q = 16, q0 = 4: L-orbit lengths on W\0: [15, 60] (bound q0^2-1 = 15); orders of L-invariant subgroups: [1, 16, 256]; largest proper 16 (bound q^2/q0^2 = 16)
q = 25, q0 = 5: L-orbit lengths on W\0: [24, 120] (bound q0^2-1 = 24); orders of L-invariant subgroups: [1, 25, 625]; largest proper 25 (bound q^2/q0^2 = 25)
