12n
0381
(K12n
0381
)
A knot diagram
1
Linearized knot diagam
3 6 8 10 2 11 5 12 5 9 6 8
Solving Sequence
2,5
6
3,11
7 8 12 9 10 1 4
c
5
c
2
c
6
c
7
c
11
c
8
c
9
c
1
c
4
c
3
, c
10
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.36468 × 10
56
u
46
− 1.46395 × 10
57
u
45
+ ··· + 1.51320 × 10
57
b − 1.91371 × 10
57
,
− 7.99348 × 10
54
u
46
− 2.59401 × 10
55
u
45
+ ··· + 4.32343 × 10
55
a − 1.46564 × 10
56
, u
47
+ 3u
46
+ ··· − 5u
2
+ 1i
I
u
2
= h−u
17
+ 2u
16
+ ··· + b + 2, −u
17
+ 4u
16
+ ··· + a + 1, u
18
− 2u
17
+ ··· − u + 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−2.36 × 10
56
u
46
− 1.46 × 10
57
u
45
+ · · · + 1.51 × 10
57
b − 1.91 ×
10
57
, −7.99 × 10
54
u
46
− 2.59 × 10
55
u
45
+ · · · + 4.32 × 10
55
a − 1.47 ×
10
56
, u
47
+ 3u
46
+ · · · − 5u
2
+ 1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
3
=
−u
−u
3
+ u
a
11
=
0.184887u
46
+ 0.599989u
45
+ ··· + 7.65952u + 3.38998
0.156270u
46
+ 0.967456u
45
+ ··· − 6.23699u + 1.26468
a
7
=
−0.392620u
46
− 1.26417u
45
+ ··· + 0.374970u − 5.61900
−0.486693u
46
− 1.16240u
45
+ ··· − 4.45856u + 0.810275
a
8
=
0.0940733u
46
− 0.101769u
45
+ ··· + 4.83353u − 6.42928
−0.486693u
46
− 1.16240u
45
+ ··· − 4.45856u + 0.810275
a
12
=
−0.0450287u
46
− 0.465608u
45
+ ··· + 13.7116u + 2.07998
0.351089u
46
+ 1.56063u
45
+ ··· − 6.00707u + 1.64053
a
9
=
−1.71992u
46
− 4.82180u
45
+ ··· − 8.94537u − 0.160735
−0.541339u
46
− 1.45857u
45
+ ··· − 1.17123u + 0.611126
a
10
=
−1.17858u
46
− 3.36324u
45
+ ··· − 7.77415u − 0.771861
−0.541339u
46
− 1.45857u
45
+ ··· − 1.17123u + 0.611126
a
1
=
u
3
u
5
− u
3
+ u
a
4
=
−0.0281343u
46
+ 0.124133u
45
+ ··· + 4.75548u + 3.17124
0.912499u
46
+ 2.86257u
45
+ ··· − 1.94007u + 1.59134
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2.80868u
46
− 7.60191u
45
+ ··· − 15.3938u + 3.54968
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
47
+ 9u
46
+ ··· + 10u + 1
c
2
, c
5
u
47
+ 3u
46
+ ··· − 5u
2
+ 1
c
3
u
47
+ 32u
45
+ ··· + 305u + 3721
c
4
, c
9
u
47
+ u
46
+ ··· − 9u + 1
c
6
, c
11
u
47
+ 2u
46
+ ··· − 1808u + 163
c
7
u
47
− 3u
46
+ ··· + 37265u + 230749
c
8
, c
12
u
47
+ 4u
46
+ ··· + 474u + 73
c
10
u
47
− 35u
46
+ ··· + 37u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
47
+ 67y
46
+ ··· − 62y −1
c
2
, c
5
y
47
− 9y
46
+ ··· + 10y −1
c
3
y
47
+ 64y
46
+ ··· − 273936299y −13845841
c
4
, c
9
y
47
+ 35y
46
+ ··· + 37y −1
c
6
, c
11
y
47
+ 46y
46
+ ··· + 1197786y −26569
c
7
y
47
+ 97y
46
+ ··· − 501554609163y −53245101001
c
8
, c
12
y
47
+ 46y
45
+ ··· + 210660y −5329
c
10
y
47
− 37y
46
+ ··· − 1687y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.762370 + 0.649452I
