11a
178
(K11a
178
)
A knot diagram
1
Linearized knot diagam
6 1 11 10 9 2 3 4 5 8 7
Solving Sequence
2,6
7 1 3 8 11 4 9 5 10
c
6
c
1
c
2
c
7
c
11
c
3
c
8
c
5
c
10
c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hu
61
− u
60
+ ··· − u + 1i
* 1 irreducible components of dim
C
= 0, with total 61 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
= hu
61
− u
60
+ · · · − u + 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
1
=
u
u
a
3
=
−u
3
−u
3
+ u
a
8
=
u
8
− u
6
+ u
4
+ 1
u
8
− 2u
6
+ 2u
4
a
11
=
u
3
u
5
− u
3
+ u
a
4
=
u
11
− 2u
9
+ 2u
7
− u
3
u
13
− 3u
11
+ 5u
9
− 4u
7
+ 2u
5
− u
3
+ u
a
9
=
u
32
− 7u
30
+ ··· + 2u
12
+ 1
u
34
− 8u
32
+ ··· + 4u
6
+ u
2
a
5
=
−u
55
+ 12u
53
+ ··· − 5u
7
− 2u
3
−u
55
+ 13u
53
+ ··· − 2u
3
+ u
a
10
=
u
21
− 4u
19
+ 9u
17
− 12u
15
+ 12u
13
− 10u
11
+ 9u
9
− 6u
7
+ 3u
5
+ u
u
21
− 5u
19
+ 13u
17
− 20u
15
+ 20u
13
− 13u
11
+ 7u
9
− 4u
7
+ 3u
5
− u
3
+ u
a
10
=
u
21
− 4u
19
+ 9u
17
− 12u
15
+ 12u
13
− 10u
11
+ 9u
9
− 6u
7
+ 3u
5
+ u
u
21
− 5u
19
+ 13u
17
− 20u
15
+ 20u
13
− 13u
11
+ 7u
9
− 4u
7
+ 3u
5
− u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
59
− 56u
57
+ ··· + 8u − 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
61
− u
60
+ ··· − u + 1
c
2
u
61
+ 29u
60
+ ··· + 3u + 1
c
3
u
61
+ 7u
60
+ ··· + 433u + 37
c
4
, c
5
, c
9
u
61
+ u
60
+ ··· + 3u + 1
c
7
u
61
+ u
60
+ ··· − 211u + 61
c
8
u
61
− u
60
+ ··· + 11u + 2
c
10
u
61
− 13u
60
+ ··· − 3083u + 283
c
11
u
61
− 3u
60
+ ··· − 89u + 56
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
61
− 29y
60
+ ··· + 3y −1
c
2
y
61
+ 7y
60
+ ··· − y −1
c
3
y
61
+ 11y
60
+ ··· − 18009y −1369
c
4
, c
5
, c
9
y
61
+ 55y
60
+ ··· + 3y −1
c
7
y
61
− 13y
60
+ ··· + 176159y −3721
c
8
y
61
+ 3y
60
+ ··· + 57y −4
c
10
y
61
+ 19y
60
+ ··· − 760653y −80089
c
11
y
61
+ 15y
60
+ ··· − 75183y −3136
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.033100 + 0.187577I
3.27959 − 1.47237I −3.77294 + 0.98684I
u = 1.033100 − 0.187577I
3.27959 + 1.47237I −3.77294 − 0.98684I
u = 0.621785 + 0.658999I
7.14477 − 7.36689I 1.83265 + 6.49541I
u = 0.621785 − 0.658999I
7.14477 + 7.36689I 1.83265 − 6.49541I
u = −0.957071 + 0.545546I
0.605205 + 0.585495I −3.92457 + 0.I
u = −0.957071 − 0.545546I
0.605205 − 0.585495I −3.92457 + 0.I
u = 0.948153 + 0.574834I
6.18322 + 2.55917I 0
u = 0.948153 − 0.574834I
6.18322 − 2.55917I 0
u = −0.612486 + 0.631132I
1.61526 + 4.05129I −2.39277 − 6.82409I
u = −0.612486 − 0.631132I
1.61526 − 4.05129I −2.39277 + 6.82409I
u = −1.089710 + 0.268806I
−2.65665 + 0.24134I −8.01162 + 0.I
u = −1.089710 − 0.268806I
−2.65665 − 0.24134I −8.01162 + 0.I
u = −0.541944 + 0.674012I
8.48817 − 1.61774I 3.86252 + 0.20232I
u = −0.541944 − 0.674012I
8.48817 + 1.61774I 3.86252 − 0.20232I
u = 1.003470 + 0.545968I
1.15617 − 4.09014I 0
u = 1.003470 − 0.545968I
1.15617 + 4.09014I 0
u = 1.120400 + 0.239796I
−4.20404 + 3.36287I 0
u = 1.120400 − 0.239796I
−4.20404 − 3.36287I 0
u = −1.129610 + 0.223326I
1.12751 − 6.89407I 0
u = −1.129610 − 0.223326I
1.12751 + 6.89407I 0
