11a
366
(K11a
366
)
A knot diagram
1
Linearized knot diagam
8 7 10 9 1 11 2 3 4 5 6
Solving Sequence
1,8 2,6
5 7 3 9 4 11 10
c
1
c
5
c
7
c
2
c
8
c
4
c
11
c
10
c
3
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hb − u, −u
5
− u
4
− 3u
3
− 2u
2
+ a − u, u
6
+ u
5
+ 4u
4
+ 3u
3
+ 4u
2
+ 2u − 1i
I
u
2
= hb − u, u
9
+ 3u
7
+ u
5
− 4u
3
+ a − u + 1, u
10
− u
9
+ 5u
8
− 5u
7
+ 9u
6
− 9u
5
+ 6u
4
− 6u
3
+ u
2
+ 1i
I
u
3
= hu
9
− u
8
+ 5u
7
− 4u
6
+ 9u
5
− 6u
4
+ 6u
3
− 4u
2
+ b + u − 1,
− u
9
+ u
8
− 5u
7
+ 5u
6
− 9u
5
+ 9u
4
− 6u
3
+ 6u
2
+ a − u,
u
10
− u
9
+ 5u
8
− 5u
7
+ 9u
6
− 9u
5
+ 6u
4
− 6u
3
+ u
2
+ 1i
I
u
4
= hu
9
+ u
8
+ 3u
7
+ 2u
6
+ 3u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ b + 2u + 1,
− u
9
− 2u
8
− 5u
7
− 6u
6
− 7u
5
− 6u
4
− 4u
3
− 4u
2
+ 2a − 3u − 3,
u
10
+ 2u
9
+ 5u
8
+ 6u
7
+ 7u
6
+ 6u
5
+ 4u
4
+ 4u
3
+ 3u
2
+ 3u + 2i
I
u
5
= hb + u, a − u + 1, u
2
+ 1i
I
u
6
= hb
2
+ bu + u
2
+ 1, −u
2
+ a − 1, u
3
+ u + 1i
* 6 irreducible components of dim
C
= 0, with total 44 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I.
I
u
1
= hb − u, −u
5
− u
4
− 3u
3
− 2u
2
+ a − u, u
6
+ u
5
+ 4u
4
+ 3u
3
+ 4u
2
+ 2u − 1i
(i) Arc colorings
a
1
=
1
0
a
8
=
0
u
a
2
=
1
u
2
a
6
=
u
5
+ u
4
+ 3u
3
+ 2u
2
+ u
u
a
5
=
u
5
+ u
4
+ 3u
3
+ 2u
2
+ 2u
u
a
7
=
u
u
3
+ u
a
3
=
u
2
+ 1
u
4
+ 2u
2
a
9
=
−u
5
− 2u
3
− u
−u
4
− u
3
− 2u
2
− 2u + 1
a
4
=
−u
4
− u
2
+ 1
u
5
+ u
4
+ 2u
3
+ 2u
2
a
11
=
u
4
+ u
3
+ 3u
2
+ 2u
−u
2
a
10
=
u
3
+ 2u
−u
4
− 2u
2
a
10
=
u
3
+ 2u
−u
4
− 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6u
4
− 6u
3
− 18u
2
− 12u − 16
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
9
, c
11
u
6
− u
5
+ 4u
4
− 3u
3
+ 4u
2
− 2u − 1
c
8
, c
10
u
6
+ u
5
− u
4
+ 3u
3
+ 4u
2
− 12u − 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
9
, c
11
y
6
+ 7y
5
+ 18y
4
+ 17y
3
− 4y
2
− 12y + 1
c
8
, c
10
y
6
− 3y
5
+ 3y
4
− y
3
+ 96y
2
− 176y + 16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.800464
a = −0.975734
b = −0.800464
−5.50851 −17.3140
u = −0.37587 + 1.37813I
a = −1.38712 − 1.74048I
b = −0.37587 + 1.37813I
7.7894 + 12.7681I −4.48012 − 7.54465I
u = −0.37587 − 1.37813I
