acb_dirichlet_lerch_phi(1, s, a, prec) is inconsistent with acb_dirichlet_hurwitz(s, a, prec)

[jaganmn]

By definition, $\zeta(s, a) = \Phi(1, s, a)$ and $\zeta(s) = \Phi(1, s, 1)$. acb_dirichlet_lerch_phi(1, s, a, prec) is indeterminate for s with real part less than or equal to 1, but acb_dirichlet_hurwitz(s, a, prec) is not.

#include <flint/flint.h>
#include <flint/acb.h>
#include <flint/acb_dirichlet.h>

int main()
{
	acb_t res, z, s, a;
	slong prec = 53;
	acb_init(res);
	acb_init(z);
	acb_init(s);
	acb_init(a);
	acb_set_d(z,  1.0);
	acb_set_d(s, -1.0);
	acb_set_d(a,  1.0);
	acb_dirichlet_zeta     (res,    s,    prec);
	flint_printf("     zeta: %{acb}\n", res);
	acb_dirichlet_hurwitz  (res,    s, a, prec);
	flint_printf("  hurwitz: %{acb}\n", res);
	acb_dirichlet_lerch_phi(res, z, s, a, prec);
	flint_printf("lerch_phi: %{acb}\n", res);
	acb_clear(res);
	acb_clear(z);
	acb_clear(s);
	acb_clear(a);
	return 0;
}

$ clang -lflint -lmpfr -lgmp test.c -o test.o && ./test.o
     zeta: [-0.0833333 +/- 3.34e-8]
  hurwitz: [-0.0833333 +/- 3.34e-8]
lerch_phi: nan + nan * i

The above seems to come from this part of acb_dirichlet/lerch_phi.c:

    if (acb_is_one(z))
    {
        arb_t one;
        arb_init(one);
        if (arb_gt(acb_realref(s), one))
            acb_dirichlet_hurwitz(res, s, a, prec);
        else
            acb_indeterminate(res);
        arb_clear(one);
        return;
    }

where perhaps the check for arb_gt(acb_realref(s), one) is no longer needed.