A014755 3 and -3 are both 4th powers (one implies other) mod these primes p=1 mod 8.

193, 313, 433, 577, 601, 673, 769, 937, 1201, 1297, 1321, 1657, 1801, 1993, 2137, 2473, 2521, 2593, 2833, 2953, 3169, 3529, 3673, 3697, 3769, 3889, 4057, 4129, 4153, 4297, 4441, 4513, 4561, 4801, 4969, 5113, 5209, 5233, 5281, 5449, 5521