/2, "8" -> -1 + Nc^2, 
     "c0c2" -> ((-1 + Nc)*Nc)/2, "6bar" -> (Nc*(1 + Nc))/2, 
     "c3c0" -> (Nc*(2 - 3*Nc + Nc^2))/6, "c21c0" -> (Nc*(-1 + Nc^2))/3, 
     "c111c0" -> (Nc*(2 + 3*Nc + Nc^2))/6, "c2c1" -> (Nc*(-2 - Nc + Nc^2))/2, 
     "15" -> (Nc*(-2 + Nc + Nc^2))/2, "c1c2" -> (Nc*(-2 - Nc + Nc^2))/2, 
     "15bar" -> (Nc*(-2 + Nc + Nc^2))/2, "c0c3" -> (Nc*(2 - 3*Nc + Nc^2))/6, 
     "c0c21" -> (Nc*(-1 + Nc^2))/3, "c0c111" -> (Nc*(2 + 3*Nc + Nc^2))/6, 
     "c4c0" -> (Nc*(-6 + 11*Nc - 6*Nc^2 + Nc^3))/24, 
     "c31c0" -> (Nc*(2 - Nc - 2*Nc^2 + Nc^3))/8, 
     "c22c0" -> (Nc^2*(-1 + Nc^2))/12, "c211c0" -> 
      (Nc*(-2 - Nc + 2*Nc^2 + Nc^3))/8, "c1111c0" -> 
      (Nc*(6 + 11*Nc + 6*Nc^2 + Nc^3))/24, 
     "c3c1" -> (Nc*(3 - Nc - 3*Nc^2 + Nc^3))/6, 
     "c21c1" -> (Nc^2*(-4 + Nc^2))/3, "24" -> (Nc*(-3 - Nc + 3*Nc^2 + Nc^3))/
       6, "0" -> (Nc^2*(-3 - 2*Nc + Nc^2))/4, 
     "10bar" -> (4 - 5*Nc^2 + Nc^4)/4, "10" -> (4 - 5*Nc^2 + Nc^4)/4, 
     "27" -> (Nc^2*(-3 + 2*Nc + Nc^2))/4, 
     "c1c3" -> (Nc*(3 - Nc - 3*Nc^2 + Nc^3))/6, 
     "c1c21" -> (Nc^2*(-4 + Nc^2))/3, "24bar" -> 
      (Nc*(-3 - Nc + 3*Nc^2 + Nc^3))/6, 
     "c0c4" -> (Nc*(-6 + 11*Nc - 6*Nc^2 + Nc^3))/24, 
     "c0c31" -> (Nc*(2 - Nc - 2*Nc^2 + Nc^3))/8, 
     "c0c22" -> (Nc^2*(-1 + Nc^2))/12, "c0c211" -> 
      (Nc*(-2 - Nc + 2*Nc^2 + Nc^3))/8, "c0c1111" -> 
      (Nc*(6 + 11*Nc + 6*Nc^2 + Nc^3))/24, 
     "35" -> (Nc^2*(16 - 12*Nc - 8*Nc^2 + 3*Nc^3 + Nc^4))/18, 
     "35bar" -> (Nc^2*(16 - 12*Nc - 8*Nc^2 + 3*Nc^3 + Nc^4))/18, 
     "64" -> (Nc^2*(1 + Nc)^2*(-5 + 4*Nc + Nc^2))/36, 
     "c111c3" -> (-36 + 49*Nc^2 - 14*Nc^4 + Nc^6)/36, 
     "c21c21" -> ((-9 + Nc^2)*(-1 + Nc^2)^2)/9, 
     "c21c3" -> (Nc^2*(16 + 12*Nc - 8*Nc^2 - 3*Nc^3 + Nc^4))/18, 
     "c3c111" -> (-36 + 49*Nc^2 - 14*Nc^4 + Nc^6)/36, 
     "c3c21" -> (Nc^2*(16 + 12*Nc - 8*Nc^2 - 3*Nc^3 + Nc^4))/18, 
     "c3c3" -> ((-1 + Nc)^2*Nc^2*(-5 - 4*Nc + Nc^2))/36}
 
BirdTrackOfWignerCoefficient[{\[Alpha]_, \[Beta]_, \[Gamma]_, \[Delta]_, 
      \[Epsilon]_, \[Zeta]_}, {v1_, v2_, v3_, v4_}] := 
    Module[{edgeConnections = {1 -> 2, 2 -> 3, 3 -> 1, 4 -> 2, 4 -> 3, 
        1 -> 4}, edgeRepresentations = {\[Gamma], \[Alpha], \[Beta], 
        \[Epsilon], \[Zeta], \[Delta]}, vLabels = 
       {1 -> Placed[ToString[v1], Center], 2 -> Placed[ToString[v2], Center], 
        3 -> Placed[ToString[v3], Center], 4 -> Placed[ToString[v4], 
          Center]}}, Graph[edgeConnections, EdgeStyle -> Thick, 
      EdgeLabels -> Table[edgeConnections[[i]] -> edgeRepresentations[[i]], 
        {i, Length[edgeConnections]}], VertexShapeFunction -> "Circle", 
      EdgeLabelStyle -> Directive[30, Background -> White], 
      VertexLabels -> vLabels, VertexStyle -> White, VertexSize -> 0.1, 
      VertexCoordinates -> {{1, 0}, {0.5, 1}, {0, 0}, {0.5, 0.4}}]]
 
DebugWignerCoefficientFunctions = False
 
AllowedRepresentations = {"1", "3", "3bar", "8", "6", "c2c0", "6bar", "c0c2", 
     "15", "c2c1", "15bar", "c1c2", "c111c0", "c21c0", "c3c0", "c0c111", 
     "c0c21", "c0c3", "27", "10", "10bar", "0", "24", "c21c1", "c3c1", 
     "24bar", "c1c21", "c1c3", "c1111c0", "c22c0", "c211c0", "c31c0", "c4c0", 
     "c0c1111", "c0c22", "c0c211", "c0c31", "c0c4", "64", "35", "35bar", 
     "c21c21", "c111c3", "c3c111", "c21c3", "c3c21", "c3c3"}
 
SortingRepresentationsNumbers = {"c3c3" -> 1, "c21c3" -> 2, "c3c21" -> 3, 
     "c21c21" -> 4, "c111c3" -> 5, "c3c111" -> 6, "35" -> 7, "35bar" -> 8, 
     "64" -> 9, "c4c0" -> 10, "c0c4" -> 11, "c3c1" -> 12, "c1c3" -> 13, 
     "0" -> 14, "c31c0" -> 15, "c0c31" -> 16, "c21c1" -> 17, "c1c21" -> 18, 
     "10" -> 19, "10bar" -> 20, "c22c0" -> 21, "c211c0" -> 22, "c0c22" -> 23, 
     "c0c211" -> 24, "24" -> 25, "24bar" -> 26, "27" -> 27, "c1111c0" -> 28, 
     "c0c1111" -> 29, "c3c0" -> 30, "c0c3" -> 31, "c2c1" -> 32, "c1c2" -> 33, 
     "c21c0" -> 34, "c0c21" -> 35, "15" -> 36, "15bar" -> 37, "c111c0" -> 38, 
     "c0c111" -> 39, "c2c0" -> 40, "c0c2" -> 41, "6" -> 42, "6bar" -> 43, 
     "3" -> 44, "3bar" -> 45, "1" -> 46, "8" -> 47}
 
RotateWignerCoefficientCounterclockwise[Wigner_] := 
    Module[{\[Alpha] = Wigner[[1]][[1]], \[Beta] = Wigner[[1]][[2]], 
      \[Gamma] = Wigner[[1]][[3]], \[Delta] = Wigner[[1]][[4]], 
      \[Epsilon] = Wigner[[1]][[5]], \[Zeta] = Wigner[[1]][[6]]}, 
     Return[{{\[Gamma], \[Alpha], \[Beta], \[Zeta] /. ConjugationRules, 
        \[Delta] /. ConjugationRules, \[Epsilon]}, 
       Wigner[[2]][[{3, 1, 2, 4}]]}]]
 
ConjugationRules = {"1" -> "1", "3" -> "3bar", "3bar" -> "3", 
     "c2c0" -> "c0c2", "6" -> "6bar", "8" -> "8", "c0c2" -> "c2c0", 
     "6bar" -> "6", "c3c0" -> "c0c3", "c21c0" -> "c0c21", 
     "c111c0" -> "c0c111", "c2c1" -> "c1c2", "15" -> "15bar", 
     "c1c2" -> "c2c1", "15bar" -> "15", "c0c3" -> "c3c0", "c0c21" -> "c21c0", 
     "c0c111" -> "c111c0", "c4c0" -> "c0c4", "c31c0" -> "c0c31", 
     "c22c0" -> "c0c22", "c211c0" -> "c0c211", "c1111c0" -> "c0c1111", 
     "c3c1" -> "c1c3", "c21c1" -> "c1c21", "24" -> "24bar", "0" -> "0", 
     "10bar" -> "10", "10" -> "10bar", "27" -> "27", "c1c3" -> "c3c1", 
     "c1c21" -> "c21c1", "24bar" -> "24", "c0c4" -> "c4c0", 
     "c0c31" -> "c31c0", "c0c22" -> "c22c0", "c0c211" -> "c211c0", 
     "c0c1111" -> "c1111c0", "35" -> "35bar", "35bar" -> "35", "64" -> "64", 
     "c111c3" -> "c3c111", "c21c21" -> "c21c21", "c21c3" -> "c3c21", 
     "c3c111" -> "c111c3", "c3c21" -> "c21c3", "c3c3" -> "c3c3"}
 
