12n
0181
(K12n
0181
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 10 9 11 4 6 12 8 10
Solving Sequence
5,10 3,6
2 1 4 9 7 8 12 11
c
5
c
2
c
1
c
4
c
9
c
6
c
8
c
12
c
10
c
3
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.89597 × 10
103
u
52
+ 7.97404 × 10
103
u
51
+ ··· + 3.42001 × 10
105
b − 2.68164 × 10
105
,
− 2.24253 × 10
103
u
52
+ 6.90313 × 10
103
u
51
+ ··· + 1.36801 × 10
105
a − 2.45570 × 10
105
,
u
53
− 3u
52
+ ··· − 49u + 49i
I
u
2
= h−1878a
5
u + 2600a
4
u + ··· + 23830a − 8647,
a
6
− 3a
5
u − 4a
5
+ 7a
4
u − a
4
− a
3
u − 3a
3
+ 9a
2
u + 5a
2
− 6au + 2a + u, u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 65 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
= h−2.90 × 10
103
u
52
+ 7.97 × 10
103
u
51
+ · · · + 3.42 × 10
105
b − 2.68 ×
10
105
, −2.24 × 10
103
u
52
+ 6.90 × 10
103
u
51
+ · · · + 1.37 × 10
105
a − 2.46 ×
10
105
, u
53
− 3u
52
+ · · · − 49u + 49i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
3
=
0.0163927u
52
− 0.0504613u
51
+ ··· + 4.67289u + 1.79509
0.00846773u
52
− 0.0233158u
51
+ ··· + 3.33538u + 0.784101
a
6
=
1
−u
2
a
2
=
0.0248604u
52
− 0.0737771u
51
+ ··· + 8.00826u + 2.57919
0.00846773u
52
− 0.0233158u
51
+ ··· + 3.33538u + 0.784101
a
1
=
−0.00350318u
52
+ 0.0151353u
51
+ ··· − 5.53251u + 4.45074
0.00290112u
52
− 0.00548627u
51
+ ··· − 1.43147u + 1.55122
a
4
=
−0.0134120u
52
+ 0.0381751u
51
+ ··· − 12.1908u + 0.357746
−0.00827306u
52
+ 0.0265007u
51
+ ··· − 4.74375u + 0.368964
a
9
=
−u
u
3
+ u
a
7
=
u
2
+ 1
−u
4
− 2u
2
a
8
=
0.0238148u
52
− 0.0757412u
51
+ ··· + 15.3375u − 0.149255
0.0114699u
52
− 0.0338179u
51
+ ··· + 7.34993u − 0.181045
a
12
=
−0.00350318u
52
+ 0.0151353u
51
+ ··· − 5.53251u + 4.45074
0.00182181u
52
− 0.00371679u
51
+ ··· − 1.82979u + 1.77789
a
11
=
−0.0209597u
52
+ 0.0608672u
51
+ ··· − 11.6241u − 1.93839
−0.00957219u
52
+ 0.0293318u
51
+ ··· − 5.11792u − 0.541740
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0668454u
52
− 0.159654u
51
+ ··· + 29.7015u + 4.20227
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
53
+ 33u
52
+ ··· − 47u + 1
c
2
, c
4
u
53
− 5u
52
+ ··· − u + 1
c
3
, c
8
u
53
+ u
52
+ ··· − 3u + 1
c
5
, c
6
, c
9
u
53
+ 3u
52
+ ··· − 49u − 49
c
7
, c
11
u
53
+ 3u
52
+ ··· − 55u − 17
c
10
, c
12
u
53
+ 31u
52
+ ··· − 613u + 289
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
53
− 21y
52
+ ··· + 1053y −1
c
2
, c
4
y
53
− 33y
52
+ ··· − 47y −1
c
3
, c
8
y
53
− 9y
52
+ ··· + 25y −1
c
5
, c
6
, c
9
