12n
0014
(K12n
0014
)
A knot diagram
1
Linearized knot diagam
3 5 6 7 2 10 5 12 6 8 9 11
Solving Sequence
5,7 8,10
11 4 6 3 2 1 9 12
c
7
c
10
c
4
c
6
c
3
c
2
c
1
c
9
c
11
c
5
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−3.93906 × 10
169
u
53
+ 8.11692 × 10
169
u
52
+ ··· + 2.56580 × 10
172
b + 5.59119 × 10
173
,
2.70535 × 10
172
u
53
+ 1.41390 × 10
173
u
52
+ ··· + 1.43685 × 10
174
a + 5.91275 × 10
175
,
u
54
+ 5u
53
+ ··· + 2048u + 1024i
I
v
1
= ha, 8286v
9
− 14092v
8
+ ··· + 8095b + 12581,
v
10
− v
9
− 2v
8
− 19v
7
+ 12v
6
+ 35v
5
+ 50v
4
+ 34v
3
+ 17v
2
+ 5v + 1i
* 2 irreducible components of dim
C
= 0, with total 64 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−3.94 × 10
169
u
53
+ 8.12 × 10
169
u
52
+ · · · + 2.57 × 10
172
b + 5.59 ×
10
173
, 2.71 × 10
172
u
53
+ 1.41 × 10
173
u
52
+ · · · + 1.44 × 10
174
a + 5.91 ×
10
175
, u
54
+ 5u
53
+ · · · + 2048u + 1024i
(i) Arc colorings
a
5
=
0
u
a
7
=
1
0
a
8
=
1
−u
2
a
10
=
−0.0188284u
53
− 0.0984027u
52
+ ··· − 57.6613u − 41.1508
0.00153522u
53
− 0.00316351u
52
+ ··· + 2.45774u − 21.7912
a
11
=
−0.0323517u
53
− 0.147501u
52
+ ··· − 88.1255u − 23.7227
0.0109343u
53
+ 0.0438860u
52
+ ··· + 26.5354u − 2.82844
a
4
=
−u
u
a
6
=
−0.0118561u
53
− 0.0590764u
52
+ ··· − 36.2368u − 21.2553
0.0134039u
53
+ 0.0620483u
52
+ ··· + 36.4660u + 13.4608
a
3
=
0.00441031u
53
+ 0.0172727u
52
+ ··· + 10.8004u − 5.96037
0.00533450u
53
+ 0.0282151u
52
+ ··· + 13.6825u + 15.5729
a
2
=
0.00441031u
53
+ 0.0172727u
52
+ ··· + 10.8004u − 5.96037
0.00669340u
53
+ 0.0361984u
52
+ ··· + 18.9533u + 20.4664
a
1
=
−0.00154779u
53
− 0.00297199u
52
+ ··· − 0.229176u + 7.79450
0.0169009u
53
+ 0.0786020u
52
+ ··· + 44.6438u + 18.3421
a
9
=
−0.00933751u
53
− 0.0594844u
52
+ ··· − 30.9568u − 43.0824
−0.0225428u
53
− 0.0990264u
52
+ ··· − 54.4975u − 12.8121
a
12
=
−0.0399571u
53
− 0.175227u
52
+ ··· − 100.366u − 19.0531
0.00625323u
53
+ 0.0325196u
52
+ ··· + 12.5340u + 17.1289
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.00845297u
53
− 0.0644904u
52
+ ··· − 23.1790u − 60.4595
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
54
+ 14u
53
+ ··· − 53u + 1
c
2
, c
5
u
54
+ 6u
53
+ ··· + 15u + 1
c
3
u
54
− 6u
53
+ ··· + 11895099u + 596177
c
4
, c
7
u
54
+ 5u
53
+ ··· + 2048u + 1024
c
6
, c
9
u
54
+ 3u
53
+ ··· + 4u
2
+ 1
c
8
, c
11
u
54
+ 3u
53
+ ··· − 2u + 1
c
10
u
54
− 3u
53
+ ··· − 8544u + 1217
c
12
u
54
+ 23u
53
+ ··· + 8u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
54
+ 58y
53
+ ··· + 2411y + 1
c
2
, c
5
y
54
+ 14y
53
+ ··· − 53y + 1
c
3
y
54
+ 102y
53
+ ··· − 14429377332621y + 355427015329
c
4
, c
7
