12a
0725
(K12a
0725
)
A knot diagram
1
Linearized knot diagam
3 8 9 10 11 12 1 2 5 4 7 6
Solving Sequence
5,9
10 4 11 6
2,3
1 8 7 12
c
9
c
4
c
10
c
5
c
3
c
1
c
8
c
7
c
12
c
2
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
15
− 8u
13
+ 2u
12
− 26u
11
+ 12u
10
− 41u
9
+ 28u
8
− 26u
7
+ 28u
6
+ 5u
5
+ 6u
4
+ 8u
3
− 5u
2
+ 2b − 3u + 1,
− u
15
− 8u
13
− 26u
11
+ 2u
10
− 41u
9
+ 10u
8
− 26u
7
+ 20u
6
+ 5u
5
+ 18u
4
+ 8u
3
+ 5u
2
+ 2a − 3u − 1,
u
16
− u
15
+ ··· − 2u + 1i
I
u
2
= h−u
11
− 4u
9
− u
8
− 5u
7
− 3u
6
− u
5
− 2u
4
+ u
3
+ b − 1,
− u
13
+ 2u
12
− 5u
11
+ 6u
10
− 9u
9
+ 4u
8
− 6u
7
− 6u
6
− 8u
4
+ u
3
− 2u
2
+ 2a − u − 1,
u
14
+ 5u
12
+ 2u
11
+ 9u
10
+ 8u
9
+ 6u
8
+ 10u
7
+ 2u
5
− u
4
− 2u
3
+ u
2
+ u + 2i
I
u
3
= hb − u, a − u, u
12
− u
11
+ 4u
10
− 4u
9
+ 7u
8
− 7u
7
+ 5u
6
− 5u
5
+ u
4
− u
3
+ 1i
I
u
4
= h8u
5
a + 22u
4
a + 37u
5
+ 14u
3
a + 29u
4
− 8u
2
a + 89u
3
+ 2au + 60u
2
+ 97b − 37a + 82u + 35,
u
5
− 2u
3
a + 4u
4
− 2u
2
a + 6u
3
+ a
2
− 3au + 10u
2
− 2a + 6u + 7, u
6
+ u
5
+ 3u
4
+ 2u
3
+ 2u
2
+ u − 1i
I
u
5
= hb − u, a − u, u
6
+ u
5
+ 3u
4
+ 2u
3
+ 2u
2
+ u − 1i
I
u
6
= hb − u, a − u + 1, u
2
+ 1i
* 6 irreducible components of dim
C
= 0, with total 62 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
= h−u
15
−8u
13
+· · ·+2b+1, −u
15
−8u
13
+· · ·+2a−1, u
16
−u
15
+· · ·−2u+1i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
4
=
u
u
3
+ u
a
11
=
u
2
+ 1
u
4
+ 2u
2
a
6
=
−u
5
− 2u
3
− u
−u
7
− 3u
5
− 2u
3
+ u
a
2
=
1
2
u
15
+ 4u
13
+ ··· +
3
2
u +
1
2
1
2
u
15
+ 4u
13
+ ··· +
3
2
u −
1
2
a
3
=
u
3
+ 2u
u
3
+ u
a
1
=
−u
6
− 3u
4
− 2u
2
+ 1
1
2
u
15
− u
14
+ ··· +
3
2
u −
1
2
a
8
=
−u
9
− 4u
7
− 5u
5
+ 3u
−
1
2
u
15
− 3u
13
+ ··· −
1
2
u −
1
2
a
7
=
u
3
+ 2u
−
1
2
u
15
− 3u
13
+ ··· −
1
2
u −
1
2
a
12
=
−u
4
− u
2
+ 1
1
2
u
15
− u
14
+ ··· +
3
2
u −
1
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
15
− 4u
14
+ 30u
13
− 28u
12
+ 90u
11
− 76u
10
+ 122u
9
− 88u
8
+
40u
7
− 16u
6
− 64u
5
+ 36u
4
− 34u
3
+ 22u − 16
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
16
+ 8u
15
+ ··· + 11u + 4
c
2
, c
8
u
16
− 2u
15
+ ··· − 3u + 2
c
3
, c
5
, c
7
u
16
+ 2u
15
+ ··· + 12u + 8
c
4
, c
6
, c
9
c
10
, c
11
, c
12
u
16
