Computing Zeta Functions of Table Algebra Orders Using Local Zeta Integrals

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