12a
0753
(K12a
0753
)
A knot diagram
1
Linearized knot diagam
3 8 10 9 12 11 2 1 4 7 6 5
Solving Sequence
5,9
4 10
1,3
8 2 7 12 6 11
c
4
c
9
c
3
c
8
c
2
c
7
c
12
c
5
c
11
c
1
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h3.47678 × 10
21
u
49
− 1.33799 × 10
21
u
48
+ ··· + 1.34820 × 10
22
b − 3.88891 × 10
22
,
2.21158 × 10
21
u
49
− 1.62283 × 10
21
u
48
+ ··· + 1.34820 × 10
22
a − 4.79098 × 10
22
, u
50
− u
49
+ ··· − 4u + 4i
I
u
2
= hb
2
− bu + 1, a
2
+ a + 1, u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 58 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
= h3.48 × 10
21
u
49
− 1.34 × 10
21
u
48
+ · · · + 1.35 × 10
22
b − 3.89 × 10
22
, 2.21 ×
10
21
u
49
−1.62×10
21
u
48
+· · ·+1.35×10
22
a−4.79×10
22
, u
50
−u
49
+· · ·−4u+4i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
10
=
u
u
3
+ u
a
1
=
−0.164040u
49
+ 0.120370u
48
+ ··· + 8.84293u + 3.55361
−0.257882u
49
+ 0.0992428u
48
+ ··· + 2.87776u + 2.88452
a
3
=
u
2
+ 1
u
4
+ 2u
2
a
8
=
0.570562u
49
− 0.676764u
48
+ ··· − 8.50993u − 2.63929
0.00372260u
49
+ 0.222580u
48
+ ··· − 6.74010u − 1.68097
a
2
=
0.137529u
49
− 0.0400013u
48
+ ··· + 4.53679u + 1.15498
−0.233430u
49
+ 0.0703666u
48
+ ··· + 1.46685u + 2.29315
a
7
=
0.836099u
49
− 0.448168u
48
+ ··· − 24.1572u − 6.13765
−0.144284u
49
+ 0.0267194u
48
+ ··· − 0.748206u − 1.92710
a
12
=
0.0938429u
49
+ 0.0211270u
48
+ ··· + 5.96518u + 0.669092
−0.257882u
49
+ 0.0992428u
48
+ ··· + 2.87776u + 2.88452
a
6
=
0.122630u
49
− 0.215276u
48
+ ··· − 0.518300u − 8.94249
0.297613u
49
− 0.201245u
48
+ ··· − 3.06461u + 0.521412
a
11
=
−0.0377076u
49
− 0.204943u
48
+ ··· − 5.37290u − 2.05267
−0.215869u
49
+ 0.420688u
48
+ ··· + 7.63220u + 1.46112
(ii) Obstruction class = −1
(iii) Cusp Shapes =
6041655765283033164853
3370503149641393660032
u
49
−
2696370501616779290413
1685251574820696830016
u
48
+ ··· −
15380340131345433270079
421312893705174207504
u −
15926907601216017826235
842625787410348415008
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
50
+ 27u
49
+ ··· + 131u + 25
c
2
, c
7
u
50
+ u
49
+ ··· + u + 5
c
3
, c
4
, c
9
u
50
+ u
49
+ ··· + 4u + 4
c
5
, c
6
, c
10
c
11
, c
12
u
50
− u
49
+ ··· + 9u + 1
c
8
u
50
+ 3u
49
+ ··· + 519u + 345
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
50
− 3y
49
+ ··· + 89y + 625
c
2
, c
7
y
50
− 27y
49
+ ··· − 131y + 25
c
3
, c
4
, c
9
y
50
+ 53y
49
+ ··· − 8y + 16
c
5
, c
6
, c
10
c
11
, c
12
y
50
+ 69y
49
+ ··· − 39y + 1
c
8
y
50
+ 33y
49
+ ··· − 1916391y + 119025
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.825284 + 0.564850I
