This paper explores the leading terms of equivariant Artin L-functions at \(s=0\) for finite abelian extensions F/k, where k is an imaginary quadratic number field. We introduce a module constructed from these leading terms and the Dirichlet regulator, and compute its generalized index relative to the torsion-free part of the unit group of F. The main result establishes that this index equals the ratio of class numbers \(h_F/h_k\) multiplied by an explicit annihilator index involving roots of unity. For primes p not dividing the Galois group order, we provide a p-adic refinement using idempotents from higher Stark theory. As consequences, we derive obstructions to the existence of integral higher Stark elements mapping to the equivariant L-value and prove class number divisibility under non-decomposition conditions for ramified places. These findings contribute to the verification of equivariant Stark-type conjectures and offer new insights into class number relations in abelian extensions.
