where c l (E, γ) are the expansion coefficients, which encode the finite-width spectral function and the energy grid point, E, on which it is evaluated. In practice, the infinite sum over Chebyshev moments is truncated to N cheb terms, which is treated as a convergence parameter. The action of Tl ( Ĥ) on an arbitrary vector |λ ⟩ is defined as Tl ( Ĥ)|λ l-1 ⟩ = |λ l ( Ĥ)⟩. The coefficients are evaluated by discrete Fourier transform as,