# A list of promising (a, b, c) triples, where the full 5-parameters are (a, b,
# c, 0, 0).
HopefulZ3 := [[0, 0, 0], [1, 1, 0], [2, 2, 0], [1/4, -1, -1/14], [-1/4, -1, -1/14], [0, -2, -1/14], [-1/7, -2, -1/
14], [-1/4, -2, -1/14], [-1/2, -2, -1/14], [1, -2, -1/14], [2, -2, -1/14], [1/2, -2, -1/14], [1/4, -2,
-1/14], [1/7, -2, -1/14], [2/7, -2, -1/14], [1/14, -2, -1/14], [-1/14, -1, -1/7], [-1/2, -1, -1/7], [1
/2, -1, -1/7], [1/14, -1, -1/7], [0, -2, -1/7], [1/14, -2, -1/7], [1/7, -2, -1/7], [2/7, -2, -1/7], [1
/2, -2, -1/7], [1, -2, -1/7], [2, -2, -1/7], [-1/2, -2, -1/7], [-2/7, -2, -1/7], [-1/14, -2, -1/7], [0
, -1, -2/13], [2/13, -1, -2/13], [1/2, -1, -2/13], [2, -1, -2/13], [-1/2, -1, -2/13], [0, -2, -2/13],
[-1/13, -2, -2/13], [-1/2, -2, -2/13], [1, -2, -2/13], [2, -2, -2/13], [1/2, -2, -2/13], [1/13, -2, -2
/13], [2/13, -2, -2/13], [-1/2, -1, -1/13], [1/2, -1, -1/13], [0, -2, -1/13], [2/13, -2, -1/13], [1/13
, -2, -1/13], [1/2, -2, -1/13], [1, -2, -1/13], [2, -2, -1/13], [-1/2, -2, -1/13], [-2/13, -2, -1/13],
[1/8, -1, -1/12], [-1/8, -1, -1/12], [0, -2, -1/12], [-1/6, -2, -1/12], [-1/8, -2, -1/12], [-1/4, -2,
-1/12], [-1/3, -2, -1/12], [-1/2, -2, -1/12], [-2/3, -2, -1/12], [1, -2, -1/12], [2, -2, -1/12], [1/2,
-2, -1/12], [1/3, -2, -1/12], [2/3, -2, -1/12], [1/4, -2, -1/12], [1/6, -2, -1/12], [1/8, -2, -1/12],
[1/12, -2, -1/12], [-1/12, -1, -1/6], [-2/9, -1, -1/6], [-1/9, -1, -1/6], [-1/4, -1, -1/6], [1/4, -1,
-1/6], [1/9, -1, -1/6], [2/9, -1, -1/6], [1/12, -1, -1/6], [0, -2, -1/6], [1/12, -2, -1/6], [1/6, -2,
-1/6], [2/9, -2, -1/6], [1/9, -2, -1/6], [1/4, -2, -1/6], [1/3, -2, -1/6], [1/2, -2, -1/6], [2/3, -2,
-1/6], [1, -2, -1/6], [2, -2, -1/6], [-1/2, -2, -1/6], [-1/3, -2, -1/6], [-2/3, -2, -1/6], [-1/4, -2,
-1/6], [-1/9, -2, -1/6], [-2/9, -2, -1/6], [-1/12, -2, -1/6], [0, -1, -2/11], [2/11, -1, -2/11], [1/2,
-1, -2/11], [2, -1, -2/11], [-1/2, -1, -2/11], [0, -2, -2/11], [-1/11, -2, -2/11], [-1/2, -2, -2/11],
[1, -2, -2/11], [2, -2, -2/11], [1/2, -2, -2/11], [1/11, -2, -2/11], [2/11, -2, -2/11], [-1/2, -1, -1/
11], [1/2, -1, -1/11], [0, -2, -1/11], [2/11, -2, -1/11], [1/11, -2, -1/11], [1/2, -2, -1/11], [1, -2,
-1/11], [-1/2, -2, -1/11], [-2/11, -2, -1/11], [1/4, -1, -1/10], [-1/4, -1, -1/10], [0, -2, -1/10], [-\
1/5, -2, -1/10], [-1/4, -2, -1/10], [-2/5, -2, -1/10], [-1/2, -2, -1/10], [1, -2, -1/10], [2, -2, -1/
10], [1/2, -2, -1/10], [1/4, -2, -1/10], [1/5, -2, -1/10], [2/5, -2, -1/10], [1/10, -2, -1/10], [-1/10
, -1, -1/5], [-1/2, -1, -1/5], [1/2, -1, -1/5], [1/10, -1, -1/5], [0, -2, -1/5], [1/10, -2, -1/5], [1/
