12a
0368
(K12a
0368
)
A knot diagram
1
Linearized knot diagam
3 6 9 10 2 11 12 5 4 1 8 7
Solving Sequence
8,11
12 7 1
2,6
3 5 9 10 4
c
11
c
7
c
12
c
6
c
2
c
5
c
8
c
10
c
4
c
1
, c
3
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h3.30973 × 10
28
u
91
− 8.40338 × 10
28
u
90
+ ··· + 5.98098 × 10
28
b + 1.59798 × 10
28
,
− 2.69784 × 10
28
u
91
+ 1.86728 × 10
28
u
90
+ ··· + 5.98098 × 10
28
a − 7.90169 × 10
28
, u
92
− 2u
91
+ ··· + 4u − 1i
I
u
2
= h−au − u
2
+ b + u − 1, −2u
2
a + a
2
− 3u
2
− 2a + u − 4, u
3
− u
2
+ 2u − 1i
I
u
3
= h−2u
2
+ b − 2u − 2, −u
2
+ a − 1, u
3
+ u
2
+ 2u + 1i
* 3 irreducible components of dim
C
= 0, with total 101 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
= h3.31×10
28
u
91
−8.40×10
28
u
90
+· · ·+5.98×10
28
b+1.60×10
28
, −2.70×
10
28
u
91
+1.87×10
28
u
90
+· · ·+5.98×10
28
a−7.90×10
28
, u
92
−2u
91
+· · ·+4u−1i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
7
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
4
+ 2u
2
a
2
=
0.451070u
91
− 0.312203u
90
+ ··· − 7.08977u + 1.32114
−0.553376u
91
+ 1.40502u
90
+ ··· + 1.50461u − 0.267177
a
6
=
u
3
+ 2u
u
3
+ u
a
3
=
0.735415u
91
− 0.771047u
90
+ ··· − 8.70172u + 2.30497
−0.222428u
91
+ 0.315787u
90
+ ··· − 0.399025u + 0.493332
a
5
=
0.362177u
91
− 0.986787u
90
+ ··· + 4.35986u + 1.44942
0.858220u
91
− 2.63949u
90
+ ··· − 1.81332u + 0.982411
a
9
=
−0.918301u
91
+ 2.21912u
90
+ ··· − 3.90930u − 1.54472
−0.0236999u
91
+ 0.263544u
90
+ ··· + 0.339475u − 0.202110
a
10
=
−u
6
− 3u
4
− 2u
2
+ 1
−u
8
− 4u
6
− 4u
4
a
4
=
1.29625u
91
− 2.48311u
90
+ ··· + 0.388481u + 2.80304
0.918260u
91
− 2.71085u
90
+ ··· − 2.13551u + 1.23180
(ii) Obstruction class = −1
(iii) Cusp Shapes = −1.75950u
91
+ 3.08333u
90
+ ··· − 2.35105u − 16.2139
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
92
+ 46u
91
+ ··· + 1255u + 49
c
2
, c
5
u
92
+ 4u
91
+ ··· − 67u − 7
c
3
, c
4
, c
9
u
92
− u
91
+ ··· − 24u − 8
c
6
u
92
− 2u
91
+ ··· − 312u − 29
c
7
, c
11
, c
12
u
92
+ 2u
91
+ ··· − 4u − 1
c
8
u
92
+ 3u
91
+ ··· + 49864u + 10856
c
10
u
92
− 20u
91
+ ··· − 103152u + 12161
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
92
+ 10y
91
+ ··· − 468507y + 2401
c
2
, c
5
y
92
− 46y
91
+ ··· − 1255y + 49
c
3
, c
4
, c
9
y
92
− 85y
91
+ ··· + 448y + 64
c
6
y
92
+ 4y
91
+ ··· + 28748y + 841
c
7
, c
11
, c
12
y
92
+ 84y
91
+ ··· − 16y + 1
c
8
y
92
− y
91
+ ··· − 514447808y + 117852736
c
10
y
92
+ 28y
91
+ ··· − 3573140208y + 147889921
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.034848 + 1.070820I
a = 1.16142 + 1.64957I
b = 0.39105 − 1.62169I
−6.16629 + 0.50321I 0
u = −0.034848 − 1.070820I
a = 1.16142 − 1.64957I