SwapVerticesInWignerCoefficient[Wigner_] := 
    Module[{\[Alpha] = Wigner[[1]][[1]], \[Beta] = Wigner[[1]][[2]], 
      \[Gamma] = Wigner[[1]][[3]], \[Delta] = Wigner[[1]][[4]], 
      \[Epsilon] = Wigner[[1]][[5]], \[Zeta] = Wigner[[1]][[6]]}, 
     Return[{{\[Gamma] /. ConjugationRules, \[Delta], \[Epsilon], \[Zeta], 
        \[Alpha] /. ConjugationRules, \[Beta]}, Wigner[[2]][[{4, 2, 1, 3}]]}]]
 
Sort3RepresentationList[{{\[Alpha]_, \[Beta]_, \[Gamma]_, "8", "8", "8"}, 
      {vertex1_, vertex2_, vertex3_, vertex4_}}] := 
    Module[{SortedList = {{\[Alpha], vertex3}, {\[Beta], vertex1}, 
        {\[Gamma], vertex2}}, SortingList, SortedListReverse, 
      SortingListReverse, Representations, RepresentationsConjugated, 
      AllEqualPermutations, AllEqualPermutationsOrdering, 
      WasItConjugated = False, OutputWigner}, 
     Representations = Sort[{SortedList[[1]][[1]], SortedList[[2]][[1]], 
          SortedList[[3]][[1]]} /. SortingRepresentationsNumbers]; 
      RepresentationsConjugated = 
       Sort[{SortedList[[1]][[1]], SortedList[[2]][[1]], SortedList[[3]][[
            1]]} /. ConjugationRules /. SortingRepresentationsNumbers]; 
      If[Sort[{Representations, RepresentationsConjugated}][[1]] == 
         RepresentationsConjugated && Representations != 
         RepresentationsConjugated, 
       SortedList = SortedList /. ConjugationRules; WasItConjugated = True]; 
      SortedListReverse = {{SortedList[[3]][[1]], SortedList[[2]][[2]]}, 
        {SortedList[[2]][[1]], SortedList[[1]][[2]]}, {SortedList[[1]][[1]], 
         SortedList[[3]][[2]]}}; SortingList = 
       Table[{SortedList[[i]][[1]] /. SortingRepresentationsNumbers, 
         SortedList[[i]][[2]]}, {i, Length[SortedList]}]; 
      SortingListReverse = Table[{SortedListReverse[[i]][[1]] /. 
          SortingRepresentationsNumbers, SortedListReverse[[i]][[2]]}, 
        {i, Length[SortedListReverse]}]; AllEqualPermutations = 
       Join[NestList[#1[[{3, 1, 2}]] & , SortedList, 2], 
        NestList[#1[[{3, 1, 2}]] & , SortedListReverse, 2]]; 
      AllEqualPermutationsOrdering = Ordering[
        Join[NestList[#1[[{3, 1, 2}]] & , SortingList, 2], 
         NestList[#1[[{3, 1, 2}]] & , SortingListReverse, 2]]]; 
      SortedList = AllEqualPermutations[[AllEqualPermutationsOrdering[[1]]]]; 
      OutputWigner = {{SortedList[[1]][[1]], SortedList[[2]][[1]], 
         SortedList[[3]][[1]], "8", "8", "8"}, {SortedList[[2]][[2]], 
         SortedList[[3]][[2]], SortedList[[1]][[2]], vertex4}}; 
      Return[{OutputWigner, WasItConjugated}]]
 
Sort3RepresentationCoefficient[Wigner_] := 
    Module[{InternalWigner = Wigner, v1, v2, v3, v4, v1Conj, v2Conj, v3Conj, 
      v4Conj, vertices, NumberOfAntisymmetricTripleGluonVertices, 
      NumberOfSymmetricTripleGluonVertices, NumberOfQQbarGVertices, 
      NumberOfRotations = 0, TripleGluonVertexToAccept, 
      QuarkCoefficient = False, QuarkVertices, SortedWigner, Conjugated}, 
     v1Conj[{b_, c_, d_}] := {b, c /. ConjugationRules, 
        d /. ConjugationRules}; v2Conj[{a_, e_, c_}] := 
       {a /. ConjugationRules, e, c}; v3Conj[{a_, b_, f_}] := 
       {a, b /. ConjugationRules, f}; v4Conj[{d_, e_, f_}] := 
       {d, e /. ConjugationRules, f /. ConjugationRules}; 
      v1 := {Sort[v1Conj[InternalWigner[[1]][[{2, 3, 4}]]]], 
        InternalWigner[[2]][[1]]}; 
      v2 := {Sort[v2Conj[InternalWigner[[1]][[{1, 5, 3}]]]], 
        InternalWigner[[2]][[2]]}; 
      v3 := {Sort[v3Conj[InternalWigner[[1]][[{1, 2, 6}]]]], 
        InternalWigner[[2]][[3]]}; 
      v4 := {Sort[v4Conj[InternalWigner[[1]][[{4, 5, 6}]]]], 
        InternalWigner[[2]][[4]]}; vertices := {v1, v2, v3, v4}; 
      NumberOfAntisymmetricTripleGluonVertices = Count[vertices, 
        {{"8", "8", "8"}, 1}]; NumberOfSymmetricTripleGluonVertices = 
       Count[vertices, {{"8", "8", "8"}, 2}]; NumberOfQQbarGVertices = 
       Count[vertices, {{"3", "3bar", "8"}, 1}]; 
      Which[NumberOfAntisymmetricTripleGluonVertices > 0, 
       TripleGluonVertexToAccept = 1, NumberOfSymmetricTripleGluonVertices > 
        0, TripleGluonVertexToAccept = 2, NumberOfQQbarGVertices > 0, 
       QuarkCoefficient = True, True, 
       PrintWig[
         "Warning! Sort3RepresentationCoefficient encountered an error."]; 
        Return[]]; If[QuarkCoefficient, 
       QuarkVertices = Table[{p, 1}, {p, Permutations[{"3", "3bar", "8"}]}]; 
        While[FreeQ[QuarkVertices, v4] && NumberOfRotations < 4, 
         NumberOfRotations++; If[MemberQ[QuarkVertices, v3], 
           InternalWigner = SwapVerticesInWignerCoefficient[InternalWigner], 
           InternalWigner = RotateWignerCoefficientCounterclockwise[
             InternalWigner]]]; {SortedWigner, Conjugated} = 
         Sort3RepresentationQuarkList[InternalWigner]; , 
       While[v4 != {{"8", "8", "8"}, TripleGluonVertexToAccept} && 
          NumberOfRotations < 4, NumberOfRotations++; 
          If[v3 == {{"8", "8", "8"}, TripleGluonVertexToAccept}, 
           InternalWigner = SwapVerticesInWignerCoefficient[InternalWigner], 
           InternalWigner = RotateWignerCoefficientCounterclockwise[
             InternalWigner]]]; {SortedWigner, Conjugated} = 
         Sort3RepresentationList[InternalWigner]; ]; 
      Clear[v1Conj, v2Conj, v3Conj, v4Conj, vertices, v1, v2, v3, v4, 
       InternalWigner]; Return[{SortedWigner, Conjugated}]]
 
PrintWig[args___] := If[WignerVerbosity > 0, Print[args]]
 
