UNITARY IRRATIONAL CENTRAL CHARGE ON COMPACT g I: $({\rm simply\mbox{-}laced~} g_x)_{\# \,}^{q \ge 2}$

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Following the recent construction of unitary irrational central charge on compact affine g, we begin a series of papers to report further solutions of the Virasoro master equation and related topics in irrational conformal field theory. This paper completes the maximal-symmetric subansatz by obtaining the three-parameter unitary irrational construction [Formula: see text], which contains the known solution [Formula: see text] and involves a root of a root generically.