12a
0338
(K12a
0338
)
A knot diagram
1
Linearized knot diagam
3 6 8 12 10 2 9 4 7 1 5 11
Solving Sequence
2,7
6 3
1,10
11 5 9 8 4 12
c
6
c
2
c
1
c
10
c
5
c
9
c
7
c
3
c
12
c
4
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.78002 × 10
173
u
104
+ 5.41973 × 10
173
u
103
+ ··· + 1.18953 × 10
174
b − 3.63788 × 10
175
,
− 9.01231 × 10
174
u
104
− 1.44968 × 10
175
u
103
+ ··· + 5.94763 × 10
174
a + 4.58982 × 10
176
,
u
105
+ u
104
+ ··· − 125u − 25i
I
u
2
= h28a
5
− 43a
4
u + 70a
4
− 86a
3
u + 36a
3
− 27a
2
u − 16a
2
+ 16au + 215b + 189a − 114u − 8,
a
6
− 2a
5
u + 3a
5
− 5a
4
u + a
4
− 2a
3
u − 3a
3
+ 2a
2
u + 3a
2
− 5au + 5a − 3u + 4, u
2
+ 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−2.78 × 10
173
u
104
+ 5.42 × 10
173
u
103
+ · · · + 1.19 × 10
174
b − 3.64 ×
10
175
, −9.01 × 10
174
u
104
− 1.45 × 10
175
u
103
+ · · · + 5.95 × 10
174
a + 4.59 ×
10
176
, u
105
+ u
104
+ · · · − 125u − 25i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
10
=
1.51528u
104
+ 2.43741u
103
+ ··· − 342.962u − 77.1705
0.233708u
104
− 0.455620u
103
+ ··· + 106.022u + 30.5826
a
11
=
1.41422u
104
+ 3.00688u
103
+ ··· − 376.935u − 86.2579
−0.102232u
104
− 0.503588u
103
+ ··· + 107.840u + 27.3085
a
5
=
0.107162u
104
+ 0.439090u
103
+ ··· − 68.2154u − 12.9715
−1.66904u
104
− 0.358595u
103
+ ··· + 71.3230u + 2.74449
a
9
=
1.74898u
104
+ 1.98179u
103
+ ··· − 236.940u − 46.5879
0.233708u
104
− 0.455620u
103
+ ··· + 106.022u + 30.5826
a
8
=
0.0840748u
104
+ 0.942451u
103
+ ··· − 98.0344u − 26.0878
0.100962u
104
− 0.744433u
103
+ ··· + 141.226u + 39.8498
a
4
=
−0.990500u
104
− 3.18401u
103
+ ··· + 407.098u + 90.6155
2.57023u
104
+ 0.861705u
103
+ ··· − 126.916u − 11.1131
a
12
=
0.301371u
104
+ 2.46302u
103
+ ··· − 344.399u − 88.0238
−1.21240u
104
− 0.508503u
103
+ ··· + 118.564u + 20.5025
(ii) Obstruction class = −1
(iii) Cusp Shapes = −3.34744u
104
− 4.63397u
103
+ ··· + 773.517u + 167.231
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
105
+ 51u
104
+ ··· − 1225u − 625
c
2
, c
6
u
105
− u
104
+ ··· − 125u + 25
c
3
, c
8
u
105
− u
104
+ ··· + 9u + 1
c
4
, c
11
u
105
+ u
104
+ ··· − 7u + 1
c
5
u
105
− 5u
104
+ ··· − 422719u + 60663
c
7
, c
9
u
105
+ 35u
104
+ ··· − 43u + 1
c
10
, c
12
u
105
− 35u
104
+ ··· + 39u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
105
+ 19y
104
+ ··· + 36351875y −390625
c
2
, c
6
y
105
+ 51y
104
+ ··· − 1225y −625
c
3
, c
8
y
105
− 35y
104
+ ··· − 43y −1
c
4
, c
11
y
105
+ 35y
104
+ ··· + 39y −1
c
5
y
105
+ 15y
104
+ ··· + 108021991111y −3679999569
c
7
, c
9
y
105
+ 77y
104
+ ··· − 5759y −1
c
10
, c
12
y
105
+ 75y
104
+ ··· + 951y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.749218 + 0.639499I
