For e a positive integer, we find restrictions modulo 2e on the
coefficients of the characteristic polynomial ΟSβ(x) of a Seidel matrix
S. We show that, for a Seidel matrix of order n even (resp. odd), there are
at most 2(2eβ2β) (resp. 2(2eβ2β)+1) possibilities for
the congruence class of ΟSβ(x) modulo 2eZ[x]. As an application
of these results, we obtain an improvement to the upper bound for the number of
equiangular lines in R17, that is, we reduce the known upper bound
from 50 to 49.Comment: 21 pages, fixed typo in Lemma 2.