Canonical momenta from a Lagrangian with a velocity-coupling term

The Lagrangian of a dynamical system is given by $L(q_1,q_2,\dot q_1,\dot q_2)=\dfrac m2(\dot q_1^2+\dot q_2^2) +a(q_1\dot q_2-q_2\dot q_1)$ where $m$ and $a$ are constants. Then canonical momenta of the system are given by: