  The long range Bethe Ansatz solution of the mixing problem in N=4 SYM allows
to compute in a very efficient way multiloop anomalous dimensions of various
composite operators. In the case of sl(2) twist operators it is important to
obtain closed expressions for the anomalous dimensions in terms of the Lorentz
spin. Conjectures are available altough analytical proofs are missing beyond
one-loop. In this paper, we will present a method to expand at large spin the
solution of the long range Baxter equation in twist 2 and 3. We will also
propose sum rules for special singlet states at higher twist.