a = −1.38712 + 1.74048I
b = −0.37587 − 1.37813I
7.7894 − 12.7681I −4.48012 + 7.54465I
u = 0.13297 + 1.45639I
a = 0.61041 − 2.42559I
b = 0.13297 + 1.45639I
14.9383 − 4.7754I −0.31743 + 3.39879I
u = 0.13297 − 1.45639I
a = 0.61041 + 2.42559I
b = 0.13297 − 1.45639I
14.9383 + 4.7754I −0.31743 − 3.39879I
u = 0.286259
a = 0.529157
b = 0.286259
−0.468566 −21.0910
5
II. I
u
2
= hb − u, u
9
+ 3u
7
+ u
5
− 4u
3
+ a − u + 1, u
10
− u
9
+ · · · + u
2
+ 1i
(i) Arc colorings
a
1
=
1
0
a
8
=
0
u
a
2
=
1
u
2
a
6
=
−u
9
− 3u
7
− u
5
+ 4u
3
+ u − 1
u
a
5
=
−u
9
− 3u
7
− u
5
+ 4u
3
+ 2u − 1
u
a
7
=
u
u
3
+ u
a
3
=
u
2
+ 1
u
4
+ 2u
2
a
9
=
−u
5
− 2u
3
− u
−u
7
− 3u
5
− 2u
3
+ u
a
4
=
−2u
9
− 8u
7
− 10u
5
+ u
4
− u
3
+ 3u
2
+ 4u + 1
−u
9
− 5u
7
+ u
6
− 9u
5
+ 4u
4
− 5u
3
+ 5u
2
+ 2u + 1
a
11
=
u
9
− 2u
8
+ 5u
7
− 8u
6
+ 9u
5
− 10u
4
+ 6u
3
− 2u
2
+ u
−u
2
a
10
=
u
9
− 2u
8
+ 5u
7
− 8u
6
+ 9u
5
− 11u
4
+ 6u
3
− 5u
2
+ u
−u
4
− 2u
2
a
10
=
u
9
− 2u
8
+ 5u
7
− 8u
6
+ 9u
5
− 11u
4
+ 6u
3
− 5u
2
+ u
−u
4
− 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
8
+ 16u
6
− 4u
5
+ 20u
4
− 12u
3
+ 4u
2
− 12u − 10
6
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
7
, c
11
u
10
+ u
9
+ 5u
8
+ 5u
7
+ 9u
6
+ 9u
5
+ 6u
4
+ 6u
3
+ u
2
+ 1
c
3
, c
4
, c
9
u
10
− 2u
9
+ 5u
8
− 6u
7
+ 7u
6
− 6u
5
+ 4u
4
− 4u
3
+ 3u
2
− 3u + 2
c
8
, c
10
u
10
+ 2u
9
− u
8
− 5u
7
− 3u
6
+ 4u
5
+ 12u
4
+ 13u
3
+ 5u
2
+ u + 2
7
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
7
, c
11
y
10
+ 9y
9
+ 33y
8
+ 59y
7
+ 41y
6
− 21y
5
− 44y
4
− 6y
3
+ 13y
2
+ 2y + 1
c
3
, c
4
, c
9
y
10
+ 6y
9
+ 15y
8
+ 18y
7
+ 7y
6
− 6y
5
− 6y
4
+ y
2
+ 3y + 4
c
8
, c
10
y
10
− 6y
9
+ ··· + 19y + 4
8
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.800451 + 0.099834I
a = 0.984240 + 0.025977I
b = 0.800451 + 0.099834I
−1.58679 − 4.14585I −12.98134 + 3.97600I
u = 0.800451 − 0.099834I
a = 0.984240 − 0.025977I
b = 0.800451 − 0.099834I
−1.58679 + 4.14585I −12.98134 − 3.97600I
u = −0.280829 + 1.292560I
a = −1.76028 − 2.20870I
b = −0.280829 + 1.292560I
5.70347 + 3.47839I −4.80497 − 2.79515I
u = −0.280829 − 1.292560I
a = −1.76028 + 2.20870I
b = −0.280829 − 1.292560I
