12n
0798
(K12n
0798
)
A knot diagram
1
Linearized knot diagam
4 12 11 9 3 12 3 1 4 1 7 5
Solving Sequence
1,4 2,10
11 3 9 5 6 8 7 12
c
1
c
10
c
3
c
9
c
4
c
5
c
8
c
7
c
12
c
2
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h1283u
12
− 662u
11
+ ··· + 5739b + 1160, −630u
12
+ 3164u
11
+ ··· + 1913a − 753,
u
13
− 3u
12
+ 8u
11
− 20u
10
+ 36u
9
− 61u
8
+ 84u
7
− 97u
6
+ 97u
5
− 68u
4
+ 41u
3
− 13u
2
+ 3u + 1i
I
u
2
= h−1.18123 × 10
153
u
55
− 4.51937 × 10
153
u
54
+ ··· + 2.08930 × 10
155
b − 7.05789 × 10
155
,
8.87232 × 10
153
u
55
+ 3.38341 × 10
154
u
54
+ ··· + 6.26789 × 10
155
a + 3.97690 × 10
156
,
u
56
+ 4u
55
+ ··· + 1346u + 111i
I
u
3
= h−135214u
15
+ 515373u
14
+ ··· + 267063b + 30946,
− 570167u
15
+ 1972254u
14
+ ··· + 1335315a − 4248919, u
16
− 4u
15
+ ··· − u + 1i
I
u
4
= h−u
3
+ u
2
+ b − u, u
2
+ a − u + 2, u
4
− u
3
+ 2u
2
+ 1i
I
u
5
= h−u
2
+ b + u, a + u, u
4
− u
3
+ u
2
− u + 1i
* 5 irreducible components of dim
C
= 0, with total 93 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
= h1283u
12
− 662u
11
+ · · · + 5739b + 1160, −630u
12
+ 3164u
11
+ · · · +
1913a − 753, u
13
− 3u
12
+ · · · + 3u + 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
10
=
0.329326u
12
− 1.65395u
11
+ ··· − 12.3325u + 0.393623
−0.223558u
12
+ 0.115351u
11
+ ··· − 2.77749u − 0.202126
a
11
=
0.552884u
12
− 1.76930u
11
+ ··· − 9.55497u + 0.595748
−0.223558u
12
+ 0.115351u
11
+ ··· − 2.77749u − 0.202126
a
3
=
−0.744555u
12
+ 1.43562u
11
+ ··· − 4.66423u + 0.635477
−0.238021u
12
+ 0.958355u
11
+ ··· + 3.13870u + 0.798048
a
9
=
0.329326u
12
− 1.65395u
11
+ ··· − 12.3325u + 0.393623
−0.499042u
12
+ 1.07667u
11
+ ··· − 1.10890u + 0.463844
a
5
=
1.02248u
12
− 2.20178u
11
+ ··· + 4.08207u − 1.12075
−0.110646u
12
+ 0.148284u
11
+ ··· − 1.06290u − 0.552884
a
6
=
0.905558u
12
− 2.55532u
11
+ ··· − 1.63164u − 1.70971
−0.659697u
12
+ 2.22426u
11
+ ··· + 3.05646u + 0.706743
a
8
=
0.828367u
12
− 2.73062u
11
+ ··· − 11.2236u − 0.0702213
−0.499042u
12
+ 1.07667u
11
+ ··· − 1.10890u + 0.463844
a
7
=
1.44642u
12
− 3.28646u
11
+ ··· − 1.18400u + 1.06691
0.158564u
12
− 1.31486u
11
+ ··· − 7.38230u − 1.25492
a
12
=
−0.364523u
12
+ 1.83813u
11
+ ··· + 7.51403u + 3.57066
0.798048u
12
− 2.15612u
11
+ ··· − 2.86914u − 0.744555
(ii) Obstruction class = −1
(iii) Cusp Shapes =
27061
5739
u
12
−
84808
5739
u
11
+ ··· −
197266
5739
u +
6865
5739
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
u
13
+ 3u
12
+ ··· + 3u − 1
c
3
, c
12
u
13
+ u
12
+ ··· − 3u − 1
c
4
, c
6
, c
9
c
11
u
13
− 2u
12
+ ··· + 7u
3
− 1
c
5
, c
10
u
13
− u
12
+ ··· + 3u − 3
c
7
, c
8
u
13
+ 3u
12
+ ··· − 8u − 3
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
y
13
+ 7y
12
+ ··· + 35y −1
c
3
, c
