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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 nd that the large spectral parameter asymptotics and some analyticity properties have to be modi ed, but the functional relations are unchanged. As a demonstration, we nd an all-loop analytic expression for the rst two nontrivial terms in the small j j 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.
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