12n
0730
(K12n
0730
)
A knot diagram
1
Linearized knot diagam
4 10 8 10 1 3 10 12 3 1 8 6
Solving Sequence
3,8 4,10
2 1 7 6 5 9 12 11
c
3
c
2
c
1
c
7
c
6
c
5
c
9
c
12
c
11
c
4
, c
8
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h1.44280 × 10
94
u
39
+ 8.50468 × 10
94
u
38
+ ··· + 1.31536 × 10
97
b − 5.65969 × 10
97
,
− 7.99853 × 10
97
u
39
− 1.12262 × 10
98
u
38
+ ··· + 2.19271 × 10
100
a − 2.21181 × 10
101
,
u
40
+ 3u
39
+ ··· + 1016u − 1667i
I
u
2
= h−7910373u
16
+ 432236197u
15
+ ··· + 1605075802b + 422623648,
996003064u
16
− 1757434994u
15
+ ··· + 1605075802a + 2036147287, u
17
− 2u
16
+ ··· − u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 57 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
= h1.44 × 10
94
u
39
+ 8.50 × 10
94
u
38
+ · · · + 1.32 × 10
97
b − 5.66 ×
10
97
, −8.00 × 10
97
u
39
− 1.12 × 10
98
u
38
+ · · · + 2.19 × 10
100
a − 2.21 ×
10
101
, u
40
+ 3u
39
+ · · · + 1016u − 1667i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
u
2
a
10
=
0.00364778u
39
+ 0.00511977u
38
+ ··· − 16.1044u + 10.0871
−0.00109689u
39
− 0.00646565u
38
+ ··· + 1.45140u + 4.30276
a
2
=
−0.00182775u
39
+ 0.0000852465u
38
+ ··· + 7.45312u − 9.20414
0.00494909u
39
+ 0.0143198u
38
+ ··· − 7.75640u + 2.00982
a
1
=
0.000306195u
39
+ 0.0113462u
38
+ ··· + 8.40116u − 16.4770
0.00369323u
39
+ 0.00540172u
38
+ ··· − 9.13598u + 10.1100
a
7
=
−0.0149546u
39
− 0.0418621u
38
+ ··· + 30.1162u − 7.15726
0.00556849u
39
+ 0.0195206u
38
+ ··· − 7.34714u − 3.04686
a
6
=
−0.00938611u
39
− 0.0223414u
38
+ ··· + 22.7690u − 10.2041
0.00556849u
39
+ 0.0195206u
38
+ ··· − 7.34714u − 3.04686
a
5
=
0.00482950u
39
+ 0.0248160u
38
+ ··· + 0.583500u − 13.7252
−0.00213394u
39
− 0.0112609u
38
+ ··· − 0.948044u + 7.27286
a
9
=
0.00255090u
39
− 0.00134588u
38
+ ··· − 14.6530u + 14.3899
−0.00109689u
39
− 0.00646565u
38
+ ··· + 1.45140u + 4.30276
a
12
=
−0.00391056u
39
− 0.0175058u
38
+ ··· + 6.93355u + 8.56793
−0.00163120u
39
− 0.00313351u
38
+ ··· + 5.54321u − 3.60264
a
11
=
−0.00391056u
39
− 0.0175058u
38
+ ··· + 6.93355u + 8.56793
0.00128477u
39
+ 0.0119254u
38
+ ··· + 4.89087u − 13.2282
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0225460u
39
+ 0.0929089u
38
+ ··· + 1.19705u − 39.3928
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
40
− 6u
39
+ ··· − 585u + 81
c
2
, c
9
u
40
+ u
39
+ ··· − 1593u − 281
c
3
u
40
− 3u
39
+ ··· − 1016u − 1667
c
4
u
40
− 2u
39
+ ··· + 18u − 7
c
5
, c
12
u
40
+ 2u
39
+ ··· + 45u − 181
c
6
u
40
+ 23u
38
+ ··· + 72246u − 10339
c
7
u
40
− u
39
+ ··· + 119u + 7
c
8
, c
11
u
40
− 4u
39
+ ··· + 159u + 39
c
10
u
40
− 3u
39
+ ··· + 77u + 49
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
40
− 22y
39
+ ··· − 215217y + 6561
