12n
0644
(K12n
0644
)
A knot diagram
1
Linearized knot diagam
3 8 12 9 11 10 2 5 3 6 5 9
Solving Sequence
5,9
4
1,8
12 3 2 7 11 6 10
c
4
c
8
c
12
c
3
c
2
c
7
c
11
c
5
c
10
c
1
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−9649326548650u
14
+ 50820393580641u
13
+ ··· + 871991330612b + 276658983707276,
− 98118943388815u
14
+ 517725352137249u
13
+ ··· + 1743982661224a + 2846447135872992,
u
15
− 5u
14
+ ··· − 36u − 8i
I
u
2
= h37u
11
− 4u
10
− 19u
9
− 51u
8
− 94u
7
+ 35u
6
+ 152u
5
− 47u
4
+ 184u
3
− 53u
2
+ 86b − 97u − 25,
11u
11
− 7u
10
− u
9
− 14u
8
− 14u
7
+ 29u
6
+ 51u
5
− 7u
4
+ 64u
3
− 82u
2
+ 43a − 30u − 76,
u
12
+ u
11
+ u
10
− 3u
8
− 3u
7
− u
6
− 3u
5
+ 3u
4
+ u
3
− 1i
* 2 irreducible components of dim
C
= 0, with total 27 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−9.65 × 10
12
u
14
+ 5.08 × 10
13
u
13
+ · · · + 8.72 × 10
11
b + 2.77 ×
10
14
, −9.81 × 10
13
u
14
+ 5.18 × 10
14
u
13
+ · · · + 1.74 × 10
12
a + 2.85 ×
10
15
, u
15
− 5u
14
+ · · · − 36u − 8i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
4
=
1
−u
2
a
1
=
56.2614u
14
− 296.864u
13
+ ··· − 1427.56u − 1632.15
11.0659u
14
− 58.2808u
13
+ ··· − 271.998u − 317.273
a
8
=
u
u
a
12
=
56.2614u
14
− 296.864u
13
+ ··· − 1427.56u − 1632.15
6.82466u
14
− 35.8416u
13
+ ··· − 162.048u − 192.819
a
3
=
−64.6576u
14
+ 341.081u
13
+ ··· + 1634.51u + 1875.21
−3.15293u
14
+ 16.6942u
13
+ ··· + 82.5222u + 92.8366
a
2
=
−59.9171u
14
+ 316.162u
13
+ ··· + 1519.44u + 1740.30
1.58748u
14
− 8.22498u
13
+ ··· − 32.5463u − 42.0757
a
7
=
−69.1241u
14
+ 364.539u
13
+ ··· + 1748.19u + 2001.69
−2.05249u
14
+ 10.7120u
13
+ ··· + 51.5981u + 57.9377
a
11
=
63.0861u
14
− 332.705u
13
+ ··· − 1589.61u − 1824.97
6.82466u
14
− 35.8416u
13
+ ··· − 162.048u − 192.819
a
6
=
31.2918u
14
− 165.106u
13
+ ··· − 792.337u − 906.764
0.796083u
14
− 4.30252u
13
+ ··· − 26.8018u − 26.2397
a
10
=
81.7883u
14
− 431.479u
13
+ ··· − 2072.39u − 2372.03
7.57555u
14
− 40.0591u
13
+ ··· − 195.899u − 222.593
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
23777727583517
217997832653
u
14
−
125538144456213
217997832653
u
13
+ ··· −
605427961030606
217997832653
u −
696103351358110
217997832653
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
15
+ 23u
14
+ ··· + 6467u + 961
c
2
, c
7
u
15
+ u
14
+ ··· + 71u + 31
c
3
u
15
− 4u
14
+ ··· + 312u + 49
c
4
, c
8
u
15
− 5u
14
+ ··· − 36u − 8
c
5
, c
6
, c
10
c
11
u
15
+ u
14
+ ··· − 6u − 1
c
9
u
15
− u
14
+ ··· − 167u − 151
c
12
u
15
+ 3u
14
+ ··· − 10u − 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
