12a
0084
(K12a
0084
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 9 11 10 4 1 12 7 6
Solving Sequence
7,12
11 6
1,3
2 10 8 4 9 5
c
11
c
6
c
12
c
1
c
10
c
7
c
3
c
9
c
5
c
2
, c
4
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
107
+ u
106
+ ··· + b + u, 3u
107
− 3u
106
+ ··· + a + 1, u
108
− 2u
107
+ ··· + 3u − 1i
I
u
2
= hu
3
+ b − u − 1, −u
7
+ 2u
5
+ u
4
− 2u
3
− u
2
+ a + 1, u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1i
* 2 irreducible components of dim
C
= 0, with total 117 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−u
107
+u
106
+· · ·+b+u, 3u
107
−3u
106
+· · ·+a+1, u
108
−2u
107
+· · ·+3u−1i
(i) Arc colorings
a
7
=
0
u
a
12
=
1
0
a
11
=
1
u
2
a
6
=
−u
−u
3
+ u
a
1
=
u
4
− u
2
+ 1
u
6
− 2u
4
+ u
2
a
3
=
−3u
107
+ 3u
106
+ ··· + 4u − 1
u
107
− u
106
+ ··· + 3u
2
− u
a
2
=
2u
107
− 2u
106
+ ··· − 3u + 1
−u
107
+ u
106
+ ··· − 2u
2
+ u
a
10
=
−u
2
+ 1
u
2
a
8
=
−u
5
+ 2u
3
− u
u
5
− u
3
+ u
a
4
=
−u
107
+ u
106
+ ··· + 3u
3
− 3u
2
u
107
− u
106
+ ··· − 4u
4
+ u
2
a
9
=
−u
12
+ 3u
10
− 5u
8
+ 4u
6
− 2u
4
− u
2
+ 1
−u
14
+ 4u
12
− 7u
10
+ 6u
8
− 2u
6
+ u
2
a
5
=
u
23
− 6u
21
+ ··· + 2u
3
− 2u
u
25
− 7u
23
+ ··· − 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 14u
107
− 15u
106
+ ··· − 29u + 15
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
108
+ 50u
107
+ ··· + 43u + 1
c
2
, c
4
u
108
− 10u
107
+ ··· + 11u − 1
c
3
, c
8
u
108
+ u
107
+ ··· − 7424u
2
+ 512
c
5
u
108
− 2u
107
+ ··· + 2153835u − 699025
c
6
, c
11
u
108
− 2u
107
+ ··· + 3u − 1
c
7
, c
12
u
108
− 6u
107
+ ··· + 11u − 1
c
9
u
108
+ 14u
107
+ ··· + 4453u + 349
c
10
u
108
− 58u
107
+ ··· + u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
108
+ 26y
107
+ ··· − 1883y + 1
c
2
, c
4
y
108
− 50y
107
+ ··· − 43y + 1
c
3
, c
8
y
108
− 57y
107
+ ··· − 7602176y + 262144
c
5
y
108
− 42y
107
+ ··· − 6625342064775y + 488635950625
c
6
, c
11
y
108
− 58y
107
+ ··· + y + 1
c
7
, c
12
y
108
+ 86y
107
+ ··· + 121y + 1
c
9
y
108
− 6y
107
+ ··· − 1457151y + 121801
c
10
y
108
− 14y
107
+ ··· − 7y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.996236 + 0.045280I
a = −0.116744 + 1.006360I
b = −0.406874 + 0.889939I
1.66851 + 2.03339I 0
u = 0.996236 − 0.045280I
a = −0.116744 − 1.006360I
b = −0.406874 − 0.889939I
1.66851 − 2.03339I 0
u = −0.862530 + 0.521960I
a = 1.133140 + 0.012092I
b = 0.830795 − 0.379581I
−2.08646 − 5.96170I 0
u = −0.862530 − 0.521960I
a = 1.133140 − 0.012092I
b = 0.830795 + 0.379581I
−2.08646 + 5.96170I 0
u = 0.844591 + 0.507051I
a = 0.59353 + 1.36298I
b = 0.270864 − 0.952687I
−2.96700 + 3.56740I 0
u = 0.844591 − 0.507051I
a = 0.59353 − 1.36298I
b = 0.270864 + 0.952687I
−2.96700 − 3.56740I 0
u = −0.794168 + 0.557145I
a = 0.266509 − 0.777339I
b = 0.464499 − 0.344043I
−2.97176 − 0.64254I 0
u = −0.794168 − 0.557145I
a = 0.266509 + 0.777339I
b = 0.464499 + 0.344043I
−2.97176 + 0.64254I 0
u = 0.885383 + 0.534389I
a = −0.603383 − 0.155335I
