What could be the source of this sine wave distortion, visible as equally spaced lines in FFT?
I've hooked up a lab signal generator to the input of the scope to compare it to the measured signal and surprisingly saw the exactly same spectrum in it's FFT. Turning up the frequency the subharmonics went away at 1250 Hz. Changing memory depth in the "Aquire" settings from Auto to 6K removed the effect. It seems like some kind of an aliasing problem is going on in the FFT of the DS1054Z. 

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EDIT:
Looking carefully at the image you will see a sampling rate of 5kHz shown over the FFT window. It would have been too less to sample the DAC output before the filter. It's surprising that it still looks the same if provided with a clean 1120Hz signal, as it's still below the niquist frequency.