12n
0584
(K12n
0584
)
A knot diagram
1
Linearized knot diagam
3 7 12 11 8 2 10 11 3 6 4 10
Solving Sequence
2,7 3,10
8 1 6 11 5 4 9 12
c
2
c
7
c
1
c
6
c
10
c
5
c
4
c
9
c
12
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.84207 × 10
81
u
60
2.95633 × 10
81
u
59
+ ··· + 5.11199 × 10
81
b 2.88400 × 10
82
,
1.14386 × 10
81
u
60
4.62548 × 10
81
u
59
+ ··· + 1.06887 × 10
82
a 7.85278 × 10
82
,
u
61
+ u
60
+ ··· 22u 23i
I
u
2
= h−17u
15
11u
14
+ ··· + 5b + 24, 38u
15
24u
14
+ ··· + 5a + 51,
u
16
4u
14
u
13
+ 10u
12
+ 4u
11
18u
10
8u
9
+ 25u
8
+ 9u
7
23u
6
6u
5
+ 14u
4
+ 3u
3
5u
2
u + 1i
* 2 irreducible components of dim
C
= 0, with total 77 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−2.84 × 10
81
u
60
2.96 × 10
81
u
59
+ · · · + 5.11 × 10
81
b 2.88 ×
10
82
, 1.14 × 10
81
u
60
4.63 × 10
81
u
59
+ · · · + 1.07 × 10
82
a 7.85 ×
10
82
, u
61
+ u
60
+ · · · 22u 23i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
u
2
a
10
=
0.107015u
60
+ 0.432744u
59
+ ··· + 11.5924u + 7.34680
0.555961u
60
+ 0.578313u
59
+ ··· + 13.5777u + 5.64164
a
8
=
1.63482u
60
0.434066u
59
+ ··· 3.95439u + 24.4321
1.20730u
60
0.120843u
59
+ ··· + 1.65510u + 29.0484
a
1
=
u
2
+ 1
u
4
a
6
=
u
u
a
11
=
0.525349u
60
+ 0.268729u
59
+ ··· + 7.94097u + 14.3245
0.0764035u
60
+ 0.414298u
59
+ ··· + 9.92621u + 12.6193
a
5
=
0.132466u
60
0.942714u
59
+ ··· 27.4934u 9.73617
0.157167u
60
0.596294u
59
+ ··· 18.0455u 3.48263
a
4
=
1.08158u
60
0.482855u
59
+ ··· 14.9772u + 30.5122
0.233874u
60
0.223864u
59
+ ··· 8.46851u 1.44589
a
9
=
0.504826u
60
+ 0.228474u
59
+ ··· + 7.64215u + 9.19693
0.303905u
60
+ 0.301421u
59
+ ··· + 8.47187u + 15.0158
a
12
=
1.28481u
60
+ 0.424922u
59
+ ··· + 11.1040u + 38.8528
0.877631u
60
0.0161271u
59
+ ··· + 0.455782u + 24.0747
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0.265475u
60
+ 0.396204u
59
+ ··· + 11.1890u 16.1033
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
61
+ 37u
60
+ ··· + 3014u + 529
c
2
, c
6
u
61
u
60
+ ··· 22u + 23
c
3
, c
4
, c
11
u
61
3u
60
+ ··· u + 1
c
5
u
61
+ 5u
60
+ ··· + 128u + 56
c
7
u
61
+ u
60
+ ··· + 4795u 1559
c
8
u
61
+ 3u
60
+ ··· + 1189u 103
c
9
u
61
u
60
+ ··· 4288u + 1856
c
10
u
61
+ u
60
+ ··· 19u + 1
c
12
u
61
u
60
+ ··· 120835u + 26113
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
61
17y
60
+ ··· + 10572802y 279841
c
2
, c
6
y
61
37y
60
