# Manifold: Census Knot K5_13

# Number of Tetrahedra: 5

# Number Field
x^5 + 4*x^4 + 4*x^3 - 9*x^2 + 5*x - 1 

# Approximate Field Generator
0.369908768847230 - 0.281337020237160*I

# Shape Parameters
-7/4*y^4 - 33/4*y^3 - 51/4*y^2 + 15/2*y - 5/4

-7/4*y^4 - 33/4*y^3 - 51/4*y^2 + 15/2*y - 5/4

-1/4*y^4 - 5/4*y^3 - 9/4*y^2 - 1/4

-5/4*y^4 - 23/4*y^3 - 33/4*y^2 + 13/2*y - 7/4

-1/8*y^4 - 7/8*y^3 - 17/8*y^2 - 5/4*y + 13/8


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

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

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

# f Combinatorial flattening
{0, 0, 1, 0, 1}

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

# 1 Loop Invariant
4*y^4 + 15*y^3 + 11*y^2 - 46*y + 16

# 2 Loop Invariant
27902129/206318976*y^4 + 115108391/206318976*y^3 + 136652561/206318976*y^2 - 103991183/103159488*y + 21676169/68772992

# 3 Loop Invariant
-16729526263/806569650176*y^4 - 68994343665/806569650176*y^3 - 90984939231/806569650176*y^2 + 50247249185/403284825088*y - 32414600749/806569650176

# 4 Loop Invariant
-39017184807728026493/416026560742476349440*y^4 - 176360490408931047947/416026560742476349440*y^3 - 245569060681067971477/416026560742476349440*y^2 + 365229039132082733993/624039841113714524160*y - 252005953401503963197/1248079682227429048320

# 5 Loop Invariant
-167369497405877229688933/975831900877552525246464*y^4 - 245411890236400859847841/325277300292517508415488*y^3 - 325192844693390205538751/325277300292517508415488*y^2 + 490292530237014172182587/487915950438776262623232*y - 340034898075654667756471/975831900877552525246464