Since the seminal work of Bazhanov, Lukyanov and Zamolodchikov, diagonalization of integrals of motion has been an important issue in conformal field theory. Feigin,Kojima,Shiraishi and Watanabe introduced a commutative family of operators for the q-deformed Virasoro algebra. It turns out that their first Hamiltonian (and most likely all others) is derived from the transfer matrix acting on Fock representations of the toroidal gl(1) algebra. Making use of the shuffle algebra realization, we show that its spectrum is described by a Bethe-type equation. noindent This is a joint work with B.Feigin, T.Miwa and E.Mukhin.