12n
0214
(K12n
0214
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 9 11 4 6 12 5 8 10
Solving Sequence
4,7 8,11
12 3 6 9 5 2 1 10
c
7
c
11
c
3
c
6
c
8
c
5
c
2
c
1
c
10
c
4
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.09571 × 10
30
u
16
− 2.07081 × 10
30
u
15
+ ··· + 6.08382 × 10
33
b + 8.49226 × 10
32
,
− 1.33922 × 10
32
u
16
− 1.76390 × 10
32
u
15
+ ··· + 6.08382 × 10
34
a − 1.49809 × 10
35
,
u
17
+ u
16
+ ··· + 384u − 256i
I
u
2
= hb, −u
8
+ u
7
− 3u
6
+ u
5
− 4u
4
+ u
3
− 4u
2
+ a − 2, u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1i
I
v
1
= ha, −941v
7
+ 2551v
6
− 1791v
5
− 6184v
4
+ 16309v
3
+ 15249v
2
+ 887b − 4192v −1842,
v
8
− 2v
7
+ 8v
5
− 13v
4
− 28v
3
− 7v
2
+ 3v + 1i
* 3 irreducible components of dim
C
= 0, with total 34 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−2.10 × 10
30
u
16
− 2.07 × 10
30
u
15
+ · · · + 6.08 × 10
33
b + 8.49 ×
10
32
, −1.34 × 10
32
u
16
− 1.76 × 10
32
u
15
+ · · · + 6.08 × 10
34
a − 1.50 ×
10
35
, u
17
+ u
16
+ · · · + 384u − 256i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
11
=
0.00220128u
16
+ 0.00289932u
15
+ ··· − 5.85108u + 2.46242
0.000344472u
16
+ 0.000340380u
15
+ ··· − 1.54619u − 0.139587
a
12
=
0.00303342u
16
+ 0.00362610u
15
+ ··· − 7.69275u + 2.14413
0.000425453u
16
+ 0.000210059u
15
+ ··· − 1.29270u − 0.166559
a
3
=
u
u
3
+ u
a
6
=
−0.00104394u
16
− 0.000502159u
15
+ ··· − 0.986241u − 0.762867
−0.000208289u
16
− 0.000242907u
15
+ ··· + 0.747325u − 0.207566
a
9
=
−0.00179545u
16
− 0.00185026u
15
+ ··· + 2.21680u + 0.967939
−0.000259975u
16
− 0.000427010u
15
+ ··· + 0.794841u + 0.0755036
a
5
=
−0.00105718u
16
− 0.000691805u
15
+ ··· − 2.07890u + 0.560650
−0.000380922u
16
− 0.000264026u
15
+ ··· + 0.424147u + 0.138080
a
2
=
0.000938601u
16
+ 0.000588558u
15
+ ··· + 2.91399u − 0.516106
0.000131921u
16
+ 0.0000766562u
15
+ ··· + 1.20979u − 0.0450674
a
1
=
0.000676260u
16
+ 0.000427780u
15
+ ··· + 2.50305u − 0.422569
−0.000161339u
16
− 0.0000449155u
15
+ ··· + 0.692685u + 0.0744692
a
10
=
0.00254189u
16
+ 0.00306982u
15
+ ··· − 5.29234u + 2.34906
0.000191963u
16
+ 6.02751 × 10
−6
u
15
+ ··· − 0.601447u − 0.0925424
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0102860u
16
+ 0.00859873u
15
+ ··· + 17.8393u + 1.47057
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
17
+ 37u
16
+ ··· + u + 1
c
2
, c
4
u
17
− 15u
16
+ ··· + 3u − 1
c
3
, c
7
u
17
+ u
16
+ ··· + 384u − 256
c
5
, c
8
u
17
+ 2u
16
+ ··· + 3u + 1
c
6
u
17
+ u
16
+ ··· − 512u − 512
c
9
, c
12
u
17
+ 16u
16
+ ··· − 11u + 1
c
10
u
17
− 3u
16
+ ··· − 167922u − 192217
c
11
u
17
− 6u
16
+ ··· − 19686u + 2393
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
17
− 57y
16
+ ··· − 7859y −1
c
2
, c
4
y
17
− 37y
16
+ ··· + y −1
c
3
, c
7
y
17
− 33y
16
+ ··· + 245760y −65536
c
5
, c
8
y
17
+ 12y
16
+ ··· + 25y −1
c
6
y
17
− 39y
16
+ ··· + 3670016y −262144
c
9
, c
12
y
17
− 40y
16
+ ··· + 221y −1
c
10
y
17
− 45y
16
+ ··· + 806894237728y −36947375089
c
11
y
17
− 38y
16
+ ··· + 475084108y −5726449
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.634179 + 0.647207I
a = −0.59964 + 1.28467I
