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: [x+(j-i/p)]0≤ i,j≤ p-1/2=cases (2/p)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".