12n
0482
(K12n
0482
)
A knot diagram
1
Linearized knot diagam
3 5 10 7 2 12 1 3 4 9 6 4
Solving Sequence
3,10 4,5
2 6 1 9 11 8 7 12
c
3
c
2
c
5
c
1
c
9
c
10
c
8
c
7
c
12
c
4
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= hb + u, 135u
10
− 671u
9
+ ··· + 493a + 107,
u
11
− 2u
10
+ 3u
9
− 4u
8
+ 8u
7
− 11u
6
+ 12u
5
− 11u
4
+ 5u
3
− 3u
2
− 1i
I
u
2
= h1.98818 × 10
32
u
37
+ 5.18591 × 10
31
u
36
+ ··· + 3.87572 × 10
32
b − 1.54819 × 10
32
,
4.74622 × 10
33
u
37
+ 1.04073 × 10
33
u
36
+ ··· + 3.87572 × 10
32
a − 3.08284 × 10
33
, u
38
+ u
37
+ ··· + 11u + 1i
I
u
3
= hb + u, −3u
4
+ 3u
3
− 2u
2
+ a + 5u − 2, u
5
− u
4
+ u
3
− 2u
2
+ u − 1i
I
u
4
= hb + u, a + 2u + 2, u
2
+ u + 1i
I
u
5
= h−u
13
− 2u
12
− 3u
11
− 8u
10
− 7u
9
− 16u
8
− 10u
7
− 21u
6
− 13u
5
− 18u
4
− 9u
3
− 11u
2
+ b − 3u − 2,
3u
13
− u
12
+ 10u
11
+ 19u
9
+ 2u
8
+ 22u
7
+ 8u
6
+ 19u
5
+ 5u
4
+ 12u
3
+ 3u
2
+ a + 2u,
u
14
+ 4u
12
+ u
11
+ 9u
10
+ 3u
9
+ 13u
8
+ 6u
7
+ 14u
6
+ 6u
5
+ 11u
4
+ 4u
3
+ 5u
2
+ u + 1i
* 5 irreducible components of dim
C
= 0, with total 70 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
= hb + u, 135u
10
− 671u
9
+ · · · + 493a + 107, u
11
− 2u
10
+ · · · − 3u
2
− 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
−u
2
a
5
=
−0.273834u
10
+ 1.36105u
9
+ ··· + 3.25761u − 0.217039
−u
a
2
=
−0.813387u
10
+ 1.76876u
9
+ ··· + 0.217039u + 1.27383
u
2
a
6
=
−0.415822u
10
+ 1.36308u
9
+ ··· + 1.98377u + 0.596349
−u
3
− u
a
1
=
−0.813387u
10
+ 1.76876u
9
+ ··· + 0.217039u + 1.27383
u
2
a
9
=
−u
u
3
+ u
a
11
=
−u
3
u
5
+ u
3
+ u
a
8
=
u
3
u
3
+ u
a
7
=
0.0263692u
10
− 0.271805u
9
+ ··· − 3.30629u + 1.00609
0.0953347u
10
− 0.444219u
9
+ ··· + 0.969574u − 0.131846
a
12
=
−1.09533u
10
+ 2.44422u
9
+ ··· + 1.03043u + 1.13185
−0.150101u
10
+ 0.316430u
9
+ ··· + 0.281947u − 0.111562
(ii) Obstruction class = −1
(iii) Cusp Shapes =
1818
493
u
10
−
2167
493
u
9
+
2637
493
u
8
−
3733
493
u
7
+
10857
493
u
6
−
10419
493
u
5
+
8712
493
u
4
−
7389
493
u