5.70347 − 3.47839I −4.80497 + 2.79515I
u = −0.057928 + 1.351670I
a = −0.46648 − 3.19340I
b = −0.057928 + 1.351670I
8.22706 + 2.31006I −3.13631 − 3.52133I
u = −0.057928 − 1.351670I
a = −0.46648 + 3.19340I
b = −0.057928 − 1.351670I
8.22706 − 2.31006I −3.13631 + 3.52133I
u = 0.347624 + 1.331990I
a = 1.56700 − 1.85631I
b = 0.347624 + 1.331990I
2.90872 − 8.28632I −8.17560 + 6.14881I
u = 0.347624 − 1.331990I
a = 1.56700 + 1.85631I
b = 0.347624 − 1.331990I
2.90872 + 8.28632I −8.17560 − 6.14881I
u = −0.309318 + 0.396943I
a = −0.824473 + 0.630441I
b = −0.309318 + 0.396943I
2.84181 + 1.23169I −8.90177 − 5.44908I
u = −0.309318 − 0.396943I
a = −0.824473 − 0.630441I
b = −0.309318 − 0.396943I
2.84181 − 1.23169I −8.90177 + 5.44908I
9
III.
I
u
3
= hu
9
− u
8
+ · · · + b − 1, −u
9
+ u
8
+ · · · + a − u, u
10
− u
9
+ · · · + u
2
+ 1i
(i) Arc colorings
a
1
=
1
0
a
8
=
0
u
a
2
=
1
u
2
a
6
=
u
9
− u
8
+ 5u
7
− 5u
6
+ 9u
5
− 9u
4
+ 6u
3
− 6u
2
+ u
−u
9
+ u
8
− 5u
7
+ 4u
6
− 9u
5
+ 6u
4
− 6u
3
+ 4u
2
− u + 1
a
5
=
−u
6
− 3u
4
− 2u
2
+ 1
−u
9
+ u
8
− 5u
7
+ 4u
6
− 9u
5
+ 6u
4
− 6u
3
+ 4u
2
− u + 1
a
7
=
u
u
3
+ u
a
3
=
u
2
+ 1
u
4
+ 2u
2
a
9
=
−u
5
− 2u
3
− u
−u
7
− 3u
5
− 2u
3
+ u
a
4
=
−u
4
− u
2
+ 1
−u
9
+ 2u
8
− 5u
7
+ 7u
6
− 9u
5
+ 8u
4
− 6u
3
+ 3u
2
− u + 1
a
11
=
−u
9
− 4u
7
− 5u
5
+ 3u
−u
7
− 3u
5
− 2u
3
+ u
2
+ u + 2
a
10
=
u
3
+ 2u
u
9
+ 3u
7
+ 2u
5
− u
3
+ 1
a
10
=
u
3
+ 2u
u
9
+ 3u
7
+ 2u
5
− u
3
+ 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
8
+ 16u
6
− 4u
5
+ 20u
4
− 12u
3
+ 4u
2
− 12u − 10
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
7
, c
9
u
10
+ u
9
+ 5u
8
+ 5u
7
+ 9u
6
+ 9u
5
+ 6u
4
+ 6u
3
+ u
2
+ 1
c
5
, c
6
, c
11
u
10
− 2u
9
+ 5u
8
− 6u
7
+ 7u
6
− 6u
5
+ 4u
4
− 4u
3
+ 3u
2
− 3u + 2
c
8
, c
10
u
10
+ 2u
9
− u
8
− 5u
7
− 3u
6
+ 4u
5
+ 12u
4
+ 13u
3
+ 5u
2
+ u + 2
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
7
, c
9
y
10
+ 9y
9
+ 33y
8
+ 59y
7
+ 41y
6
− 21y
5
− 44y
4
− 6y
3
+ 13y
2
+ 2y + 1
c
5
, c
6
, c
11
y
10
+ 6y
9
+ 15y
8
+ 18y
7
+ 7y
6
− 6y
5
− 6y
4
+ y
2
+ 3y + 4
c
8
, c
10
y
10
− 6y
9
+ ··· + 19y + 4
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.800451 + 0.099834I