y
54
− 55y
53
+ ··· − 4194304y + 1048576
c
6
, c
9
y
54
− 5y
53
+ ··· + 8y + 1
c
8
, c
11
y
54
+ 23y
53
+ ··· + 8y + 1
c
10
y
54
+ 15y
53
+ ··· + 18080344y + 1481089
c
12
y
54
+ 19y
53
+ ··· − 160y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.968225 + 0.607102I
a = −0.164875 − 0.865628I
b = 0.789588 + 0.453320I
−3.62207 − 1.88435I 0
u = −0.968225 − 0.607102I
a = −0.164875 + 0.865628I
b = 0.789588 − 0.453320I
−3.62207 + 1.88435I 0
u = 0.556588 + 0.619363I
a = 0.901194 + 0.566536I
b = 0.051996 − 0.642624I
0.99939 + 1.40813I 3.91416 − 3.69919I
u = 0.556588 − 0.619363I
a = 0.901194 − 0.566536I
b = 0.051996 + 0.642624I
0.99939 − 1.40813I 3.91416 + 3.69919I
u = −0.661385 + 0.335932I
a = 1.52538 − 0.28332I
b = −0.395578 + 0.434236I
−0.24598 + 2.82121I 1.02280 − 2.27971I
u = −0.661385 − 0.335932I
a = 1.52538 + 0.28332I
b = −0.395578 − 0.434236I
−0.24598 − 2.82121I 1.02280 + 2.27971I
u = −0.569346 + 0.474090I
a = 1.99530 − 0.80720I
b = 0.663565 − 0.017228I
0.611788 + 1.006080I −3.88173 − 0.39430I
u = −0.569346 − 0.474090I
a = 1.99530 + 0.80720I
b = 0.663565 + 0.017228I
0.611788 − 1.006080I −3.88173 + 0.39430I
u = 0.511621 + 0.452929I
a = −0.55984 − 1.59306I
b = 0.023415 + 0.808214I
−1.18484 − 1.48546I −2.98046 + 1.14168I
u = 0.511621 − 0.452929I
a = −0.55984 + 1.59306I
b = 0.023415 − 0.808214I
−1.18484 + 1.48546I −2.98046 − 1.14168I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.423245 + 0.528845I
a = 0.207901 + 0.031710I
b = 1.208630 − 0.192759I
−2.63355 + 1.15153I −2.76262 + 2.47931I
u = −0.423245 − 0.528845I
a = 0.207901 − 0.031710I
b = 1.208630 + 0.192759I
−2.63355 − 1.15153I −2.76262 − 2.47931I
u = −0.362967 + 0.571541I
a = 0.026420 + 0.236077I
b = −1.351430 − 0.085409I
−6.34508 − 2.87510I −9.60101 + 6.45832I
u = −0.362967 − 0.571541I
a = 0.026420 − 0.236077I
b = −1.351430 + 0.085409I
−6.34508 + 2.87510I −9.60101 − 6.45832I
u = −0.376666 + 0.551588I
a = −3.09962 + 1.34006I
b = −0.581470 + 0.039436I
0.57291 − 3.72246I −7.65423 + 7.89265I
u = −0.376666 − 0.551588I
a = −3.09962 − 1.34006I
b = −0.581470 − 0.039436I
0.57291 + 3.72246I −7.65423 − 7.89265I
u = −0.443126 + 0.469766I
a = 0.023144 − 0.202231I
b = −1.41853 + 0.34093I
−5.84105 + 5.81566I −4.21669 + 1.36326I
u = −0.443126 − 0.469766I
a = 0.023144 + 0.202231I
b = −1.41853 − 0.34093I
−5.84105 − 5.81566I −4.21669 − 1.36326I
u = 0.604914 + 0.174580I
a = −0.76546 − 3.52241I
b = 0.255821 + 0.548310I
−0.60959 + 4.26256I 4.62783 − 4.73451I
u = 0.604914 − 0.174580I
a = −0.76546 + 3.52241I
b = 0.255821 − 0.548310I
−0.60959 − 4.26256I 4.62783 + 4.73451I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.41543 + 0.25569I
