11a
237
(K11a
237
)
A knot diagram
1
Linearized knot diagam
7 1 10 9 11 8 2 3 4 6 5
Solving Sequence
6,10 4,11
3 5 1 2 9 8 7
c
10
c
3
c
5
c
11
c
2
c
9
c
8
c
6
c
1
, c
4
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= hb − u, u
19
− u
18
+ ··· + 4a + 1, u
20
+ 11u
18
+ ··· + 3u − 1i
I
u
2
= h−159484971u
29
+ 121594878u
28
+ ··· + 95716253b + 570195911, −u
29
+ u
28
+ ··· + a + 6,
u
30
− u
29
+ ··· − 6u + 1i
I
u
3
= hb + u, a
2
− 2au − a + u, u
2
+ 1i
* 3 irreducible components of dim
C
= 0, with total 54 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
19
− u
18
+ · · · + 4a + 1, u
20
+ 11u
18
+ · · · + 3u − 1i
(i) Arc colorings
a
6
=
0
u
a
10
=
1
0
a
4
=
−
1
4
u
19
+
1
4
u
18
+ ··· + 3u −
1
4
u
a
11
=
1
u
2
a
3
=
−
1
4
u
19
+
1
4
u
18
+ ··· + 4u −
1
4
u
a
5
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
4
+ 2u
2
a
2
=
−
1
4
u
19
+
1
4
u
18
+ ··· + 5u −
1
4
1
4
u
19
−
1
4
u
18
+ ··· + u
2
+
1
4
a
9
=
−
1
4
u
19
−
1
4
u
18
+ ··· −
1
2
u +
5
4
−u
2
a
8
=
−
1
4
u
19
−
1
4
u
18
+ ··· −
1
2
u +
5
4
−u
4
− 2u
2
a
7
=
1
2
u
19
+
1
2
u
18
+ ··· +
5
2
u
2
− 2u
1
4
u
19
−
1
4
u
18
+ ··· + u
2
+
1
4
a
7
=
1
2
u
19
+
1
2
u
18
+ ··· +
5
2
u
2
− 2u
1
4
u
19
−
1
4
u
18
+ ··· + u
2
+
1
4
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2u
19
− 21u
17
− 3u
16
− 91u
15
− 30u
14
− 202u
13
− 119u
12
−
224u
11
− 227u
10
− 84u
9
− 181u
8
+ 22u
7
+ 14u
6
− 22u
5
+ 64u
4
− 28u
3
− 25u
2
+ 12u − 19
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
20
+ 3u
19
+ ··· − 9u − 2
c
2
, c
6
u
20
+ 7u
19
+ ··· + 33u + 4
c
3
, c
4
, c
5
c
9
, c
10
, c
11
u
20
+ 11u
18
+ ··· − 3u − 1
c
8
u
20
− 3u
19
+ ··· − 48u − 32
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
20
− 7y
19
+ ··· − 33y + 4
c
2
, c
6
y
20
+ 13y
19
+ ··· − 561y + 16
c
3
, c
4
, c
5
c
9
, c
10
, c
11
y
20
+ 22y
19
+ ··· − 5y + 1
c
8
y
20
− y
19
+ ··· + 3328y + 1024
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.711644 + 0.213665I
a = −0.992229 + 0.085972I
b = −0.711644 + 0.213665I
−0.77253 + 5.59830I −13.4954 − 6.8250I
u = −0.711644 − 0.213665I
a = −0.992229 − 0.085972I
b = −0.711644 − 0.213665I
−0.77253 − 5.59830I −13.4954 + 6.8250I
u = −0.714807
a = −0.946170
b = −0.714807
−4.75848 −19.2850
u = 0.147507 + 1.344930I
a = 1.07486 − 2.87571I
b = 0.147507 + 1.344930I
5.87096 + 0.28405I −5.48153 − 0.41216I
u = 0.147507 − 1.344930I
a = 1.07486 + 2.87571I
b = 0.147507 − 1.344930I
5.87096 − 0.28405I −5.48153 + 0.41216I
u = 0.601815 + 0.228236I
a = 0.950028 + 0.149217I
b = 0.601815 + 0.228236I
0.157185 − 0.414126I −12.01664 + 2.08787I
u = 0.601815 − 0.228236I
a = 0.950028 − 0.149217I
b = 0.601815 − 0.228236I
0.157185 + 0.414126I −12.01664 − 2.08787I
u = 0.280299 + 1.365240I
a = 1.37177 − 2.14002I
b = 0.280299 + 1.365240I
3.92725 − 7.17367I −8.70322 + 5.73165I
u = 0.280299 − 1.365240I
