Ratios Conjecture prediction for the 1-level density of Dirichlet L-functions

Let $q$ be a modulus, let $f$ be the test function used in the 1-level density, and let $D_{1;q}(\widehat{f})$ denote the corresponding density with scaling parameter $Q=q$. Write $\gamma$ for Euler's constant and let the sum over $p\mid q$ run over primes dividing $q$. Ratios Conjecture's prediction. The 1-level density equals

$$D_{1;q}(\widehat{f})=f(0)\left(1-\frac{\log(8\pi e^{\gamma})}{\log q}-\frac{\sum_{p\mid q}\frac{\log p}{p-1}}{\log q}\right)+\int_0^{\infty}\frac{f(0)-f(t)}{q^{t/2}-q^{-t/2}}\,dt+O_{\epsilon}\left(q^{-\frac12+\epsilon}\right).$$

This is the lower-order prediction obtained by extending the Ratios Conjecture to general moduli; the paper compares its proven density calculations with this formula where both are available.