12a
0099
(K12a
0099
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 10 11 9 4 1 12 7 6
Solving Sequence
7,12
11 6
1,3
2 10 5 4 9 8
c
11
c
6
c
12
c
1
c
10
c
5
c
4
c
9
c
7
c
2
, c
3
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= hu
113
+ u
112
+ ··· + b + u, −u
113
− u
112
+ ··· + a + u, u
114
+ 2u
113
+ ··· + 3u + 1i
I
u
2
= hu
5
+ u
4
− u
3
− u
2
+ b, a, u
6
+ u
5
− u
4
− 2u
3
+ u + 1i
* 2 irreducible components of dim
C
= 0, with total 120 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
= hu
113
+u
112
+· · ·+b+u, −u
113
−u
112
+· · ·+a+u, u
114
+2u
113
+· · ·+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
=
u
113
+ u
112
+ ··· + 2u
3
− u
−u
113
− u
112
+ ··· − 2u
2
− u
a
2
=
−u
59
+ 14u
57
+ ··· − 2u
2
− 2u
−u
112
− u
111
+ ··· − u
2
− u
a
10
=
−u
2
+ 1
u
2
a
5
=
−u
7
+ 2u
5
− 2u
3
u
7
− u
5
+ u
a
4
=
−u
113
− u
112
+ ··· − 3u − 1
u
113
− u
112
+ ··· + 2u
5
+ u
3
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
8
=
u
25
− 6u
23
+ ··· − 2u
3
+ u
u
27
− 7u
25
+ ··· + u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 12u
113
+ 14u
112
+ ··· + 20u + 10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
114
+ 61u
113
+ ··· + 8u + 1
c
2
, c
4
u
114
− 7u
113
+ ··· − 8u + 1
c
3
, c
8
u
114
+ u
113
+ ··· − 64u + 64
c
5
u
114
+ 2u
113
+ ··· − 60045u + 5113
c
6
, c
11
u
114
− 2u
113
+ ··· − 3u + 1
c
7
u
114
− 39u
113
+ ··· − 114688u + 4096
c
9
u
114
− 14u
113
+ ··· − 4339u + 349
c
10
u
114
− 54u
113
+ ··· + u + 1
c
12
u
114
− 6u
113
+ ··· − 13547u + 1585
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
114
− 9y
113
+ ··· − 16y + 1
c
2
, c
4
y
114
− 61y
113
+ ··· − 8y + 1
c
3
, c
8
y
114
− 39y
113
+ ··· − 114688y + 4096
c
5
y
114
− 30y
113
+ ··· − 2610115671y + 26142769
c
6
, c
11
y
114
− 54y
113
+ ··· + y + 1
c
7
y
114
+ 61y
113
+ ··· − 486539264y + 16777216
c
9
y
114
+ 6y
113
+ ··· + 2982089y + 121801
c
10
y
114
+ 14y
113
+ ··· + 9y + 1
c
12
y
114
+ 26y
113
+ ··· + 126216321y + 2512225
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.802895 + 0.478978I
a = 0.648034 + 0.661607I
b = 1.081410 − 0.794048I
1.73492 + 0.06692I 0
u = −0.802895 − 0.478978I
a = 0.648034 − 0.661607I
b = 1.081410 + 0.794048I
1.73492 − 0.06692I 0
u = −0.621442 + 0.675702I
a = −2.36173 − 0.66170I
b = 0.38621 + 2.96578I
−4.92367 − 10.31030I 0
u = −0.621442 − 0.675702I
a = −2.36173 + 0.66170I
b = 0.38621 − 2.96578I
−4.92367 + 10.31030I 0
u = −1.075240 + 0.161250I
a = 0.221621 − 0.332650I
b = 0.442594 + 1.153370I
−0.60639 − 3.57403I 0
u = −1.075240 − 0.161250I
a = 0.221621 + 0.332650I
b = 0.442594 − 1.153370I
−0.60639 + 3.57403I 0
u = −1.071530 + 0.244885I
a = 1.110960 − 0.154532I
b = −0.631824 − 0.105891I
2.19637 − 0.24343I 0
u = −1.071530 − 0.244885I
a = 1.110960 + 0.154532I
b = −0.631824 + 0.105891I
2.19637 + 0.24343I 0
u = −0.886335 + 0.160699I
a = 0.590127 + 0.021652I
b = 0.224427 − 0.276342I
