12a
0599
(K12a
0599
)
A knot diagram
1
Linearized knot diagam
3 7 9 11 12 2 10 1 6 8 5 4
Solving Sequence
4,11
5 12 6
1,9
3 2 8 10 7
c
4
c
11
c
5
c
12
c
3
c
1
c
8
c
10
c
7
c
2
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−6.18140 × 10
106
u
103
− 1.68839 × 10
107
u
102
+ ··· + 8.40136 × 10
106
b − 8.56625 × 10
106
,
1.80765 × 10
105
u
103
+ 2.28944 × 10
105
u
102
+ ··· + 1.68027 × 10
106
a − 7.57112 × 10
105
, u
104
+ 3u
103
+ ··· + 2u + 1i
* 1 irreducible components of dim
C
= 0, with total 104 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−6.18 × 10
106
u
103
− 1.69 × 10
107
u
102
+ · · · + 8.40 × 10
106
b − 8.57 ×
10
106
, 1.81 × 10
105
u
103
+ 2.29 × 10
105
u
102
+ · · · + 1.68 × 10
106
a − 7.57 ×
10
105
, u
104
+ 3u
103
+ · · · + 2u + 1i
(i) Arc colorings
a
4
=
1
0
a
11
=
0
u
a
5
=
1
−u
2
a
12
=
u
−u
3
+ u
a
6
=
−u
2
+ 1
u
4
− 2u
2
a
1
=
−u
3
+ 2u
−u
3
+ u
a
9
=
−0.107581u
103
− 0.136254u
102
+ ··· + 5.30403u + 0.450589
0.735762u
103
+ 2.00966u
102
+ ··· + 2.25110u + 1.01963
a
3
=
0.540322u
103
+ 0.963064u
102
+ ··· − 4.53621u − 0.0896284
−0.874844u
103
− 2.38227u
102
+ ··· − 2.60814u − 2.37733
a
2
=
1.88927u
103
+ 5.89937u
102
+ ··· − 0.482302u + 0.853416
1.41968u
103
+ 4.11081u
102
+ ··· + 1.60811u + 0.823482
a
8
=
−0.340032u
103
− 0.0211301u
102
+ ··· + 4.20707u − 1.59516
2.19574u
103
+ 4.81322u
102
+ ··· + 3.24526u + 1.19118
a
10
=
0.540859u
103
+ 2.31345u
102
+ ··· + 5.26158u − 0.675638
2.57621u
103
+ 6.00112u
102
+ ··· + 4.56913u + 1.82368
a
7
=
−2.37733u
103
− 6.25714u
102
+ ··· − 0.753556u − 2.14652
−0.657904u
103
− 2.25986u
102
+ ··· − 1.17027u − 0.540322
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.01554u
103
+ 4.88122u
102
+ ··· − 15.4275u + 5.37327
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
104
+ 39u
103
+ ··· + 4u + 1
c
2
, c
6
u
104
− 3u
103
+ ··· − 4u + 1
c
3
u
104
− u
103
+ ··· − 22u − 1
c
4
, c
5
, c
11
u
104
− 3u
103
+ ··· − 2u + 1
c
7
, c
10
u
104
+ u
103
+ ··· + 34u − 1
c
8
u
104
+ 43u
103
+ ··· + 121854u + 32269
c
9
u
104
+ 5u
103
+ ··· − 325970u + 195737
c
12
u
104
+ 9u
103
+ ··· − 5770u − 725
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
104
+ 53y
103
+ ··· + 28y + 1
c
2
, c
6
y
104
− 39y
103
+ ··· − 4y + 1
c
3
y
104
− 3y
103
+ ··· − 100y + 1
c
4
, c
5
, c
11
y
104
− 91y
103
+ ··· − 4y + 1
c
7
, c
10
y
104
− 71y
103
+ ··· + 844y + 1
c
8
y
104
− 575y
103
+ ··· − 55858036808y + 1041288361
c
9
y
104
+ 501y
103
+ ··· − 1559554340176y + 38312973169
c
12
y
104
+ 17y
103
+ ··· + 2768600y + 525625
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.989526 + 0.131041I
a = 0.883619 − 0.264649I
b = 0.740437 − 1.108110I
−0.14536 − 4.59513I 0
u = 0.989526 − 0.131041I
a = 0.883619 + 0.264649I
b = 0.740437 + 1.108110I
−0.14536 + 4.59513I 0
u = −0.846433 + 0.492394I
a = 0.824251 + 0.236983I
b = 0.921699 + 0.805391I
5.21407 + 3.81898I 0
