  We investigate Solomon's zeta function for orders in the special case of
orders generated by the standard basis of an integral table algebra, a special
case of which is the integral adjacency algebra of an association scheme. As
Solomon's elementary method for computing this zeta function runs into
computational difficulties for ranks $3$ or more, a more efficient method is
desired. We give several examples to illustrate how the local zeta integral
approach proposed by Bushnell and Reiner can be applied to compute explicit
zeta functions for these orders.