3
+
2214
493
u
2
−
3255
493
u −
301
493
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
11
+ 2u
10
+ ··· − 6u − 1
c
2
, c
3
, c
5
c
9
u
11
− 2u
10
+ 3u
9
− 4u
8
+ 8u
7
− 11u
6
+ 12u
5
− 11u
4
+ 5u
3
− 3u
2
− 1
c
4
, c
6
, c
11
u
11
− u
10
− u
9
+ u
8
+ 5u
7
− 3u
6
− 4u
5
+ u
4
+ 3u
3
− u
2
+ 3u − 1
c
7
u
11
+ u
10
+ ··· − 51u − 17
c
8
u
11
− 4u
10
+ ··· − 16u − 1
c
12
u
11
+ 8u
10
+ ··· − 320u − 64
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
11
+ 14y
10
+ ··· − 26y −1
c
2
, c
3
, c
5
c
9
y
11
+ 2y
10
+ ··· − 6y −1
c
4
, c
6
, c
11
y
11
− 3y
10
+ ··· + 7y −1
c
7
y
11
− 15y
10
+ ··· − 425y −289
c
8
y
11
+ 20y
10
+ ··· + 92y −1
c
12
y
11
− 22y
10
+ ··· − 10240y −4096
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.069055 + 1.000350I
a = −0.981312 − 0.304041I
b = −0.069055 − 1.000350I
−5.87879 + 3.62795I −10.28819 − 4.50965I
u = 0.069055 − 1.000350I
a = −0.981312 + 0.304041I
b = −0.069055 + 1.000350I
−5.87879 − 3.62795I −10.28819 + 4.50965I
u = 0.457197 + 0.753480I
a = 0.883878 − 0.436496I
b = −0.457197 − 0.753480I
0.73694 + 2.00002I 2.64478 − 3.99897I
u = 0.457197 − 0.753480I
a = 0.883878 + 0.436496I
b = −0.457197 + 0.753480I
0.73694 − 2.00002I 2.64478 + 3.99897I
u = 1.21408
a = 0.899878
b = −1.21408
2.41788 20.6200
u = 1.06044 + 0.99031I
a = 1.37322 − 0.35892I
b = −1.06044 − 0.99031I
10.12310 + 0.00215I 1.32048 + 0.53124I
u = 1.06044 − 0.99031I
a = 1.37322 + 0.35892I
b = −1.06044 + 0.99031I
10.12310 − 0.00215I 1.32048 − 0.53124I
u = −0.92863 + 1.13891I
a = −1.51448 − 0.57303I
b = 0.92863 − 1.13891I
8.9020 − 15.0293I −0.32227 + 7.97448I
u = −0.92863 − 1.13891I
a = −1.51448 + 0.57303I
b = 0.92863 + 1.13891I
8.9020 + 15.0293I −0.32227 − 7.97448I
u = −0.265103 + 0.402117I
a = 1.28876 + 2.59793I
b = 0.265103 − 0.402117I
−1.93271 + 1.18056I −1.16495 − 2.63475I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.265103 − 0.402117I
a = 1.28876 − 2.59793I
b = 0.265103 + 0.402117I
−1.93271 − 1.18056I −1.16495 + 2.63475I
6
II.
