One major achievement in mathematics of last century is the classification of finite simple groups. Their character tables are provided in the famous big red book, the ATLAS of Finite Simple Groups; the ATLAS of Brauer Tables list the modular irreducible characters. In a joint project with Thomas Breuer and Richard Parker we computed the discriminants of the invariant quadratic forms for all even degree absolutely irreducible indicator + characters of most of the groups in these two books. For finite fields this gives the additional information which of the two possible orthogonal groups contains the image of the representation. The talk will comment on the theoretical and computational methods used to obtain these discriminants and how to work with the database of orthogonal discriminants of characters.