b = −0.186633 − 0.343696I
−4.28789 + 1.16759I −4.15148 + 0.42617I
u = 0.634179 − 0.647207I
a = −0.59964 − 1.28467I
b = −0.186633 + 0.343696I
−4.28789 − 1.16759I −4.15148 − 0.42617I
u = −0.690024 + 0.240704I
a = 0.236937 − 1.076210I
b = 0.762159 + 0.184291I
−1.52593 + 2.30609I 0.84073 − 4.41351I
u = −0.690024 − 0.240704I
a = 0.236937 + 1.076210I
b = 0.762159 − 0.184291I
−1.52593 − 2.30609I 0.84073 + 4.41351I
u = −0.442272
a = 1.85319
b = 0.249683
−1.26971 −9.85470
u = 0.408620
a = 1.30764
b = −0.594904
1.02663 10.5660
u = 0.149177 + 0.310693I
a = 0.71057 − 3.54706I
b = −0.479273 − 0.632626I
0.959539 − 1.013620I 4.00582 − 0.77460I
u = 0.149177 − 0.310693I
a = 0.71057 + 3.54706I
b = −0.479273 + 0.632626I
0.959539 + 1.013620I 4.00582 + 0.77460I
u = 2.13688 + 2.10608I
a = 0.445317 + 0.501364I
b = −2.32289 + 2.38769I
−16.2212 − 7.3387I 3.75665 + 2.42096I
u = 2.13688 − 2.10608I
a = 0.445317 − 0.501364I
b = −2.32289 − 2.38769I
−16.2212 + 7.3387I 3.75665 − 2.42096I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −2.02549 + 2.27905I
a = −0.511301 + 0.473424I
b = 2.09738 + 2.40856I
19.0196 + 12.9458I 0.98224 − 5.00778I
u = −2.02549 − 2.27905I
a = −0.511301 − 0.473424I
b = 2.09738 − 2.40856I
19.0196 − 12.9458I 0.98224 + 5.00778I
u = −2.36097 + 2.01644I
a = −0.370113 + 0.467612I
b = 2.49326 + 2.18000I
19.0497 + 1.6784I 0.985857 + 0.191287I
u = −2.36097 − 2.01644I
a = −0.370113 − 0.467612I
b = 2.49326 − 2.18000I
19.0497 − 1.6784I 0.985857 − 0.191287I
u = −3.15648
a = 0.0710901
b = 3.69863
3.68181 3.55300
u = 3.25130 + 0.32944I
a = −0.0277291 + 0.0915040I
b = −3.54070 + 0.36634I
−0.61891 − 5.84472I 0.94829 + 2.62397I
u = 3.25130 − 0.32944I
a = −0.0277291 − 0.0915040I
b = −3.54070 − 0.36634I
−0.61891 + 5.84472I 0.94829 − 2.62397I
6
II. I
u
2
= hb, −u
8
+ u
7
− 3u
6
+ u
5
− 4u
4
+ u
3
− 4u
2
+ a − 2, u
9
− u
8
+ 2u
7
−
u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
11
=
u
8
− u
7
+ 3u
6
− u
5
+ 4u
4
− u
3
+ 4u
2
+ 2
0
a
12
=
−u
7
+ 2u
6
− u
5
+ 2u
4
− u
3
+ 3u
2
+ u + 2
u
7
+ 2u
5
+ 3u
3
+ u
2
+ 2u + 1
a
3
=
u
u
3
+ u
a
6
=
1
0
a
9
=
u
2
+ 1
u
2
a
5
=
u
4
+ u
2
+ 1
u
4
a
2
=
−u
6
− u
4
− 2u
2
− 1
−u
8
− 2u
6
− 2u
4
− 2u
2
a
1
=
−u
2
− 1
−u
2
a
10
=
−u
7
+ 2u
6
− u
5
+ 2u
4
− u
3
+ 4u
2
+ u + 3
u
7
+ 2u
5
+ 3u
3
+ 2u
2
+ 2u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
8
+ 8u
7
− 13u
6
+ 9u
5
− 17u
4
+ 16u
3
− 13u
2
+ 4u − 4
7
(iv) u-Polynomials at the component
8
Crossings u-Polynomials at each crossing
c
1
u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1
c
2
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1
c
3
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1
c
4
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
c
5
u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1
c
6
u
9
c
7
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
8
u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1
c
9
(u + 1)
9
c
10
u
9
+ 2u
8
+ 5u
7
+ 22u
6
+ 52u
5
+ 63u
4
+ 41u
3
+ 10u
2
− 2u − 1
c
11
u
9
+ 3u
8
+ 3u
7
− 2u
6
+ u
5
− 9u
4
+ 3u
3
+ 2u − 1
c
12
(u − 1)
9
9
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1
