12a
0158
(K12a
0158
)
A knot diagram
1
Linearized knot diagam
3 5 9 2 11 12 10 4 8 1 6 7
Solving Sequence
4,8
9
1,10
11 3 2 5 7 12 6
c
8
c
9
c
10
c
3
c
1
c
4
c
7
c
12
c
6
c
2
, c
5
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−4.37013 × 10
32
u
60
+ 1.07931 × 10
33
u
59
+ ··· + 2.13053 × 10
33
b + 2.55159 × 10
32
,
− 1.77317 × 10
32
u
60
+ 4.83859 × 10
32
u
59
+ ··· + 1.06527 × 10
33
a + 3.22263 × 10
33
, u
61
− u
60
+ ··· + 8u + 4i
I
v
1
= ha, b + v + 1, v
2
+ v −1i
* 2 irreducible components of dim
C
= 0, with total 63 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−4.37×10
32
u
60
+1.08×10
33
u
59
+· · ·+2.13×10
33
b+2.55×10
32
, −1.77×
10
32
u
60
+4.84×10
32
u
59
+· · ·+1.07×10
33
a+3.22×10
33
, u
61
−u
60
+· · ·+8u+4i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
1
=
0.166453u
60
− 0.454214u
59
+ ··· − 5.04302u − 3.02519
0.205119u
60
− 0.506592u
59
+ ··· + 1.80715u − 0.119763
a
10
=
u
2
+ 1
u
2
a
11
=
−0.0499331u
60
− 0.0191878u
59
+ ··· + 4.34689u + 1.61382
0.531140u
60
− 0.796906u
59
+ ··· + 4.86494u + 0.379014
a
3
=
u
u
3
+ u
a
2
=
0.308153u
60
− 0.583793u
59
+ ··· − 4.74082u − 3.17923
0.351153u
60
− 0.680255u
59
+ ··· + 1.44558u − 0.322290
a
5
=
0.152571u
60
− 0.191082u
59
+ ··· + 5.21389u + 1.75438
0.319024u
60
− 0.645296u
59
+ ··· + 0.170875u − 1.27081
a
7
=
u
4
+ u
2
+ 1
u
4
a
12
=
0.394171u
60
− 0.666399u
59
+ ··· − 4.85797u − 3.23772
0.323761u
60
− 0.610161u
59
+ ··· − 0.328448u − 1.25482
a
6
=
−0.711527u
60
+ 0.890795u
59
+ ··· − 2.81563u − 0.209751
−0.127525u
60
+ 0.512045u
59
+ ··· − 3.76247u − 1.00960
(ii) Obstruction class = −1
(iii) Cusp Shapes = −1.26579u
60
+ 1.94808u
59
+ ··· + 11.8662u − 2.65853
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
61
+ 35u
60
+ ··· + 40u + 1
c
2
, c
4
u
61
− 3u
60
+ ··· + 2u + 1
c
3
, c
8
u
61
− u
60
+ ··· + 8u + 4
c
5
, c
6
, c
11
c
12
u
61
+ 2u
60
+ ··· + u + 1
c
7
, c
9
u
61
− 15u
60
+ ··· − 88u + 16
c
10
u
61
− 20u
60
+ ··· − 33811u + 6497
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
61
− 15y
60
+ ··· + 992y −1
c
2
, c
4
y
61
− 35y
60
+ ··· + 40y −1
c
3
, c
8
y
61
+ 15y
60
+ ··· − 88y −16
c
5
, c
6
, c
11
c
12
y
61
− 72y
60
+ ··· + 13y −1
c
7
, c
9
y
61
+ 59y
60
+ ··· + 9760y −256
c
10
y
61
− 36y
60
+ ··· − 229814295y −42211009
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.238487 + 0.953197I
a = −0.003755 + 0.877090I
b = −0.178706 + 0.107732I
2.09116 + 2.27253I −4.25062 − 5.15678I
u = −0.238487 − 0.953197I
a = −0.003755 − 0.877090I
b = −0.178706 − 0.107732I
2.09116 − 2.27253I −4.25062 + 5.15678I
u = −0.307970 + 0.970251I
a = 0.0336117 − 0.1292320I
b = 0.942071 + 0.219289I
