  We study the correction-to-scaling exponents for the two-dimensional
self-avoiding walk, using a combination of series-extrapolation and Monte Carlo
methods. We enumerate all self-avoiding walks up to 59 steps on the square
lattice, and up to 40 steps on the triangular lattice, measuring the
mean-square end-to-end distance, the mean-square radius of gyration and the
mean-square distance of a monomer from the endpoints. The complete endpoint
distribution is also calculated for self-avoiding walks up to 32 steps (square)
and up to 22 steps (triangular). We also generate self-avoiding walks on the
square lattice by Monte Carlo, using the pivot algorithm, obtaining the
mean-square radii to ~0.01% accuracy up to N = 4000. We give compelling
evidence that the first non-analytic correction term for two-dimensional
self-avoiding walks is Delta_1 = 3/2. We compute several moments of the
endpoint distribution function, finding good agreement with the field-theoretic
predictions. Finally, we study a particular invariant ratio that can be shown,
by conformal-field-theory arguments, to vanish asymptotically, and we find the
cancellation of the leading analytic correction.
