  We consider twist-3 operators in the sl(2) sector of N=4 SYM built out of
three scalar fields with derivatives. We extract from the Bethe Ansatz
equations of this sector the exact lowest anomalous dimension gamma(s) of
scaling fields for several values of the operator spin s. We propose compact
closed expressions for the spin dependence of gamma(s) up to the four loop
level and show that they obey a simple new twist-3 transcendentality principle.
As a check, we reproduce the four loop universal cusp anomalous dimension
governing the logarithmic large spin limit of gamma(s).
