∀ {M N : ℕ} [NeZero N] (hMN : M ∣ N) (χ : DirichletCharacter ℂ M) {s : ℂ},
  1 < s.re →
    LSeries (fun n => ((DirichletCharacter.changeLevel hMN) χ) ↑n) s =
      LSeries (fun n => χ ↑n) s * ∏ p ∈ N.primeFactors, (1 - χ ↑p * ↑p ^ (-s))