12a
0012
(K12a
0012
)
A knot diagram
1
Linearized knot diagam
3 5 6 8 2 11 9 4 1 12 7 10
Solving Sequence
7,12
11
3,6
4 10 1 2 5 9 8
c
11
c
6
c
3
c
10
c
12
c
1
c
5
c
9
c
8
c
2
, c
4
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= h3u
88
− 2u
87
+ ··· + 2b − 4, −3u
88
+ 6u
87
+ ··· + 2a − 5, u
89
− 3u
88
+ ··· + 3u
2
− 1i
I
u
2
= h−u
2
a − au + b, a
2
− au + u
2
, u
3
+ u
2
− 1i
* 2 irreducible components of dim
C
= 0, with total 95 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
=
h3u
88
−2u
87
+· · ·+2b−4, −3u
88
+6u
87
+· · ·+2a−5, u
89
−3u
88
+· · ·+3u
2
−1i
(i) Arc colorings
a
7
=
0
u
a
12
=
1
0
a
11
=
1
u
2
a
3
=
3
2
u
88
− 3u
87
+ ··· −
11
2
u
2
+
5
2
−
3
2
u
88
+ u
87
+ ··· + u + 2
a
6
=
−u
−u
3
+ u
a
4
=
4u
88
− 8u
87
+ ··· − 10u
2
+ 3
−3u
88
+
1
2
u
87
+ ··· +
7
2
u + 4
a
10
=
−u
2
+ 1
u
2
a
1
=
u
4
− u
2
+ 1
−u
4
a
2
=
1
2
u
88
− u
87
+ ··· − u +
1
2
−
1
2
u
88
+ u
87
+ ··· +
1
2
u
2
+ u
a
5
=
4u
88
− 8u
87
+ ··· − u + 1
−2u
88
+
1
2
u
87
+ ··· + u
2
+
9
2
u
a
9
=
−u
6
+ u
4
− 2u
2
+ 1
u
6
+ u
2
a
8
=
−u
13
+ 2u
11
− 5u
9
+ 6u
7
− 6u
5
+ 4u
3
− u
u
13
− u
11
+ 3u
9
− 2u
7
+ 2u
5
− u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes =
9
2
u
88
− 7u
87
+ ··· + 10u +
25
2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
89
+ 42u
88
+ ··· + 31u − 1
c
2
, c
5
u
89
+ 4u
88
+ ··· − u − 1
c
3
u
89
− 4u
88
+ ··· + 14621u − 1153
c
4
, c
8
u
89
− u
88
+ ··· + 224u − 64
c
6
, c
11
u
89
− 3u
88
+ ··· + 3u
2
− 1
c
7
u
89
+ 35u
88
+ ··· − 68608u − 4096
c
9
, c
10
, c
12
u
89
− 23u
88
+ ··· + 6u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
89
+ 14y
88
+ ··· + 1271y −1
c
2
, c
5
y
89
+ 42y
88
+ ··· + 31y −1
c
3
y
89
− 14y
88
+ ··· + 87088919y −1329409
c
4
, c
8
y
89
+ 35y
88
+ ··· − 68608y −4096
c
6
, c
11
y
89
− 23y
88
+ ··· + 6y −1
c
7
y
89
+ 27y
88
+ ··· + 739246080y −16777216
c
9
, c
10
, c
12
y
89
+ 89y
88
+ ··· + 46y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.984195 + 0.195609I
a = 0.284066 + 0.070833I
b = −0.868179 − 0.697870I
3.78188 − 0.84858I 0
u = 0.984195 − 0.195609I
a = 0.284066 − 0.070833I
b = −0.868179 + 0.697870I
3.78188 + 0.84858I 0
u = 0.939086 + 0.312963I
a = −1.39245 − 1.37113I
b = 0.291029 + 0.718996I
2.25621 + 6.04954I 0
u = 0.939086 − 0.312963I
a = −1.39245 + 1.37113I
b = 0.291029 − 0.718996I
2.25621 − 6.04954I 0
u = −0.946105 + 0.284359I
a = 0.0319019 − 0.1300720I
b = −0.790886 + 1.103430I
3.90708 − 4.17956I 0
u = −0.946105 − 0.284359I
a = 0.0319019 + 0.1300720I
b = −0.790886 − 1.103430I
3.90708 + 4.17956I 0
u = 0.944001 + 0.270938I
a = 1.034510 + 0.828787I
b = −0.365300 − 0.762985I
3.98448 + 1.20777I 0
u = 0.944001 − 0.270938I
a = 1.034510 − 0.828787I
b = −0.365300 + 0.762985I
3.98448 − 1.20777I 0
u = −0.669121 + 0.711417I
