We study the Coulomb pseudogap for tunneling into the two-dimensional electron system of high-mobility (Al,Ga)As/GaAs heterojunctions subjected to a quantizing magnetic field at filling factor ν<~1. Tunnel current-voltage characteristics show that for the double maximum observed in the tunnel resistance at ν≈1 the pseudogap is linear in energy with a slope that depends on filling-factor, magnetic field, and temperature. We give a qualitative account of the filling-factor dependence of the pseudogap slope, and we confirm the recently reported appearance of another relaxation time for tunneling at ν≈1. For the tunnel resistance peaks at ν=1/3 and 2/3 a completely different behavior of the current-voltage curves is found and interpreted as manifestation of the fractional gap.