1.57240 − 0.20684I 0
u = −0.886335 − 0.160699I
a = 0.590127 − 0.021652I
b = 0.224427 + 0.276342I
1.57240 + 0.20684I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.615559 + 0.654054I
a = 1.149110 + 0.493027I
b = 0.323910 − 1.111660I
−1.96215 − 5.30707I 0
u = −0.615559 − 0.654054I
a = 1.149110 − 0.493027I
b = 0.323910 + 1.111660I
−1.96215 + 5.30707I 0
u = 0.555986 + 0.695044I
a = −0.550268 − 0.848925I
b = 0.910033 + 0.620226I
−6.14855 − 3.85204I 0
u = 0.555986 − 0.695044I
a = −0.550268 + 0.848925I
b = 0.910033 − 0.620226I
−6.14855 + 3.85204I 0
u = −0.953795 + 0.568317I
a = −0.282187 − 0.766041I
b = −0.60170 + 1.43220I
−0.966330 + 0.533951I 0
u = −0.953795 − 0.568317I
a = −0.282187 + 0.766041I
b = −0.60170 − 1.43220I
−0.966330 − 0.533951I 0
u = 0.595625 + 0.658860I
a = −2.67140 + 0.35318I
b = 0.69157 − 3.12827I
−6.05660 + 4.18679I 0
u = 0.595625 − 0.658860I
a = −2.67140 − 0.35318I
b = 0.69157 + 3.12827I
−6.05660 − 4.18679I 0
u = 1.095250 + 0.218908I
a = 0.058489 + 0.349819I
b = 0.63782 − 1.28155I
−0.723969 − 1.165160I 0
u = 1.095250 − 0.218908I
a = 0.058489 − 0.349819I
b = 0.63782 + 1.28155I
−0.723969 + 1.165160I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.689875 + 0.550108I
a = −1.176930 + 0.040814I
b = 0.58857 + 1.87664I
1.38535 − 4.29767I 0
u = −0.689875 − 0.550108I
a = −1.176930 − 0.040814I
b = 0.58857 − 1.87664I
1.38535 + 4.29767I 0
u = −0.951843 + 0.590636I
a = 0.69211 + 1.66566I
b = 2.25251 − 2.22982I
−3.94828 + 5.40705I 0
u = −0.951843 − 0.590636I
a = 0.69211 − 1.66566I
b = 2.25251 + 2.22982I
−3.94828 − 5.40705I 0
u = −0.579857 + 0.659260I
a = −0.729257 + 0.753579I
b = 0.921755 − 0.547684I
−6.31930 − 1.45178I 0
u = −0.579857 − 0.659260I
a = −0.729257 − 0.753579I
b = 0.921755 + 0.547684I
−6.31930 + 1.45178I 0
u = −1.078320 + 0.313731I
a = −0.002798 − 1.411830I
b = −0.029617 + 0.558469I
2.74778 − 0.59864I 0
u = −1.078320 − 0.313731I
a = −0.002798 + 1.411830I
b = −0.029617 − 0.558469I
2.74778 + 0.59864I 0
u = 1.068360 + 0.356754I
a = −0.350823 + 0.046731I
b = 1.38032 − 1.28074I
0.59192 + 1.98551I 0
u = 1.068360 − 0.356754I
a = −0.350823 − 0.046731I
b = 1.38032 + 1.28074I
0.59192 − 1.98551I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.972416 + 0.571723I
a = 0.43804 − 1.84169I
b = 2.88407 + 2.12586I
−4.94611 + 0.60813I 0
u = 0.972416 − 0.571723I
a = 0.43804 + 1.84169I
b = 2.88407 − 2.12586I
−4.94611 − 0.60813I 0
u = −1.110340 + 0.219144I
a = −1.90855 − 1.39379I
b = 1.207020 + 0.431034I
−0.29000 + 3.83040I 0
u = −1.110340 − 0.219144I
a = −1.90855 + 1.39379I
b = 1.207020 − 0.431034I
−0.29000 − 3.83040I 0
u = −0.984881 + 0.571424I
a = −0.687429 + 0.727612I
b = 0.329495 + 0.273234I
−5.12521 − 3.34234I 0
u = −0.984881 − 0.571424I
a = −0.687429 − 0.727612I
b = 0.329495 − 0.273234I
−5.12521 + 3.34234I 0
u = 0.398789 + 0.754071I
a = 0.675107 + 0.339066I
