# Manifold: Census Knot K7_81

# Number of Tetrahedra: 7

# Number Field
x^9 + x^8 - 19*x^6 - 27*x^5 - 30*x^4 - 15*x^3 + x^2 + 4*x + 1 

# Approximate Field Generator
-0.249348404184789 - 1.01279545786180*I

# Shape Parameters
67895/133191*y^8 + 31631/44397*y^7 + 11056/44397*y^6 - 1275140/133191*y^5 - 2336152/133191*y^4 - 2880230/133191*y^3 - 2164063/133191*y^2 - 28485/4933*y - 19840/133191

-699994/1780813*y^8 + 51083/1780813*y^7 + 287589/1780813*y^6 + 13062922/1780813*y^5 + 4818774/1780813*y^4 + 9524769/1780813*y^3 - 3924546/1780813*y^2 - 3532815/1780813*y + 661765/1780813

31184/44397*y^8 + 3540/4933*y^7 - 432/4933*y^6 - 594881/44397*y^5 - 850006/44397*y^4 - 867191/44397*y^3 - 408454/44397*y^2 + 15845/14799*y + 144269/44397

31184/44397*y^8 + 3540/4933*y^7 - 432/4933*y^6 - 594881/44397*y^5 - 850006/44397*y^4 - 867191/44397*y^3 - 408454/44397*y^2 + 15845/14799*y + 144269/44397

-y^8 - y^7 + 19*y^5 + 27*y^4 + 30*y^3 + 15*y^2 - y - 3

432/4933*y^8 + 697/4933*y^7 - 269/4933*y^6 - 8727/4933*y^5 - 16435/4933*y^4 - 9533/4933*y^3 + 1021/4933*y^2 + 6528/4933*y + 8473/4933

-y^8 - y^7 + 19*y^5 + 27*y^4 + 30*y^3 + 15*y^2 - y - 3


# A Gluing Matrix
{{-1,-2,-2,0,-2,2,0},{-2,-3,-4,0,-4,4,0},{0,0,1,0,0,1,-1},{0,0,0,1,-1,1,0},{-2,-4,-5,-1,-4,4,0},{0,0,-1,1,-1,2,1},{-2,-4,-6,0,-5,4,1}}

# B Gluing Matrix
{{1,0,0,0,0,0,2},{0,1,0,0,0,0,4},{0,0,1,0,0,0,0},{0,0,0,1,0,0,0},{0,0,0,0,1,0,5},{0,0,0,0,0,1,2},{0,0,0,0,0,0,6}}

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

# f Combinatorial flattening
{3, -1, 1, -1, 0, 2, 0}

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

# 1 Loop Invariant
-26472/4933*y^8 - 19964/4933*y^7 + 12921/4933*y^6 + 499418/4933*y^5 + 581492/4933*y^4 + 504959/4933*y^3 + 241363/4933*y^2 - 43201/4933*y - 67289/4933

# 2 Loop Invariant
1027699442204823359019475/7071920978789697791660136*y^8 + 305870423287103949122345/2357306992929899263886712*y^7 - 19697235875158219294439/589326748232474815971678*y^6 - 38880017754583716856892423/14143841957579395583320272*y^5 - 25542747141495056310118073/7071920978789697791660136*y^4 - 25589133312971970021053365/7071920978789697791660136*y^3 - 25117883552996583180281401/14143841957579395583320272*y^2 + 1668346126573731123080629/4714613985859798527773424*y + 12022269183690310813066199/14143841957579395583320272

# 3 Loop Invariant
81555304722962524186869771219853651/757348090284561754921801773064133184*y^8 + 16246789346848995195570026205631531/252449363428187251640600591021377728*y^7 - 2176319827585819500320527290557257/63112340857046812910150147755344432*y^6 - 386521096575614538396198742178405413/189337022571140438730450443266033296*y^5 - 394760669765900865942554761348852883/189337022571140438730450443266033296*y^4 - 422323596091993724722416198178957087/189337022571140438730450443266033296*y^3 - 364564287713285389879393295408674829/757348090284561754921801773064133184*y^2 + 2994865665996582379295305986539351/5259361738087234409179178979612036*y + 281082932753106699775498894730690737/757348090284561754921801773064133184