a = −1.50637 + 1.24868I
b = −0.989488 − 0.131338I
5.23780 − 6.46320I −1.46400 + 8.28387I
u = 0.762370 − 0.649452I
a = −1.50637 − 1.24868I
b = −0.989488 + 0.131338I
5.23780 + 6.46320I −1.46400 − 8.28387I
u = −0.969690 + 0.156566I
a = −0.78768 + 1.48941I
b = −0.170053 + 0.274049I
1.28197 + 2.91902I −6.17943 − 3.54883I
u = −0.969690 − 0.156566I
a = −0.78768 − 1.48941I
b = −0.170053 − 0.274049I
1.28197 − 2.91902I −6.17943 + 3.54883I
u = −0.999768 + 0.303365I
a = −0.822827 + 0.875403I
b = 0.047491 + 1.410890I
−3.50808 + 0.30720I −13.9878 − 2.1509I
u = −0.999768 − 0.303365I
a = −0.822827 − 0.875403I
b = 0.047491 − 1.410890I
−3.50808 − 0.30720I −13.9878 + 2.1509I
u = 0.927859 + 0.501471I
a = 0.391994 + 0.880414I
b = −1.15238 + 1.05300I
−2.42036 − 5.43835I −10.53298 + 5.82034I
u = 0.927859 − 0.501471I
a = 0.391994 − 0.880414I
b = −1.15238 − 1.05300I
−2.42036 + 5.43835I −10.53298 − 5.82034I
u = −0.538449 + 0.740127I
a = 0.51120 + 1.74597I
b = 0.835490 + 0.313643I
2.12448 + 2.88678I −5.05632 − 3.90476I
u = −0.538449 − 0.740127I
a = 0.51120 − 1.74597I
b = 0.835490 − 0.313643I
2.12448 − 2.88678I −5.05632 + 3.90476I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.812709 + 0.407282I
a = 0.917456 − 0.540115I
b = 1.22892 − 0.77634I
4.89911 + 2.22864I −0.91069 + 1.26993I
u = 0.812709 − 0.407282I
a = 0.917456 + 0.540115I
b = 1.22892 + 0.77634I
4.89911 − 2.22864I −0.91069 − 1.26993I
u = 0.356859 + 1.085610I
a = −0.123516 + 1.294310I
b = −0.684132 + 0.610771I
6.45758 − 0.19356I 1.61840 + 0.58039I
u = 0.356859 − 1.085610I
a = −0.123516 − 1.294310I
b = −0.684132 − 0.610771I
6.45758 + 0.19356I 1.61840 − 0.58039I
u = −1.112960 + 0.392492I
a = −0.993882 − 0.188437I
b = −1.275610 − 0.507155I
0.02525 + 1.58346I −5.18804 − 1.00520I
u = −1.112960 − 0.392492I
a = −0.993882 + 0.188437I
b = −1.275610 + 0.507155I
0.02525 − 1.58346I −5.18804 + 1.00520I
u = 0.599789 + 0.540388I
a = −0.036112 + 0.593518I
b = 0.363889 − 0.014702I
2.07065 − 1.88289I −2.57014 + 4.18704I
u = 0.599789 − 0.540388I
a = −0.036112 − 0.593518I
b = 0.363889 + 0.014702I
2.07065 + 1.88289I −2.57014 − 4.18704I
u = −0.897826 + 0.816897I
a = 0.478130 − 0.208097I
b = 0.010006 − 0.790312I
8.49975 + 3.05476I 3.70184 − 1.92364I
u = −0.897826 − 0.816897I
a = 0.478130 + 0.208097I
b = 0.010006 + 0.790312I
8.49975 − 3.05476I 3.70184 + 1.92364I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.935406 + 0.903350I
a = −0.061964 + 0.510432I
b = 0.129870 − 0.075176I
4.37878 − 3.33131I 0
u = 0.935406 − 0.903350I
a = −0.061964 − 0.510432I
b = 0.129870 + 0.075176I
