Side note on encoding something like that with a lossy codec: In a practical implementation you'd high-pass filter the frequencies coing into the higher order SH terms; the narrower the beam/lobe the less directional it becomes for lower frequencies (basic diffraction physics). For practical numeric implementation you'd choose approximations of the base functions, that are quick to evaluate with a couple of bit-shifts and arithmetic (avoid LUTs where possible!) and accept the cross-talk.