a = −1.38941 − 0.41251I
b = 0.750171 + 0.466489I
−4.15772 − 6.05772I 0
u = −0.669121 − 0.711417I
a = −1.38941 + 0.41251I
b = 0.750171 − 0.466489I
−4.15772 + 6.05772I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.012480 + 0.174891I
a = 0.102594 + 0.161802I
b = 1.26707 + 0.65083I
1.84877 − 5.70019I 0
u = 1.012480 − 0.174891I
a = 0.102594 − 0.161802I
b = 1.26707 − 0.65083I
1.84877 + 5.70019I 0
u = −0.955117 + 0.380078I
a = 0.089571 + 1.140090I
b = 0.447280 − 0.603455I
−1.84135 − 4.39709I 0
u = −0.955117 − 0.380078I
a = 0.089571 − 1.140090I
b = 0.447280 + 0.603455I
−1.84135 + 4.39709I 0
u = 0.956090 + 0.086124I
a = 0.184317 − 0.631357I
b = 0.612157 − 0.217712I
−0.213474 + 0.971536I 0
u = 0.956090 − 0.086124I
a = 0.184317 + 0.631357I
b = 0.612157 + 0.217712I
−0.213474 − 0.971536I 0
u = −0.992264 + 0.337163I
a = 0.678914 − 0.851212I
b = −0.177904 + 0.843661I
2.95432 − 6.73111I 0
u = −0.992264 − 0.337163I
a = 0.678914 + 0.851212I
b = −0.177904 − 0.843661I
2.95432 + 6.73111I 0
u = −0.917872 + 0.249970I
a = 0.374348 − 0.014019I
b = 1.22174 − 1.01315I
2.64050 + 0.85670I 0
u = −0.917872 − 0.249970I
a = 0.374348 + 0.014019I
b = 1.22174 + 1.01315I
2.64050 − 0.85670I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.010850 + 0.350168I
a = −0.94340 + 1.21684I
b = 0.007723 − 0.659253I
0.81793 − 11.84480I 0
u = −1.010850 − 0.350168I
a = −0.94340 − 1.21684I
b = 0.007723 + 0.659253I
0.81793 + 11.84480I 0
u = −0.891457 + 0.611031I
a = −1.070120 − 0.032846I
b = 0.140570 + 0.381892I
−4.10237 − 5.74107I 0
u = −0.891457 − 0.611031I
a = −1.070120 + 0.032846I
b = 0.140570 − 0.381892I
−4.10237 + 5.74107I 0
u = −0.800386 + 0.753263I
a = 0.215588 + 0.897331I
b = 0.615256 − 0.454722I
−2.23330 − 1.98424I 0
u = −0.800386 − 0.753263I
a = 0.215588 − 0.897331I
b = 0.615256 + 0.454722I
−2.23330 + 1.98424I 0
u = −0.653820 + 0.533473I
a = 0.680786 + 0.229763I
b = 0.055291 + 0.139974I
−1.77091 − 1.96389I 2.42047 + 4.44234I
u = −0.653820 − 0.533473I
a = 0.680786 − 0.229763I
b = 0.055291 − 0.139974I
−1.77091 + 1.96389I 2.42047 − 4.44234I
u = −0.826529 + 0.827935I
a = −1.55195 + 1.53702I
b = 2.78350 + 0.57949I
−2.90898 − 0.83941I 0
u = −0.826529 − 0.827935I
a = −1.55195 − 1.53702I
b = 2.78350 − 0.57949I
−2.90898 + 0.83941I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.772339 + 0.290141I
a = 0.37290 − 1.61691I
b = −0.009613 + 0.717771I
−0.0039878 − 0.0448662I 5.32263 − 2.00027I
u = 0.772339 − 0.290141I
a = 0.37290 + 1.61691I
b = −0.009613 − 0.717771I
−0.0039878 + 0.0448662I 5.32263 + 2.00027I
u = 0.825260 + 0.836613I
a = 0.399010 − 1.091970I
b = 0.324884 + 0.701428I
−3.16103 − 2.10920I 0
u = 0.825260 − 0.836613I
a = 0.399010 + 1.091970I
b = 0.324884 − 0.701428I
−3.16103 + 2.10920I 0
u = 0.842049 + 0.823858I
a = −1.168440 + 0.518558I
