The Epstein zeta function of m²+5n²: rightmost zeros, zeros beyond Re s = 1, and where its Weil negativity lives

For Z(s) = Σ′ (m²+5n²)−s: an independent ball-arithmetic enclosure of the supremum of real parts of the zeros, 1.1339063220928…, due to Bombieri and Mueller, with the constants for bad primes removed and the supremum approached from both sides (the counting-function exponent from above, lattice-built zeros reaching 1.0931 from below); a certified census to height 20,002 (54,524 zeros, 7,327 off-line pairs) with exactly three zeros of real part above one below that height, the lowest 1.011049 + 1193.946i; ten further zeros above one certified; the closed form of the prime-power defect (no prime-level defect); and, at all 52 negative off-line pairs, certified negative Weil values carried by the composite channel, with the Euler part certified positive. Explicit zeros above one are not claimed as new pending the journal version of Bombieri–Mueller (2008). Written jointly with Claude, an AI system made by Anthropic, which carried out much of the computation, the derivations and the drafting; the human author is responsible for the content. Not peer reviewed. The package contains the PDF, its LaTeX source, the scripts and result files it cites, and the dated literature-search log behind its priority statements.