  Berge in [1] defined doubly primitive knots, which yield lens spaces by Dehn
surgery. At the same paper he listed the knots into several types. In this
paper we will prove the list is complete when $\tau>1$. The invariant $\tau$ is
a quantity with regard to lens space surgery, which is defined in this paper.
Furthermore at the same time we will also prove that Table~6 in [8] is complete
as Poincar\'e homology sphere surgery when $\tau>1$.