5, -2, -1/5], [2/5, -2, -1/5], [1/2, -2, -1/5], [2, -2, -1/5], [-1/2, -2, -1/5], [-2/5, -2, -1/5], [-1
/10, -2, -1/5], [0, -1, -2/9], [1/6, -1, -2/9], [2/9, -1, -2/9], [1/2, -1, -2/9], [2/3, -1, -2/9], [2,
-1, -2/9], [-1/2, -1, -2/9], [-2/3, -1, -2/9], [-1/6, -1, -2/9], [0, -2, -2/9], [-1/6, -2, -2/9], [-1/
9, -2, -2/9], [-1/3, -2, -2/9], [-1/2, -2, -2/9], [-2/3, -2, -2/9], [1, -2, -2/9], [2, -2, -2/9], [1/2
, -2, -2/9], [1/3, -2, -2/9], [2/3, -2, -2/9], [1/6, -2, -2/9], [1/9, -2, -2/9], [2/9, -2, -2/9], [-1/
6, -1, -1/9], [-1/2, -1, -1/9], [1/2, -1, -1/9], [1/6, -1, -1/9], [0, -2, -1/9], [1/6, -2, -1/9], [2/9
, -2, -1/9], [1/9, -2, -1/9], [1/3, -2, -1/9], [1/2, -2, -1/9], [2/3, -2, -1/9], [1, -2, -1/9], [2, -2
, -1/9], [-1/2, -2, -1/9], [-1/3, -2, -1/9], [-2/3, -2, -1/9], [-1/6, -2, -1/9], [-2/9, -2, -1/9], [1/
12, -1, -1/8], [-1/12, -1, -1/8], [0, -2, -1/8], [-1/12, -2, -1/8], [-1/4, -2, -1/8], [-1/2, -2, -1/8]
, [1, -2, -1/8], [2, -2, -1/8], [1/2, -2, -1/8], [1/4, -2, -1/8], [1/8, -2, -1/8], [1/12, -2, -1/8], [
-1/14, -1, -1/4], [-1/12, -1, -1/4], [-1/6, -1, -1/4], [-1/10, -1, -1/4], [-1/8, -1, -1/4], [1/6, -1,
-1/4], [1/8, -1, -1/4], [1/10, -1, -1/4], [1/12, -1, -1/4], [1/14, -1, -1/4], [0, -2, -1/4], [1/14, -2
, -1/4], [1/12, -2, -1/4], [1/6, -2, -1/4], [1/10, -2, -1/4], [1/8, -2, -1/4], [1/4, -2, -1/4], [1/2,
-2, -1/4], [1, -2, -1/4], [2, -2, -1/4], [-1/2, -2, -1/4], [-1/6, -2, -1/4], [-1/8, -2, -1/4], [-1/10,
-2, -1/4], [-1/12, -2, -1/4], [-1/14, -2, -1/4], [0, -1, -2/7], [1/14, -1, -2/7], [2/7, -1, -2/7], [1/
2, -1, -2/7], [2, -1, -2/7], [-1/2, -1, -2/7], [-1/14, -1, -2/7], [0, -2, -2/7], [-1/14, -2, -2/7], [-\
1/7, -2, -2/7], [-1/2, -2, -2/7], [1, -2, -2/7], [2, -2, -2/7], [1/2, -2, -2/7], [1/7, -2, -2/7], [2/7
, -2, -2/7], [1/14, -2, -2/7], [-1/12, -1, -1/3], [-1/6, -1, -1/3], [-2/9, -1, -1/3], [-1/9, -1, -1/3]
, [-1/2, -1, -1/3], [1/2, -1, -1/3], [1/6, -1, -1/3], [1/9, -1, -1/3], [2/9, -1, -1/3], [1/12, -1, -1/
3], [0, -2, -1/3], [1/12, -2, -1/3], [1/6, -2, -1/3], [2/9, -2, -1/3], [1/9, -2, -1/3], [1/3, -2, -1/3
], [1/2, -2, -1/3], [1, -2, -1/3], [2, -2, -1/3], [-1/2, -2, -1/3], [-1/6, -2, -1/3], [-1/9, -2, -1/3]
, [-2/9, -2, -1/3], [-1/12, -2, -1/3], [2/3, 1/3, -1/3], [-1/3, 1/3, -1/3], [0, -1, -2/5], [1/10, -1,
-2/5], [2/5, -1, -2/5], [1/2, -1, -2/5], [2, -1, -2/5], [-1/2, -1, -2/5], [-1/10, -1, -2/5], [0, -2, -\
2/5], [-1/10, -2, -2/5], [-1/5, -2, -2/5], [-1/2, -2, -2/5], [1, -2, -2/5], [2, -2, -2/5], [1/2, -2, -\
2/5], [1/5, -2, -2/5], [2/5, -2, -2/5], [1/10, -2, -2/5], [-1/14, -1, -1/2], [-1/7, -1, -1/2], [-2/13,
