# Manifold: Census Knot K8_265

# Number of Tetrahedra: 8

# Number Field
x^7 + 3*x^6 + 9*x^5 + 11*x^4 + 12*x^3 + 2*x^2 - 3*x - 1 

# Approximate Field Generator
-0.775929629986284 + 1.76112722079363*I

# Shape Parameters
-y^6 - 3*y^5 - 9*y^4 - 10*y^3 - 11*y^2 + y + 2

-3/2*y^6 - 4*y^5 - 23/2*y^4 - 11*y^3 - 11*y^2 + 3*y + 7/2

y^6 + 2*y^5 + 7*y^4 + 5*y^3 + 8*y^2 - 3*y - 1

-1/4*y^6 - 1/2*y^5 - 7/4*y^4 - y^3 - 2*y^2 + 3/2*y + 1/4

-3/2*y^6 - 4*y^5 - 23/2*y^4 - 11*y^3 - 11*y^2 + 3*y + 7/2

-1/4*y^6 - 1/2*y^5 - 7/4*y^4 - y^3 - 2*y^2 + 3/2*y + 1/4

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

-4*y^6 - 10*y^5 - 31*y^4 - 29*y^3 - 34*y^2 + 8*y + 10


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

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

# nu Gluing Vector
{1, 0, 0, 2, 1, 2, 3, 1}

# f Combinatorial flattening
{3, -5, -3, -2, -3, -4, 0, 2}

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

# 1 Loop Invariant
-5/2*y^6 - 9*y^5 - 55/2*y^4 - 34*y^3 - 40*y^2 - 7*y + 9/2

# 2 Loop Invariant
-9388494343/20187863056*y^6 - 24866247949/20187863056*y^5 - 459045120961/121127178336*y^4 - 455194959407/121127178336*y^3 - 172810720699/40375726112*y^2 + 37799607491/40375726112*y + 524663719/2523482882

# 3 Loop Invariant
-160687626222879/2868372334448704*y^6 - 1697617470703009/11473489337794816*y^5 - 4736787164536929/11473489337794816*y^4 - 4655801264761429/11473489337794816*y^3 - 4317286677751037/11473489337794816*y^2 + 372963276787383/11473489337794816*y + 1924963315455375/11473489337794816

# 4 Loop Invariant
-905047558116838114831977253/6948756945776336113041530880*y^6 - 6351715739664844267272170359/20846270837329008339124592640*y^5 - 1115500208122588040991385407/1158126157629389352173588480*y^4 - 8275455940301973786618515471/10423135418664504169562296320*y^3 - 10599010094251216236377010491/10423135418664504169562296320*y^2 + 1327814344461173294128911211/3474378472888168056520765440*y + 168595719727461148436888743/1042313541866450416956229632