11a
156
(K11a
156
)
A knot diagram
1
Linearized knot diagam
6 1 10 7 2 4 5 11 3 8 9
Solving Sequence
1,6
2
3,9
10 4 5 11 8 7
c
1
c
2
c
9
c
3
c
5
c
11
c
8
c
7
c
4
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h1.35866 × 10
48
u
51
− 1.57104 × 10
48
u
50
+ ··· + 3.08851 × 10
48
b + 4.21202 × 10
48
,
− 1.52481 × 10
49
u
51
+ 2.17161 × 10
49
u
50
+ ··· + 6.17703 × 10
48
a − 1.53352 × 10
50
,
u
52
− 2u
51
+ ··· + 28u − 4i
I
u
2
= hb − 1, u
4
+ u
2
+ a + u + 1, u
5
− u
4
+ 2u
3
− u
2
+ u − 1i
I
v
1
= ha, b − v + 2, v
2
− 3v + 1i
* 3 irreducible components of dim
C
= 0, with total 59 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
= h1.36 × 10
48
u
51
− 1.57 × 10
48
u
50
+ · · · + 3.09 × 10
48
b + 4.21 ×
10
48
, −1.52 × 10
49
u
51
+ 2.17 × 10
49
u
50
+ · · · + 6.18 × 10
48
a − 1.53 ×
10
50
, u
52
− 2u
51
+ · · · + 28u − 4i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
u
a
2
=
1
−u
2
a
3
=
u
2
+ 1
−u
2
a
9
=
2.46852u
51
− 3.51562u
50
+ ··· − 104.235u + 24.8262
−0.439906u
51
+ 0.508672u
50
+ ··· + 10.8322u − 1.36377
a
10
=
2.84368u
51
− 4.05858u
50
+ ··· − 117.062u + 28.1494
−0.556181u
51
+ 0.655346u
50
+ ··· + 13.1982u − 1.84971
a
4
=
0.770801u
51
− 0.938728u
50
+ ··· − 26.6783u + 6.61543
−0.576000u
51
+ 0.735448u
50
+ ··· + 12.0720u − 2.35162
a
5
=
−u
u
3
+ u
a
11
=
1.96321u
51
− 3.05211u
50
+ ··· − 93.6559u + 23.1027
0.0420101u
51
+ 0.0759082u
50
+ ··· + 7.19593u − 1.40746
a
8
=
0.194801u
51
− 0.203280u
50
+ ··· − 14.6063u + 4.26381
0.243803u
51
− 0.393136u
50
+ ··· − 7.63417u + 1.60634
a
7
=
0.685271u
51
− 0.920162u
50
+ ··· − 28.4036u + 6.67530
−0.226462u
51
+ 0.539033u
50
+ ··· + 11.5948u − 1.86138
a
7
=
0.685271u
51
− 0.920162u
50
+ ··· − 28.4036u + 6.67530
−0.226462u
51
+ 0.539033u
50
+ ··· + 11.5948u − 1.86138
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6.29255u
51
+ 9.41983u
50
+ ··· + 269.288u − 54.6478
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
52
− 2u
51
+ ··· + 28u − 4
c
2
u
52
+ 18u
51
+ ··· − 72u + 16
c
3
, c
9
u
52
− 2u
51
+ ··· + 64u − 32
c
4
, c
6
, c
7
u
52
− 4u
51
+ ··· − 4u + 1
c
8
, c
10
, c
11
u
52
+ 7u
51
+ ··· + 3u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
52
+ 18y
51
+ ··· − 72y + 16
c
2
y
52
+ 30y
51
+ ··· − 41760y + 256
c
3
, c
9
y
52
− 36y
51
+ ··· − 10752y + 1024
c
4
, c
6
, c
7
y
52
− 44y
51
+ ··· − 116y + 1
c
8
, c
10
, c
11
y
52
− 53y
51
+ ··· + 13y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.075327 + 1.008500I
a = −1.022790 + 0.774917I
b = 1.190360 + 0.416488I
−3.66540 + 1.40599I −0.611498 − 0.934044I
u = 0.075327 − 1.008500I
a = −1.022790 − 0.774917I
b = 1.190360 − 0.416488I
−3.66540 − 1.40599I −0.611498 + 0.934044I
u = 0.613736 + 0.753703I
a = −1.05975 + 1.15611I
b = 0.527758 + 0.653505I
0.194027 + 1.037730I 3.66549 − 3.70521I
u = 0.613736 − 0.753703I
a = −1.05975 − 1.15611I
b = 0.527758 − 0.653505I
