# Manifold: Census Knot K8_237

# Number of Tetrahedra: 8

# Number Field
x^5 - 7*x^4 + 10*x^3 - 3*x^2 + 5*x + 25 

# Approximate Field Generator
0.215769073634576 - 1.40153123303497*I

# Shape Parameters
-y

45/269*y^4 - 189/269*y^3 - 133/269*y^2 - 346/269*y - 421/269

45/269*y^4 - 189/269*y^3 - 133/269*y^2 - 346/269*y - 421/269

-8/1345*y^4 - 74/1345*y^3 + 147/269*y^2 - 1146/1345*y + 437/269

219/1345*y^4 - 1673/1345*y^3 + 717/269*y^2 - 4607/1345*y + 1319/269

25/269*y^4 - 105/269*y^3 - 44/269*y^2 - 252/269*y + 65/269

-13/1345*y^4 + 216/1345*y^3 - 131/269*y^2 - 181/1345*y + 4/269

-159/6725*y^4 + 883/6725*y^3 - 71/1345*y^2 - 248/6725*y + 649/1345


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

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

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

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

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

# 1 Loop Invariant
657/1345*y^4 - 3674/1345*y^3 - 808/269*y^2 + 10389/1345*y + 2074/269

# 2 Loop Invariant
-46199090561273/248576143247240*y^4 + 1093913090911013/745728429741720*y^3 - 158771160350411/49715228649448*y^2 + 446246931034717/124288071623620*y - 666867854722145/149145685948344

# 3 Loop Invariant
57173432413842476376337/4684947383831640915680*y^4 - 456658780054581737447599/4684947383831640915680*y^3 + 204477110353257944329229/936989476766328183136*y^2 - 589896318343923110841523/2342473691915820457840*y + 144974844072048594324427/468494738383164091568

# 4 Loop Invariant
-133574063388100008110765206345485660589/77926359612654619050061841636390400*y^4 + 1066757208300453166517292441446402066483/77926359612654619050061841636390400*y^3 - 477569215951378989500817657781572051847/15585271922530923810012368327278080*y^2 + 1377894623758640444790122743499024335441/38963179806327309525030920818195200*y - 3762019699985699386358651839362816009/86584844014060687833402046262656