. . "The water-soluble complex dye according to claim 1, wherein in the azo compound represented by the above formula (1) or its tautomer, A1 is a group represented by either the following formula (2) or (3): (In the formulae (2) and (3), each of R3 to R6 which are independent of one another, is a hydrogen atom or a monovalent substituent.) 5." . .