b = 0.720294 − 0.819193I
−3.98819 + 3.19140I 0
u = 0.842049 − 0.823858I
a = −1.168440 − 0.518558I
b = 0.720294 + 0.819193I
−3.98819 − 3.19140I 0
u = −0.516247 + 0.636377I
a = −0.649421 + 0.541364I
b = 0.238133 − 0.874682I
−5.10938 + 1.20295I −3.30682 − 0.49087I
u = −0.516247 − 0.636377I
a = −0.649421 − 0.541364I
b = 0.238133 + 0.874682I
−5.10938 − 1.20295I −3.30682 + 0.49087I
u = −0.828598 + 0.851010I
a = 2.47396 − 2.06719I
b = −4.29930 − 1.01081I
−5.11393 + 3.82637I 0
u = −0.828598 − 0.851010I
a = 2.47396 + 2.06719I
b = −4.29930 + 1.01081I
−5.11393 − 3.82637I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.957326 + 0.706173I
a = 0.141941 + 1.214140I
b = 0.482793 − 0.912258I
−3.41751 + 0.66358I 0
u = −0.957326 − 0.706173I
a = 0.141941 − 1.214140I
b = 0.482793 + 0.912258I
−3.41751 − 0.66358I 0
u = 0.810066 + 0.871834I
a = −1.62312 − 1.44769I
b = 2.61132 − 0.61128I
−4.88917 − 4.94343I 0
u = 0.810066 − 0.871834I
a = −1.62312 + 1.44769I
b = 2.61132 + 0.61128I
−4.88917 + 4.94343I 0
u = 0.805965 + 0.882488I
a = 2.35286 + 1.59822I
b = −3.56104 + 1.09439I
−7.24505 − 10.18080I 0
u = 0.805965 − 0.882488I
a = 2.35286 − 1.59822I
b = −3.56104 − 1.09439I
−7.24505 + 10.18080I 0
u = −0.945920 + 0.743098I
a = −0.836389 − 0.374659I
b = 0.673558 + 1.024450I
−1.79139 − 3.70694I 0
u = −0.945920 − 0.743098I
a = −0.836389 + 0.374659I
b = 0.673558 − 1.024450I
−1.79139 + 3.70694I 0
u = −0.866941 + 0.836286I
a = 2.44062 + 0.04037I
b = −1.89080 − 3.09001I
−6.74064 − 3.43706I 0
u = −0.866941 − 0.836286I
a = 2.44062 − 0.04037I
b = −1.89080 + 3.09001I
−6.74064 + 3.43706I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.831113 + 0.876310I
a = 1.51874 + 0.10090I
b = −1.25014 + 1.92549I
−9.88374 − 2.08759I 0
u = 0.831113 − 0.876310I
a = 1.51874 − 0.10090I
b = −1.25014 − 1.92549I
−9.88374 + 2.08759I 0
u = 0.942881 + 0.793885I
a = 0.244590 − 1.237230I
b = 0.419746 + 0.906708I
−3.67541 + 2.86361I 0
u = 0.942881 − 0.793885I
a = 0.244590 + 1.237230I
b = 0.419746 − 0.906708I
−3.67541 − 2.86361I 0
u = −0.930101 + 0.813617I
a = 0.06817 − 2.29904I
b = −3.08373 + 2.03710I
−6.54245 − 2.71731I 0
u = −0.930101 − 0.813617I
a = 0.06817 + 2.29904I
b = −3.08373 − 2.03710I
−6.54245 + 2.71731I 0
u = −0.953878 + 0.790823I
a = −1.68540 + 1.40666I
b = 3.26711 + 0.64952I
−2.51595 − 5.21699I 0
u = −0.953878 − 0.790823I
a = −1.68540 − 1.40666I
b = 3.26711 − 0.64952I
−2.51595 + 5.21699I 0
u = 0.908323 + 0.851107I
a = −1.55606 − 1.35708I
b = 2.78869 − 0.48366I
−9.19375 + 3.15888I 0
u = 0.908323 − 0.851107I
a = −1.55606 + 1.35708I
b = 2.78869 + 0.48366I
−9.19375 − 3.15888I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.958134 + 0.795019I
a = −0.913730 + 0.566872I
b = 0.677571 − 1.009680I
−2.74969 + 8.20421I 0
u = 0.958134 − 0.795019I
