# Manifold: Census Knot K8_251

# Number of Tetrahedra: 8

# Number Field
x^6 - 2*x^5 + 2*x^4 - 2*x^3 + 2*x^2 - x + 1 

# Approximate Field Generator
1.18352641861027 + 0.507020981080684*I

# Shape Parameters
y^5 - 2*y^3 + y^2 + 2

y^4 - y^3 + y^2 - y + 1

3/11*y^5 + 2/11*y^4 - 7/11*y^3 + 12/11*y^2 - 6/11*y + 3/11

y^4 - y^3 + y^2 - y + 1

8/11*y^5 - 10/11*y^4 + 3/11*y^3 + 5/11*y + 4/11

2*y^5 - y^4 - 2*y^3 + 2*y + 3

-y^5 + y^4 + y^3 - y - 1

-y^4 + 3*y^3 - 3*y^2 + 2*y - 1


# A Gluing Matrix
{{1,1,-1,2,1,-1,2,2},{1,1,0,2,0,0,2,2},{-1,0,-2,2,2,-2,2,2},{1,1,2,0,0,2,-1,0},{1,0,2,0,0,1,0,0},{-1,0,-2,2,1,-1,1,1},{1,1,2,-1,0,1,-1,-1},{1,1,2,0,0,1,-1,0}}

# B Gluing Matrix
{{1,1,0,0,0,0,0,0},{0,2,0,0,0,0,0,0},{0,0,1,0,0,0,0,0},{0,0,0,1,0,0,0,0},{0,0,0,0,1,0,0,0},{0,0,0,0,0,1,0,0},{0,0,0,0,0,0,1,0},{0,0,0,0,0,0,0,1}}

# nu Gluing Vector
{4, 4, 2, 2, 2, 1, 1, 2}

# f Combinatorial flattening
{-34, 12, 18, -1, -9, 0, 12, 2}

# f' Combinatorial flattening
{27, 0, -4, 0, 0, 0, 0, 0}

# 1 Loop Invariant
-4*y^5 + y^4 + 2*y^3 + 12*y^2 + 3*y + 4

# 2 Loop Invariant
-79532509477/1882609068048*y^5 + 451462583467/1882609068048*y^4 - 71271621319/313768178008*y^3 + 134464263219/627536356016*y^2 - 61396341209/235326133506*y + 114400131495067/941304534024

# 3 Loop Invariant
5363246555245234611/112643557815171595936*y^5 - 13360391807145606637/225287115630343191872*y^4 + 8004687378254829553/225287115630343191872*y^3 - 4848810296195262963/112643557815171595936*y^2 - 198169741317159193/7040222363448224746*y + 12803017419807297723/112643557815171595936

# 4 Loop Invariant
-272597100107269257907626618591143/2120637834000312052602737842529280*y^5 + 163416749234838402558272676611623/1060318917000156026301368921264640*y^4 - 27660983249533173571351416541803/353439639000052008767122973754880*y^3 + 705441028948314897608310088987099/6361913502000936157808213527587840*y^2 + 7107167613549261885273096623627/1060318917000156026301368921264640*y - 1620648124533049869089081616115663/6361913502000936157808213527587840