c
2
, c
4
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
c
3
, c
7
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
c
5
, c
8
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
c
6
y
9
c
9
, c
12
(y −1)
9
c
10
y
9
+ 6y
8
+ ··· + 24y −1
c
11
y
9
− 3y
8
+ 23y
7
+ 62y
6
− 13y
5
− 57y
4
+ 9y
3
− 6y
2
+ 4y −1
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.140343 + 0.966856I
a = −0.483566 + 0.305056I
b = 0
3.42837 + 2.09337I 7.05683 − 6.62869I
u = −0.140343 − 0.966856I
a = −0.483566 − 0.305056I
b = 0
3.42837 − 2.09337I 7.05683 + 6.62869I
u = −0.628449 + 0.875112I
a = 1.022450 + 0.246780I
b = 0
1.02799 + 2.45442I 3.88318 − 3.00529I
u = −0.628449 − 0.875112I
a = 1.022450 − 0.246780I
b = 0
1.02799 − 2.45442I 3.88318 + 3.00529I
u = 0.796005 + 0.733148I
a = −1.23246 + 1.62704I
b = 0
−2.72642 + 1.33617I 1.90921 + 3.07774I
u = 0.796005 − 0.733148I
a = −1.23246 − 1.62704I
b = 0
−2.72642 − 1.33617I 1.90921 − 3.07774I
u = 0.728966 + 0.986295I
a = 0.411691 + 0.129409I
b = 0
−1.95319 − 7.08493I −2.13339 + 8.87891I
u = 0.728966 − 0.986295I
a = 0.411691 − 0.129409I
b = 0
−1.95319 + 7.08493I −2.13339 − 8.87891I
u = −0.512358
a = 3.56378
b = 0
0.446489 −13.4320
12
III. I
v
1
= ha, −941v
7
+ 2551v
6
+ · · · + 887b − 1842, v
8
− 2v
7
+ 8v
5
− 13v
4
−
28v
3
− 7v
2
+ 3v + 1i
(i) Arc colorings
a
4
=
v
0
a
7
=
1
0
a
8
=
1
0
a
11
=
0
1.06088v
7
− 2.87599v
6
+ ··· + 4.72604v + 2.07666
a
12
=
1.06088v
7
− 2.87599v
6
+ ··· + 4.72604v + 2.07666
1.06088v
7
− 2.87599v
6
+ ··· + 4.72604v + 2.07666
a
3
=
v
0
a
6
=
1
−1.62683v
7
+ 3.57497v
6
+ ··· − 1.17926v − 3.82638
a
9
=
1.62683v
7
− 3.57497v
6
+ ··· + 1.17926v + 4.82638
2.38219v
7
− 5.33258v
6
+ ··· − 1.21984v + 6.70349
a
5
=
−0.755355v
7
+ 1.75761v
6
+ ··· + 2.39910v − 1.87711
−v
7
+ 2v
6
− 8v
4
+ 13v
3
+ 28v
2
+ 7v − 3
a
2
=
0.755355v
7
− 1.75761v
6
+ ··· − 1.39910v + 1.87711
v
7
− 2v
6
+ 8v
4
− 13v
3
− 28v
2
− 7v + 3
a
1
=
0.755355v
7
− 1.75761v
6
+ ··· − 2.39910v + 1.87711
v
7
− 2v
6
+ 8v
4
− 13v
3
− 28v
2
− 7v + 3
a
10
=
0.244645v
7
− 0.242390v
6
+ ··· − 4.60090v + 1.12289
v
7
− 2v
6
+ 8v
4
− 13v
3
− 28v
2
− 7v + 3
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
7569
887
v
7
−
17105
887
v
6
+
3122
887
v
5
+
63760
887
v
4
−
119185
887
v
3
−
185558
887
v
2
+
17829
887
v +
32002
887
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
8
c
3
, c
7
u
8
c
4
(u + 1)
8
c
5
u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1
c
6
u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1
c
8
u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1
c
9
u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1
c
10
, c
12
u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1
c
11
u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
8
c
3
, c
7
y
8
c
5
, c
8
y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1
c
6
, c
11
y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1
c
9
, c
10
, c
12
y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.230330 + 0.083902I
a = 0
b = 0.855237 + 0.665892I
−3.80435 + 2.57849I −1.56478 − 3.68514I
v = −1.230330 − 0.083902I
a = 0
b = 0.855237 − 0.665892I
