Analytic class number formula

For a number field of signature $(r_1,r_2)$, roots-of-unity count $w_K$, regulator $R_K$, class number $h_K$, and discriminant $d_K$,

For an imaginary quadratic field of fundamental discriminant $D<-4$,Equivalent finite character-sum forms follow by evaluating the odd quadratic Dirichlet L-function at one.