12a
0252
(K12a
0252
)
A knot diagram
1
Linearized knot diagam
3 6 7 10 11 2 12 1 4 5 9 8
Solving Sequence
5,11 2,6
3 7 1 10 4 9 12 8
c
5
c
2
c
6
c
1
c
10
c
4
c
9
c
11
c
8
c
3
, c
7
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−3.93238 × 10
36
u
70
− 5.06587 × 10
36
u
69
+ ··· + 5.33198 × 10
36
b + 2.44647 × 10
37
,
5.07711 × 10
36
u
70
− 1.19436 × 10
37
u
69
+ ··· + 5.33198 × 10
36
a + 4.10693 × 10
37
, u
71
− u
70
+ ··· − 4u + 4i
I
u
2
= h−au + b + 1, 2a
2
+ au + 2a + 2u + 3, u
2
− 2i
I
v
1
= ha, b + v, v
2
+ v + 1i
* 3 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−3.93×10
36
u
70
−5.07×10
36
u
69
+· · ·+5.33×10
36
b+2.45×10
37
, 5.08×
10
36
u
70
−1.19×10
37
u
69
+· · ·+5.33×10
36
a+4.11×10
37
, u
71
−u
70
+· · ·−4u+4i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
2
=
−0.952200u
70
+ 2.23999u
69
+ ··· + 20.1357u − 7.70244
0.737508u
70
+ 0.950092u
69
+ ··· + 6.24797u − 4.58829
a
6
=
1
u
2
a
3
=
−0.741052u
70
+ 2.20642u
69
+ ··· + 17.4237u − 7.13958
1.16557u
70
+ 1.11369u
69
+ ··· + 6.11369u − 5.29860
a
7
=
−1.16962u
70
+ 1.25814u
69
+ ··· + 8.82584u − 2.37901
−0.630401u
70
− 0.239711u
69
+ ··· − 3.62581u + 2.09462
a
1
=
−0.429711u
70
+ 0.940016u
69
+ ··· + 10.0861u − 2.73375
0.311878u
70
− 0.164899u
69
+ ··· + 1.39448u − 0.301335
a
10
=
u
u
a
4
=
−u
2
+ 1
−u
2
a
9
=
−u
3
+ 2u
−u
3
+ u
a
12
=
−u
7
+ 4u
5
− 4u
3
−u
7
+ 3u
5
− 2u
3
+ u
a
8
=
−0.518233u
70
+ 1.13571u
69
+ ··· + 3.53681u − 1.30370
−0.0840621u
70
+ 0.422232u
69
+ ··· − 1.48260u − 0.530560
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2.34776u
70
− 2.08944u
69
+ ··· − 14.6022u − 7.88015
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
71
+ 34u
70
+ ··· + 6u − 1
c
2
, c
6
u
71
− 2u
70
+ ··· − 2u − 1
c
3
u
71
+ 2u
70
+ ··· − 3942u − 797
c
4
, c
5
, c
9
c
10
u
71
+ u
70
+ ··· − 4u − 4
c
7
, c
8
, c
12
u
71
+ 3u
70
+ ··· + 19u − 7
c
11
u
71
− 15u
70
+ ··· + 3072u − 1792
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
71
+ 10y
70
+ ··· + 62y −1
c
2
, c
6
y
71
+ 34y
70
+ ··· + 6y −1
c
3
y
71
− 14y
70
+ ··· + 18751274y −635209
c
4
, c
5
, c
9
c
10
y
71
− 81y
70
+ ··· + 176y −16
c
7
, c
8
, c
12
y
71
− 63y
70
+ ··· − 17y −49
c
11
y
71
+ 11y
70
+ ··· − 2719744y −3211264
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.974962
a = −0.132568
b = −0.762090
−6.07387 0
u = 1.041460 + 0.273367I
a = −0.83444 − 1.61294I
b = −0.309992 − 0.982745I
−9.26803 − 3.63527I 0
u = 1.041460 − 0.273367I
a = −0.83444 + 1.61294I
b = −0.309992 + 0.982745I
−9.26803 + 3.63527I 0
u = −0.683517 + 0.613751I
a = −1.85094 + 1.31765I
