12a
0752
(K12a
0752
)
A knot diagram
1
Linearized knot diagam
3 8 10 9 12 11 2 7 4 1 6 5
Solving Sequence
3,10 4,8
2 1 11 7 6 9 5 12
c
3
c
2
c
1
c
10
c
7
c
6
c
9
c
4
c
12
c
5
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h9.34661 × 10
34
u
64
− 1.16625 × 10
35
u
63
+ ··· + 2.68953 × 10
35
b + 2.48209 × 10
35
,
− 2.45811 × 10
33
u
64
+ 8.33232 × 10
33
u
63
+ ··· + 1.12064 × 10
34
a + 2.26849 × 10
34
, u
65
− u
64
+ ··· + 12u − 4i
I
u
2
= h−a
3
u − 2a
2
u − 3a
2
+ au + 2b − 4a + 3u − 1, a
4
− 4a
3
u + a
3
− 3a
2
u − 4a
2
− 4a + 2u, u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 73 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
= h9.35×10
34
u
64
−1.17×10
35
u
63
+· · ·+2.69×10
35
b+2.48×10
35
, −2.46×
10
33
u
64
+8.33×10
33
u
63
+· · ·+1.12×10
34
a+2.27×10
34
, u
65
−u
64
+· · ·+12u−4i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
u
2
a
8
=
0.219349u
64
− 0.743533u
63
+ ··· − 1.52002u − 2.02429
−0.347518u
64
+ 0.433625u
63
+ ··· + 0.00867489u − 0.922871
a
2
=
−0.263361u
64
+ 0.721780u
63
+ ··· − 1.26586u − 4.04726
−0.133396u
64
− 0.108354u
63
+ ··· + 1.92192u − 0.715761
a
1
=
−0.396757u
64
+ 0.613426u
63
+ ··· + 0.656058u − 4.76302
−0.133396u
64
− 0.108354u
63
+ ··· + 1.92192u − 0.715761
a
11
=
−0.665779u
64
+ 1.57509u
63
+ ··· + 8.10654u − 7.87229
0.118149u
64
− 0.522205u
63
+ ··· − 2.63479u − 0.297265
a
7
=
0.637359u
64
− 0.265428u
63
+ ··· + 0.870487u − 0.828079
−0.193937u
64
− 0.121331u
63
+ ··· − 2.80066u + 0.434278
a
6
=
−1.05857u
64
+ 0.511308u
63
+ ··· + 11.4864u − 2.05186
0.119417u
64
+ 0.0796398u
63
+ ··· + 2.46009u + 0.413703
a
9
=
u
u
3
+ u
a
5
=
u
2
+ 1
u
4
+ 2u
2
a
12
=
−0.353724u
64
+ 0.868730u
63
+ ··· − 0.913544u − 4.49532
−0.0369830u
64
− 0.0480797u
63
+ ··· + 2.57325u − 0.708124
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.196131u
64
+ 0.795929u
63
+ ··· + 1.11042u − 13.7264
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
65
+ 21u
64
+ ··· − 19u + 25
c
2
, c
7
u
65
+ u
64
+ ··· + 9u + 5
c
3
, c
4
, c
9
u
65
+ u
64
+ ··· + 12u + 4
c
5
, c
6
, c
11
c
12
u
65
− u
64
+ ··· − 11u + 1
c
10
u
65
− 15u
64
+ ··· + 14637u − 579
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
65
+ 51y
64
+ ··· + 23161y −625
c
2
, c
7
y
65
− 21y
64
+ ··· − 19y −25
c
3
, c
4
, c
9
y
65
+ 63y
64
+ ··· + 40y −16
c
5
, c
6
, c
11
c
12
y
65
+ 75y
64
+ ··· + 33y −1
c
10
y
65
+ 15y
64
+ ··· + 32505249y −335241
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.102835 + 0.976475I
