Research Note 27 in the "Geometry of the Critical Line" programme. RN26 identified M₂₁ (λ, m) as the η-stable Evans function. This note reports the first complex-λ zero scan for the m=4 sector and records two methodological findings: raw phase-winding of M₂₁ along contours is unreliable due to the rapid WKB rotation of arg M₂₁, and the exact variational contour integral N = (2πi) ⁻¹ ∮ (∂_λ M₂₁/M₂₁) dλ is the method of choice. For m = 4, 49 Newton-converged, η-stable Evans zeros are located, all in the lower half of the complex λ-plane. Tested upper-half-plane windows are confirmed zero-free by the exact contour integral. The asymptotic zero spacing in √ (Re λ) is numerically consistent with convergence to π/L with L = 2/k. An earlier version reported spacing 2π/L; that was an alternating-zero artifact from incomplete resolution. Chiral conjugation symmetry is verified numerically: 21/21 conjugate pairs pass to machine precision. All zero-count and zero-free statements are restricted to the tested windows and certified contours. No arithmetic interpretation is claimed. Part of a 46-paper open-access programme on the geometry of the Riemann zeta function's critical line, anchored by the SCT 5-Manifold and the cover equation Φ + e^iπ − 1/Φ = 0.
Pavel Kramarenko-Byrd (Sun,) studied this question.