12a
0112
(K12a
0112
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 11 12 9 4 1 7 6 10
Solving Sequence
1,9 4,10
8 3 2 7 11 12 6 5
c
9
c
8
c
3
c
1
c
7
c
10
c
12
c
6
c
5
c
2
, c
4
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h6.90259 × 10
236
u
87
+ 8.88875 × 10
237
u
86
+ ··· + 2.40669 × 10
238
b − 4.89965 × 10
238
,
6.80069 × 10
238
u
87
+ 9.46673 × 10
239
u
86
+ ··· + 5.53539 × 10
239
a + 2.08834 × 10
241
,
u
88
+ 14u
87
+ ··· + 3387u + 207i
I
u
2
= hb, −u
4
− u
3
− 2u
2
+ a − u − 1, u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1i
* 2 irreducible components of dim
C
= 0, with total 93 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
= h6.90 × 10
236
u
87
+ 8.89 × 10
237
u
86
+ · · · + 2.41 × 10
238
b − 4.90 ×
10
238
, 6.80 × 10
238
u
87
+ 9.47 × 10
239
u
86
+ · · · + 5.54 × 10
239
a + 2.09 ×
10
241
, u
88
+ 14u
87
+ · · · + 3387u + 207i
(i) Arc colorings
a
1
=
0
u
a
9
=
1
0
a
4
=
−0.122858u
87
− 1.71022u
86
+ ··· − 627.195u − 37.7271
−0.0286808u
87
− 0.369335u
86
+ ··· + 21.4446u + 2.03584
a
10
=
1
u
2
a
8
=
−0.00171350u
87
− 0.0279250u
86
+ ··· − 36.0867u − 5.51864
−0.0374023u
87
− 0.488646u
86
+ ··· − 233.414u − 15.5951
a
3
=
−0.0424549u
87
− 0.597700u
86
+ ··· − 379.570u − 27.2479
−0.0311366u
87
− 0.382954u
86
+ ··· + 100.315u + 8.26440
a
2
=
0.0694474u
87
+ 0.975047u
86
+ ··· + 215.246u + 12.4910
0.0385643u
87
+ 0.496854u
86
+ ··· + 44.9227u + 3.00962
a
7
=
0.0356888u
87
+ 0.460721u
86
+ ··· + 197.327u + 10.0764
−0.0374023u
87
− 0.488646u
86
+ ··· − 233.414u − 15.5951
a
11
=
0.0269231u
87
+ 0.335328u
86
+ ··· + 210.971u + 21.3838
−0.0159512u
87
− 0.217071u
86
+ ··· + 26.5351u + 1.10107
a
12
=
u
u
3
+ u
a
6
=
0.0237817u
87
+ 0.326428u
86
+ ··· + 315.117u + 18.5023
−0.0404086u
87
− 0.542338u
86
+ ··· − 222.919u − 13.8773
a
5
=
−0.0753384u
87
− 1.01734u
86
+ ··· − 399.712u − 21.7576
0.00393597u
87
+ 0.0453448u
86
+ ··· − 0.284989u − 0.354695
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.114811u
87
− 1.49279u
86
+ ··· − 618.725u − 34.0945
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
88
+ 46u
87
+ ··· + 7u + 1
c
2
, c
4
u
88
− 6u
87
+ ··· + 7u − 1
c
3
, c
8
u
88
+ u
87
+ ··· − 32u + 32
c
5
, c
6
, c
11
u
88
− 2u
87
+ ··· + u − 1
c
7
u
88
− 33u
87
+ ··· − 18944u + 1024
c
9
, c
12
u
88
− 14u
87
+ ··· − 3387u + 207
c
10
u
88
+ 6u
87
+ ··· − 4287u − 1585
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
88
− 2y
87
+ ··· + 17y + 1
c
2
, c
4
y
88
− 46y
87
+ ··· − 7y + 1
c
3
, c
8
y
88
− 33y
87
+ ··· − 18944y + 1024
c
5
, c
6
, c
11
y
88
− 82y
87
+ ··· + 11y + 1
c
7
y
88
+ 35y
87
+ ··· + 3538944y + 1048576
c
9
, c
12
y
88
+ 66y
87
+ ··· + 2032911y + 42849
c
10
y
88
− 26y
87
+ ··· − 57768789y + 2512225
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.936529 + 0.286385I
a = 0.375503 − 0.818432I
b = 0.670197 − 0.599214I
1.58963 + 0.54596I 0
u = −0.936529 − 0.286385I
a = 0.375503 + 0.818432I
b = 0.670197 + 0.599214I