WignerVerbosity = 0
 
Sort3RepresentationQuarkList[{{\[Alpha]_, \[Beta]_, \[Gamma]_, \[Delta]_, 
       \[Epsilon]_, \[Zeta]_}, {vertex1_, vertex2_, vertex3_, vertex4_}}] := 
    Module[{InternalWigner = {{\[Alpha], \[Beta], \[Gamma], \[Delta], 
         \[Epsilon], \[Zeta]}, {vertex1, vertex2, vertex3, vertex4}}, v1, v2, 
      v3, v4, v1Conj, v2Conj, v3Conj, v4Conj, vertices, 
      QuarkVertices = Table[{p, 1}, {p, Permutations[{"3", "3bar", "8"}]}], 
      WasItConjugated = False, NumberOfRotations = 0}, 
     v1Conj[{b_, c_, d_}] := {b, c /. ConjugationRules, 
        d /. ConjugationRules}; v2Conj[{a_, e_, c_}] := 
       {a /. ConjugationRules, e, c}; v3Conj[{a_, b_, f_}] := 
       {a, b /. ConjugationRules, f}; v4Conj[{d_, e_, f_}] := 
       {d, e /. ConjugationRules, f /. ConjugationRules}; 
      v1 := {Sort[v1Conj[InternalWigner[[1]][[{2, 3, 4}]]]], 
        InternalWigner[[2]][[1]]}; 
      v2 := {Sort[v2Conj[InternalWigner[[1]][[{1, 5, 3}]]]], 
        InternalWigner[[2]][[2]]}; 
      v3 := {Sort[v3Conj[InternalWigner[[1]][[{1, 2, 6}]]]], 
        InternalWigner[[2]][[3]]}; 
      v4 := {Sort[v4Conj[InternalWigner[[1]][[{4, 5, 6}]]]], 
        InternalWigner[[2]][[4]]}; vertices := {v1, v2, v3, v4}; 
      If[FreeQ[QuarkVertices, v4], PrintWig["WARNING! \
Sort3RepresentationQuarkList called with the wrong form of the Wigner \
coefficient, \nWigner = ", InternalWigner, "\nVertices = ", vertices]; 
        Return[]]; While[InternalWigner[[1,5]] != "8" && 
        NumberOfRotations < 4, NumberOfRotations++; InternalWigner = 
         RotateWignerCoefficientCounterclockwise[InternalWigner]]; 
      If[InternalWigner[[1,6]] == "3bar", WasItConjugated = True; 
        InternalWigner[[1]] = InternalWigner[[1]] /. ConjugationRules]; 
      If[(InternalWigner[[1,1]] /. SortingRepresentationsNumbers) > 
        (InternalWigner[[1,3]] /. SortingRepresentationsNumbers), 
       InternalWigner = MirrorAndConjugateWignerCoefficient[InternalWigner], 
       Null, PrintWig["Warning! Could not sort representations in \
Sort3RepresentationQuarkList, when attempting to reduce to simplest Wigner \
coefficient. Might be a problem with SortingRepresentationNumbers."]]; 
      Clear[v1Conj, v2Conj, v3Conj, v4Conj, vertices, v1, v2, v3, v4]; 
      Return[{InternalWigner, WasItConjugated}]]
 
MirrorAndConjugateWignerCoefficient[Wigner_] := 
    Module[{\[Alpha] = Wigner[[1]][[1]], \[Beta] = Wigner[[1]][[2]], 
      \[Gamma] = Wigner[[1]][[3]], \[Delta] = Wigner[[1]][[4]], 
      \[Epsilon] = Wigner[[1]][[5]], \[Zeta] = Wigner[[1]][[6]]}, 
     Return[{{\[Gamma], \[Beta], \[Alpha], \[Zeta], \[Epsilon], \[Delta]}, 
       Wigner[[2]][[{3, 2, 1, 4}]]}]]
 
Sort4RepresentationList[{{\[Alpha]_, \[Beta]_, "8", \[Gamma]_, \[Delta]_, 
       "8"}, {vertex1_, vertex2_, vertex3_, vertex4_}}] := 
    Module[{RepList = {{\[Alpha], vertex3}, {\[Beta], vertex1}, 
        {\[Gamma], vertex4}, {\[Delta], vertex2}}, RepListReverse = 
       {{\[Beta], vertex3}, {\[Alpha], vertex2}, {\[Delta], vertex4}, 
        {\[Gamma], vertex1}}, SortingList, SortingListReverse, 
      Representations, RepresentationsConjugated, AllEqualPermutations, 
      AllEqualPermutationsOrdering, WasItConjugated = False, OutputWigner}, 
     Representations = Sort[Table[RepList[[ii]][[1]], 
          {ii, Length[RepList]}] /. SortingRepresentationsNumbers]; 
      RepresentationsConjugated = 
       Sort[Table[RepList[[ii]][[1]], {ii, Length[RepList]}] /. 
          ConjugationRules /. SortingRepresentationsNumbers]; 
      If[Sort[{Representations, RepresentationsConjugated}][[1]] == 
         RepresentationsConjugated && Representations != 
         RepresentationsConjugated, RepList = RepList /. ConjugationRules; 
        RepListReverse = RepListReverse /. ConjugationRules; 
        WasItConjugated = True]; SortingList = 
       Table[{RepList[[i]][[1]] /. SortingRepresentationsNumbers, 
         RepList[[i]][[2]]}, {i, Length[RepList]}]; SortingListReverse = 
       Table[{RepListReverse[[i]][[1]] /. SortingRepresentationsNumbers, 
         RepListReverse[[i]][[2]]}, {i, Length[RepListReverse]}]; 
      AllEqualPermutations = Join[NestList[#1[[{4, 1, 2, 3}]] & , RepList, 
         3], NestList[#1[[{4, 1, 2, 3}]] & , RepListReverse, 3]]; 
      AllEqualPermutationsOrdering = Ordering[
        Join[NestList[#1[[{4, 1, 2, 3}]] & , SortingList, 3], 
         NestList[#1[[{4, 1, 2, 3}]] & , SortingListReverse, 3]]]; 
      If[EvenQ[AllEqualPermutationsOrdering[[1]]], WasItConjugated = 
         !WasItConjugated]; RepList = AllEqualPermutations[[
        AllEqualPermutationsOrdering[[1]]]]; OutputWigner = 
       {{RepList[[1]][[1]], RepList[[2]][[1]], "8", RepList[[3]][[1]], 
         RepList[[4]][[1]], "8"}, {RepList[[2]][[2]], RepList[[4]][[2]], 
         RepList[[1]][[2]], RepList[[3]][[2]]}}; 
      Return[{OutputWigner, WasItConjugated}]]
 
Sort4RepresentationCoefficient[Wigner_] := 
    Module[{InternalWigner = Wigner, v1, v2, v3, v4, v1Conj, v2Conj, v3Conj, 
      v4Conj, vertices, NumberOfRotations = 0, 
      NumberOfAntisymmetricTripleGluonVertices, 
      NumberOfSymmetricTripleGluonVertices, NumberOfQQbarGVertices, 
      GluonCoefficient, GluonQuarkCoeff, Conjugated}, 
     v1Conj[{b_, c_, d_}] := {b, c /. ConjugationRules, 
        d /. ConjugationRules}; v2Conj[{a_, e_, c_}] := 
       {a /. ConjugationRules, e, c}; v3Conj[{a_, b_, f_}] := 
       {a, b /. ConjugationRules, f}; v4Conj[{d_, e_, f_}] := 
       {d, e /. ConjugationRules, f /. ConjugationRules}; 
      v1 := {Sort[v1Conj[InternalWigner[[1]][[{2, 3, 4}]]]], 
        InternalWigner[[2]][[1]]}; 
      v2 := {Sort[v2Conj[InternalWigner[[1]][[{1, 5, 3}]]]], 
        InternalWigner[[2]][[2]]}; 
      v3 := {Sort[v3Conj[InternalWigner[[1]][[{1, 2, 6}]]]], 
        InternalWigner[[2]][[3]]}; 
      v4 := {Sort[v4Conj[InternalWigner[[1]][[{4, 5, 6}]]]], 
        InternalWigner[[2]][[4]]}; vertices := {v1, v2, v3, v4}; 
      NumberOfAntisymmetricTripleGluonVertices = Count[vertices, 
        {{"8", "8", "8"}, 1}]; NumberOfSymmetricTripleGluonVertices = 
       Count[vertices, {{"8", "8", "8"}, 2}]; NumberOfQQbarGVertices = 
       Count[vertices, {{"3", "3bar", "8"}, 1}]; 
      If[NumberOfAntisymmetricTripleGluonVertices + 
         NumberOfSymmetricTripleGluonVertices + NumberOfQQbarGVertices != 0, 
       PrintWig["WARNING! This coefficient has triple-gluon vertices or \
quark-antiquark-gluon vertices, hence it should be sorted with \
Sort3RepresentationCoefficient."]]; GluonCoefficient = 
       InternalWigner[[1,{1, 4}]] == {"8", "8"} || 
        InternalWigner[[1,{2, 5}]] == {"8", "8"} || 
        InternalWigner[[1,{3, 6}]] == {"8", "8"}; If[GluonCoefficient, 
       While[InternalWigner[[1]][[{3, 6}]] != {"8", "8"} && 
          NumberOfRotations < 4, NumberOfRotations++; InternalWigner = 
           RotateWignerCoefficientCounterclockwise[InternalWigner]]; 
        {InternalWigner, Conjugated} = Sort4RepresentationList[
          InternalWigner], GluonQuarkCoeff = 
         MemberQ[Sort /@ {InternalWigner[[1,{1, 4}]], InternalWigner[[1,
              {2, 5}]], InternalWigner[[1,{3, 6}]]}, {"3", "8"}] || 
          MemberQ[Sort /@ {InternalWigner[[1,{1, 4}]], InternalWigner[[1,
              {2, 5}]], InternalWigner[[1,{3, 6}]]}, {"3bar", "8"}]; 
        If[GluonQuarkCoeff, While[(Sort[InternalWigner[[1]][[{3, 6}]]] != 
              {"3", "8"} && Sort[InternalWigner[[1]][[{3, 6}]]] != 
              {"3bar", "8"}) && NumberOfRotations < 4, NumberOfRotations++; 
            InternalWigner = RotateWignerCoefficientCounterclockwise[
              InternalWigner]]; {InternalWigner, Conjugated} = 
           Sort4RepresentationQuarkList[InternalWigner, GluonQuarkCoeff], 
         While[FreeQ[{{"3", "3"}, {"3", "3bar"}, {"3bar", "3"}, 
              {"3bar", "3bar"}}, InternalWigner[[1]][[{3, 6}]]] && 
            NumberOfRotations < 4, NumberOfRotations++; InternalWigner = 
             RotateWignerCoefficientCounterclockwise[InternalWigner]]; 
          {InternalWigner, Conjugated} = Sort4RepresentationQuarkList[
            InternalWigner, GluonQuarkCoeff]]]; Clear[v1Conj, v2Conj, v3Conj, 
       v4Conj, vertices, v1, v2, v3, v4]; 
      Return[{InternalWigner, Conjugated}]]
 
