12n
0339
(K12n
0339
)
A knot diagram
1
Linearized knot diagam
3 6 9 10 2 10 12 3 4 1 7 11
Solving Sequence
3,9
4
6,10
7 2 1 11 5 12 8
c
3
c
9
c
6
c
2
c
1
c
10
c
5
c
12
c
7
c
4
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h1.66975 × 10
42
u
55
− 3.16547 × 10
41
u
54
+ ··· + 4.47134 × 10
42
b − 8.10923 × 10
42
,
− 1.22687 × 10
42
u
55
− 2.29862 × 10
42
u
54
+ ··· + 1.78854 × 10
43
a − 5.42549 × 10
43
, u
56
+ u
55
+ ··· − 24u − 8i
I
u
2
= hb + 1, 4a
3
+ 2a
2
u + 12a
2
+ 4au + 16a + 3u + 8, u
2
− 2i
I
v
1
= ha, b − 1, v
3
− v
2
+ 2v −1i
* 3 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
= h1.67×10
42
u
55
−3.17×10
41
u
54
+· · ·+4.47×10
42
b−8.11×10
42
, −1.23×
10
42
u
55
−2.30×10
42
u
54
+· · ·+1.79×10
43
a−5.43×10
43
, u
56
+u
55
+· · ·−24u−8i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
6
=
0.0685965u
55
+ 0.128520u
54
+ ··· + 1.30791u + 3.03348
−0.373433u
55
+ 0.0707946u
54
+ ··· + 4.21694u + 1.81360
a
10
=
−u
−u
3
+ u
a
7
=
−0.405753u
55
+ 0.122299u
54
+ ··· + 7.07171u + 5.59685
−0.513211u
55
+ 0.0509245u
54
+ ··· + 5.89345u + 2.99527
a
2
=
−0.240787u
55
+ 0.0796338u
54
+ ··· + 3.53793u + 4.36769
−0.164966u
55
+ 0.0426655u
54
+ ··· + 3.53379u + 1.22915
a
1
=
−0.405753u
55
+ 0.122299u
54
+ ··· + 7.07171u + 5.59685
−0.164966u
55
+ 0.0426655u
54
+ ··· + 3.53379u + 1.22915
a
11
=
−0.221862u
55
− 0.235942u
54
+ ··· + 14.8907u + 4.16689
−0.206006u
55
+ 0.0316302u
54
+ ··· + 0.697720u + 0.830810
a
5
=
−u
2
+ 1
−u
4
+ 2u
2
a
12
=
−1.04226u
55
− 0.0828767u
54
+ ··· + 18.0314u + 6.34714
−0.876806u
55
+ 0.0149551u
54
+ ··· + 11.0477u + 5.43910
a
8
=
−u
−u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.91247u
55
− 0.0651102u
54
+ ··· − 36.7295u − 19.6145
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
56
+ 22u
55
+ ··· + 6193u + 529
c
2
, c
5
u
56
+ 4u
55
+ ··· − 35u − 23
c
3
, c
4
, c
8
c
9
u
56
+ u
55
+ ··· − 24u − 8
c
6
u
56
− 2u
55
+ ··· − 144u − 52
c
7
, c
11
u
56
+ 2u
55
+ ··· − 12u − 1
c
10
, c
12
u
56
− 20u
55
+ ··· − 70u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
56
+ 34y
55
+ ··· − 4251793y + 279841
c
2
, c
5
y
56
− 22y
55
+ ··· − 6193y + 529
c
3
, c
4
, c
8
c
9
y
56
− 49y
55
+ ··· + 320y + 64
c
6
y
56
− 36y
55
+ ··· − 244856y + 2704
c
7
, c
11
y
56
− 20y
55
+ ··· − 70y + 1
c
10
, c
12
y
56
+ 36y
55
+ ··· − 2910y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.006180 + 0.341220I
a = −0.289797 − 0.354743I
b = 0.753588 + 0.708565I
−1.067960 − 0.006602I −5.64848 + 0.I
u = −1.006180 − 0.341220I
a = −0.289797 + 0.354743I
b = 0.753588 − 0.708565I
−1.067960 + 0.006602I −5.64848 + 0.I
u = 0.229845 + 0.885092I
a = 0.23373 + 1.60210I
b = −1.066080 − 0.785797I
2.82839 − 10.02440I −1.48494 + 7.67479I
u = 0.229845 − 0.885092I
a = 0.23373 − 1.60210I
b = −1.066080 + 0.785797I
2.82839 + 10.02440I −1.48494 − 7.67479I
u = 0.095889 + 0.905571I
a = 0.41943 + 1.46050I