12
y
13
+ 7y
12
+ ··· + 3y −1
c
4
, c
6
, c
9
c
11
y
13
+ 4y
11
+ ··· − 2y
2
− 1
c
5
, c
10
y
13
+ 15y
12
+ ··· + 39y −9
c
7
, c
8
y
13
− 3y
12
+ ··· + 34y −9
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.125889 + 0.791075I
a = −0.42819 + 1.60424I
b = 0.06421 + 1.99251I
3.78832 − 0.68098I 3.18600 + 10.56387I
u = 0.125889 − 0.791075I
a = −0.42819 − 1.60424I
b = 0.06421 − 1.99251I
3.78832 + 0.68098I 3.18600 − 10.56387I
u = 0.435895 + 1.153550I
a = −0.166988 − 0.397762I
b = −1.101790 − 0.664354I
−1.60930 − 2.98509I 6.45992 + 2.62910I
u = 0.435895 − 1.153550I
a = −0.166988 + 0.397762I
b = −1.101790 + 0.664354I
−1.60930 + 2.98509I 6.45992 − 2.62910I
u = 0.405751 + 0.538490I
a = −1.29934 − 1.45999I
b = 0.613689 − 0.351552I
−8.20006 − 2.65719I −7.53293 + 6.11651I
u = 0.405751 − 0.538490I
a = −1.29934 + 1.45999I
b = 0.613689 + 0.351552I
−8.20006 + 2.65719I −7.53293 − 6.11651I
u = −0.21582 + 1.42915I
a = 0.743610 + 0.701361I
b = 0.17608 + 1.54701I
9.07015 + 0.94105I 7.27747 − 1.09961I
u = −0.21582 − 1.42915I
a = 0.743610 − 0.701361I
b = 0.17608 − 1.54701I
9.07015 − 0.94105I 7.27747 + 1.09961I
u = 1.52678 + 0.05294I
a = 0.101352 + 0.424061I
b = −0.310928 + 0.347924I
−3.37050 + 0.66803I 1.81891 − 10.95758I
u = 1.52678 − 0.05294I
a = 0.101352 − 0.424061I
b = −0.310928 − 0.347924I
−3.37050 − 0.66803I 1.81891 + 10.95758I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.70010 + 1.56807I
a = 0.383909 − 0.789778I
b = 0.82111 − 1.72051I
7.2980 + 16.4758I 4.42093 − 8.40539I
u = −0.70010 − 1.56807I
a = 0.383909 + 0.789778I
b = 0.82111 + 1.72051I
7.2980 − 16.4758I 4.42093 + 8.40539I
u = −0.156796
a = 3.33128
b = 0.475252
0.851273 11.7390
6
II. I
u
2
= h−1.18 × 10
153
u
55
− 4.52 × 10
153
u
54
+ · · · + 2.09 × 10
155
b − 7.06 ×
10
155
, 8.87 × 10
153
u
55
+ 3.38 × 10
154
u
54
+ · · · + 6.27 × 10
155
a + 3.98 ×
10
156
, u
56
+ 4u
55
+ · · · + 1346u + 111i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
10
=
−0.0141552u
55
− 0.0539800u
54
+ ··· − 28.3025u − 6.34487
0.00565370u
55
+ 0.0216310u
54
+ ··· + 16.5561u + 3.37812
a
11
=
−0.0198089u
55
− 0.0756110u
54
+ ··· − 44.8585u − 9.72299
0.00565370u
55
+ 0.0216310u
54
+ ··· + 16.5561u + 3.37812
a
3
=
0.0144678u
55
+ 0.0586721u
54
+ ··· + 73.1975u + 12.4499
−0.00267933u
55
− 0.00908580u
54
+ ··· − 12.7090u − 3.57215
a
9
=
−0.0141552u
55
− 0.0539800u
54
+ ··· − 28.3025u − 6.34487
0.00718179u
55
+ 0.0273575u
54
+ ··· + 14.5728u + 3.08499
a
5
=
−0.00877254u
55
− 0.0387439u
54
+ ··· − 48.2032u − 6.38465
0.00314979u
55
+ 0.0134163u
54
+ ··· + 18.1770u + 2.89867
a
6
=
−0.0116448u
55
− 0.0480523u
54
+ ··· − 48.8452u + 1.49968
0.00331140u
55
+ 0.0134797u
54
+ ··· + 33.1904u + 2.23101
a
8
=
−0.0213370u
55
− 0.0813374u
