Information Ratio from a Tiny R-Squared

A model predicting next-day returns has an out-of-sample $R^2=0.003$ for each of $N=1000$ independent bets per year. Using the fundamental law of active management, $IR = IC\sqrt{N}$, where $IC$ is the information coefficient (the correlation between forecast and outcome), what is the annual information ratio? Give an exact expression or a decimal.