To compute W_xy(t+alpha zeta) modulo 2^p, first divide each retained noncentral factor t-q+alpha z by the KNOWN integer 2^(v_2(t-q)). Both resulting coefficients are integers. Cancel the remaining explicit powers of two as in the integrality proof, then invert only the odd part of C_prime(0). Evaluate the normalized product at the supplied e coordinates of zeta modulo 2^p. This works even at zeta=0, where the uncanceled rational expression might appear to divide by zero. There are O(L) factors; exact coordinate arithmetic is polynomial in s,p for the prescribed field and packet sizes.