∀ {q : ℕ} {a : ZMod q} [NeZero q],
  IsUnit a →
    ∀ (n : ℕ),
      ↑(ArithmeticFunction.vonMangoldt.residueClass a n) =
        (↑q.totient)⁻¹ * ∑ χ, χ a⁻¹ * χ ↑n * ↑(ArithmeticFunction.vonMangoldt n)