b = 0.39105 + 1.62169I
−6.16629 − 0.50321I 0
u = −0.298329 + 1.065540I
a = −0.58990 − 1.97199I
b = −0.991589 + 0.695120I
−4.70505 + 8.08259I 0
u = −0.298329 − 1.065540I
a = −0.58990 + 1.97199I
b = −0.991589 − 0.695120I
−4.70505 − 8.08259I 0
u = 0.243152 + 1.123750I
a = −0.42463 + 1.52933I
b = −0.933638 − 1.026660I
0.59647 − 4.93114I 0
u = 0.243152 − 1.123750I
a = −0.42463 − 1.52933I
b = −0.933638 + 1.026660I
0.59647 + 4.93114I 0
u = −0.099228 + 1.149160I
a = 0.342890 − 1.154020I
b = −0.53285 + 1.56071I
−0.12027 + 1.68117I 0
u = −0.099228 − 1.149160I
a = 0.342890 + 1.154020I
b = −0.53285 − 1.56071I
−0.12027 − 1.68117I 0
u = −0.223947 + 1.146940I
a = −0.050862 − 0.628559I
b = −1.036560 − 0.050910I
−2.37447 + 3.62080I 0
u = −0.223947 − 1.146940I
a = −0.050862 + 0.628559I
b = −1.036560 + 0.050910I
−2.37447 − 3.62080I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.417399 + 0.711711I
a = 0.44156 − 2.75513I
b = 0.980567 − 0.367031I
−3.83510 + 8.20507I −14.2773 − 4.2378I
u = 0.417399 − 0.711711I
a = 0.44156 + 2.75513I
b = 0.980567 + 0.367031I
−3.83510 − 8.20507I −14.2773 + 4.2378I
u = 0.743091 + 0.297468I
a = −3.30203 − 0.28673I
b = −2.63885 − 0.35083I
−5.29278 − 12.34380I −16.7373 + 9.0455I
u = 0.743091 − 0.297468I
a = −3.30203 + 0.28673I
b = −2.63885 + 0.35083I
−5.29278 + 12.34380I −16.7373 − 9.0455I
u = −0.715067 + 0.312276I
a = −2.80954 + 0.09188I
b = −2.33320 + 0.20273I
0.27317 + 8.47973I −12.3886 − 8.8422I
u = −0.715067 − 0.312276I
a = −2.80954 − 0.09188I
b = −2.33320 − 0.20273I
0.27317 − 8.47973I −12.3886 + 8.8422I
u = 0.705158 + 0.313085I
a = 0.007471 + 0.229207I
b = 0.116507 + 0.613947I
−2.69498 − 6.91327I −13.7303 + 5.8428I
u = 0.705158 − 0.313085I
a = 0.007471 − 0.229207I
b = 0.116507 − 0.613947I
−2.69498 + 6.91327I −13.7303 − 5.8428I
u = −0.755570 + 0.124061I
a = 2.75287 − 0.27400I
b = 2.13575 + 0.12130I
−7.57244 − 4.17982I −18.8339 + 3.7354I
u = −0.755570 − 0.124061I
a = 2.75287 + 0.27400I
b = 2.13575 − 0.12130I
−7.57244 + 4.17982I −18.8339 − 3.7354I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.419534 + 0.632335I
a = 0.42637 + 2.43079I
b = 0.767115 + 0.278010I
1.49754 − 4.49101I −9.57609 + 3.60714I
u = −0.419534 − 0.632335I
a = 0.42637 − 2.43079I
b = 0.767115 − 0.278010I
1.49754 + 4.49101I −9.57609 − 3.60714I
u = 0.079329 + 1.239520I
a = −0.338826 + 0.178720I
b = −0.665582 − 0.126932I
2.98419 − 1.52090I 0
u = 0.079329 − 1.239520I
a = −0.338826 − 0.178720I
b = −0.665582 + 0.126932I
2.98419 + 1.52090I 0
u = 0.416289 + 0.609604I
a = 0.554452 − 0.075964I
b = −0.353566 + 0.101596I
−1.52499 + 2.98968I −11.23647 − 0.16527I
u = 0.416289 − 0.609604I
a = 0.554452 + 0.075964I
b = −0.353566 − 0.101596I