u = −0.846433 − 0.492394I
a = 0.824251 − 0.236983I
b = 0.921699 − 0.805391I
5.21407 − 3.81898I 0
u = 0.846368 + 0.470568I
a = −0.896666 + 0.390579I
b = −0.970228 + 1.015240I
3.57729 − 9.85375I 0
u = 0.846368 − 0.470568I
a = −0.896666 − 0.390579I
b = −0.970228 − 1.015240I
3.57729 + 9.85375I 0
u = −0.345479 + 0.873329I
a = −0.329641 + 0.633256I
b = −0.515483 + 0.318246I
2.33648 − 3.25638I 0
u = −0.345479 − 0.873329I
a = −0.329641 − 0.633256I
b = −0.515483 − 0.318246I
2.33648 + 3.25638I 0
u = 0.168045 + 0.918321I
a = 0.681538 − 0.436064I
b = 0.399562 − 0.441746I
0.23249 − 3.75946I 0
u = 0.168045 − 0.918321I
a = 0.681538 + 0.436064I
b = 0.399562 + 0.441746I
0.23249 + 3.75946I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.038150 + 0.281331I
a = 0.574175 − 0.696383I
b = 0.171610 − 1.125820I
−3.13606 + 2.08755I 0
u = 1.038150 − 0.281331I
a = 0.574175 + 0.696383I
b = 0.171610 + 1.125820I
−3.13606 − 2.08755I 0
u = −1.088660 + 0.148356I
a = −0.569342 − 0.242387I
b = −0.601460 − 0.855575I
1.47163 − 0.22582I 0
u = −1.088660 − 0.148356I
a = −0.569342 + 0.242387I
b = −0.601460 + 0.855575I
1.47163 + 0.22582I 0
u = 1.021500 + 0.461685I
a = −0.132237 − 0.773987I
b = −0.637551 − 0.715827I
2.90669 + 8.60744I 0
u = 1.021500 − 0.461685I
a = −0.132237 + 0.773987I
b = −0.637551 + 0.715827I
2.90669 − 8.60744I 0
u = 0.714848 + 0.496575I
a = −0.391758 + 0.307832I
b = −0.268115 + 0.809910I
−2.18985 − 2.17775I 0
u = 0.714848 − 0.496575I
a = −0.391758 − 0.307832I
b = −0.268115 − 0.809910I
−2.18985 + 2.17775I 0
u = −0.277989 + 0.805746I
a = −0.43532 + 2.02951I
b = −1.04109 + 0.98300I
3.40888 − 8.39494I 0
u = −0.277989 − 0.805746I
a = −0.43532 − 2.02951I
b = −1.04109 − 0.98300I
3.40888 + 8.39494I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.271419 + 0.800534I
a = 0.32107 + 2.33269I
b = 1.07449 + 1.16223I
1.7395 + 14.3608I 6.00000 − 9.55805I
u = 0.271419 − 0.800534I
a = 0.32107 − 2.33269I
b = 1.07449 − 1.16223I
1.7395 − 14.3608I 6.00000 + 9.55805I
u = 0.301715 + 0.780914I
a = −0.25793 + 1.53795I
b = 0.565053 + 0.968257I
−3.64893 + 6.60879I 0. − 7.74517I
u = 0.301715 − 0.780914I
a = −0.25793 − 1.53795I
b = 0.565053 − 0.968257I
−3.64893 − 6.60879I 0. + 7.74517I
u = −1.048700 + 0.562138I
a = 0.176179 − 0.398546I
b = 0.471374 − 0.301344I
4.38851 − 2.18462I 0
u = −1.048700 − 0.562138I
a = 0.176179 + 0.398546I
b = 0.471374 + 0.301344I
4.38851 + 2.18462I 0
u = 0.162530 + 0.740437I
a = 0.17843 − 2.11043I
b = −0.437804 − 1.169340I
−5.77665 + 1.73251I −2.33025 − 1.80037I
u = 0.162530 − 0.740437I
a = 0.17843 + 2.11043I
b = −0.437804 + 1.169340I
−5.77665 − 1.73251I −2.33025 + 1.80037I
u = −1.248350 + 0.112459I
a = 0.226760 + 0.106758I
b = −0.791191 − 0.335299I
2.16662 − 0.42827I 0
u = −1.248350 − 0.112459I
a = 0.226760 − 0.106758I
b = −0.791191 + 0.335299I
2.16662 + 0.42827I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.201135 + 0.708814I
