12n
0343
(K12n
0343
)
A knot diagram
1
Linearized knot diagam
3 6 7 8 2 11 5 4 6 12 7 10
Solving Sequence
5,7 8,11
12 4 9 3 6 2 1 10
c
7
c
11
c
4
c
8
c
3
c
6
c
2
c
1
c
10
c
5
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h2.35414 × 10
25
u
37
+ 6.36686 × 10
22
u
36
+ ··· + 1.08506 × 10
26
b + 7.17457 × 10
26
,
− 6.03496 × 10
25
u
37
− 5.08818 × 10
25
u
36
+ ··· + 1.08506 × 10
26
a − 2.36548 × 10
27
, u
38
+ u
37
+ ··· + 48u + 8i
I
u
2
= h4a
2
u + 2a
2
+ 9b − 9, 4a
3
+ 4au − 2a − 5u − 2, u
2
+ 2i
I
v
1
= ha, b + v + 1, v
3
+ 2v
2
+ v + 1i
* 3 irreducible components of dim
C
= 0, with total 47 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
= h2.35×10
25
u
37
+6.37×10
22
u
36
+· · ·+1.09×10
26
b+7.17×10
26
, −6.03×
10
25
u
37
−5.09×10
25
u
36
+· · ·+1.09×10
26
a−2.37×10
27
, u
38
+u
37
+· · ·+48u+8i
(i) Arc colorings
a
5
=
0
u
a
7
=
1
0
a
8
=
1
−u
2
a
11
=
0.556188u
37
+ 0.468931u
36
+ ··· + 66.0065u + 21.8004
−0.216959u
37
− 0.000586775u
36
+ ··· − 20.1029u − 6.61215
a
12
=
0.773147u
37
+ 0.469518u
36
+ ··· + 86.1094u + 28.4126
−0.216959u
37
− 0.000586775u
36
+ ··· − 20.1029u − 6.61215
a
4
=
−u
u
3
+ u
a
9
=
u
2
+ 1
−u
4
− 2u
2
a
3
=
−u
3
− 2u
u
3
+ u
a
6
=
0.540457u
37
+ 0.513997u
36
+ ··· + 61.5142u + 18.9792
0.118184u
37
− 0.103841u
36
+ ··· − 10.8806u − 1.99927
a
2
=
−0.931000u
37
− 0.423758u
36
+ ··· − 46.4113u − 16.9685
0.272358u
37
+ 0.0136024u
36
+ ··· − 4.22233u − 0.0113747
a
1
=
−1.34851u
37
− 0.494264u
36
+ ··· − 50.4295u − 19.4015
0.448295u
37
+ 0.0937407u
36
+ ··· + 2.84945u + 2.20997
a
10
=
−0.237267u
37
− 0.770027u
36
+ ··· − 6.76734u + 5.06203
0.216015u
37
+ 0.558969u
36
+ ··· + 14.6047u + 0.926935
(ii) Obstruction class = −1
(iii) Cusp Shapes =
213942583101129059255880827
108505904310727076649467996
u
37
+
149904830321107825585617651
108505904310727076649467996
u
36
+
··· +
5023310390844651983501342066
27126476077681769162366999
u +
1400899338503733927958392044
27126476077681769162366999
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
38
+ 10u
37
+ ··· − 24u + 1
c
2
, c
5
u
38
+ 4u
37
+ ··· + 4u − 1
c
3
u
38
− u
37
+ ··· − 16u + 8
c
4
, c
7
, c
8
u
38
+ u
37
+ ··· + 48u + 8
c
6
, c
11
u
38
− 2u
37
+ ··· + u − 3
c
9
u
38
+ 2u
37
+ ··· − 3029u − 7419
c
10
, c
12
u
38
+ 8u
37
+ ··· + 85u + 9
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
38
+ 46y
37
+ ··· + 1128y + 1
c
2
, c
5
y
38
− 10y
37
+ ··· + 24y + 1
c
3
y
38
− 53y
37
+ ··· + 896y + 64
c
4
, c
7
, c
8
y
38
+ 31y
37
+ ··· − 512y + 64
c
6
, c
11
y
38
− 8y
37
+ ··· − 85y + 9
c
9
y
38
+ 120y
37
+ ··· − 2146915177y + 55041561
c
10
, c
12
y
38
+ 48y
37
+ ··· + 1091y + 81