b = 0.217889 + 0.456806I
−5.35149 + 1.39827I −5.37324 − 3.61880I
u = 0.398789 − 0.754071I
a = 0.675107 − 0.339066I
b = 0.217889 − 0.456806I
−5.35149 − 1.39827I −5.37324 + 3.61880I
u = 0.551314 + 0.650772I
a = 1.102810 − 0.442735I
b = 0.294268 + 1.016610I
−2.99674 + 0.08626I −3.37469 + 0.I
u = 0.551314 − 0.650772I
a = 1.102810 + 0.442735I
b = 0.294268 − 1.016610I
−2.99674 − 0.08626I −3.37469 + 0.I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.125210 + 0.224930I
a = 1.171490 − 0.126598I
b = −0.781136 + 0.388903I
3.98132 − 4.81965I 0
u = 1.125210 − 0.224930I
a = 1.171490 + 0.126598I
b = −0.781136 − 0.388903I
3.98132 + 4.81965I 0
u = −0.350318 + 0.776123I
a = 0.08094 − 3.05542I
b = −2.44593 + 0.87546I
−3.53427 + 12.67090I −3.32296 − 8.10951I
u = −0.350318 − 0.776123I
a = 0.08094 + 3.05542I
b = −2.44593 − 0.87546I
−3.53427 − 12.67090I −3.32296 + 8.10951I
u = 1.003680 + 0.565753I
a = −0.193038 + 0.786711I
b = −0.79242 − 1.38566I
−1.66402 + 4.66671I 0
u = 1.003680 − 0.565753I
a = −0.193038 − 0.786711I
b = −0.79242 + 1.38566I
−1.66402 − 4.66671I 0
u = 1.133970 + 0.211582I
a = −1.84896 + 1.08134I
b = 1.203520 − 0.245182I
1.17402 − 9.99443I 0
u = 1.133970 − 0.211582I
a = −1.84896 − 1.08134I
b = 1.203520 + 0.245182I
1.17402 + 9.99443I 0
u = −1.096350 + 0.368893I
a = 1.66997 + 0.65816I
b = −1.259970 − 0.207309I
1.20941 − 4.25449I 0
u = −1.096350 − 0.368893I
a = 1.66997 − 0.65816I
b = −1.259970 + 0.207309I
1.20941 + 4.25449I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.344591 + 0.763294I
a = 0.50736 + 1.70919I
b = 0.822018 − 1.012960I
−0.61002 + 7.49344I 0. − 5.08922I
u = −0.344591 − 0.763294I
a = 0.50736 − 1.70919I
b = 0.822018 + 1.012960I
−0.61002 − 7.49344I 0. + 5.08922I
u = 0.355740 + 0.756327I
a = 0.45882 + 3.35198I
b = −2.82264 − 0.66453I
−4.86402 − 6.39230I −4.93163 + 4.52879I
u = 0.355740 − 0.756327I
a = 0.45882 − 3.35198I
b = −2.82264 + 0.66453I
−4.86402 + 6.39230I −4.93163 − 4.52879I
u = 1.129870 + 0.281054I
a = −0.98753 + 1.20581I
b = 0.613503 − 0.265856I
7.30319 − 2.72734I 0
u = 1.129870 − 0.281054I
a = −0.98753 − 1.20581I
b = 0.613503 + 0.265856I
7.30319 + 2.72734I 0
u = 1.005600 + 0.592425I
a = −0.758335 − 0.529644I
b = 0.391220 − 0.513005I
−4.82071 + 8.81017I 0
u = 1.005600 − 0.592425I
a = −0.758335 + 0.529644I
b = 0.391220 + 0.513005I
−4.82071 − 8.81017I 0
u = 0.454687 + 0.696441I
a = 0.293722 − 0.478216I
b = 0.574073 + 0.723221I
−2.70846 − 1.10061I 1.79985 + 1.69816I
u = 0.454687 − 0.696441I
a = 0.293722 + 0.478216I
b = 0.574073 − 0.723221I
−2.70846 + 1.10061I 1.79985 − 1.69816I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.362970 + 0.748096I
a = 0.574247 − 0.532042I
b = 0.246848 − 0.337640I
−5.25184 + 3.63750I −5.10704 − 3.62611I
u = −0.362970 − 0.748096I
a = 0.574247 + 0.532042I
b = 0.246848 + 0.337640I
−5.25184 − 3.63750I −5.10704 + 3.62611I
u = 1.128000 + 0.306570I