Sort4RepresentationQuarkList[{{\[Alpha]_, \[Beta]_, \[Gamma]_, \[Delta]_, 
       \[Epsilon]_, \[Zeta]_}, {vertex1_, vertex2_, vertex3_, vertex4_}}, 
     GluonQuarkCoeff_] := 
    Module[{InternalWigner = {{\[Alpha], \[Beta], \[Gamma], \[Delta], 
         \[Epsilon], \[Zeta]}, {vertex1, vertex2, vertex3, vertex4}}, v1, v2, 
      v3, v4, v1Conj, v2Conj, v3Conj, v4Conj, vertices, 
      NumberOfRotations = 0, Conjugated = False, listWigner, conj}, 
     If[FreeQ[{"3", "3bar", "8"}, \[Gamma]] || FreeQ[{"3", "3bar", "8"}, 
         \[Zeta]], PrintWig["WARNING! Sort4RepresentationQuarkList called \
with the wrong form of the Wigner coefficient, Wigner = ", InternalWigner]; 
        Return[]]; v1Conj[{b_, c_, d_}] := {b, c /. ConjugationRules, 
        d /. ConjugationRules}; v2Conj[{a_, e_, c_}] := 
       {a /. ConjugationRules, e, c}; v3Conj[{a_, b_, f_}] := 
       {a, b /. ConjugationRules, f}; v4Conj[{d_, e_, f_}] := 
       {d, e /. ConjugationRules, f /. ConjugationRules}; 
      v1 := {Sort[v1Conj[InternalWigner[[1]][[{2, 3, 4}]]]], 
        InternalWigner[[2]][[1]]}; 
      v2 := {Sort[v2Conj[InternalWigner[[1]][[{1, 5, 3}]]]], 
        InternalWigner[[2]][[2]]}; 
      v3 := {Sort[v3Conj[InternalWigner[[1]][[{1, 2, 6}]]]], 
        InternalWigner[[2]][[3]]}; 
      v4 := {Sort[v4Conj[InternalWigner[[1]][[{4, 5, 6}]]]], 
        InternalWigner[[2]][[4]]}; vertices := {v1, v2, v3, v4}; 
      If[GluonQuarkCoeff, If[InternalWigner[[1]][[3]] != "8", 
         Conjugated =  !Conjugated; InternalWigner = 
           SwapVertex2And4InWignerCoefficient[InternalWigner]; 
          InternalWigner = RotateWignerCoefficientCounterclockwise[
            InternalWigner]; InternalWigner = 
           RotateWignerCoefficientCounterclockwise[InternalWigner]]; 
        If[InternalWigner[[1]][[6]] == "3bar", Conjugated =  !Conjugated; 
          InternalWigner[[1]] = InternalWigner[[1]] /. ConjugationRules]; 
        listWigner = ({{#1, False}, {SwapVertex1And2InWignerCoefficient[#1], 
             True}, {SwapVertex3And4InWignerCoefficient[#1], False}, 
            {SwapVertex1And2InWignerCoefficient[
              SwapVertex3And4InWignerCoefficient[#1]], True}} & )[
          InternalWigner]; listWigner[[3,1,1]] = listWigner[[3,1,1]] /. 
          ConjugationRules; listWigner[[4,1,1]] = listWigner[[4,1,1]] /. 
          ConjugationRules; {InternalWigner, conj} = 
         SortBy[listWigner, {#1[[1,1,1]] /. SortingRepresentationsNumbers & , 
            #1[[1,1,2]] /. SortingRepresentationsNumbers & , 
            #1[[1,1,4]] /. SortingRepresentationsNumbers & , 
            #1[[1,1,5]] /. SortingRepresentationsNumbers & }][[1]]; 
        If[conj, Conjugated =  !Conjugated], 
       If[InternalWigner[[1]][[3]] == "3bar", Conjugated =  !Conjugated; 
          InternalWigner[[1]] = InternalWigner[[1]] /. ConjugationRules]; 
        If[InternalWigner[[1]][[6]] == "3bar", Conjugated =  !Conjugated; 
          InternalWigner = SwapVertex3And4InWignerCoefficient[
            InternalWigner]]; listWigner = 
         ({{#1, False}, {SwapRepresentationsWignerCoefficient[#1], False}, 
            {SwapVertex1And2InWignerCoefficient[
              SwapVertex3And4InWignerCoefficient[#1]], True}, 
            {SwapVertex1And2InWignerCoefficient[
              SwapVertex3And4InWignerCoefficient[
               SwapRepresentationsWignerCoefficient[#1]]], True}} & )[
          InternalWigner]; listWigner[[3,1,1]] = listWigner[[3,1,1]] /. 
          ConjugationRules; listWigner[[4,1,1]] = listWigner[[4,1,1]] /. 
          ConjugationRules; {InternalWigner, conj} = 
         SortBy[listWigner, {#1[[1,1,1]] /. SortingRepresentationsNumbers & , 
            #1[[1,1,2]] /. SortingRepresentationsNumbers & , 
            #1[[1,1,4]] /. SortingRepresentationsNumbers & , 
            #1[[1,1,5]] /. SortingRepresentationsNumbers & }][[1]]; 
        If[conj, Conjugated =  !Conjugated]]; Clear[v1Conj, v2Conj, v3Conj, 
       v4Conj, vertices, v1, v2, v3, v4]; 
      Return[{InternalWigner, Conjugated}]]
 
SwapVertex2And4InWignerCoefficient[Wigner_] := 
    Module[{\[Alpha] = Wigner[[1]][[1]], \[Beta] = Wigner[[1]][[2]], 
      \[Gamma] = Wigner[[1]][[3]], \[Delta] = Wigner[[1]][[4]], 
      \[Epsilon] = Wigner[[1]][[5]], \[Zeta] = Wigner[[1]][[6]]}, 
     Return[{{\[Zeta], \[Beta], \[Delta], \[Gamma], \[Epsilon] /. 
         ConjugationRules, \[Alpha]}, Wigner[[2]][[{1, 4, 3, 2}]]}]]
 
SwapVertex1And2InWignerCoefficient[Wigner_] := 
    Module[{\[Alpha] = Wigner[[1]][[1]], \[Beta] = Wigner[[1]][[2]], 
      \[Gamma] = Wigner[[1]][[3]], \[Delta] = Wigner[[1]][[4]], 
      \[Epsilon] = Wigner[[1]][[5]], \[Zeta] = Wigner[[1]][[6]]}, 
     Return[{{\[Beta] /. ConjugationRules, \[Alpha] /. ConjugationRules, 
        \[Gamma] /. ConjugationRules, \[Epsilon] /. ConjugationRules, 
        \[Delta] /. ConjugationRules, \[Zeta]}, Wigner[[2]][[{2, 1, 3, 4}]]}]]
 
SwapVertex3And4InWignerCoefficient[Wigner_] := 
    Module[{\[Alpha] = Wigner[[1]][[1]], \[Beta] = Wigner[[1]][[2]], 
      \[Gamma] = Wigner[[1]][[3]], \[Delta] = Wigner[[1]][[4]], 
      \[Epsilon] = Wigner[[1]][[5]], \[Zeta] = Wigner[[1]][[6]]}, 
     Return[{{\[Epsilon] /. ConjugationRules, \[Delta] /. ConjugationRules, 
        \[Gamma], \[Beta] /. ConjugationRules, \[Alpha] /. ConjugationRules, 
        \[Zeta] /. ConjugationRules}, Wigner[[2]][[{1, 2, 4, 3}]]}]]
 
SwapRepresentationsWignerCoefficient[Wigner_] := 
    Module[{\[Alpha] = Wigner[[1]][[1]], \[Beta] = Wigner[[1]][[2]], 
      \[Gamma] = Wigner[[1]][[3]], \[Delta] = Wigner[[1]][[4]], 
      \[Epsilon] = Wigner[[1]][[5]], \[Zeta] = Wigner[[1]][[6]]}, 
     Return[{{\[Alpha] /. ConjugationRules, \[Epsilon] /. ConjugationRules, 
        \[Zeta], \[Delta] /. ConjugationRules, \[Beta] /. ConjugationRules, 
        \[Gamma]}, Wigner[[2]][[{3, 2, 1, 4}]]}]]
 