a = 1.37177 + 2.14002I
b = 0.280299 − 1.365240I
3.92725 + 7.17367I −8.70322 − 5.73165I
u = −0.20040 + 1.40896I
a = −1.00049 − 2.38403I
b = −0.20040 + 1.40896I
8.53664 + 4.27425I −2.38649 − 3.51536I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.20040 − 1.40896I
a = −1.00049 + 2.38403I
b = −0.20040 − 1.40896I
8.53664 − 4.27425I −2.38649 + 3.51536I
u = 0.35253 + 1.44249I
a = 1.15928 − 1.78353I
b = 0.35253 + 1.44249I
9.8480 − 13.6547I −5.09222 + 8.08354I
u = 0.35253 − 1.44249I
a = 1.15928 + 1.78353I
b = 0.35253 − 1.44249I
9.8480 + 13.6547I −5.09222 − 8.08354I
u = −0.32179 + 1.45317I
a = −1.09427 − 1.86772I
b = −0.32179 + 1.45317I
11.02130 + 7.69202I −3.25100 − 3.40395I
u = −0.32179 − 1.45317I
a = −1.09427 + 1.86772I
b = −0.32179 − 1.45317I
11.02130 − 7.69202I −3.25100 + 3.40395I
u = 0.074422 + 0.475930I
a = 0.299691 + 1.194600I
b = 0.074422 + 0.475930I
1.45151 − 2.34993I −9.21397 + 4.74077I
u = 0.074422 − 0.475930I
a = 0.299691 − 1.194600I
b = 0.074422 − 0.475930I
1.45151 + 2.34993I −9.21397 − 4.74077I
u = −0.02313 + 1.54067I
a = −0.08257 − 2.23973I
b = −0.02313 + 1.54067I
15.2534 + 3.0855I −1.70716 − 2.62885I
u = −0.02313 − 1.54067I
a = −0.08257 + 2.23973I
b = −0.02313 − 1.54067I
15.2534 − 3.0855I −1.70716 + 2.62885I
u = 0.315603
a = 0.574029
b = 0.315603
−0.553031 −18.0200
6
II. I
u
2
= h−1.59 × 10
8
u
29
+ 1.22 × 10
8
u
28
+ · · · + 9.57 × 10
7
b + 5.70 ×
10
8
, −u
29
+ u
28
+ · · · + a + 6, u
30
− u
29
+ · · · − 6u + 1i
(i) Arc colorings
a
6
=
0
u
a
10
=
1
0
a
4
=
u
29
− u
28
+ ··· + 10u − 6
1.66623u
29
− 1.27037u
28
+ ··· + 17.4027u − 5.95715
a
11
=
1
u
2
a
3
=
2.66623u
29
− 2.27037u
28
+ ··· + 27.4027u − 11.9571
1.66623u
29
− 1.27037u
28
+ ··· + 17.4027u − 5.95715
a
5
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
4
+ 2u
2
a
2
=
4.72929u
29
− 3.69976u
28
+ ··· + 46.3017u − 17.7300
2.22042u
29
− 1.73024u
28
+ ··· + 21.0519u − 7.17018
a
9
=
5.95715u
29
− 4.29092u
28
+ ··· + 56.4198u − 17.3402
0.395859u
29
+ 0.105883u
28
+ ··· + 4.04021u − 0.666227
a
8
=
5.19351u
29
− 3.62763u
28
+ ··· + 49.7650u − 14.1723
−0.367778u
29
+ 0.769175u
28
+ ··· − 2.61459u + 1.50174
a
7
=
−6.74902u
29
+ 4.86232u
28
+ ··· − 65.5259u + 23.3729
−2.01973u
29
+ 1.16256u
28
+ ··· − 17.2242u + 5.64291
a
7
=
−6.74902u
29
+ 4.86232u
28
+ ··· − 65.5259u + 23.3729
−2.01973u
29
+ 1.16256u
28
+ ··· − 17.2242u + 5.64291
(ii) Obstruction class = −1
(iii) Cusp Shapes =
583799292
95716253
u
29
−
406184408
95716253
u
28
+ ··· +
4386525380
95716253
u −
2570388306
95716253
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
15
− u
14
+ ··· + 2u − 1)
2
c
2
, c
6
(u
15
+ 5u
14
+ ··· + 12u
3
+ 1)
2
c
3
, c
4
, c
5
c
9
, c
10
, c
11
u
30
+ u
29
+ ··· + 6u + 1
c
8
(u
15
+ u
14
+ ··· − 4u − 1)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
15
− 5y
14
+ ··· + 12y
3
− 1)
2
c
2
, c
6
(y
15
+ 11y