a = 1.018290 − 0.857226I
b = 0.03252 − 1.72373I
−12.07120 − 2.72832I 1.32353 + 2.43193I
u = −0.825284 − 0.564850I
a = 1.018290 + 0.857226I
b = 0.03252 + 1.72373I
−12.07120 + 2.72832I 1.32353 − 2.43193I
u = −0.084210 + 1.043320I
a = −0.384445 − 0.811272I
b = −0.178045 + 0.054788I
−1.54403 − 2.06175I 7.89718 + 4.27454I
u = −0.084210 − 1.043320I
a = −0.384445 + 0.811272I
b = −0.178045 − 0.054788I
−1.54403 + 2.06175I 7.89718 − 4.27454I
u = −0.650825 + 0.686901I
a = −0.574983 + 0.899543I
b = −0.001959 + 1.082170I
−5.77062 + 1.33212I −3.10818 − 0.66099I
u = −0.650825 − 0.686901I
a = −0.574983 − 0.899543I
b = −0.001959 − 1.082170I
−5.77062 − 1.33212I −3.10818 + 0.66099I
u = −0.798083 + 0.491554I
a = −1.12468 + 0.88964I
b = −0.227660 + 1.067050I
−5.13290 − 6.35349I −1.14202 + 7.17760I
u = −0.798083 − 0.491554I
a = −1.12468 − 0.88964I
b = −0.227660 − 1.067050I
−5.13290 + 6.35349I −1.14202 − 7.17760I
u = 0.267440 + 1.044800I
a = −0.170870 + 0.254106I
b = −0.227134 + 0.746761I
−3.70325 + 0.50512I −4.05141 + 0.I
u = 0.267440 − 1.044800I
a = −0.170870 − 0.254106I
b = −0.227134 − 0.746761I
−3.70325 − 0.50512I −4.05141 + 0.I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.981288 + 0.514013I
a = −0.96413 − 1.07465I
b = −0.05777 − 1.74519I
−15.2476 + 7.5356I 0
u = 0.981288 − 0.514013I
a = −0.96413 + 1.07465I
b = −0.05777 + 1.74519I
−15.2476 − 7.5356I 0
u = 0.872961 + 0.773969I
a = −0.729263 − 0.828003I
b = 0.00151 − 1.74975I
−16.0293 − 1.3459I 0
u = 0.872961 − 0.773969I
a = −0.729263 + 0.828003I
b = 0.00151 + 1.74975I
−16.0293 + 1.3459I 0
u = −0.233208 + 1.157960I
a = 0.103022 − 0.205335I
b = −0.06216 − 1.60924I
−11.81320 + 0.61087I 0
u = −0.233208 − 1.157960I
a = 0.103022 + 0.205335I
b = −0.06216 + 1.60924I
−11.81320 − 0.61087I 0
u = 0.626871 + 0.455302I
a = 1.027610 + 0.620239I
b = 0.151543 + 0.964779I
−2.39825 + 2.03419I 2.27060 − 4.05066I
u = 0.626871 − 0.455302I
a = 1.027610 − 0.620239I
b = 0.151543 − 0.964779I
−2.39825 − 2.03419I 2.27060 + 4.05066I
u = 0.500054 + 0.432744I
a = −1.58264 − 0.45958I
b = −0.429197 − 0.273799I
−0.92587 + 4.11077I 5.01065 − 8.99779I
u = 0.500054 − 0.432744I
a = −1.58264 + 0.45958I
b = −0.429197 + 0.273799I
−0.92587 − 4.11077I 5.01065 + 8.99779I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.037819 + 1.343840I
a = −0.297542 + 1.152810I
b = −0.056382 − 1.024380I
−5.06538 + 2.73318I 0
u = 0.037819 − 1.343840I
a = −0.297542 − 1.152810I
b = −0.056382 + 1.024380I
−5.06538 − 2.73318I 0
u = −0.07762 + 1.41592I