+ u
15
+ ··· + 2u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
16
+ 24y
14
+ ··· − 33y + 16
c
2
, c
8
y
16
+ 8y
15
+ ··· + 11y + 4
c
3
, c
5
, c
7
y
16
− 14y
15
+ ··· + 496y + 64
c
4
, c
6
, c
9
c
10
, c
11
, c
12
y
16
+ 15y
15
+ ··· + 4y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.896754 + 0.031752I
a = 0.17672 + 2.61210I
b = −0.465246 + 1.250080I
−11.44060 − 4.76307I −15.3726 + 3.2989I
u = 0.896754 − 0.031752I
a = 0.17672 − 2.61210I
b = −0.465246 − 1.250080I
−11.44060 + 4.76307I −15.3726 − 3.2989I
u = −0.177081 + 1.342100I
a = −0.281404 + 0.454739I
b = 0.725499 − 0.391212I
8.15821 + 4.40873I 0.01113 − 3.61674I
u = −0.177081 − 1.342100I
a = −0.281404 − 0.454739I
b = 0.725499 + 0.391212I
8.15821 − 4.40873I 0.01113 + 3.61674I
u = 0.399274 + 1.311870I
a = −0.110245 + 0.614867I
b = −0.897959 − 0.093377I
0.55749 − 9.14366I −4.61411 + 5.72614I
u = 0.399274 − 1.311870I
a = −0.110245 − 0.614867I
b = −0.897959 + 0.093377I
0.55749 + 9.14366I −4.61411 − 5.72614I
u = −0.037558 + 1.371140I
a = 0.952917 + 0.035835I
b = −0.623542 − 0.745700I
9.86121 + 2.40714I 1.11944 − 3.44004I
u = −0.037558 − 1.371140I
a = 0.952917 − 0.035835I
b = −0.623542 + 0.745700I
9.86121 − 2.40714I 1.11944 + 3.44004I
u = 0.240518 + 1.356540I
a = −1.46246 − 0.89499I
b = 0.561956 − 1.036960I
6.29728 − 9.25950I −3.29029 + 8.32178I
u = 0.240518 − 1.356540I
a = −1.46246 + 0.89499I
b = 0.561956 + 1.036960I
6.29728 + 9.25950I −3.29029 − 8.32178I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.598794 + 0.151071I
a = −0.88900 + 2.25691I
b = 0.359947 + 1.044940I
−3.27788 + 3.09462I −15.6158 − 6.1007I
u = −0.598794 − 0.151071I
a = −0.88900 − 2.25691I
b = 0.359947 − 1.044940I
−3.27788 − 3.09462I −15.6158 + 6.1007I
u = −0.420730 + 1.328670I
a = 1.38895 − 1.73157I
b = −0.514655 − 1.242600I
−2.9192 + 14.2327I −7.70275 − 8.58885I
u = −0.420730 − 1.328670I
a = 1.38895 + 1.73157I
b = −0.514655 + 1.242600I
−2.9192 − 14.2327I −7.70275 + 8.58885I
u = 0.197618 + 0.311751I
a = 1.224520 + 0.293518I
b = −0.146001 + 0.823219I
−0.656687 − 0.955703I −10.53509 + 6.55993I
u = 0.197618 − 0.311751I
a = 1.224520 − 0.293518I
b = −0.146001 − 0.823219I
−0.656687 + 0.955703I −10.53509 − 6.55993I
6
II.