y
53
+ 63y
52
+ ··· − 67963y −2401
c
7
, c
11
y
53
− 31y
52
+ ··· − 613y −289
c
10
, c
12
y
53
− 11y
52
+ ··· + 7632559y −83521
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.595173 + 0.790194I
a = 0.44043 + 1.93505I
b = −1.210360 − 0.280896I
−4.60939 − 3.81170I −6.73528 + 3.84171I
u = −0.595173 − 0.790194I
a = 0.44043 − 1.93505I
b = −1.210360 + 0.280896I
−4.60939 + 3.81170I −6.73528 − 3.84171I
u = −0.065051 + 1.017050I
a = −3.30036 + 7.32048I
b = −1.027960 + 0.007177I
−3.35538 + 2.03910I 49.7365 + 13.7735I
u = −0.065051 − 1.017050I
a = −3.30036 − 7.32048I
b = −1.027960 − 0.007177I
−3.35538 − 2.03910I 49.7365 − 13.7735I
u = 0.416693 + 0.950759I
a = 1.024360 + 0.862942I
b = −0.965495 − 0.409417I
−4.11133 + 1.46427I −9.04772 − 2.35631I
u = 0.416693 − 0.950759I
a = 1.024360 − 0.862942I
b = −0.965495 + 0.409417I
−4.11133 − 1.46427I −9.04772 + 2.35631I
u = 0.729736 + 0.532396I
a = 0.16697 − 1.52278I
b = −0.010061 + 0.720357I
−1.31363 + 5.14831I −1.33330 − 6.61182I
u = 0.729736 − 0.532396I
a = 0.16697 + 1.52278I
b = −0.010061 − 0.720357I
−1.31363 − 5.14831I −1.33330 + 6.61182I
u = −0.215243 + 1.119870I
a = 0.188281 − 1.006360I
b = 0.752530 + 0.810688I
0.48114 − 2.27755I 0
u = −0.215243 − 1.119870I
a = 0.188281 + 1.006360I
b = 0.752530 − 0.810688I
0.48114 + 2.27755I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.103946 + 1.148880I
a = 0.680955 − 0.103748I
b = 0.041239 − 0.173602I
−1.46943 − 2.21311I 0
u = −0.103946 − 1.148880I
a = 0.680955 + 0.103748I
b = 0.041239 + 0.173602I
−1.46943 + 2.21311I 0
u = −0.212301 + 1.239690I
a = −0.226559 + 0.777926I
b = 1.017950 − 0.818402I
−0.28600 + 3.82525I 0
u = −0.212301 − 1.239690I
a = −0.226559 − 0.777926I
b = 1.017950 + 0.818402I
−0.28600 − 3.82525I 0
u = −0.614853 + 0.330857I
a = 0.124371 + 0.894782I
b = 0.214005 − 0.481317I
1.20368 − 0.96438I 4.48379 + 2.13228I
u = −0.614853 − 0.330857I
a = 0.124371 − 0.894782I
b = 0.214005 + 0.481317I
1.20368 + 0.96438I 4.48379 − 2.13228I
u = −0.973061 + 0.866281I
a = −0.168964 − 0.836441I
b = 1.065960 + 0.284444I
−1.16177 − 4.11245I 0
u = −0.973061 − 0.866281I
a = −0.168964 + 0.836441I
b = 1.065960 − 0.284444I
−1.16177 + 4.11245I 0
u = 1.156780 + 0.633760I
a = −0.556768 + 1.051180I
b = 1.251690 − 0.389157I
−5.12630 + 9.25985I 0
u = 1.156780 − 0.633760I
a = −0.556768 − 1.051180I
b = 1.251690 + 0.389157I
−5.12630 − 9.25985I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.200767 + 0.612944I
a = 1.72350 − 1.16204I
