  We show that there exist real numbers $\alpha_1,\alpha_2$ linearly
independent over $\mathbb{Z}$ together with 1 such that for every non-zero
integer vector $(m_1,m_2)$ with $m_1\ge 0$ and $m_2\ge 0$ one has
$||m_1\alpha_1+m_2\alpha_2|| \ge 2^{-300} (\max(m_1, m_2))^{-\sigma}$ with
$\sigma = 1.94696^+$.
