Sign conjecture for Bloch–Kato Selmer groups

Let $F$ be an imaginary quadratic field, let $\pi$ be a regular algebraic cuspidal automorphic representation of $\mathrm{GL}_n$ over $F$ satisfying $\pi^\vee\simeq\pi^c|\cdot|^{-1}$, and let $\rho_{\pi,\iota}$ be a fixed $p$-adic realization. Write $\varepsilon(\pi)=\varepsilon(0,\pi)\in\{\pm1\}$ for the sign in the functional equation of the completed $L$-function. Sign conjecture. If $\varepsilon(\pi)=-1$, then

$$H^1_f(F,\rho_{\pi,\iota})\neq 0.$$

This is presented as a very weak consequence of the Bloch–Kato conjecture, since an odd order of vanishing should force a nonzero finite cohomology group; the supplied text gives no resolution status.