`zeta(s)` and `eta(s)` return `NaN` or `Inf` for every real s < `-170.62`

For example:

```julia
julia> using SpecialFunctions

julia> zeta(-170.0)
-0.0

julia> zeta(-172.0) # true value 0 (trivial zero): https://www.wolframalpha.com/input?i=zeta%28-172%29
NaN

julia> zeta(-180.0) # true value 0 (trivial zero): https://www.wolframalpha.com/input?i=zeta%28-180%29
NaN

julia> zeta(-200.0) # true value 0 (trivial zero): https://www.wolframalpha.com/input?i=zeta%28-200%29
NaN

julia> zeta(-250.0) # true value 0 (trivial zero): https://www.wolframalpha.com/input?i=zeta%28-250%29
NaN

julia> zeta(-175.0) # true value 7.4526910304300896e177: https://www.wolframalpha.com/input?i=zeta%28-175%29
Inf

julia> zeta(-171.0) # true value 1.2819489863517886e172: https://www.wolframalpha.com/input?i=zeta%28-171%29
Inf
```

## Possible Cause (as considered by an AI)

`src/gamma.jl`, `_zeta(s::ComplexOrReal{Float64})`:

```julia
elseif real(s) < 0.5
absim = abs(imag(s))
if abs(real(s)) + absim < 1e-3 # Taylor series for small |s|
...
end
if absim > 12 # amplitude of sinpi(s/2) ≈ exp(imag(s)*π/2)
# avoid overflow/underflow (issue #128)
lg = loggamma(1 - s)
...
else
return zeta(1 - s) * gamma(1 - s) * sinpi(s*0.5) * twoπ^s * invπ
end
```

The `else` branch is the one from issue #128 that "avoids overflow" only when `absim > 12`.
On the real axis `gamma(1 - s)` is `Inf` for all `s < -170.62`, `sinpi(s*0.5)` is `∓0.0` at negative even integers, and `twoπ^s` is a tiny denormal-range factor that would have brought the product back into range had the multiplication been done in log space.

For the second regime, the `@pg_horner` macro (same file) expands to a Horner scheme whose coefficients are `m*(m+1)*…` products; for `m ≈ 5.7e19` the third such product exceeds `floatmax`.

Start in src/gamma.jl at _zeta(s::ComplexOrReal{Float64}) and inspect both the real-axis branch and the @pg_horner expansion. Reproduce the reported zeta values in Julia, then verify the relevant behavior around the gamma overflow threshold and negative even integers. Done means real inputs below -170.62 no longer incorrectly produce NaN or Inf, including the reported trivial zeros and finite values.

Written by the indexing model from the issue text.