Euler constants from primes in arithmetic progression

Many Dirichlet series of number theoretic interest can be written as a product of generating series (Formula presented), with p p≡a (mod d) ranging over all the primes in the primitive residue class modulo a (mod d), and a function H(s) well-behaved around s = 1. In such a case the corresponding Euler constant can be expressed in terms of the Euler constants γ(d, a) of the series ζd,a(s) involved and the (numerically more harmless) term H,(1)/H(1). Here we systematically study γ(d, a), their numerical evaluation and discuss some examples.