Under GRH, the count of primes p ≤ x with Frobenius trace a_{1,p}(A) = t is ≪ x to a power strictly less than 1, yielding that |a_{1,p}(A)| exceeds p to a positive power for almost all p.
Murty, Explicit formulae for the Lang-Trotter conjecture, Rocky Mountain Journal of Mathematics 15, No
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Bounds for the distribution of the Frobenius traces associated to a generic abelian variety
Under GRH, the count of primes p ≤ x with Frobenius trace a_{1,p}(A) = t is ≪ x to a power strictly less than 1, yielding that |a_{1,p}(A)| exceeds p to a positive power for almost all p.