11a
258
(K11a
258
)
A knot diagram
1
Linearized knot diagam
4 8 1 2 11 10 3 5 7 6 9
Solving Sequence
2,8 3,5
9 4 1 7 10 6 11
c
2
c
8
c
4
c
1
c
7
c
9
c
6
c
11
c
3
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h4.93541 × 10
32
u
40
+ 2.04760 × 10
32
u
39
+ ··· + 1.23008 × 10
33
b − 8.08350 × 10
33
,
1.21871 × 10
33
u
40
− 1.85520 × 10
33
u
39
+ ··· + 2.46016 × 10
33
a + 1.04083 × 10
34
, u
41
− u
40
+ ··· + 8u − 16i
I
v
1
= ha, b − 1, v
4
− v
3
+ v
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 45 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
= h4.94 × 10
32
u
40
+ 2.05 × 10
32
u
39
+ · · · + 1.23 × 10
33
b − 8.08 × 10
33
, 1.22 ×
10
33
u
40
−1.86×10
33
u
39
+· · ·+2.46×10
33
a+1.04×10
34
, u
41
−u
40
+· · ·+8u−16i
(i) Arc colorings
a
2
=
1
0
a
8
=
0
u
a
3
=
1
−u
2
a
5
=
−0.495378u
40
+ 0.754100u
39
+ ··· + 8.36593u − 4.23073
−0.401227u
40
− 0.166461u
39
+ ··· + 3.25878u + 6.57153
a
9
=
0.00964588u
40
+ 0.868205u
39
+ ··· + 3.33085u − 12.4271
−0.279000u
40
+ 0.570378u
39
+ ··· + 6.14986u − 4.36198
a
4
=
−0.896605u
40
+ 0.587639u
39
+ ··· + 11.6247u + 2.34080
−0.401227u
40
− 0.166461u
39
+ ··· + 3.25878u + 6.57153
a
1
=
−0.896605u
40
+ 0.587639u
39
+ ··· + 11.6247u + 2.34080
−0.623981u
40
+ 0.594016u
39
+ ··· + 8.61517u − 1.62808
a
7
=
−u
u
3
+ u
a
10
=
0.181324u
40
+ 0.551451u
39
+ ··· + 0.442667u − 9.89004
−0.175096u
40
+ 0.493041u
39
+ ··· + 5.13059u − 4.57783
a
6
=
−0.295942u
40
+ 0.237376u
39
+ ··· + 3.40554u + 0.455300
−0.311321u
40
− 0.0909921u
39
+ ··· + 2.02971u + 5.46031
a
11
=
−0.248888u
40
− 0.460318u
39
+ ··· − 0.398174u + 9.13315
−0.0375077u
40
− 0.244171u
39
+ ··· − 1.75912u + 2.99026
a
11
=
−0.248888u
40
− 0.460318u
39
+ ··· − 0.398174u + 9.13315
−0.0375077u
40
− 0.244171u
39
+ ··· − 1.75912u + 2.99026
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.312617u
40
+ 1.81495u
39
+ ··· + 9.58739u − 33.8289
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
u
41
− 5u
40
+ ··· − 3u + 1
c
2
, c
7
u
41
+ u
40
+ ··· + 8u + 16
c
5
, c
6
, c
9
c
10
u
41
+ 2u
40
+ ··· − 3u − 1
c
8
u
41
+ 2u
40
+ ··· − 20u − 100
c
11
u
41
− 12u
40
+ ··· + 549u − 131
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
y
41
− 41y
40
+ ··· − 13y −1
c
2
, c
7
y
41
+ 27y
40
+ ··· − 960y −256
c
5
, c
6
, c
9
c
10
y
41
+ 48y
40
+ ··· − 7y −1
c
8
y
41
− 24y
40
+ ··· − 163800y −10000
c
11
y
41
− 12y
40
+ ··· + 112237y −17161
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.04360
a = −0.918815
b = 1.34522
−3.09864 −0.703580
u = −0.280650 + 1.032300I
a = 0.113218 − 0.945326I
b = 0.451556 + 0.680540I
−0.98467 − 2.16041I 0.30534 + 3.36601I
u = −0.280650 − 1.032300I
a = 0.113218 + 0.945326I
b = 0.451556 − 0.680540I
−0.98467 + 2.16041I 0.30534 − 3.36601I
u = −0.636469 + 0.676356I
a = −0.663046 + 0.390386I
b = 1.123470 − 0.320823I
−8.62893 + 1.18234I −6.12242 + 0.09680I
u = −0.636469 − 0.676356I
a = −0.663046 − 0.390386I
b = 1.123470 + 0.320823I
−8.62893 − 1.18234I −6.12242 − 0.09680I
u = 0.067485 + 1.087720I
a = −1.345840 − 0.268602I