a = −0.154405 + 0.543190I
b = 0.077141 + 1.283560I
3.66490 − 2.51476I 0
u = −0.749218 − 0.639499I
a = −0.154405 − 0.543190I
b = 0.077141 − 1.283560I
3.66490 + 2.51476I 0
u = −0.948983 + 0.361206I
a = −0.206223 − 0.158334I
b = 0.45260 − 1.51018I
2.91142 + 11.55500I 0
u = −0.948983 − 0.361206I
a = −0.206223 + 0.158334I
b = 0.45260 + 1.51018I
2.91142 − 11.55500I 0
u = 0.922665 + 0.425326I
a = 0.413418 − 0.143561I
b = −0.183481 − 1.219410I
3.78039 − 5.61089I 0
u = 0.922665 − 0.425326I
a = 0.413418 + 0.143561I
b = −0.183481 + 1.219410I
3.78039 + 5.61089I 0
u = −0.455269 + 0.915131I
a = −1.78391 + 1.38691I
b = 0.417127 + 1.242680I
−3.63933 − 1.37243I 0
u = −0.455269 − 0.915131I
a = −1.78391 − 1.38691I
b = 0.417127 − 1.242680I
−3.63933 + 1.37243I 0
u = 0.613086 + 0.826892I
a = 1.021720 + 0.354723I
b = −0.497693 − 0.157462I
3.75864 + 2.41481I 0
u = 0.613086 − 0.826892I
a = 1.021720 − 0.354723I
b = −0.497693 + 0.157462I
3.75864 − 2.41481I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.896671 + 0.356964I
a = −0.203981 + 0.291029I
b = 0.44898 + 1.46429I
1.72233 − 5.88113I 0
u = 0.896671 − 0.356964I
a = −0.203981 − 0.291029I
b = 0.44898 − 1.46429I
1.72233 + 5.88113I 0
u = −0.914248 + 0.490333I
a = 0.128466 − 0.189595I
b = 0.33402 − 1.49335I
7.99889 + 5.30446I 0
u = −0.914248 − 0.490333I
a = 0.128466 + 0.189595I
b = 0.33402 + 1.49335I
7.99889 − 5.30446I 0
u = 0.099289 + 1.032690I
a = −0.503451 − 1.051430I
b = 0.537831 + 0.973312I
−1.75450 − 2.05061I 0
u = 0.099289 − 1.032690I
a = −0.503451 + 1.051430I
b = 0.537831 − 0.973312I
−1.75450 + 2.05061I 0
u = −0.854899 + 0.421450I
a = 0.425038 + 0.283762I
b = −0.128597 + 1.177340I
2.54200 + 0.06951I 0
u = −0.854899 − 0.421450I
a = 0.425038 − 0.283762I
b = −0.128597 − 1.177340I
2.54200 − 0.06951I 0
u = −0.031016 + 1.049550I
a = 1.113560 + 0.088475I
b = −0.0059743 − 0.0144561I
−4.65129 − 2.79161I 0
u = −0.031016 − 1.049550I
a = 1.113560 − 0.088475I
b = −0.0059743 + 0.0144561I
−4.65129 + 2.79161I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.889111 + 0.570980I
a = 0.086184 − 0.189831I
b = −0.068274 − 1.318180I
8.53906 + 0.69544I 0
u = 0.889111 − 0.570980I
a = 0.086184 + 0.189831I
b = −0.068274 + 1.318180I
8.53906 − 0.69544I 0
u = −0.840055 + 0.645863I
a = 0.575483 − 0.243329I
b = 0.19081 − 1.42878I
5.26478 − 1.27381I 0
u = −0.840055 − 0.645863I
a = 0.575483 + 0.243329I
b = 0.19081 + 1.42878I
5.26478 + 1.27381I 0
u = −0.412578 + 0.843978I
a = 2.05627 − 0.88271I
b = 0.126633 − 1.017210I
−3.33038 − 2.22358I 0
u = −0.412578 − 0.843978I
a = 2.05627 + 0.88271I
b = 0.126633 + 1.017210I
−3.33038 + 2.22358I 0
u = 0.774233 + 0.531300I
a = 0.340368 + 0.531499I
b = 0.293190 + 1.372850I
3.36600 − 3.23323I 0