a = −0.032757 + 1.095510I
b = −0.798701 − 0.498342I
1.74608 − 2.06336I 3.79758 + 4.39158I
u = 0.102835 − 0.976475I
a = −0.032757 − 1.095510I
b = −0.798701 + 0.498342I
1.74608 + 2.06336I 3.79758 − 4.39158I
u = 0.906499 + 0.335695I
a = −1.00090 + 1.11719I
b = −1.002750 − 0.732824I
−5.22317 − 9.63115I −7.07608 + 7.08853I
u = 0.906499 − 0.335695I
a = −1.00090 − 1.11719I
b = −1.002750 + 0.732824I
−5.22317 + 9.63115I −7.07608 − 7.08853I
u = −0.863103 + 0.392575I
a = 0.189374 + 0.143384I
b = −0.712709 − 0.812089I
−4.34155 + 3.82461I −5.48743 − 2.35121I
u = −0.863103 − 0.392575I
a = 0.189374 − 0.143384I
b = −0.712709 + 0.812089I
−4.34155 − 3.82461I −5.48743 + 2.35121I
u = −0.646090 + 0.839750I
a = 0.412776 + 1.185770I
b = 0.793279 − 0.769153I
−2.98842 + 1.42035I 0
u = −0.646090 − 0.839750I
a = 0.412776 − 1.185770I
b = 0.793279 + 0.769153I
−2.98842 − 1.42035I 0
u = −0.622090 + 0.690604I
a = 0.280367 + 0.412655I
b = −0.850043 − 0.730237I
2.97067 − 2.17133I −0.55827 + 3.61156I
u = −0.622090 − 0.690604I
a = 0.280367 − 0.412655I
b = −0.850043 + 0.730237I
2.97067 + 2.17133I −0.55827 − 3.61156I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.810994 + 0.423522I
a = 0.88886 + 1.24338I
b = 0.957966 − 0.730403I
2.05615 + 7.11041I −3.69386 − 8.87039I
u = −0.810994 − 0.423522I
a = 0.88886 − 1.24338I
b = 0.957966 + 0.730403I
2.05615 − 7.11041I −3.69386 + 8.87039I
u = 0.267823 + 1.055660I
a = −0.43521 + 1.61801I
b = −0.814658 + 0.091365I
−8.43583 + 0.53108I 0
u = 0.267823 − 1.055660I
a = −0.43521 − 1.61801I
b = −0.814658 − 0.091365I
−8.43583 − 0.53108I 0
u = 0.738216 + 0.505729I
a = −0.275387 + 0.232751I
b = 0.771634 − 0.765297I
2.62252 − 1.43772I −1.92916 + 3.83462I
u = 0.738216 − 0.505729I
a = −0.275387 − 0.232751I
b = 0.771634 + 0.765297I
2.62252 + 1.43772I −1.92916 − 3.83462I
u = 0.685313 + 0.553849I
a = −0.67132 + 1.35014I
b = −0.896052 − 0.725197I
2.82813 − 3.37856I −0.87863 + 2.72445I
u = 0.685313 − 0.553849I
a = −0.67132 − 1.35014I
b = −0.896052 + 0.725197I
2.82813 + 3.37856I −0.87863 − 2.72445I
u = −0.210657 + 1.099830I
a = 0.227640 + 1.282450I
b = 0.747845 − 0.100142I
−0.354198 + 0.463146I 0
u = −0.210657 − 1.099830I
a = 0.227640 − 1.282450I
b = 0.747845 + 0.100142I
−0.354198 − 0.463146I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.634423 + 0.925822I
a = −0.136818 + 0.495445I
b = 0.939159 − 0.735967I
−3.43259 + 4.27319I 0
u = 0.634423 − 0.925822I
a = −0.136818 − 0.495445I
b = 0.939159 + 0.735967I