14
+ ··· − 84y
2
− 1)
2
c
3
, c
4
, c
5
c
9
, c
10
, c
11
y
30
+ 23y
29
+ ··· − 16y + 1
c
8
(y
15
− y
14
+ ··· + 16y −1)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.171252 + 1.009920I
a = 0.163210 + 0.962498I
b = 0.318180 + 0.052816I
1.46912 − 2.07402I −11.82822 + 2.67122I
u = −0.171252 − 1.009920I
a = 0.163210 − 0.962498I
b = 0.318180 − 0.052816I
1.46912 + 2.07402I −11.82822 − 2.67122I
u = −0.607011 + 0.856391I
a = 0.550893 + 0.777218I
b = −0.108390 − 1.374740I
6.82325 + 1.50523I −3.84867 − 2.74048I
u = −0.607011 − 0.856391I
a = 0.550893 − 0.777218I
b = −0.108390 + 1.374740I
6.82325 − 1.50523I −3.84867 + 2.74048I
u = 0.879105 + 0.290763I
a = −1.025350 + 0.339134I
b = −0.28507 − 1.38638I
4.31617 − 9.21780I −8.14540 + 7.39135I
u = 0.879105 − 0.290763I
a = −1.025350 − 0.339134I
b = −0.28507 + 1.38638I
4.31617 + 9.21780I −8.14540 − 7.39135I
u = −0.836240 + 0.341718I
a = 1.024720 + 0.418737I
b = 0.241243 − 1.382540I
5.27292 + 3.51852I −6.28698 − 2.59027I
u = −0.836240 − 0.341718I
a = 1.024720 − 0.418737I
b = 0.241243 + 1.382540I
5.27292 − 3.51852I −6.28698 + 2.59027I
u = 0.587196 + 0.946781I
a = −0.473090 + 0.762799I
b = 0.171749 − 1.369410I
6.30676 + 4.09199I −4.95573 − 3.15094I
u = 0.587196 − 0.946781I
a = −0.473090 − 0.762799I
b = 0.171749 + 1.369410I
6.30676 − 4.09199I −4.95573 + 3.15094I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.269205 + 1.103370I
a = −0.208705 + 0.855397I
b = 0.269205 − 1.103370I
1.86559 −10.56339 + 0.I
u = 0.269205 − 1.103370I
a = −0.208705 − 0.855397I
b = 0.269205 + 1.103370I
1.86559 −10.56339 + 0.I
u = 0.119824 + 1.236680I
a = −0.077620 + 0.801099I
b = −0.505429 − 0.368881I
2.93870 − 1.66084I −6.48958 + 3.96405I
u = 0.119824 − 1.236680I
a = −0.077620 − 0.801099I
b = −0.505429 + 0.368881I
2.93870 + 1.66084I −6.48958 − 3.96405I
u = 0.706910 + 0.161570I
a = −1.344380 + 0.307269I
b = −0.280017 − 1.247240I
−0.91830 − 3.60340I −14.1637 + 4.4767I
u = 0.706910 − 0.161570I
a = −1.344380 − 0.307269I
b = −0.280017 + 1.247240I
−0.91830 + 3.60340I −14.1637 − 4.4767I
u = −0.280017 + 1.247240I
a = 0.171369 + 0.763299I
b = 0.706910 − 0.161570I
−0.91830 + 3.60340I −14.1637 − 4.4767I
u = −0.280017 − 1.247240I
a = 0.171369 − 0.763299I
b = 0.706910 + 0.161570I
−0.91830 − 3.60340I −14.1637 + 4.4767I
u = −0.505429 + 0.368881I
a = 1.29090 + 0.94215I
b = 0.119824 − 1.236680I
2.93870 + 1.66084I −6.48958 − 3.96405I
u = −0.505429 − 0.368881I
a = 1.29090 − 0.94215I
b = 0.119824 + 1.236680I
2.93870 − 1.66084I −6.48958 + 3.96405I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.108390 + 1.374740I
a = 0.056998 + 0.722915I
b = −0.607011 − 0.856391I
6.82325 − 1.50523I −3.84867 + 2.74048I
u = −0.108390 − 1.374740I
a = 0.056998 − 0.722915I
b = −0.607011 + 0.856391I
6.82325 + 1.50523I −3.84867 − 2.74048I
u = 0.171749 + 1.369410I
a = −0.090167 + 0.718933I
