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In general, assuming the strong form of the Riemann Hypothesis, if 0 < a, b < k are integers, gcd(a, k) = gcd(b, k) = 1, a is a quadratic residue and b is a quadratic nonresidue mod k, then Pi(k,b)(n) > Pi(k,a)(n) occurs more often than not. This phenomenon is called "Chebyshev's bias". (See Wikipedia link and especially the links in A007350.) [Edited by Peter Munn, Nov 19 2023]

Define the "Chebyshev's bias sequence mod k" to be sequence q(n), where q(n) = Sum_{b is a quadratic nonresidue mod k, gcd(b, k) = 1} Pi(k,b)(n) - (r-1)*(Sum_{a is a quadratic residue mod k, gcd(a, k) = 1} Pi(k,a)(n)), r is the number of solutions to x^2 == 1 (mod n), then this sequence is the "Chebyshev's bias sequence mod 8". Also the initial terms are nonnegative integers, a(n) is negative for some n ~ 10^28.127. See page 21 of the paper in Journal of Number Theory in the Links section below.