∀ {L : Type u} [inst : CommRing L] [inst_1 : IsDomain L] (n : ℕ) [inst_2 : NeZero n] (g : L ≃+* L)
  (c : ZMod (Fintype.card ↥(rootsOfUnity n L))),
  (∀ t ∈ rootsOfUnity n L, g ↑t = ↑t ^ c.val) → c = modularCyclotomicCharacter.toFun n g