b = 0.587196 − 0.946781I
6.30676 − 4.09199I −4.95573 + 3.15094I
u = 0.171749 − 1.369410I
a = −0.090167 − 0.718933I
b = 0.587196 + 0.946781I
6.30676 + 4.09199I −4.95573 − 3.15094I
u = 0.241243 + 1.382540I
a = −0.122482 + 0.701932I
b = −0.836240 − 0.341718I
5.27292 − 3.51852I −6.28698 + 2.59027I
u = 0.241243 − 1.382540I
a = −0.122482 − 0.701932I
b = −0.836240 + 0.341718I
5.27292 + 3.51852I −6.28698 − 2.59027I
u = −0.28507 + 1.38638I
a = 0.142301 + 0.692043I
b = 0.879105 − 0.290763I
4.31617 + 9.21780I −8.14540 − 7.39135I
u = −0.28507 − 1.38638I
a = 0.142301 − 0.692043I
b = 0.879105 + 0.290763I
4.31617 − 9.21780I −8.14540 + 7.39135I
u = 0.318180 + 0.052816I
a = −3.05860 + 0.50771I
b = −0.171252 + 1.009920I
1.46912 − 2.07402I −11.82822 + 2.67122I
u = 0.318180 − 0.052816I
a = −3.05860 − 0.50771I
b = −0.171252 − 1.009920I
1.46912 + 2.07402I −11.82822 − 2.67122I
12
III. I
u
3
= hb + u, a
2
− 2au − a + u, u
2
+ 1i
(i) Arc colorings
a
6
=
0
u
a
10
=
1
0
a
4
=
a
−u
a
11
=
1
−1
a
3
=
a − u
−u
a
5
=
u
0
a
1
=
0
−1
a
2
=
a − u
−a
a
9
=
au + 1
1
a
8
=
au + 1
1
a
7
=
au − u + 1
a
a
7
=
au − u + 1
a
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4a − 4u − 8
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
4
− u
2
+ 1
c
2
(u
2
+ u + 1)
2
c
3
, c
4
, c
5
c
9
, c
10
, c
11
(u
2
+ 1)
2
c
6
(u
2
− u + 1)
2
c
8
u
4
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
2
− y + 1)
2
c
2
, c
6
(y
2
+ y + 1)
2
c
3
, c
4
, c
5
c
9
, c
10
, c
11
(y + 1)
4
c
8
y
4
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = 0.500000 + 0.133975I
b = − 1.000000I
3.28987 + 2.02988I −6.00000 − 3.46410I
u = 1.000000I
a = 0.50000 + 1.86603I
b = − 1.000000I
3.28987 − 2.02988I −6.00000 + 3.46410I
u = − 1.000000I
a = 0.500000 − 0.133975I
b = 1.000000I
3.28987 − 2.02988I −6.00000 + 3.46410I
u = − 1.000000I
a = 0.50000 − 1.86603I
b = 1.000000I
3.28987 + 2.02988I −6.00000 − 3.46410I
16
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
4
− u
2
+ 1)(u
15
− u
14
+ ··· + 2u − 1)
2
(u
20
+ 3u
19
+ ··· − 9u − 2)
c
2
((u
2
+ u + 1)
2
)(u
15
+ 5u
14
+ ··· + 12u
3
+ 1)
2
· (u
20
+ 7u
19
+ ··· + 33u + 4)
c
3
, c
4
, c
5
c
9
, c
10
, c
11
((u
2
+ 1)
2
)(u
20
+ 11u
18
+ ··· − 3u − 1)(u
30
+ u
29
+ ··· + 6u + 1)
c
6
((u
2
− u + 1)
2
)(u
15
+ 5u
14
+ ··· + 12u
3
+ 1)
2
· (u
20
+ 7u
19
+ ··· + 33u + 4)
c
8
u
4
(u
15
+ u
14
+ ··· − 4u − 1)
2
(u
20
− 3u
19
+ ··· − 48u − 32)
17
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
((y
2
− y + 1)
2
)(y
15
− 5y
14
+ ··· + 12y
3
− 1)
2
· (y
20
− 7y
19
+ ··· − 33y + 4)
c
2
, c
6
((y
2
+ y + 1)
2
)(y
15
+ 11y
14
+ ··· − 84y
2
− 1)
2
· (y
20
+ 13y
19
+ ··· − 561y + 16)
c
3
, c
4
, c
5
c
9
, c
10
, c
11
((y + 1)
4
)(y
20
+ 22y
19
+ ··· − 5y + 1)(y
30
+ 23y
29
+ ··· − 16y + 1)
c
8
y
4
(y
15
− y
14
+ ··· + 16y −1)
2
(y
20
− y
19
+ ··· + 3328y + 1024)
18
