11a
133
(K11a
133
)
A knot diagram
1
Linearized knot diagam
5 1 8 7 2 10 4 3 11 6 9
Solving Sequence
3,8
4
1,9
2 7 5 11 10 6
c
3
c
8
c
2
c
7
c
4
c
11
c
9
c
6
c
1
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h3.79178 × 10
22
u
44
+ 3.67398 × 10
22
u
43
+ ··· + 7.16385 × 10
22
b − 6.36327 × 10
21
,
− 9.16718 × 10
20
u
44
+ 1.82694 × 10
23
u
43
+ ··· + 2.86554 × 10
23
a − 2.62927 × 10
24
, u
45
+ u
44
+ ··· − 28u
2
− 4i
I
u
2
= hb + 1, 2a
2
− au − 4a + u + 1, u
2
+ 2i
I
v
1
= ha, b + 1, v
2
+ v + 1i
* 3 irreducible components of dim
C
= 0, with total 51 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
= h3.79 × 10
22
u
44
+ 3.67 × 10
22
u
43
+ · · · + 7.16 × 10
22
b − 6.36 ×
10
21
, −9.17 × 10
20
u
44
+ 1.83 × 10
23
u
43
+ · · · + 2.87 × 10
23
a − 2.63 ×
10
24
, u
45
+ u
44
+ · · · − 28u
2
− 4i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
u
2
a
1
=
0.00319911u
44
− 0.637556u
43
+ ··· − 7.59140u + 9.17549
−0.529294u
44
− 0.512850u
43
+ ··· + 4.30006u + 0.0888247
a
9
=
−u
u
a
2
=
0.424417u
44
+ 0.198789u
43
+ ··· − 8.45475u + 5.64275
−1.00162u
44
− 1.22215u
43
+ ··· + 7.67645u + 1.88551
a
7
=
u
u
3
+ u
a
5
=
u
2
+ 1
u
4
+ 2u
2
a
11
=
0.432131u
44
+ 0.147580u
43
+ ··· − 9.69578u + 6.67824
−0.958226u
44
− 1.29799u
43
+ ··· + 6.40444u + 2.58607
a
10
=
0.729800u
44
+ 0.582734u
43
+ ··· − 6.09901u − 6.26113
−0.0344386u
44
+ 0.939991u
43
+ ··· + 4.74682u − 5.61829
a
6
=
0.432131u
44
+ 0.147580u
43
+ ··· − 9.69578u + 6.67824
0.415034u
44
+ 0.460313u
43
+ ··· − 4.67591u − 3.72428
a
6
=
0.432131u
44
+ 0.147580u
43
+ ··· − 9.69578u + 6.67824
0.415034u
44
+ 0.460313u
43
+ ··· − 4.67591u − 3.72428
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
32120453352253218896835
71638476266902618700479
u
44
+
51439144552236413356159
71638476266902618700479
u
43
+ ··· +
267057572611973423431852
71638476266902618700479
u −
630536796005845775981388
71638476266902618700479
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
45
+ 3u
44
+ ··· − 10u + 3
c
2
u
45
+ 19u
44
+ ··· + 58u + 9
c
3
, c
4
, c
7
c
8
u
45
− u
44
+ ··· + 28u
2
+ 4
c
6
, c
10
u
45
− 2u
44
+ ··· + 3u + 3
c
9
, c
11
u
45
+ 14u
44
+ ··· + 21u − 9
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
45
− 19y
44
+ ··· + 58y −9
c
2
y
45
+ 21y
44
+ ··· − 1838y −81
c
3
, c
4
, c
7
c
8
y
45
+ 55y
44
+ ··· − 224y −16
c
6
, c
10
y
45
+ 14y
44
+ ··· + 21y −9
c
9
, c
11
y
45
+ 38y
44
+ ··· + 10737y −81
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.595154 + 0.799976I
a = −0.809139 − 0.923508I
