# Manifold: Census Knot K5_21

# Number of Tetrahedra: 5

# Number Field
x^4 - 5*x^3 + 10*x^2 - 8*x + 4 

# Approximate Field Generator
0.454787400161346 - 0.715953029988023*I

# Shape Parameters
1/4*y^2 - 3/4*y + 1

-1/4*y^3 + 5/4*y^2 - 5/2*y + 2

-1/4*y^3 + 5/4*y^2 - 5/2*y + 2

-1/4*y^3 + 5/4*y^2 - 2*y + 3/2

-1/4*y^3 + 5/4*y^2 - 2*y + 3/2


# A Gluing Matrix
{{-1,1,-2,1,1},{-1,1,-2,1,1},{-1,0,-1,2,0},{-2,0,-2,2,2},{-2,1,-3,2,2}}

# B Gluing Matrix
{{1,0,0,0,3},{0,1,1,0,3},{0,0,2,0,3},{0,0,0,1,3},{0,0,0,0,4}}

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

# f Combinatorial flattening
{2, 2, 0, 2, 0}

# f' Combinatorial flattening
{0, 0, 0, 2, 0}

# 1 Loop Invariant
2*y^3 - 25/2*y^2 + 27*y - 18

# 2 Loop Invariant
8402827/182557536*y^3 - 8590303/182557536*y^2 - 9124823/91278768*y - 6897937/22819692

# 3 Loop Invariant
-7112559063/587409298336*y^3 + 3120127769/293704649168*y^2 - 4707916067/293704649168*y + 5780929437/587409298336

# 4 Loop Invariant
-131853984155650699/26808998531927265024*y^3 + 2777552129699106433/89363328439757550080*y^2 - 4701355992122512951/160853991191563590144*y + 1580398024863234727/80426995595781795072

# 5 Loop Invariant
281781875207765669043/172524841885795926184448*y^3 - 16951897572812326675109/1035149051314775557106688*y^2 + 7401566911788156685411/517574525657387778553344*y - 3566401842241818961529/345049683771591852368896