Symplectic hypergeometric groups of degree six

Our computations show that there is a total of 40 pairs degree six coprime polynomials f,g where f(x)=(x?1)6, g product cyclotomic polynomials, g(0)=1 and form primitive pair. The aim this article to determine whether the corresponding symplectic hypergeometric groups with maximally unipotent monodromy follow same dichotomy between arithmeticity thinness holds for 14 four f(x)=(x?1)4 as described above. As result we prove at least 18 these are arithmetic in Sp6. In addition, extend our search all find 458 (up scalar shifts) such groups. For 211 them, absolute values leading coefficients difference f?g most 2 follows from Singh Venkataramana, while one more group Detinko, Flannery Hulpke. article, 163 remaining 246