12n
0372
(K12n
0372
)
A knot diagram
1
Linearized knot diagam
3 6 8 10 2 11 5 1 4 6 10 9
Solving Sequence
6,10
11 7
3,12
2 1 5 8 4 9
c
10
c
6
c
11
c
2
c
1
c
5
c
7
c
4
c
9
c
3
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h1.42529 × 10
92
u
36
+ 8.72680 × 10
91
u
35
+ ··· + 1.49513 × 10
93
b + 2.35282 × 10
95
,
− 3.02051 × 10
94
u
36
− 1.75541 × 10
94
u
35
+ ··· + 6.54608 × 10
94
a − 5.25852 × 10
97
,
u
37
− 30u
35
+ ··· + 4671u − 1007i
I
u
2
= h7u
14
− 13u
13
+ ··· + b + 17, −13u
15
+ 34u
14
+ ··· + a + 20, u
16
− 3u
15
+ ··· − 4u + 1i
* 2 irreducible components of dim
C
= 0, with total 53 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
= h1.43 × 10
92
u
36
+ 8.73 × 10
91
u
35
+ · · · + 1.50 × 10
93
b + 2.35 ×
10
95
, −3.02 × 10
94
u
36
− 1.76 × 10
94
u
35
+ · · · + 6.55 × 10
94
a − 5.26 ×
10
97
, u
37
− 30u
35
+ · · · + 4671u − 1007i
(i) Arc colorings
a
6
=
0
u
a
10
=
1
0
a
11
=
1
−u
2
a
7
=
u
−u
3
+ u
a
3
=
0.461422u
36
+ 0.268162u
35
+ ··· − 2340.32u + 803.308
−0.0953284u
36
− 0.0583680u
35
+ ··· + 476.203u − 157.365
a
12
=
−u
2
+ 1
−u
2
a
2
=
0.461422u
36
+ 0.268162u
35
+ ··· − 2340.32u + 803.308
−0.250593u
36
− 0.148286u
35
+ ··· + 1264.14u − 427.405
a
1
=
0.0803873u
36
+ 0.0415081u
35
+ ··· − 433.347u + 161.373
−0.176241u
36
− 0.103850u
35
+ ··· + 897.957u − 302.093
a
5
=
−0.0247048u
36
− 0.00822526u
35
+ ··· + 139.528u − 59.8522
0.304235u
36
+ 0.170592u
35
+ ··· − 1563.50u + 546.853
a
8
=
0.326831u
36
+ 0.178171u
35
+ ··· − 1699.82u + 603.957
−0.293525u
36
− 0.170056u
35
+ ··· + 1484.90u − 508.106
a
4
=
0.279530u
36
+ 0.162367u
35
+ ··· − 1423.97u + 487.001
0.304235u
36
+ 0.170592u
35
+ ··· − 1563.50u + 546.853
a
9
=
−0.325873u
36
− 0.178662u
35
+ ··· + 1668.53u − 591.318
0.169109u
36
+ 0.102532u
35
+ ··· − 850.133u + 281.907
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.65322u
36
+ 0.965871u
35
+ ··· − 8351.56u + 2824.79
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
37
+ 7u
36
+ ··· + 33u + 1
c
2
, c
5
u
37
+ u
36
+ ··· − 5u + 1
c
3
u
37
+ u
36
+ ··· − 23u − 5
c
4
, c
9
u
37
+ 3u
35
+ ··· − 294u − 229
c
6
, c
10
u
37
− 30u
35
+ ··· + 4671u + 1007
c
7
u
37
− 7u
36
+ ··· − 207584u − 176401
c
8
, c
12
u
37
− 6u
36
+ ··· + 3u + 1
c
11
u
37
− 60u
36
+ ··· + 36901087u − 1014049
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
37
+ 53y
36
+ ··· + 369y −1
c
2
, c
5
y
37
− 7y
36
+ ··· + 33y −1
c
3
y
37
+ 3y
36
+ ··· − 131y −25
c
4
, c
9
y
37
+ 6y
36
+ ··· + 6744y −52441
c
6
, c
10
y
37
− 60y
36
+ ··· + 36901087y −1014049
c
7
y
37
+ 101y
36
+ ··· − 38906418180y −31117312801
c
8
, c
12
y
37
+ 36y
36
+ ··· + 119y −1
c
11
y
37
− 168y
36
+ ··· + 147226173534695y −1028295374401
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.840205 + 0.666551I
a = 0.340962 + 0.304853I
b = −0.13217 + 1.48071I
1.03398 − 2.73157I −7.05651 + 1.27102I
u = −0.840205 − 0.666551I
a = 0.340962 − 0.304853I
b = −0.13217 − 1.48071I