−1.52499 − 2.98968I −11.23647 + 0.16527I
u = −0.653161 + 0.337464I
a = 0.097611 + 0.186413I
b = 0.163634 − 0.406687I
2.31309 + 3.22705I −8.73500 − 4.74749I
u = −0.653161 − 0.337464I
a = 0.097611 − 0.186413I
b = 0.163634 + 0.406687I
2.31309 − 3.22705I −8.73500 + 4.74749I
u = 0.661017 + 0.308769I
a = −2.20722 + 0.54547I
b = −1.99099 + 0.22787I
−1.12232 − 4.16995I −14.2649 + 4.5495I
u = 0.661017 − 0.308769I
a = −2.20722 − 0.54547I
b = −1.99099 − 0.22787I
−1.12232 + 4.16995I −14.2649 − 4.5495I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.706111 + 0.084338I
a = 2.23611 + 0.20245I
b = 1.82332 − 0.12395I
−2.53333 + 1.38999I −14.0303 − 4.7787I
u = 0.706111 − 0.084338I
a = 2.23611 − 0.20245I
b = 1.82332 + 0.12395I
−2.53333 − 1.38999I −14.0303 + 4.7787I
u = 0.571431 + 0.417944I
a = −0.571220 + 0.056591I
b = −0.966951 + 0.051439I
0.02478 − 4.16521I −11.76282 + 7.26961I
u = 0.571431 − 0.417944I
a = −0.571220 − 0.056591I
b = −0.966951 − 0.051439I
0.02478 + 4.16521I −11.76282 − 7.26961I
u = 0.657513 + 0.255277I
a = 2.32367 + 1.60701I
b = 1.85504 + 0.58325I
−7.86767 − 3.37346I −18.8189 + 5.1242I
u = 0.657513 − 0.255277I
a = 2.32367 − 1.60701I
b = 1.85504 − 0.58325I
−7.86767 + 3.37346I −18.8189 − 5.1242I
u = −0.273151 + 1.269520I
a = −0.784454 − 0.758498I
b = −1.13550 + 1.11583I
−1.58778 + 3.32160I 0
u = −0.273151 − 1.269520I
a = −0.784454 + 0.758498I
b = −1.13550 − 1.11583I
−1.58778 − 3.32160I 0
u = −0.696747 + 0.052921I
a = 1.55611 − 0.39504I
b = 1.157240 − 0.471909I
−5.66596 − 0.20100I −16.5902 − 1.1108I
u = −0.696747 − 0.052921I
a = 1.55611 + 0.39504I
b = 1.157240 + 0.471909I
−5.66596 + 0.20100I −16.5902 + 1.1108I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.474451 + 0.495892I
a = 0.186792 + 0.006945I
b = −0.533837 − 0.088452I
3.02224 + 0.50785I −6.50995 − 2.67224I
u = −0.474451 − 0.495892I
a = 0.186792 − 0.006945I
b = −0.533837 + 0.088452I
3.02224 − 0.50785I −6.50995 + 2.67224I
u = −0.641532 + 0.227372I
a = −2.77674 − 2.05080I
b = −2.40013 − 1.11814I
−8.25229 + 2.34538I −18.8507 − 6.3358I
u = −0.641532 − 0.227372I
a = −2.77674 + 2.05080I
b = −2.40013 + 1.11814I
−8.25229 − 2.34538I −18.8507 + 6.3358I
u = 0.546620 + 0.394137I
a = 0.376941 − 0.947222I
b = 0.321957 + 0.123725I
0.037398 + 0.490858I −11.59345 − 0.06446I
u = 0.546620 − 0.394137I
a = 0.376941 + 0.947222I
b = 0.321957 − 0.123725I
0.037398 − 0.490858I −11.59345 + 0.06446I
u = 0.269413 + 1.300480I
a = −0.781329 + 0.840657I
b = −2.02613 − 0.86488I
1.77296 − 2.13369I 0
u = 0.269413 − 1.300480I
a = −0.781329 − 0.840657I
b = −2.02613 + 0.86488I
1.77296 + 2.13369I 0
u = −0.310339 + 1.325110I
a = −1.01943 − 1.08388I
b = −2.60482 + 0.61631I
