12a
0002
(K12a
0002
)
A knot diagram
1
Linearized knot diagam
3 5 6 8 2 9 11 4 12 1 7 10
Solving Sequence
7,12
11
4,8
5 9 10 1 6 3 2
c
11
c
7
c
4
c
8
c
9
c
12
c
6
c
3
c
2
c
1
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h2.87313 × 10
334
u
104
− 9.21887 × 10
334
u
103
+ ··· + 1.15405 × 10
337
b + 3.50101 × 10
336
,
− 2.56029 × 10
334
u
104
+ 5.49406 × 10
334
u
103
+ ··· + 6.59460 × 10
336
a − 2.98633 × 10
337
,
u
105
− 3u
104
+ ··· + 2048u + 1024i
I
u
2
= h−u
2
a + b − a, u
4
a + u
3
a + u
4
+ 2u
2
a + a
2
+ au + u
2
+ a − u, u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1i
I
v
1
= ha, v
3
+ 2v
2
+ b + 2v, v
4
+ 2v
3
+ 3v
2
+ v + 1i
I
v
2
= ha, −v
3
− v
2
+ b + 1, v
6
+ 3v
5
+ 4v
4
+ 2v
3
+ 1i
* 4 irreducible components of dim
C
= 0, with total 125 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
= h2.87 × 10
334
u
104
− 9.22 × 10
334
u
103
+ · · · + 1.15 × 10
337
b + 3.50 ×
10
336
, −2.56 × 10
334
u
104
+ 5.49 × 10
334
u
103
+ · · · + 6.59 × 10
336
a − 2.99 ×
10
337
, u
105
− 3u
104
+ · · · + 2048u + 1024i
(i) Arc colorings
a
7
=
0
u
a
12
=
1
0
a
11
=
1
u
2
a
4
=
0.00388240u
104
− 0.00833116u
103
+ ··· + 11.4924u + 4.52845
−0.00248959u
104
+ 0.00798824u
103
+ ··· − 4.48147u − 0.303366
a
8
=
u
u
3
+ u
a
5
=
0.00498777u
104
− 0.0112515u
103
+ ··· + 14.7026u + 5.39070
−0.00215259u
104
+ 0.00751970u
103
+ ··· − 3.21368u + 0.153629
a
9
=
−0.000519769u
104
+ 0.00481996u
103
+ ··· + 4.67049u + 3.48978
−0.00119259u
104
+ 0.00216389u
103
+ ··· − 4.22800u − 2.41288
a
10
=
0.000672817u
104
+ 0.00265608u
103
+ ··· + 8.89849u + 5.90266
−0.00119259u
104
+ 0.00216389u
103
+ ··· − 4.22800u − 2.41288
a
1
=
0.000672817u
104
+ 0.00265608u
103
+ ··· + 8.89849u + 5.90266
−0.00129632u
104
+ 0.00157290u
103
+ ··· − 6.03440u − 2.37383
a
6
=
−0.00489883u
104
+ 0.0141883u
103
+ ··· − 8.53327u − 2.46195
0.00235848u
104
− 0.00763297u
103
+ ··· + 4.80576u + 0.638462
a
3
=
−0.00606696u
104
+ 0.0253348u
103
+ ··· + 2.81502u + 4.85586
0.00220680u
104
− 0.0101609u
103
+ ··· − 3.08436u − 1.82736
a
2
=
−0.00434510u
104
+ 0.0185156u
103
+ ··· − 0.931222u + 2.88768
−0.000320191u
104
− 0.00175592u
103
+ ··· − 9.30691u − 3.74997
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.00265333u
104
+ 0.00375222u
103
+ ··· − 32.4877u − 13.5243
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
105
+ 53u
104
+ ··· − 7u − 1
c
2
, c
5
u
105
+ 7u
104
+ ··· − 7u − 1
c
3
u
105
− 7u
104
+ ··· − 40152u − 14308
c
4
, c
8
u
105
− 2u
104
+ ··· − 2048u − 1024
c
6
u
105
− 4u
104
+ ··· − 66488u − 52489
c
7
, c
11
u
105
− 3u
104
+ ··· + 2048u + 1024
c
9
, c
10
, c
12
u
105
− 13u
104
+ ··· − 7u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