a = −0.913730 − 0.566872I
b = 0.677571 + 1.009680I
−2.74969 − 8.20421I 0
u = 0.899654 + 0.869048I
a = 1.33039 + 2.02355I
b = −3.61876 − 0.43635I
−12.74330 − 1.02952I 0
u = 0.899654 − 0.869048I
a = 1.33039 − 2.02355I
b = −3.61876 + 0.43635I
−12.74330 + 1.02952I 0
u = −0.962482 + 0.804421I
a = 2.23438 − 2.28958I
b = −4.75869 − 0.68092I
−4.69683 − 9.99405I 0
u = −0.962482 − 0.804421I
a = 2.23438 + 2.28958I
b = −4.75869 + 0.68092I
−4.69683 + 9.99405I 0
u = 0.926091 + 0.858251I
a = 2.20383 + 1.17824I
b = −3.17389 + 1.66679I
−12.6600 + 7.4254I 0
u = 0.926091 − 0.858251I
a = 2.20383 − 1.17824I
b = −3.17389 − 1.66679I
−12.6600 − 7.4254I 0
u = 0.982575 + 0.806408I
a = −1.56913 − 1.42962I
b = 3.21737 − 0.34502I
−4.34954 + 11.17710I 0
u = 0.982575 − 0.806408I
a = −1.56913 + 1.42962I
b = 3.21737 + 0.34502I
−4.34954 − 11.17710I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.973466 + 0.819696I
a = 0.16054 + 1.43750I
b = −2.24771 − 1.27213I
−9.43596 + 8.37985I 0
u = 0.973466 − 0.819696I
a = 0.16054 − 1.43750I
b = −2.24771 + 1.27213I
−9.43596 − 8.37985I 0
u = 0.990000 + 0.809599I
a = 1.79298 + 2.17207I
b = −4.21652 + 0.13308I
−6.6675 + 16.4559I 0
u = 0.990000 − 0.809599I
a = 1.79298 − 2.17207I
b = −4.21652 − 0.13308I
−6.6675 − 16.4559I 0
u = −0.150757 + 0.682122I
a = −1.46918 − 0.43941I
b = 0.496150 − 0.695454I
−1.91804 + 8.20078I 0.63570 − 6.56551I
u = −0.150757 − 0.682122I
a = −1.46918 + 0.43941I
b = 0.496150 + 0.695454I
−1.91804 − 8.20078I 0.63570 + 6.56551I
u = −0.246131 + 0.627367I
a = −1.055150 − 0.559293I
b = 0.862529 + 0.232798I
−4.05476 + 0.74742I −3.00857 − 0.36398I
u = −0.246131 − 0.627367I
a = −1.055150 + 0.559293I
b = 0.862529 − 0.232798I
−4.05476 − 0.74742I −3.00857 + 0.36398I
u = −0.139471 + 0.635853I
a = 1.39651 + 0.34800I
b = −0.294766 + 0.248460I
0.29648 + 3.27892I 3.84119 − 2.78924I
u = −0.139471 − 0.635853I
a = 1.39651 − 0.34800I
b = −0.294766 − 0.248460I
0.29648 − 3.27892I 3.84119 + 2.78924I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.646770
a = 0.860949
b = −0.235839
0.883017 11.7070
u = 0.482237 + 0.354828I
a = −2.04164 + 1.20936I
b = 0.972083 − 0.349406I
−0.87269 + 2.73014I 2.40287 − 5.98665I
u = 0.482237 − 0.354828I
a = −2.04164 − 1.20936I
b = 0.972083 + 0.349406I
−0.87269 − 2.73014I 2.40287 + 5.98665I
u = −0.566823 + 0.093243I
a = 0.204694 + 1.214440I
b = 0.399147 + 1.066770I
0.65478 − 2.26477I −1.92948 + 7.19355I
u = −0.566823 − 0.093243I
a = 0.204694 − 1.214440I
b = 0.399147 − 1.066770I
0.65478 + 2.26477I −1.92948 − 7.19355I
u = −0.017736 + 0.501459I
a = 1.67869 − 0.08674I
b = −0.134465 − 0.518010I
1.29764 + 1.42827I 5.30898 − 3.39968I
u = −0.017736 − 0.501459I
a = 1.67869 + 0.08674I
b = −0.134465 + 0.518010I
1.29764 − 1.42827I 5.30898 + 3.39968I