b = −0.910114 − 0.875500I
7.54385 − 3.22762I 3.27833 + 3.06176I
u = 0.095889 − 0.905571I
a = 0.41943 − 1.46050I
b = −0.910114 + 0.875500I
7.54385 + 3.22762I 3.27833 − 3.06176I
u = 0.987650 + 0.502370I
a = −0.286230 + 0.250539I
b = 0.881358 − 0.804502I
0.47314 + 5.10436I 0
u = 0.987650 − 0.502370I
a = −0.286230 − 0.250539I
b = 0.881358 + 0.804502I
0.47314 − 5.10436I 0
u = −0.062857 + 0.881765I
a = 0.58725 + 1.29532I
b = −0.690478 − 0.924886I
3.98324 + 3.71635I 0.54832 − 2.83161I
u = −0.062857 − 0.881765I
a = 0.58725 − 1.29532I
b = −0.690478 + 0.924886I
3.98324 − 3.71635I 0.54832 + 2.83161I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.786679 + 0.359198I
a = 0.432713 − 0.772670I
b = 0.471201 + 0.699941I
−0.08460 − 3.96138I −1.83399 + 7.39744I
u = 0.786679 − 0.359198I
a = 0.432713 + 0.772670I
b = 0.471201 − 0.699941I
−0.08460 + 3.96138I −1.83399 − 7.39744I
u = −0.202973 + 0.835141I
a = 0.31939 − 1.67631I
b = −1.011030 + 0.737718I
1.39627 + 4.40461I −3.28369 − 3.30771I
u = −0.202973 − 0.835141I
a = 0.31939 + 1.67631I
b = −1.011030 − 0.737718I
1.39627 − 4.40461I −3.28369 + 3.30771I
u = −1.15688
a = −1.40454
b = −1.29717
−3.09499 0
u = 0.002274 + 0.798617I
a = 0.67122 − 1.43784I
b = −0.729713 + 0.782717I
2.26056 + 1.36637I −1.86008 − 2.59968I
u = 0.002274 − 0.798617I
a = 0.67122 + 1.43784I
b = −0.729713 − 0.782717I
2.26056 − 1.36637I −1.86008 + 2.59968I
u = −1.230490 + 0.202314I
a = −1.221100 − 0.322026I
b = −1.341000 − 0.107492I
−6.99348 + 5.20308I 0
u = −1.230490 − 0.202314I
a = −1.221100 + 0.322026I
b = −1.341000 + 0.107492I
−6.99348 − 5.20308I 0
u = −1.253730 + 0.113458I
a = −0.29240 + 1.67063I
b = 0.798165 − 0.447170I
−7.89052 − 1.16203I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.253730 − 0.113458I
a = −0.29240 − 1.67063I
b = 0.798165 + 0.447170I
−7.89052 + 1.16203I 0
u = 1.183640 + 0.457210I
a = −0.399011 + 0.254230I
b = 0.686195 − 0.927663I
4.20004 − 1.62927I 0
u = 1.183640 − 0.457210I
a = −0.399011 − 0.254230I
b = 0.686195 + 0.927663I
4.20004 + 1.62927I 0
u = 1.265580 + 0.146299I
a = −0.06646 − 1.75568I
b = 0.843815 + 0.469241I
−8.04174 − 4.90764I 0
u = 1.265580 − 0.146299I
a = −0.06646 + 1.75568I
b = 0.843815 − 0.469241I
−8.04174 + 4.90764I 0
u = −1.208550 + 0.422798I
a = 0.571547 + 1.151150I
b = 0.889236 − 0.816585I
0.452903 + 0.953294I 0
u = −1.208550 − 0.422798I
a = 0.571547 − 1.151150I
b = 0.889236 + 0.816585I
0.452903 − 0.953294I 0
u = −0.686053 + 0.086131I
a = 0.079007 − 0.372551I
b = 0.701986 + 0.419047I
−1.231800 − 0.090410I −7.02973 − 0.67945I
u = −0.686053 − 0.086131I
a = 0.079007 + 0.372551I
b = 0.701986 − 0.419047I
−1.231800 + 0.090410I −7.02973 + 0.67945I
u = 1.302460 + 0.169792I
a = −1.133380 + 0.246466I
b = −1.285030 + 0.150211I
−7.79470 − 0.02282I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.302460 − 0.169792I
a = −1.133380 − 0.246466I
