Wavelength dependent properties of the p-Ge THz laser are reported for pulsed as well as for mode locked operation. The original small mirror laser outcoupler has been replaced by a mesh outcoupler, resulting in clear improvements of laser action. The optical output has been analyzed using a grating spectrometer and fast Schottky diode detectors. FOr 0.25 <EQ B <EQ 0.6T, 170-185 micrometers emission occurs. Laser action starts at short wavelength; during the pulse, longer wavelength components gain intensity, until simultaneous emission across the whole band occurs. With the mesh outcoupler instead of a small mirror, the small signal gain is found to increase, for instance from 0.015 cm-1 to 0.04 cm-1 at 172 micrometers . With the rf field modulation applied, 770 MHz mode locking of the laser is achieved at 172 micrometers , yielding a train of 100 ps FWHM pulses. For 0.5 <EQ B <EQ 1.4T, 75-120 micrometers emission is observed, dependent on both B and E field. Time-and wavelength dependence is complicated; often an oscillatory behavior of spectral components is seen. Although this effect complicates the formation of stable pulse trains under mode locked conditions, 140 ps pulses have been produced.