a = −1.230160 + 0.153429I
b = −0.350885 − 1.264620I
−1.58679 − 4.14585I −12.98134 + 3.97600I
u = 0.800451 − 0.099834I
a = −1.230160 − 0.153429I
b = −0.350885 + 1.264620I
−1.58679 + 4.14585I −12.98134 − 3.97600I
u = −0.280829 + 1.292560I
a = 0.160513 + 0.738786I
b = −0.480814 − 1.084510I
5.70347 + 3.47839I −4.80497 − 2.79515I
u = −0.280829 − 1.292560I
a = 0.160513 − 0.738786I
b = −0.480814 + 1.084510I
5.70347 − 3.47839I −4.80497 + 2.79515I
u = −0.057928 + 1.351670I
a = 0.031648 + 0.738467I
b = 0.642886 − 0.580182I
8.22706 + 2.31006I −3.13631 − 3.52133I
u = −0.057928 − 1.351670I
a = 0.031648 − 0.738467I
b = 0.642886 + 0.580182I
8.22706 − 2.31006I −3.13631 + 3.52133I
u = 0.347624 + 1.331990I
a = −0.183438 + 0.702881I
b = −0.871979 − 0.168588I
2.90872 − 8.28632I −8.17560 + 6.14881I
u = 0.347624 − 1.331990I
a = −0.183438 − 0.702881I
b = −0.871979 + 0.168588I
2.90872 + 8.28632I −8.17560 − 6.14881I
u = −0.309318 + 0.396943I
a = 1.22144 + 1.56745I
b = 0.060791 − 1.179490I
2.84181 + 1.23169I −8.90177 − 5.44908I
u = −0.309318 − 0.396943I
a = 1.22144 − 1.56745I
b = 0.060791 + 1.179490I
2.84181 − 1.23169I −8.90177 + 5.44908I
13
IV.
I
u
4
= hu
9
+ u
8
+ · · · + b + 1, −u
9
− 2u
8
+ · · · + 2a − 3, u
10
+ 2u
9
+ · · · + 3u + 2i
(i) Arc colorings
a
1
=
1
0
a
8
=
0
u
a
2
=
1
u
2
a
6
=
1
2
u
9
+ u
8
+ ··· +
3
2
u +
3
2
−u
9
− u
8
− 3u
7
− 2u
6
− 3u
5
− 2u
4
− 2u
3
− 2u
2
− 2u − 1
a
5
=
−
1
2
u
9
−
1
2
u
7
+ ··· −
1
2
u +
1
2
−u
9
− u
8
− 3u
7
− 2u
6
− 3u
5
− 2u
4
− 2u
3
− 2u
2
− 2u − 1
a
7
=
u
u
3
+ u
a
3
=
u
2
+ 1
u
4
+ 2u
2
a
9
=
−u
5
− 2u
3
− u
−u
7
− 3u
5
− 2u
3
+ u
a
4
=
1
2
u
9
+
5
2
u
7
+ ··· −
1
2
u +
5
2
u
9
+ 3u
7
+ 3u
5
+ 2u
4
+ u
3
+ 4u
2
+ 1
a
11
=
1
2
u
9
+
3
2
u
7
+ ··· −
1
2
u +
1
2
u
9
+ 2u
8
+ 4u
7
+ 4u
6
+ 4u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 3
a
10
=
1
2
u
9
+
1
2
u
7
+ ··· −
1
2
u −
1
2
u
9
+ 2u
8
+ 3u
7
+ 4u
6
+ 2u
5
+ 3u
4
+ u
3
+ 2u
2
+ 2u + 1
a
10
=
1
2
u
9
+
1
2
u
7
+ ··· −
1
2
u −
1
2
u
9
+ 2u
8
+ 3u
7
+ 4u
6
+ 2u
5
+ 3u
4
+ u
3
+ 2u
2
+ 2u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
7
− 8u
5
− 4u
3
+ 4u − 10
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