Wigner6jCoefficient[{rep\[Alpha]_, rep\[Beta]_, rep\[Gamma]_, rep\[Delta]_, 
      rep\[Epsilon]_, rep\[Zeta]_}, {vertexa_, vertexb_, vertexc_, vertexd_}, 
     {ordera_, orderb_, orderc_, orderd_}, OutputRepresentations_] := 
    Module[{InternalWigner = {{rep\[Alpha], rep\[Beta], rep\[Gamma], 
         rep\[Delta], rep\[Epsilon], rep\[Zeta]}, {vertexa, vertexb, vertexc, 
         vertexd}}, v1, v2, v3, v4, v1Conj, v2Conj, v3Conj, v4Conj, nv, 
      vertices, vertexOrders, is3RepWig, sign = 1, ConjugatedFlag}, 
     v1Conj[{b_, c_, d_}] := {b, c /. ConjugationRules, 
        d /. ConjugationRules}; v2Conj[{a_, e_, c_}] := 
       {a /. ConjugationRules, e, c}; v3Conj[{a_, b_, f_}] := 
       {a, b /. ConjugationRules, f}; v4Conj[{d_, e_, f_}] := 
       {d, e /. ConjugationRules, f /. ConjugationRules}; 
      v1 := {Sort[v1Conj[InternalWigner[[1]][[{2, 3, 4}]]]], 
        InternalWigner[[2]][[1]]}; 
      v2 := {Sort[v2Conj[InternalWigner[[1]][[{1, 5, 3}]]]], 
        InternalWigner[[2]][[2]]}; 
      v3 := {Sort[v3Conj[InternalWigner[[1]][[{1, 2, 6}]]]], 
        InternalWigner[[2]][[3]]}; 
      v4 := {Sort[v4Conj[InternalWigner[[1]][[{4, 5, 6}]]]], 
        InternalWigner[[2]][[4]]}; vertices := {v1, v2, v3, v4}; 
      vertexOrders = {ordera, orderb, orderc, orderd}; 
      If[Complement[InternalWigner[[1]], AllowedRepresentations] =!= {}, 
       PrintWig["Error! Invalid representations in the argument of \
Wigner6jCoefficient! The invalid representations were ", 
         Complement[InternalWigner[[1]], AllowedRepresentations], 
         ".\nSee AllowedRepresentations for valid representations."]\
; Clear[v1Conj, v2Conj, v3Conj, v4Conj, vertices, v1, v2, v3, v4]; 
        Return[Wig6j[{rep\[Alpha], rep\[Beta], rep\[Gamma], rep\[Delta], 
           rep\[Epsilon], rep\[Zeta]}, {vertexa, vertexb, vertexc, vertexd}, 
          {ordera, orderb, orderc, orderd}]]]; nv = NVertices /@ vertices; 
      If[MemberQ[nv, 0], Return[0]]; If[MemberQ[nv, Null], 
       PrintWig["Error! Invalid vertices in the argument of \
Wigner6jCoefficient! The invalid vertices were: ", 
         (StringJoin["v", ToString[#1]] & ) /@ Flatten[Position[nv, Null]], 
         ".\nSee VertexSymmetriesRules for valid vertices."]; 
        Clear[v1Conj, v2Conj, v3Conj, v4Conj, vertices, v1, v2, v3, v4]; 
        Return[Null]]; If[Complement[vertexOrders, {1, -1}] =!= {}, 
       PrintWig["Error! Invalid vertex orders in the argument of \
Wigner6jCoefficient! The invalid vertex orders were ", 
         Complement[vertexOrders, {1, -1}], 
         ".\nThe vertex orders should be +1 or -1."]; Clear[v1Conj, v2Conj, 
         v3Conj, v4Conj, vertices, v1, v2, v3, v4]; Return[Null]]; 
      If[OutputRepresentations =!= True && OutputRepresentations =!= False, 
       PrintWig["Error! Invalid option for OutputRepresentations, it should \
be True or False, it was ", OutputRepresentations, "."]; 
        Clear[v1Conj, v2Conj, v3Conj, v4Conj, vertices, v1, v2, v3, v4]; 
        Return[Null]]; If[MemberQ[NVertices /@ vertices, 0], 
       Clear[v1Conj, v2Conj, v3Conj, v4Conj, vertices, v1, v2, v3, v4]; 
        Return[0]]; If[(InternalWigner[[1]] /. ConjugationRules) == 
         InternalWigner[[1]] && Product[VertexSymmetriesAllIngoing[
           vertices[[ii]]], {ii, 4}] == -1, Return[0]]; 
      is3RepWig = MemberQ[vertices, {{"3", "3bar", "8"}, 1}] || 
        MemberQ[vertices, {{"8", "8", "8"}, 1}] || MemberQ[vertices, 
         {{"8", "8", "8"}, 2}]; sign *= Product[If[vertexOrders[[ii]] == -1, 
         VertexSymmetriesAllIngoing[vertices[[ii]]], 1], {ii, 4}]; 
      If[DebugWignerCoefficientFunctions, 
       Print["The sign from vertex orders is ", sign]]; 
      If[is3RepWig, If[DebugWignerCoefficientFunctions, 
         Print[
          "It is a Wigner 6j coefficient with 3 arbitrary representations!"]]\
; {InternalWigner, ConjugatedFlag} = Sort3RepresentationCoefficient[
          InternalWigner]; sign *= Product[VertexSymmetriesAllIngoing[
           vertices[[ii]]], {ii, 4}], If[DebugWignerCoefficientFunctions, 
         Print[
          "It is a Wigner 6j coefficient with 4 arbitrary representations!"]]\
; {InternalWigner, ConjugatedFlag} = Sort4RepresentationCoefficient[
          InternalWigner]; sign *= Product[VertexSymmetriesAllIngoing[
           vertices[[ii]]], {ii, 3, 4}]]; If[ConjugatedFlag, 
       sign *= Product[VertexSymmetriesAllIngoing[vertices[[ii]]], {ii, 4}]]; 
      If[DebugWignerCoefficientFunctions, Print[{InternalWigner, sign}]]; 
      If[OutputRepresentations, Clear[v1Conj, v2Conj, v3Conj, v4Conj, 
         vertices, v1, v2, v3, v4]; Return[{sign*Wig6j[InternalWigner], 
          InternalWigner}]]; Clear[v1Conj, v2Conj, v3Conj, v4Conj, vertices, 
       v1, v2, v3, v4]; Return[sign*Wig6j[InternalWigner]]]
 
Wigner6jCoefficient[{rep\[Alpha]_, rep\[Beta]_, rep\[Gamma]_, rep\[Delta]_, 
      rep\[Epsilon]_, rep\[Zeta]_}, {vertexa_, vertexb_, vertexc_, vertexd_}, 
     {ordera_, orderb_, orderc_, orderd_}] := Wigner6jCoefficient[
     {rep\[Alpha], rep\[Beta], rep\[Gamma], rep\[Delta], rep\[Epsilon], 
      rep\[Zeta]}, {vertexa, vertexb, vertexc, vertexd}, 
     {ordera, orderb, orderc, orderd}, False]
 
NVertices[{r1_, r2_, r3_}] := NVertices[{r1, r2, r3}, False]
 
NVertices[{r1_, r2_, r3_}, returnReps_] := 
    Module[{octet = FirstPosition[{r1, r2, r3}, "8"], 
      q = FirstPosition[{r1, r2, r3}, "3"], 
      qbar = FirstPosition[{r1, r2, r3}, "3bar"], rep, octetQ, qQ, qbarQ, 
      otherReps = {r1, r2, r3}, nv}, octetQ = octet =!= Missing["NotFound"]; 
      qQ = q =!= Missing["NotFound"]; qbarQ = qbar =!= Missing["NotFound"]; 
      If[ !octetQ &&  !qQ &&  !qbarQ, 
       PrintWig["No 8/3/3bar representation in the vertex ", {r1, r2, r3}]; 
        Return[Null]]; Which[octetQ, otherReps = Delete[otherReps, octet]; 
        rep = "8", qQ, otherReps = Delete[otherReps, q]; rep = "3", qbarQ, 
       otherReps = Delete[otherReps, qbar]; rep = "3bar"]; 
      If[ !MemberQ[AllowedRepresentations, otherReps[[1]]], 
       PrintWig["The representation ", otherReps[[1]], " is not valid (see \
AllowedRepresentations for valid representations)."]; 
        Return[Null]; ]; If[ !MemberQ[AllowedRepresentations, 
         otherReps[[2]]], PrintWig["The representation ", otherReps[[2]], " \
is not valid (see AllowedRepresentations for valid \
representations)."]; Return[Null]; ]; Which[octetQ, 
       nv = Count[otherReps[[1]] /. ProductOfRepresentationWithGluonRules, 
         otherReps[[2]] /. ConjugationRules], qQ, 
       nv = Count[otherReps[[1]] /. ProductOfRepresentationWithQuarkRules, 
         otherReps[[2]] /. ConjugationRules], qbarQ, 
       nv = Count[otherReps[[1]] /. 
          ProductOfRepresentationWithAntiquarkRules, otherReps[[2]] /. 
          ConjugationRules]]; If[returnReps, 
       Return[{nv, {rep, otherReps[[1]], otherReps[[2]]}}], Return[nv], 
       PrintWig["Error! Invalid argument for NVertices, second argument must \
be True or False, it was ", returnReps]; Return[Null]]]
 