a = −0.65799 − 2.69199I
b = −1.17052 − 1.32325I
−2.39932 + 8.07353I 2.96084 − 8.86760I
u = 0.201135 − 0.708814I
a = −0.65799 + 2.69199I
b = −1.17052 + 1.32325I
−2.39932 − 8.07353I 2.96084 + 8.86760I
u = −0.186873 + 0.690936I
a = 0.77808 − 2.16675I
b = 1.12913 − 0.94113I
−1.00539 − 3.04538I 5.02927 + 4.37384I
u = −0.186873 − 0.690936I
a = 0.77808 + 2.16675I
b = 1.12913 + 0.94113I
−1.00539 + 3.04538I 5.02927 − 4.37384I
u = −1.280030 + 0.182164I
a = 2.30865 − 1.83870I
b = −0.533197 − 0.041483I
4.29134 − 4.85987I 0
u = −1.280030 − 0.182164I
a = 2.30865 + 1.83870I
b = −0.533197 + 0.041483I
4.29134 + 4.85987I 0
u = 1.308150 + 0.207596I
a = −12.4273 + 8.9998I
b = 0.0918274 + 0.0787198I
4.66635 + 0.78468I 0
u = 1.308150 − 0.207596I
a = −12.4273 − 8.9998I
b = 0.0918274 − 0.0787198I
4.66635 − 0.78468I 0
u = 1.320460 + 0.153660I
a = −1.46352 + 0.79473I
b = 0.811793 + 0.351138I
5.21559 + 1.16431I 0
u = 1.320460 − 0.153660I
a = −1.46352 − 0.79473I
b = 0.811793 − 0.351138I
5.21559 − 1.16431I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.310210 + 0.236069I
a = −0.157080 − 1.091820I
b = 0.160988 − 0.095874I
3.04010 − 0.83758I 0
u = −1.310210 − 0.236069I
a = −0.157080 + 1.091820I
b = 0.160988 + 0.095874I
3.04010 + 0.83758I 0
u = −1.343800 + 0.078810I
a = 0.382497 + 1.052170I
b = −1.57134 − 0.37622I
5.39810 + 4.39371I 0
u = −1.343800 − 0.078810I
a = 0.382497 − 1.052170I
b = −1.57134 + 0.37622I
5.39810 − 4.39371I 0
u = 1.342890 + 0.103976I
a = −0.658717 + 1.060560I
b = 1.54649 + 0.00805I
6.33561 + 0.56533I 0
u = 1.342890 − 0.103976I
a = −0.658717 − 1.060560I
b = 1.54649 − 0.00805I
6.33561 − 0.56533I 0
u = 1.338520 + 0.257583I
a = 0.74243 − 1.24808I
b = −0.711072 − 0.202051I
3.75246 + 5.21120I 0
u = 1.338520 − 0.257583I
a = 0.74243 + 1.24808I
b = −0.711072 + 0.202051I
3.75246 − 5.21120I 0
u = 1.345000 + 0.244038I
a = 1.001560 − 0.942439I
b = −0.814953 + 0.094462I
3.81873 + 5.22294I 0
u = 1.345000 − 0.244038I
a = 1.001560 + 0.942439I
b = −0.814953 − 0.094462I
3.81873 − 5.22294I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.353180 + 0.207483I
a = 0.161585 + 0.980965I
b = 0.347548 + 0.906497I
6.06988 − 3.47205I 0
u = −1.353180 − 0.207483I
a = 0.161585 − 0.980965I
b = 0.347548 − 0.906497I
6.06988 + 3.47205I 0
u = −0.103587 + 0.622209I
a = 0.287222 − 1.328960I
b = 0.475281 − 0.083983I
−0.80872 − 1.97143I 3.33449 + 4.65511I
u = −0.103587 − 0.622209I
a = 0.287222 + 1.328960I
b = 0.475281 + 0.083983I
−0.80872 + 1.97143I 3.33449 − 4.65511I
u = −0.142575 + 0.614426I
a = 0.280636 − 0.888346I
b = 0.811142 − 0.030751I
−0.87795 − 2.08035I 2.20405 + 5.01346I
u = −0.142575 − 0.614426I
a = 0.280636 + 0.888346I
b = 0.811142 + 0.030751I
−0.87795 + 2.08035I 2.20405 − 5.01346I
u = 0.621086 + 0.084207I
a = 0.373074 − 0.207627I
b = 0.760421 + 0.785124I
−0.13085 + 4.71370I 6.12729 − 5.66701I
u = 0.621086 − 0.084207I
