12a
0009
(K12a
0009
)
A knot diagram
1
Linearized knot diagam
3 5 6 8 2 11 4 1 12 7 10 9
Solving Sequence
4,7
8
5,11
6 3 2 1 10 12 9
c
7
c
4
c
6
c
3
c
2
c
1
c
10
c
11
c
9
c
5
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h1.86386 × 10
139
u
66
+ 4.31229 × 10
138
u
65
+ ··· + 1.98538 × 10
140
b + 5.26231 × 10
141
,
1.05918 × 10
140
u
66
− 4.57520 × 10
138
u
65
+ ··· + 7.94151 × 10
140
a + 2.63032 × 10
142
,
u
67
+ u
66
+ ··· + 384u + 256i
I
v
1
= ha, 18v
7
− 26v
6
+ 12v
5
− 78v
4
+ 71v
3
+ 30v
2
+ 19b + 6v −2, v
8
− 2v
7
+ v
6
− 4v
5
+ 6v
4
+ v
3
− 2v
2
− v + 1i
* 2 irreducible components of dim
C
= 0, with total 75 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
= h1.86 × 10
139
u
66
+ 4.31 × 10
138
u
65
+ · · · + 1.99 × 10
140
b + 5.26 ×
10
141
, 1.06 × 10
140
u
66
− 4.58 × 10
138
u
65
+ · · · + 7.94 × 10
140
a + 2.63 ×
10
142
, u
67
+ u
66
+ · · · + 384u + 256i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
5
=
−u
−u
3
+ u
a
11
=
−0.133372u
66
+ 0.00576112u
65
+ ··· − 11.7330u − 33.1212
−0.0938796u
66
− 0.0217203u
65
+ ··· − 6.32205u − 26.5053
a
6
=
0.209669u
66
+ 0.0230614u
65
+ ··· + 21.6013u + 63.8657
−0.0241755u
66
+ 0.0237769u
65
+ ··· − 9.20588u − 1.31583
a
3
=
−0.142701u
66
− 0.0190334u
65
+ ··· − 17.1447u − 45.4624
−0.0396775u
66
− 0.0112029u
65
+ ··· − 1.07906u − 14.6917
a
2
=
−0.111576u
66
+ 0.000157764u
65
+ ··· − 14.6284u − 30.1716
−0.0827762u
66
− 0.0101687u
65
+ ··· − 6.98086u − 26.9277
a
1
=
−0.185494u
66
− 0.0468383u
65
+ ··· − 12.3954u − 62.5498
−0.120165u
66
− 0.00728459u
65
+ ··· − 14.9632u − 36.8117
a
10
=
−0.227252u
66
− 0.0159592u
65
+ ··· − 18.0550u − 59.6265
−0.0938796u
66
− 0.0217203u
65
+ ··· − 6.32205u − 26.5053
a
12
=
−0.280258u
66
− 0.0158075u
65
+ ··· − 25.1937u − 78.0193
−0.194157u
66
− 0.0107796u
65
+ ··· − 23.6385u − 52.3816
a
9
=
−0.0947524u
66
− 0.0190567u
65
+ ··· − 3.59061u − 27.7303
−0.0296424u
66
− 0.00314345u
65
+ ··· − 7.50843u − 12.6063
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.257514u
66
+ 0.0210201u
65
+ ··· − 47.1768u − 88.2413
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
67
+ 35u
66
+ ··· − 6u − 1
c
2
, c
5
u
67
+ 5u
66
+ ··· + 4u + 1
c
3
u
67
− 5u
66
+ ··· − 4396u + 833
c
4
, c
7
u
67
+ u
66
+ ··· + 384u + 256
c
6
, c
10
u
67
+ 3u
66
+ ··· + 3u
2
+ 1
c
8
, c
9
, c
11
c
12
u
67
− 13u
66
+ ··· − 6u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
67
− y
66
+ ··· + 26y −1
c
2
, c
5
y
67
+ 35y
66
+ ··· − 6y −1
c
3
y
67
− 37y
66
+ ··· − 10001782y −693889
c
4
, c
7
y
67
− 45y
66
+ ··· + 770048y −65536
c
6
, c
10
y
67
+ 13y
66
+ ··· − 6y −1
c
8
, c
9
, c
11
c
12
y
67
+ 85y
66
