12n
0608
(K12n
0608
)
A knot diagram
1
Linearized knot diagam
3 7 12 9 8 2 11 5 3 7 4 10
Solving Sequence
3,12 4,7
2 1 6 11 8 5 10 9
c
3
c
2
c
1
c
6
c
11
c
7
c
5
c
10
c
9
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−4.28549 × 10
26
u
34
+ 1.62732 × 10
27
u
33
+ ··· + 1.15843 × 10
27
b + 8.44652 × 10
25
,
− 6.12275 × 10
26
u
34
+ 2.45059 × 10
27
u
33
+ ··· + 1.15843 × 10
27
a − 1.01126 × 10
28
,
u
35
− 4u
34
+ ··· + 13u − 1i
I
u
2
= h−u
8
− 2u
7
− 6u
6
− 8u
5
− 11u
4
− 10u
3
− 8u
2
+ b − 5u − 2, −5u
14
− 15u
13
+ ··· + 3a − 17,
u
15
+ 3u
14
+ ··· + 13u + 3i
* 2 irreducible components of dim
C
= 0, with total 50 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−4.29 × 10
26
u
34
+ 1.63 × 10
27
u
33
+ · · · + 1.16 × 10
27
b + 8.45 ×
10
25
, −6.12 × 10
26
u
34
+ 2.45 × 10
27
u
33
+ · · · + 1.16 × 10
27
a − 1.01 ×
10
28
, u
35
− 4u
34
+ · · · + 13u − 1i
(i) Arc colorings
a
3
=
1
0
a
12
=
0
u
a
4
=
1
u
2
a
7
=
0.528536u
34
− 2.11543u
33
+ ··· − 7.88425u + 8.72955
0.369938u
34
− 1.40475u
33
+ ··· − 4.29951u − 0.0729132
a
2
=
−0.359797u
34
+ 1.78137u
33
+ ··· + 13.8898u + 2.59083
0.722732u
34
− 2.92785u
33
+ ··· − 9.15685u + 0.471493
a
1
=
0.362935u
34
− 1.14648u
33
+ ··· + 4.73298u + 3.06233
0.722732u
34
− 2.92785u
33
+ ··· − 9.15685u + 0.471493
a
6
=
1.27580u
34
− 5.37707u
33
+ ··· − 35.0016u + 9.63485
−0.579896u
34
+ 2.31293u
33
+ ··· + 5.25837u − 0.573290
a
11
=
u
u
3
+ u
a
8
=
0.304499u
34
− 1.56526u
33
+ ··· − 9.41309u + 8.84688
−0.0982936u
34
+ 0.185494u
33
+ ··· − 1.55461u − 0.301571
a
5
=
0.406624u
34
− 2.10480u
33
+ ··· − 26.6053u + 5.81865
−0.535938u
34
+ 2.38382u
33
+ ··· + 13.8187u − 1.15100
a
10
=
−1.18951u
34
+ 4.30246u
33
+ ··· + 18.7895u − 7.62806
0.436510u
34
− 1.15451u
33
+ ··· + 10.2359u − 0.598029
a
9
=
−1.62602u
34
+ 5.45697u
33
+ ··· + 8.55359u − 7.03003
0.436510u
34
− 1.15451u
33
+ ··· + 10.2359u − 0.598029
(ii) Obstruction class = −1
(iii) Cusp Shapes =
3236202714557221663667427502
1158434840850118878760670711
u
34
−
11521304278120420457094400882
1158434840850118878760670711
u
33
+
··· −
19429751991808479469174855571
1158434840850118878760670711
u +
14832261325134485821068505741
1158434840850118878760670711
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
35
+ 52u
34
+ ··· + 1078089u + 58081
c
2
, c
6
u
35
− 2u
34
+ ··· + 133u − 241
c
3
, c
11
u
35
− 4u
