Face-on representation of the orbital evolution of the best fit of the GJ 1148 system with a time step of 9000 yr. covering a full secular cycle of the planetary eccentricities, which has a period of ≈ 72 500 yr. Ellipses illustrate the planetary orbits with the line connecting the central star (red dot) and the planetary argument of periastron ϖ. The timescale for orbital precession is ≈ 52 000 yr, thus shorter than the secular period of the system. The gray shaded disk represents the optimistic habitable zone aroundthe GJ 1148 M dwarf. Most of the time GJ 1148 b orbits mostly within the HZ.