1.65969 + 3.31321I −4.58003 − 3.95738I
u = −0.307970 − 0.970251I
a = 0.0336117 + 0.1292320I
b = 0.942071 − 0.219289I
1.65969 − 3.31321I −4.58003 + 3.95738I
u = −0.877601 + 0.378203I
a = 0.207288 − 0.357685I
b = 0.447467 + 0.371493I
−9.07110 − 3.90521I −14.6512 + 4.5873I
u = −0.877601 − 0.378203I
a = 0.207288 + 0.357685I
b = 0.447467 − 0.371493I
−9.07110 + 3.90521I −14.6512 − 4.5873I
u = 0.084785 + 0.946752I
a = −0.080363 + 0.669261I
b = 0.531909 + 0.161258I
2.57667 + 0.91135I −2.15381 − 4.08068I
u = 0.084785 − 0.946752I
a = −0.080363 − 0.669261I
b = 0.531909 − 0.161258I
2.57667 − 0.91135I −2.15381 + 4.08068I
u = 0.077209 + 1.056450I
a = 0.297681 + 0.382384I
b = −0.928442 + 0.127233I
−3.28717 − 2.31394I −7.12059 + 3.62918I
u = 0.077209 − 1.056450I
a = 0.297681 − 0.382384I
b = −0.928442 − 0.127233I
−3.28717 + 2.31394I −7.12059 − 3.62918I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.359746 + 1.016880I
a = 0.062599 + 1.101460I
b = −0.217088 + 0.019866I
−4.85916 − 4.06193I −8.00000 + 3.62400I
u = 0.359746 − 1.016880I
a = 0.062599 − 1.101460I
b = −0.217088 − 0.019866I
−4.85916 + 4.06193I −8.00000 − 3.62400I
u = 0.410008 + 1.014890I
a = −0.012002 − 0.459759I
b = −0.721661 + 0.144626I
0.62509 − 6.72372I −8.00000 + 10.31873I
u = 0.410008 − 1.014890I
a = −0.012002 + 0.459759I
b = −0.721661 − 0.144626I
0.62509 + 6.72372I −8.00000 − 10.31873I
u = 0.808032 + 0.816831I
a = 1.00805 + 1.02708I
b = 0.03711 + 1.94913I
−4.47605 + 0.47564I 0
u = 0.808032 − 0.816831I
a = 1.00805 − 1.02708I
b = 0.03711 − 1.94913I
−4.47605 − 0.47564I 0
u = −0.749510 + 0.886201I
a = −0.87056 + 1.16887I
b = 0.43430 + 1.70385I
−1.90394 + 2.84541I 0
u = −0.749510 − 0.886201I
a = −0.87056 − 1.16887I
b = 0.43430 − 1.70385I
−1.90394 − 2.84541I 0
u = −0.316577 + 0.775281I
a = 0.34310 − 2.42404I
b = −0.749506 + 0.387164I
−9.89951 + 1.70824I −13.49720 − 3.89995I
u = −0.316577 − 0.775281I
a = 0.34310 + 2.42404I
b = −0.749506 − 0.387164I
−9.89951 − 1.70824I −13.49720 + 3.89995I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.489410 + 1.059940I
a = −0.038865 − 0.755001I
b = 0.369249 + 0.129881I
−6.69274 + 8.82294I 0
u = −0.489410 − 1.059940I
a = −0.038865 + 0.755001I
b = 0.369249 − 0.129881I
−6.69274 − 8.82294I 0
u = 0.849526 + 0.813861I
a = −1.44747 − 1.16596I
b = −0.11881 − 1.83683I
−5.74001 + 1.43814I 0
u = 0.849526 − 0.813861I
a = −1.44747 + 1.16596I
b = −0.11881 + 1.83683I
−5.74001 − 1.43814I 0
u = 0.757519 + 0.305031I
a = 0.149859 − 0.548164I
b = −0.040871 + 0.285650I
−1.78875 + 2.52359I −12.4907 − 7.4949I
u = 0.757519 − 0.305031I
a = 0.149859 + 0.548164I
b = −0.040871 − 0.285650I
