On a generalization of R. Chapman's "evil determinant"

Let p be an odd prime and x be an indeterminate. Recently, Z. -W. Sun proposed the following conjecture: + (j-ip) ₀ ₈, ₉ ₏-₁₂=cases (2p) pbₚx-aₚ & if\ p 14, 1 & if\ p 34, cases where aₚ and bₚ are rational numbers related to the fundamental unit and class number of the real quadratic field Q (p). In this paper, we confirm the above conjecture of Sun based on Vsemirnov's decomposition of Chapman's "evil determinant".