We present a high resolution synthetic spectral library, INTRIGOSS, designed for studying FGK stars. The library is based on atmosphere models computed with specified individual element abundances via ATLAS12 code. Normalized SPectra (NSP) and surface Flux SPectra (FSP), in the 4830-5400 A, wavelength range, were computed with the SPECTRUM code. INTRIGOSS uses the solar composition by Grevesse et al. 2007 and four [alpha/Fe] abundance ratios and consists of 15,232 spectra. The synthetic spectra are computed with astrophysical gf-values derived by comparing synthetic predictions with a very high SNR solar spectrum and the UVES-U580 spectra of five cool giants. The validity of the NSPs is assessed by using the UVES-U580 spectra of 2212 stars observed in the framework of the Gaia-ESO Survey and characterized by homogeneous and accurate atmospheric parameter values and by detailed chemical compositions. The greater accuracy of NSPs with respect to spectra from the AMBRE, GES_Grid, PHOENIX, C14, and B17 synthetic spectral libraries is demonstrated by evaluating the consistency of the predictions of the different libraries for the UVES-U580 sample stars. The validity of the FSPs is checked by comparing their prediction with both observed spectral energy distribution and spectral indices. The comparison of FSPs with SEDs derived from ELODIE, INDO--U.S., and MILES libraries indicates that the former reproduce the observed flux distributions within a few percent and without any systematic trend. The good agreement between observational and synthetic Lick/SDSS indices shows that the predicted blanketing of FSPs well reproduces the observed one, thus confirming the reliability of INTRIGOSS FSPs.
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