We refine the statement of the denominator and evaluation conjectures foraffine Macdonald polynomials proposed by Etingof-Kirillov Jr. and prove thefirst non-trivial cases of these conjectures. Our results provide aq-deformation of the computation of genus 1 conformal blocks via ellipticSelberg integrals by Felder-Stevens-Varchenko. They allow us to give preciseformulations for the affine Macdonald conjectures in the general case which areconsistent with computer computations. Our method applies recent work of the second named author to relate theseconjectures in the case of $U_q(\widehat{\mathfrak{sl}}_2)$ to evaluations ofcertain theta hypergeometric integrals defined by Felder-Varchenko. We thenevaluate the resulting integrals, which may be of independent interest, bywell-chosen applications of the elliptic beta integral introduced bySpiridonov.
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