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We classify finite irreducible conformal modules over a class of infinite Lieconformal algebras ${\frak {B}}(p)$ of Block type, where $p$ is a nonzerocomplex number. In particular, we obtain that a finite irreducible conformalmodule over ${\frak {B}}(p)$ may be a nontrivial extension of a finiteconformal module over ${\frak {Vir}}$ if $p=-1$, where ${\frak {Vir}}$ is aVirasoro conformal subalgebra of ${\frak {B}}(p)$. As a byproduct, we alsoobtain the classification of finite irreducible conformal modules over a seriesof finite Lie conformal algebras ${\frak b}(n)$ for $n\ge1$.

Classification of finite irreducible conformal modules over a class of Lie conformal algebras of Block type