S^1: P_k(lam_k) = P_k(lam_(k+1)) = 0 exactly at all 59 gaps checked
S^2: P_k(lam_k) = P_k(lam_(k+1)) = 0 exactly at all 59 gaps checked
S^3: P_k(lam_k) = P_k(lam_(k+1)) = 0 exactly at all 24 gaps checked
S^4: P_k(lam_k) = P_k(lam_(k+1)) = 0 exactly at all 24 gaps checked
S^5: P_k(lam_k) = P_k(lam_(k+1)) = 0 exactly at all 24 gaps checked
S^6: P_k(lam_k) = P_k(lam_(k+1)) = 0 exactly at all 24 gaps checked
ALL SPHERE CHECKS PASSED