0.194027 − 1.037730I 3.66549 + 3.70521I
u = −0.772235 + 0.690068I
a = −2.53064 − 1.27133I
b = 1.378930 + 0.036041I
2.12355 + 1.28202I 4.52218 − 0.37137I
u = −0.772235 − 0.690068I
a = −2.53064 + 1.27133I
b = 1.378930 − 0.036041I
2.12355 − 1.28202I 4.52218 + 0.37137I
u = 0.455162 + 0.835894I
a = 0.863304 − 0.362503I
b = −0.263353 − 0.185170I
−0.04711 + 1.88095I −0.11775 − 4.20113I
u = 0.455162 − 0.835894I
a = 0.863304 + 0.362503I
b = −0.263353 + 0.185170I
−0.04711 − 1.88095I −0.11775 + 4.20113I
u = −0.729350 + 0.773257I
a = −0.108923 − 0.214082I
b = 0.639530 + 0.722525I
3.67881 − 0.13440I 8.39486 + 0.I
u = −0.729350 − 0.773257I
a = −0.108923 + 0.214082I
b = 0.639530 − 0.722525I
3.67881 + 0.13440I 8.39486 + 0.I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.886765 + 0.619894I
a = 0.076581 + 0.354456I
b = 0.461865 − 0.742040I
−0.14154 − 3.59160I 3.36417 + 4.10455I
u = 0.886765 − 0.619894I
a = 0.076581 − 0.354456I
b = 0.461865 + 0.742040I
−0.14154 + 3.59160I 3.36417 − 4.10455I
u = 0.619534 + 0.655112I
a = 1.82077 − 0.13795I
b = −1.62890 + 0.13929I
7.94427 + 0.70276I 6.08078 − 4.95980I
u = 0.619534 − 0.655112I
a = 1.82077 + 0.13795I
b = −1.62890 − 0.13929I
7.94427 − 0.70276I 6.08078 + 4.95980I
u = −0.906927 + 0.670128I
a = 1.75190 + 0.21463I
b = −1.55769 − 0.21556I
10.93850 + 3.24486I 10.33648 − 1.31467I
u = −0.906927 − 0.670128I
a = 1.75190 − 0.21463I
b = −1.55769 + 0.21556I
10.93850 − 3.24486I 10.33648 + 1.31467I
u = 0.732657 + 0.866743I
a = −2.26559 + 1.11526I
b = 1.43928 + 0.05940I
5.55338 + 2.78570I 8.09999 − 3.02309I
u = 0.732657 − 0.866743I
a = −2.26559 − 1.11526I
b = 1.43928 − 0.05940I
5.55338 − 2.78570I 8.09999 + 3.02309I
u = 0.635920 + 0.950705I
a = −0.338552 + 0.157448I
b = 0.792480 − 0.758107I
−0.43994 + 3.90031I 3.00000 − 3.18847I
u = 0.635920 − 0.950705I
a = −0.338552 − 0.157448I
b = 0.792480 + 0.758107I
−0.43994 − 3.90031I 3.00000 + 3.18847I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.134179 + 1.161340I
a = −0.384531 − 0.483430I
b = −1.389650 − 0.050928I
3.59908 + 2.53417I 6.05449 − 3.57963I
u = 0.134179 − 1.161340I
a = −0.384531 + 0.483430I
b = −1.389650 + 0.050928I
3.59908 − 2.53417I 6.05449 + 3.57963I
u = −0.699619 + 0.940497I
a = −0.928509 − 0.600285I
b = 0.486038 − 0.816981I
3.16600 − 5.32735I 0. + 6.25644I
u = −0.699619 − 0.940497I
a = −0.928509 + 0.600285I
b = 0.486038 + 0.816981I
3.16600 + 5.32735I 0. − 6.25644I
u = −0.155548 + 1.164430I
a = 0.234739 − 0.432223I
b = 0.000043 − 0.701161I
−7.29497 − 2.64942I −4.44338 + 3.34527I
u = −0.155548 − 1.164430I
a = 0.234739 + 0.432223I
b = 0.000043 + 0.701161I
−7.29497 + 2.64942I −4.44338 − 3.34527I
u = −0.785903 + 0.215104I
a = 0.746081 + 0.304165I
b = −0.093921 − 0.253947I
−2.53454 + 0.36656I −2.03786 + 0.85265I
u = −0.785903 − 0.215104I
a = 0.746081 − 0.304165I
b = −0.093921 + 0.253947I