c
2
, c
9
y
40
+ 55y
39
+ ··· + 1314861y + 78961
c
3
y
40
+ 35y
39
+ ··· + 25863122y + 2778889
c
4
y
40
− 38y
39
+ ··· + 10176y + 49
c
5
, c
12
y
40
+ 28y
39
+ ··· + 424773y + 32761
c
6
y
40
+ 46y
39
+ ··· − 3212684616y + 106894921
c
7
y
40
− 55y
39
+ ··· − 3745y + 49
c
8
, c
11
y
40
− 22y
39
+ ··· − 88383y + 1521
c
10
y
40
− 29y
39
+ ··· − 130291y + 2401
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.074225 + 0.995798I
a = −1.48142 − 0.88202I
b = 0.069778 + 0.251836I
−1.68029 − 6.30373I −1.75666 + 6.49211I
u = 0.074225 − 0.995798I
a = −1.48142 + 0.88202I
b = 0.069778 − 0.251836I
−1.68029 + 6.30373I −1.75666 − 6.49211I
u = −0.019908 + 1.014730I
a = 0.933442 + 0.125283I
b = 0.321710 + 0.172172I
−2.72752 − 0.30261I −4.74009 + 1.12705I
u = −0.019908 − 1.014730I
a = 0.933442 − 0.125283I
b = 0.321710 − 0.172172I
−2.72752 + 0.30261I −4.74009 − 1.12705I
u = 0.090932 + 1.056100I
a = 0.69809 − 1.51032I
b = 0.39797 + 1.53949I
8.40378 + 2.27498I −2.47436 − 4.06313I
u = 0.090932 − 1.056100I
a = 0.69809 + 1.51032I
b = 0.39797 − 1.53949I
8.40378 − 2.27498I −2.47436 + 4.06313I
u = −0.384077 + 0.999119I
a = −0.75184 − 1.68276I
b = −0.06076 + 1.71893I
9.33802 − 0.43323I −1.80383 − 1.69832I
u = −0.384077 − 0.999119I
a = −0.75184 + 1.68276I
b = −0.06076 − 1.71893I
9.33802 + 0.43323I −1.80383 + 1.69832I
u = 0.744898 + 0.775177I
a = −0.209036 − 0.214334I
b = −1.145770 + 0.121712I
−4.62154 − 2.17421I −9.73588 + 5.09039I
u = 0.744898 − 0.775177I
a = −0.209036 + 0.214334I
b = −1.145770 − 0.121712I
−4.62154 + 2.17421I −9.73588 − 5.09039I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.969293 + 0.598574I
a = 0.875542 − 0.894161I
b = −0.124340 + 0.752925I
−0.244335 − 1.176990I −6.16007 + 1.36199I
u = 0.969293 − 0.598574I
a = 0.875542 + 0.894161I
b = −0.124340 − 0.752925I
−0.244335 + 1.176990I −6.16007 − 1.36199I
u = −1.103180 + 0.358015I
a = 0.751248 + 0.156995I
b = 0.530673 − 0.765497I
−1.66991 + 2.90598I −0.37953 − 2.28494I
u = −1.103180 − 0.358015I
a = 0.751248 − 0.156995I
b = 0.530673 + 0.765497I
−1.66991 − 2.90598I −0.37953 + 2.28494I
u = −0.898417 + 0.778153I
a = 0.096570 − 0.403680I
b = −0.535046 − 0.126132I
4.45088 + 3.00898I −9.22623 + 0.17791I
u = −0.898417 − 0.778153I
a = 0.096570 + 0.403680I
b = −0.535046 + 0.126132I
4.45088 − 3.00898I −9.22623 − 0.17791I
u = 0.530454 + 1.115730I
a = −0.109870 + 0.125763I
b = 1.69402 − 0.58477I
−1.60625 + 4.02862I −2.67808 − 1.97162I
u = 0.530454 − 1.115730I
a = −0.109870 − 0.125763I
b = 1.69402 + 0.58477I
−1.60625 − 4.02862I −2.67808 + 1.97162I
u = 0.946367 + 0.805651I
a = −0.594098 + 0.206972I
b = 0.866066 − 0.936600I
0.05822 − 3.02351I −2.19172 + 2.97004I
u = 0.946367 − 0.805651I