b = −0.367723 + 0.938689I
2.59244 + 6.40382I 0
u = 0.885383 − 0.534389I
a = −0.603383 + 0.155335I
b = −0.367723 − 0.938689I
2.59244 − 6.40382I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.876654 + 0.553713I
a = 1.138340 − 0.046475I
b = 0.354844 − 0.826320I
0.41046 + 11.93020I 0
u = 0.876654 − 0.553713I
a = 1.138340 + 0.046475I
b = 0.354844 + 0.826320I
0.41046 − 11.93020I 0
u = −0.956750
a = 0.894676
b = −1.61493
0.334264 0
u = −0.839356 + 0.456799I
a = −0.506274 − 0.352044I
b = −0.973741 − 0.147203I
−0.86996 − 1.97916I 0
u = −0.839356 − 0.456799I
a = −0.506274 + 0.352044I
b = −0.973741 + 0.147203I
−0.86996 + 1.97916I 0
u = −1.048940 + 0.048886I
a = −1.133180 + 0.113072I
b = 0.343147 + 0.845942I
6.58179 − 1.97370I 0
u = −1.048940 − 0.048886I
a = −1.133180 − 0.113072I
b = 0.343147 − 0.845942I
6.58179 + 1.97370I 0
u = 0.948392 + 0.456770I
a = 0.858154 − 0.677501I
b = 0.030428 + 1.311010I
3.81145 + 3.11422I 0
u = 0.948392 − 0.456770I
a = 0.858154 + 0.677501I
b = 0.030428 − 1.311010I
3.81145 − 3.11422I 0
u = −1.058660 + 0.084126I
a = 1.191570 − 0.207622I
b = −0.44160 − 1.44697I
4.80577 − 7.59628I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.058660 − 0.084126I
a = 1.191570 + 0.207622I
b = −0.44160 + 1.44697I
4.80577 + 7.59628I 0
u = −0.736275 + 0.560642I
a = 0.509790 + 0.501835I
b = −0.391752 + 0.666181I
−3.13683 − 3.82711I 0
u = −0.736275 − 0.560642I
a = 0.509790 − 0.501835I
b = −0.391752 − 0.666181I
−3.13683 + 3.82711I 0
u = 1.051040 + 0.322763I
a = −0.87818 + 1.25855I
b = −1.10882 − 1.15799I
2.55355 − 1.82439I 0
u = 1.051040 − 0.322763I
a = −0.87818 − 1.25855I
b = −1.10882 + 1.15799I
2.55355 + 1.82439I 0
u = −0.743951 + 0.441122I
a = −0.168733 − 0.150783I
b = −0.556383 − 0.687073I
−1.16073 − 1.79746I 0. + 5.56509I
u = −0.743951 − 0.441122I
a = −0.168733 + 0.150783I
b = −0.556383 + 0.687073I
−1.16073 + 1.79746I 0. − 5.56509I
u = 1.048310 + 0.450986I
a = −1.40818 + 1.29023I
b = −0.72561 − 1.90324I
2.48243 − 1.91335I 0
u = 1.048310 − 0.450986I
a = −1.40818 − 1.29023I
b = −0.72561 + 1.90324I
2.48243 + 1.91335I 0
u = 0.624825 + 0.574772I
a = 1.028940 + 0.598373I
b = 0.699771 − 0.402827I
−0.29917 − 7.43550I −0.31843 + 4.49348I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.624825 − 0.574772I
a = 1.028940 − 0.598373I
b = 0.699771 + 0.402827I
−0.29917 + 7.43550I −0.31843 − 4.49348I
u = 0.677012 + 0.490046I
a = 1.91943 − 0.37048I
b = 0.010605 − 0.151479I
−3.45158 + 0.56668I −1.98152 + 0.95502I
u = 0.677012 − 0.490046I
a = 1.91943 + 0.37048I
b = 0.010605 + 0.151479I
−3.45158 − 0.56668I −1.98152 − 0.95502I
u = 0.143847 + 0.816906I
a = 3.60584 − 1.75236I
b = −2.72020 + 1.87600I
3.99543 − 12.45750I 3.16743 + 7.87882I
u = 0.143847 − 0.816906I
a = 3.60584 + 1.75236I
b = −2.72020 − 1.87600I
3.99543 + 12.45750I 3.16743 − 7.87882I
u = 0.131097 + 0.814628I
a = −2.82764 + 1.44556I
b = 2.19358 − 1.64273I
6.19290 − 6.68872I 6.18602 + 3.85805I