4.37878 + 3.33131I 0
u = −0.895107 + 1.020460I
a = −0.59940 − 1.56714I
b = −2.53084 − 0.17370I
15.0606 + 5.0419I 0
u = −0.895107 − 1.020460I
a = −0.59940 + 1.56714I
b = −2.53084 + 0.17370I
15.0606 − 5.0419I 0
u = 0.872024 + 1.067490I
a = 0.462555 − 1.314280I
b = 2.51393 − 0.29226I
10.96990 + 1.03471I 0
u = 0.872024 − 1.067490I
a = 0.462555 + 1.314280I
b = 2.51393 + 0.29226I
10.96990 − 1.03471I 0
u = 0.609271 + 0.090864I
a = 1.73564 + 0.80655I
b = −0.015666 − 0.339586I
−0.78577 − 2.24530I −1.90996 + 0.61737I
u = 0.609271 − 0.090864I
a = 1.73564 − 0.80655I
b = −0.015666 + 0.339586I
−0.78577 + 2.24530I −1.90996 − 0.61737I
u = −1.060760 + 0.918923I
a = 1.02378 + 1.23868I
b = 2.73250 − 0.04492I
14.5035 + 2.0770I 0
u = −1.060760 − 0.918923I
a = 1.02378 − 1.23868I
b = 2.73250 + 0.04492I
14.5035 − 2.0770I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.88048 + 1.11465I
a = −0.585508 − 1.063030I
b = −2.40490 − 0.28862I
15.6315 − 6.8243I 0
u = −0.88048 − 1.11465I
a = −0.585508 + 1.063030I
b = −2.40490 + 0.28862I
15.6315 + 6.8243I 0
u = 1.09371 + 0.92621I
a = −1.10674 + 1.32508I
b = −2.67812 − 0.20782I
10.22340 − 8.30631I 0
u = 1.09371 − 0.92621I
a = −1.10674 − 1.32508I
b = −2.67812 + 0.20782I
10.22340 + 8.30631I 0
u = −0.558280
a = −0.365775
b = −0.445102
−0.793031 −12.7680
u = 1.32146 + 0.57871I
a = 1.001920 + 0.175193I
b = 1.252130 − 0.118762I
3.13147 − 6.06944I 0
u = 1.32146 − 0.57871I
a = 1.001920 − 0.175193I
b = 1.252130 + 0.118762I
3.13147 + 6.06944I 0
u = −1.11216 + 0.94153I
a = 1.17595 + 1.33807I
b = 2.51990 − 0.19390I
14.8227 + 14.2823I 0
u = −1.11216 − 0.94153I
a = 1.17595 − 1.33807I
b = 2.51990 + 0.19390I
14.8227 − 14.2823I 0
u = −1.01074 + 1.18267I
a = −0.271199 + 1.032090I
b = −0.252566 + 0.583242I
7.80553 + 4.18941I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.01074 − 1.18267I
a = −0.271199 − 1.032090I
b = −0.252566 − 0.583242I
7.80553 − 4.18941I 0
u = 0.393275 + 0.193365I
a = 3.04506 − 1.79634I
b = 0.209999 + 0.923947I
−1.11354 + 2.17945I −8.17041 − 2.91637I
u = 0.393275 − 0.193365I
a = 3.04506 + 1.79634I
b = 0.209999 − 0.923947I
−1.11354 − 2.17945I −8.17041 + 2.91637I
u = −0.235367 + 0.361169I
a = −1.10685 − 1.57370I
b = 0.612976 − 1.024460I
4.58828 + 3.58928I −1.93036 − 7.49852I
u = −0.235367 − 0.361169I
a = −1.10685 + 1.57370I
b = 0.612976 + 1.024460I
4.58828 − 3.58928I −1.93036 + 7.49852I
u = −0.192286 + 0.378326I
a = −3.55874 − 0.28507I
b = 0.419190 + 1.143200I
−0.94050 + 2.40895I −3.87483 − 0.19612I
u = −0.192286 − 0.378326I
a = −3.55874 + 0.28507I
b = 0.419190 − 1.143200I
−0.94050 − 2.40895I −3.87483 + 0.19612I
9
II.