a = −0.594098 − 0.206972I
b = 0.866066 + 0.936600I
0.05822 + 3.02351I −2.19172 − 2.97004I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.547294 + 1.146790I
a = 0.07437 − 1.44792I
b = 0.351725 + 1.262160I
1.36525 − 2.63988I 0.758920 − 0.234307I
u = 0.547294 − 1.146790I
a = 0.07437 + 1.44792I
b = 0.351725 − 1.262160I
1.36525 + 2.63988I 0.758920 + 0.234307I
u = 0.110521 + 1.325330I
a = −0.210888 + 1.057420I
b = −0.82951 − 1.82120I
9.68403 − 3.29803I −1.76650 + 2.63916I
u = 0.110521 − 1.325330I
a = −0.210888 − 1.057420I
b = −0.82951 + 1.82120I
9.68403 + 3.29803I −1.76650 − 2.63916I
u = −0.400029 + 1.319180I
a = 0.302273 + 1.229320I
b = 0.25236 − 2.15666I
10.73370 + 3.93558I −1.98176 − 4.05917I
u = −0.400029 − 1.319180I
a = 0.302273 − 1.229320I
b = 0.25236 + 2.15666I
10.73370 − 3.93558I −1.98176 + 4.05917I
u = 0.499216
a = −0.294586
b = 0.384818
−0.791835 −13.1510
u = 0.60667 + 1.39679I
a = −0.177788 + 1.087880I
b = 0.08306 − 1.87544I
2.61258 − 4.98918I 0
u = 0.60667 − 1.39679I
a = −0.177788 − 1.087880I
b = 0.08306 + 1.87544I
2.61258 + 4.98918I 0
u = 0.057521 + 0.459196I
a = −1.04344 − 1.83286I
b = −0.049531 + 0.594009I
1.36870 − 1.27202I 0.60073 + 4.17984I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.057521 − 0.459196I
a = −1.04344 + 1.83286I
b = −0.049531 − 0.594009I
1.36870 + 1.27202I 0.60073 − 4.17984I
u = −0.451499
a = 1.24714
b = −1.34904
−7.99269 −41.4500
u = −1.71262 + 0.03239I
a = −0.625667 − 0.062971I
b = −0.701464 + 1.129030I
2.55596 − 3.89352I 0
u = −1.71262 − 0.03239I
a = −0.625667 + 0.062971I
b = −0.701464 − 1.129030I
2.55596 + 3.89352I 0
u = −0.93976 + 1.68582I
a = 0.302089 + 0.934011I
b = 0.52563 − 2.12471I
7.2434 + 13.4515I 0
u = −0.93976 − 1.68582I
a = 0.302089 − 0.934011I
b = 0.52563 + 2.12471I
7.2434 − 13.4515I 0
u = −0.75189 + 1.95033I
a = −0.179356 − 0.815834I
b = −0.24537 + 2.12821I
4.31816 + 4.85736I 0
u = −0.75189 − 1.95033I
a = −0.179356 + 0.815834I
b = −0.24537 − 2.12821I
4.31816 − 4.85736I 0
u = 0.00784 + 2.54288I
a = −0.024216 + 0.721328I
b = −0.41910 − 2.14226I
13.20450 − 2.73784I 0
u = 0.00784 − 2.54288I
a = −0.024216 − 0.721328I
b = −0.41910 + 2.14226I
13.20450 + 2.73784I 0
8
II.
I
u
2
= h−7.91 × 10
6
u
16
+ 4.32 × 10
8
u
15
+ · · · + 1.61 × 10
9
b + 4.23 × 10
8
, 9.96 ×
10
8
u
16
−1.76×10
9
u
15
+· · · +1.61×10
9
a+2.04×10
9
, u
17
−2u
16
+· · · −u
2
+1i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
u
2
a
10
=
−0.620533u
16
+ 1.09492u
15
+ ··· − 0.305972u − 1.26857
0.00492835u
16
− 0.269293u
15
+ ··· − 1.22753u − 0.263304
a
2
=
−0.151781u
16
+ 0.152336u
15
+ ··· − 4.08959u + 0.621432
−0.149622u
16
+ 0.0695177u
15
+ ··· + 1.46667u − 1.24998
a
1
=
−0.498942u
16
+ 0.618046u
15
+ ··· − 2.77470u − 0.779776
