Cody and Hillstrom (1970) provides rational approximations of the phase shift ${\sigma }_0\left(\eta \right)=\mathrm{ph}\mathrm{\Gamma }\left(1+\mathrm{i}\eta \right)$ (see (33.2.10)) for the ranges $0\le \eta \le 2$, $2\le \eta \le 4$, and $4\le \eta \le \mathrm{\infty }$. Maximum relative errors range from 1.09×10⁻²⁰ to 4.24×10⁻¹⁹.