1.58963 − 0.54596I 0
u = −0.158558 + 0.953109I
a = 1.35923 − 1.66559I
b = −0.799038 − 0.483668I
−1.208240 − 0.072119I 0
u = −0.158558 − 0.953109I
a = 1.35923 + 1.66559I
b = −0.799038 + 0.483668I
−1.208240 + 0.072119I 0
u = 0.049688 + 1.038260I
a = 0.246699 − 0.518699I
b = 0.189654 − 0.798658I
1.25966 − 1.52143I 0
u = 0.049688 − 1.038260I
a = 0.246699 + 0.518699I
b = 0.189654 + 0.798658I
1.25966 + 1.52143I 0
u = 0.957572 + 0.048444I
a = 0.18518 + 1.65682I
b = 0.704859 + 0.769906I
−5.39754 − 1.29517I 0
u = 0.957572 − 0.048444I
a = 0.18518 − 1.65682I
b = 0.704859 − 0.769906I
−5.39754 + 1.29517I 0
u = 0.672618 + 0.682873I
a = −0.400811 + 0.253113I
b = −0.747825 + 0.045261I
−0.26439 − 2.42416I 0
u = 0.672618 − 0.682873I
a = −0.400811 − 0.253113I
b = −0.747825 − 0.045261I
−0.26439 + 2.42416I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.927890 + 0.197280I
a = −0.307178 + 1.192550I
b = −0.836277 + 0.577421I
−1.73101 − 2.30754I 0
u = 0.927890 − 0.197280I
a = −0.307178 − 1.192550I
b = −0.836277 − 0.577421I
−1.73101 + 2.30754I 0
u = −0.992970 + 0.408219I
a = 0.27813 − 1.71995I
b = −0.764304 − 0.705483I
−1.77414 + 1.70120I 0
u = −0.992970 − 0.408219I
a = 0.27813 + 1.71995I
b = −0.764304 + 0.705483I
−1.77414 − 1.70120I 0
u = −0.240044 + 1.046750I
a = −0.640277 + 0.623290I
b = −0.547854 + 0.938031I
−0.63655 + 2.43655I 0
u = −0.240044 − 1.046750I
a = −0.640277 − 0.623290I
b = −0.547854 − 0.938031I
−0.63655 − 2.43655I 0
u = −0.901912
a = 0.475848
b = 0.618625
1.84548 0
u = −0.999368 + 0.482478I
a = −0.385520 + 1.298070I
b = −0.681224 + 0.844671I
−1.59853 + 4.33517I 0
u = −0.999368 − 0.482478I
a = −0.385520 − 1.298070I
b = −0.681224 − 0.844671I
−1.59853 − 4.33517I 0
u = 1.107320 + 0.199270I
a = 0.60506 − 1.33234I
b = 0.985248 − 0.683709I
−4.52658 − 6.80550I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.107320 − 0.199270I
a = 0.60506 + 1.33234I
b = 0.985248 + 0.683709I
−4.52658 + 6.80550I 0
u = −0.979582 + 0.586031I
a = 0.004868 + 1.287640I
b = 0.928514 + 0.612301I
2.32070 + 5.36796I 0
u = −0.979582 − 0.586031I
a = 0.004868 − 1.287640I
b = 0.928514 − 0.612301I
2.32070 − 5.36796I 0
u = −1.122670 + 0.270465I
a = −0.800454 + 0.947773I
b = −0.935027 + 0.654173I
−1.23452 − 3.53072I 0
u = −1.122670 − 0.270465I
a = −0.800454 − 0.947773I
b = −0.935027 − 0.654173I
−1.23452 + 3.53072I 0
u = −0.532169 + 0.647609I
a = −1.117930 + 0.206729I
b = −0.928319 + 0.547493I
−0.68637 − 4.27140I 0
u = −0.532169 − 0.647609I
a = −1.117930 − 0.206729I
b = −0.928319 − 0.547493I
−0.68637 + 4.27140I 0
u = 0.049130 + 1.172290I
a = −0.77333 − 1.57633I
b = 1.142770 − 0.685681I
7.63686 − 5.93187I 0
u = 0.049130 − 1.172290I
a = −0.77333 + 1.57633I
b = 1.142770 + 0.685681I
7.63686 + 5.93187I 0
u = −0.097525 + 1.179330I
a = 0.526131 + 0.428629I
b = 0.502102 + 0.976980I
5.60936 + 0.10985I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.097525 − 1.179330I
a = 0.526131 − 0.428629I