u = 0.774233 − 0.531300I
a = 0.340368 − 0.531499I
b = 0.293190 − 1.372850I
3.36600 + 3.23323I 0
u = −0.495537 + 0.944166I
a = −0.75412 + 1.30512I
b = 0.899731 − 1.079430I
−3.30148 − 3.57186I 0
u = −0.495537 − 0.944166I
a = −0.75412 − 1.30512I
b = 0.899731 + 1.079430I
−3.30148 + 3.57186I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.472411 + 0.959035I
a = −1.94854 − 1.12109I
b = 0.443886 − 1.273270I
−3.90875 + 7.44310I 0
u = 0.472411 − 0.959035I
a = −1.94854 + 1.12109I
b = 0.443886 + 1.273270I
−3.90875 − 7.44310I 0
u = −0.265182 + 1.035910I
a = −0.540567 + 0.578355I
b = 0.627717 + 0.218999I
−1.64134 − 0.64025I 0
u = −0.265182 − 1.035910I
a = −0.540567 − 0.578355I
b = 0.627717 − 0.218999I
−1.64134 + 0.64025I 0
u = 0.436930 + 0.990417I
a = −0.70748 − 1.31204I
b = 0.833111 + 1.105010I
−4.03635 − 1.85896I 0
u = 0.436930 − 0.990417I
a = −0.70748 + 1.31204I
b = 0.833111 − 1.105010I
−4.03635 + 1.85896I 0
u = 0.827568 + 0.728196I
a = −0.360735 − 0.251802I
b = 0.078908 − 1.395500I
5.40630 + 7.26455I 0
u = 0.827568 − 0.728196I
a = −0.360735 + 0.251802I
b = 0.078908 + 1.395500I
5.40630 − 7.26455I 0
u = 0.408500 + 1.043460I
a = −1.31979 − 0.57260I
b = 0.987712 − 0.301187I
−3.74828 + 3.33003I 0
u = 0.408500 − 1.043460I
a = −1.31979 + 0.57260I
b = 0.987712 + 0.301187I
−3.74828 − 3.33003I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.654211 + 0.587061I
a = 1.095220 + 0.206022I
b = −0.467679 + 0.101114I
0.36679 − 3.18781I 0
u = 0.654211 − 0.587061I
a = 1.095220 − 0.206022I
b = −0.467679 − 0.101114I
0.36679 + 3.18781I 0
u = −0.523776 + 0.994154I
a = −1.58817 + 0.36404I
b = 1.129100 + 0.462674I
−0.15746 − 5.39094I 0
u = −0.523776 − 0.994154I
a = −1.58817 − 0.36404I
b = 1.129100 − 0.462674I
−0.15746 + 5.39094I 0
u = 0.391092 + 0.779809I
a = 1.94937 + 1.22961I
b = 0.181158 + 1.035310I
−3.18895 − 3.79634I 0
u = 0.391092 − 0.779809I
a = 1.94937 − 1.22961I
b = 0.181158 − 1.035310I
−3.18895 + 3.79634I 0
u = −0.538943 + 0.992209I
a = 0.892504 − 0.495752I
b = −0.440179 + 0.375313I
−1.80743 − 2.63543I 0
u = −0.538943 − 0.992209I
a = 0.892504 + 0.495752I
b = −0.440179 − 0.375313I
−1.80743 + 2.63543I 0
u = 0.602258 + 0.992368I
a = 0.967009 + 0.515114I
b = −0.523841 − 0.361124I
−0.81304 + 8.09901I 0
u = 0.602258 − 0.992368I
a = 0.967009 − 0.515114I
b = −0.523841 + 0.361124I
−0.81304 − 8.09901I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.435933 + 0.697192I
a = −1.58393 − 0.14120I
b = 0.906082 + 0.759162I
−2.52613 − 0.37000I 0
u = −0.435933 − 0.697192I
a = −1.58393 + 0.14120I
b = 0.906082 − 0.759162I
−2.52613 + 0.37000I 0
u = −0.326926 + 0.753509I
a = 0.876707 − 0.161992I
b = −0.208415 + 0.097999I
−0.358551 − 1.274780I 0
u = −0.326926 − 0.753509I
