Random matrix theory has been applied to food web stability for decades, implying elliptical eigenvalue spectra and that large food webs should be unstable. Here we allow feasible food webs to self-assemble within an evolutionary process, using simple Lotka-Volterra equations and several elementary interaction types. We show that, as complex food webs evolve under 10(5) invasion attempts, the community matrix spectra become bi-modal, rather than falling onto elliptical geometries. Our results raise questions as to the applicability of random matrix theory to the analysis of food web steady states.