1.03398 + 2.73157I −7.05651 − 1.27102I
u = −0.853829 + 0.359843I
a = 0.495942 + 0.786208I
b = −0.204005 + 0.651770I
1.45153 − 1.91917I −1.09958 + 4.16671I
u = −0.853829 − 0.359843I
a = 0.495942 − 0.786208I
b = −0.204005 − 0.651770I
1.45153 + 1.91917I −1.09958 − 4.16671I
u = 0.755908 + 0.512680I
a = 0.866716 + 0.077393I
b = 0.149283 + 0.157106I
−1.45991 − 0.04960I −8.67591 + 0.36054I
u = 0.755908 − 0.512680I
a = 0.866716 − 0.077393I
b = 0.149283 − 0.157106I
−1.45991 + 0.04960I −8.67591 − 0.36054I
u = 0.979984 + 0.597364I
a = 0.036606 + 1.010950I
b = −0.161070 + 1.162890I
6.29690 − 0.93807I 0
u = 0.979984 − 0.597364I
a = 0.036606 − 1.010950I
b = −0.161070 − 1.162890I
6.29690 + 0.93807I 0
u = 0.622379 + 0.534957I
a = 0.294972 − 1.294270I
b = −0.219235 − 1.224940I
−1.91889 + 4.49439I −10.27196 − 6.08209I
u = 0.622379 − 0.534957I
a = 0.294972 + 1.294270I
b = −0.219235 + 1.224940I
−1.91889 − 4.49439I −10.27196 + 6.08209I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.139275 + 1.174200I
a = −0.196370 + 0.643239I
b = −0.451126 + 0.096722I
0.20567 − 4.24321I −9.32033 + 9.54688I
u = −0.139275 − 1.174200I
a = −0.196370 − 0.643239I
b = −0.451126 − 0.096722I
0.20567 + 4.24321I −9.32033 − 9.54688I
u = 1.180350 + 0.222094I
a = −1.046310 − 0.346221I
b = 0.263695 − 0.674015I
4.21160 − 7.05862I 0. + 5.66738I
u = 1.180350 − 0.222094I
a = −1.046310 + 0.346221I
b = 0.263695 + 0.674015I
4.21160 + 7.05862I 0. − 5.66738I
u = 0.574255
a = −1.63784
b = 1.42181
−5.56665 −18.9790
u = 0.553337 + 0.058859I
a = 1.76805 − 0.36536I
b = 0.540750 + 0.394902I
−0.707444 − 0.027731I −6.69727 − 0.68732I
u = 0.553337 − 0.058859I
a = 1.76805 + 0.36536I
b = 0.540750 − 0.394902I
−0.707444 + 0.027731I −6.69727 + 0.68732I
u = 1.45175
a = −0.159754
b = −0.988768
−2.82767 0
u = −1.28637 + 0.72968I
a = −0.771385 + 0.037127I
b = 1.24761 + 0.99067I
4.33297 + 0.28642I 0
u = −1.28637 − 0.72968I
a = −0.771385 − 0.037127I
b = 1.24761 − 0.99067I
4.33297 − 0.28642I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.404870
a = 1.84305
b = 0.402148
−0.970503 −10.8270
u = −0.383604 + 0.036914I
a = −0.83236 + 1.46023I
b = −1.274340 − 0.220333I
2.16124 + 2.73535I 0.44906 − 2.49340I
u = −0.383604 − 0.036914I
a = −0.83236 − 1.46023I
b = −1.274340 + 0.220333I
2.16124 − 2.73535I 0.44906 + 2.49340I
u = 1.73463 + 0.14709I
a = −0.525150 + 0.634018I
b = −0.43949 + 2.05393I
10.27330 + 3.72558I 0
u = 1.73463 − 0.14709I
a = −0.525150 − 0.634018I
b = −0.43949 − 2.05393I
10.27330 − 3.72558I 0
u = −1.41128 + 1.17849I
a = −0.012841 − 0.584996I
b = −0.98850 − 1.17013I
5.31029 − 5.07857I 0
u = −1.41128 − 1.17849I
a = −0.012841 + 0.584996I
b = −0.98850 + 1.17013I
5.31029 + 5.07857I 0
u = −1.89476 + 0.47022I
a = 0.403115 + 0.592404I
b = 0.19279 + 2.49482I
15.7367 − 4.5260I 0
u = −1.89476 − 0.47022I
a = 0.403115 − 0.592404I
b = 0.19279 − 2.49482I
15.7367 + 4.5260I 0
u = −2.10823 + 0.28878I