34
+ ··· + 13u − 1
c
4
, c
5
, c
8
u
35
+ 3u
34
+ ··· − 51u − 29
c
7
, c
10
u
35
− 4u
34
+ ··· − 1779u − 1003
c
9
u
35
− u
34
+ ··· + 78u − 85
c
12
u
35
+ 3u
34
+ ··· − 98428u − 11887
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
35
− 136y
34
+ ··· + 281818346229y −3373402561
c
2
, c
6
y
35
− 52y
34
+ ··· + 1078089y −58081
c
3
, c
11
y
35
+ 24y
34
+ ··· + 117y −1
c
4
, c
5
, c
8
y
35
+ 39y
34
+ ··· − 11087y −841
c
7
, c
10
y
35
+ 12y
34
+ ··· − 6831057y −1006009
c
9
y
35
+ 55y
34
+ ··· − 71946y −7225
c
12
y
35
+ 65y
34
+ ··· + 5833354824y −141300769
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.438726 + 0.895588I
a = 1.016980 − 0.315210I
b = 0.365333 − 0.481328I
−2.74914 − 4.81054I 0.81451 + 1.64077I
u = 0.438726 − 0.895588I
a = 1.016980 + 0.315210I
b = 0.365333 + 0.481328I
−2.74914 + 4.81054I 0.81451 − 1.64077I
u = −0.333888 + 1.017460I
a = 0.443838 − 0.170121I
b = −0.562059 + 0.013682I
0.88382 + 2.43047I −0.03299 − 5.13239I
u = −0.333888 − 1.017460I
a = 0.443838 + 0.170121I
b = −0.562059 − 0.013682I
0.88382 − 2.43047I −0.03299 + 5.13239I
u = 0.447884 + 0.792535I
a = −0.854818 + 0.719224I
b = 0.214078 − 0.577363I
−3.06128 + 1.10681I 2.91387 − 1.64168I
u = 0.447884 − 0.792535I
a = −0.854818 − 0.719224I
b = 0.214078 + 0.577363I
−3.06128 − 1.10681I 2.91387 + 1.64168I
u = −0.875729 + 0.155508I
a = −0.842983 + 0.299610I
b = −1.23212 − 0.73772I
−8.00593 + 0.44170I −3.85524 − 0.48096I
u = −0.875729 − 0.155508I
a = −0.842983 − 0.299610I
b = −1.23212 + 0.73772I
−8.00593 − 0.44170I −3.85524 + 0.48096I
u = −0.103177 + 0.789327I
a = −2.66688 − 0.67293I
b = −0.453226 + 0.879943I
2.14762 + 0.15223I 2.99660 + 0.57013I
u = −0.103177 − 0.789327I
a = −2.66688 + 0.67293I
b = −0.453226 − 0.879943I
2.14762 − 0.15223I 2.99660 − 0.57013I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.427929 + 1.125370I
a = −0.033088 − 0.623920I
b = 1.61731 − 0.12251I
−6.38645 − 1.24603I 1.102278 + 0.713977I
u = 0.427929 − 1.125370I
a = −0.033088 + 0.623920I
b = 1.61731 + 0.12251I
−6.38645 + 1.24603I 1.102278 − 0.713977I
u = 0.567236 + 1.078050I
a = 1.20953 − 2.15171I
b = 2.05290 + 0.23565I
−7.67580 − 6.23301I 0. + 5.36362I
u = 0.567236 − 1.078050I
a = 1.20953 + 2.15171I
b = 2.05290 − 0.23565I
−7.67580 + 6.23301I 0. − 5.36362I
u = 0.587809 + 0.459354I
a = −2.88667 + 0.34889I
b = −1.94228 − 0.11994I
