As described in the Supplementary Material, each combinatorial factor, a^{X}_{X_1,X_2,X_3,X_4,X_5,X_6,X_7}, can be expressed as a rational function of the form (c_{15}n^{15}+c_{14}n^{14}+...+c_{1}n+c_{0})/(512(n-1)^3 (n-2)^9). Each row in the data file `threeloop_a.datâ€™ represents (c_{15}, c_{14},...,c_{1},c_{0}), and the rows are tabulated with ascending index I=(2^7)*(X-1)+(2^6)*(X_1-1)+(2^5)*(X_2-1)+(2^4)*(X_3-1)+(2^3)*(X_4-1)+(2^2)*(X_5-1)+(2^1)*(X_6-1)+(2^0)*X_7. The same conventions are followed in the data file `threeloop_b.datâ€™ for b^{X}_{X1,X2,X3,X4,X5,X6,X7}.