a = 0.548000 − 0.556665I
b = −0.535084 + 0.575642I
0.04114 + 3.00401I 0
u = −1.41543 − 0.25569I
a = 0.548000 + 0.556665I
b = −0.535084 − 0.575642I
0.04114 − 3.00401I 0
u = 1.44011 + 0.26608I
a = −0.018030 + 0.946466I
b = 0.96835 − 1.18906I
3.23271 + 1.00154I 0
u = 1.44011 − 0.26608I
a = −0.018030 − 0.946466I
b = 0.96835 + 1.18906I
3.23271 − 1.00154I 0
u = −1.43048 + 0.47132I
a = 0.048317 − 0.972966I
b = 1.15296 + 1.07758I
2.63538 − 7.17562I 0
u = −1.43048 − 0.47132I
a = 0.048317 + 0.972966I
b = 1.15296 − 1.07758I
2.63538 + 7.17562I 0
u = 0.365593 + 0.176466I
a = −2.89742 − 7.37153I
b = −0.313165 + 0.318803I
−0.056183 − 0.359580I 11.4178 − 26.2253I
u = 0.365593 − 0.176466I
a = −2.89742 + 7.37153I
b = −0.313165 − 0.318803I
−0.056183 + 0.359580I 11.4178 + 26.2253I
u = 0.086973 + 0.349018I
a = 0.92423 + 1.33854I
b = 0.377234 − 0.508733I
−0.22325 + 1.43278I −1.54657 − 5.02280I
u = 0.086973 − 0.349018I
a = 0.92423 − 1.33854I
b = 0.377234 + 0.508733I
−0.22325 − 1.43278I −1.54657 + 5.02280I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.63008 + 0.27442I
a = −0.070772 − 0.883996I
b = 1.03860 + 1.15294I
7.40537 + 7.44620I 0
u = 1.63008 − 0.27442I
a = −0.070772 + 0.883996I
b = 1.03860 − 1.15294I
7.40537 − 7.44620I 0
u = −1.65228 + 0.05485I
a = 0.080653 + 0.885577I
b = 1.16375 − 1.00098I
7.65653 − 0.97520I 0
u = −1.65228 − 0.05485I
a = 0.080653 − 0.885577I
b = 1.16375 + 1.00098I
7.65653 + 0.97520I 0
u = −1.72238 + 0.16170I
a = −0.086105 + 0.916649I
b = −1.15021 − 1.02233I
9.40334 − 4.97639I 0
u = −1.72238 − 0.16170I
a = −0.086105 − 0.916649I
b = −1.15021 + 1.02233I
9.40334 + 4.97639I 0
u = 1.73138 + 0.06809I
a = 0.043882 + 0.891061I
b = −1.01279 − 1.15273I
9.47308 + 1.61822I 0
u = 1.73138 − 0.06809I
a = 0.043882 − 0.891061I
b = −1.01279 + 1.15273I
9.47308 − 1.61822I 0
u = −1.76374 + 0.21792I
a = −0.360469 − 0.631007I
b = 0.631595 + 0.625797I
−1.14583 − 7.63336I 0
u = −1.76374 − 0.21792I
a = −0.360469 + 0.631007I
b = 0.631595 − 0.625797I
−1.14583 + 7.63336I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.71169 + 0.70638I
a = −0.103752 + 0.988152I
b = −1.11053 − 1.06013I
9.11085 − 9.64421I 0
u = −1.71169 − 0.70638I
a = −0.103752 − 0.988152I
b = −1.11053 + 1.06013I
9.11085 + 9.64421I 0
u = −1.65609 + 0.87083I
a = 0.109961 − 1.010800I
b = 1.09592 + 1.06931I
7.1548 − 15.5018I 0
u = −1.65609 − 0.87083I
a = 0.109961 + 1.010800I
b = 1.09592 − 1.06931I
7.1548 + 15.5018I 0
u = 1.84254 + 0.55471I
a = −0.024388 − 0.899775I
b = −0.96048 + 1.13369I
10.02790 + 2.89871I 0
u = 1.84254 − 0.55471I
a = −0.024388 + 0.899775I
b = −0.96048 − 1.13369I