b = −1.365970 + 0.031939I
−3.50700 + 1.95785I −4.15911 − 3.79195I
u = 0.067485 − 1.087720I
a = −1.345840 + 0.268602I
b = −1.365970 − 0.031939I
−3.50700 − 1.95785I −4.15911 + 3.79195I
u = 0.053492 + 1.097010I
a = −0.119204 + 0.861224I
b = 0.644526 − 0.652721I
−3.46087 − 0.57126I −6.38744 + 1.36032I
u = 0.053492 − 1.097010I
a = −0.119204 − 0.861224I
b = 0.644526 + 0.652721I
−3.46087 + 0.57126I −6.38744 − 1.36032I
u = −0.231068 + 1.076220I
a = −1.18409 + 0.88552I
b = −1.359660 − 0.109695I
−9.84300 − 4.44580I −7.49047 + 4.00982I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.231068 − 1.076220I
a = −1.18409 − 0.88552I
b = −1.359660 + 0.109695I
−9.84300 + 4.44580I −7.49047 − 4.00982I
u = 0.575963 + 0.681143I
a = 0.654397 + 0.985833I
b = 0.064994 − 0.588385I
−5.44874 + 2.20051I −0.49288 − 3.58387I
u = 0.575963 − 0.681143I
a = 0.654397 − 0.985833I
b = 0.064994 + 0.588385I
−5.44874 − 2.20051I −0.49288 + 3.58387I
u = −1.179440 + 0.158362I
a = −0.994717 + 0.088396I
b = 1.409360 − 0.075417I
−5.20973 + 3.10308I −5.68137 − 4.55677I
u = −1.179440 − 0.158362I
a = −0.994717 − 0.088396I
b = 1.409360 + 0.075417I
−5.20973 − 3.10308I −5.68137 + 4.55677I
u = 0.353950 + 1.159500I
a = 0.079020 + 1.089230I
b = 0.450262 − 0.797995I
−2.77750 + 5.51756I −3.79773 − 7.77564I
u = 0.353950 − 1.159500I
a = 0.079020 − 1.089230I
b = 0.450262 + 0.797995I
−2.77750 − 5.51756I −3.79773 + 7.77564I
u = 0.005676 + 1.227250I
a = −0.228021 − 0.942171I
b = 0.720117 + 0.732589I
−11.55890 + 2.26622I −7.69126 − 0.18572I
u = 0.005676 − 1.227250I
a = −0.228021 + 0.942171I
b = 0.720117 − 0.732589I
−11.55890 − 2.26622I −7.69126 + 0.18572I
u = −0.383325 + 1.244490I
a = 0.043543 − 1.163710I
b = 0.463101 + 0.864387I
−10.75100 − 7.67961I −5.88345 + 5.74816I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.383325 − 1.244490I
a = 0.043543 + 1.163710I
b = 0.463101 − 0.864387I
−10.75100 + 7.67961I −5.88345 − 5.74816I
u = 1.287610 + 0.202232I
a = −1.055360 − 0.112449I
b = 1.46107 + 0.09654I
−13.2971 − 5.0740I −7.49177 + 2.86395I
u = 1.287610 − 0.202232I
a = −1.055360 + 0.112449I
b = 1.46107 − 0.09654I
−13.2971 + 5.0740I −7.49177 − 2.86395I
u = −0.637500 + 0.135734I
a = 1.71237 − 0.80495I
b = −0.363345 + 0.258087I
−7.29387 + 3.70140I 0.13489 − 3.24211I
u = −0.637500 − 0.135734I
a = 1.71237 + 0.80495I
b = −0.363345 − 0.258087I
−7.29387 − 3.70140I 0.13489 + 3.24211I
u = −0.442927 + 0.446451I
a = 0.885936 − 0.663779I
b = 0.002285 + 0.351914I
0.739118 − 0.963294I 5.38374 + 5.24951I
u = −0.442927 − 0.446451I
a = 0.885936 + 0.663779I
b = 0.002285 − 0.351914I
0.739118 + 0.963294I 5.38374 − 5.24951I
u = 0.545126 + 0.215241I
a = 1.37573 + 0.63189I
b = −0.218730 − 0.254700I
0.06188 − 1.89506I 3.00107 + 4.96508I
u = 0.545126 − 0.215241I
a = 1.37573 − 0.63189I
b = −0.218730 + 0.254700I
0.06188 + 1.89506I 3.00107 − 4.96508I
u = 0.332351 + 0.473594I
a = −0.483789 − 0.209918I
b = 0.984199 + 0.167639I
−1.84031 − 0.69258I −6.89864 − 1.74884I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.332351 − 0.473594I