u = 0.136537 + 0.480189I
a = −2.20688 + 0.22311I
b = 0.516448 + 0.846415I
−0.07110 − 3.07726I 2.85853 + 2.35963I
u = 0.136537 − 0.480189I
a = −2.20688 − 0.22311I
b = 0.516448 − 0.846415I
−0.07110 + 3.07726I 2.85853 − 2.35963I
13
II. I
u
2
= h−u
2
a − au + b, a
2
− au + u
2
, u
3
+ u
2
− 1i
(i) Arc colorings
a
7
=
0
u
a
12
=
1
0
a
11
=
1
u
2
a
3
=
a
u
2
a + au
a
6
=
−u
u
2
+ u − 1
a
4
=
0
au + a
a
10
=
−u
2
+ 1
u
2
a
1
=
u
−u
2
− u + 1
a
2
=
a
u
2
a + au − u
2
− u
a
5
=
0
au + a
a
9
=
0
u
a
8
=
0
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 2u
2
a + 2au + u
2
− a + 6u + 7
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
(u
2
− u + 1)
3
c
2
(u
2
+ u + 1)
3
c
4
, c
7
, c
8
u
6
c
6
(u
3
− u
2
+ 1)
2
c
9
, c
10
(u
3
+ u
2
+ 2u + 1)
2
c
11
(u
3
+ u
2
− 1)
2
c
12
(u
3
− u
2
+ 2u − 1)
2
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
(y
2
+ y + 1)
3
c
4
, c
7
, c
8
y
6
c
6
, c
11
(y
3
− y
2
+ 2y −1)
2
c
9
, c
10
, c
12
(y
3
+ 3y
2
+ 2y −1)
2
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.877439 + 0.744862I
a = −1.083790 − 0.387453I
b = 0.500000 + 0.866025I
−3.02413 − 4.85801I 4.03424 + 5.28153I
u = −0.877439 + 0.744862I
a = 0.206350 + 1.132320I
b = 0.500000 − 0.866025I
−3.02413 − 0.79824I 2.74410 + 0.29766I
u = −0.877439 − 0.744862I
a = −1.083790 + 0.387453I
b = 0.500000 − 0.866025I
−3.02413 + 4.85801I 4.03424 − 5.28153I
u = −0.877439 − 0.744862I
a = 0.206350 − 1.132320I
b = 0.500000 + 0.866025I
−3.02413 + 0.79824I 2.74410 − 0.29766I
u = 0.754878
a = 0.377439 + 0.653743I
b = 0.500000 + 0.866025I
1.11345 − 2.02988I 12.72167 + 1.07831I
u = 0.754878
a = 0.377439 − 0.653743I
b = 0.500000 − 0.866025I
1.11345 + 2.02988I 12.72167 − 1.07831I
17
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
3
)(u
89
+ 42u
88
+ ··· + 31u − 1)
c
2
((u
2
+ u + 1)
3
)(u
89
+ 4u
88
+ ··· − u − 1)
c
3
((u
2
− u + 1)
3
)(u
89
− 4u
88
+ ··· + 14621u − 1153)
c
4
, c
8
u
6
(u
89
− u
88
+ ··· + 224u − 64)
c
5
((u
2
− u + 1)
3
)(u
89
+ 4u
88
+ ··· − u − 1)
c
6
((u
3
− u
2
+ 1)
2
)(u
89
− 3u
88
+ ··· + 3u
2
− 1)
c
7
u
6
(u
89
+ 35u
88
+ ··· − 68608u − 4096)
c
9
, c
10
((u
3
+ u
2
+ 2u + 1)
2
)(u
89
− 23u
88
+ ··· + 6u − 1)
c
11
((u
3
+ u
2
− 1)
2
)(u
89
− 3u
88
+ ··· + 3u
2
− 1)
c
12
((u
3
− u
2
+ 2u − 1)
2
)(u
89
− 23u
88
+ ··· + 6u − 1)
18
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
3
)(y
89
+ 14y
88
+ ··· + 1271y −1)
c
2
, c
5
((y
2
+ y + 1)
3
)(y
89
+ 42y
88
+ ··· + 31y −1)
c
3
((y
2
+ y + 1)
3
)(y
89
− 14y
88
+ ··· + 8.70889 × 10
7
y −1329409)
c
4
, c
8
y
6
(y
89
+ 35y
88
+ ··· − 68608y −4096)
c
6
, c
11
((y
3
− y
2
+ 2y −1)
2
)(y
89
− 23y
88
+ ··· + 6y −1)
c
7
y
6
(y
89
+ 27y
88
+ ··· + 7.39246 × 10
8
y −1.67772 × 10
7
)
c
9
, c
10
, c
12
((y
3
+ 3y
2
+ 2y −1)
2
)(y
89
+ 89y
88
+ ··· + 46y −1)
19