10.02790 − 2.89871I 0
u = 0.32734 + 1.90477I
a = 0.068219 + 0.161006I
b = 0.209333 − 0.729341I
2.99545 + 1.06109I 0
u = 0.32734 − 1.90477I
a = 0.068219 − 0.161006I
b = 0.209333 + 0.729341I
2.99545 − 1.06109I 0
u = 1.80022 + 0.78166I
a = 0.046975 + 0.901747I
b = 0.94658 − 1.12324I
8.36288 + 8.76828I 0
u = 1.80022 − 0.78166I
a = 0.046975 − 0.901747I
b = 0.94658 + 1.12324I
8.36288 − 8.76828I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.27509 + 2.02948I
a = 0.062934 − 0.138328I
b = −0.268730 + 0.724836I
2.55849 + 5.96109I 0
u = −0.27509 − 2.02948I
a = 0.062934 + 0.138328I
b = −0.268730 − 0.724836I
2.55849 − 5.96109I 0
u = 2.03479 + 0.31103I
a = 0.038225 + 0.499273I
b = 0.020667 − 0.781951I
3.81792 + 2.50371I 0
u = 2.03479 − 0.31103I
a = 0.038225 − 0.499273I
b = 0.020667 + 0.781951I
3.81792 − 2.50371I 0
10
II. I
v
1
= ha, 8286v
9
− 14092v
8
+ · · · + 8095b + 12581, v
10
− v
9
+ · · · + 5v + 1i
(i) Arc colorings
a
5
=
v
0
a
7
=
1
0
a
8
=
1
0
a
10
=
0
−1.02359v
9
+ 1.74083v
8
+ ··· − 2.14256v −1.55417
a
11
=
1.02359v
9
− 1.74083v
8
+ ··· + 2.14256v + 1.55417
−1.02359v
9
+ 1.74083v
8
+ ··· − 2.14256v −1.55417
a
4
=
v
0
a
6
=
1
0.566770v
9
− 0.910562v
8
+ ··· + 1.12069v −2.46844
a
3
=
0.343792v
9
− 0.433107v
8
+ ··· + 6.30229v + 0.566770
−1.56677v
9
+ 1.91056v
8
+ ··· − 18.1207v −2.53156
a
2
=
0.433107v
9
− 0.556763v
8
+ ··· + 6.45448v + 0.910562
−1.56677v
9
+ 1.91056v
8
+ ··· − 18.1207v −2.53156
a
1
=
−1
−0.566770v
9
+ 0.910562v
8
+ ··· − 1.12069v + 2.46844
a
9
=
−1.02359v
9
+ 1.74083v
8
+ ··· − 2.14256v −1.55417
−0.515256v
9
+ 0.785300v
8
+ ··· − 0.966523v + 2.10241
a
12
=
−1.96479v
9
+ 3.18777v
8
+ ··· − 3.92341v + 1.99444
1.39802v
9
− 2.27721v
8
+ ··· + 2.80272v −0.526004
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
20287
1619
v
9
+
28878
1619
v
8
+
30807
1619
v
7
+
368475
1619
v
6
−
403029
1619
v
5
−
583117
1619
v
4
−
710653
1619
v
3
−
322767
1619
v
2
−
137041
1619
v −
22786
1619
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
(u
2
− u + 1)
5
c
2
(u
2
+ u + 1)
5
c
4
, c
7
u
10
c
6
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
c
8
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
2
c
9
, c
10
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
c
11
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
2
c
12
(u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)
2
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
(y
2
+ y + 1)
5
c
4
, c
7
y
10
c
6
, c
9
, c
10
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
c
8
, c
11
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
c
12
