Let m ≥ 2 m\geq 2 be a natural number and let A \mathcal {A} be an ideal class of an imaginary quadratic number field. Zagier and Gangl constructed C / Q ( m ) \mathbb {C}/\mathbb {Q}(m) -valued invariants I m ( A ) I_{m}(\mathcal {A}) which they named “the enhanced zeta value”, since the real part of i m − 1 I m ( A ) i^{m-1}I_{m}(\mathcal {A}) , after being multiplied by a certain elementary factor in terms of a factorial and a power of 2 π 2\pi , equals the partial zeta value ζ ( m , A ) \zeta (m,\mathcal {A}) . They also constructed the enhanced polylogarithm, a C / Q ( m ) \mathbb {C}/\mathbb {Q}(m) -valued function on the m m -th Bloch group B m ( C ) \mathcal {B}_{m}(\mathbb {C}) , and formulated an enhanced conjecture for I m ( A ) I_{m}(\mathcal {A}) that gives a natural lift of the polylogarithm conjecture for ζ ( m , A ) \zeta (m,\mathcal {A}) to a conjectural equality in C / Q ( m ) \mathbb {C}/\mathbb {Q}(m) . In this article, we define the Shintani L-function of two variables which is naturally regarded as a two-variable analog of the partial zeta function for imaginary quadratic fields. Then we study its analytic properties in order to construct C / Q ( 1 ) \mathbb {C}/\mathbb {Q}(1) -valued invariants Λ i ( 1 − m , A ) \Lambda _{i}(1-m,\mathcal {A}) ( i ∈ { 1 , 2 } i\in \{1,2\} ) for a ray class A \mathcal {A} using the first partial derivative of the Shintani L-function at ( 1 − m , 1 − m ) (1-m,1-m) . From the construction, Λ 1 ( 1 − m , A ) \Lambda _{1}(1-m,\mathcal {A}) and Λ 2 ( 1 − m , A ) \Lambda _{2}(1-m,\mathcal {A}) are complex conjugate invariants that satisfy ζ ′ ( 1 − m , A ) = Λ 1 ( 1 − m , A ) + Λ 2 ( 1 − m , A ) \zeta ’(1-m,\mathcal {A})=\Lambda _{1}(1-m,\mathcal {A})+\Lambda _{2}(1-m,\mathcal {A}) . Then we prove the main theorem of this article about the equality between Zagier and Gangl’s enhanced zeta value I m ( A ) I_{m}(\mathcal {A}) and Λ 1 ( 1 − m , A ) \Lambda _{1}(1-m,\mathcal {A}) , by explicit calculation of the Fourier expansion of the partial derivative of the Shintani L-function. Finally, we formulate the enhanced conjecture for the ray class invariants Λ i ( 1 − m , A ) \Lambda _{i}(1-m,\mathcal {A}) , by which we expand Zagier-Gangl’s original conjecture. We also give several numerical examples to verify the correctness of our enhanced conjecture.