54
+ ··· − 42.8753u − 9.42987
0.00718179u
55
+ 0.0273575u
54
+ ··· + 14.5728u + 3.08499
a
7
=
0.0106076u
55
+ 0.0439229u
54
+ ··· + 51.7711u + 2.93855
−0.00286600u
55
− 0.0111012u
54
+ ··· − 25.2269u − 2.36948
a
12
=
−0.00420227u
55
− 0.0147886u
54
+ ··· − 32.7418u − 2.34305
0.00309502u
55
+ 0.0110761u
54
+ ··· + 17.1401u + 2.03269
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.000431876u
55
− 0.00131056u
54
+ ··· − 42.1688u + 5.52954
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
u
56
− 4u
55
+ ··· − 1346u + 111
c
3
, c
12
u
56
+ 2u
54
+ ··· + 907u + 193
c
4
, c
6
, c
9
c
11
u
56
+ u
55
+ ··· + 13u + 3
c
5
, c
10
u
56
+ 2u
55
+ ··· + 82u + 37
c
7
, c
8
u
56
− u
55
+ ··· + 29361u + 1951
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
y
56
+ 50y
55
+ ··· − 249724y + 12321
c
3
, c
12
y
56
+ 4y
55
+ ··· − 242491y + 37249
c
4
, c
6
, c
9
c
11
y
56
+ 15y
55
+ ··· + 275y + 9
c
5
, c
10
y
56
+ 52y
55
+ ··· − 39284y + 1369
c
7
, c
8
y
56
− 31y
55
+ ··· − 114413905y + 3806401
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.973175 + 0.358698I
a = 0.223686 + 0.715699I
b = −0.141495 − 0.212809I
−2.35105 − 1.37665I 0. + 4.49216I
u = 0.973175 − 0.358698I
a = 0.223686 − 0.715699I
b = −0.141495 + 0.212809I
−2.35105 + 1.37665I 0. − 4.49216I
u = −0.847096 + 0.638226I
a = −0.404462 + 0.469747I
b = 0.15766 + 1.46714I
1.93596 + 5.90600I 0. − 3.51945I
u = −0.847096 − 0.638226I
a = −0.404462 − 0.469747I
b = 0.15766 − 1.46714I
1.93596 − 5.90600I 0. + 3.51945I
u = −0.561985 + 0.926870I
a = 0.331742 − 1.143620I
b = 0.25987 − 1.69030I
−3.01211 + 5.08083I 8.72700 + 0.I
u = −0.561985 − 0.926870I
a = 0.331742 + 1.143620I
b = 0.25987 + 1.69030I
−3.01211 − 5.08083I 8.72700 + 0.I
u = −0.401455 + 0.819963I
a = 0.524050 − 0.252083I
b = −0.232565 − 1.287120I
3.14992 − 0.89303I 3.36391 + 1.60851I
u = −0.401455 − 0.819963I
a = 0.524050 + 0.252083I
b = −0.232565 + 1.287120I
3.14992 + 0.89303I 3.36391 − 1.60851I
u = 0.428842 + 0.782748I
a = 1.39747 + 0.43456I
b = −0.093467 − 0.473397I
−2.65912 − 0.69416I 5.49287 + 3.59719I
u = 0.428842 − 0.782748I
a = 1.39747 − 0.43456I
b = −0.093467 + 0.473397I
−2.65912 + 0.69416I 5.49287 − 3.59719I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.293234 + 1.071580I
a = −0.398636 + 1.032790I
b = 0.105708 + 1.267210I
3.14992 + 0.89303I 4.00000 + 0.I
u = −0.293234 − 1.071580I
a = −0.398636 − 1.032790I
b = 0.105708 − 1.267210I
3.14992 − 0.89303I 4.00000 + 0.I
u = −0.087731 + 1.118910I
a = −0.686073 + 0.991907I
b = 0.06046 + 1.60533I
3.57949 + 0.97368I 7.35348 − 5.23167I
u = −0.087731 − 1.118910I
a = −0.686073 − 0.991907I
b = 0.06046 − 1.60533I
3.57949 − 0.97368I 7.35348 + 5.23167I
u = 0.683985 + 0.326867I
a = 0.76677 + 1.25863I
