12n
0151
(K12n
0151
)
A knot diagram
1
Linearized knot diagam
3 5 9 2 9 10 11 3 1 12 7 6
Solving Sequence
3,9 4,5
6 2 1 10 7 12 11 8
c
3
c
5
c
2
c
1
c
9
c
6
c
12
c
11
c
7
c
4
, c
8
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h3.12647 × 10
124
u
58
+ 4.88388 × 10
124
u
57
+ ··· + 1.00387 × 10
125
b + 4.11276 × 10
127
,
− 3.26562 × 10
125
u
58
− 5.01296 × 10
125
u
57
+ ··· + 2.00773 × 10
125
a − 4.08050 × 10
128
,
u
59
+ u
58
+ ··· + 2048u + 1024i
I
v
1
= ha, b − 1, v
4
+ v
2
− v + 1i
I
v
2
= ha, b − 1, v
6
+ v
5
+ 2v
4
+ 2v
3
+ 2v
2
+ 2v + 1i
* 3 irreducible components of dim
C
= 0, with total 69 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
= h3.13 × 10
124
u
58
+ 4.88 × 10
124
u
57
+ · · · + 1.00 × 10
125
b + 4.11 ×
10
127
, −3.27 × 10
125
u
58
− 5.01 × 10
125
u
57
+ · · · + 2.01 × 10
125
a − 4.08 ×
10
128
, u
59
+ u
58
+ · · · + 2048u + 1024i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
5
=
1.62652u
58
+ 2.49682u
57
+ ··· + 8071.87u + 2032.39
−0.311443u
58
− 0.486506u
57
+ ··· − 1587.44u − 409.691
a
6
=
1.62652u
58
+ 2.49682u
57
+ ··· + 8071.87u + 2032.39
0.364133u
58
+ 0.570656u
57
+ ··· + 1860.49u + 481.501
a
2
=
1.62652u
58
+ 2.49682u
57
+ ··· + 8071.87u + 2032.39
−0.364133u
58
− 0.570656u
57
+ ··· − 1860.49u − 481.501
a
1
=
1.26239u
58
+ 1.92617u
57
+ ··· + 6211.38u + 1550.89
−0.364133u
58
− 0.570656u
57
+ ··· − 1860.49u − 481.501
a
10
=
2.30700u
58
+ 0.360471u
57
+ ··· − 4216.20u − 4797.17
−0.565229u
58
− 0.116297u
57
+ ··· + 894.169u + 1106.32
a
7
=
5.81545u
58
+ 7.39875u
57
+ ··· + 21563.7u + 3635.94
1.51836u
58
+ 2.56526u
57
+ ··· + 8651.47u + 2450.59
a
12
=
−5.75244u
58
− 8.42872u
57
+ ··· − 26627.9u − 6229.64
−1.53789u
58
− 2.31822u
57
+ ··· − 7427.88u − 1819.55
a
11
=
−4.22067u
58
− 3.95119u
57
+ ··· − 8869.99u + 637.146
−2.04332u
58
− 2.01780u
57
+ ··· − 4729.36u + 74.4945
a
8
=
−u
−u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 12.9922u
58
+ 16.4987u
57
+ ··· + 46831.5u + 7718.14
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
59
+ 15u
58
+ ··· + 15u + 1
c
2
, c
4
u
59
− 11u
58
+ ··· − 11u + 1
c
3
, c
8
u
59
+ u
58
+ ··· + 2048u + 1024
c
5
u
59
− 2u
58
+ ··· + 2u + 1
c
6
u
59
+ 2u
58
+ ··· + 480u + 72
c
7
, c
11
u
59
− 2u
58
+ ··· − 4u
2
+ 1
c
9
u
59
+ 8u
58
+ ··· + 2958u + 53
c
10
u
59
+ 28u
58
+ ··· + 8u − 1
c
12
u
59
− 10u
58
+ ··· − 1216u + 193
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
59
+ 69y
58
+ ··· − 13y −1
c
2
, c
4
y
59
− 15y
58
+ ··· + 15y −1
c
3
, c
8
y
59
+ 63y
58
+ ··· − 22544384y −1048576
c
5
y
59
− 68y
58
+ ··· + 8y −1
c
6
y
59
− 12y
58
+ ··· + 184464y −5184
c
7
, c
11
y
59
+ 28y
58
+ ··· + 8y −1
c
9
y
59
− 8y
58
+ ··· + 8867000y −2809
c
10
y
59
+ 8y
