Cody and Hillstrom (1970) provides rational approximations of the phase shift σ0(η)=phΓ(1+iη) (see (33.2.10)) for the ranges 0≤η≤2, 2≤η≤4, and 4≤η≤∞. Maximum relative errors range from 1.09×10⁻²⁰ to 4.24×10⁻¹⁹.