b = −0.876249 − 0.500129I
−4.38515 − 0.94897I −10.21959 + 1.75938I
u = 0.683985 − 0.326867I
a = 0.76677 − 1.25863I
b = −0.876249 + 0.500129I
−4.38515 + 0.94897I −10.21959 − 1.75938I
u = −0.463157 + 1.179820I
a = −0.692781 − 0.317187I
b = −0.447756 − 0.568276I
−2.65912 − 0.69416I 0
u = −0.463157 − 1.179820I
a = −0.692781 + 0.317187I
b = −0.447756 + 0.568276I
−2.65912 + 0.69416I 0
u = −1.250640 + 0.306528I
a = 0.350610 + 0.608692I
b = −0.076204 + 0.243308I
3.22350 + 2.16516I 0
u = −1.250640 − 0.306528I
a = 0.350610 − 0.608692I
b = −0.076204 − 0.243308I
3.22350 − 2.16516I 0
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.150720 + 1.306260I
a = 0.728240 + 0.063856I
b = 1.105270 + 0.474638I
−0.60047 − 5.02443I 0
u = −0.150720 − 1.306260I
a = 0.728240 − 0.063856I
b = 1.105270 − 0.474638I
−0.60047 + 5.02443I 0
u = 0.118150 + 1.326950I
a = 0.824150 + 0.704249I
b = −0.25793 + 1.46755I
7.25514 0
u = 0.118150 − 1.326950I
a = 0.824150 − 0.704249I
b = −0.25793 − 1.46755I
7.25514 0
u = 0.855631 + 1.049130I
a = −0.036172 − 0.766616I
b = −0.62639 − 1.44617I
−0.60047 − 5.02443I 0
u = 0.855631 − 1.049130I
a = −0.036172 + 0.766616I
b = −0.62639 + 1.44617I
−0.60047 + 5.02443I 0
u = 0.110352 + 0.636373I
a = −2.55589 − 0.04098I
b = −0.423182 + 0.031837I
−3.01211 + 5.08083I 8.72700 − 0.16788I
u = 0.110352 − 0.636373I
a = −2.55589 + 0.04098I
b = −0.423182 − 0.031837I
−3.01211 − 5.08083I 8.72700 + 0.16788I
u = −0.002625 + 1.377270I
a = 0.508986 − 0.612116I
b = −0.09477 − 1.51750I
3.22350 − 2.16516I 0
u = −0.002625 − 1.377270I
a = 0.508986 + 0.612116I
b = −0.09477 + 1.51750I
3.22350 + 2.16516I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.150210 + 0.569344I
a = −0.824610 − 0.889775I
b = −1.046740 + 0.070502I
−2.35105 − 1.37665I −0.14056 + 4.49216I
u = 0.150210 − 0.569344I
a = −0.824610 + 0.889775I
b = −1.046740 − 0.070502I
−2.35105 + 1.37665I −0.14056 − 4.49216I
u = −0.23885 + 1.42021I
a = −0.724589 − 0.727418I
b = 0.07102 − 1.58823I
8.32665 + 8.69653I 0
u = −0.23885 − 1.42021I
a = −0.724589 + 0.727418I
b = 0.07102 + 1.58823I
8.32665 − 8.69653I 0
u = 0.46400 + 1.40989I
a = 0.467280 + 0.871972I
b = 0.93856 + 1.51643I
2.96962 − 6.50699I 0
u = 0.46400 − 1.40989I
a = 0.467280 − 0.871972I
b = 0.93856 − 1.51643I
2.96962 + 6.50699I 0
u = 0.12171 + 1.48953I
a = −0.732149 − 0.618254I
b = 0.02724 − 1.64380I
8.61168 − 6.87817I 0
u = 0.12171 − 1.48953I
a = −0.732149 + 0.618254I
b = 0.02724 + 1.64380I
8.61168 + 6.87817I 0
u = 0.46868 + 1.43810I
a = 0.529642 + 0.769097I
b = 0.656517 + 1.172790I
1.93596 − 5.90600I 0
u = 0.46868 − 1.43810I
a = 0.529642 − 0.769097I
b = 0.656517 − 1.172790I
1.93596 + 5.90600I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.61255 + 1.47138I