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.053800 + 0.148639I
a = −0.35198 − 1.75546I
b = 0.976993 + 0.905951I
12.2690 − 7.2289I −0.96626 + 4.68407I
u = −1.053800 − 0.148639I
a = −0.35198 + 1.75546I
b = 0.976993 − 0.905951I
12.2690 + 7.2289I −0.96626 − 4.68407I
u = −0.057390 + 0.931497I
a = 0.49812 + 1.63735I
b = −0.893541 − 0.823917I
0.10554 − 3.06762I −6.46786 + 2.97828I
u = −0.057390 − 0.931497I
a = 0.49812 − 1.63735I
b = −0.893541 + 0.823917I
0.10554 + 3.06762I −6.46786 − 2.97828I
u = 1.064480 + 0.094759I
a = −0.73343 − 1.41153I
b = 0.912968 + 0.941319I
12.47990 + 0.43824I −0.562427 − 0.044649I
u = 1.064480 − 0.094759I
a = −0.73343 + 1.41153I
b = 0.912968 − 0.941319I
12.47990 − 0.43824I −0.562427 + 0.044649I
u = 0.156341 + 1.111710I
a = 1.23758 + 0.87855I
b = 0.929752 − 0.586434I
−1.21085 + 3.08073I −5.55249 − 3.17627I
u = 0.156341 − 1.111710I
a = 1.23758 − 0.87855I
b = 0.929752 + 0.586434I
−1.21085 − 3.08073I −5.55249 + 3.17627I
u = −0.191591 + 1.141470I
a = −1.71195 + 0.26865I
b = −1.018780 + 0.030482I
−4.76428 − 2.22122I −10.55897 + 3.42071I
u = −0.191591 − 1.141470I
a = −1.71195 − 0.26865I
b = −1.018780 − 0.030482I
−4.76428 + 2.22122I −10.55897 − 3.42071I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.271471 + 0.749945I
a = −0.032046 − 0.267481I
b = 0.626757 − 0.614277I
−0.20728 + 1.53818I −4.56900 − 2.28483I
u = −0.271471 − 0.749945I
a = −0.032046 + 0.267481I
b = 0.626757 + 0.614277I
−0.20728 − 1.53818I −4.56900 + 2.28483I
u = 0.418841 + 1.156790I
a = −0.417466 − 0.176902I
b = 0.386654 + 0.764550I
0.11970 + 3.73317I −2.97329 − 3.30525I
u = 0.418841 − 1.156790I
a = −0.417466 + 0.176902I
b = 0.386654 − 0.764550I
0.11970 − 3.73317I −2.97329 + 3.30525I
u = 0.714927 + 0.180259I
a = 0.324913 − 1.250580I
b = −0.617135 + 0.730511I
3.04719 + 0.49757I 1.21153 − 1.20838I
u = 0.714927 − 0.180259I
a = 0.324913 + 1.250580I
b = −0.617135 − 0.730511I
3.04719 − 0.49757I 1.21153 + 1.20838I
u = 0.227184 + 0.682533I
a = 0.429035 + 0.360906I
b = 0.320049 − 0.507052I
−0.238421 + 1.266880I −2.42303 − 5.08329I
u = 0.227184 − 0.682533I
a = 0.429035 − 0.360906I
b = 0.320049 + 0.507052I
−0.238421 − 1.266880I −2.42303 + 5.08329I
u = −0.092432 + 1.311290I
a = 0.14750 − 1.68723I
b = 0.688190 + 0.376073I
−6.50773 − 1.47983I −9.20328 + 4.48160I
u = −0.092432 − 1.311290I
a = 0.14750 + 1.68723I
b = 0.688190 − 0.376073I
−6.50773 + 1.47983I −9.20328 − 4.48160I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.366037 + 1.277380I
a = 1.32644 − 1.19862I
b = 1.025390 + 0.488331I
−1.99066 − 8.34590I −7.38920 + 8.20539I
u = −0.366037 − 1.277380I
a = 1.32644 + 1.19862I
b = 1.025390 − 0.488331I
−1.99066 + 8.34590I −7.38920 − 8.20539I