+ ··· + 3014y 529
c
3
, c
4
, c
11
y
61
+ 45y
60
+ ··· 61y 1
c
5
y
61
+ 47y
60
+ ··· 214112y 3136
c
7
y
61
31y
60
+ ··· + 107411875y 2430481
c
8
y
61
+ 49y
60
+ ··· + 350761y 10609
c
9
y
61
+ 51y
60
+ ··· 57040896y 3444736
c
10
y
61
+ 15y
60
+ ··· + 51y 1
c
12
y
61
+ 55y
60
+ ··· + 971678005y 681888769
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.959151 + 0.188873I
a = 0.71607 2.11317I
b = 0.427222 1.250120I
0.40672 + 5.49798I 3.46413 7.66192I
u = 0.959151 0.188873I
a = 0.71607 + 2.11317I
b = 0.427222 + 1.250120I
0.40672 5.49798I 3.46413 + 7.66192I
u = 0.934743 + 0.424563I
a = 0.220618 + 0.026435I
b = 1.043970 + 0.429854I
1.60124 + 2.09731I 0.52172 3.57800I
u = 0.934743 0.424563I
a = 0.220618 0.026435I
b = 1.043970 0.429854I
1.60124 2.09731I 0.52172 + 3.57800I
u = 0.205719 + 0.937770I
a = 0.007890 1.331690I
b = 0.780566 0.133806I
2.24217 + 2.51722I 4.13220 2.03658I
u = 0.205719 0.937770I
a = 0.007890 + 1.331690I
b = 0.780566 + 0.133806I
2.24217 2.51722I 4.13220 + 2.03658I
u = 0.162902 + 1.031490I
a = 0.260817 1.260900I
b = 0.544283 0.172289I
6.40462 + 3.64805I 6.12698 2.44450I
u = 0.162902 1.031490I
a = 0.260817 + 1.260900I
b = 0.544283 + 0.172289I
6.40462 3.64805I 6.12698 + 2.44450I
u = 0.941999 + 0.077674I
a = 1.08751 1.37046I
b = 1.055650 0.247755I
1.84937 1.06710I 7.68501 + 0.20822I
u = 0.941999 0.077674I
a = 1.08751 + 1.37046I
b = 1.055650 + 0.247755I
1.84937 + 1.06710I 7.68501 0.20822I
5
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.937483 + 0.102090I
a = 0.484123 + 0.573834I
b = 0.98031 1.45346I
4.81378 + 0.51083I 5.07863 + 3.86372I
u = 0.937483 0.102090I
a = 0.484123 0.573834I
b = 0.98031 + 1.45346I
4.81378 0.51083I 5.07863 3.86372I
u = 1.008430 + 0.362616I
a = 1.000510 0.605838I
b = 2.33129 0.84687I
0.01276 7.14753I 2.20400 + 9.04049I
u = 1.008430 0.362616I
a = 1.000510 + 0.605838I
b = 2.33129 + 0.84687I
0.01276 + 7.14753I 2.20400 9.04049I
u = 0.643141 + 0.668518I
a = 0.716958 + 0.049390I
b = 0.318873 + 0.601995I
1.75152 2.53902I 1.27559 + 4.14078I
u = 0.643141 0.668518I
a = 0.716958 0.049390I
b = 0.318873 0.601995I
1.75152 + 2.53902I 1.27559 4.14078I
u = 0.753203 + 0.517931I
a = 0.102774 + 0.952076I
b = 0.367431 + 1.094570I
1.66195 1.20234I 8.53362 + 3.15271I
u = 0.753203 0.517931I
a = 0.102774 0.952076I
b = 0.367431 1.094570I
1.66195 + 1.20234I 8.53362 3.15271I
u = 0.910915
a = 0.473770
