12n
0011
(K12n
0011
)
A knot diagram
1
Linearized knot diagam
3 5 6 8 2 11 5 6 12 7 10 9
Solving Sequence
5,7
8
4,11
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
= h−5.71616 × 10
69
u
37
+ 1.11175 × 10
70
u
36
+ ··· + 3.33891 × 10
72
b + 1.88016 × 10
72
,
4.07046 × 10
70
u
37
− 5.21445 × 10
70
u
36
+ ··· + 1.33556 × 10
73
a − 1.19377 × 10
73
,
u
38
− u
37
+ ··· + 128u + 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 46 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−5.72 × 10
69
u
37
+ 1.11 × 10
70
u
36
+ · · · + 3.34 × 10
72
b + 1.88 ×
10
72
, 4.07 × 10
70
u
37
− 5.21 × 10
70
u
36
+ · · · + 1.34 × 10
73
a − 1.19 ×
10
73
, u
38
− u
37
+ · · · + 128u + 256i
(i) Arc colorings
a
5
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
4
=
u
u
3
+ u
a
11
=
−0.00304774u
37
+ 0.00390431u
36
+ ··· − 2.13353u + 0.893835
0.00171198u
37
− 0.00332968u
36
+ ··· − 0.453692u − 0.563107
a
6
=
0.00130957u
37
+ 0.00189335u
36
+ ··· − 1.90974u + 2.64338
−0.00109847u
37
+ 0.00183184u
36
+ ··· − 0.794202u − 0.211610
a
3
=
0.00359002u
37
− 0.00745031u
36
+ ··· + 4.56333u − 0.957202
0.00112443u
37
− 0.000480799u
36
+ ··· + 0.826261u + 0.801763
a
2
=
0.00359002u
37
− 0.00745031u
36
+ ··· + 4.56333u − 0.957202
0.00209211u
37
− 0.000172711u
36
+ ··· + 0.401334u + 1.79000
a
1
=
−0.000952567u
37
− 0.000976781u
36
+ ··· + 1.86076u − 2.03505
0.000357004u
37
+ 0.000916565u
36
+ ··· − 0.0489786u + 0.608337
a
10
=
−0.00133576u
37
+ 0.000574632u
36
+ ··· − 2.58722u + 0.330728
0.00171198u
37
− 0.00332968u
36
+ ··· − 0.453692u − 0.563107
a
12
=
0.000400109u
37
+ 0.00305192u
36
+ ··· − 3.11755u + 1.84992
0.00136835u
37
− 0.000426605u
36
+ ··· − 0.970171u − 0.257429
a
9
=
−0.00313189u
37
+ 0.00425632u
36
+ ··· − 0.691749u + 0.425379
−0.00175985u
37
+ 0.00256836u
36
+ ··· + 0.691063u − 0.518052
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.0107565u
37
+ 0.0115767u
36
+ ··· − 16.3471u − 2.84993
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
38
+ 9u
37
+ ··· + 15u + 1
c
2
, c
5
u
38
+ 5u
37
+ ··· + 3u + 1
c
3
u
38
− 5u
37
+ ··· + 90147u + 15489
c
4
, c
7
u
38
− u
37
+ ··· + 128u + 256
c
6
, c
10
u
38
+ 3u
37
+ ··· − u + 1
c
8
u
38
+ 3u
37
+ ··· + u + 1
c
9
, c
11
, c
12
u
38
− 11u
37
+ ··· − 11u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
38
+ 45y
37
+ ··· + 91y + 1
c
2
, c
5
y
38
+ 9y
37
+ ··· + 15y + 1
c
3
y
38
+ 81y
37
+ ··· + 7556564583y + 239909121
c
4
, c
7
y
38
+ 45y
37
+ ··· + 344064y + 65536
c
6
, c
10
y
38
+ 11y
37
+ ··· + 11y + 1
c
8
y
38
− 65y
37
+ ··· + 11y + 1
c
9
, c
11
, c
12
y
38
+ 35y
37
+ ··· + 131y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.801035 + 0.695463I
a = 0.79350 − 1.46806I
b = 0.025706 + 0.900927I
2.72429 − 1.49580I 6.88383 + 3.00756I
u = 0.801035 − 0.695463I
a = 0.79350 + 1.46806I
b = 0.025706 − 0.900927I
2.72429 + 1.49580I 6.88383 − 3.00756I