a = 1.52405 − 0.17746I
b = −1.121760 + 0.190253I
7.58019 + 2.42692I 0
u = 1.128000 − 0.306570I
a = 1.52405 + 0.17746I
b = −1.121760 − 0.190253I
7.58019 − 2.42692I 0
u = 1.120950 + 0.362820I
a = −0.265496 + 0.759296I
b = −0.0971877 + 0.0095791I
5.45218 + 4.81121I 0
u = 1.120950 − 0.362820I
a = −0.265496 − 0.759296I
b = −0.0971877 − 0.0095791I
5.45218 − 4.81121I 0
u = 0.367330 + 0.726409I
a = 0.65012 − 1.54514I
b = 0.801978 + 1.047490I
−2.12917 − 2.13709I −2.06723 + 0.57279I
u = 0.367330 − 0.726409I
a = 0.65012 + 1.54514I
b = 0.801978 − 1.047490I
−2.12917 + 2.13709I −2.06723 − 0.57279I
u = 1.083910 + 0.500725I
a = −1.58095 − 0.11969I
b = 2.63236 − 2.83333I
0.35657 + 2.97809I 0
u = 1.083910 − 0.500725I
a = −1.58095 + 0.11969I
b = 2.63236 + 2.83333I
0.35657 − 2.97809I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.131430 + 0.381437I
a = 1.43868 − 0.48924I
b = −1.246310 + 0.163466I
3.04654 + 9.86154I 0
u = 1.131430 − 0.381437I
a = 1.43868 + 0.48924I
b = −1.246310 − 0.163466I
3.04654 − 9.86154I 0
u = −1.083400 + 0.524828I
a = 0.321930 + 0.284450I
b = −0.732120 + 0.450506I
−0.59072 − 5.01689I 0
u = −1.083400 − 0.524828I
a = 0.321930 − 0.284450I
b = −0.732120 − 0.450506I
−0.59072 + 5.01689I 0
u = 1.065770 + 0.574128I
a = −0.350867 + 0.162190I
b = −0.325909 − 1.146450I
−0.91046 + 5.99898I 0
u = 1.065770 − 0.574128I
a = −0.350867 − 0.162190I
b = −0.325909 + 1.146450I
−0.91046 − 5.99898I 0
u = −1.120160 + 0.466519I
a = −1.083030 − 0.174179I
b = 1.81133 + 2.21947I
2.47594 + 2.10647I 0
u = −1.120160 − 0.466519I
a = −1.083030 + 0.174179I
b = 1.81133 − 2.21947I
2.47594 − 2.10647I 0
u = −1.112160 + 0.490659I
a = 0.330739 − 0.672558I
b = −1.61305 − 0.21868I
4.59732 − 2.80846I 0
u = −1.112160 − 0.490659I
a = 0.330739 + 0.672558I
b = −1.61305 + 0.21868I
4.59732 + 2.80846I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.287071 + 0.729040I
a = 0.92347 − 1.89592I
b = −1.82438 − 0.15813I
3.09127 + 5.67737I 2.39216 − 6.13027I
u = −0.287071 − 0.729040I
a = 0.92347 + 1.89592I
b = −1.82438 + 0.15813I
3.09127 − 5.67737I 2.39216 + 6.13027I
u = 1.100550 + 0.534307I
a = 0.70949 + 1.44621I
b = −3.54581 − 0.41915I
1.23499 + 6.66667I 0
u = 1.100550 − 0.534307I
a = 0.70949 − 1.44621I
b = −3.54581 + 0.41915I
1.23499 − 6.66667I 0
u = 1.106770 + 0.565812I
a = −1.138090 + 0.576922I
b = 0.45698 − 2.42716I
0.03653 + 7.06812I 0
u = 1.106770 − 0.565812I
a = −1.138090 − 0.576922I
b = 0.45698 + 2.42716I
0.03653 − 7.06812I 0
u = −1.124910 + 0.530888I
a = −1.35614 − 0.48373I
b = 1.24665 + 2.77559I
6.06724 − 5.32291I 0
u = −1.124910 − 0.530888I
a = −1.35614 + 0.48373I
b = 1.24665 − 2.77559I
6.06724 + 5.32291I 0
u = 1.101210 + 0.583983I
a = 0.287855 + 0.382193I
b = −0.987534 − 1.005520I
−3.28003 + 3.67128I 0
u = 1.101210 − 0.583983I
a = 0.287855 − 0.382193I
b = −0.987534 + 1.005520I
−3.28003 − 3.67128I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.113080 + 0.572032I