I
u
2
= h1.99 × 10
32
u
37
+ 5.19 × 10
31
u
36
+ · · · + 3.88 × 10
32
b − 1.55 × 10
32
, 4.75 ×
10
33
u
37
+1.04×10
33
u
36
+· · ·+3.88×10
32
a−3.08×10
33
, u
38
+u
37
+· · ·+11u+1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
−u
2
a
5
=
−12.2460u
37
− 2.68526u
36
+ ··· + 1.99894u + 7.95423
−0.512982u
37
− 0.133805u
36
+ ··· + 0.536992u + 0.399459
a
2
=
7.74425u
37
+ 4.31734u
36
+ ··· + 215.566u + 26.2164
0.565194u
37
+ 2.66371u
36
+ ··· + 55.8911u + 6.22476
a
6
=
−11.1078u
37
− 6.54371u
36
+ ··· − 143.314u − 12.5852
3.29534u
37
+ 2.38055u
36
+ ··· + 112.115u + 12.6582
a
1
=
8.30944u
37
+ 6.98105u
36
+ ··· + 271.458u + 32.4411
0.565194u
37
+ 2.66371u
36
+ ··· + 55.8911u + 6.22476
a
9
=
−u
u
3
+ u
a
11
=
−u
3
u
5
+ u
3
+ u
a
8
=
u
3
u
3
+ u
a
7
=
2.38323u
37
+ 1.44709u
36
+ ··· + 51.2510u + 3.28992
1.45749u
37
+ 1.85739u
36
+ ··· + 1.74398u − 1.81804
a
12
=
7.40661u
37
+ 4.29257u
36
+ ··· + 209.264u + 24.8880
−1.35180u
37
+ 1.74929u
36
+ ··· + 35.3462u + 4.43912
(ii) Obstruction class = −1
(iii) Cusp Shapes = 25.3622u
37
+ 20.1574u
36
+ ··· + 887.101u + 105.896
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
38
+ 7u
37
+ ··· − 3u + 1
c
2
, c
3
, c
5
c
9
u
38
+ u
37
+ ··· + 11u + 1
c
4
, c
6
, c
11
u
38
+ u
37
+ ··· − 13u + 1
c
7
u
38
+ 6u
37
+ ··· + 279558u + 34943
c
8
u
38
+ 2u
37
+ ··· + 31225u + 84625
c
12
(u
19
− 4u
18
+ ··· + 182u − 103)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
38
+ 47y
37
+ ··· + 41y + 1
c
2
, c
3
, c
5
c
9
y
38
+ 7y
37
+ ··· − 3y + 1
c
4
, c
6
, c
11
y
38
− 7y
37
+ ··· − 27y + 1
c
7
y
38
− 54y
37
+ ··· + 19424324302y + 1221013249
c
8
y
38
+ 90y
37
+ ··· + 115039950625y + 7161390625
c
12
(y
19
− 18y
18
+ ··· − 49070y −10609)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.004590 + 0.172131I
a = 0.883738 − 0.151424I
b = −1.004590 + 0.172131I
2.25367 8.32597 + 0.I
u = 1.004590 − 0.172131I
a = 0.883738 + 0.151424I
b = −1.004590 − 0.172131I
2.25367 8.32597 + 0.I
u = −0.769998 + 0.586991I
a = 1.117170 + 0.263942I
b = −0.49939 + 1.38926I
−1.95090 − 5.96839I 0.62541 + 10.55313I
u = −0.769998 − 0.586991I
a = 1.117170 − 0.263942I
b = −0.49939 − 1.38926I
−1.95090 + 5.96839I 0.62541 − 10.55313I
u = −0.250368 + 0.928587I
a = 0.922332 + 0.890681I
b = 0.516346 + 1.055000I
−3.76429 + 1.96233I −6.97090 − 0.90766I
u = −0.250368 − 0.928587I
a = 0.922332 − 0.890681I
b = 0.516346 − 1.055000I
−3.76429 − 1.96233I −6.97090 + 0.90766I
u = 0.685299 + 0.877713I
a = 0.431131 + 0.017894I
b = 0.221102 − 0.581236I
0.80155 + 2.69495I 4.30397 − 0.26494I
u = 0.685299 − 0.877713I
a = 0.431131 − 0.017894I
b = 0.221102 + 0.581236I
0.80155 − 2.69495I 4.30397 + 0.26494I
u = −0.151590 + 0.840331I
a = 1.15667 + 1.14014I
b = 0.319310 + 0.249382I
−1.87491 + 1.48071I −3.81413 − 3.72384I
u = −0.151590 − 0.840331I
a = 1.15667 − 1.14014I