a = 0.876707 + 0.161992I
b = −0.208415 − 0.097999I
−0.358551 + 1.274780I 0
u = 0.727147 + 0.929674I
a = 1.332630 + 0.067450I
b = −0.073439 + 1.279710I
4.78389 − 1.49312I 0
u = 0.727147 − 0.929674I
a = 1.332630 − 0.067450I
b = −0.073439 − 1.279710I
4.78389 + 1.49312I 0
u = −0.642428 + 0.994707I
a = 1.58181 − 0.06710I
b = −0.120516 − 1.169660I
2.58651 − 2.77147I 0
u = −0.642428 − 0.994707I
a = 1.58181 + 0.06710I
b = −0.120516 + 1.169660I
2.58651 + 2.77147I 0
u = −0.291339 + 1.147920I
a = −1.07904 + 1.33880I
b = 0.880929 − 0.060855I
−7.29427 + 3.25905I 0
u = −0.291339 − 1.147920I
a = −1.07904 − 1.33880I
b = 0.880929 + 0.060855I
−7.29427 − 3.25905I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.318480 + 1.149160I
a = −1.20502 − 1.21024I
b = 0.937266 + 0.014042I
−7.80378 + 2.53380I 0
u = 0.318480 − 1.149160I
a = −1.20502 + 1.21024I
b = 0.937266 − 0.014042I
−7.80378 − 2.53380I 0
u = −0.394685 + 0.681817I
a = −0.74179 + 1.24370I
b = 0.858018 − 0.849099I
1.00451 + 1.38416I 0
u = −0.394685 − 0.681817I
a = −0.74179 − 1.24370I
b = 0.858018 + 0.849099I
1.00451 − 1.38416I 0
u = −0.696432 + 0.998477I
a = −1.363000 + 0.182789I
b = 0.36242 + 1.47257I
4.19020 − 4.43268I 0
u = −0.696432 − 0.998477I
a = −1.363000 − 0.182789I
b = 0.36242 − 1.47257I
4.19020 + 4.43268I 0
u = 0.525892 + 1.105600I
a = −1.70195 − 0.58889I
b = 1.227660 − 0.311645I
−6.36079 + 5.15428I 0
u = 0.525892 − 1.105600I
a = −1.70195 + 0.58889I
b = 1.227660 + 0.311645I
−6.36079 − 5.15428I 0
u = −0.557253 + 1.100040I
a = −1.75299 + 0.53655I
b = 1.264240 + 0.349874I
−5.43018 − 10.86880I 0
u = −0.557253 − 1.100040I
a = −1.75299 − 0.53655I
b = 1.264240 − 0.349874I
−5.43018 + 10.86880I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.633066 + 1.062180I
a = −1.71464 − 0.17211I
b = 0.45172 − 1.45583I
1.76945 + 8.55794I 0
u = 0.633066 − 1.062180I
a = −1.71464 + 0.17211I
b = 0.45172 + 1.45583I
1.76945 − 8.55794I 0
u = −0.157329 + 1.256680I
a = 0.153650 − 1.003600I
b = 0.055397 + 0.979337I
−3.05816 − 2.74237I 0
u = −0.157329 − 1.256680I
a = 0.153650 + 1.003600I
b = 0.055397 − 0.979337I
−3.05816 + 2.74237I 0
u = −0.659194 + 0.320658I
a = −0.514042 + 0.767799I
b = 1.036400 − 0.466896I
−3.24371 + 6.12777I −6.15771 − 5.80608I
u = −0.659194 − 0.320658I
a = −0.514042 − 0.767799I
b = 1.036400 + 0.466896I
−3.24371 − 6.12777I −6.15771 + 5.80608I
u = 0.705819 + 1.068090I
a = 1.55412 − 0.13299I
b = −0.223821 + 1.220860I
7.02983 + 5.17717I 0
u = 0.705819 − 1.068090I
a = 1.55412 + 0.13299I
b = −0.223821 − 1.220860I
7.02983 − 5.17717I 0
u = −0.638249 + 1.127680I
a = 1.71290 + 0.16233I
b = −0.276567 − 1.120920I
0.42944 − 5.60887I 0
u = −0.638249 − 1.127680I
a = 1.71290 − 0.16233I
b = −0.276567 + 1.120920I
