A family of hypergeometric motives can be determined by a coprime pair of products of cyclotomic polynomials, each product having the same degree d. For each t not 0, 1, or infinity, one can then (following Katz) associate a motive M_t to this data. At each prime p, one obtains an Euler factor by considering the monodromy action (over Q_p) on the solution space of the associated hypergeometric differential equation. For good primes, this can be explicitly calculated by a trace formula (again see Katz). There are three kinds of bad primes. The wild primes are those which divide one of the indices of the cyclotomic polynomials. The tame primes are with v_p(t) nonzero, and the "multiplicative" primes are those with v_p(t – 1) nonzero. These last are the easiest to understand, in the complex case they correspond to the fact that there are (d – 1) independent holomorphic solutions about t = 1. Indeed, one can consider the formal motive M₁ at t = 1 – as an example, in the case of Φ₅ and Φ₁⁴, one obtains the weight 4 modular form of level 25.

We report specifically on a "database" of t = 1 degenerations, including all choices (about 1500 total) of cyclotomic data up through degree 6. In each case, we are able to numerically determine the wild Euler factors and verify the functional equation of the L-function to (say) 15 digits of precision. Of additional interest is the fact that approximately half the relevant (odd motivic weight) examples of even parity appear to have analytic rank 2.