Generalized Grothendieck period conjecture for 1-motives

Let $M$ be a 1-motive defined over a sub-field $K$ of $\mathbb{C}$. Its periods are the coefficients of the comparison isomorphism between its De Rham and Hodge realizations, and let $\mathcal{G}_{\mathrm{mot}}(M)$ denote its motivic Galois group. Generalized Grothendieck period conjecture for 1-motives. One should have

$$\operatorname{tr.deg}_{\mathbb{Q}} K(\operatorname{periods}(M))\geq \dim \mathcal{G}_{\mathrm{mot}}(M),$$

where $K(\operatorname{periods}(M))$ is the field generated over $K$ by the periods of $M$. This is the 1-motivic specialization of André's generalized form of Grothendieck's period conjecture; its status is not resolved in the supplied source.