−3.80435 − 2.57849I −1.56478 + 3.68514I
v = −0.370895 + 0.073482I
a = 0
b = −1.031810 + 0.655470I
0.73474 − 6.44354I 8.02705 + 7.90662I
v = −0.370895 − 0.073482I
a = 0
b = −1.031810 − 0.655470I
0.73474 + 6.44354I 8.02705 − 7.90662I
v = 0.337834
a = 0
b = 1.09818
4.85780 14.7400
v = 1.21928 + 2.03110I
a = 0
b = −0.570868 + 0.730671I
−0.604279 + 1.131230I −3.30729 + 4.28492I
v = 1.21928 − 2.03110I
a = 0
b = −0.570868 − 0.730671I
−0.604279 − 1.131230I −3.30729 − 4.28492I
v = 2.42604
a = 0
b = −0.603304
−0.799899 9.95010
16
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
8
(u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1)
· (u
17
+ 37u
16
+ ··· + u + 1)
c
2
(u − 1)
8
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
· (u
17
− 15u
16
+ ··· + 3u − 1)
c
3
u
8
(u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1)
· (u
17
+ u
16
+ ··· + 384u − 256)
c
4
(u + 1)
8
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
· (u
17
− 15u
16
+ ··· + 3u − 1)
c
5
(u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1)
· (u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
17
+ 2u
16
+ ··· + 3u + 1)
c
6
u
9
(u
8
+ u
7
+ ··· − 2u − 1)(u
17
+ u
16
+ ··· − 512u − 512)
c
7
u
8
(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
· (u
17
+ u
16
+ ··· + 384u − 256)
c
8
(u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1)
· (u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
· (u
17
+ 2u
16
+ ··· + 3u + 1)
c
9
(u + 1)
9
(u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1)
· (u
17
+ 16u
16
+ ··· − 11u + 1)
c
10
(u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1)
· (u
9
+ 2u
8
+ 5u
7
+ 22u
6
+ 52u
5
+ 63u
4
+ 41u
3
+ 10u
2
− 2u − 1)
· (u
17
− 3u
16
+ ··· − 167922u − 192217)
c
11
(u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1)
· (u
9
+ 3u
8
+ 3u
7
− 2u
6
+ u
5
− 9u
4
+ 3u
3
+ 2u − 1)
· (u
17
− 6u
16
+ ··· − 19686u + 2393)
c
12
(u − 1)
9
(u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1)
· (u
17
+ 16u
16
+ ··· − 11u + 1)
17
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y − 1)
8
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y − 1)
· (y
17
− 57y
16
+ ··· − 7859y − 1)
c
2
, c
4
(y − 1)
8
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y − 1)
· (y
17
− 37y
16
+ ··· + y − 1)
c
3
, c
7
y
8
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y − 1)
· (y
17
− 33y
16
+ ··· + 245760y − 65536)
c
5
, c
8
(y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
· (y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y − 1)
· (y
17
+ 12y
16
+ ··· + 25y − 1)
c
6
y
9
(y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
· (y
17
− 39y
16
+ ··· + 3670016y − 262144)
c
9
, c
12
(y − 1)
9
(y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
· (y
17
− 40y
16
+ ··· + 221y − 1)
c
10
(y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
· (y
9
+ 6y
8
+ ··· + 24y − 1)
· (y
17
− 45y
16
+ ··· + 806894237728y − 36947375089)
c
11
(y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
· (y
9
− 3y
8
+ 23y
7
+ 62y
6
− 13y
5
− 57y
4
+ 9y
3
− 6y
2
+ 4y − 1)
· (y
17
− 38y
16
+ ··· + 475084108y − 5726449)
18