b = 0.360642 + 0.541603I
−4.89636 + 11.68020I 0
u = −0.683517 − 0.613751I
a = −1.85094 − 1.31765I
b = 0.360642 − 0.541603I
−4.89636 − 11.68020I 0
u = −0.744307 + 0.516977I
a = 0.718389 − 1.009080I
b = −0.783067 + 0.302046I
−7.31151 + 3.80947I −16.8222 + 0.I
u = −0.744307 − 0.516977I
a = 0.718389 + 1.009080I
b = −0.783067 − 0.302046I
−7.31151 − 3.80947I −16.8222 + 0.I
u = 0.661129 + 0.571595I
a = −0.138662 − 0.821456I
b = −0.180040 − 0.537662I
−2.56545 − 6.56727I −10.30221 + 5.89278I
u = 0.661129 − 0.571595I
a = −0.138662 + 0.821456I
b = −0.180040 + 0.537662I
−2.56545 + 6.56727I −10.30221 − 5.89278I
u = 0.617792 + 0.529373I
a = −2.11045 − 1.58230I
b = 0.257256 − 0.453919I
0.22354 − 7.65304I −8.99939 + 9.03031I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.617792 − 0.529373I
a = −2.11045 + 1.58230I
b = 0.257256 + 0.453919I
0.22354 + 7.65304I −8.99939 − 9.03031I
u = −0.288994 + 0.715682I
a = 0.753951 + 0.022023I
b = 0.23407 − 1.43165I
−3.71427 − 7.22650I −11.76200 + 4.77338I
u = −0.288994 − 0.715682I
a = 0.753951 − 0.022023I
b = 0.23407 + 1.43165I
−3.71427 + 7.22650I −11.76200 − 4.77338I
u = −0.555286 + 0.514091I
a = 0.029022 + 0.997262I
b = −0.126622 + 0.427682I
2.23050 + 2.79648I −5.08952 − 4.76680I
u = −0.555286 − 0.514091I
a = 0.029022 − 0.997262I
b = −0.126622 − 0.427682I
2.23050 − 2.79648I −5.08952 + 4.76680I
u = 0.555198 + 0.441849I
a = 1.154400 + 0.039318I
b = 0.802206 − 0.072715I
−1.00765 − 4.12329I −9.75666 + 7.48395I
u = 0.555198 − 0.441849I
a = 1.154400 − 0.039318I
b = 0.802206 + 0.072715I
−1.00765 + 4.12329I −9.75666 − 7.48395I
u = 0.284882 + 0.644950I
a = 1.080530 + 0.041177I
b = 0.317243 + 0.055472I
−1.45298 + 2.44652I −8.12987 − 0.62519I
u = 0.284882 − 0.644950I
a = 1.080530 − 0.041177I
b = 0.317243 − 0.055472I
−1.45298 − 2.44652I −8.12987 + 0.62519I
u = 0.611937 + 0.345920I
a = 1.19608 + 1.32035I
b = −0.493119 − 0.166503I
−1.94003 − 0.80211I −13.09901 + 4.19449I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.611937 − 0.345920I
a = 1.19608 − 1.32035I
b = −0.493119 + 0.166503I
−1.94003 + 0.80211I −13.09901 − 4.19449I
u = −0.148480 + 0.684433I
a = 0.856675 − 0.243803I
b = −0.146478 + 1.028510I
−5.49853 + 0.20966I −14.2031 − 1.3385I
u = −0.148480 − 0.684433I
a = 0.856675 + 0.243803I
b = −0.146478 − 1.028510I
−5.49853 − 0.20966I −14.2031 + 1.3385I
u = 1.281050 + 0.223593I
a = −0.145673 + 1.042540I
b = −1.317600 + 0.481811I
−8.63854 + 3.81527I 0
u = 1.281050 − 0.223593I
a = −0.145673 − 1.042540I
b = −1.317600 − 0.481811I
−8.63854 − 3.81527I 0
u = −0.399835 + 0.531286I
