For any Schur function s_ν, the associated delta operator Δ'_sν is a linear operator on the ring of symmetric functions which has the modified Macdonald polynomials as an eigenbasis. When ν = (1^n-1) is a column of length n-1, the symmetric function Δ'_en-1e_n appears in the Shuffle Theorem of Carlsson and Mellit. More generally, when ν = (1^k-1) is any column the polynomial Δ'_ek-1e_n is the symmetric function side of the Delta Conjecture of Haglund, Remmel, and Wilson. We give an expansion of ωΔ'_sνe_n at t=0 in the dual Hall-Littlewood basis for any partition ν. The Delta Conjecture at t=0 was recently proven by Garsia, Haglund, Remmel, and Yoo; our methods give a new proof of this result. We give an algebraic interpretation of ωΔ'_sνe_n at t=0 in terms of a Hom-space.