15
− 51y
14
+ ··· + 52633339y −923521
c
2
, c
7
y
15
− 23y
14
+ ··· + 6467y −961
c
3
y
15
− 36y
14
+ ··· + 43640y −2401
c
4
, c
8
y
15
− 27y
14
+ ··· + 1936y −64
c
5
, c
6
, c
10
c
11
y
15
+ 11y
14
+ ··· + 18y −1
c
9
y
15
− 41y
14
+ ··· + 123925y −22801
c
12
y
15
− 25y
14
+ ··· + 428y −16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.923660 + 0.494347I
a = −1.70164 + 0.17855I
b = −0.448573 + 0.379515I
−2.23565 + 4.29534I −10.91630 − 6.10915I
u = −0.923660 − 0.494347I
a = −1.70164 − 0.17855I
b = −0.448573 − 0.379515I
−2.23565 − 4.29534I −10.91630 + 6.10915I
u = −0.091749 + 1.089930I
a = 0.084694 − 0.589048I
b = −0.422185 + 0.856949I
2.00776 + 2.59269I −13.6766 − 6.5009I
u = −0.091749 − 1.089930I
a = 0.084694 + 0.589048I
b = −0.422185 − 0.856949I
2.00776 − 2.59269I −13.6766 + 6.5009I
u = 1.049060 + 0.386860I
a = −0.493644 + 0.394908I
b = −0.75538 + 1.81023I
9.65742 + 0.83037I −11.42036 − 0.07756I
u = 1.049060 − 0.386860I
a = −0.493644 − 0.394908I
b = −0.75538 − 1.81023I
9.65742 − 0.83037I −11.42036 + 0.07756I
u = 0.824524 + 0.143621I
a = 0.906560 + 0.197657I
b = 0.295936 − 0.760130I
2.39036 − 1.70688I −6.78199 + 3.68703I
u = 0.824524 − 0.143621I
a = 0.906560 − 0.197657I
b = 0.295936 + 0.760130I
2.39036 + 1.70688I −6.78199 − 3.68703I
u = −0.275761
a = 7.05043
b = 0.964667
−7.21918 −7.10970
u = −0.275217
a = 0.940995
b = −0.225404
−0.524379 −18.9810
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 2.11029 + 0.07886I
a = −0.765111 − 0.046752I
b = −2.21963 − 1.07578I
−5.55478 + 1.31578I −12.00000 − 1.63162I
u = 2.11029 − 0.07886I
a = −0.765111 + 0.046752I
b = −2.21963 + 1.07578I
−5.55478 − 1.31578I −12.00000 + 1.63162I
u = −1.95045 + 1.42970I
a = 0.695006 + 0.403378I
b = 2.77095 − 1.36080I
−14.3627 + 9.6247I −10.73924 − 3.33714I
u = −1.95045 − 1.42970I
a = 0.695006 − 0.403378I
b = 2.77095 + 1.36080I
−14.3627 − 9.6247I −10.73924 + 3.33714I
u = 3.51497
a = 0.556839
b = 4.81849
19.0038 0
6
II. I
u
2
=
h37u
11
−4u
10
+· · ·+86b−25, 11u
11
−7u
10
+· · ·+43a−76, u
12
+u
11
+· · ·+u
3
−1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
4
=
1
−u
2
a
1
=
−0.255814u
11
+ 0.162791u
10
+ ··· + 0.697674u + 1.76744
−0.430233u
11
+ 0.0465116u
10
+ ··· + 1.12791u + 0.290698
a
8
=
u
u
a
12
=
−0.255814u
11
+ 0.162791u
10
+ ··· + 0.697674u + 1.76744
−0.290698u
11
+ 0.139535u
10
+ ··· + 1.38372u − 0.127907
a
3
=
−u
10
− u
9
− u
8
+ 3u
6
+ 3u
5
+ u
4
+ 3u
3
− 3u
2
− u
−0.430233u
11
− 0.953488u
10
+ ··· + 0.127907u + 1.29070
a
2
=
0.174419u
11
− 0.883721u