a = −0.411818 + 0.844957I
b = −0.66961 + 1.79906I
8.32665 + 8.69653I 0
u = −0.61255 − 1.47138I
a = −0.411818 − 0.844957I
b = −0.66961 − 1.79906I
8.32665 − 8.69653I 0
u = 0.57163 + 1.63667I
a = −0.425730 − 0.627977I
b = −0.67894 − 1.58354I
2.19558 − 8.29138I 0
u = 0.57163 − 1.63667I
a = −0.425730 + 0.627977I
b = −0.67894 + 1.58354I
2.19558 + 8.29138I 0
u = −0.021719 + 0.263335I
a = 0.31401 + 2.13706I
b = −1.29778 − 0.84140I
3.57949 − 0.97368I 7.35348 + 5.23167I
u = −0.021719 − 0.263335I
a = 0.31401 − 2.13706I
b = −1.29778 + 0.84140I
3.57949 + 0.97368I 7.35348 − 5.23167I
u = −0.37410 + 1.70455I
a = 0.285913 − 0.668539I
b = 0.58599 − 1.56113I
9.99346 0
u = −0.37410 − 1.70455I
a = 0.285913 + 0.668539I
b = 0.58599 + 1.56113I
9.99346 0
u = −1.78299 + 0.07540I
a = −0.258059 − 0.376840I
b = 0.170261 + 0.007329I
2.19558 + 8.29138I 0
u = −1.78299 − 0.07540I
a = −0.258059 + 0.376840I
b = 0.170261 − 0.007329I
2.19558 − 8.29138I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.47184 + 1.75013I
a = −0.252592 + 0.650075I
b = −0.71080 + 1.36535I
8.61168 + 6.87817I 0
u = −0.47184 − 1.75013I
a = −0.252592 − 0.650075I
b = −0.71080 − 1.36535I
8.61168 − 6.87817I 0
u = 0.76269 + 1.66617I
a = 0.168983 + 0.041887I
b = 0.580641 + 0.363782I
−4.38515 − 0.94897I 0
u = 0.76269 − 1.66617I
a = 0.168983 − 0.041887I
b = 0.580641 − 0.363782I
−4.38515 + 0.94897I 0
u = −0.148356 + 0.045126I
a = −3.00896 − 2.49575I
b = 1.95470 + 0.87168I
2.96962 + 6.50699I 13.7787 − 5.9700I
u = −0.148356 − 0.045126I
a = −3.00896 + 2.49575I
b = 1.95470 − 0.87168I
2.96962 − 6.50699I 13.7787 + 5.9700I
15
III.
I
u
3
= h−1.35 × 10
5
u
15
+ 5.15 × 10
5
u
14
+ · · · + 2.67 × 10
5
b + 3.09 × 10
4
, −5.70 ×
10
5
u
15
+ 1.97× 10
6
u
14
+ · · · + 1.34 × 10
6
a −4.25 × 10
6
, u
16
− 4u
15
+ · · · − u + 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
10
=
0.426991u
15
− 1.47700u
14
+ ··· − 1.64833u + 3.18196
0.506300u
15
− 1.92978u
14
+ ··· + 0.204210u − 0.115875
a
11
=
−0.0793094u
15
+ 0.452785u
14
+ ··· − 1.85254u + 3.29784
0.506300u
15
− 1.92978u
14
+ ··· + 0.204210u − 0.115875
a
3
=
−1.66162u
15
+ 5.75525u
14
+ ··· − 9.16104u − 0.00841824
−0.194335u
15
+ 1.26058u
14
+ ··· − 0.801647u + 0.663182
a
9
=
0.426991u
15
− 1.47700u
14
+ ··· − 1.64833u + 3.18196
0.510721u
15
− 1.77893u
14
+ ··· + 0.00818683u − 0.346843
a
5
=
1.53255u
15
− 6.54843u
14
+ ··· + 13.1760u − 1.49836
0.0802492u
15
− 0.689561u
14
+ ··· + 1.26250u − 0.425375
a
6
=
−1.07106u
15
+ 2.28793u
14
+ ··· + 12.6165u − 5.85293
−0.0709555u
15
+ 0.340250u
14
+ ··· + 2.32523u − 1.20232
a
8
=
−0.0837301u
15
+ 0.301938u
14
+ ··· − 1.65651u + 3.52880
0.510721u
15
− 1.77893u
14
+ ··· + 0.00818683u − 0.346843
a
7
=
0.636679u
15
− 3.36717u
14
+ ··· + 10.0876u − 2.20527