b = 0.319310 − 0.249382I
−1.87491 − 1.48071I −3.81413 + 3.72384I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.479231 + 1.064790I
a = −1.79535 − 0.55808I
b = 0.350575 − 0.499346I
−3.82831 − 4.84634I −7.70612 + 6.88664I
u = −0.479231 − 1.064790I
a = −1.79535 + 0.55808I
b = 0.350575 + 0.499346I
−3.82831 + 4.84634I −7.70612 − 6.88664I
u = 0.908346 + 0.735932I
a = −0.339798 − 0.249688I
b = 0.400909 + 0.103737I
1.01937 + 3.04219I 4.58994 − 7.02078I
u = 0.908346 − 0.735932I
a = −0.339798 + 0.249688I
b = 0.400909 − 0.103737I
1.01937 − 3.04219I 4.58994 + 7.02078I
u = −0.516346 + 1.055000I
a = −0.088440 + 1.046130I
b = 0.250368 + 0.928587I
−3.76429 − 1.96233I −6.97090 + 0.90766I
u = −0.516346 − 1.055000I
a = −0.088440 − 1.046130I
b = 0.250368 − 0.928587I
−3.76429 + 1.96233I −6.97090 − 0.90766I
u = −1.044560 + 0.842557I
a = −0.811923 − 0.654907I
b = 1.044560 + 0.842557I
10.6548 0
u = −1.044560 − 0.842557I
a = −0.811923 + 0.654907I
b = 1.044560 − 0.842557I
10.6548 0
u = 0.976290 + 0.949251I
a = −1.63572 + 0.33244I
b = 0.887628 + 1.095510I
9.80034 + 7.08036I 0. − 4.76593I
u = 0.976290 − 0.949251I
a = −1.63572 − 0.33244I
b = 0.887628 − 1.095510I
9.80034 − 7.08036I 0. + 4.76593I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.221102 + 0.581236I
a = 0.427232 − 0.643816I
b = −0.685299 − 0.877713I
0.80155 + 2.69495I 4.30397 − 0.26494I
u = −0.221102 − 0.581236I
a = 0.427232 + 0.643816I
b = −0.685299 + 0.877713I
0.80155 − 2.69495I 4.30397 + 0.26494I
u = 0.950416 + 1.005200I
a = 0.568027 − 0.600769I
b = −0.950416 + 1.005200I
9.62378 0
u = 0.950416 − 1.005200I
a = 0.568027 + 0.600769I
b = −0.950416 − 1.005200I
9.62378 0
u = −0.350575 + 0.499346I
a = −3.57554 − 0.40279I
b = 0.479231 − 1.064790I
−3.82831 − 4.84634I −7.70612 + 6.88664I
u = −0.350575 − 0.499346I
a = −3.57554 + 0.40279I
b = 0.479231 + 1.064790I
−3.82831 + 4.84634I −7.70612 − 6.88664I
u = −0.887628 + 1.095510I
a = 1.53068 + 0.50554I
b = −0.976290 + 0.949251I
9.80034 − 7.08036I 0
u = −0.887628 − 1.095510I
a = 1.53068 − 0.50554I
b = −0.976290 − 0.949251I
9.80034 + 7.08036I 0
u = −1.14162 + 0.84482I
a = 0.714096 + 0.478108I
b = −1.00890 − 1.04517I
9.91517 + 7.54398I 0
u = −1.14162 − 0.84482I
a = 0.714096 − 0.478108I
b = −1.00890 + 1.04517I
9.91517 − 7.54398I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00890 + 1.04517I
a = −0.554397 + 0.631289I
b = 1.14162 − 0.84482I
9.91517 + 7.54398I 0
u = 1.00890 − 1.04517I
a = −0.554397 − 0.631289I
b = 1.14162 + 0.84482I
9.91517 − 7.54398I 0
u = 0.49939 + 1.38926I
a = −0.521072 + 0.543402I
b = 0.769998 + 0.586991I
−1.95090 + 5.96839I 0
u = 0.49939 − 1.38926I
a = −0.521072 − 0.543402I
b = 0.769998 − 0.586991I
−1.95090 − 5.96839I 0
u = −0.400909 + 0.103737I
a = 0.580462 − 1.039280I
b = −0.908346 + 0.735932I
1.01937 − 3.04219I 4.58994 + 7.02078I
u = −0.400909 − 0.103737I
