coefficient[Annular[S[n_],Z[i_]],S[n_]~join[1]~S[n_]]/;OddQ[n]:=Conjugate[coefficient[Annular[S[n],W[((n+3)/2)]],AnnularDual[S[n],Z[i]]]]InnerProduct[S[n]~join[1]~S[n],Annular[S[n],W[((n+3)/2)]]]+Conjugate[coefficient[Annular[S[n],Z[n+2]],AnnularDual[S[n],Z[i]]]]InnerProduct[S[n]~join[1]~S[n],Annular[S[n],Z[n+2]]]

coefficient[Annular[S[n_],W[i_]],AnnularDual[S[n_],Z[j_]]]:=