−2.53454 − 0.36656I −2.03786 − 0.85265I
u = −1.19620
a = 1.56251
b = −1.37476
1.56846 5.85290
u = 0.638094 + 1.019660I
a = 1.08345 − 1.78360I
b = −1.50936 − 0.23396I
6.79512 + 4.31192I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.638094 − 1.019660I
a = 1.08345 + 1.78360I
b = −1.50936 + 0.23396I
6.79512 − 4.31192I 0
u = 0.056951 + 0.784785I
a = 0.767881 + 0.964864I
b = 0.115114 + 0.367824I
−1.14630 + 1.33765I −2.67722 − 5.83204I
u = 0.056951 − 0.784785I
a = 0.767881 − 0.964864I
b = 0.115114 − 0.367824I
−1.14630 − 1.33765I −2.67722 + 5.83204I
u = −0.702251 + 0.998907I
a = −2.13606 − 0.96284I
b = 1.48399 − 0.13222I
1.19040 − 6.87281I 0
u = −0.702251 − 0.998907I
a = −2.13606 + 0.96284I
b = 1.48399 + 0.13222I
1.19040 + 6.87281I 0
u = −0.513163 + 1.119450I
a = 0.818574 + 0.287487I
b = −0.443701 + 0.321088I
−5.16137 − 5.07594I 0
u = −0.513163 − 1.119450I
a = 0.818574 − 0.287487I
b = −0.443701 − 0.321088I
−5.16137 + 5.07594I 0
u = 1.064470 + 0.691714I
a = 1.70299 − 0.26759I
b = −1.50643 + 0.26773I
6.26071 − 7.29271I 0
u = 1.064470 − 0.691714I
a = 1.70299 + 0.26759I
b = −1.50643 − 0.26773I
6.26071 + 7.29271I 0
u = 0.722743 + 1.064410I
a = −0.814403 + 0.358577I
b = 0.440375 + 0.908105I
−1.50501 + 9.54274I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.722743 − 1.064410I
a = −0.814403 − 0.358577I
b = 0.440375 − 0.908105I
−1.50501 − 9.54274I 0
u = −0.753203 + 1.063150I
a = 1.45173 + 1.51990I
b = −1.52645 + 0.29210I
9.71492 − 9.38312I 0
u = −0.753203 − 1.063150I
a = 1.45173 − 1.51990I
b = −1.52645 − 0.29210I
9.71492 + 9.38312I 0
u = 0.620392
a = 1.74300
b = −1.55182
7.82641 14.3530
u = 0.813568 + 1.125730I
a = 1.56036 − 1.27231I
b = −1.52286 − 0.33951I
4.8388 + 14.0856I 0
u = 0.813568 − 1.125730I
a = 1.56036 + 1.27231I
b = −1.52286 + 0.33951I
4.8388 − 14.0856I 0
u = −0.34754 + 1.37165I
a = 0.417284 + 0.592951I
b = −1.303780 + 0.146210I
−3.43276 − 5.51955I 0
u = −0.34754 − 1.37165I
a = 0.417284 − 0.592951I
b = −1.303780 − 0.146210I
−3.43276 + 5.51955I 0
u = −0.145020 + 0.564037I
a = −0.17797 − 2.25336I
b = 1.043790 − 0.148422I
1.28226 − 0.71509I 4.69271 − 2.87667I
u = −0.145020 − 0.564037I
a = −0.17797 + 2.25336I
b = 1.043790 + 0.148422I
1.28226 + 0.71509I 4.69271 + 2.87667I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.390440
a = −9.46557
b = 0.911724
−0.325570 41.4780
u = 0.308678
a = 0.604187
b = 0.507949
0.870137 11.8930
10
II. I
u
2
= hb − 1, u
4
+ u
2
+ a + u + 1, u
5
− u
4
+ 2u
3
− u
2
+ u − 1i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
u
a
2
=
1
−u
2
a
3
=
u
2
+ 1
−u
2
a
9
=
−u
4
− u
2
− u − 1
1
a
10
=
−u
4
− u
2
− u − 1
1
a
4
=
u
2
+ 1
−u
2
a
5
=
−u
u
3
+ u
a
11
=
−u
4
− u
2
− u
1
a
8
=
−1
0
a
7
=
−u
4
− u
2
− 1
u
4
− u
3
+ u
2
+ 1
a
7
=
−u
4
− u
2
− 1
u
4
− u
3
+ u
2
+ 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2u
4
+ 5u
3
− 7u
2
+ 5u
