identity det(zI-A-BKC) * kappa = det[V(z); [K|I] g^{-1}] verified on 6 random K: True  kappa = 378
n = 9  common denominator of (A,B,C): 378
written ../out/cert_33_nice.ABC.json
A =
   ['-4/21', '-10/7', '4/9', '1', '0', '0', '0', '0', '0']
   ['-103/63', '26/21', '13/27', '0', '1', '0', '0', '0', '0']
   ['103/63', '-5/21', '-4/27', '0', '0', '1', '0', '0', '0']
   ['-35/18', '-4/3', '10/27', '0', '0', '0', '1', '0', '0']
   ['89/63', '65/21', '-53/27', '0', '0', '0', '0', '1', '0']
   ['29/126', '-11/21', '-10/27', '0', '0', '0', '0', '0', '1']
   ['193/126', '5/21', '16/27', '0', '0', '0', '0', '0', '0']
   ['23/21', '12/7', '-8/9', '0', '0', '0', '0', '0', '0']
   ['-26/63', '19/21', '-46/27', '0', '0', '0', '0', '0', '0']
B =
   ['-73/63', '-716/63', '-1475/63']
   ['5066/189', '-1805/189', '1630/189']
   ['-1916/189', '3758/189', '-622/189']
   ['1249/54', '-1022/27', '-287/27']
   ['-2329/189', '6229/189', '7351/189']
   ['-1345/378', '-460/189', '-16/189']
   ['-6731/378', '2248/189', '-2129/189']
   ['-520/63', '2647/63', '664/63']
   ['1888/189', '-118/189', '3296/189']
C =
   ['1', '0', '0', '0', '0', '0', '0', '0', '0']
   ['0', '1', '0', '0', '0', '0', '0', '0', '0']
   ['0', '0', '1', '0', '0', '0', '0', '0', '0']