u = 0.131097 − 0.814628I
a = −2.82764 − 1.44556I
b = 2.19358 + 1.64273I
6.19290 + 6.68872I 6.18602 − 3.85805I
u = −0.638302 + 0.513402I
a = 0.298195 − 0.327642I
b = 0.150510 + 1.281760I
−2.71730 + 1.71656I −2.69239 − 1.49770I
u = −0.638302 − 0.513402I
a = 0.298195 + 0.327642I
b = 0.150510 − 1.281760I
−2.71730 − 1.71656I −2.69239 + 1.49770I
u = 0.084734 + 0.810618I
a = −0.281035 + 0.148733I
b = 0.451303 − 0.663859I
7.50477 − 2.37218I 7.60940 + 2.45508I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.084734 − 0.810618I
a = −0.281035 − 0.148733I
b = 0.451303 + 0.663859I
7.50477 + 2.37218I 7.60940 − 2.45508I
u = 0.062002 + 0.809107I
a = −0.694063 + 0.273767I
b = 0.216786 + 0.332131I
6.29498 + 3.41320I 6.03563 − 2.91284I
u = 0.062002 − 0.809107I
a = −0.694063 − 0.273767I
b = 0.216786 − 0.332131I
6.29498 − 3.41320I 6.03563 + 2.91284I
u = 0.597470 + 0.547708I
a = −0.948340 − 0.065977I
b = −0.633409 + 0.082605I
1.79154 − 2.04029I 2.75012 + 0.45973I
u = 0.597470 − 0.547708I
a = −0.948340 + 0.065977I
b = −0.633409 − 0.082605I
1.79154 + 2.04029I 2.75012 − 0.45973I
u = −0.130219 + 0.799256I
a = 1.52061 + 2.52254I
b = −0.66932 − 1.91757I
1.23189 + 6.19452I 2.03888 − 5.46938I
u = −0.130219 − 0.799256I
a = 1.52061 − 2.52254I
b = −0.66932 + 1.91757I
1.23189 − 6.19452I 2.03888 + 5.46938I
u = 0.124021 + 0.786804I
a = 1.37622 − 2.82570I
b = −1.15779 + 2.57523I
0.12959 − 3.69092I 3.30927 + 4.30775I
u = 0.124021 − 0.786804I
a = 1.37622 + 2.82570I
b = −1.15779 − 2.57523I
0.12959 + 3.69092I 3.30927 − 4.30775I
u = −0.102979 + 0.784283I
a = −1.95071 − 1.53814I
b = 1.05096 + 1.30453I
2.11051 + 1.68118I 3.82795 − 0.19790I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.102979 − 0.784283I
a = −1.95071 + 1.53814I
b = 1.05096 − 1.30453I
2.11051 − 1.68118I 3.82795 + 0.19790I
u = 1.162950 + 0.364150I
a = 1.036500 − 0.765772I
b = 0.37000 + 1.58101I
3.58952 + 2.14988I 0
u = 1.162950 − 0.364150I
a = 1.036500 + 0.765772I
b = 0.37000 − 1.58101I
3.58952 − 2.14988I 0
u = −0.178445 + 0.755692I
a = −0.96043 + 1.86608I
b = 0.99543 − 1.15166I
−0.33248 + 1.46092I 3.18525 + 1.98059I
u = −0.178445 − 0.755692I
a = −0.96043 − 1.86608I
b = 0.99543 + 1.15166I
−0.33248 − 1.46092I 3.18525 − 1.98059I
u = −1.136950 + 0.452088I
a = 0.02675 − 2.17145I
b = −3.00297 + 0.76343I
0.82492 − 2.79638I 0
u = −1.136950 − 0.452088I
a = 0.02675 + 2.17145I
b = −3.00297 − 0.76343I
0.82492 + 2.79638I 0
u = 1.155100 + 0.420420I
a = 0.09813 − 1.43768I
b = 1.40058 + 0.80355I
4.17176 + 2.11595I 0
u = 1.155100 − 0.420420I
a = 0.09813 + 1.43768I
b = 1.40058 − 0.80355I
4.17176 − 2.11595I 0
u = 1.145120 + 0.469099I
a = −0.19347 + 2.77467I
b = −2.56390 − 1.37308I
0.67784 + 5.12770I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.145120 − 0.469099I
a = −0.19347 − 2.77467I
b = −2.56390 + 1.37308I
0.67784 − 5.12770I 0
u = 0.757499
a = −0.645860
b = −0.119944
1.00529 10.9620
u = −1.141430 + 0.505632I