105
+ 5y
104
+ ··· + 33y −1
c
2
, c
5
y
105
+ 53y
104
+ ··· − 7y −1
c
3
y
105
− 43y
104
+ ··· + 5145658168y −204718864
c
4
, c
8
y
105
+ 60y
104
+ ··· − 16777216y −1048576
c
6
y
105
− 62y
104
+ ··· − 163409354104y −2755095121
c
7
, c
11
y
105
+ 69y
104
+ ··· − 9961472y −1048576
c
9
, c
10
, c
12
y
105
− 105y
104
+ ··· − 33y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.268285 + 0.949256I
a = 0.872590 + 0.818513I
b = −0.525404 − 0.588907I
−5.18965 − 8.64562I 0
u = −0.268285 − 0.949256I
a = 0.872590 − 0.818513I
b = −0.525404 + 0.588907I
−5.18965 + 8.64562I 0
u = 0.445627 + 0.931879I
a = 0.200127 + 0.084474I
b = −0.298515 − 0.395878I
−0.21716 + 2.22153I 0
u = 0.445627 − 0.931879I
a = 0.200127 − 0.084474I
b = −0.298515 + 0.395878I
−0.21716 − 2.22153I 0
u = −0.198192 + 1.018210I
a = −0.605963 − 1.018640I
b = 0.512264 + 0.694594I
−3.26753 − 3.83052I 0
u = −0.198192 − 1.018210I
a = −0.605963 + 1.018640I
b = 0.512264 − 0.694594I
−3.26753 + 3.83052I 0
u = −0.627731 + 0.833901I
a = −0.281088 − 0.037619I
b = −0.96977 + 1.12758I
−5.08057 + 5.13162I 0
u = −0.627731 − 0.833901I
a = −0.281088 + 0.037619I
b = −0.96977 − 1.12758I
−5.08057 − 5.13162I 0
u = 0.705026 + 0.644209I
a = −0.425448 − 0.094462I
b = 0.635657 + 0.076444I
−1.48237 + 6.07517I 0
u = 0.705026 − 0.644209I
a = −0.425448 + 0.094462I
b = 0.635657 − 0.076444I
−1.48237 − 6.07517I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.634957 + 0.835508I
a = −0.302189 − 0.088053I
b = 0.575178 + 0.266330I
−2.06078 − 1.03844I 0
u = 0.634957 − 0.835508I
a = −0.302189 + 0.088053I
b = 0.575178 − 0.266330I
−2.06078 + 1.03844I 0
u = −0.808540 + 0.675363I
a = −0.251435 + 0.002877I
b = −1.08572 + 1.01249I
−5.33745 − 2.51054I 0
u = −0.808540 − 0.675363I
a = −0.251435 − 0.002877I
b = −1.08572 − 1.01249I
−5.33745 + 2.51054I 0
u = −1.06632
a = 0.163913
b = 1.12178
−2.99893 0
u = −0.205855 + 1.066340I
a = 2.19332 + 0.21215I
b = 0.710064 − 1.124110I
−1.54671 + 0.30676I 0
u = −0.205855 − 1.066340I
a = 2.19332 − 0.21215I
b = 0.710064 + 1.124110I
−1.54671 − 0.30676I 0
u = −0.877564 + 0.252033I
a = 0.177938 − 0.052301I
b = 0.901469 − 0.560381I
−2.76612 + 0.46150I 0
u = −0.877564 − 0.252033I
a = 0.177938 + 0.052301I
b = 0.901469 + 0.560381I
−2.76612 − 0.46150I 0
u = 0.280688 + 1.057980I
a = 0.186025 + 0.149043I
b = −0.059742 − 0.689656I
−0.86784 + 2.21470I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.280688 − 1.057980I
a = 0.186025 − 0.149043I
b = −0.059742 + 0.689656I
−0.86784 − 2.21470I 0
u = −0.016037 + 1.111550I
a = −0.12718 − 1.49148I
b = 0.684949 + 1.038480I
−2.96866 − 1.50877I 0
u = −0.016037 − 1.111550I
a = −0.12718 + 1.49148I
b = 0.684949 − 1.038480I