−3.43259 − 4.27319I 0
u = 0.696261 + 0.218895I
a = 1.85017 + 0.05497I
b = 1.039610 + 0.156898I
−10.84640 − 4.13320I −13.21141 + 4.39737I
u = 0.696261 − 0.218895I
a = 1.85017 − 0.05497I
b = 1.039610 − 0.156898I
−10.84640 + 4.13320I −13.21141 − 4.39737I
u = 0.042531 + 1.303050I
a = −0.259174 + 0.846936I
b = −1.051340 − 0.358180I
2.32426 − 1.84830I 0
u = 0.042531 − 1.303050I
a = −0.259174 − 0.846936I
b = −1.051340 + 0.358180I
2.32426 + 1.84830I 0
u = −0.543909 + 0.434620I
a = −0.224764 + 0.261112I
b = −0.162639 + 0.576900I
−7.07962 + 1.85589I −6.10075 − 3.40773I
u = −0.543909 − 0.434620I
a = −0.224764 − 0.261112I
b = −0.162639 − 0.576900I
−7.07962 − 1.85589I −6.10075 + 3.40773I
u = 0.046525 + 1.337050I
a = −1.26413 − 2.52442I
b = 0.872078 + 0.710596I
−5.01392 − 2.72133I 0
u = 0.046525 − 1.337050I
a = −1.26413 + 2.52442I
b = 0.872078 − 0.710596I
−5.01392 + 2.72133I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.179831 + 1.357410I
a = 0.400953 + 0.852353I
b = 1.104970 − 0.245801I
1.60426 + 5.26138I 0
u = −0.179831 − 1.357410I
a = 0.400953 − 0.852353I
b = 1.104970 + 0.245801I
1.60426 − 5.26138I 0
u = 0.129798 + 1.375160I
a = 0.191467 + 0.722569I
b = 1.111650 − 0.471770I
−3.93915 + 0.11450I 0
u = 0.129798 − 1.375160I
a = 0.191467 − 0.722569I
b = 1.111650 + 0.471770I
−3.93915 − 0.11450I 0
u = −0.589848 + 0.142876I
a = −1.71897 + 0.20675I
b = −0.945800 + 0.132751I
−3.13502 + 2.54263I −12.19167 − 6.47264I
u = −0.589848 − 0.142876I
a = −1.71897 − 0.20675I
b = −0.945800 − 0.132751I
−3.13502 − 2.54263I −12.19167 + 6.47264I
u = 0.26288 + 1.39636I
a = −0.486577 + 0.820787I
b = −1.156320 − 0.188953I
−5.67735 − 7.60097I 0
u = 0.26288 − 1.39636I
a = −0.486577 − 0.820787I
b = −1.156320 + 0.188953I
−5.67735 + 7.60097I 0
u = 0.05852 + 1.42211I
a = −0.020754 + 0.973316I
b = −0.067011 − 0.763857I
5.50108 − 1.93754I 0
u = 0.05852 − 1.42211I
a = −0.020754 − 0.973316I
b = −0.067011 + 0.763857I
5.50108 + 1.93754I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.17975 + 1.44172I
a = 0.063972 + 0.963885I
b = 0.192321 − 0.811399I
−1.08595 + 4.44930I 0
u = −0.17975 − 1.44172I
a = 0.063972 − 0.963885I
b = 0.192321 + 0.811399I
−1.08595 − 4.44930I 0
u = −0.10818 + 1.48887I
a = 0.53625 − 1.98157I
b = −0.926383 + 0.789415I
4.95976 + 3.21067I 0
u = −0.10818 − 1.48887I
a = 0.53625 + 1.98157I
b = −0.926383 − 0.789415I
4.95976 − 3.21067I 0
u = 0.499570
a = 1.32716
b = 0.807460
−1.30268 −6.90340
u = 0.04216 + 1.51719I
a = 0.87256 − 1.55666I