b = 0.502102 − 0.976980I
5.60936 − 0.10985I 0
u = −0.271686 + 1.161130I
a = −0.66534 + 1.39246I
b = 1.092670 + 0.554601I
3.72025 + 3.22037I 0
u = −0.271686 − 1.161130I
a = −0.66534 − 1.39246I
b = 1.092670 − 0.554601I
3.72025 − 3.22037I 0
u = −0.178894 + 1.179540I
a = −1.51426 − 1.29003I
b = 0.862175 − 0.410472I
4.87067 + 2.63124I 0
u = −0.178894 − 1.179540I
a = −1.51426 + 1.29003I
b = 0.862175 + 0.410472I
4.87067 − 2.63124I 0
u = 0.345533 + 1.154470I
a = −0.219535 − 0.551957I
b = −0.324272 − 0.793372I
0.97891 − 2.18458I 0
u = 0.345533 − 1.154470I
a = −0.219535 + 0.551957I
b = −0.324272 + 0.793372I
0.97891 + 2.18458I 0
u = −0.618566 + 1.037550I
a = 0.280639 + 0.194471I
b = 0.760975 + 0.164149I
4.80573 + 5.40225I 0
u = −0.618566 − 1.037550I
a = 0.280639 − 0.194471I
b = 0.760975 − 0.164149I
4.80573 − 5.40225I 0
u = −0.383860 + 1.157030I
a = 0.47369 − 1.62147I
b = −1.114180 − 0.702529I
1.12733 + 8.44671I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.383860 − 1.157030I
a = 0.47369 + 1.62147I
b = −1.114180 + 0.702529I
1.12733 − 8.44671I 0
u = −0.021394 + 1.229940I
a = 0.87335 + 1.30563I
b = −1.134670 + 0.531246I
10.11390 − 0.59412I 0
u = −0.021394 − 1.229940I
a = 0.87335 − 1.30563I
b = −1.134670 − 0.531246I
10.11390 + 0.59412I 0
u = −1.104080 + 0.603800I
a = −0.27187 − 1.45375I
b = −1.021110 − 0.711171I
−0.53124 + 10.13980I 0
u = −1.104080 − 0.603800I
a = −0.27187 + 1.45375I
b = −1.021110 + 0.711171I
−0.53124 − 10.13980I 0
u = 0.679458 + 1.091510I
a = 0.670170 + 0.284575I
b = 0.843455 + 0.544076I
−1.84267 + 0.64548I 0
u = 0.679458 − 1.091510I
a = 0.670170 − 0.284575I
b = 0.843455 − 0.544076I
−1.84267 − 0.64548I 0
u = −0.237285 + 1.275700I
a = −0.223312 − 0.483493I
b = −0.181216 − 0.887325I
7.25991 + 4.32353I 0
u = −0.237285 − 1.275700I
a = −0.223312 + 0.483493I
b = −0.181216 + 0.887325I
7.25991 − 4.32353I 0
u = 0.456039 + 1.231780I
a = −1.04841 − 1.46067I
b = 0.864810 − 0.542688I
−1.77594 − 3.72393I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.456039 − 1.231780I
a = −1.04841 + 1.46067I
b = 0.864810 + 0.542688I
−1.77594 + 3.72393I 0
u = 0.022099 + 1.329330I
a = −0.686226 + 0.293109I
b = 1.221780 + 0.085487I
6.41930 + 0.59704I 0
u = 0.022099 − 1.329330I
a = −0.686226 − 0.293109I
b = 1.221780 − 0.085487I
6.41930 − 0.59704I 0
u = 0.157039 + 1.370650I
a = 0.658441 + 0.215863I
b = −1.225890 + 0.135801I
6.31625 − 4.73507I 0
u = 0.157039 − 1.370650I
a = 0.658441 − 0.215863I
b = −1.225890 − 0.135801I
6.31625 + 4.73507I 0
u = 0.465964 + 1.299550I
a = 0.468359 + 0.706801I
b = 0.590340 + 0.969623I
−1.23104 − 6.37786I 0
u = 0.465964 − 1.299550I
a = 0.468359 − 0.706801I
b = 0.590340 − 0.969623I
−1.23104 + 6.37786I 0
u = 0.44859 + 1.37548I
a = 0.573859 + 1.243100I
b = −1.099580 + 0.597714I
3.15715 − 7.30484I 0
u = 0.44859 − 1.37548I
a = 0.573859 − 1.243100I
b = −1.099580 − 0.597714I
3.15715 + 7.30484I 0
u = −0.15862 + 1.43810I
a = 0.756590 + 0.287532I
