Residue classes containing an unexpected number of primes

We fix a nonzero integer a and consider arithmetic progressions amodq, with q varying over a given range. We show that, for certain specific values of a, the arithmetic progressions amodq contain, on average, significantly fewer primes than expected. We improve on results of Fouvry, Bombieri, Friedlander, Iwaniec, Granville, Hildebrandt, and Maier.