-1, -1/2], [-1/13, -1, -1/2], [-1/12, -1, -1/2], [-1/6, -1, -1/2], [-2/11, -1, -1/2], [-1/11, -1, -1/2
], [-1/10, -1, -1/2], [-1/5, -1, -1/2], [-2/9, -1, -1/2], [-1/9, -1, -1/2], [-1/8, -1, -1/2], [-2/7, -\
1, -1/2], [-1/3, -1, -1/2], [-2/5, -1, -1/2], [-2/3, -1, -1/2], [1/3, -1, -1/2], [2/3, -1, -1/2], [1/4
, -1, -1/2], [1/5, -1, -1/2], [2/5, -1, -1/2], [1/6, -1, -1/2], [1/7, -1, -1/2], [2/7, -1, -1/2], [1/8
, -1, -1/2], [1/9, -1, -1/2], [2/9, -1, -1/2], [1/10, -1, -1/2], [1/11, -1, -1/2], [2/11, -1, -1/2], [
1/12, -1, -1/2], [1/13, -1, -1/2], [2/13, -1, -1/2], [1/14, -1, -1/2], [0, -2, -1/2], [1/14, -2, -1/2]
, [1/7, -2, -1/2], [2/13, -2, -1/2], [1/13, -2, -1/2], [1/12, -2, -1/2], [1/6, -2, -1/2], [2/11, -2, -\
1/2], [1/11, -2, -1/2], [1/10, -2, -1/2], [1/5, -2, -1/2], [2/9, -2, -1/2], [1/9, -2, -1/2], [1/8, -2,
-1/2], [1/4, -2, -1/2], [2/7, -2, -1/2], [1/3, -2, -1/2], [2/5, -2, -1/2], [2/3, -2, -1/2], [1, -2, -1
/2], [-1/3, -2, -1/2], [-2/3, -2, -1/2], [-1/4, -2, -1/2], [-1/5, -2, -1/2], [-2/5, -2, -1/2], [-1/6,
-2, -1/2], [-1/7, -2, -1/2], [-2/7, -2, -1/2], [-1/8, -2, -1/2], [-1/9, -2, -1/2], [-2/9, -2, -1/2], [
-1/10, -2, -1/2], [-1/11, -2, -1/2], [-2/11, -2, -1/2], [-1/12, -2, -1/2], [-1/13, -2, -1/2], [-2/13,
-2, -1/2], [-1/14, -2, -1/2], [1/2, 1/2, -1/2], [1/3, 2/3, -2/3], [-2/3, 2/3, -2/3], [0, -1, -2/3], [1
/12, -1, -2/3], [1/6, -1, -2/3], [2/9, -1, -2/3], [1/2, -1, -2/3], [2/3, -1, -2/3], [2, -1, -2/3], [-1
/2, -1, -2/3], [-1/6, -1, -2/3], [-1/9, -1, -2/3], [-2/9, -1, -2/3], [-1/12, -1, -2/3], [0, -2, -2/3],
[-1/12, -2, -2/3], [-1/6, -2, -2/3], [-2/9, -2, -2/3], [-1/9, -2, -2/3], [-1/2, -2, -2/3], [1, -2, -2/
3], [2, -2, -2/3], [1/2, -2, -2/3], [2/3, -2, -2/3], [1/6, -2, -2/3], [1/9, -2, -2/3], [2/9, -2, -2/3]
, [1/12, -2, -2/3], [0, 0, 1], [1, 0, 1], [-1/2, 1, 1], [1, 1, 1], [2, 1, 1], [1/2, 2, 1], [2, 2, 1],
[-1/2, 2, 1], [1/14, -1, 1], [1/7, -1, 1], [2/13, -1, 1], [1/13, -1, 1], [1/12, -1, 1], [1/6, -1, 1],
[2/11, -1, 1], [1/11, -1, 1], [1/10, -1, 1], [1/5, -1, 1], [2/9, -1, 1], [1/9, -1, 1], [1/8, -1, 1], [
1/4, -1, 1], [2/7, -1, 1], [1/3, -1, 1], [2/5, -1, 1], [1/2, -1, 1], [2/3, -1, 1], [-1/2, -1, 1], [-1/
3, -1, 1], [-2/3, -1, 1], [-1/4, -1, 1], [-1/5, -1, 1], [-2/5, -1, 1], [-1/6, -1, 1], [-1/7, -1, 1], [
-2/7, -1, 1], [-1/8, -1, 1], [-1/9, -1, 1], [-2/9, -1, 1], [-1/10, -1, 1], [-1/11, -1, 1], [-2/11, -1,
1], [-1/12, -1, 1], [-1/13, -1, 1], [-2/13, -1, 1], [-1/14, -1, 1], [2, -1/2, 1], [0, 0, 2], [1, 0, 2]
, [2, 0, 2], [2, -1/2, 2], [0, -1, 2], [-1/14, -1, 2], [-1/7, -1, 2], [-2/13, -1, 2], [-1/13, -1, 2],
