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+0.000000j) (0.000000-0.235702j) (0.235702+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+0.333333j) (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+0.000000j) (0.000000+0.235702j) (0.235702+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) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (-0.317821+0.000000j) (0.000000-0.158910j) 
8 2 -1 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.158910+0.000000j) (0.000000+0.158910j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 2 0 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (-0.449467+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+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (-0.158910+0.000000j) (0.000000+0.158910j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 2 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) (-0.317821+0.000000j) (0.000000+0.158910j) 
8 3 -3 (0.000000+0.000000j) (0.000000+0.000000j) (-0.000000-0.160557j) (-0.160557+0.000000j) (0.000000+0.000000j) (0.182055+0.000000j) (-0.000000-0.182055j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 3 -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) (0.000000-0.297294j) 
8 3 -1 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.124367j) (-0.124367+0.000000j) (0.000000+0.000000j) (-0.235032+0.000000j) (-0.000000-0.235032j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 3 0 (0.000000+0.000000j) (0.000000+0.287213j) (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+0.000000j) (0.000000-0.124367j) (-0.124367+0.000000j) (0.000000+0.000000j) (-0.235032+0.000000j) (-0.000000+0.235032j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 3 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) (0.000000-0.297294j) 
8 3 3 (0.000000+0.000000j) (0.000000+0.000000j) (-0.000000+0.160557j) (-0.160557+0.000000j) (0.000000+0.000000j) (0.182055+0.000000j) (-0.000000+0.182055j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 4 -4 (0.218154+0.000000j) (0.000000+0.168982j) (0.000000+0.000000j) (0.000000+0.000000j) (-0.036875+0.000000j) (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+0.059744j) (0.059744+0.000000j) (0.000000+0.000000j) (0.293554+0.000000j) (0.000000-0.293554j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 4 -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) (-0.048280+0.000000j) (0.000000+0.313823j) 
8 4 -1 (0.000000+0.000000j) (0.000000+0.000000j) (-0.000000+0.158068j) (-0.158068+0.000000j) (0.000000+0.000000j) (0.110953+0.000000j) (-0.000000+0.110953j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 4 0 (0.365042+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.044074+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+0.000000j) (-0.000000+0.158068j) (0.158068+0.000000j) (0.000000+0.000000j) (-0.110953+0.000000j) (-0.000000+0.110953j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 4 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) (-0.048280+0.000000j) (0.000000-0.313823j) 
8 4 3 (0.000000+0.000000j) (0.000000+0.000000j) (-0.000000+0.059744j) (-0.059744+0.000000j) (0.000000+0.000000j) (-0.293554+0.000000j) (0.000000-0.293554j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 4 4 (0.218154+0.000000j) (0.000000-0.168982j) (0.000000+0.000000j) (0.000000+0.000000j) (-0.036875+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 5 -5 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000-0.118416j) (0.118416+0.000000j) (0.000000+0.000000j) (0.044757+0.000000j) (-0.000000+0.044757j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 5 -4 (0.000000+0.000000j) (0.000000+0.299572j) (0.000000+0.000000j) (0.000000+0.000000j) (-0.392232+0.000000j) (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) (0.000000-0.194177j) (-0.194177+0.000000j) (0.000000+0.000000j) (-0.020016+0.000000j) (-0.000000+0.020016j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 5 -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) (0.392232+0.000000j) (0.000000+0.065372j) 
8 5 -1 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000-0.212459j) (0.212459+0.000000j) (0.000000+0.000000j) (-0.043240+0.000000j) (0.000000-0.043240j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 5 0 (0.000000+0.000000j) (0.000000+0.119352j) (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+0.000000j) (0.000000+0.212459j) (0.212459+0.000000j) (0.000000+0.000000j) (-0.043240+0.000000j) (0.000000+0.043240j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 5 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) (-0.392232+0.000000j) (0.000000+0.065372j) 
8 5 3 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.194177j) (-0.194177+0.000000j) (0.000000+0.000000j) (-0.020016+0.000000j) (-0.000000-0.020016j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 5 4 (0.000000+0.000000j) (0.000000+0.299572j) (0.000000+0.000000j) (0.000000+0.000000j) (0.392232+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 5 5 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.118416j) (0.118416+0.000000j) (0.000000+0.000000j) (0.044757+0.000000j) (-0.000000-0.044757j) (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) (-0.166667+0.000000j) (0.000000-0.166667j) 
8 6 -5 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.190941j) (-0.190941+0.000000j) (0.000000+0.000000j) (-0.072169+0.000000j) (-0.000000-0.072169j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 6 -4 (0.420437+0.000000j) (-0.000000+0.325669j) (0.000000+0.000000j) (0.000000+0.000000j) (-0.071067+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+0.222971j) (0.222971+0.000000j) (0.000000+0.000000j) (-0.140458+0.000000j) (0.000000+0.140458j) (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) (-0.112367+0.000000j) (-0.000000+0.112367j) 
