The tuned domes:

A dome of the modulo-30 wheel is the multiplicative window (p, rp] on the primes. Ittransmits each zero ρ =12 + iγ of ζ(s) with the transfer function rρ − 1 [1]. We combineJ domes with the ratios rj = ej∆ and complex weights cj = wj r−1/2je−iγ∗j∆, where w is awindow. The transfer function then becomes the Fourier transform of the window, centredat a tuning frequency γ∗: the combined domes pass the zero at γ∗ and mute all others. With300 domes (∆ = 0.02, ratios up to e6) and 103 ≤ p ≤ 106, a scan of γ∗shows fourteen peaks,one at each zero up to 61, within 0.014; between the zeros the output stays below 1.3% ofthe maximum. Tuned to a zero, the domes isolate it, with a leak to any other zero of atmost 8% and mostly below 3%. The zero is then read from the phase of the output alone,without a spectrum, with errors between 0.0003 and 0.013 for the first twelve zeros. Thespacing ∆ must be small, since the filter repeats with period 2π/∆. As a companion tool,a matrix pencil applied to the same wheel signals separates the dense zeros that the Fourierspectrum merges: all 26 zeros of L(s, χ15) below 45 and all 52 of L(s, ψ15) with |t| < 45.The work rests on the explicit formula and makes no claim about the Riemann hypothesis.