−2.96866 + 1.50877I 0
u = 1.123720 + 0.056254I
a = −0.18963 − 2.18372I
b = −0.21888 − 4.11381I
−3.53447 − 2.64383I 0
u = 1.123720 − 0.056254I
a = −0.18963 + 2.18372I
b = −0.21888 + 4.11381I
−3.53447 + 2.64383I 0
u = −0.293441 + 1.107970I
a = −2.16101 + 0.16158I
b = −0.45521 + 1.39470I
−1.30226 − 4.97324I 0
u = −0.293441 − 1.107970I
a = −2.16101 − 0.16158I
b = −0.45521 − 1.39470I
−1.30226 + 4.97324I 0
u = −0.555516 + 0.642632I
a = 0.321795 − 0.007589I
b = 0.947740 − 1.036810I
−2.35481 + 1.07727I −4.10629 + 0.I
u = −0.555516 − 0.642632I
a = 0.321795 + 0.007589I
b = 0.947740 + 1.036810I
−2.35481 − 1.07727I −4.10629 + 0.I
u = 0.068982 + 1.152660I
a = −0.13772 + 1.68779I
b = −0.84014 − 1.26733I
−4.49778 + 3.58279I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.068982 − 1.152660I
a = −0.13772 − 1.68779I
b = −0.84014 + 1.26733I
−4.49778 − 3.58279I 0
u = 0.133289 + 1.147960I
a = −0.207378 − 0.161416I
b = −0.094944 + 0.926840I
−3.87382 − 1.25509I 0
u = 0.133289 − 1.147960I
a = −0.207378 + 0.161416I
b = −0.094944 − 0.926840I
−3.87382 + 1.25509I 0
u = 0.577291 + 0.590200I
a = 0.455697 − 0.020258I
b = −0.542949 − 0.042937I
0.76544 + 1.83227I 2.97063 − 4.30547I
u = 0.577291 − 0.590200I
a = 0.455697 + 0.020258I
b = −0.542949 + 0.042937I
0.76544 − 1.83227I 2.97063 + 4.30547I
u = −0.486058 + 1.084780I
a = 0.530495 + 0.114300I
b = −0.451814 − 0.304162I
−6.71480 − 2.28994I 0
u = −0.486058 − 1.084780I
a = 0.530495 − 0.114300I
b = −0.451814 + 0.304162I
−6.71480 + 2.28994I 0
u = 0.019738 + 1.215440I
a = 1.58587 + 0.35008I
b = 0.264532 − 0.433564I
−4.96141 + 2.10767I 0
u = 0.019738 − 1.215440I
a = 1.58587 − 0.35008I
b = 0.264532 + 0.433564I
−4.96141 − 2.10767I 0
u = −1.212520 + 0.089544I
a = −0.175810 + 0.003726I
b = −1.378360 + 0.143579I
−5.80757 + 3.81804I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.212520 − 0.089544I
a = −0.175810 − 0.003726I
b = −1.378360 − 0.143579I
−5.80757 − 3.81804I 0
u = 0.299648 + 1.178790I
a = −0.201498 − 0.148660I
b = 0.162017 + 0.863030I
−3.49667 + 6.31468I 0
u = 0.299648 − 1.178790I
a = −0.201498 + 0.148660I
b = 0.162017 − 0.863030I
−3.49667 − 6.31468I 0
u = −0.020338 + 0.774375I
a = 0.307442 + 0.318165I
b = 0.688910 − 0.608860I
−1.50574 + 1.45150I −6.88231 − 3.91032I
u = −0.020338 − 0.774375I
a = 0.307442 − 0.318165I
b = 0.688910 + 0.608860I
−1.50574 − 1.45150I −6.88231 + 3.91032I
u = 0.070255 + 1.259590I
a = −1.50047 − 0.35184I
b = −0.147458 + 0.318912I
−7.80115 + 7.15839I 0
u = 0.070255 − 1.259590I
a = −1.50047 + 0.35184I
b = −0.147458 − 0.318912I
−7.80115 − 7.15839I 0
u = −0.053874 + 1.280380I
a = −1.58471 − 0.21128I
b = −0.108135 + 0.620275I
−9.46339 − 1.53906I 0