a = 0.409485 − 0.276988I
b = −1.038680 + 0.866746I
−3.04837 − 8.64260I 0
u = −1.113080 − 0.572032I
a = 0.409485 + 0.276988I
b = −1.038680 − 0.866746I
−3.04837 + 8.64260I 0
u = −1.127510 + 0.545345I
a = 1.35109 − 0.60924I
b = −3.12800 − 1.78113I
5.52623 − 10.50810I 0
u = −1.127510 − 0.545345I
a = 1.35109 + 0.60924I
b = −3.12800 + 1.78113I
5.52623 + 10.50810I 0
u = −0.255630 + 0.700510I
a = 0.66059 + 2.00188I
b = 0.928667 − 0.890697I
3.58451 + 0.63311I 3.90774 + 0.20235I
u = −0.255630 − 0.700510I
a = 0.66059 − 2.00188I
b = 0.928667 + 0.890697I
3.58451 − 0.63311I 3.90774 − 0.20235I
u = 1.117670 + 0.572842I
a = 2.39020 + 0.19166I
b = −3.74786 + 3.86765I
−2.62401 + 11.41900I 0
u = 1.117670 − 0.572842I
a = 2.39020 − 0.19166I
b = −3.74786 − 3.86765I
−2.62401 − 11.41900I 0
u = −1.123200 + 0.571908I
a = −1.218990 − 0.485290I
b = 0.78507 + 2.29582I
1.67983 − 12.53120I 0
u = −1.123200 − 0.571908I
a = −1.218990 + 0.485290I
b = 0.78507 − 2.29582I
1.67983 + 12.53120I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.125270 + 0.577644I
a = 2.16421 + 0.09260I
b = −3.04949 − 3.82760I
−1.2476 − 17.7637I 0
u = −1.125270 − 0.577644I
a = 2.16421 − 0.09260I
b = −3.04949 + 3.82760I
−1.2476 + 17.7637I 0
u = 0.318716 + 0.645599I
a = 2.15930 + 0.86166I
b = −1.27930 + 1.37397I
−0.99213 − 2.05244I −1.42867 + 4.32429I
u = 0.318716 − 0.645599I
a = 2.15930 − 0.86166I
b = −1.27930 − 1.37397I
−0.99213 + 2.05244I −1.42867 − 4.32429I
u = −0.371248 + 0.579272I
a = −0.468365 − 0.530701I
b = 0.674075 − 0.274514I
−2.64408 + 0.56153I 0.57264 + 1.51030I
u = −0.371248 − 0.579272I
a = −0.468365 + 0.530701I
b = 0.674075 + 0.274514I
−2.64408 − 0.56153I 0.57264 − 1.51030I
u = −0.085626 + 0.660140I
a = 0.42627 + 2.05389I
b = 0.787350 − 0.512326I
−0.37884 − 6.25642I −0.31749 + 5.34510I
u = −0.085626 − 0.660140I
a = 0.42627 − 2.05389I
b = 0.787350 + 0.512326I
−0.37884 + 6.25642I −0.31749 − 5.34510I
u = −0.141705 + 0.628686I
a = 0.763417 − 0.441676I
b = −0.799689 − 0.229027I
1.97525 − 1.44614I 3.45027 + 1.23411I
u = −0.141705 − 0.628686I
a = 0.763417 + 0.441676I
b = −0.799689 + 0.229027I
1.97525 + 1.44614I 3.45027 − 1.23411I
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.469682 + 0.440328I
a = −0.27281 − 1.87269I
b = 1.68197 − 0.69139I
−1.66871 + 1.06570I −4.19233 − 3.72073I
u = 0.469682 − 0.440328I
a = −0.27281 + 1.87269I
b = 1.68197 + 0.69139I
−1.66871 − 1.06570I −4.19233 + 3.72073I
u = 0.088644 + 0.519773I
a = 0.29013 − 2.32275I
b = 0.970827 + 0.307157I
−1.94299 + 1.02992I −2.91322 − 0.80496I
u = 0.088644 − 0.519773I
a = 0.29013 + 2.32275I
b = 0.970827 − 0.307157I
−1.94299 − 1.02992I −2.91322 + 0.80496I
16
II. I
u
2
= hu
5
+ u
4
− u
3
− u
2
+ b, a, u
6
+ u
5
− u
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
5
− u
4
+ 2u
3
+ u
2
− u − 1
a
3
=
0
−u
5
− u
4
+ u
3
+ u
2
a
2
=
u
4
− u
2
+ 1