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
5
− u
4
+ 2u
3
− u
2
+ u − 1
c
2
u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1
c
3
, c
9
u
5
c
4
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
c
5
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1
c
6
, c
7
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
c
8
(u + 1)
5
c
10
, c
11
(u − 1)
5
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1
c
2
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1
c
3
, c
9
y
5
c
4
, c
6
, c
7
y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1
c
8
, c
10
, c
11
(y −1)
5
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.339110 + 0.822375I
a = −0.103562 − 0.890762I
b = 1.00000
1.31583 − 1.53058I 5.47076 + 5.40154I
u = −0.339110 − 0.822375I
a = −0.103562 + 0.890762I
b = 1.00000
1.31583 + 1.53058I 5.47076 − 5.40154I
u = 0.766826
a = −2.70062
b = 1.00000
−0.756147 1.28100
u = 0.455697 + 1.200150I
a = −0.546130 + 0.402731I
b = 1.00000
−4.22763 + 4.40083I 0.88874 − 1.16747I
u = 0.455697 − 1.200150I
a = −0.546130 − 0.402731I
b = 1.00000
−4.22763 − 4.40083I 0.88874 + 1.16747I
14
III. I
v
1
= ha, b − v + 2, v
2
− 3v + 1i
(i) Arc colorings
a
1
=
1
0
a
6
=
v
0
a
2
=
1
0
a
3
=
1
0
a
9
=
0
v − 2
a
10
=
v − 2
v − 2
a
4
=
v − 2
v − 3
a
5
=
v
0
a
11
=
1
−v + 3
a
8
=
−v + 2
−v + 3
a
7
=
2
−v + 3
a
7
=
2
−v + 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −1
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
u
2
c
3
, c
10
, c
11
u
2
+ u − 1
c
4
(u − 1)
2
c
6
, c
7
(u + 1)
2
c
8
, c
9
u
2
− u − 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
y
2
c
3
, c
8
, c
9
c
10
, c
11
y
2
− 3y + 1
c
4
, c
6
, c
7
(y − 1)
2
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.381966
a = 0
b = −1.61803
7.23771 −1.00000
v = 2.61803
a = 0
b = 0.618034
−0.657974 −1.00000
18
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
2
(u
5
− u
4
+ ··· + u − 1)(u
52
− 2u
51
+ ··· + 28u − 4)
c
2
u
2
(u
5
+ 3u
4
+ ··· − u − 1)(u
52
+ 18u
51
+ ··· − 72u + 16)
c
3
u
5
(u
2
+ u − 1)(u
52
− 2u
51
+ ··· + 64u − 32)
c
4
((u − 1)
2
)(u
5
+ u
4
+ ··· + u − 1)(u
52
− 4u
51
+ ··· − 4u + 1)
c
5
u
2
(u
5
+ u
4
+ ··· + u + 1)(u
52
− 2u
51
+ ··· + 28u − 4)
c
6
, c
7
((u + 1)
2
)(u
5
− u
4
+ ··· + u + 1)(u
52
− 4u
51
+ ··· − 4u + 1)
c
8
((u + 1)
5
)(u
2
− u − 1)(u
52
+ 7u
51
+ ··· + 3u + 1)
c
9
u
5
(u
2
− u − 1)(u
52
− 2u
51
+ ··· + 64u − 32)
c
10
, c
11
((u − 1)
5
)(u
2
+ u − 1)(u
52
+ 7u
51
+ ··· + 3u + 1)
19
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
2
(y
5
+ 3y
4
+ ··· − y − 1)(y
52
+ 18y
51
+ ··· − 72y + 16)
c
2
y
2
(y
5
− y
4
+ ··· + 3y − 1)(y
52
+ 30y
51
+ ··· − 41760y + 256)
c
3
, c
9
y
5
(y
2
− 3y + 1)(y
52
− 36y
51
+ ··· − 10752y + 1024)
c
4
, c
6
, c
7
((y − 1)
2
)(y
5
− 5y
4
+ ··· − y − 1)(y
52
− 44y
51
+ ··· − 116y + 1)
c
8
, c
10
, c
11
((y − 1)
5
)(y
2
− 3y + 1)(y
52
− 53y
51
+ ··· + 13y + 1)
20