u
10
− 2u
9
+ 5u
8
− 6u
7
+ 7u
6
− 6u
5
+ 4u
4
− 4u
3
+ 3u
2
− 3u + 2
c
3
, c
4
, c
5
c
6
, c
9
, c
11
u
10
+ u
9
+ 5u
8
+ 5u
7
+ 9u
6
+ 9u
5
+ 6u
4
+ 6u
3
+ u
2
+ 1
c
8
, c
10
u
10
+ 2u
9
− u
8
− 5u
7
− 3u
6
+ 4u
5
+ 12u
4
+ 13u
3
+ 5u
2
+ u + 2
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
7
y
10
+ 6y
9
+ 15y
8
+ 18y
7
+ 7y
6
− 6y
5
− 6y
4
+ y
2
+ 3y + 4
c
3
, c
4
, c
5
c
6
, c
9
, c
11
y
10
+ 9y
9
+ 33y
8
+ 59y
7
+ 41y
6
− 21y
5
− 44y
4
− 6y
3
+ 13y
2
+ 2y + 1
c
8
, c
10
y
10
− 6y
9
+ ··· + 19y + 4
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.871979 + 0.168588I
a = 1.105490 + 0.213735I
b = 0.347624 − 1.331990I
2.90872 + 8.28632I −8.17560 − 6.14881I
u = −0.871979 − 0.168588I
a = 1.105490 − 0.213735I
b = 0.347624 + 1.331990I
2.90872 − 8.28632I −8.17560 + 6.14881I
u = 0.642886 + 0.580182I
a = −0.857280 + 0.773665I
b = −0.057928 − 1.351670I
8.22706 − 2.31006I −3.13631 + 3.52133I
u = 0.642886 − 0.580182I
a = −0.857280 − 0.773665I
b = −0.057928 + 1.351670I
8.22706 + 2.31006I −3.13631 − 3.52133I
u = 0.060791 + 1.179490I
a = −0.043581 + 0.845578I
b = −0.309318 − 0.396943I
2.84181 − 1.23169I −8.90177 + 5.44908I
u = 0.060791 − 1.179490I
a = −0.043581 − 0.845578I
b = −0.309318 + 0.396943I
2.84181 + 1.23169I −8.90177 − 5.44908I
u = −0.480814 + 1.084510I
a = 0.341647 + 0.770609I
b = −0.280829 − 1.292560I
5.70347 − 3.47839I −4.80497 + 2.79515I
u = −0.480814 − 1.084510I
a = 0.341647 − 0.770609I
b = −0.280829 + 1.292560I
5.70347 + 3.47839I −4.80497 − 2.79515I
u = −0.350885 + 1.264620I
a = 0.203721 + 0.734227I
b = 0.800451 − 0.099834I
−1.58679 + 4.14585I −12.98134 − 3.97600I
u = −0.350885 − 1.264620I
a = 0.203721 − 0.734227I
b = 0.800451 + 0.099834I
−1.58679 − 4.14585I −12.98134 + 3.97600I
17
V. I
u
5
= hb + u, a − u + 1, u
2
+ 1i
(i) Arc colorings
a
1
=
1
0
a
8
=
0
u
a
2
=
1
−1
a
6
=
u − 1
−u
a
5
=
−1
−u
a
7
=
u
0
a
3
=
0
−1
a
9
=
0
u
a
4
=
−1
−u − 1
a
11
=
−u
1
a
10
=
−u
1
a
10
=
−u
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
9
, c
11
u
2
+ 1
c
8
, c
10
u
2
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
9
, c
11
(y + 1)
2
c
8
, c
10
y
2
