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We give an explicit version of a result due to D. Burgess. Let χ be a non-principal Dirichlet character modulo a prime p. We show that the maximum number of consecutive integers for which χ takes on a particular value is less than πe √ 6 3 + o(1) p 1/4 log p, where the o(1) term is given explicitly.doi:10.7169/facm/2012.46.2.10 fatcat:wmhwaa4etvcgbl33ef2tdkrqzy