  An iterative procedure perturbatively solving the quantum spectral curve of
planar N=4 SYM for any operator in the sl(2) sector is presented. A Mathematica
notebook executing this procedure is enclosed. The obtained results include
10-loop computations of the conformal dimensions of more than ten different
operators.
  We prove that the conformal dimensions are always expressed, at any loop
order, in terms of multiple zeta-values with coefficients from an algebraic
number field determined by the one-loop Baxter equation. We observe that all
the perturbative results that were computed explicitly are given in terms of a
smaller algebra: single-valued multiple zeta-values times the algebraic
numbers.
