What is the justification for the theoretical value of the adiabatic index of $rm CO_2$ of 1.30 at room temperature?

I’m currently investigating an experiment to determine the adiabatic index of helium, nitrogen and carbon dioxide at room temperature and am attempting to come up with / justify theoretical values of their adiabatic indices / ratios of their heat capacities. Nitrogen and helium are easy, but for carbon dioxide, I am attempting to take account of some vibrational degrees of freedom. To do so, I have looked into vibrational partition functions, but I can’t really make sense of how to extract additional degrees of freedom from the partition function. Any help in justifying where 1.30 comes from would be much appreciated,