We examine the phase relation between two orthogonal electric field components for several hundred waveform measurements of intense electron plasma waves in the terrestrial electron foreshock. In general, the phase shift at the carrier frequency is not zero or π as would be expected if the waves were purely electrostatic Langmuir waves, but is a function of the angle between the antennas and the interplanetary magnetic field (IMF). When the antennas are field aligned, the phase shift between the components is large; this value recedes smoothly to zero as the antenna is rotated away from the IMF direction. When solar wind density fluctuations are considered, this is consistent with the dispersion of the electromagnetic z-mode and we assert that the electron foreshock is populated by transverse z-mode waves, not purely longitudinal Langmuir waves. This has implications for conversion to freely propagating modes and large-amplitude saturation mechanisms.