b = −1.285030 − 0.150211I
−7.79470 + 0.02282I 0
u = 1.283110 + 0.353977I
a = 0.62422 − 1.32590I
b = 0.971987 + 0.717214I
−1.73554 − 5.51211I 0
u = 1.283110 − 0.353977I
a = 0.62422 + 1.32590I
b = 0.971987 − 0.717214I
−1.73554 + 5.51211I 0
u = −1.284720 + 0.360060I
a = −0.496822 − 0.268927I
b = 0.497181 + 0.900810I
−1.75826 + 2.80506I 0
u = −1.284720 − 0.360060I
a = −0.496822 + 0.268927I
b = 0.497181 − 0.900810I
−1.75826 − 2.80506I 0
u = 1.317840 + 0.407750I
a = −0.487396 + 0.226625I
b = 0.496076 − 0.988968I
−0.32844 − 8.33898I 0
u = 1.317840 − 0.407750I
a = −0.487396 − 0.226625I
b = 0.496076 + 0.988968I
−0.32844 + 8.33898I 0
u = 1.38998
a = −1.03411
b = −1.06011
−6.53389 0
u = −1.346720 + 0.418450I
a = 0.78256 + 1.22776I
b = 1.071450 − 0.792956I
3.02423 + 7.97264I 0
u = −1.346720 − 0.418450I
a = 0.78256 − 1.22776I
b = 1.071450 + 0.792956I
3.02423 − 7.97264I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.39916 + 0.36081I
a = 0.90858 − 1.34750I
b = 1.137040 + 0.699212I
−3.68128 − 8.73528I 0
u = 1.39916 − 0.36081I
a = 0.90858 + 1.34750I
b = 1.137040 − 0.699212I
−3.68128 + 8.73528I 0
u = −0.071746 + 0.541437I
a = −0.0956064 − 0.0169262I
b = 1.239380 + 0.055514I
−3.47352 − 2.49924I −1.84511 + 2.12132I
u = −0.071746 − 0.541437I
a = −0.0956064 + 0.0169262I
b = 1.239380 − 0.055514I
−3.47352 + 2.49924I −1.84511 − 2.12132I
u = −1.41936 + 0.37849I
a = 0.94833 + 1.29184I
b = 1.171180 − 0.721786I
−2.4029 + 14.5849I 0
u = −1.41936 − 0.37849I
a = 0.94833 − 1.29184I
b = 1.171180 + 0.721786I
−2.4029 − 14.5849I 0
u = 0.267258 + 0.452591I
a = 0.981532 − 0.698076I
b = −0.137372 + 0.470727I
1.38052 + 0.70261I 3.81139 − 1.05801I
u = 0.267258 − 0.452591I
a = 0.981532 + 0.698076I
b = −0.137372 − 0.470727I
1.38052 − 0.70261I 3.81139 + 1.05801I
u = −1.47532
a = −0.898246
b = −0.558622
−4.26438 0
u = 1.51089 + 0.06240I
a = −0.880755 + 0.098234I
b = −0.890378 + 0.394410I
−8.44146 − 0.83388I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.51089 − 0.06240I
a = −0.880755 − 0.098234I
b = −0.890378 − 0.394410I
−8.44146 + 0.83388I 0
u = −1.52798 + 0.02835I
a = −0.851707 − 0.066826I
b = −0.756667 − 0.444461I
−7.94390 − 4.32216I 0
u = −1.52798 − 0.02835I
a = −0.851707 + 0.066826I
b = −0.756667 + 0.444461I
−7.94390 + 4.32216I 0
u = −0.014467 + 0.397572I
a = 4.05108 − 0.61951I
b = −0.737254 + 0.042361I
−4.09903 + 2.92617I 2.95211 − 3.95214I
u = −0.014467 − 0.397572I
a = 4.05108 + 0.61951I
b = −0.737254 − 0.042361I
−4.09903 − 2.92617I 2.95211 + 3.95214I
u = −0.390682
a = 0.117034
b = 0.806447
−1.01597 −12.5900
10
II. I
u
2
= hb + 1, 4a
3
+ 2a
2
u + 12a
2
+ 4au + 16a + 3u + 8, u
2
− 2i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
2
a
6
=
a
−1
a
10
=
−u
−u
a
7
=
−a − 2
−2a − 3
a
2
=
a + 1
−1
a
1
=
a
−1
a
11
=
−a
2
u − au − u
au
a
5
=
−1
0
a
12
=
−a
2
u − 2a
2
− 2au − 3a −
3
2
u − 2
−2a
2
− 2a − 1
a
8
=
u