a = 1.09724 − 1.94822I
b = −2.74030 − 0.37394I
1.52022 − 9.42870I 0
u = −1.141430 − 0.505632I
a = 1.09724 + 1.94822I
b = −2.74030 + 0.37394I
1.52022 + 9.42870I 0
u = −1.164500 + 0.479359I
a = −0.09977 + 1.55618I
b = 2.06379 − 0.72550I
3.74724 − 6.11973I 0
u = −1.164500 − 0.479359I
a = −0.09977 − 1.55618I
b = 2.06379 + 0.72550I
3.74724 + 6.11973I 0
u = −1.202640 + 0.391140I
a = 1.83220 − 1.20176I
b = −1.91566 − 2.36399I
4.05037 − 0.30836I 0
u = −1.202640 − 0.391140I
a = 1.83220 + 1.20176I
b = −1.91566 + 2.36399I
4.05037 + 0.30836I 0
u = −0.222565 + 0.698008I
a = 2.26836 − 0.90098I
b = −1.87082 + 0.17421I
−1.13913 + 4.84842I 0.19053 − 6.61375I
u = −0.222565 − 0.698008I
a = 2.26836 + 0.90098I
b = −1.87082 − 0.17421I
−1.13913 − 4.84842I 0.19053 + 6.61375I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.209040 + 0.385166I
a = 1.71742 + 0.62467I
b = −1.83241 + 1.49495I
5.22886 − 2.18421I 0
u = 1.209040 − 0.385166I
a = 1.71742 − 0.62467I
b = −1.83241 − 1.49495I
5.22886 + 2.18421I 0
u = 1.204680 + 0.402555I
a = −1.26758 − 1.07962I
b = 1.95466 − 0.62458I
5.96030 + 2.39991I 0
u = 1.204680 − 0.402555I
a = −1.26758 + 1.07962I
b = 1.95466 + 0.62458I
5.96030 − 2.39991I 0
u = −1.218960 + 0.373729I
a = 1.28881 − 2.33294I
b = −3.43800 − 0.73078I
8.12114 + 8.44678I 0
u = −1.218960 − 0.373729I
a = 1.28881 + 2.33294I
b = −3.43800 + 0.73078I
8.12114 − 8.44678I 0
u = −1.169270 + 0.512657I
a = −1.59144 + 0.40697I
b = 1.37778 + 1.55667I
2.55887 − 6.19584I 0
u = −1.169270 − 0.512657I
a = −1.59144 − 0.40697I
b = 1.37778 − 1.55667I
2.55887 + 6.19584I 0
u = −1.218850 + 0.382506I
a = −1.11458 + 1.98277I
b = 2.71467 + 0.72532I
10.26200 + 2.62921I 0
u = −1.218850 − 0.382506I
a = −1.11458 − 1.98277I
b = 2.71467 − 0.72532I
10.26200 − 2.62921I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.219230 + 0.410203I
a = −0.293141 + 0.611641I
b = 0.165616 + 0.496896I
11.39680 − 1.85953I 0
u = −1.219230 − 0.410203I
a = −0.293141 − 0.611641I
b = 0.165616 − 0.496896I
11.39680 + 1.85953I 0
u = −1.218670 + 0.421998I
a = −0.0530124 − 0.0106381I
b = 0.796121 − 0.443440I
10.10610 − 7.72026I 0
u = −1.218670 − 0.421998I
a = −0.0530124 + 0.0106381I
b = 0.796121 + 0.443440I
10.10610 + 7.72026I 0
u = −1.193200 + 0.495711I
a = 0.85770 + 1.66666I
b = 1.37649 − 2.19377I
5.29844 − 6.37819I 0
u = −1.193200 − 0.495711I
a = 0.85770 − 1.66666I
b = 1.37649 + 2.19377I
5.29844 + 6.37819I 0
u = 1.190870 + 0.503297I
a = −2.33474 + 1.75949I
b = −1.22260 − 3.21110I
3.25616 + 8.43967I 0
u = 1.190870 − 0.503297I
a = −2.33474 − 1.75949I
b = −1.22260 + 3.21110I
3.25616 − 8.43967I 0
u = −1.193950 + 0.507765I
a = −1.59403 − 1.60536I
b = −0.71201 + 2.91016I
4.36216 − 10.99680I 0
u = −1.193950 − 0.507765I
a = −1.59403 + 1.60536I
b = −0.71201 − 2.91016I
4.36216 + 10.99680I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.373685 + 0.593371I
a = 0.99356 − 2.18083I
b = 0.10408 + 1.63116I
0.56829 + 6.09045I 0.26032 − 5.28921I
