The maximal Tori of finite exceptional groups of Lie type

Let G(q) be a twisted or untwisted finite exceptional group of Lie type over GF(q), either adjoint or simply connected, and let W be the Weyl group of G(q). This paper compiles an extensive data set on the maximal tori of G(q). A systematic labeling is given, via the corresponding conjugacy classes of W, together with a complete list of the structures of the maximal tori in terms of their torsion coefficient decomposition. Additionally the associated admissible graphs and the structure or shape of centralizers of elements in W are given as well as compatible computer files. Also various apparent inconsistencies in the current literature on simply connected groups are discussed and resolved.