b = −0.847474 + 0.830941I
5.21368 + 2.83714I 0
u = 0.04216 − 1.51719I
a = 0.87256 + 1.55666I
b = −0.847474 − 0.830941I
5.21368 − 2.83714I 0
u = 0.35569 + 1.47673I
a = 0.29387 − 2.00895I
b = 1.050800 + 0.751869I
0.5934 − 14.1941I 0
u = 0.35569 − 1.47673I
a = 0.29387 + 2.00895I
b = 1.050800 − 0.751869I
0.5934 + 14.1941I 0
u = −0.32039 + 1.49216I
a = −0.995709 − 0.809498I
b = 0.677206 + 0.890530I
1.74717 + 8.10835I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.32039 − 1.49216I
a = −0.995709 + 0.809498I
b = 0.677206 − 0.890530I
1.74717 − 8.10835I 0
u = −0.29726 + 1.49890I
a = −0.10605 − 2.00465I
b = −1.025040 + 0.769571I
8.28669 + 11.14520I 0
u = −0.29726 − 1.49890I
a = −0.10605 + 2.00465I
b = −1.025040 − 0.769571I
8.28669 − 11.14520I 0
u = 0.22688 + 1.51321I
a = −0.11620 − 1.98583I
b = 0.991790 + 0.785678I
9.55198 − 6.67114I 0
u = 0.22688 − 1.51321I
a = −0.11620 + 1.98583I
b = 0.991790 − 0.785678I
9.55198 + 6.67114I 0
u = 0.24946 + 1.51401I
a = 0.995693 − 0.981031I
b = −0.725795 + 0.880563I
9.21413 − 5.02177I 0
u = 0.24946 − 1.51401I
a = 0.995693 + 0.981031I
b = −0.725795 − 0.880563I
9.21413 + 5.02177I 0
u = −0.17017 + 1.52793I
a = −0.96695 − 1.18510I
b = 0.776005 + 0.866492I
10.22350 + 0.53227I 0
u = −0.17017 − 1.52793I
a = −0.96695 + 1.18510I
b = 0.776005 − 0.866492I
10.22350 − 0.53227I 0
u = 0.244758 + 0.351804I
a = 0.155281 + 0.307568I
b = 0.120495 + 0.345871I
−0.138519 − 0.946103I −2.87476 + 7.19365I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.244758 − 0.351804I
a = 0.155281 − 0.307568I
b = 0.120495 − 0.345871I
−0.138519 + 0.946103I −2.87476 − 7.19365I
u = 0.282593 + 0.153006I
a = −4.08925 − 1.68114I
b = −0.949049 + 0.506277I
−8.95062 + 1.80203I −12.10355 − 2.75353I
u = 0.282593 − 0.153006I
a = −4.08925 + 1.68114I
b = −0.949049 − 0.506277I
−8.95062 − 1.80203I −12.10355 + 2.75353I
u = −0.180687 + 0.202078I
a = 0.02811 + 3.86747I
b = 0.881222 − 0.565760I
−0.97228 + 2.21380I −11.07503 − 3.04073I
u = −0.180687 − 0.202078I
a = 0.02811 − 3.86747I
b = 0.881222 + 0.565760I
−0.97228 − 2.21380I −11.07503 + 3.04073I
11
II. I
u
2
= h−a
3
u − 2a
2
u − 3a
2
+ au + 2b − 4a + 3u − 1, a
4
− 4a
3
u + a
3
−
3a
2
u − 4a
2
− 4a + 2u, u
2
+ 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
−1
a
8
=
a
1
2
a
3
u + a
2
u + ··· + 2a +
1
2
a
2
=
−
1
2
a
3
u −
3
2
a
2
u + ··· −
1
2
a
2
−
1
2
a
3
2
a
2
u + 2au + ··· +
1
2
a +
1
2
a
1
=
−
1
2
a
3
u +
3
2
au + ··· −
3
2
a
2
+
1
2
3
2
a
2
u + 2au + ··· +
1
2
a +
1
2
a