u = 0.373685 − 0.593371I
a = 0.99356 + 2.18083I
b = 0.10408 − 1.63116I
0.56829 − 6.09045I 0.26032 + 5.28921I
u = 1.208280 + 0.482125I
a = −0.332020 − 0.609645I
b = 0.114022 + 0.174059I
9.67754 + 1.26401I 0
u = 1.208280 − 0.482125I
a = −0.332020 + 0.609645I
b = 0.114022 − 0.174059I
9.67754 − 1.26401I 0
u = 1.206020 + 0.492028I
a = 0.468494 − 0.213799I
b = 0.702505 + 0.491534I
10.81450 + 7.11198I 0
u = 1.206020 − 0.492028I
a = 0.468494 + 0.213799I
b = 0.702505 − 0.491534I
10.81450 − 7.11198I 0
u = −0.103369 + 0.689509I
a = −1.77124 + 0.01238I
b = 1.153010 + 0.351986I
0.73695 + 1.71605I 3.77885 − 4.08947I
u = −0.103369 − 0.689509I
a = −1.77124 − 0.01238I
b = 1.153010 − 0.351986I
0.73695 − 1.71605I 3.77885 + 4.08947I
u = 1.199320 + 0.511223I
a = 0.85148 − 2.56521I
b = 2.77014 + 2.25841I
9.3507 + 11.5458I 0
u = 1.199320 − 0.511223I
a = 0.85148 + 2.56521I
b = 2.77014 − 2.25841I
9.3507 − 11.5458I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.197420 + 0.516487I
a = −0.85661 + 3.27243I
b = −3.39472 − 2.66789I
7.1127 + 17.3483I 0
u = 1.197420 − 0.516487I
a = −0.85661 − 3.27243I
b = −3.39472 + 2.66789I
7.1127 − 17.3483I 0
u = 0.420708 + 0.535584I
a = −0.92459 + 1.42942I
b = −0.269487 − 1.012120I
2.34630 + 0.88690I 3.32220 − 0.66120I
u = 0.420708 − 0.535584I
a = −0.92459 − 1.42942I
b = −0.269487 + 1.012120I
2.34630 − 0.88690I 3.32220 + 0.66120I
u = 0.135866 + 0.578350I
a = 2.77684 − 1.08354I
b = −1.55817 + 0.48586I
−2.14700 − 0.95478I −2.72488 − 0.71056I
u = 0.135866 − 0.578350I
a = 2.77684 + 1.08354I
b = −1.55817 − 0.48586I
−2.14700 + 0.95478I −2.72488 + 0.71056I
u = −0.267648 + 0.455125I
a = 1.52493 − 0.19731I
b = −1.085270 − 0.811385I
−1.84189 − 1.02568I −3.36402 + 1.61311I
u = −0.267648 − 0.455125I
a = 1.52493 + 0.19731I
b = −1.085270 + 0.811385I
−1.84189 + 1.02568I −3.36402 − 1.61311I
15
II. I
u
2
= hu
3
+ b − u − 1, −u
7
+ 2u
5
+ u
4
− 2u
3
− u
2
+ a + 1, u
9
+ u
8
− 2u
7
−
3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1i
(i) Arc colorings
a
7
=
0
u
a
12
=
1
0
a
11
=
1
u
2
a
6
=
−u
−u
3
+ u
a
1
=
u
4
− u
2
+ 1
u
6
− 2u
4
+ u
2
a
3
=
u
7
− 2u
5
− u
4
+ 2u
3
+ u
2
− 1
−u
3
+ u + 1
a
2
=
u
7
− 2u
5
+ 2u
3
u
6
− 2u
4
− u
3
+ u
2
+ u + 1
a
10
=
−u
2
+ 1
u
2
a
8
=
−u
5
+ 2u
3
− u
u
5
− u
3
+ u
a
4
=
u
7
− 2u
5
− u
4
+ 2u
3
+ u
2
− 1
−u
3
+ u + 1
a
9
=
−u
5
+ 2u
3
− u
u
5
− u
3
+ u
a
5
=
−u
4
+ u
2
− 1
−u
6
+ 2u
4
− u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −u
8
+ 2u
7
+ u
6
− 4u
5
− 3u
4
+ 6u
3
+ u
2
+ u − 2
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
9
c
3
, c
8
u
9
c
4
(u + 1)
9
c
5
, c
9
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
6
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
c
7
u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1
c
10
u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1
c
11
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1
c
12
u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