a = 0.580462 + 1.039280I
b = −0.908346 − 0.735932I
1.01937 + 3.04219I 4.58994 − 7.02078I
u = −0.319310 + 0.249382I
a = 0.99071 + 3.27648I
b = 0.151590 + 0.840331I
−1.87491 − 1.48071I −3.81413 + 3.72384I
u = −0.319310 − 0.249382I
a = 0.99071 − 3.27648I
b = 0.151590 − 0.840331I
−1.87491 + 1.48071I −3.81413 − 3.72384I
13
III. I
u
3
= hb + u, −3u
4
+ 3u
3
− 2u
2
+ a + 5u − 2, u
5
− u
4
+ u
3
− 2u
2
+ u − 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
−u
2
a
5
=
3u
4
− 3u
3
+ 2u
2
− 5u + 2
−u
a
2
=
u
3
− u
2
+ u − 2
u
2
a
6
=
2u
4
− 2u
3
+ u
2
− 3u + 2
−u
3
− u
a
1
=
u
3
+ u − 2
u
2
a
9
=
−u
u
3
+ u
a
11
=
−u
3
u
4
+ 2u
2
+ 1
a
8
=
u
3
u
3
+ u
a
7
=
u
4
+ u
3
− u
2
− 2u − 1
u
3
− u
2
+ u − 1
a
12
=
−u
4
+ u
3
− u
2
+ 2u − 3
u
4
+ 3u
2
+ 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
4
− 2u
3
− 7u
2
− u − 12
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
5
− u
4
− u
3
+ 4u
2
− 3u + 1
c
2
, c
9
u
5
+ u
4
+ u
3
+ 2u
2
+ u + 1
c
3
, c
5
u
5
− u
4
+ u
3
− 2u
2
+ u − 1
c
4
, c
6
u
5
− 2u
3
+ u
2
+ 2u − 1
c
7
u
5
+ 2u
4
+ 2u
3
+ 3u
2
+ 2u + 1
c
8
u
5
+ 5u
4
+ 6u
3
+ 3u
2
+ u + 1
c
10
u
5
+ u
4
− u
3
− 4u
2
− 3u − 1
c
11
u
5
− 2u
3
− u
2
+ 2u + 1
c
12
u
5
+ 6u
4
+ 9u
3
+ 8u
2
+ 4u + 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
5
− 3y
4
+ 3y
3
− 8y
2
+ y −1
c
2
, c
3
, c
5
c
9
y
5
+ y
4
− y
3
− 4y
2
− 3y −1
c
4
, c
6
, c
11
y
5
− 4y
4
+ 8y
3
− 9y
2
+ 6y −1
c
7
y
5
− 4y
3
− 5y
2
− 2y −1
c
8
y
5
− 13y
4
+ 8y
3
− 7y
2
− 5y −1
c
12
y
5
− 18y
4
− 7y
3
− 4y
2
− 1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.428550 + 1.039280I
a = −1.54944 − 0.53709I
b = 0.428550 − 1.039280I
−5.20316 − 6.77491I −7.90607 + 7.89291I
u = −0.428550 − 1.039280I
a = −1.54944 + 0.53709I
b = 0.428550 + 1.039280I
−5.20316 + 6.77491I −7.90607 − 7.89291I
u = 0.276511 + 0.728237I
a = 1.09747 − 3.27495I
b = −0.276511 − 0.728237I
−2.50012 − 0.60716I −8.21805 − 3.47460I
u = 0.276511 − 0.728237I
a = 1.09747 + 3.27495I
b = −0.276511 + 0.728237I
−2.50012 + 0.60716I −8.21805 + 3.47460I
u = 1.30408
a = 0.903937
b = −1.30408
2.24708 −26.7520
17
IV. I
u
4
= hb + u, a + 2u + 2, u
2
+ u + 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
u + 1
a
5
=
−2u − 2
−u
a
2
=
−1
−u − 1
a
6
=
−u − 2
−u − 1
a
1
=
−u − 2
−u − 1
a
9
=
−u
u + 1
a
11
=
−1
0
a
8
=
1
u + 1
a
7
=
−u + 2
u + 2
a
12
=
−2u − 2
−u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 12u + 6
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
9
, c
10
, c
11
c
12
u
2
+ u + 1
c
7
, c
8
u
2
− u + 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
8
, c
9
c
10
, c
11
, c
12
y
2
+ y + 1
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = −1.00000 − 1.73205I
b = 0.500000 − 0.866025I
− 6.08965I 0. + 10.39230I
u = −0.500000 − 0.866025I
a = −1.00000 + 1.73205I
b = 0.500000 + 0.866025I
6.08965I 0. − 10.39230I
21
V.
