Large gap between nontrivial zeros (awaiting review)

The degree 4 L-function with conductor 1 and spectral parameters approximately $\pm 4.7209 i, \pm 12.4687 i$ has the surprising property that its first nontrivial zeros have imaginary part $\pm 14.496\ldots$.

This is surprising because the Riemann zeta function has its first zeros with imaginary part $\pm 14.134\ldots$, which is a gap of $28.269\ldots$. It had been proven [MR:1890648] that the Riemann zeta function has the largest gap among L-functions with real spectral parameters. It had been (mistakenly) thought that the zeta function should have the largest gap among all L-functions, but this example illustrates how the trivial zeros, which come from the spectral parameters, can create a larger gap between the nontrivial zeros.