b = 1.07394
1.32772 8.18480
u = 0.153240 + 1.083330I
a = 0.430101 1.162100I
b = 0.365491 0.155347I
2.13464 9.66628I 2.68073 + 5.89377I
6
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.153240 1.083330I
a = 0.430101 + 1.162100I
b = 0.365491 + 0.155347I
2.13464 + 9.66628I 2.68073 5.89377I
u = 1.115530 + 0.094811I
a = 1.368590 + 0.050906I
b = 2.09969 0.80379I
3.09183 0.94578I 8.08189 0.53980I
u = 1.115530 0.094811I
a = 1.368590 0.050906I
b = 2.09969 + 0.80379I
3.09183 + 0.94578I 8.08189 + 0.53980I
u = 0.768294 + 0.427994I
a = 0.233622 0.672878I
b = 0.887371 + 0.068293I
1.25803 + 1.85767I 3.29586 4.00259I
u = 0.768294 0.427994I
a = 0.233622 + 0.672878I
b = 0.887371 0.068293I
1.25803 1.85767I 3.29586 + 4.00259I
u = 0.223321 + 0.842928I
a = 0.897998 + 0.077975I
b = 0.036178 + 0.399582I
3.62908 + 2.32516I 4.48467 2.65480I
u = 0.223321 0.842928I
a = 0.897998 0.077975I
b = 0.036178 0.399582I
3.62908 2.32516I 4.48467 + 2.65480I
u = 0.889016 + 0.747517I
a = 0.607385 0.821852I
b = 1.395130 + 0.149616I
9.07136 2.85087I 9.78334 + 0.I
u = 0.889016 0.747517I
a = 0.607385 + 0.821852I
b = 1.395130 0.149616I
9.07136 + 2.85087I 9.78334 + 0.I
u = 1.130530 + 0.481440I
a = 1.302640 + 0.202022I
b = 1.82636 + 0.28273I
3.38137 2.36705I 0
7
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.130530 0.481440I
a = 1.302640 0.202022I
b = 1.82636 0.28273I
3.38137 + 2.36705I 0
u = 1.164240 + 0.451221I
a = 1.44291 0.32158I
b = 2.22996 0.29926I
3.53482 + 5.70296I 0
u = 1.164240 0.451221I
a = 1.44291 + 0.32158I
b = 2.22996 + 0.29926I
3.53482 5.70296I 0
u = 0.686059 + 0.293330I
a = 1.01986 + 1.45708I
b = 0.74714 + 1.69501I
0.27896 3.26826I 2.74807 0.82015I
u = 0.686059 0.293330I
a = 1.01986 1.45708I
b = 0.74714 1.69501I
0.27896 + 3.26826I 2.74807 + 0.82015I
u = 1.228430 + 0.253328I
a = 1.293940 0.408857I
b = 2.05763 0.91740I
3.69197 + 4.91295I 0
u = 1.228430 0.253328I
a = 1.293940 + 0.408857I
b = 2.05763 + 0.91740I
3.69197 4.91295I 0
u = 1.225300 + 0.340151I
a = 1.215390 0.430859I
b = 1.97241 0.78995I
3.61600 + 4.89193I 0
u = 1.225300 0.340151I
a = 1.215390 + 0.430859I
b = 1.97241 + 0.78995I
3.61600 4.89193I 0
u = 1.306570 + 0.385321I
a = 0.772428 + 0.105070I
b = 1.58309 0.82825I
6.95611 6.96468I 0
8
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.306570 0.385321I
a = 0.772428 0.105070I
b = 1.58309 + 0.82825I