a = 1.111270 − 0.044872I
b = 0.493071 + 0.030498I
2.68818 + 0.83256I −3.03948 − 3.39872I
u = −0.399835 − 0.531286I
a = 1.111270 + 0.044872I
b = 0.493071 − 0.030498I
2.68818 − 0.83256I −3.03948 + 3.39872I
u = −0.562198 + 0.354555I
a = −2.26602 + 2.56094I
b = 0.071941 + 0.357866I
−2.07090 + 3.34227I −13.0075 − 6.0861I
u = −0.562198 − 0.354555I
a = −2.26602 − 2.56094I
b = 0.071941 − 0.357866I
−2.07090 − 3.34227I −13.0075 + 6.0861I
u = −0.662402 + 0.022295I
a = 0.32012 − 2.79437I
b = −0.334133 − 0.224554I
−2.89598 − 2.84826I −16.4142 + 5.1408I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.662402 − 0.022295I
a = 0.32012 + 2.79437I
b = −0.334133 + 0.224554I
−2.89598 + 2.84826I −16.4142 − 5.1408I
u = 0.319547 + 0.564821I
a = 0.815652 + 0.018623I
b = 0.373590 + 1.327950I
1.09698 + 3.88412I −5.83336 − 2.81724I
u = 0.319547 − 0.564821I
a = 0.815652 − 0.018623I
b = 0.373590 − 1.327950I
1.09698 − 3.88412I −5.83336 + 2.81724I
u = −1.382810 + 0.085315I
a = −0.770899 + 0.369521I
b = −1.73606 + 0.52292I
−6.41810 + 0.14375I 0
u = −1.382810 − 0.085315I
a = −0.770899 − 0.369521I
b = −1.73606 − 0.52292I
−6.41810 − 0.14375I 0
u = −0.509163 + 0.332791I
a = 0.901210 − 0.137186I
b = 0.70921 − 1.26609I
−1.87792 − 0.91954I −12.51300 − 2.70436I
u = −0.509163 − 0.332791I
a = 0.901210 + 0.137186I
b = 0.70921 + 1.26609I
−1.87792 + 0.91954I −12.51300 + 2.70436I
u = 0.396419 + 0.434178I
a = 0.55903 − 1.50302I
b = −0.056466 − 0.287345I
−0.545124 + 0.994643I −7.84415 + 1.46512I
u = 0.396419 − 0.434178I
a = 0.55903 + 1.50302I
b = −0.056466 + 0.287345I
−0.545124 − 0.994643I −7.84415 − 1.46512I
u = −1.44238 + 0.08576I
a = −0.349916 − 0.860243I
b = −1.51352 − 0.74219I
−4.43692 − 1.78201I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.44238 − 0.08576I
a = −0.349916 + 0.860243I
b = −1.51352 + 0.74219I
−4.43692 + 1.78201I 0
u = 1.48243 + 0.11601I
a = −0.503110 − 0.588443I
b = −1.54844 − 0.83999I
−3.44891 − 3.00583I 0
u = 1.48243 − 0.11601I
a = −0.503110 + 0.588443I
b = −1.54844 + 0.83999I
−3.44891 + 3.00583I 0
u = −1.52603 + 0.07657I
a = −0.792598 − 0.307607I
b = −1.30084 − 0.77169I
−6.95261 + 0.55649I 0
u = −1.52603 − 0.07657I
a = −0.792598 + 0.307607I
b = −1.30084 + 0.77169I
−6.95261 − 0.55649I 0
u = 1.55290 + 0.14230I
a = −0.540917 + 0.452635I
b = −0.733603 + 1.181220I
−4.83267 − 5.13999I 0
u = 1.55290 − 0.14230I
a = −0.540917 − 0.452635I
b = −0.733603 − 1.181220I
−4.83267 + 5.13999I 0
u = 1.55861 + 0.09132I
a = −0.303039 + 0.740752I
b = −1.64578 + 0.75593I
−8.96219 − 0.58402I 0
u = 1.55861 − 0.09132I
