K. = NumberField(x^2 +1); (4*a+7).norm() 65 mod (65,4) 1
factor(4a+7) (-3a - 2) * (a - 2)
(4*a+7).multiplicative_order(); +Infinity
K.elements_of_norm(65);factor(-8a + 1);K.prime_factors(4a -7);
-8a - 1, 4a - 7, 4a + 7, -8a + 1] (a - 2) * (3a - 2) [Fractional ideal (3a - 2), Fractional ideal (-a - 2)] [Fractional ideal (a - 2), Fractional ideal (3*a - 2)]