8 6 -1 (0.000000+0.000000j) (0.000000+0.000000j) (-0.000000-0.141019j) (0.141019+0.000000j) (0.000000+0.000000j) (0.124367+0.000000j) (0.000000+0.124367j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 6 0 (-0.224733+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (-0.265908+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+0.000000j) (-0.000000-0.141019j) (-0.141019+0.000000j) (0.000000+0.000000j) (-0.124367+0.000000j) (0.000000+0.124367j) (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) (-0.112367+0.000000j) (-0.000000-0.112367j) 
8 6 3 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.222971j) (-0.222971+0.000000j) (0.000000+0.000000j) (0.140458+0.000000j) (0.000000+0.140458j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 6 4 (0.420437+0.000000j) (-0.000000-0.325669j) (0.000000+0.000000j) (0.000000+0.000000j) (-0.071067+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+0.190941j) (0.190941+0.000000j) (0.000000+0.000000j) (0.072169+0.000000j) (-0.000000-0.072169j) (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) (-0.166667+0.000000j) (0.000000+0.166667j) 
8 7 -7 (0.000000+0.000000j) (0.000000+0.000000j) (-0.000000-0.080687j) (-0.080687+0.000000j) (0.000000+0.000000j) (0.213478+0.000000j) (-0.000000-0.213478j) (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) (0.228218+0.000000j) (-0.000000+0.228218j) 
8 7 -5 (0.000000+0.000000j) (0.000000+0.000000j) (-0.000000-0.177625j) (0.177625+0.000000j) (0.000000+0.000000j) (0.067136+0.000000j) (0.000000+0.067136j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 7 -4 (0.000000+0.000000j) (-0.000000+0.236833j) (0.000000+0.000000j) (0.000000+0.000000j) (-0.310087+0.000000j) (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+0.017852j) (0.017852+0.000000j) (0.000000+0.000000j) (-0.317128+0.000000j) (0.000000+0.317128j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 7 -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) (-0.209930+0.000000j) (0.000000-0.324437j) 
8 7 -1 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.133989j) (-0.133989+0.000000j) (0.000000+0.000000j) (-0.081808+0.000000j) (-0.000000-0.081808j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 7 0 (0.000000+0.000000j) (-0.000000+0.022037j) (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+0.000000j) (0.000000-0.133989j) (-0.133989+0.000000j) (0.000000+0.000000j) (-0.081808+0.000000j) (-0.000000+0.081808j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 7 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) (0.209930+0.000000j) (0.000000-0.324437j) 
8 7 3 (0.000000+0.000000j) (0.000000+0.000000j) (0.000000-0.017852j) (0.017852+0.000000j) (0.000000+0.000000j) (-0.317128+0.000000j) (0.000000-0.317128j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 7 4 (0.000000+0.000000j) (-0.000000+0.236833j) (0.000000+0.000000j) (0.000000+0.000000j) (0.310087+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+0.177625j) (0.177625+0.000000j) (0.000000+0.000000j) (0.067136+0.000000j) (0.000000-0.067136j) (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) (-0.228218+0.000000j) (-0.000000+0.228218j) 
8 7 7 (0.000000+0.000000j) (0.000000+0.000000j) (-0.000000+0.080687j) (-0.080687+0.000000j) (0.000000+0.000000j) (0.213478+0.000000j) (-0.000000+0.213478j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 8 -8 (0.208333+0.000000j) (0.000000+0.322749j) (0.000000+0.000000j) (0.000000+0.000000j) (-0.246503+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+0.080687j) (0.080687+0.000000j) (0.000000+0.000000j) (-0.213478+0.000000j) (-0.000000+0.213478j) (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) (-0.155902+0.000000j) (-0.000000-0.155902j) 
8 8 -5 (0.000000+0.000000j) (0.000000+0.000000j) (-0.000000+0.095470j) (-0.095470+0.000000j) (0.000000+0.000000j) (-0.036084+0.000000j) (0.000000-0.036084j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 8 -4 (0.136735+0.000000j) (0.000000+0.105915j) (0.000000+0.000000j) (0.000000+0.000000j) (-0.023113+0.000000j) (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+0.102552j) (0.102552+0.000000j) (0.000000+0.000000j) (-0.167964+0.000000j) (-0.000000+0.167964j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 8 -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) (-0.286268+0.000000j) (-0.000000-0.248099j) 
8 8 -1 (0.000000+0.000000j) (0.000000+0.000000j) (-0.000000+0.298735j) (-0.298735+0.000000j) (0.000000+0.000000j) (-0.103787+0.000000j) (0.000000-0.103787j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 8 0 (0.363609+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.299856+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+0.000000j) (-0.000000+0.298735j) (0.298735+0.000000j) (0.000000+0.000000j) (0.103787+0.000000j) (0.000000-0.103787j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 8 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) (-0.286268+0.000000j) (-0.000000+0.248099j) 
8 8 3 (0.000000+0.000000j) (0.000000+0.000000j) (-0.000000+0.102552j) (-0.102552+0.000000j) (0.000000+0.000000j) (0.167964+0.000000j) (-0.000000+0.167964j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 8 4 (0.136735+0.000000j) (0.000000-0.105915j) (0.000000+0.000000j) (0.000000+0.000000j) (-0.023113+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+0.095470j) (0.095470+0.000000j) (0.000000+0.000000j) (0.036084+0.000000j) (0.000000-0.036084j) (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) (-0.155902+0.000000j) (-0.000000+0.155902j) 
8 8 7 (0.000000+0.000000j) (0.000000+0.000000j) (-0.000000+0.080687j) (-0.080687+0.000000j) (0.000000+0.000000j) (0.213478+0.000000j) (-0.000000+0.213478j) (0.000000+0.000000j) (0.000000+0.000000j) 
8 8 8 (0.208333+0.000000j) (0.000000-0.322749j) (0.000000+0.000000j) (0.000000+0.000000j) (-0.246503+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) (0.000000+0.000000j) 
