Planck 2013 results. III. LFI systematic uncertainties

We present the current estimate of instrumental and systematic effect uncertainties for the Planck-Low Frequency Instrument relevant to the firstrelease of the Planck cosmological results.We give an overview of the main effects and of the tools and methods applied to assess residuals in mapsand power spectra.We also present an overall budget of known systematic effect uncertainties, which are dominated by sidelobe straylight pick-upand imperfect calibration. However, even these two effects are at least two orders of magnitude weaker than the cosmic microwave backgroundfluctuations as measured in terms of the angular temperature power spectrum. A residual signal above the noise level is present in the multipolerange ∫ < 20, most notably at 30GHz, and is probably caused by residual Galactic straylight contamination. Current analysis aims to further reducethe level of spurious signals in the data and to improve the systematic effects modelling, in particular with respect to straylight and calibrationuncertainties.