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 $E.$