+ ··· − 214y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.056677 + 1.011830I
a = 0.252444 + 1.241020I
b = −0.625082 − 0.683742I
−2.90819 + 1.25830I −6.22598 − 0.52297I
u = 0.056677 − 1.011830I
a = 0.252444 − 1.241020I
b = −0.625082 + 0.683742I
−2.90819 − 1.25830I −6.22598 + 0.52297I
u = 0.906722 + 0.307406I
a = −0.59144 + 2.02468I
b = −0.162929 − 0.884018I
1.04581 − 2.21513I 3.46945 + 4.65316I
u = 0.906722 − 0.307406I
a = −0.59144 − 2.02468I
b = −0.162929 + 0.884018I
1.04581 + 2.21513I 3.46945 − 4.65316I
u = −0.259205 + 1.013680I
a = 0.20161 + 1.64344I
b = −0.585248 − 0.823431I
−2.45553 − 5.81631I −4.24111 + 7.61398I
u = −0.259205 − 1.013680I
a = 0.20161 − 1.64344I
b = −0.585248 + 0.823431I
−2.45553 + 5.81631I −4.24111 − 7.61398I
u = −1.05818
a = −0.130055
b = −0.564378
−1.77256 −5.82730
u = 0.024549 + 1.103900I
a = 0.011764 + 1.076850I
b = 0.892018 − 0.929882I
−8.60500 + 3.29350I 0
u = 0.024549 − 1.103900I
a = 0.011764 − 1.076850I
b = 0.892018 + 0.929882I
−8.60500 − 3.29350I 0
u = 0.850621 + 0.246223I
a = 2.15946 − 0.58175I
b = 0.531404 + 0.791131I
−0.45674 − 4.58253I −3.79920 + 9.11658I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.850621 − 0.246223I
a = 2.15946 + 0.58175I
b = 0.531404 − 0.791131I
−0.45674 + 4.58253I −3.79920 − 9.11658I
u = −1.117870 + 0.087817I
a = −0.34576 + 1.97594I
b = −0.269852 − 0.943591I
−2.13038 + 1.08941I 0
u = −1.117870 − 0.087817I
a = −0.34576 − 1.97594I
b = −0.269852 + 0.943591I
−2.13038 − 1.08941I 0
u = −1.168910 + 0.077988I
a = −1.115420 − 0.446467I
b = −0.898793 − 0.925547I
−9.32041 − 0.45884I 0
u = −1.168910 − 0.077988I
a = −1.115420 + 0.446467I
b = −0.898793 + 0.925547I
−9.32041 + 0.45884I 0
u = 1.169990 + 0.122396I
a = −1.54997 + 0.03674I
b = −0.893032 − 0.937574I
−9.28166 − 6.15285I 0
u = 1.169990 − 0.122396I
a = −1.54997 − 0.03674I
b = −0.893032 + 0.937574I
−9.28166 + 6.15285I 0
u = −0.801751 + 0.037628I
a = 1.81454 − 0.67480I
b = 0.533091 − 0.711518I
−0.726291 − 0.492318I −6.66330 − 1.23227I
u = −0.801751 − 0.037628I
a = 1.81454 + 0.67480I
b = 0.533091 + 0.711518I
−0.726291 + 0.492318I −6.66330 + 1.23227I
u = 0.565014 + 0.542577I
a = −1.22383 + 2.12227I
b = −0.010154 − 0.774344I
2.09008 − 1.39139I 6.88883 + 3.94894I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.565014 − 0.542577I
a = −1.22383 − 2.12227I
b = −0.010154 + 0.774344I
2.09008 + 1.39139I 6.88883 − 3.94894I
u = −1.166070 + 0.351089I
a = −0.46834 − 2.13436I
b = −0.162727 + 0.958944I
−1.53806 + 6.56529I 0
u = −1.166070 − 0.351089I
a = −0.46834 + 2.13436I
b = −0.162727 − 0.958944I
−1.53806 − 6.56529I 0
u = 0.209708 + 0.728648I
a = −0.02695 − 1.51557I
b = −0.495464 + 0.766624I
−0.11293 + 1.90039I 0.16873 − 4.13136I