[-1/12, -1, 2], [-1/6, -1, 2], [-2/11, -1, 2], [-1/11, -1, 2], [-1/10, -1, 2], [-1/5, -1, 2], [-2/9, -\
1, 2], [-1/9, -1, 2], [-1/8, -1, 2], [-1/4, -1, 2], [-2/7, -1, 2], [-1/3, -1, 2], [-2/5, -1, 2], [-1/2
, -1, 2], [-2/3, -1, 2], [1/2, -1, 2], [1/3, -1, 2], [2/3, -1, 2], [1/4, -1, 2], [1/5, -1, 2], [2/5, -\
1, 2], [1/6, -1, 2], [1/7, -1, 2], [2/7, -1, 2], [1/8, -1, 2], [1/9, -1, 2], [2/9, -1, 2], [1/10, -1,
2], [1/11, -1, 2], [2/11, -1, 2], [1/12, -1, 2], [1/13, -1, 2], [2/13, -1, 2], [1/14, -1, 2], [0, -2,
2], [1/14, -2, 2], [1/7, -2, 2], [2/13, -2, 2], [1/13, -2, 2], [1/12, -2, 2], [1/6, -2, 2], [2/11, -2,
2], [1/11, -2, 2], [1/10, -2, 2], [1/5, -2, 2], [2/9, -2, 2], [1/9, -2, 2], [1/8, -2, 2], [1/4, -2, 2]
, [2/7, -2, 2], [1/3, -2, 2], [2/5, -2, 2], [1/2, -2, 2], [2/3, -2, 2], [-1/2, -2, 2], [-1/3, -2, 2],
[-2/3, -2, 2], [-1/4, -2, 2], [-1/5, -2, 2], [-2/5, -2, 2], [-1/6, -2, 2], [-1/7, -2, 2], [-2/7, -2, 2
], [-1/8, -2, 2], [-1/9, -2, 2], [-2/9, -2, 2], [-1/10, -2, 2], [-1/11, -2, 2], [-2/11, -2, 2], [-1/12
, -2, 2], [-1/13, -2, 2], [-2/13, -2, 2], [-1/14, -2, 2], [1, 1, 2], [2, 1, 2], [-1/2, 1, 2], [-1/2, 2
, 2], [2, 2, 2], [1/2, 2, 2], [-1/2, -1/2, 1/2], [1/2, -1/2, 1/2], [-1/14, -1, 1/2], [-1/7, -1, 1/2],
[-2/13, -1, 1/2], [-1/13, -1, 1/2], [-1/12, -1, 1/2], [-1/6, -1, 1/2], [-2/11, -1, 1/2], [-1/11, -1, 1
/2], [-1/10, -1, 1/2], [-1/5, -1, 1/2], [-2/9, -1, 1/2], [-1/9, -1, 1/2], [-1/8, -1, 1/2], [-1/4, -1,
1/2], [-2/7, -1, 1/2], [-1/3, -1, 1/2], [-2/5, -1, 1/2], [-2/3, -1, 1/2], [1/3, -1, 1/2], [2/3, -1, 1/
2], [1/4, -1, 1/2], [1/5, -1, 1/2], [2/5, -1, 1/2], [1/6, -1, 1/2], [1/7, -1, 1/2], [2/7, -1, 1/2], [1
/8, -1, 1/2], [1/9, -1, 1/2], [2/9, -1, 1/2], [1/10, -1, 1/2], [1/11, -1, 1/2], [2/11, -1, 1/2], [1/12
, -1, 1/2], [1/13, -1, 1/2], [2/13, -1, 1/2], [1/14, -1, 1/2], [1/14, -2, 1/2], [1/7, -2, 1/2], [2/13,
-2, 1/2], [1/13, -2, 1/2], [1/12, -2, 1/2], [1/6, -2, 1/2], [2/11, -2, 1/2], [1/11, -2, 1/2], [1/10, -\
2, 1/2], [1/5, -2, 1/2], [2/9, -2, 1/2], [1/9, -2, 1/2], [1/8, -2, 1/2], [1/4, -2, 1/2], [2/7, -2, 1/2
], [1/3, -2, 1/2], [2/5, -2, 1/2], [2/3, -2, 1/2], [1, -2, 1/2], [-1/3, -2, 1/2], [-1/4, -2, 1/2], [-1
/5, -2, 1/2], [-2/5, -2, 1/2], [-1/6, -2, 1/2], [-1/7, -2, 1/2], [-2/7, -2, 1/2], [-1/8, -2, 1/2], [-1
/9, -2, 1/2], [-2/9, -2, 1/2], [-1/10, -2, 1/2], [-1/11, -2, 1/2], [-2/11, -2, 1/2], [-1/12, -2, 1/2],
[-1/13, -2, 1/2], [-2/13, -2, 1/2], [-1/14, -2, 1/2], [1/2, 1/2, 1/2], [1/3, 2/3, 1/3], [-2/3, 2/3, 1/
3], [1/12, -1, 1/3], [1/6, -1, 1/3], [2/9, -1, 1/3], [1/9, -1, 1/3], [1/2, -1, 1/3], [-1/2, -1, 1/3],
