Leading transcendental contribution to the four-loop universal anomalous dimension in N=4 SYM

We present the result of a full direct component calculation for the term proportional to ζ5 in the four-loop universal anomalous dimension of the twist-2 operators in N=4 supersymmetric Yang-Mills theory for the first three even moments. We suggest the general form such contribution for the arbitrary Lorentz spin of the twist-2 operators.