u = 0.209708 − 0.728648I
a = −0.02695 + 1.51557I
b = −0.495464 − 0.766624I
−0.11293 − 1.90039I 0.16873 + 4.13136I
u = −0.464969 + 0.565453I
a = −0.299278 − 0.865709I
b = −0.434046 + 0.466211I
−0.85344 + 1.32721I −6.30018 − 4.02616I
u = −0.464969 − 0.565453I
a = −0.299278 + 0.865709I
b = −0.434046 − 0.466211I
−0.85344 − 1.32721I −6.30018 + 4.02616I
u = 1.191720 + 0.459562I
a = 1.14460 − 1.50739I
b = 0.580446 + 0.918238I
−3.08979 − 6.51525I 0
u = 1.191720 − 0.459562I
a = 1.14460 + 1.50739I
b = 0.580446 − 0.918238I
−3.08979 + 6.51525I 0
u = −1.240190 + 0.334781I
a = 0.053213 + 0.132726I
b = 0.717680 + 0.579006I
−4.20067 + 1.70229I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.240190 − 0.334781I
a = 0.053213 − 0.132726I
b = 0.717680 − 0.579006I
−4.20067 − 1.70229I 0
u = −0.601061 + 0.371818I
a = 0.128143 + 0.972761I
b = 0.851577 − 0.886506I
−7.28010 + 1.81664I −8.55201 − 4.80888I
u = −0.601061 − 0.371818I
a = 0.128143 − 0.972761I
b = 0.851577 + 0.886506I
−7.28010 − 1.81664I −8.55201 + 4.80888I
u = 1.281160 + 0.200682I
a = 0.0251805 + 0.1116100I
b = −0.659788 − 0.071314I
−4.97897 − 4.12056I 0
u = 1.281160 − 0.200682I
a = 0.0251805 − 0.1116100I
b = −0.659788 + 0.071314I
−4.97897 + 4.12056I 0
u = −1.280000 + 0.267333I
a = 0.84169 + 1.26843I
b = 0.647196 − 0.914761I
−7.47404 + 3.11915I 0
u = −1.280000 − 0.267333I
a = 0.84169 − 1.26843I
b = 0.647196 + 0.914761I
−7.47404 − 3.11915I 0
u = 0.565494 + 0.375805I
a = 0.148591 + 1.093030I
b = 0.839438 − 0.928418I
−7.15245 + 4.47005I −7.71055 + 0.32064I
u = 0.565494 − 0.375805I
a = 0.148591 − 1.093030I
b = 0.839438 + 0.928418I
−7.15245 − 4.47005I −7.71055 − 0.32064I
u = −0.394937 + 0.543945I
a = −2.11231 − 2.23101I
b = 0.104773 + 0.712271I
0.99271 − 2.93977I 4.97131 + 1.61882I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.394937 − 0.543945I
a = −2.11231 + 2.23101I
b = 0.104773 − 0.712271I
0.99271 + 2.93977I 4.97131 − 1.61882I
u = 0.183363 + 1.320840I
a = −0.033195 − 1.055920I
b = 0.911335 + 0.923319I
−11.93250 + 0.86287I 0
u = 0.183363 − 1.320840I
a = −0.033195 + 1.055920I
b = 0.911335 − 0.923319I
−11.93250 − 0.86287I 0
u = −0.222777 + 1.317480I
a = −0.010363 − 1.118770I
b = 0.898644 + 0.948171I
−11.85170 − 7.53264I 0
u = −0.222777 − 1.317480I
a = −0.010363 + 1.118770I
b = 0.898644 − 0.948171I
−11.85170 + 7.53264I 0
u = 0.508545 + 0.407974I
a = −0.23707 − 1.67495I
b = −0.386976 + 0.820574I
0.19428 + 1.92540I −0.71393 − 3.09643I
u = 0.508545 − 0.407974I
a = −0.23707 + 1.67495I
b = −0.386976 − 0.820574I
0.19428 − 1.92540I −0.71393 + 3.09643I
u = 1.375410 + 0.137221I
a = 0.136625 + 0.141678I
b = 0.765167 − 0.641306I
−8.37009 + 2.07396I 0
u = 1.375410 − 0.137221I