a = −0.839838 − 0.126193I
b = −0.589212 + 0.356243I
−4.18150 − 1.91267I 0
u = −0.07762 − 1.41592I
a = −0.839838 + 0.126193I
b = −0.589212 − 0.356243I
−4.18150 + 1.91267I 0
u = −0.04588 + 1.49852I
a = −0.286588 − 1.290620I
b = −0.01350 + 1.73889I
−15.0633 − 3.0141I 0
u = −0.04588 − 1.49852I
a = −0.286588 + 1.290620I
b = −0.01350 − 1.73889I
−15.0633 + 3.0141I 0
u = −0.04118 + 1.50695I
a = 0.857242 + 0.055781I
b = 0.641940 + 0.482037I
−7.87180 − 2.16186I 0
u = −0.04118 − 1.50695I
a = 0.857242 − 0.055781I
b = 0.641940 − 0.482037I
−7.87180 + 2.16186I 0
u = 0.20411 + 1.49822I
a = −0.995020 + 0.295616I
b = −0.332774 − 1.115340I
−8.78560 + 5.06490I 0
u = 0.20411 − 1.49822I
a = −0.995020 − 0.295616I
b = −0.332774 + 1.115340I
−8.78560 − 5.06490I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.15926 + 1.50725I
a = 0.985140 − 0.130046I
b = 0.692157 + 0.316900I
−7.37205 + 6.50901I 0
u = 0.15926 − 1.50725I
a = 0.985140 + 0.130046I
b = 0.692157 − 0.316900I
−7.37205 − 6.50901I 0
u = −0.453530 + 0.155768I
a = 1.294160 − 0.225533I
b = 0.381984 − 0.104645I
0.863945 − 0.260084I 11.81001 + 2.51028I
u = −0.453530 − 0.155768I
a = 1.294160 + 0.225533I
b = 0.381984 + 0.104645I
0.863945 + 0.260084I 11.81001 − 2.51028I
u = 0.002331 + 0.475435I
a = −1.31229 − 1.31457I
b = −0.222613 − 0.360188I
−1.29560 − 1.71128I 3.62337 − 0.57980I
u = 0.002331 − 0.475435I
a = −1.31229 + 1.31457I
b = −0.222613 + 0.360188I
−1.29560 + 1.71128I 3.62337 + 0.57980I
u = −0.10985 + 1.56287I
a = 0.745097 + 0.121175I
b = 0.305737 − 1.232150I
−13.35830 − 1.13064I 0
u = −0.10985 − 1.56287I
a = 0.745097 − 0.121175I
b = 0.305737 + 1.232150I
−13.35830 + 1.13064I 0
u = −0.26983 + 1.54338I
a = 1.117940 + 0.149645I
b = 0.408507 − 1.113900I
−11.8242 − 10.2576I 0
u = −0.26983 − 1.54338I
a = 1.117940 − 0.149645I
b = 0.408507 + 1.113900I
−11.8242 + 10.2576I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.28876 + 1.56911I
a = −1.116410 − 0.382260I
b = −0.08858 + 1.75569I
−19.0611 − 6.8576I 0
u = −0.28876 − 1.56911I
a = −1.116410 + 0.382260I
b = −0.08858 − 1.75569I
−19.0611 + 6.8576I 0
u = 0.36007 + 1.57989I
a = 1.221070 − 0.154749I
b = 0.11163 + 1.75687I
17.4391 + 12.4733I 0
u = 0.36007 − 1.57989I
a = 1.221070 + 0.154749I
b = 0.11163 − 1.75687I
17.4391 − 12.4733I 0
u = 0.329455 + 0.007485I
a = 2.30065 − 0.55846I
b = 0.177809 − 0.666151I
−0.77656 − 1.82163I 4.80979 + 5.42360I
u = 0.329455 − 0.007485I
a = 2.30065 + 0.55846I
b = 0.177809 + 0.666151I
−0.77656 + 1.82163I 4.80979 − 5.42360I
u = 0.22272 + 1.66105I
a = 0.730785 − 0.308803I