a = 0.373074 + 0.207627I
b = 0.760421 − 0.785124I
−0.13085 − 4.71370I 6.12729 + 5.66701I
u = −0.241643 + 0.573906I
a = 2.38786 + 0.68773I
b = 1.52226 + 0.87466I
2.66071 − 5.66668I 8.90037 + 9.71585I
u = −0.241643 − 0.573906I
a = 2.38786 − 0.68773I
b = 1.52226 − 0.87466I
2.66071 + 5.66668I 8.90037 − 9.71585I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.376580 + 0.166688I
a = −1.39265 + 1.24070I
b = 0.99625 + 1.78378I
8.70992 − 0.92166I 0
u = 1.376580 − 0.166688I
a = −1.39265 − 1.24070I
b = 0.99625 − 1.78378I
8.70992 + 0.92166I 0
u = −1.378030 + 0.177745I
a = 1.41515 + 1.05782I
b = −0.55253 + 1.95449I
8.91266 − 4.20677I 0
u = −1.378030 − 0.177745I
a = 1.41515 − 1.05782I
b = −0.55253 − 1.95449I
8.91266 + 4.20677I 0
u = −1.357880 + 0.299840I
a = −1.12463 − 1.04934I
b = 0.614318 − 1.177360I
−0.97490 − 5.49155I 0
u = −1.357880 − 0.299840I
a = −1.12463 + 1.04934I
b = 0.614318 + 1.177360I
−0.97490 + 5.49155I 0
u = 0.264003 + 0.545428I
a = −0.773141 − 0.191095I
b = −0.147180 + 0.538599I
−1.60451 − 1.80811I 0.324463 − 0.433644I
u = 0.264003 − 0.545428I
a = −0.773141 + 0.191095I
b = −0.147180 − 0.538599I
−1.60451 + 1.80811I 0.324463 + 0.433644I
u = 1.370800 + 0.278221I
a = 0.91185 − 1.51022I
b = −1.39185 − 1.01737I
3.93475 + 6.56935I 0
u = 1.370800 − 0.278221I
a = 0.91185 + 1.51022I
b = −1.39185 + 1.01737I
3.93475 − 6.56935I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.381400 + 0.222297I
a = 0.824612 − 0.474541I
b = 1.46910 + 1.43358I
8.29547 − 3.50526I 0
u = −1.381400 − 0.222297I
a = 0.824612 + 0.474541I
b = 1.46910 − 1.43358I
8.29547 + 3.50526I 0
u = 1.383110 + 0.231040I
a = −0.666482 − 0.888282I
b = −1.83700 + 1.13231I
7.81652 + 8.64316I 0
u = 1.383110 − 0.231040I
a = −0.666482 + 0.888282I
b = −1.83700 − 1.13231I
7.81652 − 8.64316I 0
u = −0.031347 + 0.595167I
a = −6.20853 − 6.78983I
b = 0.207524 − 0.127759I
0.49697 + 2.09340I 27.5744 + 57.2719I
u = −0.031347 − 0.595167I
a = −6.20853 + 6.78983I
b = 0.207524 + 0.127759I
0.49697 − 2.09340I 27.5744 − 57.2719I
u = 0.242443 + 0.543233I
a = −2.10102 + 1.43682I
b = −1.17748 + 1.11016I
3.14800 + 0.65168I 10.52306 − 3.36761I
u = 0.242443 − 0.543233I
a = −2.10102 − 1.43682I
b = −1.17748 − 1.11016I
3.14800 − 0.65168I 10.52306 + 3.36761I
u = −1.376820 + 0.285343I
a = −1.15345 − 1.60765I
b = 1.39674 − 1.41467I
2.60570 − 11.68300I 0
u = −1.376820 − 0.285343I
a = −1.15345 + 1.60765I
b = 1.39674 + 1.41467I
2.60570 + 11.68300I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.41904 + 0.32371I
a = 1.07007 + 1.52516I
b = −1.17872 + 1.21776I
7.1225 − 18.4287I 0
u = −1.41904 − 0.32371I
a = 1.07007 − 1.52516I
b = −1.17872 − 1.21776I
7.1225 + 18.4287I 0
u = 1.42240 + 0.32497I
a = −0.87371 + 1.42713I
b = 1.16421 + 1.04993I
8.8252 + 12.4850I 0
u = 1.42240 − 0.32497I
a = −0.87371 − 1.42713I
b = 1.16421 − 1.04993I
8.8252 − 12.4850I 0
u = −1.42942 + 0.31413I
