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 $3times 10^{15}$ and $1times 10^{17}$ 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.
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