Density and concentration of hydroiodic acid
In 1981, Nishikata et al. published Viscosities of Aqueous Hydrochloric Acid Solutions, and Densities
and Viscosities of Aqueous Hydroiodic Acid Solutions in the Journal of Chemical Engineering Data.

Table III from this paper shows what you are after.



I don't know what temperature you used to make your density measurement, but assuming it was 20&nbsp;&deg;C, then your $\ce{HI}$ looks to have a concentration of about 39 weight percent.