The wave equation ofofϕ = 0 is studied in the exterior of a Schwarzschild black hole, r > 2M. By assuming stationary-spherically symmetric solutions the wave equation reduces to the Schrodinger equation where r* = r + 2M ln(r/2M - 1). The potential V has a single maximum near r = 3M for each l]N, so a family of top resonances is expected to exist. It is demonstrated that there are spectral resonances where kϵN0 is a parameter of the harmonic oscillator, and where The resonant states orbit near the radius rlmax ∼ 3M(1-(3l)-2) for large l > 0. A modification of the standard complex scaling technique is required for the analysis.