−3.03208 − 0.33318I 0
u = −0.310339 − 1.325110I
a = −1.01943 + 1.08388I
b = −2.60482 − 0.61631I
−3.03208 + 0.33318I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.415028 + 0.472095I
a = 0.75019 − 1.77462I
b = 0.575771 − 0.027505I
−0.218277 + 0.609351I −11.98707 + 1.52989I
u = 0.415028 − 0.472095I
a = 0.75019 + 1.77462I
b = 0.575771 + 0.027505I
−0.218277 − 0.609351I −11.98707 − 1.52989I
u = −0.179121 + 1.366470I
a = −0.12914 − 1.42459I
b = −1.56586 − 0.31542I
−1.99612 + 2.07721I 0
u = −0.179121 − 1.366470I
a = −0.12914 + 1.42459I
b = −1.56586 + 0.31542I
−1.99612 − 2.07721I 0
u = −0.579053 + 0.183948I
a = 1.62434 − 1.20227I
b = 1.59468 − 0.33025I
−2.81344 + 0.87191I −13.8407 − 7.5603I
u = −0.579053 − 0.183948I
a = 1.62434 + 1.20227I
b = 1.59468 + 0.33025I
−2.81344 − 0.87191I −13.8407 + 7.5603I
u = 0.154946 + 1.389070I
a = −0.705627 − 0.180625I
b = −1.89247 − 2.47520I
−1.10166 − 1.43797I 0
u = 0.154946 − 1.389070I
a = −0.705627 + 0.180625I
b = −1.89247 + 2.47520I
−1.10166 + 1.43797I 0
u = −0.224481 + 1.380800I
a = −1.105640 − 0.260499I
b = −2.45703 + 1.93955I
2.20340 + 3.80841I 0
u = −0.224481 − 1.380800I
a = −1.105640 + 0.260499I
b = −2.45703 − 1.93955I
2.20340 − 3.80841I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.250427 + 1.390150I
a = −0.05424 + 1.79635I
b = 3.21719 + 0.62495I
−3.09254 + 5.59897I 0
u = −0.250427 − 1.390150I
a = −0.05424 − 1.79635I
b = 3.21719 − 0.62495I
−3.09254 − 5.59897I 0
u = 0.25774 + 1.40096I
a = −1.43971 + 0.38823I
b = −2.95919 − 1.83047I
−2.58142 − 6.71431I 0
u = 0.25774 − 1.40096I
a = −1.43971 − 0.38823I
b = −2.95919 + 1.83047I
−2.58142 + 6.71431I 0
u = 0.21684 + 1.42847I
a = 0.161711 + 0.522717I
b = 0.0833315 + 0.0472455I
5.80760 − 2.34021I 0
u = 0.21684 − 1.42847I
a = 0.161711 − 0.522717I
b = 0.0833315 − 0.0472455I
5.80760 + 2.34021I 0
u = 0.16115 + 1.43675I
a = 0.477907 + 0.872217I
b = −0.029713 + 1.077500I
5.81438 − 1.56102I 0
u = 0.16115 − 1.43675I
a = 0.477907 − 0.872217I
b = −0.029713 − 1.077500I
5.81438 + 1.56102I 0
u = 0.25769 + 1.42277I
a = 0.556379 − 1.170280I
b = 2.91233 + 0.46867I
4.41930 − 7.53188I 0
u = 0.25769 − 1.42277I
a = 0.556379 + 1.170280I
b = 2.91233 − 0.46867I
4.41930 + 7.53188I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.25175 + 1.43126I
a = 0.017549 − 0.211376I
b = 0.277668 + 0.504813I
7.97667 + 6.53923I 0
u = −0.25175 − 1.43126I
a = 0.017549 + 0.211376I
b = 0.277668 − 0.504813I
7.97667 − 6.53923I 0
u = 0.12926 + 1.44782I
a = −0.431462 + 0.092527I
b = 0.103286 + 0.465531I
4.93332 + 1.15748I 0
u = 0.12926 − 1.44782I
a = −0.431462 − 0.092527I
b = 0.103286 − 0.465531I
4.93332 − 1.15748I 0
u = 0.27416 + 1.42782I