u = −0.053874 − 1.280380I
a = −1.58471 + 0.21128I
b = −0.108135 − 0.620275I
−9.46339 + 1.53906I 0
u = −0.697952 + 0.137916I
a = 0.03495 + 2.03419I
b = 0.003394 + 1.178190I
−3.25405 + 8.33976I 0.04715 − 7.24075I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.697952 − 0.137916I
a = 0.03495 − 2.03419I
b = 0.003394 − 1.178190I
−3.25405 − 8.33976I 0.04715 + 7.24075I
u = 1.278710 + 0.215842I
a = −0.39628 − 1.68073I
b = −0.31459 − 3.54098I
−6.66508 − 4.90614I 0
u = 1.278710 − 0.215842I
a = −0.39628 + 1.68073I
b = −0.31459 + 3.54098I
−6.66508 + 4.90614I 0
u = −0.395632 + 1.237840I
a = −1.74409 + 0.40492I
b = 0.00591 + 1.44676I
−4.09455 − 7.49095I 0
u = −0.395632 − 1.237840I
a = −1.74409 − 0.40492I
b = 0.00591 − 1.44676I
−4.09455 + 7.49095I 0
u = −0.166036 + 1.294570I
a = −0.159030 + 0.898530I
b = −0.095823 − 1.086560I
−8.00836 − 2.78848I 0
u = −0.166036 − 1.294570I
a = −0.159030 − 0.898530I
b = −0.095823 + 1.086560I
−8.00836 + 2.78848I 0
u = −0.533755 + 1.206200I
a = −0.347377 + 0.158220I
b = 0.477048 − 0.032193I
−5.70848 − 5.64417I 0
u = −0.533755 − 1.206200I
a = −0.347377 − 0.158220I
b = 0.477048 + 0.032193I
−5.70848 + 5.64417I 0
u = −0.336147 + 1.282090I
a = 1.68636 − 0.25958I
b = −0.030211 − 1.283740I
−8.88944 − 4.03584I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.336147 − 1.282090I
a = 1.68636 + 0.25958I
b = −0.030211 + 1.283740I
−8.88944 + 4.03584I 0
u = −0.428396 + 1.265900I
a = 1.66072 − 0.44565I
b = −0.09249 − 1.47226I
−6.7884 − 12.7058I 0
u = −0.428396 − 1.265900I
a = 1.66072 + 0.44565I
b = −0.09249 + 1.47226I
−6.7884 + 12.7058I 0
u = −0.644479 + 0.156070I
a = 0.01947 − 2.09237I
b = −0.064347 − 1.144410I
−0.72998 + 3.43108I 3.23111 − 3.53029I
u = −0.644479 − 0.156070I
a = 0.01947 + 2.09237I
b = −0.064347 + 1.144410I
−0.72998 − 3.43108I 3.23111 + 3.53029I
u = 1.314130 + 0.258446I
a = 0.42118 + 1.59065I
b = 0.29191 + 3.44936I
−9.44734 − 10.06730I 0
u = 1.314130 − 0.258446I
a = 0.42118 − 1.59065I
b = 0.29191 − 3.44936I
−9.44734 + 10.06730I 0
u = 1.334250 + 0.147531I
a = 0.24745 + 1.64891I
b = 0.17768 + 3.57162I
−11.34640 − 1.32441I 0
u = 1.334250 − 0.147531I
a = 0.24745 − 1.64891I
b = 0.17768 − 3.57162I
−11.34640 + 1.32441I 0
u = −0.622293 + 0.071084I
a = 0.05136 + 2.18813I
b = 0.009203 + 1.059750I
−5.03370 + 0.34144I −2.24738 − 0.66837I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.622293 − 0.071084I
a = 0.05136 − 2.18813I
b = 0.009203 − 1.059750I
−5.03370 − 0.34144I −2.24738 + 0.66837I
u = 0.457823 + 0.346017I
a = 0.781432 − 0.194359I
b = −0.485789 + 0.019245I
1.18816 + 0.97679I 5.99668 − 2.87740I
u = 0.457823 − 0.346017I
a = 0.781432 + 0.194359I
b = −0.485789 − 0.019245I