58
+ ··· + 108y −1
c
12
y
59
+ 20y
58
+ ··· − 93136y −37249
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.998103 + 0.081236I
a = 0.553279 + 0.202090I
b = 0.594657 − 0.582462I
−2.75669 + 1.28193I 0
u = −0.998103 − 0.081236I
a = 0.553279 − 0.202090I
b = 0.594657 + 0.582462I
−2.75669 − 1.28193I 0
u = 0.909539 + 0.365168I
a = 0.613308 − 0.288519I
b = 0.335049 + 0.628049I
2.24694 − 1.52880I 0
u = 0.909539 − 0.365168I
a = 0.613308 + 0.288519I
b = 0.335049 − 0.628049I
2.24694 + 1.52880I 0
u = −0.837696 + 0.475366I
a = 0.645204 + 0.335171I
b = 0.220526 − 0.634040I
0.76048 − 3.15014I 0
u = −0.837696 − 0.475366I
a = 0.645204 − 0.335171I
b = 0.220526 + 0.634040I
0.76048 + 3.15014I 0
u = 0.390732 + 0.845943I
a = 0.442369 + 0.035951I
b = 1.245730 − 0.182507I
−2.98778 + 6.48838I −4.00000 − 4.86755I
u = 0.390732 − 0.845943I
a = 0.442369 − 0.035951I
b = 1.245730 + 0.182507I
−2.98778 − 6.48838I −4.00000 + 4.86755I
u = 1.053350 + 0.234621I
a = 0.555069 − 0.252023I
b = 0.493660 + 0.678179I
1.56089 − 3.52655I 0
u = 1.053350 − 0.234621I
a = 0.555069 + 0.252023I
b = 0.493660 − 0.678179I
1.56089 + 3.52655I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.745671 + 0.508578I
a = 0.475006 + 0.082153I
b = 1.044090 − 0.353528I
−2.42601 − 4.17459I −6.95458 + 5.22656I
u = 0.745671 − 0.508578I
a = 0.475006 − 0.082153I
b = 1.044090 + 0.353528I
−2.42601 + 4.17459I −6.95458 − 5.22656I
u = 0.832959 + 0.249451I
a = 0.514927 + 0.109936I
b = 0.857363 − 0.396544I
−3.69687 + 2.56822I −10.58010 − 3.67403I
u = 0.832959 − 0.249451I
a = 0.514927 − 0.109936I
b = 0.857363 + 0.396544I
−3.69687 − 2.56822I −10.58010 + 3.67403I
u = −1.115200 + 0.205953I
a = 0.535395 + 0.248456I
b = 0.536821 − 0.713179I
−0.53472 + 8.44391I 0
u = −1.115200 − 0.205953I
a = 0.535395 − 0.248456I
b = 0.536821 + 0.713179I
−0.53472 − 8.44391I 0
u = −0.401206 + 0.746571I
a = 0.452052 − 0.037776I
b = 1.196800 + 0.183576I
−0.90878 − 1.77655I −1.72770 + 0.28396I
u = −0.401206 − 0.746571I
a = 0.452052 + 0.037776I
b = 1.196800 − 0.183576I
−0.90878 + 1.77655I −1.72770 − 0.28396I
u = 0.186981 + 0.800482I
a = 0.447704 + 0.017000I
b = 1.230400 − 0.084694I
−4.74840 − 0.55711I −7.85243 + 1.55883I
u = 0.186981 − 0.800482I
a = 0.447704 − 0.017000I
b = 1.230400 + 0.084694I
−4.74840 + 0.55711I −7.85243 − 1.55883I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.585460 + 0.521675I
a = 0.476336 − 0.060057I
b = 1.066510 + 0.260549I
−0.552842 − 0.321059I −2.73785 − 1.45340I
u = −0.585460 − 0.521675I
a = 0.476336 + 0.060057I
b = 1.066510 − 0.260549I
−0.552842 + 0.321059I −2.73785 + 1.45340I
u = −0.344966 + 0.584974I
a = 0.989053 + 0.444757I
b = −0.158993 − 0.378184I
−0.25427 + 2.25151I −0.88439 − 3.01856I