u = −0.669684 + 0.020164I
a = −0.022217 + 1.347390I
b = −0.937251 − 0.595896I
1.98177 − 4.45651I −1.06472 + 6.47147I
u = −0.669684 − 0.020164I
a = −0.022217 − 1.347390I
b = −0.937251 + 0.595896I
1.98177 + 4.45651I −1.06472 − 6.47147I
u = −0.618417 + 1.229390I
a = 0.511319 − 0.554883I
b = −0.923330 + 0.927636I
8.97672 + 1.36657I −4.00000 + 0.I
u = −0.618417 − 1.229390I
a = 0.511319 + 0.554883I
b = −0.923330 − 0.927636I
8.97672 − 1.36657I −4.00000 + 0.I
u = 0.590971 + 1.277150I
a = −0.48725 − 1.50500I
b = −0.961686 + 0.907689I
8.85183 + 5.38651I 0
u = 0.590971 − 1.277150I
a = −0.48725 + 1.50500I
b = −0.961686 − 0.907689I
8.85183 − 5.38651I 0
u = 0.02483 + 1.43079I
a = 0.637356 + 0.570357I
b = 0.863543 − 0.756976I
−1.89195 + 2.85204I −4.00000 + 0.I
u = 0.02483 − 1.43079I
a = 0.637356 − 0.570357I
b = 0.863543 + 0.756976I
−1.89195 − 2.85204I −4.00000 + 0.I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.03651 + 1.47301I
a = −1.199870 + 0.246838I
b = −0.661912 + 0.244654I
−7.07448 + 0.98863I 0
u = −0.03651 − 1.47301I
a = −1.199870 − 0.246838I
b = −0.661912 − 0.244654I
−7.07448 − 0.98863I 0
u = 0.50808 + 1.40664I
a = 0.592702 + 0.296009I
b = −0.857340 − 0.944975I
7.77909 + 6.04150I 0
u = 0.50808 − 1.40664I
a = 0.592702 − 0.296009I
b = −0.857340 + 0.944975I
7.77909 − 6.04150I 0
u = −0.48076 + 1.42977I
a = −0.81361 + 1.56632I
b = −1.004820 − 0.868136I
7.2987 − 12.7112I 0
u = −0.48076 − 1.42977I
a = −0.81361 − 1.56632I
b = −1.004820 + 0.868136I
7.2987 + 12.7112I 0
u = −0.406334
a = 0.579971
b = 0.878349
−1.62488 −3.64530
u = −0.328792
a = 4.54970
b = −0.587341
−2.40058 5.69880
8
II. I
u
2
= h4a
2
u + 2a
2
+ 9b − 9, 4a
3
+ 4au − 2a − 5u − 2, u
2
+ 2i
(i) Arc colorings
a
5
=
0
u
a
7
=
1
0
a
8
=
1
2
a
11
=
a
−
4
9
a
2
u −
2
9
a
2
+ 1
a
12
=
4
9
a
2
u +
2
9
a
2
+ a − 1
−
4
9
a
2
u −
2
9
a
2
+ 1
a
4
=
−u
−u
a
9
=
−1
0
a
3
=
0
−u
a
6
=
1
2
u
4
9
a
2
u +
2
9
a
2
+
1
3
au +
2
3
a − 1
a
2
=
1
2
u
4
9
a
2
u +
1
3
au + ··· +
2
3
a − 1
a
1
=
1
2
u
4
9
a
2
u +
2
9
a
2
+
1
3
au +
2
3
a − 1
a
10
=
−
1
9
a
2
u −
1
3
au + ··· +
1
3
a − 1
1
3
au +
2
3
a + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
16
9
a
2
u −
8
9
a
2
− 8
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u − 1)
6
c
2
(u + 1)
6
c
3
, c
4
, c
7
c
8
(u
2
+ 2)
3
c
6
(u
3
− u
2
+ 1)
2
c
9
, c
10
(u
3
− u
2
+ 2u − 1)
2
c
11
(u
3
+ u
2
− 1)
2
c
12
(u
3
+ u
2
+ 2u + 1)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y −1)
6
c
3
, c
4
, c
7
c
8
(y + 2)
6
c
6
, c
11
(y
3
− y
2
+ 2y −1)
2
c
9
, c
10
, c
12
(y
3
+ 3y
2
+ 2y −1)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.414210I
a = 0.264767 − 1.030640I