I
u
2
= h−u
11
−4u
9
+· · ·+b−1, −u
13
+2u
12
+· · ·+2a−1, u
14
+5u
12
+· · ·+u+2i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
4
=
u
u
3
+ u
a
11
=
u
2
+ 1
u
4
+ 2u
2
a
6
=
−u
5
− 2u
3
− u
−u
7
− 3u
5
− 2u
3
+ u
a
2
=
1
2
u
13
− u
12
+ ··· +
1
2
u +
1
2
u
11
+ 4u
9
+ u
8
+ 5u
7
+ 3u
6
+ u
5
+ 2u
4
− u
3
+ 1
a
3
=
u
3
+ 2u
u
3
+ u
a
1
=
−
1
2
u
13
−
3
2
u
11
+ ··· +
1
2
u +
1
2
u
12
+ u
11
+ 4u
10
+ 4u
9
+ 6u
8
+ 5u
7
+ 3u
6
− u
4
− 2u
3
+ u + 1
a
8
=
1
2
u
13
+
3
2
u
11
+ ··· −
1
2
u −
1
2
−u
12
− 4u
10
− u
9
− 5u
8
− 3u
7
− u
6
− 2u
5
+ u
4
− u
2
− u − 1
a
7
=
−
1
2
u
13
−
3
2
u
11
+ ··· −
1
2
u +
1
2
u
12
+ u
11
+ 4u
10
+ 4u
9
+ 6u
8
+ 5u
7
+ 3u
6
− u
4
− 2u
3
+ u + 1
a
12
=
1
2
u
13
+
7
2
u
11
+ ··· +
1
2
u +
5
2
u
13
+ 5u
11
+ 9u
9
+ 5u
7
− 3u
5
+ 2u
4
− 3u
3
+ 4u
2
+ 1
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 4u
12
− 4u
11
+ 16u
10
− 8u
9
+ 20u
8
+ 4u
7
+ 4u
6
+ 20u
5
− 4u
4
+ 12u
3
− 6
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
7
+ 4u
6
+ 8u
5
+ 7u
4
+ 2u
3
− 3u
2
− 2u − 1)
2
c
2
, c
8
(u
7
+ 2u
5
− u
4
+ 2u
3
− u
2
− 1)
2
c
3
, c
5
, c
7
(u
7
− 3u
6
+ u
5
+ 2u
4
+ 2u
3
− 3u
2
+ u − 2)
2
c
4
, c
6
, c
9
c
10
, c
11
, c
12
u
14
+ 5u
12
+ ··· − u + 2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
7
+ 12y
5
+ 3y
4
+ 22y
3
− 3y
2
− 2y −1)
2
c
2
, c
8
(y
7
+ 4y
6
+ 8y
5
+ 7y
4
+ 2y
3
− 3y
2
− 2y −1)
2
c
3
, c
5
, c
7
(y
7
− 7y
6
+ 17y
5
− 16y
4
+ 6y
3
+ 3y
2
− 11y −4)
2
c
4
, c
6
, c
9
c
10
, c
11
, c
12
y
14
+ 10y
13
+ ··· + 3y + 4
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.909403 + 0.064443I
a = −0.15740 + 2.55157I
b = 0.489252 + 1.239920I
−7.27584 + 9.47458I −11.52754 − 6.21855I
u = −0.909403 − 0.064443I
a = −0.15740 − 2.55157I
b = 0.489252 − 1.239920I
−7.27584 − 9.47458I −11.52754 + 6.21855I
u = 0.004458 + 1.241100I
a = −1.103090 + 0.868476I
b = 0.391915 − 0.631080I
3.69786 − 1.46776I −2.58766 + 4.85424I
u = 0.004458 − 1.241100I
a = −1.103090 − 0.868476I
b = 0.391915 + 0.631080I
3.69786 + 1.46776I −2.58766 − 4.85424I
u = 0.689055 + 0.275978I
a = 0.52249 + 2.02022I
b = −0.468927 + 1.008510I
1.13946 − 6.00484I −8.26608 + 8.08638I
u = 0.689055 − 0.275978I
a = 0.52249 − 2.02022I
b = −0.468927 − 1.008510I
1.13946 + 6.00484I −8.26608 − 8.08638I
u = −0.396373 + 0.610024I
a = −0.351244 + 1.089890I
b = 0.391915 + 0.631080I
3.69786 + 1.46776I −2.58766 − 4.85424I
u = −0.396373 − 0.610024I
a = −0.351244 − 1.089890I
b = 0.391915 − 0.631080I
3.69786 − 1.46776I −2.58766 + 4.85424I