1.18816 − 0.97679I 5.99668 + 2.87740I
u = −0.317562 + 0.458650I
a = −0.08848 + 2.24799I
b = 0.812978 + 0.897740I
0.26703 − 2.76145I 2.39627 + 0.24825I
u = −0.317562 − 0.458650I
a = −0.08848 − 2.24799I
b = 0.812978 − 0.897740I
0.26703 + 2.76145I 2.39627 − 0.24825I
u = −0.451679 + 0.297070I
a = 0.18981 − 2.20906I
b = −0.382918 − 1.024900I
1.09706 + 1.79646I 4.50707 − 4.72051I
u = −0.451679 − 0.297070I
a = 0.18981 + 2.20906I
b = −0.382918 + 1.024900I
1.09706 − 1.79646I 4.50707 + 4.72051I
u = 0.075882 + 0.532508I
a = 1.165090 + 0.438248I
b = 1.61513 − 0.31149I
−1.30443 + 1.41880I −9.48971 − 7.96647I
u = 0.075882 − 0.532508I
a = 1.165090 − 0.438248I
b = 1.61513 + 0.31149I
−1.30443 − 1.41880I −9.48971 + 7.96647I
u = −0.53134 + 1.37400I
a = −0.342719 + 0.387464I
b = 0.675891 − 0.459262I
−7.27145 − 5.73841I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.53134 − 1.37400I
a = −0.342719 − 0.387464I
b = 0.675891 + 0.459262I
−7.27145 + 5.73841I 0
u = 0.50261 + 1.39495I
a = −2.21661 + 0.24791I
b = 0.46456 − 3.43991I
−8.15890 + 3.07952I 0
u = 0.50261 − 1.39495I
a = −2.21661 − 0.24791I
b = 0.46456 + 3.43991I
−8.15890 − 3.07952I 0
u = 0.487122 + 0.146522I
a = −1.089400 + 0.057239I
b = 0.417296 − 0.034703I
−0.44889 − 3.10218I 2.70006 + 3.61407I
u = 0.487122 − 0.146522I
a = −1.089400 − 0.057239I
b = 0.417296 + 0.034703I
−0.44889 + 3.10218I 2.70006 − 3.61407I
u = 0.55448 + 1.38660I
a = 2.18485 + 0.09212I
b = −0.71711 + 3.38390I
−7.75540 + 8.66586I 0
u = 0.55448 − 1.38660I
a = 2.18485 − 0.09212I
b = −0.71711 − 3.38390I
−7.75540 − 8.66586I 0
u = −0.47683 + 1.45135I
a = 0.353718 − 0.458048I
b = −0.702962 + 0.689832I
−10.89430 − 2.15329I 0
u = −0.47683 − 1.45135I
a = 0.353718 + 0.458048I
b = −0.702962 − 0.689832I
−10.89430 + 2.15329I 0
u = −0.58357 + 1.41607I
a = 0.387162 − 0.398248I
b = −0.835172 + 0.462307I
−10.0756 − 10.2328I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.58357 − 1.41607I
a = 0.387162 + 0.398248I
b = −0.835172 − 0.462307I
−10.0756 + 10.2328I 0
u = 0.66226 + 1.40562I
a = 1.78137 + 0.44979I
b = −0.87217 + 3.06337I
−10.4930 + 11.8093I 0
u = 0.66226 − 1.40562I
a = 1.78137 − 0.44979I
b = −0.87217 − 3.06337I
−10.4930 − 11.8093I 0
u = 0.69338 + 1.40653I
a = −1.68629 − 0.51434I
b = 0.88007 − 2.99623I
−13.1444 + 17.1838I 0
u = 0.69338 − 1.40653I
a = −1.68629 + 0.51434I
b = 0.88007 + 2.99623I
−13.1444 − 17.1838I 0
u = 0.334255 + 0.268885I
a = −2.00226 − 0.37579I
b = −2.98510 − 0.26969I
−1.88065 − 2.35835I 10.0083 − 15.2059I
u = 0.334255 − 0.268885I
a = −2.00226 + 0.37579I
b = −2.98510 + 0.26969I
−1.88065 + 2.35835I 10.0083 + 15.2059I
u = 0.37185 + 1.53450I
a = −1.43684 + 0.60839I
b = 0.24963 − 2.78944I