b = −0.66293 + 1.48925I
3.82469 + 9.97213I −4.07711 − 8.66746I
u = −0.595154 − 0.799976I
a = −0.809139 + 0.923508I
b = −0.66293 − 1.48925I
3.82469 − 9.97213I −4.07711 + 8.66746I
u = 0.542227 + 0.847104I
a = −0.624429 + 0.873722I
b = −0.49486 − 1.41856I
4.60680 − 4.00969I −2.37481 + 3.81201I
u = 0.542227 − 0.847104I
a = −0.624429 − 0.873722I
b = −0.49486 + 1.41856I
4.60680 + 4.00969I −2.37481 − 3.81201I
u = 0.449130 + 0.919217I
a = 0.997189 − 0.562134I
b = 0.360475 + 0.942383I
5.31668 − 4.26099I −1.24439 + 3.98671I
u = 0.449130 − 0.919217I
a = 0.997189 + 0.562134I
b = 0.360475 − 0.942383I
5.31668 + 4.26099I −1.24439 − 3.98671I
u = −0.372392 + 1.006660I
a = 0.981655 + 0.526640I
b = 0.139519 − 1.024240I
5.57757 − 1.59310I −0.70414 + 1.88658I
u = −0.372392 − 1.006660I
a = 0.981655 − 0.526640I
b = 0.139519 + 1.024240I
5.57757 + 1.59310I −0.70414 − 1.88658I
u = 0.203852 + 0.752739I
a = 0.411257 + 1.253590I
b = −0.370857 − 0.767483I
1.25627 − 2.00304I −0.90089 + 4.84629I
u = 0.203852 − 0.752739I
a = 0.411257 − 1.253590I
b = −0.370857 + 0.767483I
1.25627 + 2.00304I −0.90089 − 4.84629I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.756562 + 0.151657I
a = 0.353008 − 0.645751I
b = −0.400769 − 1.209730I
1.87890 − 5.45220I −5.89309 + 4.91113I
u = −0.756562 − 0.151657I
a = 0.353008 + 0.645751I
b = −0.400769 + 1.209730I
1.87890 + 5.45220I −5.89309 − 4.91113I
u = −0.411509 + 0.629213I
a = −0.48287 − 1.77369I
b = −0.759126 + 0.924061I
−2.33846 + 4.64978I −9.14624 − 8.10002I
u = −0.411509 − 0.629213I
a = −0.48287 + 1.77369I
b = −0.759126 − 0.924061I
−2.33846 − 4.64978I −9.14624 + 8.10002I
u = 0.739174 + 0.066659I
a = 0.432504 + 0.605344I
b = −0.183861 + 1.069320I
2.24775 − 0.28638I −4.98856 + 0.17511I
u = 0.739174 − 0.066659I
a = 0.432504 − 0.605344I
b = −0.183861 − 1.069320I
2.24775 + 0.28638I −4.98856 − 0.17511I
u = 0.038629 + 1.346620I
a = 0.753383 − 0.039929I
b = −0.056494 − 0.156524I
4.91236 − 2.29181I 0
u = 0.038629 − 1.346620I
a = 0.753383 + 0.039929I
b = −0.056494 + 0.156524I
4.91236 + 2.29181I 0
u = −0.101635 + 0.590584I
a = −0.429318 − 0.140632I
b = −1.47830 − 0.11239I
−0.78716 + 2.48122I −3.04347 − 4.76589I
u = −0.101635 − 0.590584I
a = −0.429318 + 0.140632I
b = −1.47830 + 0.11239I
−0.78716 − 2.48122I −3.04347 + 4.76589I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.479511 + 0.303305I
a = 0.065872 − 0.427985I
b = −0.987241 − 0.640209I
−3.30905 − 1.49655I −13.54204 − 0.04800I
u = −0.479511 − 0.303305I
a = 0.065872 + 0.427985I