0.0721897u
15
− 0.414518u
14
+ ··· + 1.95733u − 0.879098
a
12
=
−0.445408u
15
+ 0.788567u
14
+ ··· + 7.00998u − 1.98390
0.287778u
15
− 1.19976u
14
+ ··· + 1.25399u − 0.670117
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
1668929
445105
u
15
+
8331783
445105
u
14
+ ··· −
10787371
445105
u +
3576652
445105
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
16
− 4u
15
+ ··· − u + 1
c
2
u
16
+ 4u
15
+ ··· + u + 1
c
3
u
16
+ 2u
15
+ ··· + 2u + 1
c
4
, c
6
u
16
+ u
15
+ ··· − 4u + 1
c
5
u
16
− u
15
+ ··· + 9u + 9
c
7
u
16
+ u
15
+ ··· − u + 1
c
8
u
16
− u
15
+ ··· + u + 1
c
9
, c
11
u
16
− u
15
+ ··· + 4u + 1
c
10
u
16
+ u
15
+ ··· − 9u + 9
c
12
u
16
− 2u
15
+ ··· − 2u + 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
y
16
+ 10y
15
+ ··· + 11y + 1
c
3
, c
12
y
16
+ 12y
15
+ ··· + 4y + 1
c
4
, c
6
, c
9
c
11
y
16
+ 7y
15
+ ··· + 2y + 1
c
5
, c
10
y
16
+ 13y
15
+ ··· − 927y + 81
c
7
, c
8
y
16
− y
15
+ ··· + 27y + 1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.626932 + 0.939202I
a = 0.245461 + 1.107320I
b = 0.45758 + 1.67741I
−3.44371 − 5.36963I −4.65919 + 8.71627I
u = 0.626932 − 0.939202I
a = 0.245461 − 1.107320I
b = 0.45758 − 1.67741I
−3.44371 + 5.36963I −4.65919 − 8.71627I
u = 0.561928 + 0.646656I
a = 1.122090 + 0.719975I
b = −0.824183 − 0.541509I
−3.98555 − 1.28538I 1.78219 + 9.46171I
u = 0.561928 − 0.646656I
a = 1.122090 − 0.719975I
b = −0.824183 + 0.541509I
−3.98555 + 1.28538I 1.78219 − 9.46171I
u = −0.044845 + 0.844688I
a = 0.201470 − 1.383010I
b = −0.35203 − 1.95828I
4.11885 12.68263 + 0.I
u = −0.044845 − 0.844688I
a = 0.201470 + 1.383010I
b = −0.35203 + 1.95828I
4.11885 12.68263 + 0.I
u = −0.770410 + 0.331199I
a = 0.236785 + 0.596788I
b = 1.06833 + 1.33459I
2.42763 + 6.73512I 1.81921 − 10.54756I
u = −0.770410 − 0.331199I
a = 0.236785 − 0.596788I
b = 1.06833 − 1.33459I
2.42763 − 6.73512I 1.81921 + 10.54756I
u = 1.134980 + 0.398912I
a = −0.326610 − 0.608866I
b = −0.471617 + 0.101971I
−3.98521 −7.56704 + 0.I
u = 1.134980 − 0.398912I
a = −0.326610 + 0.608866I
b = −0.471617 − 0.101971I
−3.98521 −7.56704 + 0.I
19
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.44558 + 1.49412I
a = −0.522013 − 0.746739I
b = −0.87827 − 1.36350I
2.42763 − 6.73512I 1.81921 + 10.54756I
u = 0.44558 − 1.49412I
a = −0.522013 + 0.746739I
b = −0.87827 + 1.36350I
2.42763 + 6.73512I 1.81921 − 10.54756I
u = −0.117840 + 0.420370I
a = 3.38072 − 1.31571I
b = 0.798526 − 0.197831I
−3.44371 + 5.36963I −4.65919 − 8.71627I
u = −0.117840 − 0.420370I
a = 3.38072 + 1.31571I
b = 0.798526 + 0.197831I
−3.44371 − 5.36963I −4.65919 + 8.71627I
u = 0.16367 + 1.77202I
a = 0.162097 + 0.279051I
b = 0.701667 + 0.382156I
−3.98555 − 1.28538I 1.78219 + 9.46171I
