We demonstrate a silica-based planar waveguide spatial heterodyne spectrometer incorporating 120° optical hybrid 3×3 MMI couplers as the output couplers in 32 MZIs, which enabled us to derive the spectrum without use of the previously reported dynamic phase shifting. The free spectral range was 640 GHz, and the spectral resolution was 14 GHz. We used a CO laser irradiation method to calibrate the light powers from all the output ports of the couplers and to measure the optical phases and amplitudes at the individual MZIs. We solved the resultant system of three linear equations at each MZI and performed a complex Fourier transformation to derive a narrowband light spectrum. The background noise level of the retrieved spectrum was 0.05 with respect to the peak even when no window function was applied.