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
2
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.337181 + 0.584015I
a = 0
b = 1.21774
−2.40108 + 2.02988I −0.15429 − 4.97460I
v = −0.337181 − 0.584015I
a = 0
b = 1.21774
−2.40108 − 2.02988I −0.15429 + 4.97460I
v = −0.104500 + 0.473819I
a = 0
b = −1.41878 − 0.21917I
−5.87256 − 2.37095I −0.67715 − 1.65320I
v = −0.104500 − 0.473819I
a = 0
b = −1.41878 + 0.21917I
−5.87256 + 2.37095I −0.67715 + 1.65320I
v = −0.358089 + 0.327409I
a = 0
b = −1.41878 + 0.21917I
−5.87256 + 6.43072I −5.14480 − 10.95886I
v = −0.358089 − 0.327409I
a = 0
b = −1.41878 − 0.21917I
−5.87256 − 6.43072I −5.14480 + 10.95886I
v = −1.20942 + 2.19910I
a = 0
b = 0.309916 + 0.549911I
−0.32910 − 3.56046I 2.94328 + 13.07994I
v = −1.20942 − 2.19910I
a = 0
b = 0.309916 − 0.549911I
−0.32910 + 3.56046I 2.94328 − 13.07994I
v = 2.50919 + 0.05217I
a = 0
b = 0.309916 − 0.549911I
−0.329100 − 0.499304I −6.96704 − 1.22174I
v = 2.50919 − 0.05217I
a = 0
b = 0.309916 + 0.549911I
−0.329100 + 0.499304I −6.96704 + 1.22174I
14
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
5
)(u
54
+ 14u
53
+ ··· − 53u + 1)
c
2
((u
2
+ u + 1)
5
)(u
54
+ 6u
53
+ ··· + 15u + 1)
c
3
((u
2
− u + 1)
5
)(u
54
− 6u
53
+ ··· + 1.18951 × 10
7
u + 596177)
c
4
, c
7
u
10
(u
54
+ 5u
53
+ ··· + 2048u + 1024)
c
5
((u
2
− u + 1)
5
)(u
54
+ 6u
53
+ ··· + 15u + 1)
c
6
((u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
)(u
54
+ 3u
53
+ ··· + 4u
2
+ 1)
c
8
((u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
2
)(u
54
+ 3u
53
+ ··· − 2u + 1)
c
9
((u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
)(u
54
+ 3u
53
+ ··· + 4u
2
+ 1)
c
10
((u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
)(u
54
− 3u
53
+ ··· − 8544u + 1217)
c
11
((u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
2
)(u
54
+ 3u
53
+ ··· − 2u + 1)
c
12
((u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)
2
)(u
54
+ 23u
53
+ ··· + 8u + 1)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
5
)(y
54
+ 58y
53
+ ··· + 2411y + 1)
c
2
, c
5
((y
2
+ y + 1)
5
)(y
54
+ 14y
53
+ ··· − 53y + 1)
c
3
(y
2
+ y + 1)
5
· (y
54
+ 102y
53
+ ··· − 14429377332621y + 355427015329)
c
4
, c
7
y
10
(y
54
− 55y
53
+ ··· − 4194304y + 1048576)
c
6
, c
9
((y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
)(y
54
− 5y
53
+ ··· + 8y + 1)
c
8
, c
11
((y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
)(y
54
+ 23y
53
+ ··· + 8y + 1)
c
10
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
· (y
54
+ 15y
53
+ ··· + 18080344y + 1481089)
c
12
((y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
2
)(y
54
+ 19y
53
+ ··· − 160y + 1)
16