9
c
3
, c
8
y
9
c
5
, c
9
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
c
6
, c
11
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
c
7
, c
12
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
c
10
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.772920 + 0.510351I
a = −0.855828 + 0.530357I
b = 0.084886 − 0.271383I
−3.42837 − 2.09337I −2.59545 + 4.13635I
u = −0.772920 − 0.510351I
a = −0.855828 − 0.530357I
b = 0.084886 + 0.271383I
−3.42837 + 2.09337I −2.59545 − 4.13635I
u = 0.825933
a = −0.162845
b = 1.26251
−0.446489 0.580470
u = 1.173910 + 0.391555I
a = −0.852888 − 0.566992I
b = 1.09612 − 1.16718I
2.72642 + 1.33617I 3.11790 − 0.38556I
u = 1.173910 − 0.391555I
a = −0.852888 + 0.566992I
b = 1.09612 + 1.16718I
2.72642 − 1.33617I 3.11790 + 0.38556I
u = −0.141484 + 0.739668I
a = −0.77654 − 1.46791I
b = 0.629127 + 1.099930I
−1.02799 + 2.45442I −1.02595 − 3.19656I
u = −0.141484 − 0.739668I
a = −0.77654 + 1.46791I
b = 0.629127 − 1.099930I
−1.02799 − 2.45442I −1.02595 + 3.19656I
u = −1.172470 + 0.500383I
a = 1.06667 + 0.97795I
b = 0.55861 − 1.43795I
1.95319 − 7.08493I 2.21327 + 6.71575I
u = −1.172470 − 0.500383I
a = 1.06667 − 0.97795I
b = 0.55861 + 1.43795I
1.95319 + 7.08493I 2.21327 − 6.71575I
19
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
9
)(u
108
+ 50u
107
+ ··· + 43u + 1)
c
2
((u − 1)
9
)(u
108
− 10u
107
+ ··· + 11u − 1)
c
3
, c
8
u
9
(u
108
+ u
107
+ ··· − 7424u
2
+ 512)
c
4
((u + 1)
9
)(u
108
− 10u
107
+ ··· + 11u − 1)
c
5
(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
· (u
108
− 2u
107
+ ··· + 2153835u − 699025)
c
6
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
· (u
108
− 2u
107
+ ··· + 3u − 1)
c
7
(u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
· (u
108
− 6u
107
+ ··· + 11u − 1)
c
9
(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
· (u
108
+ 14u
107
+ ··· + 4453u + 349)
c
10
(u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1)
· (u
108
− 58u
107
+ ··· + u + 1)
c
11
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
· (u
108
− 2u
107
+ ··· + 3u − 1)
c
12
(u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
108
− 6u
107
+ ··· + 11u − 1)
20
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
9
)(y
108
+ 26y
107
+ ··· − 1883y + 1)
c
2
, c
4
((y −1)
9
)(y
108
− 50y
107
+ ··· − 43y + 1)
c
3
, c
8
y
9
(y
108
− 57y
107
+ ··· − 7602176y + 262144)
c
5
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
· (y
108
− 42y
107
+ ··· − 6625342064775y + 488635950625)
c
6
, c
11
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
· (y
108
− 58y
107
+ ··· + y + 1)
c
7
, c
12
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
· (y
108
+ 86y
107
+ ··· + 121y + 1)
c
9
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
· (y
108
− 6y
107
+ ··· − 1457151y + 121801)
c
10
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1)
· (y
108
− 14y
107
+ ··· − 7y + 1)
21