0.42944 + 5.60887I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.208539 + 1.286940I
a = −0.33208 − 1.39539I
b = 0.471474 + 1.286510I
−3.77595 − 2.49413I 0
u = 0.208539 − 1.286940I
a = −0.33208 + 1.39539I
b = 0.471474 − 1.286510I
−3.77595 + 2.49413I 0
u = 0.652851 + 0.229553I
a = −0.391974 − 0.605737I
b = 1.000530 + 0.352950I
−3.94841 − 0.62805I −8.02207 + 0.40086I
u = 0.652851 − 0.229553I
a = −0.391974 + 0.605737I
b = 1.000530 − 0.352950I
−3.94841 + 0.62805I −8.02207 − 0.40086I
u = −0.045533 + 1.308020I
a = −0.118848 + 1.278670I
b = 0.274612 − 1.204280I
1.44896 + 2.66591I 0
u = −0.045533 − 1.308020I
a = −0.118848 − 1.278670I
b = 0.274612 + 1.204280I
1.44896 − 2.66591I 0
u = −0.545403 + 0.420809I
a = 1.077950 − 0.122804I
b = −0.300695 − 0.199395I
−0.34516 − 1.69194I −0.65997 + 3.30204I
u = −0.545403 − 0.420809I
a = 1.077950 + 0.122804I
b = −0.300695 + 0.199395I
−0.34516 + 1.69194I −0.65997 − 3.30204I
u = −0.684533 + 1.119160I
a = −1.68900 − 0.11987I
b = 0.47230 + 1.53335I
6.08933 − 11.17010I 0
u = −0.684533 − 1.119160I
a = −1.68900 + 0.11987I
b = 0.47230 − 1.53335I
6.08933 + 11.17010I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.119068 + 1.317990I
a = 0.138283 + 1.145170I
b = 0.060042 − 1.094540I
−2.36377 − 2.50056I 0
u = 0.119068 − 1.317990I
a = 0.138283 − 1.145170I
b = 0.060042 + 1.094540I
−2.36377 + 2.50056I 0
u = 0.628153 + 1.166960I
a = −1.95577 + 0.16084I
b = 0.54821 − 1.50960I
−0.71454 + 11.48410I 0
u = 0.628153 − 1.166960I
a = −1.95577 − 0.16084I
b = 0.54821 + 1.50960I
−0.71454 − 11.48410I 0
u = 0.661390 + 1.149150I
a = 1.69582 − 0.21098I
b = −0.310769 + 1.143510I
1.58523 + 11.41040I 0
u = 0.661390 − 1.149150I
a = 1.69582 + 0.21098I
b = −0.310769 − 1.143510I
1.58523 − 11.41040I 0
u = −0.186843 + 1.334870I
a = −0.27019 + 1.43191I
b = 0.419159 − 1.326740I
−2.94616 + 7.93415I 0
u = −0.186843 − 1.334870I
a = −0.27019 − 1.43191I
b = 0.419159 + 1.326740I
−2.94616 − 7.93415I 0
u = −0.644955 + 1.184790I
a = −1.93120 − 0.24671I
b = 0.55527 + 1.53543I
0.4062 − 17.3601I 0
u = −0.644955 − 1.184790I
a = −1.93120 + 0.24671I
b = 0.55527 − 1.53543I
0.4062 + 17.3601I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.369462 + 0.499023I
a = −1.88737 + 0.31530I
b = 0.810482 − 0.869250I
−2.57683 + 5.38819I −4.57971 − 8.38711I
u = 0.369462 − 0.499023I
a = −1.88737 − 0.31530I
b = 0.810482 + 0.869250I
−2.57683 − 5.38819I −4.57971 + 8.38711I
u = 0.481861
a = 0.400491
b = 0.607759
−1.15266 −8.89830
u = −0.342083 + 0.052573I
a = 1.61547 + 0.81293I
b = 0.374191 − 0.564968I
1.25400 + 1.74865I 2.56111 − 5.04515I
u = −0.342083 − 0.052573I
a = 1.61547 − 0.81293I
b = 0.374191 + 0.564968I
1.25400 − 1.74865I 2.56111 + 5.04515I
15
II.