u = −0.344966 − 0.584974I
a = 0.989053 − 0.444757I
b = −0.158993 + 0.378184I
−0.25427 − 2.25151I −0.88439 + 3.01856I
u = 0.005163 + 0.654757I
a = 2.15076 + 0.83999I
b = −0.596583 − 0.157556I
−3.39992 − 7.96321I −2.44045 + 7.77163I
u = 0.005163 − 0.654757I
a = 2.15076 − 0.83999I
b = −0.596583 + 0.157556I
−3.39992 + 7.96321I −2.44045 − 7.77163I
u = 0.011811 + 0.651420I
a = 2.00434 − 0.69962I
b = −0.555268 + 0.155236I
−0.95728 + 3.13895I 0.53345 − 3.94025I
u = 0.011811 − 0.651420I
a = 2.00434 + 0.69962I
b = −0.555268 − 0.155236I
−0.95728 − 3.13895I 0.53345 + 3.94025I
u = 0.111459 + 0.623363I
a = 1.42041 − 0.50057I
b = −0.373755 + 0.220699I
0.62234 + 1.80022I 1.46582 − 4.56224I
u = 0.111459 − 0.623363I
a = 1.42041 + 0.50057I
b = −0.373755 − 0.220699I
0.62234 − 1.80022I 1.46582 + 4.56224I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.001805 + 0.630170I
a = 2.24681 + 0.44360I
b = −0.571624 − 0.084577I
−5.13604 − 0.16765I −5.11369 + 0.60296I
u = −0.001805 − 0.630170I
a = 2.24681 − 0.44360I
b = −0.571624 + 0.084577I
−5.13604 + 0.16765I −5.11369 − 0.60296I
u = −0.579721
a = 0.575386
b = 0.737962
−1.10396 −8.80140
u = 0.19820 + 1.41485I
a = 0.168080 + 1.201160I
b = −0.885740 − 0.816541I
0.693286 + 0.866196I 0
u = 0.19820 − 1.41485I
a = 0.168080 − 1.201160I
b = −0.885740 + 0.816541I
0.693286 − 0.866196I 0
u = 0.33794 + 1.44689I
a = 0.034774 + 1.229800I
b = −0.977026 − 0.812488I
0.40044 − 7.01056I 0
u = 0.33794 − 1.44689I
a = 0.034774 − 1.229800I
b = −0.977026 + 0.812488I
0.40044 + 7.01056I 0
u = −0.25718 + 1.49968I
a = 0.084876 − 1.159550I
b = −0.937211 + 0.857810I
3.75772 + 3.20443I 0
u = −0.25718 − 1.49968I
a = 0.084876 + 1.159550I
b = −0.937211 − 0.857810I
3.75772 − 3.20443I 0
u = 0.04696 + 1.65800I
a = 0.193873 − 0.944416I
b = −0.791424 + 1.016040I
3.69904 − 0.23163I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.04696 − 1.65800I
a = 0.193873 + 0.944416I
b = −0.791424 − 1.016040I
3.69904 + 0.23163I 0
u = −0.50336 + 1.59145I
a = −0.123627 − 1.133430I
b = −1.095100 + 0.871905I
2.73059 + 7.14739I 0
u = −0.50336 − 1.59145I
a = −0.123627 + 1.133430I
b = −1.095100 − 0.871905I
2.73059 − 7.14739I 0
u = 0.53071 + 1.64437I
a = −0.144074 + 1.095240I
b = −1.11806 − 0.89751I
7.55867 − 9.77831I 0
u = 0.53071 − 1.64437I
a = −0.144074 − 1.095240I
b = −1.11806 + 0.89751I
7.55867 + 9.77831I 0
u = −0.55751 + 1.63560I
a = −0.163068 − 1.100950I
b = −1.13165 + 0.88881I
5.3016 + 14.9246I 0
u = −0.55751 − 1.63560I
a = −0.163068 + 1.100950I
b = −1.13165 − 0.88881I
5.3016 − 14.9246I 0
u = 0.45548 + 1.68569I
a = −0.094411 + 1.064750I
b = −1.08263 − 0.93187I
8.89235 − 7.23820I 0
u = 0.45548 − 1.68569I
a = −0.094411 − 1.064750I
b = −1.08263 + 0.93187I
