Bug in computing hypergeometric traces

[kedlaya]

Steps To Reproduce

sage: from sage.modular.hypergeometric_motive import HypergeometricData as HGData
sage: H = HGData(alpha_beta=[[1/2,1/3,2/3,1/6,5/6], [0,0,0,0,0]])
sage: H.padic_H_value(6211, 2, -512000)

Expected Behavior

Should return -184336511256141.

Actual Behavior

----> 9 cpdef hgm_coeffs(long long p, int f, int prec, gamma, m, int D,
     10                  gtable, int gtable_prec, bint use_longs):
     11     r"""
File /usr/local/sage/src/sage/modular/hypergeometric_misc.pyx:73, in sage.modular.hypergeometric_misc.hgm_coeffs()
     71     except TypeError:
     72         for r in range(q1):
---> 73             gtab2[r] = gtable[r].lift()
     74 if f == 1:
     75     for r in range(q1):
OverflowError: int too big to convert

Environment

- **OS**: Ubuntu 24.04
- **Sage Version**: 10.4b4

Checklist

• I have searched the existing issues for a bug report that matches the one I want to file, without success.
• I have read the documentation and troubleshoot guide

[kedlaya]

The issue here is that hgm_coeffs() is assuming p ** prec < 2 ** 63 in order to fit each Gauss sum into a long long.

[tscrim]

Fixed by #37911.