−9.52479 + 1.55754I −3.44973 − 0.83786I
u = 0.587809 − 0.459354I
a = −2.88667 − 0.34889I
b = −1.94228 + 0.11994I
−9.52479 − 1.55754I −3.44973 + 0.83786I
u = 1.268320 + 0.094937I
a = 1.275000 + 0.163208I
b = 2.01220 − 0.37789I
−18.8876 + 5.6310I −3.08853 − 2.13848I
u = 1.268320 − 0.094937I
a = 1.275000 − 0.163208I
b = 2.01220 + 0.37789I
−18.8876 − 5.6310I −3.08853 + 2.13848I
u = −0.186440 + 1.337960I
a = −0.04404 + 1.57716I
b = 0.940593 − 0.080776I
4.65613 + 0.77461I 3.46373 + 0.I
u = −0.186440 − 1.337960I
a = −0.04404 − 1.57716I
b = 0.940593 + 0.080776I
4.65613 − 0.77461I 3.46373 + 0.I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.503936 + 1.253380I
a = −0.455770 − 0.129160I
b = 0.822421 + 0.351035I
−4.00184 + 5.15630I 0. − 3.08603I
u = −0.503936 − 1.253380I
a = −0.455770 + 0.129160I
b = 0.822421 − 0.351035I
−4.00184 − 5.15630I 0. + 3.08603I
u = −0.625747 + 1.228040I
a = 0.94055 + 1.37055I
b = 1.06385 − 1.20619I
−4.92418 + 5.07528I 0. − 3.21102I
u = −0.625747 − 1.228040I
a = 0.94055 − 1.37055I
b = 1.06385 + 1.20619I
−4.92418 − 5.07528I 0. + 3.21102I
u = −0.522315 + 0.321404I
a = 0.487435 + 0.511559I
b = 0.583370 − 0.383300I
−1.059490 + 0.906630I −3.98870 − 3.93714I
u = −0.522315 − 0.321404I
a = 0.487435 − 0.511559I
b = 0.583370 + 0.383300I
−1.059490 − 0.906630I −3.98870 + 3.93714I
u = 0.197339 + 0.561727I
a = 0.42659 + 1.47371I
b = −1.52907 + 0.02813I
−8.60322 − 1.90217I −4.38764 + 3.16662I
u = 0.197339 − 0.561727I
a = 0.42659 − 1.47371I
b = −1.52907 − 0.02813I
−8.60322 + 1.90217I −4.38764 − 3.16662I
u = −0.11107 + 1.48262I
a = 0.238087 − 1.373730I
b = −0.853511 + 0.787626I
4.86915 + 2.91939I 0
u = −0.11107 − 1.48262I
a = 0.238087 + 1.373730I
b = −0.853511 − 0.787626I
4.86915 − 2.91939I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.67415 + 1.39583I
a = −0.48671 + 1.48073I
b = −1.98416 − 0.43518I
−14.8714 − 12.4304I 0
u = 0.67415 − 1.39583I
a = −0.48671 − 1.48073I
b = −1.98416 + 0.43518I
−14.8714 + 12.4304I 0
u = 0.60867 + 1.54226I
a = 0.026702 + 0.386347I
b = −1.94794 + 0.32252I
−13.79050 − 1.10397I 0
u = 0.60867 − 1.54226I
a = 0.026702 − 0.386347I
b = −1.94794 − 0.32252I
−13.79050 + 1.10397I 0
u = 0.0885005
a = 8.41251
b = −0.335347
1.02693 12.3950
8
II. I
u
2
=
h−u
8
−2u
7
+· · ·+b−2, −5u
14
−15u
13
+· · ·+3a−17, u
15
+3u
14
+· · ·+13u+3i
(i) Arc colorings
a
3
=
1
0
a
12
=
0
u
a