6.95611 + 6.96468I 0
u = 0.060803 + 0.628747I
a = 0.53802 + 1.47756I
b = 0.127042 + 0.473478I
0.44119 1.56470I 4.17028 + 3.88456I
u = 0.060803 0.628747I
a = 0.53802 1.47756I
b = 0.127042 0.473478I
0.44119 + 1.56470I 4.17028 3.88456I
u = 0.922764 + 1.032820I
a = 0.199690 + 0.204735I
b = 0.403670 + 0.238476I
4.00754 + 3.70557I 0
u = 0.922764 1.032820I
a = 0.199690 0.204735I
b = 0.403670 0.238476I
4.00754 3.70557I 0
u = 0.457781 + 0.408457I
a = 0.56646 + 2.03842I
b = 0.511340 0.004138I
1.59167 + 3.79186I 1.89741 1.93857I
u = 0.457781 0.408457I
a = 0.56646 2.03842I
b = 0.511340 + 0.004138I
1.59167 3.79186I 1.89741 + 1.93857I
u = 1.262930 + 0.592649I
a = 1.262610 0.329157I
b = 2.25061 + 0.25489I
5.42549 + 3.10789I 0
u = 1.262930 0.592649I
a = 1.262610 + 0.329157I
b = 2.25061 0.25489I
5.42549 3.10789I 0
u = 1.36643 + 0.38967I
a = 0.765288 0.003995I
b = 1.47807 0.79705I
11.38250 + 1.28053I 0
9
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.36643 0.38967I
a = 0.765288 + 0.003995I
b = 1.47807 + 0.79705I
11.38250 1.28053I 0
u = 1.29707 + 0.58314I
a = 1.350370 0.078787I
b = 2.35665 + 0.43807I
9.91993 9.45681I 0
u = 1.29707 0.58314I
a = 1.350370 + 0.078787I
b = 2.35665 0.43807I
9.91993 + 9.45681I 0
u = 1.31022 + 0.58889I
a = 1.322870 + 0.107133I
b = 2.34658 + 0.59048I
5.7532 + 15.6192I 0
u = 1.31022 0.58889I
a = 1.322870 0.107133I
b = 2.34658 0.59048I
5.7532 15.6192I 0
u = 1.37880 + 0.46708I
a = 0.888680 0.525147I
b = 1.34840 0.85335I
1.29850 7.17717I 0
u = 1.37880 0.46708I
a = 0.888680 + 0.525147I
b = 1.34840 + 0.85335I
1.29850 + 7.17717I 0
u = 1.42356 + 0.37284I
a = 0.707166 0.088229I
b = 1.34948 0.74233I
7.38726 + 4.45354I 0
u = 1.42356 0.37284I
a = 0.707166 + 0.088229I
b = 1.34948 + 0.74233I
7.38726 4.45354I 0
u = 0.054872 + 0.484805I
a = 1.31570 + 1.52600I
b = 0.147524 + 0.297815I
0.23274 1.52753I 1.85083 + 4.54656I
10
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.054872 0.484805I
a = 1.31570 1.52600I
b = 0.147524 0.297815I
0.23274 + 1.52753I 1.85083 4.54656I
11
II. I
u
2
= h−17u
15
11u
14
+ · · · + 5b + 24, 38u
15
24u
14
+ · · · + 5a +
51, u
16
4u
14
+ · · · u + 1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
u
2
a
10
=
38
5
u
15
+
24
5
u
14
+ ···
41
5
u
51
5
17
5
u
15
+
11
5
u
14
+ ···
14
5
u
24
5
a
8
=
3u
15
+ 2u
14
+ ··· + 2u + 1
6
5
u
15
3
5
u
14
+ ··· +
17
5
u +
27
5
a
1
=
u
2
+ 1
u
4
a
6
=