10
+ ··· − 1.43023u + 0.476744
−0.255814u
11
− 0.837209u
10
+ ··· − 0.302326u + 1.76744
a
7
=
1.34884u
11
+ 1.23256u
10
+ ··· + 0.139535u + 0.953488
−0.127907u
11
− 0.418605u
10
+ ··· − 1.15116u + 1.38372
a
11
=
−0.546512u
11
+ 0.302326u
10
+ ··· + 2.08140u + 1.63953
−0.290698u
11
+ 0.139535u
10
+ ··· + 1.38372u − 0.127907
a
6
=
0.197674u
11
+ 1.46512u
10
+ ··· + 0.779070u − 1.59302
−0.290698u
11
+ 0.139535u
10
+ ··· − 0.616279u − 2.12791
a
10
=
−u
9
− u
8
− u
7
+ 3u
5
+ 3u
4
+ u
3
+ 3u
2
− 3u − 1
1.29070u
11
+ 0.860465u
10
+ ··· − 1.38372u + 0.127907
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
121
43
u
11
−
34
43
u
10
−
11
43
u
9
−
154
43
u
8
−
326
43
u
7
+
147
43
u
6
+
346
43
u
5
−
206
43
u
4
+
747
43
u
3
−
558
43
u
2
−
115
43
u−
492
43
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
12
− 10u
11
+ ··· − 13u + 1
c
2
u
12
− 5u
10
+ u
9
+ 11u
8
− 4u
7
− 15u
6
+ 6u
5
+ 13u
4
− 5u
3
− 6u
2
+ u + 1
c
3
u
12
+ 3u
11
+ 3u
10
+ u
9
− 3u
8
− 6u
7
− u
6
+ 4u
5
+ 4u
4
+ u
3
− 3u
2
− 2u − 1
c
4
u
12
+ u
11
+ u
10
− 3u
8
− 3u
7
− u
6
− 3u
5
+ 3u
4
+ u
3
− 1
c
5
, c
6
u
12
+ 8u
10
+ 24u
8
+ 32u
6
+ u
5
+ 15u
4
+ 3u
3
− 2u
2
+ 2u − 1
c
7
u
12
− 5u
10
− u
9
+ 11u
8
+ 4u
7
− 15u
6
− 6u
5
+ 13u
4
+ 5u
3
− 6u
2
− u + 1
c
8
u
12
− u
11
+ u
10
− 3u
8
+ 3u
7
− u
6
+ 3u
5
+ 3u
4
− u
3
− 1
c
9
u
12
− u
9
− 3u
8
+ 3u
7
+ u
6
+ 3u
5
+ 3u
4
− u
2
− u − 1
c
10
, c
11
u
12
+ 8u
10
+ 24u
8
+ 32u
6
− u
5
+ 15u
4
− 3u
3
− 2u
2
− 2u − 1
c
12
u
12
− 4u
11
+ ··· + 10u + 4
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
12
− 6y
11
+ ··· − 25y + 1
c
2
, c
7
y
12
− 10y
11
+ ··· − 13y + 1
c
3
y
12
− 3y
11
+ ··· + 2y + 1
c
4
, c
8
y
12
+ y
11
− 5y
10
− 2y
9
+ 19y
8
+ y
7
− 37y
6
− 11y
5
+ 21y
4
+ y
3
− 6y
2
+ 1
c
5
, c
6
, c
10
c
11
y
12
+ 16y
11
+ ··· − 38y
2
+ 1
c
9
y
12
− 6y
10
+ y
9
+ 21y
8
− 11y
7
− 37y
6
+ y
5
+ 19y
4
− 2y
3
− 5y
2
+ y + 1
c
12
y
12
− 20y
11
+ ··· − 44y + 16
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.197166 + 1.055630I
a = 0.269314 + 0.350716I
b = −0.297880 − 0.774287I
2.52801 − 2.27257I −2.24792 + 0.35874I
u = 0.197166 − 1.055630I
a = 0.269314 − 0.350716I
b = −0.297880 + 0.774287I
2.52801 + 2.27257I −2.24792 − 0.35874I
u = 0.699703 + 0.248857I
a = 2.79474 + 0.04243I
b = 0.854478 − 0.422647I
−2.92889 − 3.37800I −15.0144 + 0.9526I
u = 0.699703 − 0.248857I
a = 2.79474 − 0.04243I
b = 0.854478 + 0.422647I
−2.92889 + 3.37800I −15.0144 − 0.9526I
u = 1.26306
a = −1.13258
b = −1.43639
−4.03974 −8.57740
u = −0.721730
a = 3.00075
b = 0.973015
−7.69678 −24.7790