[-1/6, -1, 1/3], [-1/9, -1, 1/3], [-2/9, -1, 1/3], [-1/12, -1, 1/3], [-1/12, -2, 1/3], [-1/6, -2, 1/3]
, [-2/9, -2, 1/3], [-1/9, -2, 1/3], [-1/3, -2, 1/3], [-1/2, -2, 1/3], [2, -2, 1/3], [1/2, -2, 1/3], [2
/3, -2, 1/3], [1/6, -2, 1/3], [1/9, -2, 1/3], [2/9, -2, 1/3], [1/12, -2, 1/3], [1/3, -1/3, 1/3], [-2/3
, -1/3, 1/3], [2/3, -2/3, 2/3], [-1/3, -2/3, 2/3], [0, -1, 2/3], [-1/12, -1, 2/3], [-1/6, -1, 2/3], [-\
2/9, -1, 2/3], [-1/9, -1, 2/3], [-1/2, -1, 2/3], [-2/3, -1, 2/3], [2, -1, 2/3], [1/2, -1, 2/3], [1/6,
-1, 2/3], [1/9, -1, 2/3], [2/9, -1, 2/3], [1/12, -1, 2/3], [0, -2, 2/3], [1/12, -2, 2/3], [1/6, -2, 2/
3], [2/9, -2, 2/3], [1/9, -2, 2/3], [1/3, -2, 2/3], [1/2, -2, 2/3], [2, -2, 2/3], [-1/2, -2, 2/3], [-1
/6, -2, 2/3], [-1/9, -2, 2/3], [-2/9, -2, 2/3], [-1/12, -2, 2/3], [2/3, 1/3, 2/3], [-1/3, 1/3, 2/3], [
-1/14, -1, 1/4], [-1/12, -1, 1/4], [-1/6, -1, 1/4], [-1/10, -1, 1/4], [-1/8, -1, 1/4], [1/6, -1, 1/4],
[1/8, -1, 1/4], [1/10, -1, 1/4], [1/12, -1, 1/4], [1/14, -1, 1/4], [0, -2, 1/4], [1/14, -2, 1/4], [1/
12, -2, 1/4], [1/6, -2, 1/4], [1/10, -2, 1/4], [1/8, -2, 1/4], [1/2, -2, 1/4], [-1/2, -2, 1/4], [-1/4,
-2, 1/4], [-1/6, -2, 1/4], [-1/8, -2, 1/4], [-1/10, -2, 1/4], [-1/12, -2, 1/4], [-1/14, -2, 1/4], [1/
10, -1, 1/5], [1/2, -1, 1/5], [-1/2, -1, 1/5], [-1/10, -1, 1/5], [0, -2, 1/5], [-1/10, -2, 1/5], [-1/5
, -2, 1/5], [-2/5, -2, 1/5], [-1/2, -2, 1/5], [1, -2, 1/5], [1/2, -2, 1/5], [2/5, -2, 1/5], [1/10, -2,
1/5], [0, -1, 2/5], [-1/10, -1, 2/5], [-2/5, -1, 2/5], [-1/2, -1, 2/5], [2, -1, 2/5], [1/2, -1, 2/5],
[1/10, -1, 2/5], [0, -2, 2/5], [1/10, -2, 2/5], [1/5, -2, 2/5], [1/2, -2, 2/5], [1, -2, 2/5], [2, -2,
2/5], [-1/2, -2, 2/5], [-1/5, -2, 2/5], [-2/5, -2, 2/5], [-1/10, -2, 2/5], [-1/12, -1, 1/6], [-2/9, -1
, 1/6], [-1/9, -1, 1/6], [-1/4, -1, 1/6], [1/4, -1, 1/6], [1/9, -1, 1/6], [2/9, -1, 1/6], [1/12, -1, 1
/6], [0, -2, 1/6], [1/12, -2, 1/6], [2/9, -2, 1/6], [1/9, -2, 1/6], [1/4, -2, 1/6], [1/3, -2, 1/6], [1
/2, -2, 1/6], [2/3, -2, 1/6], [1, -2, 1/6], [2, -2, 1/6], [-1/2, -2, 1/6], [-1/3, -2, 1/6], [-2/3, -2,
1/6], [-1/4, -2, 1/6], [-1/6, -2, 1/6], [-1/9, -2, 1/6], [-2/9, -2, 1/6], [-1/12, -2, 1/6], [1/14, -1,
1/7], [1/2, -1, 1/7], [-1/2, -1, 1/7], [-1/14, -1, 1/7], [0, -2, 1/7], [-1/14, -2, 1/7], [-1/7, -2, 1/
7], [-2/7, -2, 1/7], [-1/2, -2, 1/7], [1, -2, 1/7], [2, -2, 1/7], [1/2, -2, 1/7], [2/7, -2, 1/7], [1/
14, -2, 1/7], [0, -1, 2/7], [-1/14, -1, 2/7], [-2/7, -1, 2/7], [-1/2, -1, 2/7], [2, -1, 2/7], [1/2, -1
, 2/7], [1/14, -1, 2/7], [0, -2, 2/7], [1/14, -2, 2/7], [1/7, -2, 2/7], [1/2, -2, 2/7], [1, -2, 2/7],