I
u
2
= h−43a
4
u − 86a
3
u + · · · + 189a − 8, −2a
5
u − 5a
4
u + · · · + 5a + 4, u
2
+ 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
−1
a
3
=
u
0
a
1
=
−u
u
a
10
=
a
0.200000a
4
u + 0.400000a
3
u + ··· − 0.879070a + 0.0372093
a
11
=
−0.200000a
4
u − 0.400000a
3
u + ··· + 0.879070a − 0.0372093
0.400000a
4
u + 0.800000a
3
u + ··· − 0.758140a + 0.0744186
a
5
=
0.0604651a
5
u + 0.251163a
4
u + ··· − 0.688372a + 0.479070
0.0604651a
5
u + 0.0511628a
4
u + ··· + 0.190698a − 0.558140
a
9
=
0.200000a
4
u + 0.400000a
3
u + ··· + 0.120930a + 0.0372093
0.200000a
4
u + 0.400000a
3
u + ··· − 0.879070a + 0.0372093
a
8
=
−0.0604651a
5
u − 0.0511628a
4
u + ··· − 0.190698a + 0.558140
0.200000a
4
u + 0.400000a
3
u + ··· − 0.879070a − 0.962791
a
4
=
−au
0.130233a
5
u + 0.325581a
4
u + ··· − 0.0744186a + 0.530233
a
12
=
−0.0651163a
5
u − 0.362791a
4
u + ··· + 0.195349a − 0.139535
0.0651163a
5
u + 0.762791a
4
u + ··· − 0.511628a − 0.111628
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
8
215
a
5
u −
112
215
a
5
+
152
215
a
4
u −
108
215
a
4
+
88
215
a
3
u +
40
43
a
3
−
256
215
a
2
u −
128
215
a
2
+
312
215
au −
224
43
a +
704
215
u −
1352
215
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
12
c
2
, c
6
(u
2
+ 1)
6
c
3
, c
8
(u
4
− u
2
+ 1)
3
c
4
, c
11
(u
6
+ u
4
+ 2u
2
+ 1)
2
c
5
(u
6
− 3u
4
+ 2u
2
+ 1)
2
c
7
(u
2
− u + 1)
6
c
9
(u
2
+ u + 1)
6
c
10
(u
3
+ u
2
+ 2u + 1)
4
c
12
(u
3
− u
2
+ 2u − 1)
4
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y −1)
12
c
2
, c
6
(y + 1)
12
c
3
, c
8
(y
2
− y + 1)
6
c
4
, c
11
(y
3
+ y
2
+ 2y + 1)
4
c
5
(y
3
− 3y
2
+ 2y + 1)
4
c
7
, c
9
(y
2
+ y + 1)
6
c
10
, c
12
(y
3
+ 3y
2
+ 2y −1)
4
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = 0.807141 − 0.650946I
b = 0.500000 + 0.866025I
−4.66906 − 4.85801I −9.50976 + 6.44355I
u = 1.000000I
a = 0.807141 + 1.081110I
b = 0.500000 − 0.866025I
−4.66906 − 0.79824I −9.50976 − 0.48465I
u = 1.000000I
a = −0.500000 − 0.296185I
b = 0.500000 + 0.866025I
−0.53148 − 2.02988I −2.98049 + 3.46410I
u = 1.000000I
a = −0.50000 + 1.43587I
b = 0.500000 − 0.866025I
