# Manifold: Census Knot K8_269

# Number of Tetrahedra: 8

# Number Field
x^6 + 5*x^5 + 17*x^4 + 24*x^3 + 36*x^2 + 32*x + 16 

# Approximate Field Generator
0.107963413538813 - 1.39196867404071*I

# Shape Parameters
-1/9*y^5 - 4/9*y^4 - 13/9*y^3 - 11/9*y^2 - 25/9*y - 7/9

-1/16*y^5 - 5/16*y^4 - 17/16*y^3 - 3/2*y^2 - 9/4*y - 1

3/68*y^5 + 13/68*y^4 + 31/68*y^3 + 3/34*y^2 - 8/17*y + 1/17

-9/68*y^5 - 39/68*y^4 - 127/68*y^3 - 77/34*y^2 - 61/17*y - 37/17

-7/204*y^5 - 19/204*y^4 - 61/204*y^3 - 7/102*y^2 - 55/51*y + 26/51

-13/204*y^5 - 79/204*y^4 - 259/204*y^3 - 217/102*y^2 - 124/51*y - 112/51

7/68*y^5 + 9/17*y^4 + 28/17*y^3 + 133/68*y^2 + 38/17*y + 42/17

2/51*y^5 + 29/204*y^4 + 77/204*y^3 - 35/204*y^2 - 10/51*y + 14/51


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

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

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

# f Combinatorial flattening
{-94, 54, 44, 37, -28, -21, 8, -50}

# f' Combinatorial flattening
{62, -36, 0, 0, 0, 0, 0, 0}

# 1 Loop Invariant
69/68*y^5 + 299/68*y^4 + 747/68*y^3 - 8/17*y^2 - 286/17*y - 130/17

# 2 Loop Invariant
-105525262399/4381562700800*y^5 - 1417853820221/13144688102400*y^4 - 4454095562317/13144688102400*y^3 - 88875522791/205385751600*y^2 - 2927975182/4278869825*y + 528329372771691/547695337600

# 3 Loop Invariant
1072537630594245449/190188914791053312000*y^5 + 5509956273262783619/190188914791053312000*y^4 + 17489664365990028071/190188914791053312000*y^3 + 7435788109974170783/95094457395526656000*y^2 + 7271151142120671029/47547228697763328000*y + 372188439796215443/4754722869776332800

# 4 Loop Invariant
-1945670811621022719326557381/18382161510752395972136140800000*y^5 + 195328680400662298962719153087/18382161510752395972136140800000*y^4 + 326973003099384997144863734999/18382161510752395972136140800000*y^3 + 233796422474996642207255836927/4595540377688098993034035200000*y^2 + 71749360190852256074796851851/2297770188844049496517017600000*y + 143835469254554366073942561319/2297770188844049496517017600000