[2, -2, 2/7], [-1/2, -2, 2/7], [-1/7, -2, 2/7], [-2/7, -2, 2/7], [-1/14, -2, 2/7], [-1/12, -1, 1/8], [
1/12, -1, 1/8], [0, -2, 1/8], [1/12, -2, 1/8], [1/4, -2, 1/8], [1/2, -2, 1/8], [1, -2, 1/8], [2, -2, 1
/8], [-1/2, -2, 1/8], [-1/4, -2, 1/8], [-1/8, -2, 1/8], [-1/12, -2, 1/8], [1/6, -1, 1/9], [1/2, -1, 1/
9], [-1/2, -1, 1/9], [-1/6, -1, 1/9], [0, -2, 1/9], [-1/6, -2, 1/9], [-2/9, -2, 1/9], [-1/9, -2, 1/9],
[-1/3, -2, 1/9], [-1/2, -2, 1/9], [-2/3, -2, 1/9], [1, -2, 1/9], [2, -2, 1/9], [1/2, -2, 1/9], [1/3, -\
2, 1/9], [2/3, -2, 1/9], [1/6, -2, 1/9], [2/9, -2, 1/9], [0, -1, 2/9], [-1/6, -1, 2/9], [-2/9, -1, 2/9
], [-1/2, -1, 2/9], [-2/3, -1, 2/9], [2, -1, 2/9], [1/2, -1, 2/9], [2/3, -1, 2/9], [1/6, -1, 2/9], [0,
-2, 2/9], [1/6, -2, 2/9], [1/9, -2, 2/9], [1/3, -2, 2/9], [1/2, -2, 2/9], [2/3, -2, 2/9], [1, -2, 2/9]
, [2, -2, 2/9], [-1/2, -2, 2/9], [-1/3, -2, 2/9], [-2/3, -2, 2/9], [-1/6, -2, 2/9], [-1/9, -2, 2/9], [
-2/9, -2, 2/9], [-1/4, -1, 1/10], [1/4, -1, 1/10], [0, -2, 1/10], [1/5, -2, 1/10], [1/4, -2, 1/10], [2
/5, -2, 1/10], [1/2, -2, 1/10], [1, -2, 1/10], [2, -2, 1/10], [-1/2, -2, 1/10], [-1/4, -2, 1/10], [-1/
5, -2, 1/10], [-2/5, -2, 1/10], [-1/10, -2, 1/10], [1/2, -1, 1/11], [-1/2, -1, 1/11], [0, -2, 1/11], [
-2/11, -2, 1/11], [-1/11, -2, 1/11], [-1/2, -2, 1/11], [1, -2, 1/11], [2, -2, 1/11], [1/2, -2, 1/11],
[2/11, -2, 1/11], [0, -1, 2/11], [-2/11, -1, 2/11], [-1/2, -1, 2/11], [2, -1, 2/11], [1/2, -1, 2/11],
[0, -2, 2/11], [1/11, -2, 2/11], [1/2, -2, 2/11], [1, -2, 2/11], [2, -2, 2/11], [-1/2, -2, 2/11], [-1/
11, -2, 2/11], [-2/11, -2, 2/11], [-1/8, -1, 1/12], [1/8, -1, 1/12], [0, -2, 1/12], [1/6, -2, 1/12], [
1/8, -2, 1/12], [1/4, -2, 1/12], [1/3, -2, 1/12], [1/2, -2, 1/12], [2/3, -2, 1/12], [1, -2, 1/12], [2,
-2, 1/12], [-1/2, -2, 1/12], [-1/3, -2, 1/12], [-2/3, -2, 1/12], [-1/4, -2, 1/12], [-1/6, -2, 1/12], [
-1/8, -2, 1/12], [-1/12, -2, 1/12], [1/2, -1, 1/13], [-1/2, -1, 1/13], [0, -2, 1/13], [-2/13, -2, 1/13
], [-1/13, -2, 1/13], [-1/2, -2, 1/13], [1, -2, 1/13], [2, -2, 1/13], [1/2, -2, 1/13], [2/13, -2, 1/13
], [0, -1, 2/13], [-2/13, -1, 2/13], [-1/2, -1, 2/13], [2, -1, 2/13], [1/2, -1, 2/13], [0, -2, 2/13],
[1/13, -2, 2/13], [1/2, -2, 2/13], [1, -2, 2/13], [2, -2, 2/13], [-1/2, -2, 2/13], [-1/13, -2, 2/13],
[-2/13, -2, 2/13], [-1/4, -1, 1/14], [1/4, -1, 1/14], [0, -2, 1/14], [1/7, -2, 1/14], [1/4, -2, 1/14],
[2/7, -2, 1/14], [1/2, -2, 1/14], [1, -2, 1/14], [2, -2, 1/14], [-1/2, -2, 1/14], [-1/4, -2, 1/14], [-\
1/7, -2, 1/14], [-2/7, -2, 1/14], [-1/14, -2, 1/14]]:

# A list of promising (a, b, c) triples where the parameters are (a, b, c, 0,
# 0). Seemingly rational integrals have been discarded.
Hopeful2Z3 := [[0, 0, 0], [1, 1, 0], [2, 2, 0], [2/3, 1/3, -1/3], [-1/3, 1/3, -1/3], [1/2, 1/2, -1/2], [1/3, 2/3, -2
/3], [-2/3, 2/3, -2/3], [0, 0, 1], [1, 0, 1], [-1/2, 1, 1], [1, 1, 1], [2, 1, 1], [1/2, 2, 1], [2, 2,
1], [-1/2, 2, 1], [2, -1/2, 1], [0, 0, 2], [1, 0, 2], [2, 0, 2], [2, -1/2, 2], [1, 1, 2], [2, 1, 2], [
-1/2, 1, 2], [-1/2, 2, 2], [2, 2, 2], [1/2, 2, 2], [-1/2, -1/2, 1/2], [1/2, -1/2, 1/2], [1/2, 1/2, 1/2
], [1/3, 2/3, 1/3], [-2/3, 2/3, 1/3], [1/3, -1/3, 1/3], [-2/3, -1/3, 1/3], [2/3, -2/3, 2/3], [-1/3, -2
/3, 2/3], [2/3, 1/3, 2/3], [-1/3, 1/3, 2/3]]:

# A list of promising parameters, approximations, and deltas. Maple cannot
# identify these.
# Try:
#   GBCZ3ck(seq(Hopeful3Z3[1][1]))[1] - Hopeful3Z3[1][2];
Hopeful3Z3 :=
[[[2/3, 1/3, -1/3, 0, 0], 4.27219386650837761201750468920554958545136464595013314247214097374056668138\
382624784236149902507879897621421877337010257357927597844167506881824758956323308477529043267911443776\
41981620341993482959391, .2313109005910974730690595016677753139575211144811894533090234832026168255713\
952901025347156332982160354536276026668120716627172292404041142410909858930588532148866063064091298118\
646433887981179845048], [[-1/3, 1/3, -1/3, 0, 0], 2.14556122669832447759649906215889008290972707080997\
337150557180525188666372323475043152770019498424020475715624532597948528414480431166498623635048208735\
33830449419134641771124471603675931601303408122, .2482171662722760311471006983116729772136906822435623\
038554207518606894897375512891430892898164547076353069280635507368727802638783517631545005820198783290\
060700994113943749165576730881781360833424196], [[1/3, 2/3, -2/3, 0, 0], 5.474469917413965251935940967\
388088621589340835492940163827475614153704846069777103346444458154753545865154661282146347878984340319\
7895678251063234133820356933278370571289306310468051213186517795265352, .28354214872800805505359894825\
900853706616699913308180805057112137121357180247020882913014845359027046647578530417837202382697926933\
39090332673403187448823179247990238818587303962770639716177727749209], [[-2/3, 2/3, -2/3, 0, 0], 1.842\
154369838372828245996310461755538849333802218308760239217225884606552879361068959152778634672096616572\
1663301341467424365212699868479890691452133363772308329898160705581644404253200824157362204084, .26658\
672013857813866220246380412943764653526293689592194884619863673386177210031989689282953285779110347018\
03956401168108411566445132818054731335454167935059001029546172714171396547967968110657063922], [[2, 1,
1, 0, 0], 2.711417835055268707313114227053603989525921708904483065738688092325895100312745039451062600\
767168480841963832447369211211457728573141651648596566326187130251897149765876451177309239374391242486\
6086044, .15907130851403194542651178939954656087550909097065382618940504864410703001374271304878128661\
764929666775162582533422811014352516957341868754780920673180320464226186429973621711741530852376660952\
60329], [[1, 0, 2, 0, 0], 1.80761189003684580487540948470240265968394780593632204382579206155059673354\
183002630070840051144565389464255496491280747430515238209443443239771088412475350126476651058430078487\
28262495941616577390696, .1588603633873189650659806207923456578991742873147213681011016996135232256596\
420006962002600697348929737462776671591278450278581475312641500024799154077200476775751314176382535018\
326149665319187363055], [[2, 0, 2, 0, 0], 2.2357277061809141158586072161829950130925978638693961678266\
398845926311246090687006861717490410393989475452094407884859856778392835729354392542920922660871851285\
627926544360283634507820109468917392445, .151567653992006437178206394667221242370214970144633112119672\
665547365958321712618063198166304535228709068237453184790748312245884737898169183453897928186563999598\
4544824938809431908111462141970258943], [[1, 1, 2, 0, 0], 1.718109553259641723582514363928528013965437\
721460689245681749210232139866249673280731916532310442025544048223403507718384723028569144464468537911\
5650838263308038003121647317635876808341450100178551941, .12994451213409342521490897845219320169061220\
510306227354045647251997436109136387821763522755305365158294066834030657979852216104100344135031191657\
83919791636418124427390792435152180029462063982676322], [[2, 1, 2, 0, 0], 2.11417835055268707313114227\