a = 0.490821 − 0.416004I
b = 0.36444 − 1.90539I
16.1759 + 2.6224I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −2.10823 − 0.28878I
a = 0.490821 + 0.416004I
b = 0.36444 + 1.90539I
16.1759 − 2.6224I 0
u = 2.07718 + 0.48138I
a = 0.388719 − 0.539166I
b = 0.41767 − 2.54262I
16.2225 + 13.1708I 0
u = 2.07718 − 0.48138I
a = 0.388719 + 0.539166I
b = 0.41767 + 2.54262I
16.2225 − 13.1708I 0
u = 2.12794 + 0.24863I
a = 0.473392 + 0.439822I
b = 0.25295 + 2.11779I
16.8105 + 5.9256I 0
u = 2.12794 − 0.24863I
a = 0.473392 − 0.439822I
b = 0.25295 − 2.11779I
16.8105 − 5.9256I 0
u = −2.32958 + 0.16455I
a = −0.370401 − 0.408307I
b = −0.47684 − 2.69279I
9.70907 − 3.28908I 0
u = −2.32958 − 0.16455I
a = −0.370401 + 0.408307I
b = −0.47684 + 2.69279I
9.70907 + 3.28908I 0
8
II. I
u
2
=
h7u
14
−13u
13
+· · ·+b+17, −13u
15
+34u
14
+· · ·+a+20, u
16
−3u
15
+· · ·−4u+1i
(i) Arc colorings
a
6
=
0
u
a
10
=
1
0
a
11
=
1
−u
2
a
7
=
u
−u
3
+ u
a
3
=
13u
15
− 34u
14
+ ··· + 60u − 20
−7u
14
+ 13u
13
+ ··· + 30u − 17
a
12
=
−u
2
+ 1
−u
2
a
2
=
13u
15
− 34u
14
+ ··· + 60u − 20
u
15
− 6u
14
+ ··· + 23u − 12
a
1
=
−10u
15
+ 23u
14
+ ··· − 39u + 7
−u
15
+ 3u
14
+ ··· − 5u + 3
a
5
=
−24u
15
+ 60u
14
+ ··· − 100u + 30
2u
15
− u
14
+ ··· − 7u + 7
a
8
=
8u
15
− 14u
14
+ ··· + 12u + 8
3u
15
− 8u
14
+ ··· + 20u − 7
a
4
=
−22u
15
+ 59u
14
+ ··· − 107u + 37
2u
15
− u
14
+ ··· − 7u + 7
a
9
=
8u
15
− 21u
14
+ ··· + 38u − 13
u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −41u
15
+ 105u
14
+ 175u
13
−551u
12
−232u
11
+ 1198u
10
−68u
9
−
1621u
8
+ 634u
7
+ 1274u
6
− 884u
5
− 529u
4
+ 597u
3
+ 18u
2
− 195u + 58
9
(iv) u-Polynomials at the component
10
Crossings u-Polynomials at each crossing
c
1
u
16
− 6u
15
+ ··· − 10u + 1
c
2
u
16
− 3u
14
+ ··· − 5u
2
+ 1
c
3
u
16
− 2u
14
+ ··· + 2u − 1
c
4
u
16
− u
15
+ ··· − u − 1
c
5
u
16
− 3u
14
+ ··· − 5u
2
+ 1
c
6
u
16
+ 3u
15
+ ··· + 4u + 1
c
7
u
16
+ 5u
14
+ ··· − 9u − 1
c
8
u
16
− u
15
+ ··· − 8u − 1
c
9
u
16
+ u
15
+ ··· + u − 1
c
10
u
16
− 3u
15
+ ··· − 4u + 1
c
11
u
16
− 15u
15
+ ··· − 8u + 1
c
12
u
16
+ u
15
+ ··· + 8u − 1
11
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
16
+ 14y
15
+ ··· − 6y + 1
c
2
, c
5
y
16
− 6y
15
+ ··· − 10y + 1
c
3
y
16
− 4y
15
+ ··· + 10y + 1
c
4
, c
9
y
16
− 13y
15
+ ··· − 9y + 1
c
6
, c
10
y
16
− 15y
15
+ ··· − 8y + 1
c
7
y
16
+ 10y
15
+ ··· + 11y + 1
c
8
, c
12
y
16
+ 9y
15
+ ··· − 88y + 1
c
11
y
16
− 31y
15
+ ··· + 20y + 1
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.708860 + 0.704443I
a = 0.196590 − 0.655681I
b = −1.03433 − 1.08957I
1.20037 + 3.52175I −4.53497 − 9.11963I
u = 0.708860 − 0.704443I
a = 0.196590 + 0.655681I
b = −1.03433 + 1.08957I
1.20037 − 3.52175I −4.53497 + 9.11963I
u = −0.950066
a = 0.979926
b = −1.63593
−4.89306 −6.14970
u = −0.840814 + 0.418418I
a = −0.583883 − 1.131830I
b = 0.09781 − 1.66739I
−0.53914 − 4.66397I −3.81832 + 4.87682I
u = −0.840814 − 0.418418I