−0.274767u
16
+ 0.350118u
15
+ ··· + 1.81383u − 1.02137
a
7
=
−0.537305u
16
+ 1.17062u
15
+ ··· − 0.571419u + 2.57166
−0.151225u
16
+ 0.499990u
15
+ ··· + 0.621432u + 0.151781
a
6
=
−0.688530u
16
+ 1.67061u
15
+ ··· + 0.0500138u + 2.72344
−0.151225u
16
+ 0.499990u
15
+ ··· + 0.621432u + 0.151781
a
5
=
0.247793u
16
− 0.451462u
15
+ ··· + 6.66125u + 1.91587
0.347162u
16
− 0.465710u
15
+ ··· − 1.31489u + 1.40121
a
9
=
−0.615605u
16
+ 0.825630u
15
+ ··· − 1.53350u − 1.53187
0.00492835u
16
− 0.269293u
15
+ ··· − 1.22753u − 0.263304
a
12
=
0.606095u
16
− 1.10067u
15
+ ··· + 2.24416u + 1.10418
−0.0253392u
16
+ 0.352876u
15
+ ··· + 3.62140u − 1.08505
a
11
=
0.606095u
16
− 1.10067u
15
+ ··· + 2.24416u + 1.10418
−0.171636u
16
+ 0.583572u
15
+ ··· + 3.01530u − 1.19657
(ii) Obstruction class = 1
(iii) Cusp Shapes =
7112656685
1605075802
u
16
−
7923058150
802537901
u
15
+ ··· −
29249964323
1605075802
u −
13984566
802537901
9
(iv) u-Polynomials at the component
10
Crossings u-Polynomials at each crossing
c
1
u
17
− 7u
16
+ ··· + 33u − 11
c
2
u
17
+ 6u
15
+ ··· − 9u − 1
c
3
u
17
− 2u
16
+ ··· − u
2
+ 1
c
4
u
17
+ u
16
+ ··· + 84u − 19
c
5
u
17
− u
16
+ ··· + u − 1
c
6
u
17
+ u
16
+ ··· − 14u − 1
c
7
u
17
+ 6u
16
+ ··· + 45u + 11
c
8
u
17
− 3u
16
+ ··· + u − 1
c
9
u
17
+ 6u
15
+ ··· − 9u + 1
c
10
u
17
− 4u
16
+ ··· − 5u − 1
c
11
u
17
+ 3u
16
+ ··· + u + 1
c
12
u
17
+ u
16
+ ··· + u + 1
11
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
17
− 13y
16
+ ··· + 561y −121
c
2
, c
9
y
17
+ 12y
16
+ ··· + 19y −1
c
3
y
17
+ 12y
16
+ ··· + 2y −1
c
4
y
17
− 13y
16
+ ··· + 3104y −361
c
5
, c
12
y
17
+ 9y
16
+ ··· + 11y −1
c
6
y
17
+ 11y
16
+ ··· + 72y −1
c
7
y
17
− 22y
16
+ ··· + 1321y −121
c
8
, c
11
y
17
− 9y
16
+ ··· + 7y −1
c
10
y
17
− 12y
16
+ ··· + 11y −1
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.020499 + 0.998308I
a = 0.37175 − 1.89988I
b = 0.18081 + 1.72832I
9.62563 + 1.51829I 1.39343 − 3.45515I
u = 0.020499 − 0.998308I
a = 0.37175 + 1.89988I
b = 0.18081 − 1.72832I
9.62563 − 1.51829I 1.39343 + 3.45515I
u = −0.380557 + 0.938672I
a = 0.739410 + 0.323312I
b = 1.246230 − 0.332058I
−4.22062 + 1.12566I −5.94166 + 0.72076I
u = −0.380557 − 0.938672I
a = 0.739410 − 0.323312I
b = 1.246230 + 0.332058I
−4.22062 − 1.12566I −5.94166 − 0.72076I
u = −0.995936 + 0.621165I
a = −0.280702 − 0.424421I
b = −0.353305 − 0.553264I
5.01697 + 3.35175I 1.60696 − 5.55747I
u = −0.995936 − 0.621165I
a = −0.280702 + 0.424421I
b = −0.353305 + 0.553264I
5.01697 − 3.35175I 1.60696 + 5.55747I
u = 1.178520 + 0.479735I
a = −0.655660 + 0.253208I
b = −0.090891 − 0.717128I
−2.58072 − 3.16432I −9.05012 + 4.68936I
u = 1.178520 − 0.479735I
a = −0.655660 − 0.253208I