a = −0.483789 + 0.209918I
b = 0.984199 − 0.167639I
−1.84031 + 0.69258I −6.89864 + 1.74884I
u = 0.52227 + 1.35643I
a = −0.110639 − 1.064090I
b = −1.49556 + 0.25090I
−7.31234 + 5.60210I 0
u = 0.52227 − 1.35643I
a = −0.110639 + 1.064090I
b = −1.49556 − 0.25090I
−7.31234 − 5.60210I 0
u = −0.41034 + 1.42300I
a = −0.140257 + 0.816586I
b = −1.52685 − 0.19609I
−10.55130 − 2.41180I 0
u = −0.41034 − 1.42300I
a = −0.140257 − 0.816586I
b = −1.52685 + 0.19609I
−10.55130 + 2.41180I 0
u = −0.60199 + 1.38207I
a = 0.024627 + 1.133790I
b = −1.50901 − 0.28951I
−9.13999 − 9.48739I 0
u = −0.60199 − 1.38207I
a = 0.024627 − 1.133790I
b = −1.50901 + 0.28951I
−9.13999 + 9.48739I 0
u = 0.65669 + 1.41457I
a = 0.127888 − 1.155240I
b = −1.52575 + 0.31574I
−17.2037 + 11.9877I 0
u = 0.65669 − 1.41457I
a = 0.127888 + 1.155240I
b = −1.52575 − 0.31574I
−17.2037 − 11.9877I 0
u = 0.38128 + 1.53983I
a = 0.017651 − 0.667778I
b = −1.58265 + 0.18117I
−19.3092 + 0.9583I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.38128 − 1.53983I
a = 0.017651 + 0.667778I
b = −1.58265 − 0.18117I
−19.3092 − 0.9583I 0
9
II. I
v
1
= ha, b − 1, v
4
− v
3
+ v
2
+ 1i
(i) Arc colorings
a
2
=
1
0
a
8
=
v
0
a
3
=
1
0
a
5
=
0
1
a
9
=
v
v
a
4
=
1
1
a
1
=
0
−1
a
7
=
v
0
a
10
=
v
3
+ v
v
a
6
=
v
3
− v
2
− 1
v
3
a
11
=
−v
2
−v
2
− 1
a
11
=
−v
2
−v
2
− 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4v
2
− 5v −1
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
4
c
2
, c
7
u
4
c
3
, c
4
(u + 1)
4
c
5
, c
6
u
4
+ u
3
+ 3u
2
+ 2u + 1
c
8
, c
11
u
4
− u
3
+ u
2
+ 1
c
9
, c
10
u
4
− u
3
+ 3u
2
− 2u + 1
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
(y −1)
4
c
2
, c
7
y
4
c
5
, c
6
, c
9
c
10
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
8
, c
11
y
4
+ y
3
+ 3y
2
+ 2y + 1
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.351808 + 0.720342I
a = 0
b = 1.00000
−1.43393 + 1.41510I −0.82145 − 5.62908I
v = −0.351808 − 0.720342I
a = 0
b = 1.00000
−1.43393 − 1.41510I −0.82145 + 5.62908I
v = 0.851808 + 0.911292I
a = 0
b = 1.00000
−8.43568 − 3.16396I −5.67855 + 1.65351I
v = 0.851808 − 0.911292I
a = 0
b = 1.00000
−8.43568 + 3.16396I −5.67855 − 1.65351I
13
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
4
)(u
41
− 5u
40
+ ··· − 3u + 1)
c
2
, c
7
u
4
(u
41
+ u
40
+ ··· + 8u + 16)
c
3
, c
4
((u + 1)
4
)(u
41
− 5u
40
+ ··· − 3u + 1)
c
5
, c
6
(u
4
+ u
3
+ 3u
2
+ 2u + 1)(u
41
+ 2u
40
+ ··· − 3u − 1)
c
8
(u
4
− u
3
+ u
2
+ 1)(u
41
+ 2u
40
+ ··· − 20u − 100)
c
9
, c
10
(u
4
− u
3
+ 3u
2
− 2u + 1)(u
41
+ 2u
40
+ ··· − 3u − 1)
c
11
(u
4
− u
3
+ u
2
+ 1)(u
41
− 12u
40
+ ··· + 549u − 131)
14
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
((y −1)
4
)(y
41
− 41y
40
+ ··· − 13y −1)
c
2
, c
7
y
4
(y
41
+ 27y
40
+ ··· − 960y −256)
c
5
, c
6
, c
9
c
10
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)(y
41
+ 48y
40
+ ··· − 7y −1)
c
8
(y
4
+ y
3
+ 3y
2
+ 2y + 1)(y
41
− 24y
40
+ ··· − 163800y −10000)
c
11
(y
4
+ y
3
+ 3y
2
+ 2y + 1)(y
41
− 12y
40
+ ··· + 112237y −17161)
15