b = −0.987241 + 0.640209I
−3.30905 + 1.49655I −13.54204 + 0.04800I
u = −0.08818 + 1.43765I
a = 1.047830 + 0.106631I
b = −1.143340 − 0.464536I
2.28059 + 0.33440I 0
u = −0.08818 − 1.43765I
a = 1.047830 − 0.106631I
b = −1.143340 + 0.464536I
2.28059 − 0.33440I 0
u = −0.117374 + 0.488254I
a = 1.95300 − 2.18078I
b = −0.572552 + 0.344300I
−1.01308 − 1.54097I −3.12750 − 1.49729I
u = −0.117374 − 0.488254I
a = 1.95300 + 2.18078I
b = −0.572552 − 0.344300I
−1.01308 + 1.54097I −3.12750 + 1.49729I
u = 0.320837 + 0.380710I
a = 1.001570 − 0.386206I
b = 0.159215 + 0.077837I
−0.430811 − 1.192020I −5.27697 + 5.64355I
u = 0.320837 − 0.380710I
a = 1.001570 + 0.386206I
b = 0.159215 − 0.077837I
−0.430811 + 1.192020I −5.27697 − 5.64355I
u = −0.00060 + 1.58402I
a = 0.58858 − 1.61169I
b = −0.042622 + 0.922347I
6.21731 − 1.33164I 0
u = −0.00060 − 1.58402I
a = 0.58858 + 1.61169I
b = −0.042622 − 0.922347I
6.21731 + 1.33164I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.10202 + 1.59722I
a = 0.16838 − 2.06884I
b = −0.568246 + 1.291280I
5.28483 + 6.46491I 0
u = −0.10202 − 1.59722I
a = 0.16838 + 2.06884I
b = −0.568246 − 1.291280I
5.28483 − 6.46491I 0
u = 0.393229
a = 0.318039
b = −0.551275
−0.995192 −10.6150
u = −0.02225 + 1.60699I
a = 1.205480 + 0.019298I
b = −2.04934 − 0.12580I
6.93943 + 2.89736I 0
u = −0.02225 − 1.60699I
a = 1.205480 − 0.019298I
b = −2.04934 + 0.12580I
6.93943 − 2.89736I 0
u = 0.04744 + 1.63431I
a = 0.24569 + 1.76495I
b = −0.161409 − 1.339170I
9.56075 − 2.89885I 0
u = 0.04744 − 1.63431I
a = 0.24569 − 1.76495I
b = −0.161409 + 1.339170I
9.56075 + 2.89885I 0
u = −0.17946 + 1.64793I
a = −0.15251 − 1.95899I
b = −0.85684 + 1.76671I
12.1487 + 12.9478I 0
u = −0.17946 − 1.64793I
a = −0.15251 + 1.95899I
b = −0.85684 − 1.76671I
12.1487 − 12.9478I 0
u = 0.15594 + 1.66197I
a = −0.10012 + 1.91348I
b = −0.69213 − 1.78816I
13.2084 − 6.7061I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.15594 − 1.66197I
a = −0.10012 − 1.91348I
b = −0.69213 + 1.78816I
13.2084 + 6.7061I 0
u = 0.11988 + 1.67520I
a = 0.116060 − 1.188540I
b = 0.864414 + 1.057190I
14.2846 − 6.4583I 0
u = 0.11988 − 1.67520I
a = 0.116060 + 1.188540I
b = 0.864414 − 1.057190I
14.2846 + 6.4583I 0
u = −0.08709 + 1.68689I
a = 0.117912 + 1.285170I
b = 0.73293 − 1.22370I
14.9288 + 0.1276I 0
u = −0.08709 − 1.68689I
a = 0.117912 − 1.285170I
b = 0.73293 + 1.22370I
14.9288 − 0.1276I 0
9
II. I
u
2
= hb + 1, 2a
2
− au − 4a + u + 1, u
2
+ 2i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
−2
a
1
=
a
−1
a
9
=
−u
u
a
2
=
