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Electron bunches of high charge (up to 10 nC) are compressed in length in the Compact Linear Collider Test Facility magnetic chicane to less than 0.4 mm rms. The short bunches radiate coherently in the chicane magnetic field, and the horizontal and longitudinal phase space density distributions are affected. This paper reports the results of beam emittance and momentum measurements. Horizontal and vertical emittances and momentum spectra were measured for different bunch compression factors and bunch charges. In particular, for 10 nC bunches, the mean beam momentum decreased by about 5% while the rms momentum spread increased from 2% to 8%. The experimental results are compared with simulations made with the code TraFiC4.