a = −0.1300120 + 0.0395838I
b = 0.282499 − 0.854739I
2.87569 − 10.48030I 0
u = 0.27416 − 1.42782I
a = −0.1300120 − 0.0395838I
b = 0.282499 + 0.854739I
2.87569 + 10.48030I 0
u = 0.29266 + 1.42539I
a = 1.30505 − 1.39528I
b = 3.68027 + 1.01759I
0.2126 − 16.1064I 0
u = 0.29266 − 1.42539I
a = 1.30505 + 1.39528I
b = 3.68027 − 1.01759I
0.2126 + 16.1064I 0
u = −0.27848 + 1.42877I
a = 1.02929 + 1.23066I
b = 3.33111 − 0.89318I
5.84424 + 12.09630I 0
u = −0.27848 − 1.42877I
a = 1.02929 − 1.23066I
b = 3.33111 + 0.89318I
5.84424 − 12.09630I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.16680 + 1.44652I
a = −0.265726 + 0.042595I
b = 0.640917 − 0.522234I
9.19614 + 2.82647I 0
u = −0.16680 − 1.44652I
a = −0.265726 − 0.042595I
b = 0.640917 + 0.522234I
9.19614 − 2.82647I 0
u = −0.12335 + 1.45196I
a = 0.629226 − 0.989265I
b = 0.08446 − 1.75725I
8.05052 − 2.70837I 0
u = −0.12335 − 1.45196I
a = 0.629226 + 0.989265I
b = 0.08446 + 1.75725I
8.05052 + 2.70837I 0
u = 0.20317 + 1.44404I
a = −0.007857 − 0.306303I
b = 1.36450 + 0.57622I
5.99792 − 6.97659I 0
u = 0.20317 − 1.44404I
a = −0.007857 + 0.306303I
b = 1.36450 − 0.57622I
5.99792 + 6.97659I 0
u = 0.09348 + 1.45829I
a = 0.634030 + 1.073110I
b = 0.04616 + 2.20336I
3.02046 + 6.72210I 0
u = 0.09348 − 1.45829I
a = 0.634030 − 1.073110I
b = 0.04616 − 2.20336I
3.02046 − 6.72210I 0
u = 0.177561 + 0.406838I
a = 0.57829 + 3.07822I
b = 0.784807 + 0.211756I
−6.49085 + 0.26451I −15.4855 + 1.1209I
u = 0.177561 − 0.406838I
a = 0.57829 − 3.07822I
b = 0.784807 − 0.211756I
−6.49085 − 0.26451I −15.4855 − 1.1209I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.320885
a = 5.19890
b = 1.47791
−6.71117 −12.0740
u = 0.319174
a = 1.19589
b = 0.236656
−0.557113 −17.6120
14
II.
I
u
2
= h−au − u
2
+ b + u − 1, −2u
2
a + a
2
− 3u
2
− 2a + u − 4, u
3
− u
2
+ 2u − 1i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
7
=
u
u
2
− u + 1
a
1
=
u
2
+ 1
u
2
− u + 1
a
2
=
a
au + u
2
− u + 1
a
6
=
u
2
+ 1
u
2
− u + 1
a
3
=
−u
2
+ a − 1
au
a
5
=
u
2
− a + 1
−au
a
9
=
−2u
2
+ 2u − 4
au − a + 2u − 2
a
10
=
0
−u
a
4
=
u
2
− a + 1
u
2
a − au + u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
2
+ 4u − 24
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u − 1)
6
c
2
(u + 1)
6
c
3
, c
4
, c
8
c
9
(u
2
− 2)
3
c
6
(u
3
− u
2
+ 1)
2
c
7
(u
3
+ u
2
+ 2u + 1)
2
c
10
(u
3
+ u
2
− 1)
2
c
11
, c
12
(u
3
− u
2
+ 2u − 1)
2
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y −1)
6
c
3
, c
4
, c
8
c
9
(y −2)
6
c
6
, c
10
(y
3
− y
2
+ 2y −1)
2
c
7
, c
11
, c
12
(y
3
+ 3y
2
+ 2y −1)
2
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 + 1.307140I
a = −0.489031 − 0.491114I
b = −0.34066 − 1.48972I
