Contour plots of the cosmographic free parameters a_i for the non-orthogonal (left panel) and orthogonal (right panel) logarithmic fits to the fifth-order. Purple contours are the confidence levels at 1σ and 2σ. Best-fit values are very different in the two cases except for a₅, which is consistent within the errors. This is expected from Eq. (1) as a₅ is not multiplied by any factor k_ij and so must be equal to the same coefficient in the non-orthogonal formula. The apparent correlation in the (a₃, a₄) and (a₄, a₅) planes in the right panel is due to the prior D_L > 0, which allows only specific values of a_i.