8.89235 + 7.23820I 0
u = −0.06440 + 1.74963I
a = 0.164970 + 0.902532I
b = −0.804022 − 1.072170I
8.58017 + 2.61249I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.06440 − 1.74963I
a = 0.164970 − 0.902532I
b = −0.804022 + 1.072170I
8.58017 − 2.61249I 0
u = −0.40556 + 1.70511I
a = −0.064015 − 1.047870I
b = −1.05808 + 0.95077I
7.86608 + 2.22410I 0
u = −0.40556 − 1.70511I
a = −0.064015 + 1.047870I
b = −1.05808 − 0.95077I
7.86608 − 2.22410I 0
u = 0.10531 + 1.75148I
a = 0.178722 − 0.887018I
b = −0.781712 + 1.083390I
6.43786 − 7.75949I 0
u = 0.10531 − 1.75148I
a = 0.178722 + 0.887018I
b = −0.781712 − 1.083390I
6.43786 + 7.75949I 0
u = 0.04475 + 1.76538I
a = 0.116249 + 0.933213I
b = −0.868556 − 1.055190I
9.59397 + 0.00079I 0
u = 0.04475 − 1.76538I
a = 0.116249 − 0.933213I
b = −0.868556 + 1.055190I
9.59397 − 0.00079I 0
u = −0.10471 + 1.77099I
a = 0.087935 − 0.948757I
b = −0.903142 + 1.045030I
8.37962 + 5.04404I 0
u = −0.10471 − 1.77099I
a = 0.087935 + 0.948757I
b = −0.903142 − 1.045030I
8.37962 − 5.04404I 0
10
II. I
v
1
= ha, b − 1, v
4
+ v
2
− v + 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
v
0
a
4
=
1
0
a
5
=
0
1
a
6
=
v
2
1
a
2
=
1
−1
a
1
=
0
−1
a
10
=
v
−v
a
7
=
v
2
− v + 1
v
a
12
=
v
2
− v + 1
−v
2
− 1
a
11
=
v
3
+ 1
−1
a
8
=
v
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −5v
3
− 4v
2
− v − 6
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
8
u
4
c
4
(u + 1)
4
c
5
, c
7
, c
9
u
4
+ u
2
+ u + 1
c
6
u
4
+ 3u
3
+ 4u
2
+ 3u + 2
c
10
u
4
− 2u
3
+ 3u
2
− u + 1
c
11
u
4
+ u
2
− u + 1
c
12
u
4
+ 2u
3
+ 3u
2
+ u + 1
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
4
c
3
, c
8
y
4
c
5
, c
7
, c
9
c
11
y
4
+ 2y
3
+ 3y
2
+ y + 1
c
6
y
4
− y
3
+ 2y
2
+ 7y + 4
c
10
, c
12
y
4
+ 2y
3
+ 7y
2
+ 5y + 1
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.547424 + 0.585652I
a = 0
b = 1.00000
−0.66484 + 1.39709I −4.37800 − 4.77865I
v = 0.547424 − 0.585652I
a = 0
b = 1.00000
−0.66484 − 1.39709I −4.37800 + 4.77865I
v = −0.547424 + 1.120870I
a = 0
b = 1.00000
−4.26996 − 7.64338I −11.12200 + 5.79053I
v = −0.547424 − 1.120870I
a = 0
b = 1.00000
−4.26996 + 7.64338I −11.12200 − 5.79053I
14
III. I
v
2
= ha, b − 1, v
6
+ v
5
+ 2v
4
+ 2v
3
+ 2v
2
+ 2v + 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
v
0
a
4
=
1
0
a
5
=
0
1
a
6
=
v
2
1
a
2
=
1
−1
a
1
=
0
−1
a
10
=
v
−v
a
7
=
−v
4
v
4
+ v
2
+ 1
a
12
=
−v
4
−v
2
− 1
a
11
=
v
5
+ v
3
+ v
2
+ v
v
5
+ 2v
3
+ v + 1
a
8
=
v
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 2v
5
+ v
4
− v
3
+ 3v
2
− 2v − 8
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
6
c
3
, c
8
u
6
c
4
(u + 1)
6
c
5
, c
7
, c
9
u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1
c
6
(u
3
− u
2
+ 1)
2
c
10