−2u
5
− 2u
4
+ 3u
3
+ 2u
2
− u − 1
a
10
=
−u
2
+ 1
u
2
a
5
=
−u
4
+ u
2
− 1
u
5
+ u
4
− 2u
3
− u
2
+ u + 1
a
4
=
0
−u
5
− u
4
+ u
3
+ u
2
a
9
=
0
u
a
8
=
0
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
4
+ 5u
2
+ 5u − 7
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
6
c
3
, c
7
, c
8
u
6
c
4
(u + 1)
6
c
5
, c
9
, c
11
u
6
+ u
5
− u
4
− 2u
3
+ u + 1
c
6
u
6
− u
5
− u
4
+ 2u
3
− u + 1
c
10
, c
12
u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
6
c
3
, c
7
, c
8
y
6
c
5
, c
6
, c
9
c
11
y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1
c
10
, c
12
y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.002190 + 0.295542I
a = 0
b = 1.000940 − 0.863088I
0.245672 + 0.924305I 0.635956 + 0.093695I
u = 1.002190 − 0.295542I
a = 0
b = 1.000940 + 0.863088I
0.245672 − 0.924305I 0.635956 − 0.093695I
u = −0.428243 + 0.664531I
a = 0
b = 0.573013 − 0.494098I
−3.53554 + 0.92430I −9.40317 − 0.69886I
u = −0.428243 − 0.664531I
a = 0
b = 0.573013 + 0.494098I
−3.53554 − 0.92430I −9.40317 + 0.69886I
u = −1.073950 + 0.558752I
a = 0
b = −0.573950 + 0.818891I
−1.64493 − 5.69302I −5.23279 + 4.86918I
u = −1.073950 − 0.558752I
a = 0
b = −0.573950 − 0.818891I
−1.64493 + 5.69302I −5.23279 − 4.86918I
20
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
6
)(u
114
+ 61u
113
+ ··· + 8u + 1)
c
2
((u − 1)
6
)(u
114
− 7u
113
+ ··· − 8u + 1)
c
3
, c
8
u
6
(u
114
+ u
113
+ ··· − 64u + 64)
c
4
((u + 1)
6
)(u
114
− 7u
113
+ ··· − 8u + 1)
c
5
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)(u
114
+ 2u
113
+ ··· − 60045u + 5113)
c
6
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)(u
114
− 2u
113
+ ··· − 3u + 1)
c
7
u
6
(u
114
− 39u
113
+ ··· − 114688u + 4096)
c
9
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)(u
114
− 14u
113
+ ··· − 4339u + 349)
c
10
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)(u
114
− 54u
113
+ ··· + u + 1)
c
11
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)(u
114
− 2u
113
+ ··· − 3u + 1)
c
12
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
· (u
114
− 6u
113
+ ··· − 13547u + 1585)
21
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
6
)(y
114
− 9y
113
+ ··· − 16y + 1)
c
2
, c
4
((y −1)
6
)(y
114
− 61y
113
+ ··· − 8y + 1)
c
3
, c
8
y
6
(y
114
− 39y
113
+ ··· − 114688y + 4096)
c
5
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· (y
114
− 30y
113
+ ··· − 2610115671y + 26142769)
c
6
, c
11
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)(y
114
− 54y
113
+ ··· + y + 1)
c
7
y
6
(y
114
+ 61y
113
+ ··· − 4.86539 × 10
8
y + 1.67772 × 10
7
)
c
9
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· (y
114
+ 6y
113
+ ··· + 2982089y + 121801)
c
10
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)(y
114
+ 14y
113
+ ··· + 9y + 1)
c
12
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
· (y
114
+ 26y
113
+ ··· + 126216321y + 2512225)
22