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8a
2
+ 4au + 16a + 4u + 4
11
(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
8
c
9
(u
2
− 2)
3
c
6
, c
12
(u
3
− u
2
+ 2u − 1)
2
c
7
(u
3
+ u
2
− 1)
2
c
10
(u
3
+ u
2
+ 2u + 1)
2
c
11
(u
3
− u
2
+ 1)
2
12
(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
8
c
9
(y −2)
6
c
6
, c
10
, c
12
(y
3
+ 3y
2
+ 2y −1)
2
c
7
, c
11
(y
3
− y
2
+ 2y −1)
2
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.41421
a = −1.40294
b = −1.00000
−5.46628 −4.98050
u = 1.41421
a = −1.15208 + 0.92429I
b = −1.00000
−9.60386 − 2.82812I −11.50976 + 2.97945I
u = 1.41421
a = −1.15208 − 0.92429I
b = −1.00000
−9.60386 + 2.82812I −11.50976 − 2.97945I
u = −1.41421
a = −0.847916 + 0.924288I
b = −1.00000
−9.60386 + 2.82812I −11.50976 − 2.97945I
u = −1.41421
a = −0.847916 − 0.924288I
b = −1.00000
−9.60386 − 2.82812I −11.50976 + 2.97945I
u = −1.41421
a = −0.597062
b = −1.00000
−5.46628 −4.98050
14
III. I
v
1
= ha, b − 1, v
3
− v
2
+ 2v − 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
v
0
a
4
=
1
0
a
6
=
0
1
a
10
=
v
0
a
7
=
v
2
1
a
2
=
1
−1
a
1
=
0
−1
a
11
=
v
−v
a
5
=
1
0
a
12
=
v
2
−v
2
− 1
a
8
=
v
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 10v
2
− 6v + 6
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
3
c
3
, c
4
, c
8
c
9
u
3
c
5
(u + 1)
3
c
6
, c
10
u
3
+ u
2
+ 2u + 1
c
7
u
3
− u
2
+ 1
c
11
u
3
+ u
2
− 1
c
12
u
3
− u
2
+ 2u − 1
16
(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
8
c
9
y
3
c
6
, c
10
, c
12
y
3
+ 3y
2
+ 2y − 1
c
7
, c
11
y
3
− y
2
+ 2y − 1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.215080 + 1.307140I
a = 0
b = 1.00000
−4.66906 + 2.82812I −11.91407 − 2.22005I
v = 0.215080 − 1.307140I
a = 0
b = 1.00000
−4.66906 − 2.82812I −11.91407 + 2.22005I
v = 0.569840
a = 0
b = 1.00000
−0.531480 5.82810
18
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
9
)(u
56
+ 22u
55
+ ··· + 6193u + 529)
c
2
((u − 1)
3
)(u + 1)
6
(u
56
+ 4u
55
+ ··· − 35u − 23)
c
3
, c
4
, c
8
c
9
u
3
(u
2
− 2)
3
(u
56
+ u
55
+ ··· − 24u − 8)
c
5
((u − 1)
6
)(u + 1)
3
(u
56
+ 4u
55
+ ··· − 35u − 23)
c
6
((u
3
− u
2
+ 2u − 1)
2
)(u
3
+ u
2
+ 2u + 1)(u
56
− 2u
55
+ ··· − 144u − 52)
c
7
(u
3
− u
2
+ 1)(u
3
+ u
2
− 1)
2
(u
56
+ 2u
55
+ ··· − 12u − 1)
c
10
((u
3
+ u
2
+ 2u + 1)
3
)(u
56
− 20u
55
+ ··· − 70u + 1)
c
11
((u
3
− u
2
+ 1)
2
)(u
3
+ u
2
− 1)(u
56
+ 2u
55
+ ··· − 12u − 1)
c
12
((u
3
− u
2
+ 2u − 1)
3
)(u
56
− 20u
55
+ ··· − 70u + 1)
19
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
9
)(y
56
+ 34y
55
+ ··· − 4251793y + 279841)
c
2
, c
5
((y − 1)
9
)(y
56
− 22y
55
+ ··· − 6193y + 529)
c
3
, c
4
, c
8
c
9
y
3
(y − 2)
6
(y
56
− 49y
55
+ ··· + 320y + 64)
c
6
((y
3
+ 3y
2
+ 2y − 1)
3
)(y
56
− 36y
55
+ ··· − 244856y + 2704)
c
7
, c
11
((y
3
− y
2
+ 2y − 1)
3
)(y
56
− 20y
55
+ ··· − 70y + 1)
c
10
, c
12
((y
3
+ 3y
2
+ 2y − 1)
3
)(y
56
+ 36y
55
+ ··· − 2910y + 1)
20