u = 0.16367 − 1.77202I
a = 0.162097 − 0.279051I
b = 0.701667 − 0.382156I
−3.98555 + 1.28538I 1.78219 − 9.46171I
20
IV. I
u
4
= h−u
3
+ u
2
+ b − u, u
2
+ a − u + 2, u
4
− u
3
+ 2u
2
+ 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
10
=
−u
2
+ u − 2
u
3
− u
2
+ u
a
11
=
−u
3
− 2
u
3
− u
2
+ u
a
3
=
−2u
3
+ 3u
2
− 5u + 1
2u − 1
a
9
=
−u
2
+ u − 2
u
3
− u
2
+ u + 1
a
5
=
2u
3
− 2u
2
+ 3u + 1
−u
3
+ 2u
2
− 2u + 1
a
6
=
2u
3
+ u + 4
−2u
3
+ u
2
− 3u − 1
a
8
=
−u
3
− 3
u
3
− u
2
+ u + 1
a
7
=
−3u
3
+ 5u
2
− 7u + 1
−2u
2
+ 2u − 2
a
12
=
2u
2
− 3u + 5
−u
3
+ u
2
− u − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
3
+ 3u
2
+ 4u + 7
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
4
− u
3
+ 2u
2
+ 1
c
2
u
4
+ u
3
+ 2u
2
+ 1
c
3
u
4
+ u
3
+ 4u
2
+ 2u + 3
c
4
, c
6
u
4
+ 2u
2
+ u + 1
c
5
u
4
+ u
3
+ 1
c
7
u
4
− 3u
3
+ 3u
2
− u + 1
c
8
u
4
+ 3u
3
+ 3u
2
+ u + 1
c
9
, c
11
u
4
+ 2u
2
− u + 1
c
10
u
4
− u
3
+ 1
c
12
u
4
− u
3
+ 4u
2
− 2u + 3
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
y
4
+ 3y
3
+ 6y
2
+ 4y + 1
c
3
, c
12
y
4
+ 7y
3
+ 18y
2
+ 20y + 9
c
4
, c
6
, c
9
c
11
y
4
+ 4y
3
+ 6y
2
+ 3y + 1
c
5
, c
10
y
4
− y
3
+ 2y
2
+ 1
c
7
, c
8
y
4
− 3y
3
+ 5y
2
+ 5y + 1
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.175098 + 0.691825I
a = −1.72714 + 0.93410I
b = 0.518913 + 0.666610I
−7.71788 + 2.37936I 5.93992 + 0.97052I
u = −0.175098 − 0.691825I
a = −1.72714 − 0.93410I
b = 0.518913 − 0.666610I
−7.71788 − 2.37936I 5.93992 − 0.97052I
u = 0.675098 + 1.227920I
a = −0.272864 − 0.430014I
b = −1.018910 − 0.602565I
−2.15173 − 3.38562I −4.43992 + 9.19530I
u = 0.675098 − 1.227920I
a = −0.272864 + 0.430014I
b = −1.018910 + 0.602565I
−2.15173 + 3.38562I −4.43992 − 9.19530I
24
V. I
u
5
= h−u
2
+ b + u, a + u, u
4
− u
3
+ u
2
− u + 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
10
=
−u
u
2
− u
a
11
=
−u
2
u
2
− u
a
3
=
1
−u
3
+ u
2
a
9
=
−u
−u
3
+ u
2
− u
a
5
=
u
3
u
2
a
6
=
u
3
− u
2
+ u − 1
2u
2
− 2u + 1
a
8
=
u
3
− u
2
−u
3
+ u
2
− u
a
7
=
u
3
− u
2
+ u − 1
u
2
− 2u + 1
a
12
=
0
u
3
− u
2
+ u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 6u
3
− 6u
2
− 1
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
9
c
11
u
4
− u
3
+ u
2
− u + 1
c
2
, c
4
, c
6
c
12
u
4
+ u
3
+ u
2
+ u + 1
c
5
u
4
+ 2u
3
+ 4u
2
+ 3u + 1
c
7
u
4
+ 3u
3
+ 4u
2
+ 2u + 1
c
8
u
4
− 3u
3
+ 4u
2
− 2u + 1
c
10
u
4
− 2u
3
+ 4u
2
− 3u + 1
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
6
, c
9
c
11
, c
12
y
4
+ y
3
+ y
2
+ y + 1
c
5
, c
10
y
4
+ 4y
3
+ 6y
2
− y + 1
c
7
, c
8
y
4
− y
3
+ 6y
2
+ 4y + 1
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.309017 + 0.951057I
a = 0.309017 − 0.951057I
b = −0.50000 − 1.53884I
3.94784 8.70820 + 0.I
u = −0.309017 − 0.951057I