a = −0.303039 − 0.740752I
b = −1.64578 − 0.75593I
−8.96219 + 0.58402I 0
u = 0.437893
a = 0.702032
b = −0.178433
−0.692654 −14.1050
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.56098 + 0.11999I
a = −0.416452 + 0.590189I
b = −1.56200 + 0.90423I
−8.16520 + 6.12024I 0
u = −1.56098 − 0.11999I
a = −0.416452 − 0.590189I
b = −1.56200 − 0.90423I
−8.16520 − 6.12024I 0
u = 1.56896 + 0.10229I
a = 1.02180 + 2.69391I
b = 2.15590 + 5.82172I
−9.34889 − 5.00736I 0
u = 1.56896 − 0.10229I
a = 1.02180 − 2.69391I
b = 2.15590 − 5.82172I
−9.34889 + 5.00736I 0
u = −1.57483 + 0.09927I
a = −0.75369 + 2.16400I
b = −0.95108 + 4.45781I
−9.36775 + 2.43571I 0
u = −1.57483 − 0.09927I
a = −0.75369 − 2.16400I
b = −0.95108 − 4.45781I
−9.36775 − 2.43571I 0
u = 1.58020 + 0.03046I
a = −0.41422 − 2.66376I
b = −0.43461 − 5.57845I
−10.52460 + 2.50482I 0
u = 1.58020 − 0.03046I
a = −0.41422 + 2.66376I
b = −0.43461 + 5.57845I
−10.52460 − 2.50482I 0
u = −1.57417 + 0.15470I
a = 1.25068 − 2.27271I
b = 2.53079 − 5.06207I
−7.14402 + 10.15450I 0
u = −1.57417 − 0.15470I
a = 1.25068 + 2.27271I
b = 2.53079 + 5.06207I
−7.14402 − 10.15450I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.58909 + 0.17273I
a = −0.405664 − 0.412866I
b = −0.391537 − 1.150890I
−10.12550 + 9.32824I 0
u = −1.58909 − 0.17273I
a = −0.405664 + 0.412866I
b = −0.391537 + 1.150890I
−10.12550 − 9.32824I 0
u = 0.089398 + 0.387096I
a = 0.988618 + 0.088778I
b = 0.248296 − 0.842415I
−0.50745 − 1.65056I −4.58929 + 3.33883I
u = 0.089398 − 0.387096I
a = 0.988618 − 0.088778I
b = 0.248296 + 0.842415I
−0.50745 + 1.65056I −4.58929 − 3.33883I
u = 1.59787 + 0.18877I
a = 1.18769 + 2.00228I
b = 2.37919 + 4.60569I
−12.5488 − 14.6759I 0
u = 1.59787 − 0.18877I
a = 1.18769 − 2.00228I
b = 2.37919 − 4.60569I
−12.5488 + 14.6759I 0
u = 1.61397 + 0.14947I
a = −0.59553 − 1.87276I
b = −0.44662 − 3.91654I
−15.3002 − 6.3034I 0
u = 1.61397 − 0.14947I
a = −0.59553 + 1.87276I
b = −0.44662 + 3.91654I
−15.3002 + 6.3034I 0
u = 1.63502
a = −0.507683
b = −0.526412
−14.8851 0
u = −1.65827 + 0.02787I
a = 0.21619 − 2.25531I
b = 0.81168 − 5.01290I
−18.5709 + 4.4255I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.65827 − 0.02787I
a = 0.21619 + 2.25531I
b = 0.81168 + 5.01290I
−18.5709 − 4.4255I 0
12
II. I
u
2
= h−au + b + 1, 2a
2
+ au + 2a + 2u + 3, u
2
− 2i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
2
=
a
au − 1
a
6
=
1
2
a
3
=
au − a − 1
3au − 4a − 3
a
7
=
−
1
2
u
au − 2a − u
a
1
=
−
1
2
u
au − 2a − u
a
10
=
u
u
a
4
=
−1
−2
a
9
=
0
−u
a
12
=
0
u
a
8
=
−
1
2
u