b = −1.257530 + 0.061097I
12.66800 + 2.43863I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.15862 − 1.43810I
a = 0.756590 − 0.287532I
b = −1.257530 − 0.061097I
12.66800 − 2.43863I 0
u = −0.547508
a = −3.18325
b = 0.650133
1.52279 9.62570
u = −0.094475 + 0.535440I
a = 0.347771 − 1.278000I
b = 1.033350 + 0.461461I
5.45652 + 5.74955I 8.27153 − 6.35837I
u = −0.094475 − 0.535440I
a = 0.347771 + 1.278000I
b = 1.033350 − 0.461461I
5.45652 − 5.74955I 8.27153 + 6.35837I
u = −0.40315 + 1.41421I
a = 0.190985 − 0.550246I
b = 0.348570 − 0.863292I
6.81786 + 5.34505I 0
u = −0.40315 − 1.41421I
a = 0.190985 + 0.550246I
b = 0.348570 + 0.863292I
6.81786 − 5.34505I 0
u = 0.52142 + 1.40786I
a = −0.41170 − 1.42636I
b = 1.117850 − 0.729506I
0.43903 − 12.59080I 0
u = 0.52142 − 1.40786I
a = −0.41170 + 1.42636I
b = 1.117850 + 0.729506I
0.43903 + 12.59080I 0
u = −0.62249 + 1.37484I
a = −0.533773 + 0.267110I
b = −0.794629 + 0.526308I
3.66078 + 2.71789I 0
u = −0.62249 − 1.37484I
a = −0.533773 − 0.267110I
b = −0.794629 − 0.526308I
3.66078 − 2.71789I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.452328 + 0.182517I
a = −0.775066 + 0.069599I
b = 0.182906 − 0.784119I
2.76640 + 1.62363I 5.37285 − 3.69344I
u = −0.452328 − 0.182517I
a = −0.775066 − 0.069599I
b = 0.182906 + 0.784119I
2.76640 − 1.62363I 5.37285 + 3.69344I
u = −0.23658 + 1.50088I
a = −0.697005 + 0.179142I
b = 1.259650 + 0.155114I
12.4798 + 7.9130I 0
u = −0.23658 − 1.50088I
a = −0.697005 − 0.179142I
b = 1.259650 − 0.155114I
12.4798 − 7.9130I 0
u = −0.398905 + 0.257394I
a = 1.275610 + 0.173707I
b = 0.796240 − 0.210293I
1.231150 − 0.339540I 8.48317 + 1.18283I
u = −0.398905 − 0.257394I
a = 1.275610 − 0.173707I
b = 0.796240 + 0.210293I
1.231150 + 0.339540I 8.48317 − 1.18283I
u = −0.45854 + 1.47063I
a = 1.03639 − 1.31302I
b = −0.907266 − 0.539160I
4.03499 + 7.02654I 0
u = −0.45854 − 1.47063I
a = 1.03639 + 1.31302I
b = −0.907266 + 0.539160I
4.03499 − 7.02654I 0
u = −0.45869 + 1.51594I
a = −0.391021 + 0.671604I
b = −0.594978 + 0.999319I
4.62335 + 9.74269I 0
u = −0.45869 − 1.51594I
a = −0.391021 − 0.671604I
b = −0.594978 − 0.999319I
4.62335 − 9.74269I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.43792 + 1.56540I
a = −0.592932 + 1.155750I
b = 1.121840 + 0.613720I
9.08319 + 10.71720I 0
u = −0.43792 − 1.56540I
a = −0.592932 − 1.155750I
b = 1.121840 − 0.613720I
9.08319 − 10.71720I 0
u = −0.48396 + 1.59795I
a = 0.448307 − 1.330000I
b = −1.130750 − 0.741204I
6.3330 + 16.0842I 0
u = −0.48396 − 1.59795I
a = 0.448307 + 1.330000I
b = −1.130750 + 0.741204I
6.3330 − 16.0842I 0
u = −0.148251 + 0.239950I
a = 1.71349 + 3.10527I
b = −1.043500 − 0.215301I
6.92468 + 1.07292I 11.82072 − 0.64085I
u = −0.148251 − 0.239950I
a = 1.71349 − 3.10527I
b = −1.043500 + 0.215301I
6.92468 − 1.07292I 11.82072 + 0.64085I
u = 0.093432 + 0.176931I
a = 3.34527 − 2.60951I
b = −0.284902 − 0.457886I
−1.69196 − 0.57556I −4.55877 − 0.73024I
