Are number fields determined by Artin L-functions?

Let k   be a number field, K/kK/k a finite Galois extension with Galois group G, χ a faithful character of G. We prove that the Artin L  -function L(s,χ,K/k)L(s,χ,K/k) determines the Galois closure of K   over QQ. In the special case k=Qk=Q it also determines the character χ.