Let $L/K$ be any finite Galois extension of number fields with Galois group $G$ . For any conjugacy class $C \subset G$ , the subset of prime ideals $\mathfrak{p} \subset K$ which are unramified in $L$ and satisfy the property $$ [L/K,\mathfrak{P}] \in C\ \text{for any prime }\ \mathfrak{P} \subset L\ \text{containing }\ \mathfrak{p} $$ has analytic density $\frac{|C|}{|G|}$ , where $[L/K,\mathfrak{P}]$ denotes the Artin symbol at $\mathfrak{P}$ .

Note that the conjugacy class of $[L/K,\mathfrak{P}]$ is independent of the choice of prime $\mathfrak{P}$ lying over $\mathfrak{p}$ , since any two such choices of primes are related by a Galois automorphism and their corresponding Artin symbols are conjugate by this same automorphism.