random Seifert matrices tested: 4000 (of which |det| = 1: 141); (i), (ii), (iii) hold in all cases.
signature histogram: {-8: 129, -6: 251, -4: 293, -2: 554, 0: 1486, 2: 572, 4: 302, 6: 261, 8: 152}
PYTHONDONTWRITEBYTECODE=1 python3 necessity_check.py 4000  5.42s user 0.03s system 99% cpu 5.459 total