au − 2a − 2u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4au − 8a − 16
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u
2
− u + 1)
2
c
3
, c
6
(u
2
+ u + 1)
2
c
4
, c
5
, c
9
c
10
(u
2
− 2)
2
c
7
, c
8
(u + 1)
4
c
11
u
4
c
12
(u − 1)
4
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
6
(y
2
+ y + 1)
2
c
4
, c
5
, c
9
c
10
(y −2)
4
c
7
, c
8
, c
12
(y −1)
4
c
11
y
4
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.41421
a = −0.85355 + 1.47840I
b = −2.20711 + 2.09077I
−6.57974 + 2.02988I −14.0000 − 3.4641I
u = 1.41421
a = −0.85355 − 1.47840I
b = −2.20711 − 2.09077I
−6.57974 − 2.02988I −14.0000 + 3.4641I
u = −1.41421
a = −0.146447 + 0.253653I
b = −0.792893 − 0.358719I
−6.57974 + 2.02988I −14.0000 − 3.4641I
u = −1.41421
a = −0.146447 − 0.253653I
b = −0.792893 + 0.358719I
−6.57974 − 2.02988I −14.0000 + 3.4641I
16
III. I
v
1
= ha, b + v, v
2
+ v + 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
v
0
a
2
=
0
−v
a
6
=
1
0
a
3
=
−v
−v
a
7
=
1
v + 1
a
1
=
−1
−v − 1
a
10
=
v
0
a
4
=
1
0
a
9
=
v
0
a
12
=
v
0
a
8
=
v + 1
v + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4v − 10
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
u
2
− u + 1
c
2
u
2
+ u + 1
c
4
, c
5
, c
9
c
10
, c
11
u
2
c
7
, c
8
(u − 1)
2
c
12
(u + 1)
2
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
6
y
2
+ y + 1
c
4
, c
5
, c
9
c
10
, c
11
y
2
c
7
, c
8
, c
12
(y − 1)
2
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.500000 + 0.866025I
a = 0
b = 0.500000 − 0.866025I
−1.64493 − 2.02988I −12.00000 + 3.46410I
v = −0.500000 − 0.866025I
a = 0
b = 0.500000 + 0.866025I
−1.64493 + 2.02988I −12.00000 − 3.46410I
20
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
3
)(u
71
+ 34u
70
+ ··· + 6u − 1)
c
2
((u
2
− u + 1)
2
)(u
2
+ u + 1)(u
71
− 2u
70
+ ··· − 2u − 1)
c
3
(u
2
− u + 1)(u
2
+ u + 1)
2
(u
71
+ 2u
70
+ ··· − 3942u − 797)
c
4
, c
5
, c
9
c
10
u
2
(u
2
− 2)
2
(u
71
+ u
70
+ ··· − 4u − 4)
c
6
(u
2
− u + 1)(u
2
+ u + 1)
2
(u
71
− 2u
70
+ ··· − 2u − 1)
c
7
, c
8
((u − 1)
2
)(u + 1)
4
(u
71
+ 3u
70
+ ··· + 19u − 7)
c
11
u
6
(u
71
− 15u
70
+ ··· + 3072u − 1792)
c
12
((u − 1)
4
)(u + 1)
2
(u
71
+ 3u
70
+ ··· + 19u − 7)
21
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
3
)(y
71
+ 10y
70
+ ··· + 62y − 1)
c
2
, c
6
((y
2
+ y + 1)
3
)(y
71
+ 34y
70
+ ··· + 6y − 1)
c
3
((y
2
+ y + 1)
3
)(y
71
− 14y
70
+ ··· + 1.87513 × 10
7
y − 635209)
c
4
, c
5
, c
9
c
10
y
2
(y − 2)
4
(y
71
− 81y
70
+ ··· + 176y − 16)
c
7
, c
8
, c
12
((y − 1)
6
)(y
71
− 63y
70
+ ··· − 17y − 49)
c
11
y
6
(y
71
+ 11y
70
+ ··· − 2719744y − 3211264)
22
