Telluric correction and template generation of the M dwarf GJ 588 for two different chunks. First row: CRIRES⁺ observation from 8 August 2022 of the star (red) overlaid with the best-fit telluric model obtained with viper (blue). Second row: Telluric-corrected spectrum. Third row: individual telluric-corrected spectra taken between March and August 2022. Last row: co-added spectrum using the average of the individual observations from the plot above. This represents the final stellar template, which is used as reference for the RV determination.