We present the first census of the interstellar Complex Organic Molecules (iCOMs) in the low-mass Class I protostar SVS13-A, obtained by analysing data from the IRAM-30m Large Project ASAI (Astrochemical Surveys At IRAM). They consist of an high-sensitivity unbiased spectral survey at the 1mm, 2mm and 3mm IRAM bands. We detected five iCOMs: acetaldehyde (CH 3 CHO), methyl formate (HCOOCH 3 ), dimethyl ether (CH 3 OCH 3 ), ethanol (CH 3 CH 2 OH) and formamide (NH 2 CHO). In addition we searched for other iCOMs and ketene (H 2 CCO), formic acid (HCOOH) and methoxy (CH 3 O), whose only ketene was detected. The numerous detected lines, from 5 to 37 depending on the species, cover a large upper level energy range, between 15 and 254 K. This allowed us to carry out a rotational diagram analysis and derive rotational temperatures between 35 and 110 K, and column densities between 3 × 10 15 and 1 × 10 17 cm −2 on the 0. 3 size previously determined by interferometric observations of glycolaldehyde. These new observations clearly demonstrate the presence of a rich chemistry in the hot corino towards SVS13-A. The measured iCOMs abundances were compared to other Class 0 and I hot corinos, as well as comets, previously published in the literature. We find evidence that (i) SVS13-A is as chemically rich as younger Class 0 protostars, and (ii) the iCOMs relative abundances do not substantially evolve during the protostellar phase.