I am trying to understand whether something non trivial is known about the following $$\sum_{n \leq x} \mu(n) \chi(n),$$ as a function of $x$.

Here $\chi$ is a Dirichlet character modulo $q$ and $q > (\log x)^2$ (for example).

I am trying to understand whether some non trivial explicit estimate is known about the following $$\sum_{n \leq x} \mu(n) \chi(n)$$ as a function of $x$.

Here $\chi$ is a Dirichlet character modulo $q$ and $q > (\log x)^2$ (for example).

I am trying to understand whether something non trivial is known about $$\sum_{n \leq X} \mu(n) \chi(n).$$ Here $\chi$ is a Dirichlet character modulo $q$ and $q > (\log x)^2$ (for example).

I am trying to understand whether something non trivial is known about the following $$\sum_{n \leq x} \mu(n) \chi(n),$$ as a function of $x$.

Here $\chi$ is a Dirichlet character modulo $q$ and $q > (\log x)^2$ (for example).