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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-30 m Large Project ASAI (Astrochemical Surveys At IRAM). They consist of a high-sensitivity unbiased spectral survey at the 1mm, 2mm, and 3mm IRAM bands. We detected five iCOMs: acetaldehyde (CH₃CHO), methyl formate (HCOOCH₃), dimethyl ether (CH₃OCH₃), ethanol (CH₃CH₂OH), and formamide (NH₂CHO). In addition, we searched for other iCOMs and ketene (H₂CCO), formic acid (HCOOH) and methoxy (CH₃O), 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 x 10¹⁵ and 1 x 10¹⁷ cm^–2 on the 0.3 arcsec 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.