You need Magma to load these .m files, specifically, a version of Magma
that is new enough to have the command AlgorithmicFunctionField.

We've covered all N <= 40 precisely, i.e., the lower bound is the
same as the gonality.  In this folder we skip N <= 22 because the
gonalities for N <= 22 and N = 24 were already known.

In the folder X1_42_57 we compute lower bounds that are almost
certainly not sharp, namely:
	gon_Q(X1(42)) >= 9
	gon_Q(X1(43)) >= 17
	gon_Q(X1(44)) >= 9
	gon_Q(X1(46)) >= 9
	gon_Q(X1(48)) >= 9
	gon_Q(X1(53)) >= 17
	gon_Q(X1(57)) >= 17
These bounds are used in Section 5 of the paper, in order to determine
(for d <= 8) all N for which X1(N) has infinitely many places of degree d over Q.

For N = 42, 44, 46, 48 we can rule out infinitely many places of degree <= 8
by showing that the Q-gonality is at least 9, because the Jacobian is finite
in these cases.  For N = 43, 53, 57 the Jacobian has positive rank, hence
we need a higher bound, >= 17, so that we can use Frey's theorem.