# Manifold: Census Knot K8_275

# Number of Tetrahedra: 8

# Number Field
x^5 - 19*x^4 + 2*x^3 - 30*x^2 - 3*x + 17 

# Approximate Field Generator
0.0313778039410122 + 1.42456089346275*I

# Shape Parameters
-3/340*y^4 + 219/1360*y^3 + 7/80*y^2 + 853/1360*y + 61/80

7/340*y^4 - 149/340*y^3 + 9/10*y^2 - 23/340*y + 39/20

15/136*y^4 - 295/136*y^3 + 13/8*y^2 - 501/136*y + 3

-3/136*y^4 + 59/136*y^3 - 3/8*y^2 + 209/136*y + 1/4

-1/16*y^4 + 9/8*y^3 + y^2 + 23/8*y + 33/16

35/544*y^4 - 165/136*y^3 - 1/16*y^2 - 237/136*y - 9/32

1/2*y + 1/2

-9/272*y^4 + 11/17*y^3 - 61/136*y^2 + 55/34*y - 21/272


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

# B Gluing Matrix
{{1,1,0,0,0,0,2,0},{0,2,0,0,0,0,0,0},{0,0,1,0,0,0,3,0},{0,0,0,1,0,0,4,0},{0,0,0,0,1,0,3,0},{0,0,0,0,0,1,2,0},{0,0,0,0,0,0,5,0},{0,0,0,0,0,0,0,1}}

# nu Gluing Vector
{5, 2, 4, 6, 4, 3, 5, 2}

# f Combinatorial flattening
{0, -244, -40, -81, 42, 204, 285, -81}

# f' Combinatorial flattening
{0, 285, 0, 0, 0, 0, 0, 0}

# 1 Loop Invariant
111/272*y^4 - 1151/136*y^3 + 111/8*y^2 - 577/136*y - 101/16

# 2 Loop Invariant
1135469/169111172*y^4 - 266652589/2029334064*y^3 + 9838697/119372592*y^2 - 103627925/676444688*y + 1036436109215/119372592

# 3 Loop Invariant
-5901499777/17068052367616*y^4 + 27382156631/8534026183808*y^3 + 8346158847/125500385056*y^2 - 50855852587/8534026183808*y + 145173416209/1004003080448

# 4 Loop Invariant
138148848168913425169/30561864772710881710080*y^4 - 1315645956866396505841/15280932386355440855040*y^3 + 922588836034694423/149813062611327851520*y^2 - 2631722282649874250987/15280932386355440855040*y - 26221139488983981421/1797756751335934218240