If an hydrogen atom energy level is in the continuum quantum state....?

If the electron is no longer in a bound state, where the energy levels of the atom are the discrete values E_n = E_1 / n^2 < 0 (E_1 = - alpha^2 m c^2 / 2, with alpha the fine structure constant, m the electron m, and c the speed of light), then it is in a tering state, where the energy can take on any positive value. So, the answer to your question is E > 0.