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Artin representations were computed with Magma by Tim Dokchitser and John Jones.

Bounds for completeness of computations come from [MR:3669395, 10.1007/s40993-017-0079-5, arXiv:1610.01228] . In each case, the LMFDB contains all faithful representations for a given group and irreducible representation with conductor less than or equal to the stated bound. Representations are distinguished by their dimension, and the smallest containing permutation representation.