u = 0.412241 + 1.228750I
a = −0.088236 + 0.731499I
b = −0.824481
−0.0577569 −5.23744 + 0.I
u = 0.412241 − 1.228750I
a = −0.088236 − 0.731499I
b = −0.824481
−0.0577569 −5.23744 + 0.I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.220128 + 1.284480I
a = 1.90275 − 0.76301I
b = −0.468927 − 1.008510I
1.13946 + 6.00484I −8.26608 − 8.08638I
u = −0.220128 − 1.284480I
a = 1.90275 + 0.76301I
b = −0.468927 + 1.008510I
1.13946 − 6.00484I −8.26608 + 8.08638I
u = 0.420151 + 1.304360I
a = −1.47527 − 1.77944I
b = 0.489252 − 1.239920I
−7.27584 − 9.47458I −11.52754 + 6.21855I
u = 0.420151 − 1.304360I
a = −1.47527 + 1.77944I
b = 0.489252 + 1.239920I
−7.27584 + 9.47458I −11.52754 − 6.21855I
11
III. I
u
3
= hb − u, a − u, u
12
− u
11
+ · · · − u
3
+ 1i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
4
=
u
u
3
+ u
a
11
=
u
2
+ 1
u
4
+ 2u
2
a
6
=
−u
5
− 2u
3
− u
−u
7
− 3u
5
− 2u
3
+ u
a
2
=
u
u
a
3
=
u
3
+ 2u
u
3
+ u
a
1
=
u
5
+ 2u
3
+ u
u
5
+ u
3
+ u
a
8
=
u
2
+ 1
u
2
a
7
=
−u
8
− 3u
6
− 3u
4
+ 1
−u
8
− 2u
6
− 2u
4
a
12
=
−2u
11
− 8u
9
− 13u
7
− 6u
5
+ u
4
+ 4u
3
+ 3u
2
+ 4u + 3
−2u
11
− 8u
9
− 13u
7
+ u
6
− 7u
5
+ 4u
4
+ 2u
3
+ 5u
2
+ 3u + 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
9
+ 12u
7
+ 12u
5
− 4u
3
− 8u − 10
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
12
+ 7u
11
+ ··· + 2u
2
+ 1
c
2
, c
4
, c
8
c
9
, c
10
u
12
+ u
11
+ 4u
10
+ 4u
9
+ 7u
8
+ 7u
7
+ 5u
6
+ 5u
5
+ u
4
+ u
3
+ 1
c
3
, c
5
, c
7
(u
6
+ u
5
− 3u
4
− 2u
3
+ 2u
2
− u − 1)
2
c
6
, c
11
, c
12
(u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
− u − 1)
2
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
12
− 5y
11
+ ··· + 4y + 1
c
2
, c
4
, c
8
c
9
, c
10
y
12
+ 7y
11
+ ··· + 2y
2
+ 1
c
3
, c
5
, c
7
(y
6
− 7y
5
+ 17y
4
− 16y
3
+ 6y
2
− 5y + 1)
2
c
6
, c
11
, c
12
(y
6
+ 5y
5
+ 9y
4
+ 4y
3
− 6y
2
− 5y + 1)
2
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.386547 + 0.899125I
a = 0.386547 + 0.899125I
b = 0.386547 + 0.899125I
2.96024 + 1.97241I −4.57572 − 3.68478I
u = 0.386547 − 0.899125I
a = 0.386547 − 0.899125I
b = 0.386547 − 0.899125I
2.96024 − 1.97241I −4.57572 + 3.68478I
u = −0.206575 + 1.062080I
a = −0.206575 + 1.062080I
b = −0.206575 + 1.062080I
−0.738851 −13.41678 + 0.I
u = −0.206575 − 1.062080I
a = −0.206575 − 1.062080I
b = −0.206575 − 1.062080I
−0.738851 −13.41678 + 0.I
u = 0.869654 + 0.049931I
a = 0.869654 + 0.049931I
b = 0.869654 + 0.049931I
−3.69558 − 4.59213I −8.58114 + 3.20482I
u = 0.869654 − 0.049931I
a = 0.869654 − 0.049931I
