theorem AddChar.map_zmod_smul {R : Type u_1} {M : Type u_2} [Semiring R] {q : ℕ} [AddCommMonoid M] [Module (ZMod q) M] (γ : AddChar M R) (r : ZMod q) (x : M) [NeZero q] : γ (r • x) = γ x ^ r.val