I
u
2
= h−u
17
+2u
16
+· · ·+b+2, −u
17
+4u
16
+· · ·+a+1, u
18
−2u
17
+· · ·−u+1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
3
=
−u
−u
3
+ u
a
11
=
u
17
− 4u
16
+ ··· − 3u − 1
u
17
− 2u
16
+ ··· − 4u − 2
a
7
=
−u
16
+ 2u
15
+ ··· − 3u + 4
−3u
17
+ 4u
16
+ ··· − u + 3
a
8
=
3u
17
− 5u
16
+ ··· − 2u + 1
−3u
17
+ 4u
16
+ ··· − u + 3
a
12
=
−u
17
− u
16
+ ··· − 2u + 3
u
17
− 2u
16
+ ··· − 3u − 1
a
9
=
u
17
− 2u
16
+ ··· + 4u − 1
−3u
17
+ 4u
16
+ ··· − 25u
2
+ 5
a
10
=
4u
17
− 6u
16
+ ··· + 4u − 6
−3u
17
+ 4u
16
+ ··· − 25u
2
+ 5
a
1
=
u
3
u
5
− u
3
+ u
a
4
=
2u
17
− 6u
16
+ ··· − 8u − 2
u
17
− 4u
15
+ ··· + 2u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −13u
17
+ 22u
16
+ 25u
15
− 68u
14
− 46u
13
+ 148u
12
+ 58u
11
−
256u
10
− 31u
9
+ 318u
8
− 64u
7
− 247u
6
+ 114u
5
+ 95u
4
− 79u
3
− 9u
2
+ 20u − 12
10
(iv) u-Polynomials at the component
11
Crossings u-Polynomials at each crossing
c
1
u
18
− 8u
17
+ ··· − 11u + 1
c
2
u
18
+ 2u
17
+ ··· + u + 1
c
3
u
18
− u
17
+ ··· − 2u + 1
c
4
u
18
+ 6u
16
+ ··· + 4u + 1
c
5
u
18
− 2u
17
+ ··· − u + 1
c
6
u
18
+ u
17
+ ··· − 3u + 1
c
7
u
18
+ 2u
17
+ ··· + 4u + 1
c
8
u
18
+ 3u
17
+ ··· − u + 1
c
9
u
18
+ 6u
16
+ ··· − 4u + 1
c
10
u
18
− 12u
17
+ ··· − 2u + 1
c
11
u
18
− u
17
+ ··· + 3u + 1
c
12
u
18
− 3u
17
+ ··· + u + 1
12
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
18
+ 12y
17
+ ··· + 5y + 1
c
2
, c
5
y
18
− 8y
17
+ ··· − 11y + 1
c
3
y
18
+ 17y
17
+ ··· + 22y + 1
c
4
, c
9
y
18
+ 12y
17
+ ··· + 2y + 1
c
6
, c
11
y
18
+ 7y
17
+ ··· + 13y + 1
c
7
y
18
+ 14y
17
+ ··· − 22y + 1
c
8
, c
12
y
18
+ 13y
17
+ ··· + 7y + 1
c
10
y
18
− 4y
17
+ ··· − 18y + 1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.938607 + 0.177796I
a = −1.277810 + 0.352527I
b = −0.532976 − 0.231640I
−1.49224 + 2.44774I −13.11338 − 3.83957I
u = −0.938607 − 0.177796I
a = −1.277810 − 0.352527I
b = −0.532976 + 0.231640I
−1.49224 − 2.44774I −13.11338 + 3.83957I
u = −0.991070 + 0.379386I
a = −0.386409 + 0.925899I
b = 0.55160 + 1.88537I
−2.57337 − 0.15300I −5.91487 + 0.60575I
u = −0.991070 − 0.379386I
a = −0.386409 − 0.925899I
b = 0.55160 − 1.88537I
−2.57337 + 0.15300I −5.91487 − 0.60575I
u = 0.664659 + 0.594539I
a = 2.33242 − 0.85415I
b = 0.95795 + 1.08548I
−0.212595 + 1.383300I −3.10748 + 0.84622I
u = 0.664659 − 0.594539I
a = 2.33242 + 0.85415I
b = 0.95795 − 1.08548I
−0.212595 − 1.383300I −3.10748 − 0.84622I
u = 1.010780 + 0.560346I
a = 0.108550 + 1.284390I
b = −1.31489 + 1.78640I
−1.34156 − 5.99798I −4.55960 + 7.13102I
u = 1.010780 − 0.560346I
a = 0.108550 − 1.284390I
b = −1.31489 − 1.78640I
−1.34156 + 5.99798I −4.55960 − 7.13102I
u = 1.157390 + 0.449657I
a = 1.48723 + 0.18657I