u = −0.213839 + 1.135170I
a = −0.421285 − 0.668176I
b = 0.784497 + 0.822982I
−4.44084 + 0.93436I −3.64457 − 1.20353I
u = −0.213839 − 1.135170I
a = −0.421285 + 0.668176I
b = 0.784497 − 0.822982I
−4.44084 − 0.93436I −3.64457 + 1.20353I
u = −1.159340 + 0.148885I
a = −1.361450 + 0.030633I
b = −0.708036 + 0.833117I
−1.60611 − 0.16717I −2.00112 − 0.51691I
u = −1.159340 − 0.148885I
a = −1.361450 − 0.030633I
b = −0.708036 − 0.833117I
−1.60611 + 0.16717I −2.00112 + 0.51691I
u = −0.358418 + 0.734904I
a = 1.30197 + 2.31889I
b = −0.136751 − 0.822464I
1.16926 − 3.17447I 5.84543 + 3.28927I
u = −0.358418 − 0.734904I
a = 1.30197 − 2.31889I
b = −0.136751 + 0.822464I
1.16926 + 3.17447I 5.84543 − 3.28927I
u = 0.183194 + 1.207340I
a = 0.229775 + 1.020680I
b = 0.677081 − 0.878596I
−0.69910 + 2.61127I 1.65431 − 3.00859I
u = 0.183194 − 1.207340I
a = 0.229775 − 1.020680I
b = 0.677081 + 0.878596I
−0.69910 − 2.61127I 1.65431 + 3.00859I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.083408 + 1.218640I
a = 0.31884 − 1.60799I
b = 0.755833 + 0.932426I
−4.10208 − 6.74360I −2.53206 + 6.49784I
u = 0.083408 − 1.218640I
a = 0.31884 + 1.60799I
b = 0.755833 − 0.932426I
−4.10208 + 6.74360I −2.53206 − 6.49784I
u = 1.262280 + 0.110410I
a = −1.310290 + 0.231935I
b = −0.705134 − 0.909841I
−1.36537 − 5.58839I −0.94341 + 6.04268I
u = 1.262280 − 0.110410I
a = −1.310290 − 0.231935I
b = −0.705134 + 0.909841I
−1.36537 + 5.58839I −0.94341 − 6.04268I
u = −0.533596 + 0.416988I
a = −0.970594 − 0.091212I
b = −0.856400 + 0.889730I
−7.10344 + 1.95919I −5.95273 − 5.24866I
u = −0.533596 − 0.416988I
a = −0.970594 + 0.091212I
b = −0.856400 − 0.889730I
−7.10344 − 1.95919I −5.95273 + 5.24866I
u = 0.525705 + 0.422944I
a = −0.981407 − 0.165229I
b = −0.842922 + 0.929719I
−6.97962 + 4.35433I −5.02974 + 0.36700I
u = 0.525705 − 0.422944I
a = −0.981407 + 0.165229I
b = −0.842922 − 0.929719I
−6.97962 − 4.35433I −5.02974 − 0.36700I
u = −0.437849 + 0.512305I
a = 0.779426 + 0.427405I
b = 0.391315 − 0.479189I
−0.621022 + 1.245300I −4.66633 − 4.67696I
u = −0.437849 − 0.512305I
a = 0.779426 − 0.427405I
b = 0.391315 + 0.479189I
−0.621022 − 1.245300I −4.66633 + 4.67696I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.517700 + 0.295561I
a = 0.655146 + 0.862409I
b = 0.360279 − 0.813117I
0.31192 + 1.82341I 0.28789 − 3.69490I
u = 0.517700 − 0.295561I
a = 0.655146 − 0.862409I
b = 0.360279 + 0.813117I
0.31192 − 1.82341I 0.28789 + 3.69490I
u = −0.304409 + 0.498073I
a = 1.074620 − 0.335260I
b = −0.237341 − 0.266456I
−0.29515 + 1.55177I −2.39420 − 5.36172I
u = −0.304409 − 0.498073I
a = 1.074620 + 0.335260I
b = −0.237341 + 0.266456I
−0.29515 − 1.55177I −2.39420 + 5.36172I
u = −0.54647 + 1.64480I
a = 0.0641318 + 0.0863728I
b = 0.904591 + 0.748202I
3.59603 + 6.55252I 0
u = −0.54647 − 1.64480I
a = 0.0641318 − 0.0863728I
b = 0.904591 − 0.748202I