4
=
1
u
2
a
7
=
5
3
u
14
+ 5u
13
+ ··· +
62
3
u +
17
3
u
8
+ 2u
7
+ 6u
6
+ 8u
5
+ 11u
4
+ 10u
3
+ 8u
2
+ 5u + 2
a
2
=
−
4
3
u
14
− 3u
13
+ ··· −
13
3
u −
1
3
−u
14
− 3u
13
+ ··· − 4u − 1
a
1
=
−
7
3
u
14
− 6u
13
+ ··· −
25
3
u −
4
3
−u
14
− 3u
13
+ ··· − 4u − 1
a
6
=
2u
14
+ 6u
13
+ ··· + 27u + 7
u
13
+ 3u
12
+ ··· + 11u + 3
a
11
=
u
u
3
+ u
a
8
=
5
3
u
14
+ 5u
13
+ ··· +
68
3
u +
17
3
u
13
+ 2u
12
+ ··· + 7u + 2
a
5
=
2
3
u
14
+ 2u
13
+ ··· +
35
3
u +
11
3
u
13
+ 3u
12
+ ··· + 8u + 2
a
10
=
4
3
u
14
+ 4u
13
+ ··· +
43
3
u +
13
3
u
3
+ u
2
+ 2u + 1
a
9
=
4
3
u
14
+ 4u
13
+ ··· +
37
3
u +
10
3
u
3
+ u
2
+ 2u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −u
14
−5u
13
−18u
12
−46u
11
−94u
10
−159u
9
−225u
8
−278u
7
−
294u
6
− 274u
5
− 220u
4
− 148u
3
− 86u
2
− 39u − 12
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
15
− 13u
14
+ ··· + 7u − 1
c
2
u
15
− u
14
+ ··· + u − 1
c
3
u
15
+ 3u
14
+ ··· + 13u + 3
c
4
, c
5
u
15
+ 2u
14
+ ··· + 7u + 1
c
6
u
15
+ u
14
+ ··· + u + 1
c
7
u
15
− 3u
14
+ ··· + u + 1
c
8
u
15
− 2u
14
+ ··· + 7u − 1
c
9
u
15
+ 9u
13
+ ··· + 6u + 1
c
10
u
15
+ 3u
14
+ ··· + u − 1
c
11
u
15
− 3u
14
+ ··· + 13u − 3
c
12
u
15
− 2u
14
+ ··· + 3u
2
− 1
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
15
− 21y
14
+ ··· + 7y −1
c
2
, c
6
y
15
− 13y
14
+ ··· + 7y −1
c
3
, c
11
y
15
+ 15y
14
+ ··· − 17y −9
c
4
, c
5
, c
8
y
15
+ 14y
14
+ ··· + 15y −1
c
7
, c
10
y
15
− 9y
14
+ ··· + 9y −1
c
9
y
15
+ 18y
14
+ ··· + 36y −1
c
12
y
15
+ 8y
14
+ ··· + 6y −1
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.294054 + 0.902067I
a = −1.74741 + 1.25285I
b = 0.163721 + 0.772718I
2.05778 + 1.28386I 1.55430 − 4.57112I
u = −0.294054 − 0.902067I
a = −1.74741 − 1.25285I
b = 0.163721 − 0.772718I
2.05778 − 1.28386I 1.55430 + 4.57112I
u = 0.335661 + 0.850330I
a = −0.644931 + 0.229416I
b = −1.51635 − 0.09643I
−7.89532 + 0.50711I −0.469805 + 0.654815I
u = 0.335661 − 0.850330I
a = −0.644931 − 0.229416I
b = −1.51635 + 0.09643I
−7.89532 − 0.50711I −0.469805 − 0.654815I
u = −0.765432 + 0.446059I
a = −0.993036 − 0.607246I
b = −0.655190 − 0.030645I
−4.48804 − 1.42220I −2.69080 + 1.40736I
u = −0.765432 − 0.446059I
a = −0.993036 + 0.607246I
b = −0.655190 + 0.030645I
−4.48804 + 1.42220I −2.69080 − 1.40736I
u = 0.300700 + 1.077460I
a = −0.789534 − 0.997684I
b = 1.62235 − 0.19645I
