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Asheim and Huybrechs considered these polynomials in connection with complex Gaussian quadrature for oscillatory integrals. They observed that the zeros are complex and accumulate as $n \\to \\infty$ near the vertical line $\\textrm{Re}\\, z = \\frac{\\nu \\pi}{2}$. We prove this fact for the case $0 \\leq \\nu \\leq 1/2$ from strong asymptotic formulas that we derive for the polynomials $P_n$ in the complex plane. 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