3.59603 − 6.55252I 0
u = 0.34197 + 1.69965I
a = 0.1067440 + 0.0256339I
b = 0.889409 − 0.715074I
4.26554 + 0.00326I 0
u = 0.34197 − 1.69965I
a = 0.1067440 − 0.0256339I
b = 0.889409 + 0.715074I
4.26554 − 0.00326I 0
u = −0.13035 + 1.76573I
a = −0.0597378 − 0.0404559I
b = −0.799015 − 0.032415I
8.11017 + 3.32648I 0
u = −0.13035 − 1.76573I
a = −0.0597378 + 0.0404559I
b = −0.799015 + 0.032415I
8.11017 − 3.32648I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.62652 + 1.70416I
a = 1.02467 − 1.15119I
b = 0.788823 + 1.027640I
4.47409 − 12.81500I 0
u = 0.62652 − 1.70416I
a = 1.02467 + 1.15119I
b = 0.788823 − 1.027640I
4.47409 + 12.81500I 0
u = −0.43365 + 1.79825I
a = 0.88940 + 1.14293I
b = 0.765371 − 1.032090I
5.25384 + 6.12703I 0
u = −0.43365 − 1.79825I
a = 0.88940 − 1.14293I
b = 0.765371 + 1.032090I
5.25384 − 6.12703I 0
u = 0.32788 + 1.90698I
a = −0.52275 + 1.62668I
b = −0.300160 − 1.097060I
11.67940 − 7.06576I 0
u = 0.32788 − 1.90698I
a = −0.52275 − 1.62668I
b = −0.300160 + 1.097060I
11.67940 + 7.06576I 0
u = −0.05179 + 1.95040I
a = −0.36069 − 1.63993I
b = −0.257145 + 1.102200I
11.94710 + 0.17151I 0
u = −0.05179 − 1.95040I
a = −0.36069 + 1.63993I
b = −0.257145 − 1.102200I
11.94710 − 0.17151I 0
8
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
5
=
v
0
a
7
=
1
0
a
8
=
1
0
a
4
=
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
9
(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
11
, c
12
(u
4
− u
3
+ 3u
2
− 2u + 1)
2
c
9
(u
4
+ u
3
+ 3u
2
+ 2u + 1)
2
c
10
(u
4
− u
3
+ u
2
+ 1)
2
10
(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
11
(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
12
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
4
)(u
38
+ 9u
37
+ ··· + 15u + 1)
c
2
((u
2
+ u + 1)
4
)(u
38
+ 5u
37
+ ··· + 3u + 1)
c
3
((u
2
− u + 1)
4
)(u
38
− 5u
37
+ ··· + 90147u + 15489)
c
4
, c
7
u
8
(u
38
− u
37
+ ··· + 128u + 256)
c
5
((u
2
− u + 1)
4
)(u
38
+ 5u
37
+ ··· + 3u + 1)
c
6
((u
4
+ u
3
+ u
2
+ 1)
2
)(u
38
+ 3u
37
+ ··· − u + 1)
c
8
((u
4
− u
3
+ 3u
2
− 2u + 1)
2
)(u
38
+ 3u
37
+ ··· + u + 1)
c
9
((u
4
+ u
3
+ 3u
2
+ 2u + 1)
2
)(u
38
− 11u
37
+ ··· − 11u + 1)
c
10
((u
4
− u
3
+ u
2
+ 1)
2
)(u
38
+ 3u
37
+ ··· − u + 1)
c
11
, c
12
((u
4
− u
3
+ 3u
2
− 2u + 1)
2
)(u
38
− 11u
37
+ ··· − 11u + 1)
13
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
4
)(y
38
+ 45y
37
+ ··· + 91y + 1)
c
2
, c
5
((y
2
+ y + 1)
4
)(y
38
+ 9y
37
+ ··· + 15y + 1)
c
3
((y
2
+ y + 1)
4
)(y
38
+ 81y
37
+ ··· + 7.55656 × 10
9
y + 2.39909 × 10
8
)
c
4
, c
7
y
8
(y
38
+ 45y
37
+ ··· + 344064y + 65536)
c
6
, c
10
((y
4
+ y
3
+ 3y
2
+ 2y + 1)
2
)(y
38
+ 11y
37
+ ··· + 11y + 1)
c
8
((y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
2
)(y
38
− 65y
37
+ ··· + 11y + 1)
c
9
, c
11
, c
12
((y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
2
)(y
38
+ 35y
37
+ ··· + 131y + 1)
14