11
=
1
2
a
3
u −
3
2
au + ··· +
3
2
a
2
−
1
2
−a + 2u
a
7
=
3
2
a
2
u −
1
2
u + ··· +
3
2
a +
1
2
1
2
a
3
u + a
2
u + ··· + 2a +
1
2
a
6
=
−
3
2
a
2
u +
1
2
u + ··· −
3
2
a +
1
2
−
3
2
a
2
u + au + ··· −
3
2
a +
1
2
a
9
=
u
0
a
5
=
0
−1
a
12
=
−
1
2
a
3
u +
3
2
au + ··· −
3
2
a
2
+
1
2
−
1
2
a
3
u +
3
2
a
2
u + ··· +
1
2
a + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 2a
3
− 6a
2
u + 4a
2
− 8au − 2a − 2u − 10
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)
4
c
2
, c
7
(u
4
− u
2
+ 1)
2
c
3
, c
4
, c
9
(u
2
+ 1)
4
c
5
, c
6
, c
11
c
12
(u
4
+ 3u
2
+ 1)
2
c
8
(u
2
+ u + 1)
4
c
10
(u
2
+ u − 1)
4
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
(y
2
+ y + 1)
4
c
2
, c
7
(y
2
− y + 1)
4
c
3
, c
4
, c
9
(y + 1)
8
c
5
, c
6
, c
11
c
12
(y
2
+ 3y + 1)
4
c
10
(y
2
− 3y + 1)
4
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −0.809017 − 0.401259I
b = −0.866025 − 0.500000I
−7.23771 − 2.02988I −6.00000 + 3.46410I
u = 1.000000I
a = 0.309017 + 0.464767I
b = 0.866025 − 0.500000I
0.65797 + 2.02988I −6.00000 − 3.46410I
u = 1.000000I
a = 0.30902 + 1.53523I
b = −0.866025 − 0.500000I
0.65797 − 2.02988I −6.00000 + 3.46410I
u = 1.000000I
a = −0.80902 + 2.40126I
b = 0.866025 − 0.500000I
−7.23771 + 2.02988I −6.00000 − 3.46410I
u = − 1.000000I
a = −0.809017 + 0.401259I
b = −0.866025 + 0.500000I
−7.23771 + 2.02988I −6.00000 − 3.46410I
u = − 1.000000I
a = 0.309017 − 0.464767I
b = 0.866025 + 0.500000I
0.65797 − 2.02988I −6.00000 + 3.46410I
u = − 1.000000I
a = 0.30902 − 1.53523I
b = −0.866025 + 0.500000I
0.65797 + 2.02988I −6.00000 − 3.46410I
u = − 1.000000I
a = −0.80902 − 2.40126I
b = 0.866025 + 0.500000I
−7.23771 − 2.02988I −6.00000 + 3.46410I
15
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
4
)(u
65
+ 21u
64
+ ··· − 19u + 25)
c
2
, c
7
((u
4
− u
2
+ 1)
2
)(u
65
+ u
64
+ ··· + 9u + 5)
c
3
, c
4
, c
9
((u
2
+ 1)
4
)(u
65
+ u
64
+ ··· + 12u + 4)
c
5
, c
6
, c
11
c
12
((u
4
+ 3u
2
+ 1)
2
)(u
65
− u
64
+ ··· − 11u + 1)
c
8
((u
2
+ u + 1)
4
)(u
65
+ 21u
64
+ ··· − 19u + 25)
c
10
((u
2
+ u − 1)
4
)(u
65
− 15u
64
+ ··· + 14637u − 579)
16
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
8
((y
2
+ y + 1)
4
)(y
65
+ 51y
64
+ ··· + 23161y −625)
c
2
, c
7
((y
2
− y + 1)
4
)(y
65
− 21y
64
+ ··· − 19y −25)
c
3
, c
4
, c
9
((y + 1)
8
)(y
65
+ 63y
64
+ ··· + 40y −16)
c
5
, c
6
, c
11
c
12
((y
2
+ 3y + 1)
4
)(y
65
+ 75y
64
+ ··· + 33y −1)
c
10
((y
2
− 3y + 1)
4
)(y
65
+ 15y
64
+ ··· + 3.25052 × 10
7
y −335241)
17