−1.78875 − 2.52359I −12.4907 + 7.4949I
u = −0.874218 + 0.804569I
a = −1.15410 + 0.99565I
b = −0.28100 + 2.30195I
−12.87930 − 2.42278I 0
u = −0.874218 − 0.804569I
a = −1.15410 − 0.99565I
b = −0.28100 − 2.30195I
−12.87930 + 2.42278I 0
u = −0.821847 + 0.871851I
a = 1.56651 − 1.37568I
b = −0.35452 − 2.07289I
−8.17948 + 2.03351I 0
u = −0.821847 − 0.871851I
a = 1.56651 + 1.37568I
b = −0.35452 + 2.07289I
−8.17948 − 2.03351I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.241710 + 0.747099I
a = −0.465874 + 0.305697I
b = −1.270210 + 0.529709I
−1.94835 − 1.41549I −11.33185 + 4.43113I
u = 0.241710 − 0.747099I
a = −0.465874 − 0.305697I
b = −1.270210 − 0.529709I
−1.94835 + 1.41549I −11.33185 − 4.43113I
u = 0.772724 + 0.137846I
a = 0.672930 + 0.110054I
b = 0.895434 − 0.127416I
−7.72551 + 0.23364I −12.50787 + 1.31729I
u = 0.772724 − 0.137846I
a = 0.672930 − 0.110054I
b = 0.895434 + 0.127416I
−7.72551 − 0.23364I −12.50787 − 1.31729I
u = −0.909481 + 0.809234I
a = 1.55609 − 0.96630I
b = 0.57813 − 2.04844I
−8.07107 − 4.97454I 0
u = −0.909481 − 0.809234I
a = 1.55609 + 0.96630I
b = 0.57813 + 2.04844I
−8.07107 + 4.97454I 0
u = 0.836848 + 0.884467I
a = −1.10413 − 1.59303I
b = −0.05000 − 2.92120I
−16.6735 − 2.0703I 0
u = 0.836848 − 0.884467I
a = −1.10413 + 1.59303I
b = −0.05000 + 2.92120I
−16.6735 + 2.0703I 0
u = −0.805476 + 0.918966I
a = 0.92783 − 1.56312I
b = −0.19783 − 2.45697I
−8.03154 + 4.05119I 0
u = −0.805476 − 0.918966I
a = 0.92783 + 1.56312I
b = −0.19783 + 2.45697I
−8.03154 − 4.05119I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.776141 + 0.950673I
a = 0.90967 + 1.32399I
b = −0.83918 + 1.88849I
−4.06730 − 6.42529I 0
u = 0.776141 − 0.950673I
a = 0.90967 − 1.32399I
b = −0.83918 − 1.88849I
−4.06730 + 6.42529I 0
u = 0.824923 + 0.918769I
a = −1.71708 − 1.47330I
b = 0.63383 − 2.39142I
−16.5663 − 4.1225I 0
u = 0.824923 − 0.918769I
a = −1.71708 + 1.47330I
b = 0.63383 + 2.39142I
−16.5663 + 4.1225I 0
u = 0.797214 + 0.969907I
a = −0.74216 − 1.63736I
b = 0.66652 − 2.12988I
−5.25621 − 7.57674I 0
u = 0.797214 − 0.969907I
a = −0.74216 + 1.63736I
b = 0.66652 + 2.12988I
−5.25621 + 7.57674I 0
u = 0.949600 + 0.823547I
a = −1.68518 − 0.86336I
b = −0.86700 − 2.32515I
−16.4115 + 7.1396I 0
u = 0.949600 − 0.823547I
a = −1.68518 + 0.86336I
b = −0.86700 + 2.32515I
−16.4115 − 7.1396I 0
u = −0.806362 + 0.985930I
a = −0.96958 + 1.42164I
b = 1.10553 + 2.10803I
−12.3142 + 8.6618I 0
u = −0.806362 − 0.985930I
a = −0.96958 − 1.42164I
b = 1.10553 − 2.10803I
−12.3142 − 8.6618I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.823074 + 1.001050I
a = 0.68683 − 1.78798I
b = −1.13111 − 2.20407I
−7.46084 + 11.37220I 0