−12.72110 + 1.04025I 0
u = 0.37185 − 1.53450I
a = −1.43684 − 0.60839I
b = 0.24963 + 2.78944I
−12.72110 − 1.04025I 0
u = 0.64364 + 1.45743I
a = −1.69453 − 0.26926I
b = 0.76095 − 3.05481I
−15.5796 + 8.3556I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.64364 − 1.45743I
a = −1.69453 + 0.26926I
b = 0.76095 + 3.05481I
−15.5796 − 8.3556I 0
u = 0.33215 + 1.58221I
a = 1.271400 − 0.600285I
b = −0.31232 + 2.64286I
−15.9138 − 4.0187I 0
u = 0.33215 − 1.58221I
a = 1.271400 + 0.600285I
b = −0.31232 − 2.64286I
−15.9138 + 4.0187I 0
u = 0.44101 + 1.56678I
a = 1.45585 − 0.39191I
b = −0.41727 + 2.86735I
−17.1532 + 5.1373I 0
u = 0.44101 − 1.56678I
a = 1.45585 + 0.39191I
b = −0.41727 − 2.86735I
−17.1532 − 5.1373I 0
15
II. I
u
2
= h−u
2
a + b − a, u
4
a + u
3
a + u
4
+ 2u
2
a + a
2
+ au + u
2
+ a − u, u
5
+
u
4
+ 2u
3
+ u
2
+ u + 1i
(i) Arc colorings
a
7
=
0
u
a
12
=
1
0
a
11
=
1
u
2
a
4
=
a
u
2
a + a
a
8
=
u
u
3
+ u
a
5
=
a
u
2
a + a
a
9
=
u
u
3
+ u
a
10
=
−u
3
u
3
+ u
a
1
=
−u
3
u
4
+ u
3
+ u
2
+ 1
a
6
=
u
3
−u
4
− u
3
− u
2
− 1
a
3
=
−u
4
a + a
−u
3
a
a
2
=
−u
4
a + u
4
+ u
3
+ 2u
2
+ a + u + 1
−u
3
a + u
4
+ u
3
+ 2u
2
+ 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −u
4
a − 3u
3
a + u
4
− u
2
a − 3u
3
+ 2au − u
2
− 3u − 4
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
(u
2
− u + 1)
5
c
2
(u
2
+ u + 1)
5
c
4
, c
8
u
10
c
6
(u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)
2
c
7
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
2
c
9
, c
10
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
c
11
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
2
c
12
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
(y
2
+ y + 1)
5
c
4
, c
8
y
10
c
6
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
2
c
7
, c
11
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
c
9
, c
10
, c
12
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.339110 + 0.822375I
a = 1.114310 − 0.148503I
b = 0.571671 + 0.556363I
−0.32910 + 3.56046I −2.43337 − 7.40396I
u = 0.339110 + 0.822375I
a = −0.685764 − 0.890773I
b = 0.195989 − 0.773263I
−0.329100 − 0.499304I 1.41726 − 0.48644I
u = 0.339110 − 0.822375I
a = 1.114310 + 0.148503I
b = 0.571671 − 0.556363I
−0.32910 − 3.56046I −2.43337 + 7.40396I
u = 0.339110 − 0.822375I
a = −0.685764 + 0.890773I
b = 0.195989 + 0.773263I
−0.329100 + 0.499304I 1.41726 + 0.48644I
u = −0.766826
a = −0.652039 + 1.129360I
b = −1.03545 + 1.79345I
−2.40108 + 2.02988I 0.137791 − 1.258916I
u = −0.766826
a = −0.652039 − 1.129360I
b = −1.03545 − 1.79345I
−2.40108 − 2.02988I 0.137791 + 1.258916I
u = −0.455697 + 1.200150I
a = 0.492416 − 0.603584I
b = −0.774795 − 0.398153I
