# Manifold: Census Knot K6_8

# Number of Tetrahedra: 6

# Number Field
x^8 + 6*x^7 + 8*x^6 + 17*x^5 + 27*x^4 + 13*x^3 + x^2 + 2*x - 1 

# Approximate Field Generator
-0.00463871401123240 + 0.467197298382156*I

# Shape Parameters
-167/354*y^7 - 1405/531*y^6 - 959/354*y^5 - 7277/1062*y^4 - 5462/531*y^3 - 1274/531*y^2 - 211/1062*y - 1265/531

10/177*y^7 + 9/59*y^6 - 74/177*y^5 + 131/177*y^4 - 121/177*y^3 - 43/177*y^2 + 323/177*y + 86/59

-110/1239*y^7 - 1894/3717*y^6 - 86/177*y^5 - 3202/3717*y^4 - 854/531*y^3 + 1891/3717*y^2 + 3973/3717*y + 277/3717

-272/531*y^7 - 587/177*y^6 - 2837/531*y^5 - 5050/531*y^4 - 9028/531*y^3 - 5521/531*y^2 - 148/531*y - 109/177

-241/1062*y^7 - 1459/1062*y^6 - 1969/1062*y^5 - 655/177*y^4 - 6223/1062*y^3 - 1538/531*y^2 + 635/1062*y + 697/1062

-68/531*y^7 - 278/531*y^6 + 220/531*y^5 - 19/59*y^4 + 457/531*y^3 + 2440/531*y^2 + 1438/531*y + 464/531


# A Gluing Matrix
{{-1,0,-2,0,0,-2},{0,0,-2,0,0,-2},{-2,-2,-6,1,0,-6},{0,0,1,0,1,2},{0,0,0,1,0,-1},{-2,-2,-6,2,-1,-6}}

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

# nu Gluing Vector
{-3, -2, -8, 2, 0, -8}

# f Combinatorial flattening
{-81, -51, 62, -20, -20, -20}

# f' Combinatorial flattening
{0, 82, 0, 0, 0, 0}

# 1 Loop Invariant
1693/531*y^7 + 9946/531*y^6 + 11827/531*y^5 + 8146/177*y^4 + 38674/531*y^3 + 9364/531*y^2 - 7685/531*y + 1931/531

# 2 Loop Invariant
1121695940594273/1782192424227050754*y^7 - 72300474744908695/4752513131272135344*y^6 - 261117331411106519/3564384848454101508*y^5 + 579678564950332583/14257539393816406032*y^4 - 659040412032840301/3564384848454101508*y^3 + 30287144340090113/14257539393816406032*y^2 + 142048321971135275/891096212113525377*y + 2472121728856695424813/4752513131272135344

# 3 Loop Invariant
-8825683242787090254757451/449611827954893290724323392*y^7 - 44804653720015697909351195/449611827954893290724323392*y^6 - 31196567846519800040647415/449611827954893290724323392*y^5 - 7348417866911163416168683/24978434886382960595795744*y^4 - 7671612234813892433345089/26447754585581958277901376*y^3 - 23276890674416268101519303/449611827954893290724323392*y^2 - 30106138721896821296009303/449611827954893290724323392*y + 369671620416862307244235/56201478494361661340540424