I
u
5
= h−u
13
−2u
12
+· · ·+b−2, 3u
13
−u
12
+· · ·+a+2u, u
14
+4u
12
+· · ·+u+1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
−u
2
a
5
=
−3u
13
+ u
12
+ ··· − 3u
2
− 2u
u
13
+ 2u
12
+ ··· + 3u + 2
a
2
=
3u
13
− u
12
+ ··· + 6u + 1
−u
13
− u
12
+ ··· − 4u − 3
a
6
=
−2u
13
+ 2u
12
+ ··· − 4u + 2
u
13
+ 2u
12
+ ··· + 6u + 4
a
1
=
2u
13
− 2u
12
+ ··· + 2u − 2
−u
13
− u
12
+ ··· − 4u − 3
a
9
=
−u
u
3
+ u
a
11
=
−u
3
u
5
+ u
3
+ u
a
8
=
u
3
u
3
+ u
a
7
=
2u
13
− u
12
+ ··· + 4u + 2
u
11
− u
10
+ 3u
9
− 2u
8
+ 5u
7
− 3u
6
+ 5u
5
− u
4
+ 4u
3
− u
2
+ 3u
a
12
=
3u
13
− 2u
12
+ ··· + 6u − 1
−u
13
− u
12
+ ··· − 3u − 3
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 5u
13
+7u
12
+16u
11
+31u
10
+38u
9
+65u
8
+56u
7
+90u
6
+72u
5
+79u
4
+53u
3
+50u
2
+18u+4
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
14
− 8u
13
+ ··· − 9u + 1
c
2
, c
9
u
14
+ 4u
12
+ ··· − u + 1
c
3
, c
5
u
14
+ 4u
12
+ ··· + u + 1
c
4
, c
6
u
14
− 2u
13
+ ··· + u + 1
c
7
u
14
− 3u
13
+ ··· − 2u + 1
c
8
u
14
− 3u
13
+ ··· − 3u + 1
c
10
u
14
+ 8u
13
+ ··· + 9u + 1
c
11
u
14
+ 2u
13
+ ··· − u + 1
c
12
(u
7
− 2u
6
+ 2u
5
− u
4
+ 2u
2
− 2u + 1)
2
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
14
+ 4y
13
+ ··· − 3y + 1
c
2
, c
3
, c
5
c
9
y
14
+ 8y
13
+ ··· + 9y + 1
c
4
, c
6
, c
11
y
14
− 6y
13
+ ··· − 11y + 1
c
7
y
14
+ 11y
13
+ ··· + 2y + 1
c
8
y
14
+ 3y
13
+ ··· + 17y + 1
c
12
(y
7
+ 3y
4
− 2y
2
− 1)
2
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.716205 + 0.619830I
a = 1.50526 + 0.73982I
b = −0.417581 + 1.200450I
−2.50419 − 5.00992I −2.87922 + 5.19233I
u = −0.716205 − 0.619830I
a = 1.50526 − 0.73982I
b = −0.417581 − 1.200450I
−2.50419 + 5.00992I −2.87922 − 5.19233I
u = 0.369492 + 1.060950I
a = −1.074490 − 0.287225I
b = 0.355639 − 0.671652I
−3.83313 + 3.38801I −5.24712 − 4.06276I
u = 0.369492 − 1.060950I
a = −1.074490 + 0.287225I
b = 0.355639 + 0.671652I