b = −0.266010 + 0.219165I
−1.61832 − 1.52147I −1.349487 − 0.343641I
u = 0.200767 − 0.612944I
a = 1.72350 + 1.16204I
b = −0.266010 − 0.219165I
−1.61832 + 1.52147I −1.349487 + 0.343641I
u = 0.215983 + 0.479163I
a = 0.36339 − 2.19939I
b = −1.001170 + 0.213875I
−1.87227 + 0.78178I −5.10778 + 0.42163I
u = 0.215983 − 0.479163I
a = 0.36339 + 2.19939I
b = −1.001170 − 0.213875I
−1.87227 − 0.78178I −5.10778 − 0.42163I
u = −0.520458
a = 0.390996
b = −1.18658
−2.71524 0.0344960
u = −0.358766 + 0.278704I
a = −0.700349 − 0.576141I
b = 0.792821 − 0.657219I
3.09917 + 0.31720I 4.50890 + 0.69651I
u = −0.358766 − 0.278704I
a = −0.700349 + 0.576141I
b = 0.792821 + 0.657219I
3.09917 − 0.31720I 4.50890 − 0.69651I
u = −0.17201 + 1.54745I
a = −0.061046 + 0.762953I
b = 0.008072 − 1.011800I
−5.20565 − 3.69410I 0
u = −0.17201 − 1.54745I
a = −0.061046 − 0.762953I
b = 0.008072 + 1.011800I
−5.20565 + 3.69410I 0
u = 1.28535 + 0.92715I
a = −0.443268 + 0.275722I
b = 1.172440 + 0.025439I
−5.51056 − 1.44071I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.28535 − 0.92715I
a = −0.443268 − 0.275722I
b = 1.172440 − 0.025439I
−5.51056 + 1.44071I 0
u = 0.372202 + 0.136798I
a = 1.90070 + 2.55797I
b = −0.643573 − 0.317372I
−1.22108 − 1.50910I −1.59355 + 4.23824I
u = 0.372202 − 0.136798I
a = 1.90070 − 2.55797I
b = −0.643573 + 0.317372I
−1.22108 + 1.50910I −1.59355 − 4.23824I
u = 0.05090 + 1.61029I
a = −0.299743 − 0.901123I
b = −1.32748 + 0.50601I
−9.35172 + 1.68194I 0
u = 0.05090 − 1.61029I
a = −0.299743 + 0.901123I
b = −1.32748 − 0.50601I
−9.35172 − 1.68194I 0
u = 0.27323 + 1.60285I
a = −0.259024 − 0.912712I
b = 0.100537 + 1.137500I
−8.46780 + 9.00006I 0
u = 0.27323 − 1.60285I
a = −0.259024 + 0.912712I
b = 0.100537 − 1.137500I
−8.46780 − 9.00006I 0
u = 0.03952 + 1.64660I
a = 0.182459 − 0.963991I
b = −0.203341 + 1.088210I
−9.72111 − 0.68351I 0
u = 0.03952 − 1.64660I
a = 0.182459 + 0.963991I
b = −0.203341 − 1.088210I
−9.72111 + 0.68351I 0
u = −0.17859 + 1.67997I
a = −0.076726 + 1.173520I
b = −1.31892 − 0.63562I
−13.1597 − 6.8790I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.17859 − 1.67997I
a = −0.076726 − 1.173520I
b = −1.31892 + 0.63562I
−13.1597 + 6.8790I 0
u = 0.08259 + 1.69794I
a = −0.054404 + 0.572818I
b = −1.45600 − 0.45286I
−13.53370 + 3.26626I 0
u = 0.08259 − 1.69794I
a = −0.054404 − 0.572818I
b = −1.45600 + 0.45286I
−13.53370 − 3.26626I 0
u = 0.42803 + 1.65107I
a = 0.184242 + 1.247230I
b = 1.35580 − 0.58825I
−12.4103 + 15.1230I 0