u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1
c
11
u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1
c
12
u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
6
c
3
, c
8
y
6
c
5
, c
7
, c
9
c
11
y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1
c
6
(y
3
− y
2
+ 2y − 1)
2
c
10
, c
12
y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = 0.498832 + 1.001300I
a = 0
b = 1.00000
−1.91067 + 2.82812I −7.72532 − 2.61835I
v = 0.498832 − 1.001300I
a = 0
b = 1.00000
−1.91067 − 2.82812I −7.72532 + 2.61835I
v = −0.284920 + 1.115140I
a = 0
b = 1.00000
−6.04826 −14.8442 − 0.2733I
v = −0.284920 − 1.115140I
a = 0
b = 1.00000
−6.04826 −14.8442 + 0.2733I
v = −0.713912 + 0.305839I
a = 0
b = 1.00000
−1.91067 + 2.82812I −4.93045 − 2.21599I
v = −0.713912 − 0.305839I
a = 0
b = 1.00000
−1.91067 − 2.82812I −4.93045 + 2.21599I
18
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
10
)(u
59
+ 15u
58
+ ··· + 15u + 1)
c
2
((u − 1)
10
)(u
59
− 11u
58
+ ··· − 11u + 1)
c
3
, c
8
u
10
(u
59
+ u
58
+ ··· + 2048u + 1024)
c
4
((u + 1)
10
)(u
59
− 11u
58
+ ··· − 11u + 1)
c
5
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
59
− 2u
58
+ ··· + 2u + 1)
c
6
((u
3
− u
2
+ 1)
2
)(u
4
+ 3u
3
+ ··· + 3u + 2)(u
59
+ 2u
58
+ ··· + 480u + 72)
c
7
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
59
− 2u
58
+ ··· − 4u
2
+ 1)
c
9
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
59
+ 8u
58
+ ··· + 2958u + 53)
c
10
(u
4
− 2u
3
+ 3u
2
− u + 1)(u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1)
· (u
59
+ 28u
58
+ ··· + 8u − 1)
c
11
(u
4
+ u
2
− u + 1)(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
· (u
59
− 2u
58
+ ··· − 4u
2
+ 1)
c
12
(u
4
+ 2u
3
+ 3u
2
+ u + 1)(u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1)
· (u
59
− 10u
58
+ ··· − 1216u + 193)
19
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
10
)(y
59
+ 69y
58
+ ··· − 13y − 1)
c
2
, c
4
((y − 1)
10
)(y
59
− 15y
58
+ ··· + 15y − 1)
c
3
, c
8
y
10
(y
59
+ 63y
58
+ ··· − 2.25444 × 10
7
y − 1048576)
c
5
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
59
− 68y
58
+ ··· + 8y − 1)
c
6
(y
3
− y
2
+ 2y − 1)
2
(y
4
− y
3
+ 2y
2
+ 7y + 4)
· (y
59
− 12y
58
+ ··· + 184464y − 5184)
c
7
, c
11
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
59
+ 28y
58
+ ··· + 8y − 1)
c
9
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
59
− 8y
58
+ ··· + 8867000y − 2809)
c
10
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)(y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
· (y
59
+ 8y
58
+ ··· + 108y − 1)
c
12
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)(y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
· (y
59
+ 20y
58
+ ··· − 93136y − 37249)
20