u = −0.823074 − 1.001050I
a = 0.68683 + 1.78798I
b = −1.13111 + 2.20407I
−7.46084 − 11.37220I 0
u = 0.848261 + 1.018330I
a = −0.67747 − 1.91157I
b = 1.48348 − 2.35344I
−15.7786 − 13.7453I 0
u = 0.848261 − 1.018330I
a = −0.67747 + 1.91157I
b = 1.48348 + 2.35344I
−15.7786 + 13.7453I 0
u = −0.308299 + 0.596152I
a = 0.945489 + 0.457470I
b = 2.00842 + 0.79172I
−10.52170 + 0.86189I −12.7781 − 7.9081I
u = −0.308299 − 0.596152I
a = 0.945489 − 0.457470I
b = 2.00842 − 0.79172I
−10.52170 − 0.86189I −12.7781 + 7.9081I
u = 0.254491 + 0.574517I
a = 0.11821 − 2.36867I
b = 0.311978 + 0.275962I
−2.54655 − 0.75490I −10.56290 + 9.15741I
u = 0.254491 − 0.574517I
a = 0.11821 + 2.36867I
b = 0.311978 − 0.275962I
−2.54655 + 0.75490I −10.56290 − 9.15741I
u = −0.612829 + 0.106029I
a = −0.809358 − 0.377022I
b = −0.294046 + 0.149479I
−1.002850 − 0.150257I −9.43253 − 1.75186I
u = −0.612829 − 0.106029I
a = −0.809358 + 0.377022I
b = −0.294046 − 0.149479I
−1.002850 + 0.150257I −9.43253 + 1.75186I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.415187
a = −0.415618
b = −0.410931
−0.737929 −13.3140
11
II. I
v
1
= ha, b + v + 1, v
2
+ v − 1i
(i) Arc colorings
a
4
=
v
0
a
8
=
1
0
a
9
=
1
0
a
1
=
0
−v − 1
a
10
=
1
0
a
11
=
1
v + 2
a
3
=
v
0
a
2
=
v
−v − 1
a
5
=
0
v + 1
a
7
=
1
0
a
12
=
−v − 1
−v − 1
a
6
=
−v − 1
−v − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −15
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
2
c
3
, c
7
, c
8
c
9
u
2
c
4
(u + 1)
2
c
5
, c
6
, c
10
u
2
+ u − 1
c
11
, c
12
u
2
− u − 1
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
2
c
3
, c
7
, c
8
c
9
y
2
c
5
, c
6
, c
10
c
11
, c
12
y
2
− 3y + 1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.618034
a = 0
b = −1.61803
−10.5276 −15.0000
v = −1.61803
a = 0
b = 0.618034
−2.63189 −15.0000
15
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
2
)(u
61
+ 35u
60
+ ··· + 40u + 1)
c
2
((u − 1)
2
)(u
61
− 3u
60
+ ··· + 2u + 1)
c
3
, c
8
u
2
(u
61
− u
60
+ ··· + 8u + 4)
c
4
((u + 1)
2
)(u
61
− 3u
60
+ ··· + 2u + 1)
c
5
, c
6
(u
2
+ u − 1)(u
61
+ 2u
60
+ ··· + u + 1)
c
7
, c
9
u
2
(u
61
− 15u
60
+ ··· − 88u + 16)
c
10
(u
2
+ u − 1)(u
61
− 20u
60
+ ··· − 33811u + 6497)
c
11
, c
12
(u
2
− u − 1)(u
61
+ 2u
60
+ ··· + u + 1)
16
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
2
)(y
61
− 15y
60
+ ··· + 992y − 1)
c
2
, c
4
((y − 1)
2
)(y
61
− 35y
60
+ ··· + 40y − 1)
c
3
, c
8
y
2
(y
61
+ 15y
60
+ ··· − 88y − 16)
c
5
, c
6
, c
11
c
12
(y
2
− 3y + 1)(y
61
− 72y
60
+ ··· + 13y − 1)
c
7
, c
9
y
2
(y
61
+ 59y
60
+ ··· + 9760y − 256)
c
10
(y
2
− 3y + 1)(y
61
− 36y
60
+ ··· − 2.29814 × 10
8
y − 4.22110 × 10
7
)
17