b = 0.869654 − 0.049931I
−3.69558 + 4.59213I −8.58114 − 3.20482I
u = −0.460851 + 1.226450I
a = −0.460851 + 1.226450I
b = −0.460851 + 1.226450I
−3.69558 − 4.59213I −8.58114 + 3.20482I
u = −0.460851 − 1.226450I
a = −0.460851 − 1.226450I
b = −0.460851 − 1.226450I
−3.69558 + 4.59213I −8.58114 − 3.20482I
u = 0.436607 + 1.253750I
a = 0.436607 + 1.253750I
b = 0.436607 + 1.253750I
−7.66009 −12.26950 + 0.I
u = 0.436607 − 1.253750I
a = 0.436607 − 1.253750I
b = 0.436607 − 1.253750I
−7.66009 −12.26950 + 0.I
15
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.525382 + 0.335320I
a = −0.525382 + 0.335320I
b = −0.525382 + 0.335320I
2.96024 + 1.97241I −4.57572 − 3.68478I
u = −0.525382 − 0.335320I
a = −0.525382 − 0.335320I
b = −0.525382 − 0.335320I
2.96024 − 1.97241I −4.57572 + 3.68478I
16
IV. I
u
4
= h8u
5
a + 37u
5
+ · · · − 37a + 35, u
5
+ 4u
4
+ · · · − 2a + 7, u
6
+ u
5
+
3u
4
+ 2u
3
+ 2u
2
+ u − 1i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
4
=
u
u
3
+ u
a
11
=
u
2
+ 1
u
4
+ 2u
2
a
6
=
−u
5
− 2u
3
− u
−u
5
− u
4
− 2u
3
− u
2
− u + 1
a
2
=
a
−0.0824742au
5
− 0.381443u
5
+ ··· + 0.381443a − 0.360825
a
3
=
u
3
+ 2u
u
3
+ u
a
1
=
0.247423au
5
− 0.855670u
5
+ ··· + 0.855670a + 0.0824742
0.412371au
5
− 1.09278u
5
+ ··· + 0.0927835a − 0.195876
a
8
=
0.381443au
5
− 0.360825u
5
+ ··· + 0.360825a − 2.20619
0.144330au
5
− 0.0824742u
5
+ ··· + 0.0824742a − 0.618557
a
7
=
0.247423au
5
− 0.855670u
5
+ ··· − 0.144330a − 0.917526
−0.412371au
5
+ 0.0927835u
5
+ ··· − 0.0927835a + 0.195876
a
12
=
0.670103au
5
− 0.525773u
5
+ ··· + 0.525773a − 0.443299
0.422680au
5
− 0.670103u
5
+ ··· − 0.329897a − 0.525773
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
4
− 4u
3
− 8u
2
− 4u − 10
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
12
+ 7u
11
+ ··· + 2u
2
+ 1
c
2
, c
6
, c
8
c
11
, c
12
u
12
+ u
11
+ 4u
10
+ 4u
9
+ 7u
8
+ 7u
7
+ 5u
6
+ 5u
5
+ u
4
+ u
3
+ 1
c
3
, c
5
, c
7
(u
6
+ u
5
− 3u
4
− 2u
3
+ 2u
2
− u − 1)
2
c
4
, c
9
, c
10
(u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
− u − 1)
2
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
12
− 5y
11
+ ··· + 4y + 1
c
2
, c
6
, c
8
c
11
, c
12
y
12
+ 7y
11
+ ··· + 2y
2
+ 1
c
3
, c
5
, c
7
(y
6
− 7y
5
+ 17y
4
− 16y
3
+ 6y
2
− 5y + 1)
2
c
4
, c
9
, c
10
(y
6
+ 5y
5
+ 9y
4
+ 4y
3
− 6y
2
− 5y + 1)
2
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.873214
a = −0.21315 + 2.67643I
b = 0.436607 + 1.253750I
−7.66009 −12.2690
u = −0.873214
a = −0.21315 − 2.67643I
b = 0.436607 − 1.253750I