u = −0.154674 + 0.692367I
a = 0.726797 + 0.523291I
b = −0.171464 + 1.286840I
10.64100 + 1.46286I −4.09278 − 4.80437I
u = −0.154674 − 0.692367I
a = 0.726797 − 0.523291I
b = −0.171464 − 1.286840I
10.64100 − 1.46286I −4.09278 + 4.80437I
u = −1.246550 + 0.486161I
a = −1.067620 − 0.103337I
b = −1.343420 − 0.224193I
0.66596 + 2.08092I −11.59767 − 2.54425I
u = −1.246550 − 0.486161I
a = −1.067620 + 0.103337I
b = −1.343420 + 0.224193I
0.66596 − 2.08092I −11.59767 + 2.54425I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.266310 + 1.357680I
a = −0.157319 − 0.900117I
b = −0.310027 + 0.519410I
4.83179 + 2.98242I −8.86878 − 3.33225I
u = −0.266310 − 1.357680I
a = −0.157319 + 0.900117I
b = −0.310027 − 0.519410I
4.83179 − 2.98242I −8.86878 + 3.33225I
11
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
12
− 10u
11
+ ··· − 13u + 1)(u
15
+ 23u
14
+ ··· + 6467u + 961)
c
2
(u
12
− 5u
10
+ u
9
+ 11u
8
− 4u
7
− 15u
6
+ 6u
5
+ 13u
4
− 5u
3
− 6u
2
+ u + 1)
· (u
15
+ u
14
+ ··· + 71u + 31)
c
3
(u
12
+ 3u
11
+ 3u
10
+ u
9
− 3u
8
− 6u
7
− u
6
+ 4u
5
+ 4u
4
+ u
3
− 3u
2
− 2u − 1)
· (u
15
− 4u
14
+ ··· + 312u + 49)
c
4
(u
12
+ u
11
+ u
10
− 3u
8
− 3u
7
− u
6
− 3u
5
+ 3u
4
+ u
3
− 1)
· (u
15
− 5u
14
+ ··· − 36u − 8)
c
5
, c
6
(u
12
+ 8u
10
+ 24u
8
+ 32u
6
+ u
5
+ 15u
4
+ 3u
3
− 2u
2
+ 2u − 1)
· (u
15
+ u
14
+ ··· − 6u − 1)
c
7
(u
12
− 5u
10
− u
9
+ 11u
8
+ 4u
7
− 15u
6
− 6u
5
+ 13u
4
+ 5u
3
− 6u
2
− u + 1)
· (u
15
+ u
14
+ ··· + 71u + 31)
c
8
(u
12
− u
11
+ u
10
− 3u
8
+ 3u
7
− u
6
+ 3u
5
+ 3u
4
− u
3
− 1)
· (u
15
− 5u
14
+ ··· − 36u − 8)
c
9
(u
12
− u
9
− 3u
8
+ 3u
7
+ u
6
+ 3u
5
+ 3u
4
− u
2
− u − 1)
· (u
15
− u
14
+ ··· − 167u − 151)
c
10
, c
11
(u
12
+ 8u
10
+ 24u
8
+ 32u
6
− u
5
+ 15u
4
− 3u
3
− 2u
2
− 2u − 1)
· (u
15
+ u
14
+ ··· − 6u − 1)
c
12
(u
12
− 4u
11
+ ··· + 10u + 4)(u
15
+ 3u
14
+ ··· − 10u − 4)
12
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
12
− 6y
11
+ ··· − 25y + 1)
· (y
15
− 51y
14
+ ··· + 52633339y −923521)
c
2
, c
7
(y
12
− 10y
11
+ ··· − 13y + 1)(y
15
− 23y
14
+ ··· + 6467y −961)
c
3
(y
12
− 3y
11
+ ··· + 2y + 1)(y
15
− 36y
14
+ ··· + 43640y −2401)
c
4
, c
8
(y
12
+ y
11
− 5y
10
− 2y
9
+ 19y
8
+ y
7
− 37y
6
− 11y
5
+ 21y
4
+ y
3
− 6y
2
+ 1)
· (y
15
− 27y
14
+ ··· + 1936y −64)
c
5
, c
6
, c
10
c
11
(y
12
+ 16y
11
+ ··· − 38y
2
+ 1)(y
15
+ 11y
14
+ ··· + 18y −1)
c
9
(y
12
− 6y
10
+ y
9
+ 21y
8
− 11y
7
− 37y
6
+ y
5
+ 19y
4
− 2y
3
− 5y
2
+ y + 1)
· (y
15
− 41y
14
+ ··· + 123925y −22801)
c
12
(y
12
− 20y
11
+ ··· − 44y + 16)(y
15
− 25y
14
+ ··· + 428y −16)
13