u = 0.42803 − 1.65107I
a = 0.184242 − 1.247230I
b = 1.35580 + 0.58825I
−12.4103 − 15.1230I 0
u = −0.33416 + 1.67478I
a = 0.281652 − 1.015890I
b = 1.33173 + 0.51061I
−9.32017 − 9.12278I 0
u = −0.33416 − 1.67478I
a = 0.281652 + 1.015890I
b = 1.33173 − 0.51061I
−9.32017 + 9.12278I 0
u = −0.014001 + 0.282926I
a = 2.23005 + 0.68964I
b = 0.877923 + 0.687381I
2.87265 − 4.91482I 4.21582 + 6.57376I
u = −0.014001 − 0.282926I
a = 2.23005 − 0.68964I
b = 0.877923 − 0.687381I
2.87265 + 4.91482I 4.21582 − 6.57376I
u = 0.07007 + 1.82145I
a = 0.350617 − 0.045144I
b = 1.120840 + 0.120521I
−4.27518 − 3.61779I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.07007 − 1.82145I
a = 0.350617 + 0.045144I
b = 1.120840 − 0.120521I
−4.27518 + 3.61779I 0
u = 0.27553 + 1.82009I
a = 0.038306 + 0.719874I
b = 1.42013 − 0.39452I
−15.0358 + 4.4925I 0
u = 0.27553 − 1.82009I
a = 0.038306 − 0.719874I
b = 1.42013 + 0.39452I
−15.0358 − 4.4925I 0
10
II. I
u
2
= h−1878a
5
u + 2600a
4
u + · · · + 23830a − 8647, −3a
5
u + 7a
4
u + · · · +
5a
2
+ 2a, u
2
+ 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
3
=
a
0.313575a
5
u − 0.434129a
4
u + ··· − 3.97896a + 1.44381
a
6
=
1
1
a
2
=
0.313575a
5
u − 0.434129a
4
u + ··· − 2.97896a + 1.44381
0.313575a
5
u − 0.434129a
4
u + ··· − 3.97896a + 1.44381
a
1
=
0.230422a
5
u − 0.782267a
4
u + ··· − 1.18901a + 0.965103
−0.165136a
5
u + 0.977292a
4
u + ··· + 0.0687928a + 1.64168
a
4
=
−0.183336a
5
u − 0.225413a
4
u + ··· + 3.74169a − 0.115712
−0.478711a
5
u + 1.41142a
4
u + ··· + 4.04775a − 0.802137
a
9
=
−u
0
a
7
=
0
1
a
8
=
−0.0719653a
5
u + 0.813157a
4
u + ··· − 0.816330a − 0.315913
−0.231758a
5
u + 0.583904a
4
u + ··· + 0.201703a + 0.493071
a
12
=
0.230422a
5
u − 0.782267a
4
u + ··· − 1.18901a + 0.965103
0.0652864a
5
u + 0.195024a
4
u + ··· − 1.12022a + 2.60678
a
11
=
0.230422a
5
u − 0.782267a
4
u + ··· − 1.18901a + 0.965103
0.00250459a
5
u − 0.128068a
4
u + ··· + 0.476206a + 1.14093
(ii) Obstruction class = 1
(iii) Cusp Shapes =
9236
5989
a
5
u −
3388
5989
a
5
−
29880
5989
a
4
u +
35892
5989
a
4
−
2204
5989
a
3
u −
43908
5989
a
3
−
72924
5989
a
2
u +
25744
5989
a
2
+
27704
5989
au −
75764
5989
a −
12196
5989
u −
5756
5989
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
3
− u
2
+ 2u − 1)
4
c
2
(u
3
+ u
2
− 1)
4
c
3
, c
8
(u
6
− 3u
4
+ 2u
2
+ 1)
2
c
4
(u
3
− u
2
+ 1)
4
c
5
, c
6
, c
9
(u
2
+ 1)
6
c
7
, c
11
(u
4
− u
2
+ 1)
3
c
10
(u
2
− u + 1)
6
c
12
(u
2
+ u + 1)
6
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