−7.66009 −12.2690
u = 0.138835 + 1.234450I
a = 0.371706 + 0.742110I
b = −0.525382 − 0.335320I
2.96024 − 1.97241I −4.57572 + 3.68478I
u = 0.138835 + 1.234450I
a = −2.22839 + 0.02729I
b = 0.386547 − 0.899125I
2.96024 − 1.97241I −4.57572 + 3.68478I
u = 0.138835 − 1.234450I
a = 0.371706 − 0.742110I
b = −0.525382 + 0.335320I
2.96024 + 1.97241I −4.57572 − 3.68478I
u = 0.138835 − 1.234450I
a = −2.22839 − 0.02729I
b = 0.386547 + 0.899125I
2.96024 + 1.97241I −4.57572 − 3.68478I
u = −0.408802 + 1.276380I
a = 0.105118 + 0.668457I
b = 0.869654 − 0.049931I
−3.69558 + 4.59213I −8.58114 − 3.20482I
u = −0.408802 + 1.276380I
a = 1.60377 − 1.80541I
b = −0.460851 − 1.226450I
−3.69558 + 4.59213I −8.58114 − 3.20482I
u = −0.408802 − 1.276380I
a = 0.105118 − 0.668457I
b = 0.869654 + 0.049931I
−3.69558 − 4.59213I −8.58114 + 3.20482I
u = −0.408802 − 1.276380I
a = 1.60377 + 1.80541I
b = −0.460851 + 1.226450I
−3.69558 − 4.59213I −8.58114 + 3.20482I
20
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.413150
a = 1.86094 + 2.87653I
b = −0.206575 + 1.062080I
−0.738851 −13.4170
u = 0.413150
a = 1.86094 − 2.87653I
b = −0.206575 − 1.062080I
−0.738851 −13.4170
21
V. I
u
5
= hb − u, a − u, u
6
+ u
5
+ 3u
4
+ 2u
3
+ 2u
2
+ u − 1i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
4
=
u
u
3
+ u
a
11
=
u
2
+ 1
u
4
+ 2u
2
a
6
=
−u
5
− 2u
3
− u
−u
5
− u
4
− 2u
3
− u
2
− u + 1
a
2
=
u
u
a
3
=
u
3
+ 2u
u
3
+ u
a
1
=
u
5
+ 2u
3
+ u
u
5
+ u
3
+ u
a
8
=
u
2
+ 1
u
2
a
7
=
u
3
+ 2u
−u
5
− 2u
4
− u
3
− 2u
2
+ u
a
12
=
−u
4
− u
2
+ 1
u
5
− u
4
− u
2
− u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
4
− 4u
3
− 8u
2
− 4u − 10
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
6
+ 5u
5
+ 9u
4
+ 4u
3
− 6u
2
− 5u + 1
c
2
, c
4
, c
6
c
8
, c
9
, c
10
c
11
, c
12
u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
− u − 1
c
3
, c
5
, c
7
u
6
+ u
5
− 3u
4
− 2u
3
+ 2u
2
− u − 1
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
6
− 7y
5
+ 29y
4
− 72y
3
+ 94y
2
− 37y + 1
c
2
, c
4
, c
6
c
8
, c
9
, c
10
c
11
, c
12
y
6
+ 5y
5
+ 9y
4
+ 4y
3
− 6y
2
− 5y + 1
c
3
, c
5
, c
7
y
6
− 7y
5
+ 17y
4
− 16y
3
+ 6y
2
− 5y + 1
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.873214
a = −0.873214
b = −0.873214
−7.66009 −12.2690
u = 0.138835 + 1.234450I
a = 0.138835 + 1.234450I
b = 0.138835 + 1.234450I
2.96024 − 1.97241I −4.57572 + 3.68478I
u = 0.138835 − 1.234450I
a = 0.138835 − 1.234450I
b = 0.138835 − 1.234450I
2.96024 + 1.97241I −4.57572 − 3.68478I
u = −0.408802 + 1.276380I
