Finding elements in GL_2(R) with specific orders

[jackmell]

Hi,

Is there a way to find elements in $GL_2(\mathbb{R})$ with an arbitrary order other than by trial and error? Suppose I wanted to find $A\in GL_2(\mathbb{R}):\; o(A)=165$. Is there no methodical way to find this? Is it possible perhaps I can find a product of matricies, each individually relatively easy to determine the order, such that the order of the product is the order I need?

Thanks,
Jack

 

[Infrared]

How about a rotation by an angle of $2\pi/165$?