a = 0.136625 − 0.141678I
b = 0.765167 + 0.641306I
−8.37009 − 2.07396I 0
u = −1.297480 + 0.545966I
a = 0.99218 + 1.66578I
b = 0.578591 − 0.954312I
−5.83001 + 11.50930I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.297480 − 0.545966I
a = 0.99218 − 1.66578I
b = 0.578591 + 0.954312I
−5.83001 − 11.50930I 0
u = 1.36159 + 0.46010I
a = −0.1117340 − 0.0569109I
b = 0.759058 − 0.543606I
−7.18404 − 6.58171I 0
u = 1.36159 − 0.46010I
a = −0.1117340 + 0.0569109I
b = 0.759058 + 0.543606I
−7.18404 + 6.58171I 0
u = −0.226790 + 0.512847I
a = −1.193550 + 0.040521I
b = 0.239619 + 0.182955I
−0.33336 + 1.65382I −2.71310 − 4.65579I
u = −0.226790 − 0.512847I
a = −1.193550 − 0.040521I
b = 0.239619 − 0.182955I
−0.33336 − 1.65382I −2.71310 + 4.65579I
u = 1.38489 + 0.55760I
a = −1.17727 + 1.10112I
b = −0.891489 − 0.970679I
−12.8397 − 9.2457I 0
u = 1.38489 − 0.55760I
a = −1.17727 − 1.10112I
b = −0.891489 + 0.970679I
−12.8397 + 9.2457I 0
u = −1.39960 + 0.53092I
a = −0.017508 − 0.147534I
b = −0.927330 − 0.902590I
−13.06210 + 2.54998I 0
u = −1.39960 − 0.53092I
a = −0.017508 + 0.147534I
b = −0.927330 + 0.902590I
−13.06210 − 2.54998I 0
u = −1.42700 + 0.68349I
a = −1.05188 − 1.26038I
b = −0.889746 + 0.979952I
−15.7150 + 14.6442I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.42700 − 0.68349I
a = −1.05188 + 1.26038I
b = −0.889746 − 0.979952I
−15.7150 − 14.6442I 0
u = 1.44635 + 0.66308I
a = 0.138752 + 0.035309I
b = −0.935151 + 0.894911I
−15.9934 − 7.9304I 0
u = 1.44635 − 0.66308I
a = 0.138752 − 0.035309I
b = −0.935151 − 0.894911I
−15.9934 + 7.9304I 0
u = −1.55039 + 0.42301I
a = −0.949405 − 0.872633I
b = −0.906199 + 0.967999I
−17.8393 + 5.4177I 0
u = −1.55039 − 0.42301I
a = −0.949405 + 0.872633I
b = −0.906199 − 0.967999I
−17.8393 − 5.4177I 0
u = 1.56628 + 0.38972I
a = −0.218508 − 0.080153I
b = −0.933842 + 0.917694I
−18.0048 + 1.3484I 0
u = 1.56628 − 0.38972I
a = −0.218508 + 0.080153I
b = −0.933842 − 0.917694I
−18.0048 − 1.3484I 0
11
II.
I
v
1
= ha, 18v
7
−26v
6
+· · · + 19b − 2, v
8
−2v
7
+v
6
−4v
5
+6v
4
+v
3
−2v
2
−v +1i
(i) Arc colorings
a
4
=
v
0
a
7
=
1
0
a
8
=
1
0
a
5
=
v
0
a
11
=
0
−0.947368v
7
+ 1.36842v
6
+ ··· − 0.315789v + 0.105263
a
6
=
1
−1.26316v
7
+ 2.15789v
6
+ ··· − 0.421053v + 1.47368
a
3
=
0.368421v
7
− 0.421053v
6
+ ··· + 0.789474v −1.26316
0.263158v
7
− 0.157895v
6
+ ··· + 2.42105v −0.473684
a
2
=
0.0526316v
7
+ 0.368421v
6
+ ··· + 0.684211v −0.894737
0.263158v
7
− 0.157895v
6
+ ··· + 2.42105v −0.473684
a
1
=
−1
1.26316v
7
− 2.15789v
6
+ ··· + 0.421053v −1.47368
a
10
=
−0.947368v
7
+ 1.36842v
6
+ ··· − 0.315789v + 0.105263
−0.947368v
7
+ 1.36842v
6
+ ··· − 0.315789v + 0.105263
a
12
=
−0.789474v
7
+ 1.47368v
6