b = 0.06984 + 1.78630I
15.1658 + 2.7485I 0
u = 0.22272 − 1.66105I
a = 0.730785 + 0.308803I
b = 0.06984 − 1.78630I
15.1658 − 2.7485I 0
u = −0.186126 + 0.264782I
a = 2.72769 + 2.04868I
b = 0.01181 − 1.64054I
−8.93133 − 2.25545I 4.66563 + 3.82510I
u = −0.186126 − 0.264782I
a = 2.72769 − 2.04868I
b = 0.01181 + 1.64054I
−8.93133 + 2.25545I 4.66563 − 3.82510I
9
II. I
u
2
= hb
2
− bu + 1, a
2
+ a + 1, u
2
+ 1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
4
=
1
−1
a
10
=
u
0
a
1
=
a
b
a
3
=
0
−1
a
8
=
au + u
−bau + u
a
2
=
a
b + a
a
7
=
au
bu
a
12
=
−b + a
b
a
6
=
−ba + bu
−bu + 1
a
11
=
bau + u
−b − u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4a − 4
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)
4
c
2
, c
7
, c
8
(u
4
− u
2
+ 1)
2
c
3
, c
4
, c
9
(u
2
+ 1)
4
c
5
, c
6
, c
10
c
11
, c
12
(u
4
+ 3u
2
+ 1)
2
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
2
+ y + 1)
4
c
2
, c
7
, c
8
(y
2
− y + 1)
4
c
3
, c
4
, c
9
(y + 1)
8
c
5
, c
6
, c
10
c
11
, c
12
(y
2
+ 3y + 1)
4
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −0.500000 + 0.866025I
b = − 0.618034I
−2.63189 + 2.02988I −2.00000 − 3.46410I
u = 1.000000I
a = −0.500000 + 0.866025I
b = 1.61803I
−10.52760 + 2.02988I −2.00000 − 3.46410I
u = 1.000000I
a = −0.500000 − 0.866025I
b = − 0.618034I
−2.63189 − 2.02988I −2.00000 + 3.46410I
u = 1.000000I
a = −0.500000 − 0.866025I
b = 1.61803I
−10.52760 − 2.02988I −2.00000 + 3.46410I
u = − 1.000000I
a = −0.500000 + 0.866025I
b = 0.618034I
−2.63189 + 2.02988I −2.00000 − 3.46410I
u = − 1.000000I
a = −0.500000 + 0.866025I
b = − 1.61803I
−10.52760 + 2.02988I −2.00000 − 3.46410I
u = − 1.000000I
a = −0.500000 − 0.866025I
b = 0.618034I
−2.63189 − 2.02988I −2.00000 + 3.46410I
u = − 1.000000I
a = −0.500000 − 0.866025I
b = − 1.61803I
−10.52760 − 2.02988I −2.00000 + 3.46410I
13
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
4
)(u
50
+ 27u
49
+ ··· + 131u + 25)
c
2
, c
7
((u
4
− u
2
+ 1)
2
)(u
50
+ u
49
+ ··· + u + 5)
c
3
, c
4
, c
9
((u
2
+ 1)
4
)(u
50
+ u
49
+ ··· + 4u + 4)
c
5
, c
6
, c
10
c
11
, c
12
((u
4
+ 3u
2
+ 1)
2
)(u
50
− u
49
+ ··· + 9u + 1)
c
8
((u
4
− u
2
+ 1)
2
)(u
50
+ 3u
49
+ ··· + 519u + 345)
14
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
4
)(y
50
− 3y
49
+ ··· + 89y + 625)
c
2
, c
7
((y
2
− y + 1)
4
)(y
50
− 27y
49
+ ··· − 131y + 25)
c
3
, c
4
, c
9
((y + 1)
8
)(y
50
+ 53y
49
+ ··· − 8y + 16)
c
5
, c
6
, c
10
c
11
, c
12
((y
2
+ 3y + 1)
4
)(y
50
+ 69y
49
+ ··· − 39y + 1)
c
8
((y
2
− y + 1)
4
)(y
50
+ 33y
49
+ ··· − 1916391y + 119025)
15
