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Context. Complex organic species are known to be abundant toward low- and high-mass protostars. No statistical study of these species toward a large sample of high-mass protostars with the Atacama Large Millimeter/submillimeter Array (ALMA) has been carried out so far. Aims. We aim to study six N-bearing species: methyl cyanide (CH₃CN), isocyanic acid (HNCO), formamide (NH₂CHO), ethyl cyanide (C₂H₅CN), vinyl cyanide (C₂H₃CN) and methylamine (CH₃NH₂) in a large sample of line-rich high-mass protostars. Methods. From the ALMA Evolutionary study of High Mass Protocluster Formation in the Galaxy survey, 37 of the most line-rich hot molecular cores with ∼1" angular resolution are selected. Next, we fit their spectra and find column densities and excitation temperatures of the N-bearing species mentioned above, in addition to methanol (CH₃OH) to be used as a reference species. Finally, we compare our column densities with those in other low- and high-mass protostars. Results. CH₃OH, CH₃CN and HNCO are detected in all sources in our sample, whereas C₂H₃CN and CH₃NH₂ are (tentatively) detected in ∼78 and ∼32% of the sources. We find three groups of species when comparing their excitation temperatures: hot (NH₂CHO; T_ex ≳ 250 K), warm (C₂H₃CN, HN¹³CO and CH₃¹³CN; 100 K ≲ T_ex ≲ 250 K) and cold species (CH₃OH and CH₃NH₂; T_ex ≲ 100 K). This temperature segregation reflects the trend seen in the sublimation temperature of these molecules and validates the idea that complex organic emission shows an onion-like structure around protostars. Moreover, the molecules studied here show constant column density ratios across low- and high-mass protostars with scatter less than a factor ∼3 around the mean. Conclusions. The constant column density ratios point to a common formation environment of complex organics or their precursors, most likely in the pre-stellar ices. The scatter around the mean of the ratios, although small, varies depending on the species considered. This spread can either have a physical origin (source structure, line or dust optical depth) or a chemical one. Formamide is most prone to the physical effects as it is tracing the closest regions to the protostars, whereas such effects are small for other species. Assuming that all molecules form in the pre-stellar ices, the scatter variations could be explained by differences in lifetimes or physical conditions of the pre-stellar clouds. If the pre-stellar lifetimes are the main factor, they should be similar for low- and high-mass protostars (within factors ∼2-3).