  Witten's top Chern class is a particular cohomology class on the moduli space
of Riemann surfaces endowed with r-spin structures. It plays a key role in
Witten's conjecture relating to the intersection theory on these moduli spaces.
  Our first goal is to compute the integral of Witten's class over the
so-called double ramification cycles in genus 1. We obtain a simple closed
formula for these integrals.
  This allows us, using the methods of [15], to find an algorithm for computing
the intersection numbers of the Witten class with powers of the \psi-classes
(or tautological classes) over any moduli space of r-spin structures, in short,
all numbers involved in Witten's conjecture.
