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A<sc>bstract</sc> We employ semiclassical quantization to calculate spectrum of quantum KdV charges in the limit of large central chargec. Classically, KdV chargesQ_2n−1generate completely integrable dynamics on the co-adjoint orbit of the Virasoro algebra. They can be expressed in terms of action variablesI_k, e.g. as a power series expansion. Quantum-mechanically this series becomes the expansion in 1/c, while action variables become integer-valued quantum numbersn_i. Crucially, classical expression, which is homogeneous inI_k, acquires quantum corrections that include terms of subleading powers inn_k. At first two non-trivial orders in 1/cexpansion these “quantum” terms can be fixed from the analytic form ofQ_2n−1acting on the primary states. In this way we find explicit expression for the spectrum ofQ_2n−1up to first three orders in 1/cexpansion. We apply this result to study thermal expectation values ofQ_2n−1and free energy of the KdV Generalized Gibbs Ensemble.