+ ··· − 0.263158v + 2.42105
−1.73684v
7
+ 2.84211v
6
+ ··· − 0.578947v + 2.52632
a
9
=
1.26316v
7
− 2.15789v
6
+ ··· + 0.421053v −0.473684
0.473684v
7
− 0.684211v
6
+ ··· + 0.157895v + 1.94737
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
23
19
v
7
−
9
19
v
6
+
67
19
v
5
+
49
19
v
4
+
94
19
v
3
−
298
19
v
2
+
43
19
v +
11
19
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
(u
2
− u + 1)
4
c
2
(u
2
+ u + 1)
4
c
4
, c
7
u
8
c
6
(u
4
+ u
3
+ u
2
+ 1)
2
c
8
, c
9
(u
4
+ u
3
+ 3u
2
+ 2u + 1)
2
c
10
(u
4
− u
3
+ u
2
+ 1)
2
c
11
, c
12
(u
4
− u
3
+ 3u
2
− 2u + 1)
2
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
(y
2
+ y + 1)
4
c
4
, c
7
y
8
c
6
, c
10
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
2
c
8
, c
9
, c
11
c
12
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
2
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.576953 + 0.283088I
a = 0
b = −0.851808 − 0.911292I
−6.79074 − 1.13408I −2.09237 − 2.48762I
v = 0.576953 − 0.283088I
a = 0
b = −0.851808 + 0.911292I
−6.79074 + 1.13408I −2.09237 + 2.48762I
v = −0.533637 + 0.358112I
a = 0
b = −0.851808 − 0.911292I
−6.79074 − 5.19385I −2.75261 + 7.88731I
v = −0.533637 − 0.358112I
a = 0
b = −0.851808 + 0.911292I
−6.79074 + 5.19385I −2.75261 − 7.88731I
v = 1.54112 + 0.21492I
a = 0
b = 0.351808 − 0.720342I
0.211005 − 0.614778I 2.55284 − 0.89520I
v = 1.54112 − 0.21492I
a = 0
b = 0.351808 + 0.720342I
0.211005 + 0.614778I 2.55284 + 0.89520I
v = −0.58443 + 1.44211I
a = 0
b = 0.351808 + 0.720342I
0.21101 − 3.44499I −2.20786 + 6.97475I
v = −0.58443 − 1.44211I
a = 0
b = 0.351808 − 0.720342I
0.21101 + 3.44499I −2.20786 − 6.97475I
15
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
4
)(u
67
+ 35u
66
+ ··· − 6u − 1)
c
2
((u
2
+ u + 1)
4
)(u
67
+ 5u
66
+ ··· + 4u + 1)
c
3
((u
2
− u + 1)
4
)(u
67
− 5u
66
+ ··· − 4396u + 833)
c
4
, c
7
u
8
(u
67
+ u
66
+ ··· + 384u + 256)
c
5
((u
2
− u + 1)
4
)(u
67
+ 5u
66
+ ··· + 4u + 1)
c
6
((u
4
+ u
3
+ u
2
+ 1)
2
)(u
67
+ 3u
66
+ ··· + 3u
2
+ 1)
c
8
, c
9
((u
4
+ u
3
+ 3u
2
+ 2u + 1)
2
)(u
67
− 13u
66
+ ··· − 6u + 1)
c
10
((u
4
− u
3
+ u
2
+ 1)
2
)(u
67
+ 3u
66
+ ··· + 3u
2
+ 1)
c
11
, c
12
((u
4
− u
3
+ 3u
2
− 2u + 1)
2
)(u
67
− 13u
66
+ ··· − 6u + 1)
16
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
4
)(y
67
− y
66
+ ··· + 26y −1)
c
2
, c
5
((y
2
+ y + 1)
4
)(y
67
+ 35y
66
+ ··· − 6y −1)
c
3
((y
2
+ y + 1)
4
)(y
67
− 37y
66
+ ··· − 1.00018 × 10
7
y −693889)
c
4
, c
7
y
8
(y
67
− 45y
66
+ ··· + 770048y −65536)
c
6
, c
10
((y
4
+ y
3
+ 3y
2
+ 2y + 1)
2
)(y
67
+ 13y
66
+ ··· − 6y −1)
c
8
, c
9
, c
11
c
12
((y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
2
)(y
67
+ 85y
66
+ ··· − 214y −1)
17
