tl;dr: you don’t get exact answers from floating-point arithmetic.
There are numerous approximations in this calculation that will result in not-exactly-zero values for things that are exactly zero in principle. There’s finite-timestep integration of ODEs, approximating an infinite-time average with a long finite-time sum, maybe using finite-differencing to approximate a Jacobian, doing linear algebra on moderately poorly-conditioned linear algebra in finite-precision arithmetic, and plain old floating-point round-off. For this calculation it looks like you’re getting about seven digits of precision (1e-06 compared to 11.88), which is as good as you can get if the Jacobians are 1st-order finite-difference (square root of machine epsilon, 1e-16).