  We show that the Quantum Spectral Curve (QSC) formalism, initially formulated
for the spectrum of anomalous dimensions of all local single trace operators in
N=4 SYM, can be extended to the generalized cusp anomalous dimension for all
values of the parameters. We find that the large spectral parameter asymptotics
and some analyticity properties have to be modified, but the functional
relations are unchanged. As a demonstration, we find an all-loop analytic
expression for the first two nontrivial terms in the small |phi \pm theta|
expansion. We also present nonperturbative numerical results at generic angles
which match perfectly 4-loop perturbation theory and the classical string
prediction.
  The reformulation of the problem in terms of the QSC opens the possibility to
explore many open questions. We attach to this paper several Mathematica
notebooks which should facilitate future studies.