b = −0.090891 + 0.717128I
−2.58072 + 3.16432I −9.05012 − 4.68936I
u = 0.692730 + 0.052899I
a = 1.72978 + 0.41261I
b = −0.232122 − 0.090819I
0.745228 + 0.220813I −1.69301 + 1.79583I
u = 0.692730 − 0.052899I
a = 1.72978 − 0.41261I
b = −0.232122 + 0.090819I
0.745228 − 0.220813I −1.69301 − 1.79583I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.531547 + 1.299730I
a = 0.013837 − 1.218520I
b = 0.113827 + 1.336070I
0.72305 − 3.21935I −6.16546 + 5.06885I
u = 0.531547 − 1.299730I
a = 0.013837 + 1.218520I
b = 0.113827 − 1.336070I
0.72305 + 3.21935I −6.16546 − 5.06885I
u = 0.016024 + 0.519282I
a = −1.90689 − 1.51776I
b = −1.092870 + 0.142474I
−2.88743 − 5.63292I −6.98267 + 4.20336I
u = 0.016024 − 0.519282I
a = −1.90689 + 1.51776I
b = −1.092870 − 0.142474I
−2.88743 + 5.63292I −6.98267 − 4.20336I
u = −0.346914
a = −1.87486
b = 1.39658
−7.87029 24.2710
u = 0.11063 + 2.21488I
a = −0.074096 + 0.817459I
b = −0.46997 − 2.10827I
13.9624 − 2.5342I 2.69679 + 0.52341I
u = 0.11063 − 2.21488I
a = −0.074096 − 0.817459I
b = −0.46997 + 2.10827I
13.9624 + 2.5342I 2.69679 − 0.52341I
15
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
17
− 7u
16
+ ··· + 33u − 11)(u
40
− 6u
39
+ ··· − 585u + 81)
c
2
(u
17
+ 6u
15
+ ··· − 9u − 1)(u
40
+ u
39
+ ··· − 1593u − 281)
c
3
(u
17
− 2u
16
+ ··· − u
2
+ 1)(u
40
− 3u
39
+ ··· − 1016u − 1667)
c
4
(u
17
+ u
16
+ ··· + 84u − 19)(u
40
− 2u
39
+ ··· + 18u − 7)
c
5
(u
17
− u
16
+ ··· + u − 1)(u
40
+ 2u
39
+ ··· + 45u − 181)
c
6
(u
17
+ u
16
+ ··· − 14u − 1)(u
40
+ 23u
38
+ ··· + 72246u − 10339)
c
7
(u
17
+ 6u
16
+ ··· + 45u + 11)(u
40
− u
39
+ ··· + 119u + 7)
c
8
(u
17
− 3u
16
+ ··· + u − 1)(u
40
− 4u
39
+ ··· + 159u + 39)
c
9
(u
17
+ 6u
15
+ ··· − 9u + 1)(u
40
+ u
39
+ ··· − 1593u − 281)
c
10
(u
17
− 4u
16
+ ··· − 5u − 1)(u
40
− 3u
39
+ ··· + 77u + 49)
c
11
(u
17
+ 3u
16
+ ··· + u + 1)(u
40
− 4u
39
+ ··· + 159u + 39)
c
12
(u
17
+ u
16
+ ··· + u + 1)(u
40
+ 2u
39
+ ··· + 45u − 181)
16
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
17
− 13y
16
+ ··· + 561y −121)
· (y
40
− 22y
39
+ ··· − 215217y + 6561)
c
2
, c
9
(y
17
+ 12y
16
+ ··· + 19y −1)(y
40
+ 55y
39
+ ··· + 1314861y + 78961)
c
3
(y
17
+ 12y
16
+ ··· + 2y −1)
· (y
40
+ 35y
39
+ ··· + 25863122y + 2778889)
c
4
(y
17
− 13y
16
+ ··· + 3104y −361)(y
40
− 38y
39
+ ··· + 10176y + 49)
c
5
, c
12
(y
17
+ 9y
16
+ ··· + 11y −1)(y
40
+ 28y
39
+ ··· + 424773y + 32761)
c
6
(y
17
+ 11y
16
+ ··· + 72y −1)
· (y
40
+ 46y
39
+ ··· − 3212684616y + 106894921)
c
7
(y
17
− 22y
16
+ ··· + 1321y −121)(y
40
− 55y
39
+ ··· − 3745y + 49)
c
8
, c
11
(y
17
− 9y
16
+ ··· + 7y −1)(y
40
− 22y
39
+ ··· − 88383y + 1521)
c
10
(y
17
− 12y
16
+ ··· + 11y −1)(y
40
− 29y
39
+ ··· − 130291y + 2401)
17
