Non-orientable 3-manifolds of complexity up to 7

We classify all closed non-orientable P 2 -irreducible 3-manifolds with complexity up to 7, fixing two mistakes in our previous complexity-up-to-6 classification. We show that there is no such manifold with complexity less than 6, five with complexity 6 (the four flat ones and the filled Gieseking manifold, which is of type Sol), and three with complexity 7 (one manifold of type Sol, and the two manifolds of type H 2 × R with smallest base orbifolds).