/*  

 N=3
 M=1

 unique solution

 length of multipoles: 
   [ 1/4, 0, 1/4, 1/2 ]

 cumulative squared lengths A_M:
        [ 0, 1/4, 3/4 ]

 equitorial triangle

 symmetry group S_3

 configuration:

   [-1.0,  0.0,                             0.0 ],
   [ 0.5, -0.866025403784438646763723170755 0.0 ],
   [ 0.5,  0.866025403784438646763723170755 0.0 ]


*/

psi3:=[ 1/2*Sqrt(2),0,0, 1/2*Sqrt(2) ];