−3.83313 − 3.38801I −5.24712 + 4.06276I
u = 0.764704 + 0.855799I
a = −0.685493 − 0.365462I
b = −0.064397 + 0.681658I
0.24628 + 2.90027I −9.12896 − 4.50234I
u = 0.764704 − 0.855799I
a = −0.685493 + 0.365462I
b = −0.064397 − 0.681658I
0.24628 − 2.90027I −9.12896 + 4.50234I
u = −0.544331 + 1.111970I
a = 0.113385 + 0.231625I
b = 0.544331 + 1.111970I
−4.26728 −4.48940 + 0.I
u = −0.544331 − 1.111970I
a = 0.113385 − 0.231625I
b = 0.544331 − 1.111970I
−4.26728 −4.48940 + 0.I
u = −0.355639 + 0.671652I
a = −1.39220 + 0.87457I
b = −0.369492 − 1.060950I
−3.83313 + 3.38801I −5.24712 − 4.06276I
u = −0.355639 − 0.671652I
a = −1.39220 − 0.87457I
b = −0.369492 + 1.060950I
−3.83313 − 3.38801I −5.24712 + 4.06276I
25
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.417581 + 1.200450I
a = −0.696781 + 1.037670I
b = 0.716205 + 0.619830I
−2.50419 + 5.00992I −2.87922 − 5.19233I
u = 0.417581 − 1.200450I
a = −0.696781 − 1.037670I
b = 0.716205 − 0.619830I
−2.50419 − 5.00992I −2.87922 + 5.19233I
u = 0.064397 + 0.681658I
a = 1.230320 + 0.426410I
b = −0.764704 + 0.855799I
0.24628 − 2.90027I −9.12896 + 4.50234I
u = 0.064397 − 0.681658I
a = 1.230320 − 0.426410I
b = −0.764704 − 0.855799I
0.24628 + 2.90027I −9.12896 − 4.50234I
26
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
+ u + 1)(u
5
− u
4
+ ··· − 3u + 1)(u
11
+ 2u
10
+ ··· − 6u − 1)
· (u
14
− 8u
13
+ ··· − 9u + 1)(u
38
+ 7u
37
+ ··· − 3u + 1)
c
2
, c
9
(u
2
+ u + 1)(u
5
+ u
4
+ u
3
+ 2u
2
+ u + 1)
· (u
11
− 2u
10
+ 3u
9
− 4u
8
+ 8u
7
− 11u
6
+ 12u
5
− 11u
4
+ 5u
3
− 3u
2
− 1)
· (u
14
+ 4u
12
+ ··· − u + 1)(u
38
+ u
37
+ ··· + 11u + 1)
c
3
, c
5
(u
2
+ u + 1)(u
5
− u
4
+ u
3
− 2u
2
+ u − 1)
· (u
11
− 2u
10
+ 3u
9
− 4u
8
+ 8u
7
− 11u
6
+ 12u
5
− 11u
4
+ 5u
3
− 3u
2
− 1)
· (u
14
+ 4u
12
+ ··· + u + 1)(u
38
+ u
37
+ ··· + 11u + 1)
c
4
, c
6
(u
2
+ u + 1)(u
5
− 2u
3
+ u
2
+ 2u − 1)
· (u
11
− u
10
− u
9
+ u