b = 1.178190 + 0.178057I
1.91663 − 5.91874I −6.80744 + 5.83665I
u = 1.157390 − 0.449657I
a = 1.48723 − 0.18657I
b = 1.178190 − 0.178057I
1.91663 + 5.91874I −6.80744 − 5.83665I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.851063 + 0.965985I
a = −0.103785 + 0.850001I
b = −0.108161 + 0.557031I
7.22994 + 3.50970I −2.55016 − 2.04029I
u = −0.851063 − 0.965985I
a = −0.103785 − 0.850001I
b = −0.108161 − 0.557031I
7.22994 − 3.50970I −2.55016 + 2.04029I
u = 0.912172 + 0.926718I
a = −0.316703 + 0.525825I
b = 0.003727 − 0.356760I
5.15374 − 3.38704I 1.14776 + 3.09347I
u = 0.912172 − 0.926718I
a = −0.316703 − 0.525825I
b = 0.003727 + 0.356760I
5.15374 + 3.38704I 1.14776 − 3.09347I
u = 0.637201 + 0.247045I
a = −0.552936 + 0.306520I
b = −0.835105 + 1.116970I
4.10299 + 2.87051I −7.47106 − 1.58702I
u = 0.637201 − 0.247045I
a = −0.552936 − 0.306520I
b = −0.835105 − 1.116970I
4.10299 − 2.87051I −7.47106 + 1.58702I
u = −0.601462 + 0.303618I
a = −2.79057 + 1.63140I
b = 0.099665 + 0.804647I
−1.26899 + 3.08403I −10.1238 − 9.9181I
u = −0.601462 − 0.303618I
a = −2.79057 − 1.63140I
b = 0.099665 − 0.804647I
−1.26899 − 3.08403I −10.1238 + 9.9181I
16
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
18
− 8u
17
+ ··· − 11u + 1)(u
47
+ 9u
46
+ ··· + 10u + 1)
c
2
(u
18
+ 2u
17
+ ··· + u + 1)(u
47
+ 3u
46
+ ··· − 5u
2
+ 1)
c
3
(u
18
− u
17
+ ··· − 2u + 1)(u
47
+ 32u
45
+ ··· + 305u + 3721)
c
4
(u
18
+ 6u
16
+ ··· + 4u + 1)(u
47
+ u
46
+ ··· − 9u + 1)
c
5
(u
18
− 2u
17
+ ··· − u + 1)(u
47
+ 3u
46
+ ··· − 5u
2
+ 1)
c
6
(u
18
+ u
17
+ ··· − 3u + 1)(u
47
+ 2u
46
+ ··· − 1808u + 163)
c
7
(u
18
+ 2u
17
+ ··· + 4u + 1)(u
47
− 3u
46
+ ··· + 37265u + 230749)
c
8
(u
18
+ 3u
17
+ ··· − u + 1)(u
47
+ 4u
46
+ ··· + 474u + 73)
c
9
(u
18
+ 6u
16
+ ··· − 4u + 1)(u
47
+ u
46
+ ··· − 9u + 1)
c
10
(u
18
− 12u
17
+ ··· − 2u + 1)(u
47
− 35u
46
+ ··· + 37u + 1)
c
11
(u
18
− u
17
+ ··· + 3u + 1)(u
47
+ 2u
46
+ ··· − 1808u + 163)
c
12
(u
18
− 3u
17
+ ··· + u + 1)(u
47
+ 4u
46
+ ··· + 474u + 73)
17
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
18
+ 12y
17
+ ··· + 5y + 1)(y
47
+ 67y
46
+ ··· − 62y −1)
c
2
, c
5
(y
18
− 8y
17
+ ··· − 11y + 1)(y
47
− 9y
46
+ ··· + 10y −1)
c
3
(y
18
+ 17y
17
+ ··· + 22y + 1)
· (y
47
+ 64y
46
+ ··· − 273936299y −13845841)
c
4
, c
9
(y
18
+ 12y
17
+ ··· + 2y + 1)(y
47
+ 35y
46
+ ··· + 37y −1)
c
6
, c
11
(y
18
+ 7y
17
+ ··· + 13y + 1)(y
47
+ 46y
46
+ ··· + 1197786y −26569)
c
7
(y
18
+ 14y
17
+ ··· − 22y + 1)
· (y
47
+ 97y
46
+ ··· − 501554609163y −53245101001)
c
8
, c
12
(y
18
+ 13y
17
+ ··· + 7y + 1)(y
47
+ 46y
45
+ ··· + 210660y −5329)
c
10
(y
18
− 4y
17
+ ··· − 18y + 1)(y
47
− 37y
46
+ ··· − 1687y −1)
18
