# real analysis – To find zero set of an convolution of two characteristics function

For $$E=(0,1)setminus mathbb{Q}, ~l>0$$ and consider the function
$$chi_{(-l,l)}*chi_E(x)=int_{-l}^{l}chi_E(x-t)dt.$$
What is the zero set of the above function (in terms of $$l$$ may be)?

Notations: $$mathbb{Q}$$ is the set of rationals. $$chi_E$$ is the characteristic function of $$E.$$