There are two parts to computing Artin representations: one computes the number fields of interest, and then for each such field, one computes the data for each irreducible complex representation of the Galois group.

The number fields came from the LMFDB number field collection, or were computed by J. Jones and D. Roberts. The Artin representation data for each field was computed using programs written by Tim Dokchitser by Dokchitser and Jones.