a = −0.583883 + 1.131830I
b = 0.09781 + 1.66739I
−0.53914 + 4.66397I −3.81832 − 4.87682I
u = 0.844267 + 0.334993I
a = 1.174390 − 0.186478I
b = 0.377070 + 0.021427I
−0.583413 + 1.042030I −4.30767 − 6.39777I
u = 0.844267 − 0.334993I
a = 1.174390 + 0.186478I
b = 0.377070 − 0.021427I
−0.583413 − 1.042030I −4.30767 + 6.39777I
u = −0.982942 + 0.541373I
a = −0.920141 + 0.267122I
b = −0.392078 + 0.640196I
0.100312 + 0.914322I −3.55487 − 1.69871I
u = −0.982942 − 0.541373I
a = −0.920141 − 0.267122I
b = −0.392078 − 0.640196I
0.100312 − 0.914322I −3.55487 + 1.69871I
u = 0.498706 + 0.460819I
a = −1.46137 + 0.05858I
b = 0.99657 − 1.37404I
2.66837 + 1.50137I −3.18048 − 1.01850I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.498706 − 0.460819I
a = −1.46137 − 0.05858I
b = 0.99657 + 1.37404I
2.66837 − 1.50137I −3.18048 + 1.01850I
u = 0.523977 + 0.369468I
a = −0.64585 + 1.67216I
b = −1.188670 + 0.328805I
2.03016 + 6.51826I −5.41677 − 6.68837I
u = 0.523977 − 0.369468I
a = −0.64585 − 1.67216I
b = −1.188670 − 0.328805I
2.03016 − 6.51826I −5.41677 + 6.68837I
u = −1.52435
a = 0.344430
b = 0.923126
−3.18638 −21.1730
u = 1.98515 + 0.20040I
a = −0.421911 + 0.508878I
b = −0.49997 + 2.32848I
9.03267 + 3.39525I −7.02573 − 2.85779I
u = 1.98515 − 0.20040I
a = −0.421911 − 0.508878I
b = −0.49997 − 2.32848I
9.03267 − 3.39525I −7.02573 + 2.85779I
15
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
16
− 6u
15
+ ··· − 10u + 1)(u
37
+ 7u
36
+ ··· + 33u + 1)
c
2
(u
16
− 3u
14
+ ··· − 5u
2
+ 1)(u
37
+ u
36
+ ··· − 5u + 1)
c
3
(u
16
− 2u
14
+ ··· + 2u − 1)(u
37
+ u
36
+ ··· − 23u − 5)
c
4
(u
16
− u
15
+ ··· − u − 1)(u
37
+ 3u
35
+ ··· − 294u − 229)
c
5
(u
16
− 3u
14
+ ··· − 5u
2
+ 1)(u
37
+ u
36
+ ··· − 5u + 1)
c
6
(u
16
+ 3u
15
+ ··· + 4u + 1)(u
37
− 30u
35
+ ··· + 4671u + 1007)
c
7
(u
16
+ 5u
14
+ ··· − 9u − 1)(u
37
− 7u
36
+ ··· − 207584u − 176401)
c
8
(u
16
− u
15
+ ··· − 8u − 1)(u
37
− 6u
36
+ ··· + 3u + 1)
c
9
(u
16
+ u
15
+ ··· + u − 1)(u
37
+ 3u
35
+ ··· − 294u − 229)
c
10
(u
16
− 3u
15
+ ··· − 4u + 1)(u
37
− 30u
35
+ ··· + 4671u + 1007)
c
11
(u
16
− 15u
15
+ ··· − 8u + 1)
· (u
37
− 60u
36
+ ··· + 36901087u − 1014049)
c
12
(u
16
+ u
15
+ ··· + 8u − 1)(u
37
− 6u
36
+ ··· + 3u + 1)
16
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
16
+ 14y
15
+ ··· − 6y + 1)(y
37
+ 53y
36
+ ··· + 369y −1)
c
2
, c
5
(y
16
− 6y
15
+ ··· − 10y + 1)(y
37
− 7y
36
+ ··· + 33y −1)
c
3
(y
16
− 4y
15
+ ··· + 10y + 1)(y
37
+ 3y
36
+ ··· − 131y −25)
c
4
, c
9
(y
16
− 13y
15
+ ··· − 9y + 1)(y
37
+ 6y
36
+ ··· + 6744y −52441)
c
6
, c
10
(y
16
− 15y
15
+ ··· − 8y + 1)
· (y
37
− 60y
36
+ ··· + 36901087y −1014049)
c
7
(y
16
+ 10y
15
+ ··· + 11y + 1)
· (y
37
+ 101y
36
+ ··· − 38906418180y −31117312801)
c
8
, c
12
(y
16
+ 9y
15
+ ··· − 88y + 1)(y
37
+ 36y
36
+ ··· + 119y −1)
c
11
(y
16
− 31y
15
+ ··· + 20y + 1)
· (y
37
− 168y
36
+ ··· + 147226173534695y −1028295374401)
17
