CYCLOTOMIC COSETS IN THE RING

We consider the ringR_(2p^n q^m )=GF(l)[x]/(x^(2p^n q^m )-1) where p,q,l are distinct odd primes,l is a primitive root both modulo p^n and q^m such that gcd(p^n),(q^m))d.Explicit expressions for all the 2(m n d+m+n+1) Cyclotomic Cosets areobtained, p does not divide q-1 .