8
+ 5u
7
− 3u
6
− 4u
5
+ u
4
+ 3u
3
− u
2
+ 3u − 1)
· (u
14
− 2u
13
+ ··· + u + 1)(u
38
+ u
37
+ ··· − 13u + 1)
c
7
(u
2
− u + 1)(u
5
+ 2u
4
+ ··· + 2u + 1)(u
11
+ u
10
+ ··· − 51u − 17)
· (u
14
− 3u
13
+ ··· − 2u + 1)(u
38
+ 6u
37
+ ··· + 279558u + 34943)
c
8
(u
2
− u + 1)(u
5
+ 5u
4
+ ··· + u + 1)(u
11
− 4u
10
+ ··· − 16u − 1)
· (u
14
− 3u
13
+ ··· − 3u + 1)(u
38
+ 2u
37
+ ··· + 31225u + 84625)
c
10
(u
2
+ u + 1)(u
5
+ u
4
+ ··· − 3u − 1)(u
11
+ 2u
10
+ ··· − 6u − 1)
· (u
14
+ 8u
13
+ ··· + 9u + 1)(u
38
+ 7u
37
+ ··· − 3u + 1)
c
11
(u
2
+ u + 1)(u
5
− 2u
3
− u
2
+ 2u + 1)
· (u
11
− u
10
− u
9
+ u
8
+ 5u
7
− 3u
6
− 4u
5
+ u
4
+ 3u
3
− u
2
+ 3u − 1)
· (u
14
+ 2u
13
+ ··· − u + 1)(u
38
+ u
37
+ ··· − 13u + 1)
c
12
(u
2
+ u + 1)(u
5
+ 6u
4
+ 9u
3
+ 8u
2
+ 4u + 1)
· ((u
7
− 2u
6
+ 2u
5
− u
4
+ 2u
2
− 2u + 1)
2
)(u
11
+ 8u
10
+ ··· − 320u − 64)
· (u
19
− 4u
18
+ ··· + 182u − 103)
2
27
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
10
(y
2
+ y + 1)(y
5
− 3y
4
+ ··· + y − 1)(y
11
+ 14y
10
+ ··· − 26y − 1)
· (y
14
+ 4y
13
+ ··· − 3y + 1)(y
38
+ 47y
37
+ ··· + 41y + 1)
c
2
, c
3
, c
5
c
9
(y
2
+ y + 1)(y
5
+ y
4
+ ··· − 3y − 1)(y
11
+ 2y
10
+ ··· − 6y − 1)
· (y
14
+ 8y
13
+ ··· + 9y + 1)(y
38
+ 7y
37
+ ··· − 3y + 1)
c
4
, c
6
, c
11
(y
2
+ y + 1)(y
5
− 4y
4
+ ··· + 6y − 1)(y
11
− 3y
10
+ ··· + 7y − 1)
· (y
14
− 6y
13
+ ··· − 11y + 1)(y
38
− 7y
37
+ ··· − 27y + 1)
c
7
(y
2
+ y + 1)(y
5
− 4y
3
+ ··· − 2y − 1)(y
11
− 15y
10
+ ··· − 425y − 289)
· (y
14
+ 11y
13
+ ··· + 2y + 1)
· (y
38
− 54y
37
+ ··· + 19424324302y + 1221013249)
c
8
(y
2
+ y + 1)(y
5
− 13y
4
+ ··· − 5y − 1)(y
11
+ 20y
10
+ ··· + 92y − 1)
· (y
14
+ 3y
13
+ ··· + 17y + 1)
· (y
38
+ 90y
37
+ ··· + 115039950625y + 7161390625)
c
12
(y
2
+ y + 1)(y
5
− 18y
4
− 7y
3
− 4y
2
− 1)(y
7
+ 3y
4
− 2y
2
− 1)
2
· (y
11
− 22y
10
+ ··· − 10240y − 4096)
· (y
19
− 18y
18
+ ··· − 49070y − 10609)
2
28