a + 1
−1
a
7
=
u
−u
a
5
=
−1
0
a
11
=
−a + 2
2a − 3
a
10
=
−au − a +
1
2
u + 1
au + 2a − u − 2
a
6
=
a
−1
a
6
=
a
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4au + 4u − 8
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u + 1)
4
c
3
, c
4
, c
7
c
8
(u
2
+ 2)
2
c
5
(u − 1)
4
c
6
, c
9
(u
2
− u + 1)
2
c
10
, c
11
(u
2
+ u + 1)
2
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y −1)
4
c
3
, c
4
, c
7
c
8
(y + 2)
4
c
6
, c
9
, c
10
c
11
(y
2
+ y + 1)
2
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.414210I
a = 0.387628 + 0.353553I
b = −1.00000
3.28987 − 2.02988I −6.00000 + 3.46410I
u = 1.414210I
a = 1.61237 + 0.35355I
b = −1.00000
3.28987 + 2.02988I −6.00000 − 3.46410I
u = − 1.414210I
a = 0.387628 − 0.353553I
b = −1.00000
3.28987 + 2.02988I −6.00000 − 3.46410I
u = − 1.414210I
a = 1.61237 − 0.35355I
b = −1.00000
3.28987 − 2.02988I −6.00000 + 3.46410I
13
III. I
v
1
= ha, b + 1, v
2
+ v + 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
v
0
a
4
=
1
0
a
1
=
0
−1
a
9
=
v
0
a
2
=
1
−1
a
7
=
v
0
a
5
=
1
0
a
11
=
v + 1
−1
a
10
=
v + 1
v
a
6
=
0
1
a
6
=
0
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4v − 14
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
2
c
2
, c
5
(u + 1)
2
c
3
, c
4
, c
7
c
8
u
2
c
6
, c
11
u
2
+ u + 1
c
9
, c
10
u
2
− u + 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y − 1)
2
c
3
, c
4
, c
7
c
8
y
2
c
6
, c
9
, c
10
c
11
y
2
+ y + 1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.500000 + 0.866025I
a = 0
b = −1.00000
−1.64493 + 2.02988I −12.00000 − 3.46410I
v = −0.500000 − 0.866025I
a = 0
b = −1.00000
−1.64493 − 2.02988I −12.00000 + 3.46410I
17
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
2
)(u + 1)
4
(u
45
+ 3u
44
+ ··· − 10u + 3)
c
2
((u + 1)
6
)(u
45
+ 19u
44
+ ··· + 58u + 9)
c
3
, c
4
, c
7
c
8
u
2
(u
2
+ 2)
2
(u
45
− u
44
+ ··· + 28u
2
+ 4)
c
5
((u − 1)
4
)(u + 1)
2
(u
45
+ 3u
44
+ ··· − 10u + 3)
c
6
((u
2
− u + 1)
2
)(u
2
+ u + 1)(u
45
− 2u
44
+ ··· + 3u + 3)
c
9
((u
2
− u + 1)
3
)(u
45
+ 14u
44
+ ··· + 21u − 9)
c
10
(u
2
− u + 1)(u
2
+ u + 1)
2
(u
45
− 2u
44
+ ··· + 3u + 3)
c
11
((u
2
+ u + 1)
3
)(u
45
+ 14u
44
+ ··· + 21u − 9)
18
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
((y − 1)
6
)(y
45
− 19y
44
+ ··· + 58y − 9)
c
2
((y − 1)
6
)(y
45
+ 21y
44
+ ··· − 1838y − 81)
c
3
, c
4
, c
7
c
8
y
2
(y + 2)
4
(y
45
+ 55y
44
+ ··· − 224y − 16)
c
6
, c
10
((y
2
+ y + 1)
3
)(y
45
+ 14y
44
+ ··· + 21y − 9)
c
9
, c
11
((y
2
+ y + 1)
3
)(y
45
+ 38y
44
+ ··· + 10737y − 81)
19