NVertices[{{r1_, r2_, r3_}, a_}] := NVertices[{{r1, r2, r3}, a}, False]
 
NVertices[{{r1_, r2_, r3_}, a_}, returnReps_] := 
    Module[{nv = NVertices[{r1, r2, r3}, returnReps]}, 
     If[nv == Null, Return[nv]]; If[ !IntegerQ[a], 
       PrintWig["In the vertex ", {{r1, r2, r3}, a}, 
         " the instance of the vertex, ", a, ", should be an integer."]; 
        Return[Null]]; If[a != 1 && (a < 1 || a > nv), 
       PrintWig["In the vertex ", {{r1, r2, r3}, a}, 
         " the instance of the vertex, ", a, ", should be an integer between \
1 and the number of possible vertices (", nv, 
         ") (for vertices that are zero the instance of the vertex (", a, 
         ") is allowed to be 1)."]; Return[Null]]; 
      If[returnReps, Return[{nv[[1]], {nv[[2]], a}}], Return[nv]]]
 
ProductOfRepresentationWithGluonRules = {"1" -> {"8"}, 
     "3" -> {"3", "15", "c2c1"}, "3bar" -> {"3bar", "15bar", "c1c2"}, 
     "c2c0" -> {"6", "c2c0", "c21c1", "c3c1"}, 
     "6" -> {"6", "24", "c2c0", "c21c1"}, 
     "8" -> {"1", "8", "8", "27", "10", "10bar", "0"}, 
     "c0c2" -> {"6bar", "c0c2", "c1c21", "c1c3"}, 
     "6bar" -> {"6bar", "c0c2", "24bar", "c1c21"}, 
     "c3c0" -> {"c21c0", "c3c0"}, "c21c0" -> {"c111c0", "c21c0", "c21c0", 
       "c3c0"}, "c111c0" -> {"c111c0", "c21c0"}, 
     "c2c1" -> {"3", "15", "c2c1", "c2c1"}, 
     "15" -> {"3", "15", "15", "c2c1"}, "c1c2" -> {"3bar", "15bar", "c1c2", 
       "c1c2"}, "15bar" -> {"3bar", "15bar", "15bar", "c1c2"}, 
     "c0c3" -> {"c0c21", "c0c3"}, "c0c21" -> {"c0c111", "c0c21", "c0c21", 
       "c0c3"}, "c0c111" -> {"c0c111", "c0c21"}, "c4c0" -> {"c31c0", "c4c0"}, 
     "c31c0" -> {"c22c0", "c211c0", "c31c0", "c31c0", "c4c0"}, 
     "c22c0" -> {"c22c0", "c211c0", "c31c0"}, 
     "c211c0" -> {"c1111c0", "c22c0", "c211c0", "c211c0", "c31c0"}, 
     "c1111c0" -> {"c1111c0", "c211c0"}, "c3c1" -> {"c2c0", "c21c1", "c3c1", 
       "c3c1"}, "c21c1" -> {"6", "24", "c2c0", "c21c1", "c21c1", "c21c1", 
       "c3c1"}, "24" -> {"6", "24", "24", "c21c1"}, 
     "0" -> {"8", "10", "10bar", "0", "0", "c21c21", "c21c3", "c3c21", 
       "c3c3"}, "10bar" -> {"8", "27", "10bar", "10bar", "0", "35bar", 
       "c21c21", "c3c111", "c3c21"}, "10" -> {"8", "27", "10", "10", "35", 
       "c111c3", "0", "c21c21", "c21c3"}, 
     "27" -> {"8", "27", "27", "10", "64", "35", "10bar", "35bar", "c21c21"}, 
     "c1c3" -> {"c0c2", "c1c21", "c1c3", "c1c3"}, 
     "c1c21" -> {"6bar", "c0c2", "24bar", "c1c21", "c1c21", "c1c21", "c1c3"}, 
     "24bar" -> {"6bar", "24bar", "24bar", "c1c21"}, 
     "c0c4" -> {"c0c31", "c0c4"}, "c0c31" -> {"c0c211", "c0c22", "c0c31", 
       "c0c31", "c0c4"}, "c0c22" -> {"c0c211", "c0c22", "c0c31"}, 
     "c0c211" -> {"c0c1111", "c0c211", "c0c211", "c0c22", "c0c31"}, 
     "c0c1111" -> {"c0c1111", "c0c211"}, "c3c3" -> {"0", "c21c3", "c3c21", 
       "c3c3", "c3c3"}, "c3c21" -> {"10bar", "0", "c21c21", "c3c111", 
       "c3c21", "c3c21", "c3c21", "c3c3"}, "c3c111" -> 
      {"10bar", "35bar", "c3c111", "c3c111", "c3c21"}, 
     "c21c3" -> {"10", "c111c3", "0", "c21c21", "c21c3", "c21c3", "c21c3", 
       "c3c3"}, "c21c21" -> {"27", "10", "35", "10bar", "0", "35bar", 
       "c21c21", "c21c21", "c21c21", "c21c21", "c21c3", "c3c21"}, 
     "35bar" -> {"27", "64", "10bar", "35bar", "35bar", "35bar", "c21c21", 
       "c3c111"}, "c111c3" -> {"10", "35", "c111c3", "c111c3", "c21c3"}, 
     "35" -> {"27", "10", "64", "35", "35", "35", "c111c3", "c21c21"}, 
     "64" -> {"27", "64", "64", "35", "35bar"}}
 
ProductOfRepresentationWithQuarkRules = {"1" -> {"3"}, "3" -> {"6", "c2c0"}, 
     "3bar" -> {"1", "8"}, "c2c0" -> {"c21c0", "c3c0"}, 
     "6" -> {"c111c0", "c21c0"}, "8" -> {"3", "15", "c2c1"}, 
     "c0c2" -> {"3bar", "c1c2"}, "6bar" -> {"3bar", "15bar"}, 
     "c3c0" -> {"c31c0", "c4c0"}, "c21c0" -> {"c22c0", "c211c0", "c31c0"}, 
     "c111c0" -> {"c1111c0", "c211c0"}, "c2c1" -> {"c2c0", "c21c1", "c3c1"}, 
     "15" -> {"6", "24", "c21c1"}, "c1c2" -> {"8", "10", "0"}, 
     "15bar" -> {"8", "27", "10bar"}, "c0c3" -> {"c0c2", "c1c3"}, 
     "c0c21" -> {"6bar", "c0c2", "c1c21"}, "c0c111" -> {"6bar", "24bar"}, 
     "c4c0" -> {}, "c31c0" -> {}, "c22c0" -> {}, "c211c0" -> {}, 
     "c1111c0" -> {}, "c3c1" -> {"c3c0"}, "c21c1" -> {"c21c0"}, 
     "24" -> {"c111c0"}, "0" -> {"c2c1"}, "10bar" -> {"c2c1"}, 
     "10" -> {"15"}, "27" -> {"15"}, "c1c3" -> {"c1c2"}, 
     "c1c21" -> {"15bar", "c1c2"}, "24bar" -> {"15bar"}, "c0c4" -> {"c0c3"}, 
     "c0c31" -> {"c0c21", "c0c3"}, "c0c22" -> {"c0c21"}, 
     "c0c211" -> {"c0c111", "c0c21"}, "c0c1111" -> {"c0c111"}}
 
ProductOfRepresentationWithAntiquarkRules = {"1" -> {"3bar"}, 
     "3" -> {"1", "8"}, "3bar" -> {"6bar", "c0c2"}, "c2c0" -> {"3", "c2c1"}, 
     "6" -> {"3", "15"}, "8" -> {"3bar", "15bar", "c1c2"}, 
     "c0c2" -> {"c0c21", "c0c3"}, "6bar" -> {"c0c111", "c0c21"}, 
     "c3c0" -> {"c2c0", "c3c1"}, "c21c0" -> {"6", "c2c0", "c21c1"}, 
     "c111c0" -> {"6", "24"}, "c2c1" -> {"8", "10bar", "0"}, 
     "15" -> {"8", "27", "10"}, "c1c2" -> {"c0c2", "c1c21", "c1c3"}, 
     "15bar" -> {"6bar", "24bar", "c1c21"}, "c0c3" -> {"c0c31", "c0c4"}, 
     "c0c21" -> {"c0c211", "c0c22", "c0c31"}, 
     "c0c111" -> {"c0c1111", "c0c211"}, "c4c0" -> {"c3c0"}, 
     "c31c0" -> {"c21c0", "c3c0"}, "c22c0" -> {"c21c0"}, 
     "c211c0" -> {"c111c0", "c21c0"}, "c1111c0" -> {"c111c0"}, 
     "c3c1" -> {"c2c1"}, "c21c1" -> {"15", "c2c1"}, "24" -> {"15"}, 
     "0" -> {"c1c2"}, "10bar" -> {"15bar"}, "10" -> {"c1c2"}, 
     "27" -> {"15bar"}, "c1c3" -> {"c0c3"}, "c1c21" -> {"c0c21"}, 
     "24bar" -> {"c0c111"}, "c0c4" -> {}, "c0c31" -> {}, "c0c22" -> {}, 
     "c0c211" -> {}, "c0c1111" -> {}}
 
