A result of Heath-Brown states: For $a_1,...,a_n$ be arbitrary complex numbers, $$\sideset{}{^*}\sum_{m\le M} \left|\sideset{}{^*}\sum_{n\le M}a_n\left(\frac{n}{m}\right)\right|^{2} \ll_{\epsilon}(MN)^{\epsilon}(M+N)\sideset{}{^*}\sum_{n\le N}|a_n|^2$$ $\sideset{}{^*}\sum$ indicates restriction to odd square free values.

Is the implied constant effective ?