a = −0.408802 + 1.276380I
b = −0.408802 + 1.276380I
−3.69558 + 4.59213I −8.58114 − 3.20482I
u = −0.408802 − 1.276380I
a = −0.408802 − 1.276380I
b = −0.408802 − 1.276380I
−3.69558 − 4.59213I −8.58114 + 3.20482I
u = 0.413150
a = 0.413150
b = 0.413150
−0.738851 −13.4170
25
VI. I
u
6
= hb − u, a − u + 1, u
2
+ 1i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
10
=
1
−1
a
4
=
u
0
a
11
=
0
−1
a
6
=
0
u
a
2
=
u − 1
u
a
3
=
u
0
a
1
=
−1
u
a
8
=
−u
−1
a
7
=
−u
−1
a
12
=
−1
u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
2
c
2
, c
4
, c
6
c
8
, c
9
, c
10
c
11
, c
12
u
2
+ 1
c
3
, c
5
, c
7
u
2
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y −1)
2
c
2
, c
4
, c
6
c
8
, c
9
, c
10
c
11
, c
12
(y + 1)
2
c
3
, c
5
, c
7
y
2
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −1.00000 + 1.00000I
b = 1.000000I
1.64493 −8.00000
u = − 1.000000I
a = −1.00000 − 1.00000I
b = − 1.000000I
1.64493 −8.00000
29
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
2
(u
6
+ 5u
5
+ 9u
4
+ 4u
3
− 6u
2
− 5u + 1)
· (u
7
+ 4u
6
+ 8u
5
+ 7u
4
+ 2u
3
− 3u
2
− 2u − 1)
2
· ((u
12
+ 7u
11
+ ··· + 2u
2
+ 1)
2
)(u
16
+ 8u
15
+ ··· + 11u + 4)
c
2
, c
8
(u
2
+ 1)(u
6
− u
5
+ ··· − u − 1)(u
7
+ 2u
5
+ ··· − u
2
− 1)
2
· (u
12
+ u
11
+ 4u
10
+ 4u
9
+ 7u
8
+ 7u
7
+ 5u
6
+ 5u
5
+ u
4
+ u
3
+ 1)
2
· (u
16
− 2u
15
+ ··· − 3u + 2)
c
3
, c
5
, c
7
u
2
(u
6
+ u
5
− 3u
4
− 2u
3
+ 2u
2
− u − 1)
5
· ((u
7
− 3u
6
+ ··· + u − 2)
2
)(u
16
+ 2u
15
+ ··· + 12u + 8)
c
4
, c
6
, c
9
c
10
, c
11
, c
12
(u
2
+ 1)(u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
− u − 1)
3
· (u
12
+ u
11
+ 4u
10
+ 4u
9
+ 7u
8
+ 7u
7
+ 5u
6
+ 5u
5
+ u
4
+ u
3
+ 1)
· (u
14
+ 5u
12
+ ··· − u + 2)(u
16
+ u
15
+ ··· + 2u + 1)
30
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y −1)
2
(y
6
− 7y
5
+ 29y
4
− 72y
3
+ 94y
2
− 37y + 1)
· (y
7
+ 12y
5
+ 3y
4
+ 22y
3
− 3y
2
− 2y −1)
2
· ((y
12
− 5y
11
+ ··· + 4y + 1)
2
)(y
16
+ 24y
14
+ ··· − 33y + 16)
c
2
, c
8
(y + 1)
2
(y
6
+ 5y
5
+ 9y
4
+ 4y
3
− 6y
2
− 5y + 1)
· (y
7
+ 4y
6
+ 8y
5
+ 7y
4
+ 2y
3
− 3y
2
− 2y −1)
2
· ((y
12
+ 7y
11
+ ··· + 2y
2
+ 1)
2
)(y
16
+ 8y
15
+ ··· + 11y + 4)
c
3
, c
5
, c
7
y
2
(y
6
− 7y
5
+ 17y
4
− 16y
3
+ 6y
2
− 5y + 1)
5
· (y
7
− 7y
6
+ 17y
5
− 16y
4
+ 6y
3
+ 3y
2
− 11y −4)
2
· (y
16
− 14y
15
+ ··· + 496y + 64)
c
4
, c
6
, c
9
c
10
, c
11
, c
12
(y + 1)
2
(y
6
+ 5y
5
+ 9y
4
+ 4y
3
− 6y
2
− 5y + 1)
3
· (y
12
+ 7y
11
+ ··· + 2y
2
+ 1)(y
14
+ 10y
13
+ ··· + 3y + 4)
· (y
16
+ 15y
15
+ ··· + 4y + 1)
31