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −1.00000 + 1.00000I
b = − 1.000000I
4.93480 −4.00000
u = − 1.000000I
a = −1.00000 − 1.00000I
b = 1.000000I
4.93480 −4.00000
21
VI. I
u
6
= hb
2
+ bu + u
2
+ 1, −u
2
+ a − 1, u
3
+ u + 1i
(i) Arc colorings
a
1
=
1
0
a
8
=
0
u
a
2
=
1
u
2
a
6
=
u
2
+ 1
b
a
5
=
u
2
+ b + 1
b
a
7
=
u
−1
a
3
=
u
2
+ 1
u
2
− u
a
9
=
u
2
+ 1
u
2
a
4
=
u
2
b + u
2
+ 2b
u
2
b + b − u − 1
a
11
=
−u
2
b − b + 1
bu + u
2
+ 1
a
10
=
−u
2
b + u
2
+ 2
bu + u
2
+ b + 1
a
10
=
−u
2
b + u
2
+ 2
bu + u
2
+ b + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −10
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
9
, c
11
(u
3
+ u − 1)
2
c
8
, c
10
(u − 1)
6
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
9
, c
11
(y
3
+ 2y
2
+ y − 1)
2
c
8
, c
10
(y − 1)
6
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 0.341164 + 1.161540I
a = −0.232786 + 0.792552I
b = 0.341164 − 1.161540I
1.64493 −10.0000
u = 0.341164 + 1.161540I
a = −0.232786 + 0.792552I
b = −0.682328
1.64493 −10.0000
u = 0.341164 − 1.161540I
a = −0.232786 − 0.792552I
b = 0.341164 + 1.161540I
1.64493 −10.0000
u = 0.341164 − 1.161540I
a = −0.232786 − 0.792552I
b = −0.682328
1.64493 −10.0000
u = −0.682328
a = 1.46557
b = 0.341164 + 1.161540I
1.64493 −10.0000
u = −0.682328
a = 1.46557
b = 0.341164 − 1.161540I
1.64493 −10.0000
25
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
9
, c
11
(u
2
+ 1)(u
3
+ u − 1)
2
(u
6
− u
5
+ 4u
4
− 3u
3
+ 4u
2
− 2u − 1)
· (u
10
− 2u
9
+ 5u
8
− 6u
7
+ 7u
6
− 6u
5
+ 4u
4
− 4u
3
+ 3u
2
− 3u + 2)
· (u
10
+ u
9
+ 5u
8
+ 5u
7
+ 9u
6
+ 9u
5
+ 6u
4
+ 6u
3
+ u
2
+ 1)
2
c
8
, c
10
u
2
(u − 1)
6
(u
6
+ u
5
− u
4
+ 3u
3
+ 4u
2
− 12u − 4)
· (u
10
+ 2u
9
− u
8
− 5u
7
− 3u
6
+ 4u
5
+ 12u
4
+ 13u
3
+ 5u
2
+ u + 2)
3
26
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
9
, c
11
((y + 1)
2
)(y
3
+ 2y
2
+ y − 1)
2
(y
6
+ 7y
5
+ ··· − 12y + 1)
· (y
10
+ 6y
9
+ 15y
8
+ 18y
7
+ 7y
6
− 6y
5
− 6y
4
+ y
2
+ 3y + 4)
· (y
10
+ 9y
9
+ 33y
8
+ 59y
7
+ 41y
6
− 21y
5
− 44y
4
− 6y
3
+ 13y
2
+ 2y + 1)
2
c
8
, c
10
y
2
(y − 1)
6
(y
6
− 3y
5
+ 3y
4
− y
3
+ 96y
2
− 176y + 16)
· (y
10
− 6y
9
+ ··· + 19y + 4)
3
27