a = 0.967730 + 0.879064I
b = −0.751390 + 0.981643I
1.87186 − 10.58530I 0
u = −1.42942 − 0.31413I
a = 0.967730 − 0.879064I
b = −0.751390 − 0.981643I
1.87186 + 10.58530I 0
u = 1.44617 + 0.33353I
a = −0.315245 + 0.785569I
b = 0.809528 + 0.474654I
8.03571 + 7.55819I 0
u = 1.44617 − 0.33353I
a = −0.315245 − 0.785569I
b = 0.809528 − 0.474654I
8.03571 − 7.55819I 0
u = 0.129827 + 0.487589I
a = 0.25714 + 2.36854I
b = −0.368575 + 0.570292I
1.33150 + 0.83954I 4.54914 + 0.82518I
u = 0.129827 − 0.487589I
a = 0.25714 − 2.36854I
b = −0.368575 − 0.570292I
1.33150 − 0.83954I 4.54914 − 0.82518I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.50071 + 0.02299I
a = −0.394330 − 0.207023I
b = 1.157920 + 0.717227I
11.3902 + 8.8099I 0
u = −1.50071 − 0.02299I
a = −0.394330 + 0.207023I
b = 1.157920 − 0.717227I
11.3902 − 8.8099I 0
u = 1.50978 + 0.01787I
a = 0.369926 − 0.133517I
b = −1.156850 + 0.453893I
13.17090 − 2.70458I 0
u = 1.50978 − 0.01787I
a = 0.369926 + 0.133517I
b = −1.156850 − 0.453893I
13.17090 + 2.70458I 0
u = 0.302753 + 0.373014I
a = −1.08166 + 3.47219I
b = 0.443702 + 1.333090I
3.69173 + 2.02129I 11.76908 − 5.97446I
u = 0.302753 − 0.373014I
a = −1.08166 − 3.47219I
b = 0.443702 − 1.333090I
3.69173 − 2.02129I 11.76908 + 5.97446I
u = −0.337844 + 0.323246I
a = 0.77129 + 3.39601I
b = −0.824085 + 1.122500I
3.45433 + 2.90974I 11.59556 − 0.92056I
u = −0.337844 − 0.323246I
a = 0.77129 − 3.39601I
b = −0.824085 − 1.122500I
3.45433 − 2.90974I 11.59556 + 0.92056I
u = −0.460462 + 0.007635I
a = 0.126962 + 0.726061I
b = −0.808530 − 0.289273I
1.167780 + 0.139175I 10.38139 − 0.59279I
u = −0.460462 − 0.007635I
a = 0.126962 − 0.726061I
b = −0.808530 + 0.289273I
1.167780 − 0.139175I 10.38139 + 0.59279I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.49255 + 0.37784I
a = 0.002911 + 0.308059I
b = −0.431301 + 0.112831I
5.52489 − 1.27377I 0
u = −1.49255 − 0.37784I
a = 0.002911 − 0.308059I
b = −0.431301 − 0.112831I
5.52489 + 1.27377I 0
u = −1.59052
a = −0.115804
b = 0.474770
5.77568 0
u = −0.321853
a = 1.46602
b = −0.616577
0.922749 11.9180
15
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
104
+ 39u
103
+ ··· + 4u + 1
c
2
, c
6
u
104
− 3u
103
+ ··· − 4u + 1
c
3
u
104
− u
103
+ ··· − 22u − 1
c
4
, c
5
, c
11
u
104
− 3u
103
+ ··· − 2u + 1
c
7
, c
10
u
104
+ u
103
+ ··· + 34u − 1
c
8
u
104
+ 43u
103
+ ··· + 121854u + 32269
c
9
u
104
+ 5u
103
+ ··· − 325970u + 195737
c
12
u
104
+ 9u
103
+ ··· − 5770u − 725
16
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
104
+ 53y
103
+ ··· + 28y + 1
c
2
, c
6
y
104
− 39y
103
+ ··· − 4y + 1
c
3
y
104
− 3y
103
+ ··· − 100y + 1
c
4
, c
5
, c
11
y
104
− 91y
103
+ ··· − 4y + 1
c
7
, c
10
y
104
− 71y
103
+ ··· + 844y + 1
c
8
y
104
− 575y
103
+ ··· − 55858036808y + 1041288361
c
9
y
104
+ 501y
103
+ ··· − 1559554340176y + 38312973169
c
12
y
104
+ 17y
103
+ ··· + 2768600y + 525625
17
