  We present algorithmic perturbative solution of $\mathcal{N}=4$ SYM quantum
spectral curve in the case of twist 2 operators, valid to in principle
arbitrary order in coupling constant. The latter treats operator spins as
arbitrary integer values and is written in terms of special class of functions
-- products of rational functions in spectral parameter with sums of Baxter
polynomials and Hurwitz functions. It is shown that this class of functions is
closed under elementary operations, such as shifts, partial fractions,
multiplication by spectral parameter and differentiation. Also, it is fully
sufficient to solve arising non-homogeneous multiloop Baxter and first order
difference equations. As an application of the proposed method we present the
computation of anomalous dimensions of twist 2 operators up to four loop order.
