Enumeration of Seidel matrices

In this paper Seidel matrices are studied, and their spectrum and several related algebraic properties are determined for order n≤13. Based on this Seidel matrices with exactly three distinct eigenvalues of order n≤23 are classified. One consequence of the computational results is that the maximum number of equiangular lines in R12 with common angle 1∕5 is exactly 20.