n l m coefficients
8 0 0 (0.333333+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 1 -1 (0.000000+0.000000j) (0.000000-0.288675j) (0.288675+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 1 0 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 1 1 (0.000000+0.000000j) (0.000000+0.288675j) (0.288675+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 2 -2 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (-0.312094+0.000000j) (0.000000-0.312094j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 2 -1 (0.000000+0.000000j) (-0.000000-0.073561j) (0.073561+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 2 0 (-0.379869+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 2 1 (0.000000+0.000000j) (-0.000000-0.073561j) (-0.073561+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 2 2 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (-0.312094+0.000000j) (0.000000+0.312094j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 3 -3 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.297294j) (-0.297294+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 3 -2 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (-0.194625+0.000000j) (0.000000-0.194625j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 3 -1 (0.000000+0.000000j) (0.000000+0.261116j) (-0.261116+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 3 0 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 3 1 (0.000000+0.000000j) (0.000000-0.261116j) (-0.261116+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 3 2 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.194625+0.000000j) (0.000000-0.194625j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 3 3 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000-0.297294j) (-0.297294+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 4 -4 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.221249+0.000000j) (0.000000+0.221249j) 
8 4 -3 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (-0.000000+0.331873j) (-0.331873+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 4 -2 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.173838+0.000000j) (0.000000+0.173838j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 4 -1 (0.000000+0.000000j) (-0.000000+0.142231j) (-0.142231+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 4 0 (0.402291+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 4 1 (0.000000+0.000000j) (-0.000000+0.142231j) (0.142231+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 4 2 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.173838+0.000000j) (0.000000-0.173838j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 4 3 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (-0.000000+0.331873j) (0.331873+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 4 4 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.221249+0.000000j) (0.000000-0.221249j) 
8 5 -5 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 5 -4 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.392232+0.000000j) (0.000000+0.392232j) 
8 5 -3 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (-0.000000+0.065372j) (-0.065372+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 5 -2 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.299572+0.000000j) (0.000000+0.299572j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 5 -1 (0.000000+0.000000j) (0.000000-0.240192j) (0.240192+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 5 0 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 5 1 (0.000000+0.000000j) (0.000000+0.240192j) (0.240192+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 5 2 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (-0.299572+0.000000j) (0.000000+0.299572j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 5 3 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (-0.000000-0.065372j) (-0.065372+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 5 4 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (-0.392232+0.000000j) (0.000000+0.392232j) 
8 5 5 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 6 -6 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 6 -5 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 6 -4 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.426401+0.000000j) (-0.000000+0.426401j) 
8 6 -3 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (-0.000000-0.275241j) (0.275241+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 6 -2 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 6 -1 (0.000000+0.000000j) (-0.000000-0.230283j) (0.230283+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 6 0 (-0.449467+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 6 1 (0.000000+0.000000j) (-0.000000-0.230283j) (-0.230283+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 6 2 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 6 3 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (-0.000000-0.275241j) (-0.275241+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 6 4 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.426401+0.000000j) (-0.000000-0.426401j) 
8 6 5 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 6 6 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 7 -7 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 7 -6 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 7 -5 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 7 -4 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.310087+0.000000j) (-0.000000+0.310087j) 
8 7 -3 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (-0.000000-0.396664j) (0.396664+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 7 -2 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (-0.349825+0.000000j) (0.000000-0.349825j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 7 -1 (0.000000+0.000000j) (0.000000+0.201972j) (-0.201972+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 7 0 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 7 1 (0.000000+0.000000j) (0.000000-0.201972j) (-0.201972+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 7 2 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.349825+0.000000j) (0.000000-0.349825j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 7 3 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (-0.000000+0.396664j) (0.396664+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 7 4 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (-0.310087+0.000000j) (-0.000000+0.310087j) 
8 7 5 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 7 6 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 7 7 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 8 -8 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 8 -7 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 8 -6 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 8 -5 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 8 -4 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.138675+0.000000j) (0.000000+0.138675j) 
8 8 -3 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000-0.253185j) (0.253185+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 8 -2 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (-0.349825+0.000000j) (-0.000000-0.349825j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 8 -1 (0.000000+0.000000j) (-0.000000+0.413919j) (-0.413919+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 8 0 (0.617034+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 8 1 (0.000000+0.000000j) (-0.000000+0.413919j) (0.413919+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 8 2 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (-0.349825+0.000000j) (-0.000000+0.349825j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 8 3 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000-0.253185j) (-0.253185+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 8 4 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.138675+0.000000j) (0.000000-0.138675j) 
8 8 5 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 8 6 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 8 7 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 8 8 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
