Describe exact Hausdorff-limit geodesic configuration for non-principal congruence groups

Describe the exact Hausdorff-limit set \overline Z_{\infty,\Gamma} of zeros in the fundamental domain as the even weight k→∞ for non-principal congruence subgroups Γ (for example Γ_0(N)), expressing the resulting finite geodesic configuration explicitly in terms of N alone.

Background

The paper proves that for any congruence subgroup Γ the zeros of the chosen Eisenstein series converge, in Hausdorff distance, to a finite union of geodesic segments, and computes this configuration explicitly for Γ(N) (with different shapes depending on whether 4|N).

For certain conjugates (e.g., Γ^0(N)) they identify specific circular segments in the limit. However, an exact closed-form description for standard non-principal groups such as Γ_0(N) remains open.