Can you please suggest a free software or website that would allow me to approximate, numerically, the first $n$ roots of the equation $ 2J\_{0}(2\alpha)+2\alpha J'\_{0}(2\alpha)=0$ ? I'm trying to find a Bessel-Fourier expansion for a function in the interval $[0,2]$ and that's the boundary condition given. As you know, I need the roots of that equation to find the eigenvalues. I've checked Maxima and Octave but I think they don't offer this-or at least it wasn't clear to me they had this feature. I need this ASAP, Thanks in advance!

Note: By $J\_{0}$ we mean the Bessel function of order $0$