−0.53148 + 2.02988I −2.98049 − 3.46410I
u = 1.000000I
a = −1.80714 − 0.65095I
b = 0.500000 + 0.866025I
−4.66906 + 0.79824I −9.50976 + 0.48465I
u = 1.000000I
a = −1.80714 + 1.08111I
b = 0.500000 − 0.866025I
−4.66906 + 4.85801I −9.50976 − 6.44355I
u = − 1.000000I
a = 0.807141 + 0.650946I
b = 0.500000 − 0.866025I
−4.66906 + 4.85801I −9.50976 − 6.44355I
u = − 1.000000I
a = 0.807141 − 1.081110I
b = 0.500000 + 0.866025I
−4.66906 + 0.79824I −9.50976 + 0.48465I
u = − 1.000000I
a = −0.500000 + 0.296185I
b = 0.500000 − 0.866025I
−0.53148 + 2.02988I −2.98049 − 3.46410I
u = − 1.000000I
a = −0.50000 − 1.43587I
b = 0.500000 + 0.866025I
−0.53148 − 2.02988I −2.98049 + 3.46410I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = − 1.000000I
a = −1.80714 + 0.65095I
b = 0.500000 − 0.866025I
−4.66906 − 0.79824I −9.50976 − 0.48465I
u = − 1.000000I
a = −1.80714 − 1.08111I
b = 0.500000 + 0.866025I
−4.66906 − 4.85801I −9.50976 + 6.44355I
20
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
12
)(u
105
+ 51u
104
+ ··· − 1225u − 625)
c
2
, c
6
((u
2
+ 1)
6
)(u
105
− u
104
+ ··· − 125u + 25)
c
3
, c
8
((u
4
− u
2
+ 1)
3
)(u
105
− u
104
+ ··· + 9u + 1)
c
4
, c
11
((u
6
+ u
4
+ 2u
2
+ 1)
2
)(u
105
+ u
104
+ ··· − 7u + 1)
c
5
((u
6
− 3u
4
+ 2u
2
+ 1)
2
)(u
105
− 5u
104
+ ··· − 422719u + 60663)
c
7
((u
2
− u + 1)
6
)(u
105
+ 35u
104
+ ··· − 43u + 1)
c
9
((u
2
+ u + 1)
6
)(u
105
+ 35u
104
+ ··· − 43u + 1)
c
10
((u
3
+ u
2
+ 2u + 1)
4
)(u
105
− 35u
104
+ ··· + 39u + 1)
c
12
((u
3
− u
2
+ 2u − 1)
4
)(u
105
− 35u
104
+ ··· + 39u + 1)
21
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
12
)(y
105
+ 19y
104
+ ··· + 3.63519 × 10
7
y −390625)
c
2
, c
6
((y + 1)
12
)(y
105
+ 51y
104
+ ··· − 1225y −625)
c
3
, c
8
((y
2
− y + 1)
6
)(y
105
− 35y
104
+ ··· − 43y −1)
c
4
, c
11
((y
3
+ y
2
+ 2y + 1)
4
)(y
105
+ 35y
104
+ ··· + 39y −1)
c
5
(y
3
− 3y
2
+ 2y + 1)
4
· (y
105
+ 15y
104
+ ··· + 108021991111y −3679999569)
c
7
, c
9
((y
2
+ y + 1)
6
)(y
105
+ 77y
104
+ ··· − 5759y −1)
c
10
, c
12
((y
3
+ 3y
2
+ 2y −1)
4
)(y
105
+ 75y
104
+ ··· + 951y −1)
22