u
u
a
11
=
42
5
u
15
+
31
5
u
14
+ ···
49
5
u
64
5
21
5
u
15
+
18
5
u
14
+ ···
22
5
u
37
5
a
5
=
11.6000u
15
7.80000u
14
+ ··· + 11.2000u + 15.2000
5.80000u
15
4.40000u
14
+ ··· + 4.60000u + 7.60000
a
4
=
6.20000u
15
4.60000u
14
+ ··· + 6.40000u + 11.4000
5.20000u
15
2.60000u
14
+ ··· + 5.40000u + 6.40000
a
9
=
33
5
u
15
+
24
5
u
14
+ ···
41
5
u
51
5
12
5
u
15
+
11
5
u
14
+ ···
9
5
u
24
5
a
12
=
14
5
u
15
+
2
5
u
14
+ ···
33
5
u
18
5
14
5
u
15
+
7
5
u
14
+ ···
28
5
u
23
5
(ii) Obstruction class = 1
(iii) Cusp Shapes =
96
5
u
15
53
5
u
14
+ 68u
13
+
301
5
u
12
752
5
u
11
166u
10
+
1158
5
u
9
+
1467
5
u
8
1404
5
u
7
1716
5
u
6
+ 204u
5
+
1261
5
u
4
501
5
u
3
611
5
u
2
+
57
5
u +
132
5
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
16
8u
15
+ ··· 11u + 1
c
2
u
16
4u
14
+ ··· u + 1
c
3
, c
4
u
16
+ 2u
15
+ ··· + 8u + 1
c
5
u
16
+ 6u
14
+ ··· + 8u
2
+ 1
c
6
u
16
4u
14
+ ··· + u + 1
c
7
u
16
12u
15
+ ··· 8u + 1
c
8
u
16
+ 4u
15
+ ··· 3u
2
+ 1
c
9
u
16
+ 6u
14
+ ··· + u + 1
c
10
u
16
+ 8u
14
+ ··· + 6u
2
+ 1
c
11
u
16
2u
15
+ ··· 8u + 1
c
12
u
16
+ 2u
14
+ ··· + 2u + 1
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
16
+ 8y
15
+ ··· 3y + 1
c
2
, c
6
y
16
8y
15
+ ··· 11y + 1
c
3
, c
4
, c
11
y
16
+ 18y
15
+ ··· 16y + 1
c
5
y
16
+ 12y
15
+ ··· + 16y + 1
c
7
y
16
2y
15
+ ··· + 24y + 1
c
8
y
16
+ 6y
15
+ ··· 6y + 1
c
9
y
16
+ 12y
15
+ ··· + 13y + 1
c
10
y
16
+ 16y
15
+ ··· + 12y + 1
c
12
y
16
+ 4y
15
+ ··· 10y + 1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.913832 + 0.235082I
a = 0.128344 0.430133I
b = 0.51462 + 1.51604I
5.04845 + 1.02692I 1.87205 8.56014I
u = 0.913832 0.235082I
a = 0.128344 + 0.430133I
b = 0.51462 1.51604I
5.04845 1.02692I 1.87205 + 8.56014I
u = 0.781665 + 0.507913I
a = 0.442004 0.379613I
b = 0.243014 + 0.419895I
0.13293 2.08915I 4.96987 + 3.94005I
u = 0.781665 0.507913I
a = 0.442004 + 0.379613I
b = 0.243014 0.419895I
0.13293 + 2.08915I 4.96987 3.94005I
u = 0.902595 + 0.772917I
a = 0.745532 + 0.878575I
b = 1.53315 0.12089I
8.66558 2.92614I 9.74877 + 4.50724I
u = 0.902595 0.772917I
a = 0.745532 0.878575I
b = 1.53315 + 0.12089I
8.66558 + 2.92614I 9.74877 4.50724I
u = 1.141260 + 0.432326I
a = 1.52602 0.04764I
b = 2.22115 0.46874I
2.53602 + 3.59932I 3.71675 3.64277I
u = 1.141260 0.432326I
a = 1.52602 + 0.04764I
b = 2.22115 + 0.46874I
2.53602 3.59932I 3.71675 + 3.64277I
