Find the solution to the following lhcc recurrence:
$a_{n} = 1 a_{n-2} \text{ for } n \geq 2$ with initial conditions $a_0 = 1, a_1 = -3$. The solution is of the form: $$a_n = \alpha_1 (r_1)^n + \alpha_2 (r_2)^n$$ for suitable constants $\alpha_1, \alpha_2, r_1, r_2$ with $r_1 \leq r_2$. Find these constants.
$r_1 =$ $r_2 =$ $\alpha_1 =$ $\alpha_2 =$