Can you hear the Euler product? Recovering the multiplicativity defect of the Davenport-Heilbronn function from its zeros

The Davenport-Heilbronn function f has the functional equation of an L-function of conductor 5 but no Euler product. Its von Mangoldt coefficients split as Lambda_f = Lambda Re chi + D, where D, the multiplicativity defect, lives on the integers built from primes congruent to 2 or 3 mod 5, and an exact identity (proved in the companion paper on the defect identity) equates a smoothed sum of D(n) n^(-1/2) to the zeros of f minus the zeros of L(s, chi), with no archimedean term. This paper inverts that identity: from the certified zeros of f below height T (all 1,268 off-line pairs and 25,078 on-line zeros below 20,000, Zenodo doi:10.5281/zenodo.23676415) and the zeros of L(s, chi), it recovers D(n) coefficient by coefficient. With predictions registered before any inversion: (i) every D(n), n <= 60, is recovered to within 1.9e-8 from T = 2000 on (2,029 zeros of f), and the integers off the support come back as |D| <= 1.7e-8; (ii) the resolution law is n* ~ T/13.0 for the direct Landau-type readout with Gaussian windows of width 6/T, and n* ~ T/pi for least squares on the integers (registered T/12.9 and T/pi); (iii) the sign pattern of D(p) on the first k defective primes needs T ~ 2.6 p_k; (iv) the departure of the off-line pairs from the line recovers only 14-17% of the defect, while the pair heights used as zeros carry about one half to three fifths of it plus 13% of the ordinary prime signal (post hoc); (v) the same readout on the zeros of L(s, chi) alone returns a defect <= 8e-9: the Euler product is heard as silence at every composite. Nothing assumes RH or GRH beyond Platt's verification for q = 5. The package contains the paper, its LaTeX source, the registered predictions, the inversion code, logs and results. Written jointly with Claude (Anthropic); the human author is responsible for the content.