VertexSymmetriesAllIngoing[{{r1_, r2_, r3_}, a_}] := 
    Module[{nv = NVertices[{{r1, r2, r3}, a}, True], sym}, 
     sym = VertexSymmetries[nv[[2]]]; If[sym == {{r1, r2, r3}, a}, 
       PrintWig["Error! Vertex symmetry could not be found for the vertex ", 
         {{r1, r2, r3}, a}, "."]; Return[Null]]; Return[sym]]
 
VertexSymmetries[{Representations_, InstanceOfVertex_}] := 
    {Sort[Representations], InstanceOfVertex} /. VertexSymmetriesIngoingRules
 
VertexSymmetriesIngoingRules = {{{"3", "3", "6bar"}, 1} -> 1, 
     {{"3", "3", "c0c2"}, 1} -> -1, {{"3bar", "3bar", "6"}, 1} -> 1, 
     {{"3bar", "3bar", "c2c0"}, 1} -> -1, {{"1", "3", "3bar"}, 1} -> 1, 
     {{"3", "3bar", "8"}, 1} -> 1, {{"3", "c0c21", "c2c0"}, 1} -> 1, 
     {{"3", "c0c3", "c2c0"}, 1} -> 1, {{"3", "6", "c0c111"}, 1} -> 1, 
     {{"3", "6", "c0c21"}, 1} -> 1, {{"15bar", "3", "8"}, 1} -> 1, 
     {{"3", "8", "c1c2"}, 1} -> 1, {{"3", "c0c2", "c2c1"}, 1} -> 1, 
     {{"15", "3", "6bar"}, 1} -> 1, {{"3", "c0c31", "c3c0"}, 1} -> 1, 
     {{"3", "c0c4", "c3c0"}, 1} -> 1, {{"3", "c0c22", "c21c0"}, 1} -> 1, 
     {{"3", "c0c211", "c21c0"}, 1} -> 1, {{"3", "c0c31", "c21c0"}, 1} -> 1, 
     {{"3", "c0c1111", "c111c0"}, 1} -> 1, {{"3", "c0c211", "c111c0"}, 1} -> 
      1, {{"3", "c1c21", "c2c1"}, 1} -> 1, {{"3", "c1c3", "c2c1"}, 1} -> 1, 
     {{"15", "24bar", "3"}, 1} -> 1, {{"15", "3", "c1c21"}, 1} -> 1, 
     {{"10bar", "3", "c1c2"}, 1} -> 1, {{"0", "3", "c1c2"}, 1} -> 1, 
     {{"15bar", "27", "3"}, 1} -> 1, {{"10", "15bar", "3"}, 1} -> 1, 
     {{"3", "c0c3", "c3c1"}, 1} -> 1, {{"3", "c0c21", "c21c1"}, 1} -> 1, 
     {{"24", "3", "c0c111"}, 1} -> 1, {{"3bar", "c1c2", "c2c0"}, 1} -> 1, 
     {{"15bar", "3bar", "6"}, 1} -> 1, {{"15", "3bar", "8"}, 1} -> 1, 
     {{"3bar", "8", "c2c1"}, 1} -> 1, {{"3bar", "c0c2", "c21c0"}, 1} -> 1, 
     {{"3bar", "c0c2", "c3c0"}, 1} -> 1, {{"3bar", "6bar", "c111c0"}, 1} -> 
      1, {{"3bar", "6bar", "c21c0"}, 1} -> 1, 
     {{"3bar", "c1c3", "c3c0"}, 1} -> 1, {{"3bar", "c1c21", "c21c0"}, 1} -> 
      1, {{"24bar", "3bar", "c111c0"}, 1} -> 1, 
     {{"10", "3bar", "c2c1"}, 1} -> 1, {{"0", "3bar", "c2c1"}, 1} -> 1, 
     {{"15", "27", "3bar"}, 1} -> 1, {{"10bar", "15", "3bar"}, 1} -> 1, 
     {{"3bar", "c1c2", "c21c1"}, 1} -> 1, {{"3bar", "c1c2", "c3c1"}, 1} -> 1, 
     {{"15bar", "24", "3bar"}, 1} -> 1, {{"15bar", "3bar", "c21c1"}, 1} -> 1, 
     {{"3bar", "c0c3", "c31c0"}, 1} -> 1, {{"3bar", "c0c3", "c4c0"}, 1} -> 1, 
     {{"3bar", "c0c21", "c211c0"}, 1} -> 1, 
     {{"3bar", "c0c21", "c22c0"}, 1} -> 1, {{"3bar", "c0c21", "c31c0"}, 1} -> 
      1, {{"3bar", "c0c111", "c1111c0"}, 1} -> 1, 
     {{"3bar", "c0c111", "c211c0"}, 1} -> 1, {{"1", "8", "8"}, 1} -> 1, 
     {{"6bar", "8", "c2c0"}, 1} -> 1, {{"8", "c0c2", "c2c0"}, 1} -> 1, 
     {{"8", "c1c21", "c2c0"}, 1} -> 1, {{"8", "c1c3", "c2c0"}, 1} -> 1, 
     {{"6", "6bar", "8"}, 1} -> 1, {{"24bar", "6", "8"}, 1} -> 1, 
     {{"6", "8", "c0c2"}, 1} -> 1, {{"6", "8", "c1c21"}, 1} -> 1, 
     {{"1", "8", "8"}, 1} -> 1, {{"8", "8", "8"}, 1} -> -1, 
     {{"8", "8", "8"}, 2} -> 1, {{"27", "8", "8"}, 1} -> 1, 
     {{"10bar", "8", "8"}, 1} -> -1, {{"10", "8", "8"}, 1} -> -1, 
     {{"0", "8", "8"}, 1} -> 1, {{"8", "c0c2", "c21c1"}, 1} -> 1, 
     {{"8", "c0c2", "c3c1"}, 1} -> 1, {{"24", "6bar", "8"}, 1} -> 1, 
     {{"6bar", "8", "c21c1"}, 1} -> 1, {{"8", "c0c21", "c3c0"}, 1} -> 1, 
     {{"8", "c0c3", "c3c0"}, 1} -> 1, {{"8", "c0c111", "c21c0"}, 1} -> 1, 
     {{"8", "c0c21", "c21c0"}, 1} -> 1, {{"8", "c0c21", "c21c0"}, 2} -> 1, 
     {{"8", "c0c3", "c21c0"}, 1} -> 1, {{"8", "c0c111", "c111c0"}, 1} -> 1, 
     {{"8", "c0c21", "c111c0"}, 1} -> 1, {{"15bar", "8", "c2c1"}, 1} -> 1, 
     {{"8", "c1c2", "c2c1"}, 1} -> 1, {{"8", "c1c2", "c2c1"}, 2} -> 1, 
     {{"15", "15bar", "8"}, 1} -> 1, {{"15", "15bar", "8"}, 2} -> 1, 
     {{"15", "8", "c1c2"}, 1} -> 1, {{"8", "c0c31", "c4c0"}, 1} -> 1, 
     {{"8", "c0c4", "c4c0"}, 1} -> 1, {{"8", "c0c22", "c31c0"}, 1} -> 1, 
     {{"8", "c0c211", "c31c0"}, 1} -> 1, {{"8", "c0c31", "c31c0"}, 1} -> 1, 
     {{"8", "c0c31", "c31c0"}, 2} -> 1, {{"8", "c0c4", "c31c0"}, 1} -> 1, 
     {{"8", "c0c22", "c22c0"}, 1} -> 1, {{"8", "c0c211", "c22c0"}, 1} -> 1, 
     {{"8", "c0c31", "c22c0"}, 1} -> 1, {{"8", "c0c1111", "c211c0"}, 1} -> 1, 
     {{"8", "c0c22", "c211c0"}, 1} -> 1, {{"8", "c0c211", "c211c0"}, 1} -> 1, 
     {{"8", "c0c211", "c211c0"}, 2} -> 1, {{"8", "c0c31", "c211c0"}, 1} -> 1, 
     {{"8", "c0c1111", "c1111c0"}, 1} -> 1, 
     {{"8", "c0c211", "c1111c0"}, 1} -> 1, {{"8", "c1c21", "c3c1"}, 1} -> 1, 
     {{"8", "c1c3", "c3c1"}, 1} -> 1, {{"8", "c1c3", "c3c1"}, 2} -> 1, 
     {{"24bar", "8", "c21c1"}, 1} -> 1, {{"8", "c1c21", "c21c1"}, 1} -> 1, 
     {{"8", "c1c21", "c21c1"}, 2} -> 1, {{"8", "c1c21", "c21c1"}, 3} -> 1, 
     {{"8", "c1c3", "c21c1"}, 1} -> 1, {{"24", "24bar", "8"}, 1} -> 1, 
     {{"24", "24bar", "8"}, 2} -> 1, {{"24", "8", "c1c21"}, 1} -> 1, 
     {{"0", "8", "8"}, 1} -> 1, {{"0", "10bar", "8"}, 1} -> 1, 
     {{"0", "10", "8"}, 1} -> 1, {{"0", "0", "8"}, 1} -> -1, 
     {{"0", "0", "8"}, 2} -> 1, {{"0", "8", "c21c21"}, 1} -> 1, 
     {{"0", "8", "c3c21"}, 1} -> 1, {{"0", "8", "c21c3"}, 1} -> 1, 
     {{"0", "8", "c3c3"}, 1} -> 1, {{"10bar", "8", "8"}, 1} -> -1, 
     {{"10bar", "27", "8"}, 1} -> 1, {{"10", "10bar", "8"}, 1} -> 1, 
     {{"10", "10bar", "8"}, 2} -> 1, {{"0", "10bar", "8"}, 1} -> 1, 
     {{"10bar", "35", "8"}, 1} -> 1, {{"10bar", "8", "c21c21"}, 1} -> 1, 
     {{"10bar", "8", "c111c3"}, 1} -> 1, {{"10bar", "8", "c21c3"}, 1} -> 1, 
     {{"10", "8", "8"}, 1} -> -1, {{"10", "27", "8"}, 1} -> 1, 
     {{"10", "10bar", "8"}, 1} -> 1, {{"10", "10bar", "8"}, 2} -> 1, 
     {{"10", "35bar", "8"}, 1} -> 1, {{"10", "8", "c3c111"}, 1} -> 1, 
     {{"0", "10", "8"}, 1} -> 1, {{"10", "8", "c21c21"}, 1} -> 1, 
     {{"10", "8", "c3c21"}, 1} -> 1, {{"27", "8", "8"}, 1} -> 1, 
     {{"27", "27", "8"}, 1} -> -1, {{"27", "27", "8"}, 2} -> 1, 
     {{"10bar", "27", "8"}, 1} -> 1, {{"27", "64", "8"}, 1} -> 1, 
     {{"27", "35bar", "8"}, 1} -> 1, {{"10", "27", "8"}, 1} -> 1, 
     {{"27", "35", "8"}, 1} -> 1, {{"27", "8", "c21c21"}, 1} -> 1, 
     {{"0", "8", "c3c3"}, 1} -> 1, {{"8", "c3c21", "c3c3"}, 1} -> 1, 
     {{"8", "c21c3", "c3c3"}, 1} -> 1, {{"8", "c3c3", "c3c3"}, 1} -> -1, 
     {{"8", "c3c3", "c3c3"}, 2} -> 1, {{"10", "8", "c3c21"}, 1} -> 1, 
     {{"0", "8", "c3c21"}, 1} -> 1, {{"8", "c21c21", "c3c21"}, 1} -> 1, 
     {{"8", "c111c3", "c3c21"}, 1} -> 1, {{"8", "c21c3", "c3c21"}, 1} -> 1, 
     {{"8", "c21c3", "c3c21"}, 2} -> 1, {{"8", "c21c3", "c3c21"}, 3} -> 1, 
     {{"8", "c3c21", "c3c3"}, 1} -> 1, {{"10", "8", "c3c111"}, 1} -> 1, 
     {{"35", "8", "c3c111"}, 1} -> 1, {{"8", "c111c3", "c3c111"}, 1} -> 1, 
     {{"8", "c111c3", "c3c111"}, 2} -> 1, {{"8", "c21c3", "c3c111"}, 1} -> 1, 
     {{"10bar", "8", "c21c3"}, 1} -> 1, {{"8", "c21c3", "c3c111"}, 1} -> 1, 
     {{"0", "8", "c21c3"}, 1} -> 1, {{"8", "c21c21", "c21c3"}, 1} -> 1, 
     {{"8", "c21c3", "c3c21"}, 1} -> 1, {{"8", "c21c3", "c3c21"}, 2} -> 1, 
     {{"8", "c21c3", "c3c21"}, 3} -> 1, {{"8", "c21c3", "c3c3"}, 1} -> 1, 
     {{"27", "8", "c21c21"}, 1} -> 1, {{"10bar", "8", "c21c21"}, 1} -> 1, 
     {{"35bar", "8", "c21c21"}, 1} -> 1, {{"10", "8", "c21c21"}, 1} -> 1, 
     {{"0", "8", "c21c21"}, 1} -> 1, {{"35", "8", "c21c21"}, 1} -> 1, 
     {{"8", "c21c21", "c21c21"}, 1} -> -1, {{"8", "c21c21", "c21c21"}, 2} -> 
      -1, {{"8", "c21c21", "c21c21"}, 3} -> 1, 
     {{"8", "c21c21", "c21c21"}, 4} -> 1, {{"8", "c21c21", "c3c21"}, 1} -> 1, 
     {{"8", "c21c21", "c21c3"}, 1} -> 1, {{"27", "35bar", "8"}, 1} -> 1, 
     {{"35bar", "64", "8"}, 1} -> 1, {{"10", "35bar", "8"}, 1} -> 1, 
     {{"35", "35bar", "8"}, 1} -> 1, {{"35", "35bar", "8"}, 2} -> 1, 
     {{"35", "35bar", "8"}, 3} -> 1, {{"35bar", "8", "c21c21"}, 1} -> 1, 
     {{"35bar", "8", "c111c3"}, 1} -> 1, {{"10bar", "8", "c111c3"}, 1} -> 1, 
     {{"35bar", "8", "c111c3"}, 1} -> 1, {{"8", "c111c3", "c3c111"}, 1} -> 1, 
     {{"8", "c111c3", "c3c111"}, 2} -> 1, {{"8", "c111c3", "c3c21"}, 1} -> 1, 
     {{"27", "35", "8"}, 1} -> 1, {{"10bar", "35", "8"}, 1} -> 1, 
     {{"35", "64", "8"}, 1} -> 1, {{"35", "35bar", "8"}, 1} -> 1, 
     {{"35", "35bar", "8"}, 2} -> 1, {{"35", "35bar", "8"}, 3} -> 1, 
     {{"35", "8", "c3c111"}, 1} -> 1, {{"35", "8", "c21c21"}, 1} -> 1, 
     {{"27", "64", "8"}, 1} -> 1, {{"64", "64", "8"}, 1} -> -1, 
     {{"64", "64", "8"}, 2} -> 1, {{"35bar", "64", "8"}, 1} -> 1, 
     {{"35", "64", "8"}, 1} -> 1}
 
