Lewis & Short

2. Fātŭus, i. m., another name for the prophesying Faunus; also called Fātŭ-ellus; while his sister, Fauna, who prophesied to females, was also called Fātŭa and Fātŭella, Lact. 1, 22, 9; Arn. 5, 18; Macr. S. 1, 12; Mart. Cap. 2, § 167; Just. 43, 1; Plin. 27, 12, 83, § 117 (dub.; Jan. fatuos).