053603989525921708904483065738688092325895100312745039451062600767168480841963832447369211211457728573\
14165164859656632618713025189714976587645117730923937439124248660860439, .1439091405275604589248993772\
016699260135924539708555539637359757662107368747048481941484362768070283787591657095640982607798345055\
539132291550778144834963168155142402672878571669639929811690682754560], [[2, 2, 2, 0, 0], 2.0447770618\
091411585860721618299501309259786386939616782663988459263112460906870068617174904103939894754520944078\
848598567783928357293543925429209226608718512856279265443602836345078201094689173924451, .133409077496\
545609627448555852870475608399807139946283715743621233923295846909775678763453363743442424344190625537\
4899777166674584718139653234679859508754613785340877610154922419808924338917669562274], [[1/3, 2/3, 1/
3, 0, 0], 2.117048761209478779039114510821329323840112532394102457412134212305572691046656550196666872\
321303187977319919232195218184765104796843517376594851200730535399917555856933959465702076819779776692\
8980279, .28412311048548355974465321904507066675815887532012985277577555860719127430365669967279098234\
689639962018396637595043879670571212926480893756838957529040123165199500290165749286380392226268004003\
94866], [[-2/3, 2/3, 1/3, 0, 0], 1.2211704876120947877903911451082132932384011253239410245741213421230\
557269104665655019666687232130318797731991923219521818476510479684351737659485120073053539991755585693\
395946570207681977977669289803, .247364382844420608069712746910996770329827881279190069951879925074145\
554609285566274765733247419984971449652107326688421995764090231727967034341487347489495838051496332628\
4389486622118163469734309871], [[1/3, -1/3, 1/3, 0, 0], 2.62765041293017374032029516305955689205329582\
253529918086262192923147576965111448326777770922623227067422669358926826060507829840105216087446838293\
30898215333608147143553468447659743934067411023673240, .2620744782648482977281870321006218209154892754\
114149683803502558969996776481455590354781034213852745207237169603596046655865487672515942275139813280\
207093866618112337479944994430477760634742182258376], [[-2/3, -1/3, 1/3, 0, 0], 1.36861747935349131298\
398524184702215539733520887323504095686890353842621151744427583661111453868838646628866532053658696974\
60850799473919562765808533455089233319592642822326577617012803296629448816338, .2821126576311225390876\
707162872910146316525073141097286668284986373583084212143435205887477497335919683319869339148207663206\
830701954337888296239884398503177864769892707913808782111605499076585075123], [[2/3, -2/3, 2/3, 0, 0],
2.8243303668051695894846833969451441127300559347936335003368766479770041537891520331379336883530560508\
958125585733011602481181335188635343147840333591321710508216208714057748669563266082200755702410533, .\
231324717163314745764981202790924006938542646662460086360583610618636604305694763869715804810790041671\
3879456052768985761646789099930658159185337812540878333394578503191084308978325030820375438360498], [[
-1/3, -2/3, 2/3, 0, 0], 1.7088775466033510448070018756822198341805458583800532569888563894962266725535\
304991369445996100315195904856875093480410294317103913766700275272990358252932339101161730716457751056\
792648136797393183756, .230570650822341322911070506610295986859055807050021418187474011939747789296367\
733640395975447432849043137612446039194143967500647435860366092428384801384136466943533948763864725769\
6380430162746637760], [[2/3, 1/3, 2/3, 0, 0], 2.216071196675929852367598473316541294478657564952795991\
914960448551900309060351204689591479526654778500498594240772154045164795547275176445183199380827894780\
2810990862614031930481614027181863142147215, .26070958568739597909339230365109805515169896170007532565\
300740987021633847086528160166869786949151104625048689909169401562678204344384868347524179257111240154\
43926639613642469925376056634559967164238], [[-1/3, 1/3, 2/3, 0, 0], 1.4366836800949734327894971864766\
702487291812124299201145167154157556599911697042512945831005849527206142714687359779384558524344129349\
949587090514462620601491348257403925313373414811027794803910224365, .226689761872946783643685305719038\
231829601259461433052701640058476758778315189900568523342138012748840997228766916906940782709214503004\
7471057025745726356898125089176633239652857350231171893146366497]]: