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We study the transition from concentration to deconcentration of roots by considering coefficients with tails behaving like $L({\\log}|t|)({\\log}|t|)^{-\\alpha}$ as $t\\to\\infty$, where $\\alpha\\geq0$, and $L$ is a slowly varying function. 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We study the transition from concentration to deconcentration of roots by considering coefficients with tails behaving like $L({\\log}|t|)({\\log}|t|)^{-\\alpha}$ as $t\\to\\infty$, where $\\alpha\\geq0$, and $L$ is a slowly varying function. 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