a = 0.309017 + 0.951057I
b = −0.50000 + 1.53884I
3.94784 8.70820 + 0.I
u = 0.809017 + 0.587785I
a = −0.809017 − 0.587785I
b = −0.500000 + 0.363271I
−3.94784 −4.70820 + 0.I
u = 0.809017 − 0.587785I
a = −0.809017 + 0.587785I
b = −0.500000 − 0.363271I
−3.94784 −4.70820 + 0.I
28
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
4
− u
3
+ u
2
− u + 1)(u
4
− u
3
+ 2u
2
+ 1)(u
13
+ 3u
12
+ ··· + 3u − 1)
· (u
16
− 4u
15
+ ··· − u + 1)(u
56
− 4u
55
+ ··· − 1346u + 111)
c
2
(u
4
+ u
3
+ u
2
+ u + 1)(u
4
+ u
3
+ 2u
2
+ 1)(u
13
+ 3u
12
+ ··· + 3u − 1)
· (u
16
+ 4u
15
+ ··· + u + 1)(u
56
− 4u
55
+ ··· − 1346u + 111)
c
3
(u
4
− u
3
+ u
2
− u + 1)(u
4
+ u
3
+ 4u
2
+ 2u + 3)(u
13
+ u
12
+ ··· − 3u − 1)
· (u
16
+ 2u
15
+ ··· + 2u + 1)(u
56
+ 2u
54
+ ··· + 907u + 193)
c
4
, c
6
(u
4
+ 2u
2
+ u + 1)(u
4
+ u
3
+ u
2
+ u + 1)(u
13
− 2u
12
+ ··· + 7u
3
− 1)
· (u
16
+ u
15
+ ··· − 4u + 1)(u
56
+ u
55
+ ··· + 13u + 3)
c
5
(u
4
+ u
3
+ 1)(u
4
+ 2u
3
+ ··· + 3u + 1)(u
13
− u
12
+ ··· + 3u − 3)
· (u
16
− u
15
+ ··· + 9u + 9)(u
56
+ 2u
55
+ ··· + 82u + 37)
c
7
(u
4
− 3u
3
+ 3u
2
− u + 1)(u
4
+ 3u
3
+ 4u
2
+ 2u + 1)
· (u
13
+ 3u
12
+ ··· − 8u − 3)(u
16
+ u
15
+ ··· − u + 1)
· (u
56
− u
55
+ ··· + 29361u + 1951)
c
8
(u
4
− 3u
3
+ 4u
2
− 2u + 1)(u
4
+ 3u
3
+ 3u
2
+ u + 1)
· (u
13
+ 3u
12
+ ··· − 8u − 3)(u
16
− u
15
+ ··· + u + 1)
· (u
56
− u
55
+ ··· + 29361u + 1951)
c
9
, c
11
(u
4
+ 2u
2
− u + 1)(u
4
− u
3
+ u
2
− u + 1)(u
13
− 2u
12
+ ··· + 7u
3
− 1)
· (u
16
− u
15
+ ··· + 4u + 1)(u
56
+ u
55
+ ··· + 13u + 3)
c
10
(u
4
− 2u
3
+ ··· − 3u + 1)(u
4
− u
3
+ 1)(u
13
− u
12
+ ··· + 3u − 3)
· (u
16
+ u
15
+ ··· − 9u + 9)(u
56
+ 2u
55
+ ··· + 82u + 37)
c
12
(u
4
− u
3
+ 4u
2
− 2u + 3)(u
4
+ u
3
+ u
2
+ u + 1)(u
13
+ u
12
+ ··· − 3u − 1)
· (u
16
− 2u
15
+ ··· − 2u + 1)(u
56
+ 2u
54
+ ··· + 907u + 193)
29
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
(y
4
+ y
3
+ y
2
+ y + 1)(y
4
+ 3y
3
+ 6y
2
+ 4y + 1)
· (y
13
+ 7y
12
+ ··· + 35y −1)(y
16
+ 10y
15
+ ··· + 11y + 1)
· (y
56
+ 50y
55
+ ··· − 249724y + 12321)
c
3
, c
12
(y
4
+ y
3
+ y
2
+ y + 1)(y
4
+ 7y
3
+ 18y
2
+ 20y + 9)
· (y
13
+ 7y
12
+ ··· + 3y −1)(y
16
+ 12y
15
+ ··· + 4y + 1)
· (y
56
+ 4y
55
+ ··· − 242491y + 37249)
c
4
, c
6
, c
9
c
11
(y
4
+ y
3
+ y
2
+ y + 1)(y
4
+ 4y
3
+ ··· + 3y + 1)(y
13
+ 4y
11
+ ··· − 2y
2
− 1)
· (y
16
+ 7y
15
+ ··· + 2y + 1)(y
56
+ 15y
55
+ ··· + 275y + 9)
c
5
, c
10
(y
4
− y
3
+ 2y
2
+ 1)(y
4
+ 4y
3
+ 6y
2
− y + 1)(y
13
+ 15y
12
+ ··· + 39y −9)
· (y
16
+ 13y
15
+ ··· − 927y + 81)(y
56
+ 52y
55
+ ··· − 39284y + 1369)
c
7
, c
8
(y
4
− 3y
3
+ 5y
2
+ 5y + 1)(y
4
− y
3
+ 6y
2
+ 4y + 1)
· (y
13
− 3y
12
+ ··· + 34y −9)(y
16
− y
15
+ ··· + 27y + 1)
· (y
56
− 31y
55
+ ··· − 114413905y + 3806401)
30
