∀ {N : ℕ} [inst : NeZero N] (Φ : ZMod N → ℂ) (s : ℂ),
  ZMod.completedLFunction₀ Φ s =
    ↑N ^ (-s) * ∑ j, Φ j * HurwitzZeta.completedHurwitzZetaEven₀ (ZMod.toAddCircle j) s +
      ↑N ^ (-s) * ∑ j, Φ j * HurwitzZeta.completedHurwitzZetaOdd (ZMod.toAddCircle j) s