3
+ 3y
2
+ 2y − 1)
4
c
2
, c
4
(y
3
− y
2
+ 2y − 1)
4
c
3
, c
8
(y
3
− 3y
2
+ 2y + 1)
4
c
5
, c
6
, c
9
(y + 1)
12
c
7
, c
11
(y
2
− y + 1)
6
c
10
, c
12
(y
2
+ y + 1)
6
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −0.450984 − 1.062990I
b = 0.877439 + 0.744862I
1.37919 − 4.85801I −2.49024 + 6.44355I
u = 1.000000I
a = 0.696107 + 0.426734I
b = 0.877439 − 0.744862I
1.37919 + 4.85801I −2.49024 − 6.44355I
u = 1.000000I
a = −0.258387 + 1.162360I
b = −0.754878
−2.75839 − 2.02988I −9.01951 + 3.46410I
u = 1.000000I
a = 0.111295 + 1.400630I
b = 0.877439 − 0.744862I
1.37919 + 0.79824I −2.49024 + 0.48465I
u = 1.000000I
a = 0.133827 − 0.089093I
b = 0.877439 + 0.744862I
1.37919 − 0.79824I −2.49024 − 0.48465I
u = 1.000000I
a = 3.76814 + 1.16236I
b = −0.754878
−2.75839 + 2.02988I −9.01951 − 3.46410I
u = − 1.000000I
a = −0.450984 + 1.062990I
b = 0.877439 − 0.744862I
1.37919 + 4.85801I −2.49024 − 6.44355I
u = − 1.000000I
a = 0.696107 − 0.426734I
b = 0.877439 + 0.744862I
1.37919 − 4.85801I −2.49024 + 6.44355I
u = − 1.000000I
a = −0.258387 − 1.162360I
b = −0.754878
−2.75839 + 2.02988I −9.01951 − 3.46410I
u = − 1.000000I
a = 0.111295 − 1.400630I
b = 0.877439 + 0.744862I
1.37919 − 0.79824I −2.49024 − 0.48465I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = − 1.000000I
a = 0.133827 + 0.089093I
b = 0.877439 − 0.744862I
1.37919 + 0.79824I −2.49024 + 0.48465I
u = − 1.000000I
a = 3.76814 − 1.16236I
b = −0.754878
−2.75839 − 2.02988I −9.01951 + 3.46410I
15
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
3
− u
2
+ 2u − 1)
4
)(u
53
+ 33u
52
+ ··· − 47u + 1)
c
2
((u
3
+ u
2
− 1)
4
)(u
53
− 5u
52
+ ··· − u + 1)
c
3
, c
8
((u
6
− 3u
4
+ 2u
2
+ 1)
2
)(u
53
+ u
52
+ ··· − 3u + 1)
c
4
((u
3
− u
2
+ 1)
4
)(u
53
− 5u
52
+ ··· − u + 1)
c
5
, c
6
, c
9
((u
2
+ 1)
6
)(u
53
+ 3u
52
+ ··· − 49u − 49)
c
7
, c
11
((u
4
− u
2
+ 1)
3
)(u
53
+ 3u
52
+ ··· − 55u − 17)
c
10
((u
2
− u + 1)
6
)(u
53
+ 31u
52
+ ··· − 613u + 289)
c
12
((u
2
+ u + 1)
6
)(u
53
+ 31u
52
+ ··· − 613u + 289)
16
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
3
+ 3y
2
+ 2y − 1)
4
)(y
53
− 21y
52
+ ··· + 1053y − 1)
c
2
, c
4
((y
3
− y
2
+ 2y − 1)
4
)(y
53
− 33y
52
+ ··· − 47y − 1)
c
3
, c
8
((y
3
− 3y
2
+ 2y + 1)
4
)(y
53
− 9y
52
+ ··· + 25y − 1)
c
5
, c
6
, c
9
((y + 1)
12
)(y
53
+ 63y
52
+ ··· − 67963y − 2401)
c
7
, c
11
((y
2
− y + 1)
6
)(y
53
− 31y
52
+ ··· − 613y − 289)
c
10
, c
12
((y
2
+ y + 1)
6
)(y
53
− 11y
52
+ ··· + 7632559y − 83521)
17
