}

    // l=2 wavefunctions (f-orbitals)
    float Y33_re(float mu, float phi)  { return -0.027814921575518937 * P33(mu) * cos(3.0*phi); }
    float Y33_im(float mu, float phi)  { return -0.027814921575518937 * P33(mu) * sin(3.0*phi); }
    float Y32_re(float mu, float phi)  { return  0.06813236509555216  * P32(mu) * cos(2.0*phi); }
    float Y32_im(float mu, float phi)  { return  0.06813236509555216  * P32(mu) * sin(2.0*phi); }
    float Y31_re(float mu, float phi)  { return -0.21545345607610045  * P31(mu)