FirstOccurrenceRules = {"1" -> {0, 0}, "3" -> {1, 0}, "3bar" -> {0, 1}, 
     "8" -> {1, 1}, "6" -> {2, 0}, "c2c0" -> {2, 0}, "6bar" -> {0, 2}, 
     "c0c2" -> {0, 2}, "15" -> {2, 1}, "c2c1" -> {2, 1}, "15bar" -> {1, 2}, 
     "c1c2" -> {1, 2}, "c111c0" -> {3, 0}, "c21c0" -> {3, 0}, 
     "c3c0" -> {3, 0}, "c0c111" -> {0, 3}, "c0c21" -> {0, 3}, 
     "c0c3" -> {0, 3}, "27" -> {2, 2}, "10" -> {2, 2}, "10bar" -> {2, 2}, 
     "0" -> {2, 2}, "24" -> {3, 1}, "c21c1" -> {3, 1}, "c3c1" -> {3, 1}, 
     "24bar" -> {1, 3}, "c1c21" -> {1, 3}, "c1c3" -> {1, 3}, 
     "c1111c0" -> {4, 0}, "c22c0" -> {4, 0}, "c211c0" -> {4, 0}, 
     "c31c0" -> {4, 0}, "c4c0" -> {4, 0}, "c0c1111" -> {0, 4}, 
     "c0c22" -> {0, 4}, "c0c211" -> {0, 4}, "c0c31" -> {0, 4}, 
     "c0c4" -> {0, 4}, "64" -> {3, 3}, "35" -> {3, 3}, "35bar" -> {3, 3}, 
     "c21c21" -> {3, 3}, "c111c3" -> {3, 3}, "c3c111" -> {3, 3}, 
     "c21c3" -> {3, 3}, "c3c21" -> {3, 3}, "c3c3" -> {3, 3}}
 
nf[rep_] := rep /. FirstOccurrenceRules
 
nfq[rep_] := nf[rep][[1]]
 
nfqbar[rep_] := nf[rep][[2]]
 
nfTot[rep_] := Total[nf[rep]]