u = −1.112280 + 0.300936I
−2.83860 + 0.05729I 0
u = −1.112280 − 0.300936I
−2.83860 − 0.05729I 0
u = 0.702655 + 0.463134I
2.64368 − 1.93405I −1.89634 + 4.21284I
u = 0.702655 − 0.463134I
2.64368 + 1.93405I −1.89634 − 4.21284I
u = 0.343323 + 0.767640I
5.74647 + 9.59086I 0.22395 − 6.02636I
u = 0.343323 − 0.767640I
5.74647 − 9.59086I 0.22395 + 6.02636I
u = −1.010660 + 0.577213I
7.10735 + 6.46891I 0
u = −1.010660 − 0.577213I
7.10735 − 6.46891I 0
u = 1.115370 + 0.342685I
−5.28239 − 3.39079I 0
u = 1.115370 − 0.342685I
−5.28239 + 3.39079I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.394147 + 0.730677I
7.77499 − 0.61886I 2.98419 + 0.41079I
u = −0.394147 − 0.730677I
7.77499 + 0.61886I 2.98419 − 0.41079I
u = 0.552270 + 0.617769I
2.48756 − 0.50881I 0.570526 − 0.185507I
u = 0.552270 − 0.617769I
2.48756 + 0.50881I 0.570526 + 0.185507I
u = −0.336261 + 0.751744I
0.27382 − 6.06188I −4.21507 + 6.02215I
u = −0.336261 − 0.751744I
0.27382 + 6.06188I −4.21507 − 6.02215I
u = −1.124710 + 0.366091I
−0.41617 + 6.80603I 0
u = −1.124710 − 0.366091I
−0.41617 − 6.80603I 0
u = 0.345416 + 0.715523I
1.53930 + 2.31744I −1.192371 − 0.636222I
u = 0.345416 − 0.715523I
1.53930 − 2.31744I −1.192371 + 0.636222I
u = 1.113390 + 0.485777I
0.382880 − 0.851377I 0
u = 1.113390 − 0.485777I
0.382880 + 0.851377I 0
u = −1.112330 + 0.510589I
−4.14943 + 4.18449I 0
u = −1.112330 − 0.510589I
−4.14943 − 4.18449I 0
u = −1.096940 + 0.573191I
5.71025 + 5.58980I 0
u = −1.096940 − 0.573191I
5.71025 − 5.58980I 0
u = 1.118690 + 0.534112I
−1.26791 − 7.55537I 0
u = 1.118690 − 0.534112I
−1.26791 + 7.55537I 0
u = 1.111260 + 0.557520I
−0.69264 − 7.18756I 0
u = 1.111260 − 0.557520I
−0.69264 + 7.18756I 0
u = 0.277033 + 0.691934I
1.13938 + 2.86125I −3.45602 − 3.52851I
u = 0.277033 − 0.691934I
1.13938 − 2.86125I −3.45602 + 3.52851I
u = −1.122410 + 0.565959I
−2.03053 + 11.04660I 0
u = −1.122410 − 0.565959I
−2.03053 − 11.04660I 0
u = 1.124890 + 0.572801I
3.4458 − 14.6424I 0
u = 1.124890 − 0.572801I
3.4458 + 14.6424I 0
u = −0.210413 + 0.629262I
−1.67346 + 0.23991I −8.17483 − 1.24926I
u = −0.210413 − 0.629262I
−1.67346 − 0.23991I −8.17483 + 1.24926I
u = 0.126206 + 0.638743I
3.06025 − 3.37781I −2.51099 + 2.74692I
u = 0.126206 − 0.638743I
3.06025 + 3.37781I −2.51099 − 2.74692I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.612895
−0.928331 −10.6740
7
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
u
61
− u
60
+ ··· − u + 1
c
2
u
61
+ 29u
60
+ ··· + 3u + 1
c
3
u
61
+ 7u
60
+ ··· + 433u + 37
c
4
, c
5
, c
9
u
61
+ u
60
+ ··· + 3u + 1
c
7
u
61
+ u
60
+ ··· − 211u + 61
c
8
u
61
− u
60
+ ··· + 11u + 2
c
10
u
61
− 13u
60
+ ··· − 3083u + 283
c
11
u
61
− 3u
60
+ ··· − 89u + 56
8
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
61
− 29y
60
+ ··· + 3y −1
c
2
y
61
+ 7y
60
+ ··· − y −1
c
3
y
61
+ 11y
60
+ ··· − 18009y −1369
c
4
, c
5
, c
9
y
61
+ 55y
60
+ ··· + 3y −1
c
7
y
61
− 13y
60
+ ··· + 176159y −3721
c
8
y
61
+ 3y
60
+ ··· + 57y −4
c
10
y
61
+ 19y
60
+ ··· − 760653y −80089
c
11
y
61
+ 15y
60
+ ··· − 75183y −3136
9
