Context. Complex organic molecules are detected in many sources in the warm inner regions of envelopes surrounding deeply embedded protostars. Exactly how these species form remains an open question.Aims. This study aims to constrain the formation of complex organic molecules through comparisons of their abundances towards the Class 0 protostellar binary IRAS 16293-2422. Methods. We utilised observations from the Atacama Large Millimetre/submillimetre Array (ALMA) Protostellar Interferometric Line Survey (PILS) of IRAS 16293-2422. The species identification and the rotational temperature and column density estimation were derived by fitting the extracted spectra towards IRAS 16293-2422 A and IRAS 16293-2422 B with synthetic spectra. The majority of the work in this paper pertains to the analysis of IRAS 16293-2422 A for a comparison with the results from the other binary component, which have already been published. Results. We detect 15 different complex species, as well as 16 isotopologues towards the most luminous companion protostar IRAS 16293-2422 A. Tentative detections of an additional 11 isotopologues are reported. We also searched for and report on the first detections of methoxymethanol (CH 3 OCH 2 OH) and trans-ethyl methyl ether (t-C 2 H 5 OCH 3 ) towards IRAS 16293-2422 B and the follow-up detection of deuterated isotopologues of acetaldehyde (CH 2 DCHO and CH 3 CDO). Twenty-four lines of doubly-deuterated methanol (CHD 2 OH) are also identified. Conclusions. The comparison between the two protostars of the binary system shows significant differences in abundance for some of the species, which are partially correlated to their spatial distribution. The spatial distribution is consistent with the sublimation temperature of the species; those with higher expected sublimation temperatures are located in the most compact region of the hot corino towards IRAS 16293-2422 A. This spatial differentiation is not resolved in IRAS 16293-2422 B and will require observations at a higher angular resolution. In parallel, the list of identified CHD 2 OH lines shows the need of accurate spectroscopic data including their line strength. Article number, page 2 of 31 S. Manigand et al.: Inventory of complex organic molecules towards IRAS 16293-2422 A Notes. (a) e 0 , o 1 and e 1 corresponds to the three first torsional states. The notation of the quantum numbers is directly taken from Mukhopadhyay (2016). (b) This corresponds to the number indicated in the top-right corner of each panel in Figures D.1 and D.2. (c) W is the integrated intensity of the unblended lines, summed over the range [ν 0 − ∆ν FWHM , ν 0 + ∆ν FWHM ], given ∆ν FWHM = ν 0 FWHM c , with FWHM equal to 2.2 and 0.8 km s −1 for IRAS 16293A and B, respectively.