The Fano plane is a tiny geometry with seven points and seven lines. Every line contains three points, and every pair of points lies on exactly one line. But its tensor spectrum is surprisingly rich. This candidate computes a characteristic polynomial of degree four hundred and forty-eight, with nineteen distinct eigenvalues. This is not the spectrum of an ordinary incidence matrix. It comes from quadratic tensor eigenvalue equations. Explicit vectors show that each listed value occurs. An exact algebraic elimination calculation supplies completeness and multiplicities. Two features stand out. The real eigenvalue two has no real eigenvector. And two complex eigenvalues have a whole smooth curve of projective eigenvectors, of degree eight and genus three. The package makes these claims inspectable through coefficients, modular residues, source programs and characteristic-zero certificates. Routine replay checks the stored arithmetic, runs symbolic geometry and makes fresh determinant evaluations. It does not repeat the entire original thirty-prime computation. A different determinant algorithm gives additional evidence, but shares some utilities, so it is not an independent implementation of the whole process. The potential value is a precise test case for spectral hypergraph theory and computer algebra. Historical priority remains uncertain, and the work has not received unaffiliated specialist validation or formal verification. This is an unrefereed Evidence Press candidate. The full paper and evidence are linked on the release page. This is an AI-generated voice summary, not additional mathematical evidence.