−7.07233 − 2.98109I −0.87550 + 3.88201I
u = 0.300700 − 1.077460I
a = −0.789534 + 0.997684I
b = 1.62235 + 0.19645I
−7.07233 + 2.98109I −0.87550 − 3.88201I
u = −0.517610 + 1.132790I
a = 0.882248 + 0.640892I
b = 0.497798 − 0.455917I
−2.37196 + 6.17336I 2.93895 − 6.71675I
u = −0.517610 − 1.132790I
a = 0.882248 − 0.640892I
b = 0.497798 + 0.455917I
−2.37196 − 6.17336I 2.93895 + 6.71675I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.15119 + 1.44529I
a = 0.12383 − 1.45888I
b = −1.004350 + 0.602621I
5.34612 + 2.25981I 6.22461 − 0.26095I
u = −0.15119 − 1.44529I
a = 0.12383 + 1.45888I
b = −1.004350 − 0.602621I
5.34612 − 2.25981I 6.22461 + 0.26095I
u = −0.482410
a = 2.25011
b = 0.780168
0.445914 −3.84240
u = −0.16687 + 1.59426I
a = −0.122895 + 1.082350I
b = 1.001930 − 0.484978I
2.68625 + 1.86325I −0.76058 − 1.55872I
u = −0.16687 − 1.59426I
a = −0.122895 − 1.082350I
b = 1.001930 + 0.484978I
2.68625 − 1.86325I −0.76058 + 1.55872I
13
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
15
− 13u
14
+ ··· + 7u − 1)(u
35
+ 52u
34
+ ··· + 1078089u + 58081)
c
2
(u
15
− u
14
+ ··· + u − 1)(u
35
− 2u
34
+ ··· + 133u − 241)
c
3
(u
15
+ 3u
14
+ ··· + 13u + 3)(u
35
− 4u
34
+ ··· + 13u − 1)
c
4
, c
5
(u
15
+ 2u
14
+ ··· + 7u + 1)(u
35
+ 3u
34
+ ··· − 51u − 29)
c
6
(u
15
+ u
14
+ ··· + u + 1)(u
35
− 2u
34
+ ··· + 133u − 241)
c
7
(u
15
− 3u
14
+ ··· + u + 1)(u
35
− 4u
34
+ ··· − 1779u − 1003)
c
8
(u
15
− 2u
14
+ ··· + 7u − 1)(u
35
+ 3u
34
+ ··· − 51u − 29)
c
9
(u
15
+ 9u
13
+ ··· + 6u + 1)(u
35
− u
34
+ ··· + 78u − 85)
c
10
(u
15
+ 3u
14
+ ··· + u − 1)(u
35
− 4u
34
+ ··· − 1779u − 1003)
c
11
(u
15
− 3u
14
+ ··· + 13u − 3)(u
35
− 4u
34
+ ··· + 13u − 1)
c
12
(u
15
− 2u
14
+ ··· + 3u
2
− 1)(u
35
+ 3u
34
+ ··· − 98428u − 11887)
14
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
15
− 21y
14
+ ··· + 7y −1)
· (y
35
− 136y
34
+ ··· + 281818346229y −3373402561)
c
2
, c
6
(y
15
− 13y
14
+ ··· + 7y −1)(y
35
− 52y
34
+ ··· + 1078089y −58081)
c
3
, c
11
(y
15
+ 15y
14
+ ··· − 17y −9)(y
35
+ 24y
34
+ ··· + 117y −1)
c
4
, c
5
, c
8
(y
15
+ 14y
14
+ ··· + 15y −1)(y
35
+ 39y
34
+ ··· − 11087y −841)
c
7
, c
10
(y
15
− 9y
14
+ ··· + 9y −1)(y
35
+ 12y
34
+ ··· − 6831057y −1006009)
c
9
(y
15
+ 18y
14
+ ··· + 36y −1)(y
35
+ 55y
34
+ ··· − 71946y −7225)
c
12
(y
15
+ 8y
14
+ ··· + 6y −1)
· (y
35
+ 65y
34
+ ··· + 5833354824y −141300769)
15