b = 0.877439 + 0.744862I
−3.55561 − 2.82812I −8.49024 + 2.97945I
u = 1.414210I
a = 1.059950 + 0.093921I
b = 0.877439 − 0.744862I
−3.55561 + 2.82812I −8.49024 − 2.97945I
u = 1.414210I
a = −1.32472 + 0.93672I
b = −0.754878
−7.69319 −15.0195 + 0.I
u = − 1.414210I
a = 0.264767 + 1.030640I
b = 0.877439 − 0.744862I
−3.55561 + 2.82812I −8.49024 − 2.97945I
u = − 1.414210I
a = 1.059950 − 0.093921I
b = 0.877439 + 0.744862I
−3.55561 − 2.82812I −8.49024 + 2.97945I
u = − 1.414210I
a = −1.32472 − 0.93672I
b = −0.754878
−7.69319 −15.0195 + 0.I
12
III. I
v
1
= ha, b + v + 1, v
3
+ 2v
2
+ v + 1i
(i) Arc colorings
a
5
=
v
0
a
7
=
1
0
a
8
=
1
0
a
11
=
0
−v − 1
a
12
=
v + 1
−v − 1
a
4
=
v
0
a
9
=
1
0
a
3
=
v
0
a
6
=
1
−v
2
− 2v − 1
a
2
=
v − 1
v
2
+ 2v + 1
a
1
=
−1
v
2
+ 2v + 1
a
10
=
−v
2
− 2v
v
2
+ v − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4v
2
+ 2v − 2
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
3
c
3
, c
4
, c
7
c
8
u
3
c
5
(u + 1)
3
c
6
u
3
+ u
2
− 1
c
9
, c
12
u
3
+ u
2
+ 2u + 1
c
10
u
3
− u
2
+ 2u − 1
c
11
u
3
− u
2
+ 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y − 1)
3
c
3
, c
4
, c
7
c
8
y
3
c
6
, c
11
y
3
− y
2
+ 2y − 1
c
9
, c
10
, c
12
y
3
+ 3y
2
+ 2y − 1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.122561 + 0.744862I
a = 0
b = −0.877439 − 0.744862I
1.37919 − 2.82812I −0.08593 + 2.22005I
v = −0.122561 − 0.744862I
a = 0
b = −0.877439 + 0.744862I
1.37919 + 2.82812I −0.08593 − 2.22005I
v = −1.75488
a = 0
b = 0.754878
−2.75839 −17.8280
16
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
9
)(u
38
+ 10u
37
+ ··· − 24u + 1)
c
2
((u − 1)
3
)(u + 1)
6
(u
38
+ 4u
37
+ ··· + 4u − 1)
c
3
u
3
(u
2
+ 2)
3
(u
38
− u
37
+ ··· − 16u + 8)
c
4
, c
7
, c
8
u
3
(u
2
+ 2)
3
(u
38
+ u
37
+ ··· + 48u + 8)
c
5
((u − 1)
6
)(u + 1)
3
(u
38
+ 4u
37
+ ··· + 4u − 1)
c
6
((u
3
− u
2
+ 1)
2
)(u
3
+ u
2
− 1)(u
38
− 2u
37
+ ··· + u − 3)
c
9
((u
3
− u
2
+ 2u − 1)
2
)(u
3
+ u
2
+ 2u + 1)(u
38
+ 2u
37
+ ··· − 3029u − 7419)
c
10
((u
3
− u
2
+ 2u − 1)
3
)(u
38
+ 8u
37
+ ··· + 85u + 9)
c
11
(u
3
− u
2
+ 1)(u
3
+ u
2
− 1)
2
(u
38
− 2u
37
+ ··· + u − 3)
c
12
((u
3
+ u
2
+ 2u + 1)
3
)(u
38
+ 8u
37
+ ··· + 85u + 9)
17
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
9
)(y
38
+ 46y
37
+ ··· + 1128y + 1)
c
2
, c
5
((y − 1)
9
)(y
38
− 10y
37
+ ··· + 24y + 1)
c
3
y
3
(y + 2)
6
(y
38
− 53y
37
+ ··· + 896y + 64)
c
4
, c
7
, c
8
y
3
(y + 2)
6
(y
38
+ 31y
37
+ ··· − 512y + 64)
c
6
, c
11
((y
3
− y
2
+ 2y − 1)
3
)(y
38
− 8y
37
+ ··· − 85y + 9)
c
9
(y
3
+ 3y
2
+ 2y − 1)
3
· (y
38
+ 120y
37
+ ··· − 2146915177y + 55041561)
c
10
, c
12
((y
3
+ 3y
2
+ 2y − 1)
3
)(y
38
+ 48y
37
+ ··· + 1091y + 81)
18