u = 1.209890 + 0.340073I
a = 1.17802 0.80444I
b = 1.80436 0.95523I
2.27641 6.22692I 5.11471 + 7.16731I
u = 1.209890 0.340073I
a = 1.17802 + 0.80444I
b = 1.80436 + 0.95523I
2.27641 + 6.22692I 5.11471 7.16731I
15
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.582099 + 0.425674I
a = 0.46849 + 2.09936I
b = 0.821727 + 0.776197I
0.501722 + 0.021541I 2.41993 1.23227I
u = 0.582099 0.425674I
a = 0.46849 2.09936I
b = 0.821727 0.776197I
0.501722 0.021541I 2.41993 + 1.23227I
u = 0.621496 + 0.095944I
a = 0.02677 + 2.57216I
b = 0.61711 + 1.29946I
0.32457 + 4.21515I 3.24854 6.32973I
u = 0.621496 0.095944I
a = 0.02677 2.57216I
b = 0.61711 1.29946I
0.32457 4.21515I 3.24854 + 6.32973I
u = 0.878460 + 1.058430I
a = 0.269474 0.056700I
b = 0.0508752 + 0.0987483I
4.30209 + 3.76450I 13.3465 7.4442I
u = 0.878460 1.058430I
a = 0.269474 + 0.056700I
b = 0.0508752 0.0987483I
4.30209 3.76450I 13.3465 + 7.4442I
16
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
16
8u
15
+ ··· 11u + 1)(u
61
+ 37u
60
+ ··· + 3014u + 529)
c
2
(u
16
4u
14
+ ··· u + 1)(u
61
u
60
+ ··· 22u + 23)
c
3
, c
4
(u
16
+ 2u
15
+ ··· + 8u + 1)(u
61
3u
60
+ ··· u + 1)
c
5
(u
16
+ 6u
14
+ ··· + 8u
2
+ 1)(u
61
+ 5u
60
+ ··· + 128u + 56)
c
6
(u
16
4u
14
+ ··· + u + 1)(u
61
u
60
+ ··· 22u + 23)
c
7
(u
16
12u
15
+ ··· 8u + 1)(u
61
+ u
60
+ ··· + 4795u 1559)
c
8
(u
16
+ 4u
15
+ ··· 3u
2
+ 1)(u
61
+ 3u
60
+ ··· + 1189u 103)
c
9
(u
16
+ 6u
14
+ ··· + u + 1)(u
61
u
60
+ ··· 4288u + 1856)
c
10
(u
16
+ 8u
14
+ ··· + 6u
2
+ 1)(u
61
+ u
60
+ ··· 19u + 1)
c
11
(u
16
2u
15
+ ··· 8u + 1)(u
61
3u
60
+ ··· u + 1)
c
12
(u
16
+ 2u
14
+ ··· + 2u + 1)(u
61
u
60
+ ··· 120835u + 26113)
17
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
16
+ 8y
15
+ ··· 3y + 1)(y
61
17y
60
+ ··· + 1.05728 × 10
7
y 279841)
c
2
, c
6
(y
16
8y
15
+ ··· 11y + 1)(y
61
37y
60
+ ··· + 3014y 529)
c
3
, c
4
, c
11
(y
16
+ 18y
15
+ ··· 16y + 1)(y
61
+ 45y
60
+ ··· 61y 1)
c
5
(y
16
+ 12y
15
+ ··· + 16y + 1)(y
61
+ 47y
60
+ ··· 214112y 3136)
c
7
(y
16
2y
15
+ ··· + 24y + 1)
· (y
61
31y
60
+ ··· + 107411875y 2430481)
c
8
(y
16
+ 6y
15
+ ··· 6y + 1)(y
61
+ 49y
60
+ ··· + 350761y 10609)
c
9
(y
16
+ 12y
15
+ ··· + 13y + 1)
· (y
61
+ 51y
60
+ ··· 57040896y 3444736)
c
10
(y
16
+ 16y
15
+ ··· + 12y + 1)(y
61
+ 15y
60
+ ··· + 51y 1)
c
12
(y
16
+ 4y
15
+ ··· 10y + 1)
· (y
61
+ 55y
60
+ ··· + 971678005y 681888769)
18