u = 0.093432 − 0.176931I
a = 3.34527 + 2.60951I
b = −0.284902 + 0.457886I
−1.69196 + 0.57556I −4.55877 + 0.73024I
13
II. I
u
2
= hb, −u
4
− u
3
− 2u
2
+ a − u − 1, u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1i
(i) Arc colorings
a
1
=
0
u
a
9
=
1
0
a
4
=
u
4
+ u
3
+ 2u
2
+ u + 1
0
a
10
=
1
u
2
a
8
=
1
0
a
3
=
u
4
+ u
3
+ 2u
2
+ u + 1
0
a
2
=
u
4
+ u
3
+ 2u
2
+ u + 1
u
a
7
=
1
0
a
11
=
u
2
+ 1
u
2
a
12
=
u
u
3
+ u
a
6
=
u
4
+ u
2
+ 1
u
4
+ u
3
+ u
2
+ 1
a
5
=
0
−u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −u
4
+ 4u
3
+ 2u
2
+ 5u + 2
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
5
c
3
, c
7
, c
8
u
5
c
4
(u + 1)
5
c
5
, c
6
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
c
9
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1
c
10
u
5
− 3u
4
+ 4u
3
− u
2
− u + 1
c
11
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
c
12
u
5
− u
4
+ 2u
3
− u
2
+ u − 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
5
c
3
, c
7
, c
8
y
5
c
5
, c
6
, c
11
y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1
c
9
, c
12
y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1
c
10
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.339110 + 0.822375I
a = −0.428550 + 1.039280I
b = 0
−1.31583 − 1.53058I −0.02714 + 4.76366I
u = 0.339110 − 0.822375I
a = −0.428550 − 1.039280I
b = 0
−1.31583 + 1.53058I −0.02714 − 4.76366I
u = −0.766826
a = 1.30408
b = 0
0.756147 −2.80750
u = −0.455697 + 1.200150I
a = 0.276511 + 0.728237I
b = 0
4.22763 + 4.40083I 4.43089 − 2.80751I
u = −0.455697 − 1.200150I
a = 0.276511 − 0.728237I
b = 0
4.22763 − 4.40083I 4.43089 + 2.80751I
17
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
5
)(u
88
+ 46u
87
+ ··· + 7u + 1)
c
2
((u − 1)
5
)(u
88
− 6u
87
+ ··· + 7u − 1)
c
3
, c
8
u
5
(u
88
+ u
87
+ ··· − 32u + 32)
c
4
((u + 1)
5
)(u
88
− 6u
87
+ ··· + 7u − 1)
c
5
, c
6
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)(u
88
− 2u
87
+ ··· + u − 1)
c
7
u
5
(u
88
− 33u
87
+ ··· − 18944u + 1024)
c
9
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)(u
88
− 14u
87
+ ··· − 3387u + 207)
c
10
(u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)(u
88
+ 6u
87
+ ··· − 4287u − 1585)
c
11
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)(u
88
− 2u
87
+ ··· + u − 1)
c
12
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)(u
88
− 14u
87
+ ··· − 3387u + 207)
18
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
5
)(y
88
− 2y
87
+ ··· + 17y + 1)
c
2
, c
4
((y −1)
5
)(y
88
− 46y
87
+ ··· − 7y + 1)
c
3
, c
8
y
5
(y
88
− 33y
87
+ ··· − 18944y + 1024)
c
5
, c
6
, c
11
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)(y
88
− 82y
87
+ ··· + 11y + 1)
c
7
y
5
(y
88
+ 35y
87
+ ··· + 3538944y + 1048576)
c
9
, c
12
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)(y
88
+ 66y
87
+ ··· + 2032911y + 42849)
c
10
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
· (y
88
− 26y
87
+ ··· − 57768789y + 2512225)
19