−5.87256 − 6.43072I −7.21285 + 8.37016I
u = −0.455697 + 1.200150I
a = −0.768927 − 0.124653I
b = 0.042587 + 0.870069I
−5.87256 − 2.37095I −1.90884 + 0.95814I
u = −0.455697 − 1.200150I
a = 0.492416 + 0.603584I
b = −0.774795 + 0.398153I
−5.87256 + 6.43072I −7.21285 − 8.37016I
u = −0.455697 − 1.200150I
a = −0.768927 + 0.124653I
b = 0.042587 − 0.870069I
−5.87256 + 2.37095I −1.90884 − 0.95814I
19
III. I
v
1
= ha, v
3
+ 2v
2
+ b + 2v , v
4
+ 2v
3
+ 3v
2
+ v + 1i
(i) Arc colorings
a
7
=
v
0
a
12
=
1
0
a
11
=
1
0
a
4
=
0
−v
3
− 2v
2
− 2v
a
8
=
v
0
a
5
=
v
3
+ v
2
+ v
−v
3
− 2v
2
− 2v
a
9
=
v
−1
a
10
=
v + 1
−1
a
1
=
−v
1
a
6
=
v
2
+ v
−v
a
3
=
−v
3
− v
2
− v − 1
−v
3
− v
2
− 2v + 1
a
2
=
−v
3
− 2v
2
− v − 1
−v
3
− v
2
− 2v
(ii) Obstruction class = 1
(iii) Cusp Shapes = −5v
3
− 6v
2
− 9v
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
4
− 2u
3
+ 3u
2
− u + 1
c
2
, c
4
u
4
+ u
2
+ u + 1
c
3
u
4
+ 3u
3
+ 4u
2
+ 3u + 2
c
5
, c
8
u
4
+ u
2
− u + 1
c
7
, c
11
u
4
c
9
, c
10
(u − 1)
4
c
12
(u + 1)
4
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
4
+ 2y
3
+ 7y
2
+ 5y + 1
c
2
, c
4
, c
5
c
8
y
4
+ 2y
3
+ 3y
2
+ y + 1
c
3
y
4
− y
3
+ 2y
2
+ 7y + 4
c
7
, c
11
y
4
c
9
, c
10
, c
12
(y − 1)
4
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.043315 + 0.641200I
a = 0
b = 0.851808 − 0.911292I
−0.66484 + 1.39709I 2.57868 − 4.13745I
v = −0.043315 − 0.641200I
a = 0
b = 0.851808 + 0.911292I
−0.66484 − 1.39709I 2.57868 + 4.13745I
v = −0.95668 + 1.22719I
a = 0
b = −0.351808 + 0.720342I
−4.26996 + 7.64338I −5.07868 − 4.56334I
v = −0.95668 − 1.22719I
a = 0
b = −0.351808 − 0.720342I
−4.26996 − 7.64338I −5.07868 + 4.56334I
23
IV. I
v
2
= ha, −v
3
− v
2
+ b + 1, v
6
+ 3v
5
+ 4v
4
+ 2v
3
+ 1i
(i) Arc colorings
a
7
=
v
0
a
12
=
1
0
a
11
=
1
0
a
4
=
0
v
3
+ v
2
− 1
a
8
=
v
0
a
5
=
v
5
+ v
4
− v
2
v
3
+ v
2
− 1
a
9
=
v
−1
a
10
=
v + 1
−1
a
1
=
−v
1
a
6
=
v
2
+ v
−v
a
3
=
−v
5
− 2v
4
− 2v
3
− v
2
− v
v
5
+ 3v
4
+ 4v
3
+ 2v
2
a
2
=
−v
3
− v
2
− v + 1
v
5
+ 2v
4
+ 2v
3
− v
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4v
5
− 7v
4
− v
3
+ 7v
2
+ 6v − 6
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1
c
2
, c
4
u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1
c
3
(u
3
− u
2
+ 1)
2
c
5
, c
8
u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1
c
7
, c
11
u
6
c
9
, c
10
(u − 1)
6
c
12
(u + 1)
6
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1
c
2
, c
4
, c
5
c
8
y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1
c
3
(y
3
− y
2
+ 2y − 1)
2
c
7
, c
11
y
6
c
9
, c
10
, c
12
(y − 1)
6
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = −0.753774 + 0.998963I
a = 0
b = 0.398606 − 0.800120I
−1.91067 + 2.82812I −1.88527 − 2.08748I