−3.55561 − 2.82812I −16.4902 + 2.9794I
u = 0.215080 + 1.307140I
a = −0.83569 + 1.61567I
b = −3.16909 − 1.48972I
−3.55561 − 2.82812I −16.4902 + 2.9794I
u = 0.215080 − 1.307140I
a = −0.489031 + 0.491114I
b = −0.34066 + 1.48972I
−3.55561 + 2.82812I −16.4902 − 2.9794I
u = 0.215080 − 1.307140I
a = −0.83569 − 1.61567I
b = −3.16909 + 1.48972I
−3.55561 + 2.82812I −16.4902 − 2.9794I
u = 0.569840
a = −1.15705
b = 0.0955418
−7.69319 −23.0200
u = 0.569840
a = 3.80649
b = 2.92397
−7.69319 −23.0200
18
III. I
u
3
= h−2u
2
+ b − 2u − 2, −u
2
+ a − 1, u
3
+ u
2
+ 2u + 1i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
7
=
u
−u
2
− u − 1
a
1
=
u
2
+ 1
u
2
+ u + 1
a
2
=
u
2
+ 1
2u
2
+ 2u + 2
a
6
=
−u
2
− 1
−u
2
− u − 1
a
3
=
0
u
2
+ u + 1
a
5
=
0
u
2
+ u + 1
a
9
=
0
u
a
10
=
0
u
a
4
=
0
u
2
+ u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2u
2
− 4u − 16
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
3
c
3
, c
4
, c
8
c
9
u
3
c
5
(u + 1)
3
c
6
, c
10
u
3
+ u
2
− 1
c
7
u
3
− u
2
+ 2u − 1
c
11
, c
12
u
3
+ u
2
+ 2u + 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y −1)
3
c
3
, c
4
, c
8
c
9
y
3
c
6
, c
10
y
3
− y
2
+ 2y −1
c
7
, c
11
, c
12
y
3
+ 3y
2
+ 2y −1
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.215080 + 1.307140I
a = −0.662359 − 0.562280I
b = −1.75488 + 1.48972I
1.37919 + 2.82812I −11.81496 − 4.10401I
u = −0.215080 − 1.307140I
a = −0.662359 + 0.562280I
b = −1.75488 − 1.48972I
1.37919 − 2.82812I −11.81496 + 4.10401I
u = −0.569840
a = 1.32472
b = 1.50976
−2.75839 −14.3700
22
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
9
)(u
92
+ 46u
91
+ ··· + 1255u + 49)
c
2
((u − 1)
3
)(u + 1)
6
(u
92
+ 4u
91
+ ··· − 67u − 7)
c
3
, c
4
, c
9
u
3
(u
2
− 2)
3
(u
92
− u
91
+ ··· − 24u − 8)
c
5
((u − 1)
6
)(u + 1)
3
(u
92
+ 4u
91
+ ··· − 67u − 7)
c
6
((u
3
− u
2
+ 1)
2
)(u
3
+ u
2
− 1)(u
92
− 2u
91
+ ··· − 312u − 29)
c
7
(u
3
− u
2
+ 2u − 1)(u
3
+ u
2
+ 2u + 1)
2
(u
92
+ 2u
91
+ ··· − 4u − 1)
c
8
u
3
(u
2
− 2)
3
(u
92
+ 3u
91
+ ··· + 49864u + 10856)
c
10
((u
3
+ u
2
− 1)
3
)(u
92
− 20u
91
+ ··· − 103152u + 12161)
c
11
, c
12
((u
3
− u
2
+ 2u − 1)
2
)(u
3
+ u
2
+ 2u + 1)(u
92
+ 2u
91
+ ··· − 4u − 1)
23
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
9
)(y
92
+ 10y
91
+ ··· − 468507y + 2401)
c
2
, c
5
((y −1)
9
)(y
92
− 46y
91
+ ··· − 1255y + 49)
c
3
, c
4
, c
9
y
3
(y −2)
6
(y
92
− 85y
91
+ ··· + 448y + 64)
c
6
((y
3
− y
2
+ 2y −1)
3
)(y
92
+ 4y
91
+ ··· + 28748y + 841)
c
7
, c
11
, c
12
((y
3
+ 3y
2
+ 2y −1)
3
)(y
92
+ 84y
91
+ ··· − 16y + 1)
c
8
y
3
(y −2)
6
(y
92
− y
91
+ ··· − 5.14448 × 10
8
y + 1.17853 × 10
8
)
c
10
(y
3
− y
2
+ 2y −1)
3
· (y
92
+ 28y
91
+ ··· − 3573140208y + 147889921)
24