v = −0.753774 − 0.998963I
a = 0
b = 0.398606 + 0.800120I
−1.91067 − 2.82812I −1.88527 + 2.08748I
v = −1.162360 + 0.635452I
a = 0
b = −0.215080 + 0.841795I
−6.04826 −10.27439 + 0.99756I
v = −1.162360 − 0.635452I
a = 0
b = −0.215080 − 0.841795I
−6.04826 −10.27439 − 0.99756I
v = 0.416133 + 0.436684I
a = 0
b = −1.183530 + 0.507021I
−1.91067 − 2.82812I −2.34034 + 5.36114I
v = 0.416133 − 0.436684I
a = 0
b = −1.183530 − 0.507021I
−1.91067 + 2.82812I −2.34034 − 5.36114I
27
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)
5
(u
4
− 2u
3
+ 3u
2
− u + 1)(u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1)
· (u
105
+ 53u
104
+ ··· − 7u − 1)
c
2
(u
2
+ u + 1)
5
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
105
+ 7u
104
+ ··· − 7u − 1)
c
3
(u
2
− u + 1)
5
(u
3
− u
2
+ 1)
2
(u
4
+ 3u
3
+ 4u
2
+ 3u + 2)
· (u
105
− 7u
104
+ ··· − 40152u − 14308)
c
4
u
10
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
105
− 2u
104
+ ··· − 2048u − 1024)
c
5
(u
2
− u + 1)
5
(u
4
+ u
2
− u + 1)(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
· (u
105
+ 7u
104
+ ··· − 7u − 1)
c
6
(u
4
− 2u
3
+ 3u
2
− u + 1)(u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)
2
· (u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1)(u
105
− 4u
104
+ ··· − 66488u − 52489)
c
7
u
10
(u
5
− u
4
+ ··· + u − 1)
2
(u
105
− 3u
104
+ ··· + 2048u + 1024)
c
8
u
10
(u
4
+ u
2
− u + 1)(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
· (u
105
− 2u
104
+ ··· − 2048u − 1024)
c
9
, c
10
((u − 1)
10
)(u
5
+ u
4
+ ··· + u − 1)
2
(u
105
− 13u
104
+ ··· − 7u + 1)
c
11
u
10
(u
5
+ u
4
+ ··· + u + 1)
2
(u
105
− 3u
104
+ ··· + 2048u + 1024)
c
12
((u + 1)
10
)(u
5
− u
4
+ ··· + u + 1)
2
(u
105
− 13u
104
+ ··· − 7u + 1)
28
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
5
)(y
4
+ 2y
3
+ ··· + 5y + 1)(y
6
− y
5
+ ··· + 8y
2
+ 1)
· (y
105
+ 5y
104
+ ··· + 33y − 1)
c
2
, c
5
(y
2
+ y + 1)
5
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
105
+ 53y
104
+ ··· − 7y − 1)
c
3
(y
2
+ y + 1)
5
(y
3
− y
2
+ 2y − 1)
2
(y
4
− y
3
+ 2y
2
+ 7y + 4)
· (y
105
− 43y
104
+ ··· + 5145658168y − 204718864)
c
4
, c
8
y
10
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
105
+ 60y
104
+ ··· − 16777216y − 1048576)
c
6
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1)
2
· (y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
· (y
105
− 62y
104
+ ··· − 163409354104y − 2755095121)
c
7
, c
11
y
10
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y − 1)
2
· (y
105
+ 69y
104
+ ··· − 9961472y − 1048576)
c
9
, c
10
, c
12
(y − 1)
10
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
2
· (y
105
− 105y
104
+ ··· − 33y − 1)
29
